MISCELLANEOUS PAPER GL-89-27 DESIGN AND CONSTRUCTION OF MAT FOUNDATIONS by '" Lawrence D.Johnson Geotechnical Laboratory DEPARTMENT OF THE ARMY to Waterways Experiment Station, Corps of Engineers 3909 Halls Ferry Road, Vicksburg, Mississippi 39180-6199 DTIC ELECTE /WA) ,. . DEC291989 ~S November 1989 Appre Fr PFinal Report 'II DEPARTMENT OF THE ARMY US Army Corps of Engineers Prepared for Washington, DC 20314-1000 -LABORATORY Under RDT&E Work Unit AT 22/AO/010 89 12 28 096 Unclassified SECURITY CLASS:F!CATiON OF :,H.SPAGE REPORT DOCUMENTATION PAGE MoNoO74-O1" lb RESTRICTIVE MARKINGS la. REPORT SECURITY CLASSIFICATION Unclassified DISTRIBUTION/AVAILABILITY OF REPORT 3 2a. SECURITY CLASSIFICATION AUTHORITY 2b DECLASSIFICATION, DOWNGRADING SCHEDULE Approved for public release; 4 PERFORMING ORGANIZATION REPORT NUMBER(S) distribution unlimited. S MONITORING ORGANIZATION REPORT NUMBER(S) Miscellaneous Paper GL-89-27 6& NAME OF PERFORMING ORGANIZATION 6b OFFICE SYMBOL 7a. NAME OF MONITORING ORGANIZATION (if applicable) USAEWES Geotechnical Laboratory 1 7b 6c. ADDRESS (City, State, and ZIP Code) ADDRESS (City, State, and ZIP Code) 3909 Halls Ferry Road Vicksburg, MS 39180-6199 8b OFFICE SYMBOL 8a NAME OF FUNDINGSPONSORING ORGANIZATION 9 PROCUREMENT INSTRUMENT IDENTIFICATION NUMBER (If applicable) US Army Corps of I Engineers 8c. ADDRESS (City, State, and ZIP Code) Washington, DC 10 SOURCE OF FUNDING NUMBERS TASK PROGRAM PROJECT WORK UNIT ELEMENT NO. ACCESSION NO NO NO. AT22/AO/01 20314-1000 Security Classification) 11 TITLE (Include Design and Construction of Mat Foundations 12 PERSONAL AUTHOR(S) Johnson, Lawrence D. 13b TIME COVERED 13a. TYPE OF REPORT FROM Final report _ TO 14 DATE OF REPORT (Year,Month,Day) November 1989 15 PAGE COUNT 354 16 SUPPLEMENTARY NOTATION This report is available from the National Tecnhnical Information Service, 3285 Port Royal Road, Springfield, VA 22161. 17 FIELD COSATI CODES SUB-GROUP GROUP I SUBJECT TERMS (Continue on reverse if necessary and identify by block number) Expansive soil Mat foundation Heave Settlement Soil-structure interaction by block number) 19 ABSTRACT (Continue on reverse if necessary and identify -Mat foundations commonly support all types of structures. Flat mats from 2 to 8 ft in thickness often containing two-way steel reinforcement top and bottom usually support multistory or heavy structures. Mats less than I ft thick often constructed with steel reinforced ribs or stiffening crossbeams usually support light one or two story structures. Man, of these mats have been designed and constructed for supporting permanent military facilities, particularly in heaving/shrinking and compressible soil. Some of these mats have experienced significant differential movement leading to cracking in the stricture and have required costly remedial work. Attempts to reduce such maintenance expenses of some structures have lead to substantially increased design and (knstruction c:sts for mat foundations. Ihis report provides information on serviceability of structures, guidelines for evaluation of soil, and some structure input parameters for design analysis and guidelines for design and construction of ribbed mat foundations in expansive soils. Methods (Cont inue'd 21 ABSTRACT SECURITY CLASSIFICATION 20 DISTRIBUTION/AVAILABILITY OF ABSTRACT Q UNCLASSIFEDfUNLIMITED 0 SAME AS RPT 22a. NA;,4E OF RESPONSIBLE INDIVIDUAL DO Form 1473. JUN 86 C3 DTIC USERS Unclassified 22b TELEPHONE (Include Area Code) Previouselitions are obsolete 22c OFFICE SYMBOL SECURITY CLASSIFICATION OF THIS PAGE Unclassified Unclassified SECURITY CLASSIFICATION OF THIS PAGE 20. ABSTRACT (Continued). have been developed for evaluation of effective soil elastic moduli and stiffness of structures. New concepts are proposed for determining some soil input parameters for design in expansive soils such as the depth of the active zone for heave and edge moisture variation distance. Several case history studies of ribbed and flat mat foundations have been investigated to assist determination of suitable procedures for calculating deformati-n behavior of mat foundations. Analysis of the performance of a large ribbed mat foundation supporting building 333, Red River Army Depot, proves the viability of selected instrumentation and methodology. The observed earth pressure distribution shows extremely large concentrations of soil pressure near the perimeter indicating rigid behavior on an elastic soil or soil shear at the perimeter. The extended distribution of earth pressures from column loads indicates the effectiveness of stiffening beams in spreading applied loads. Evidence is presented indicating that concrete shrinkage and foundation distortions during construction may sometimes let stiffening beams of ribbed mats hang in the trenches without soil support, which may contribute to mat fractures when superstructure loads are applied. Observed strains in the concrete mat were generally consistent with observed deformation patterns. A preliminary systematic damage record system was developed to catalog most frequent damages, assist identification of causes of damage from foundation movements, and assist determination of requirements for maintenance and repair of military facilities. Recommendations are made for field surveys of detailed surface soil and foundation movement patterns and other work to investigate a new frequency spectrum approach and ground modification methods to improve understanding and performance of military facilities, improve design of foundations, and reduce maintenance and repair requirements. Accession For NTIS GRA&I PTU'_ TAB Justification Di-stribut ion/Availaibility Codes S-Avail and/or Dist 9pecial Unclassified SECURITY CLASSIFICATION OF THIS PAGE PREFACE This report provides a comprehensive review and analysis of design and construction technology of mat foundations as of 1988 with guidelines for design and construction of ribbed mats in expansive soil. This report completes RDT&E Work Unit AT22/AO/010, "Mat Foundations for Intermediate and Heavy Military Structures," US Army. 1988. sponsored by the Office, Chief of Engineers (OCE), This work unit was begun in October 1982 and completed September Miscellaneous Papers GL-85-16, "BOSEF: Beam on Swelling Elastic Foundation", and Miscellaneous Paper GL-88-6, "Proceedings of the Workshop on Design, Construction, and Research for Ribbed Mat Foundations" were prepared to complete earlier phases of this study. Contract reports DACA39-87-M0835, "A Computer Program For Analysis of Transient Suction Potential in Clays," DACA39-87-M0557, "Study of Surface Deformations of Mat Foundations on Expansive Soils," and DACA39-87-M0754, "Selection of Design Parameters For Foundations on Expansive Soils," were also prepared to assist in completing this work unit. Mr. A. F. Muller, Mr. Richard F. Davidson and Mr. Wayne King were the OCE Technical Monitors. This report was prepared by Dr. Lawrence D. Johnson, Research Group, Soil Mechanics Division (SMD), Geotechnical Laboratory (GL), US Army Engineer Waterways Experiment Station (WES). The Foundation and Materials Branch, Savannah District, South Atlantic Division (SAD), contributed data for analysis of the mat supporting Fort Gordon Hospital, Georgia. The Foundation and Materials Branch, Fort Worth District (FWD), Southwestern Division (SWD), contributed data for analysis of mats supporting military facilities in San Antonio, Texas. Messrs. R. L. James and B. H. James (SWD), Mr. W. R. Stroman (FWD), Messrs. G. B. Mitchell, C. L. McAnear, and Dr. L. D. Johnson (SMD), and Mr. A. F. Muller (OCE) participated in the field trip of May 1984 to San Antonio, TX, to assess visual performance of mat foundations. Many helpful comments were provided by Dr. P. F. Hadala, Assistant Chief (CL), Mr. A. L. Branch, Jr. (FWD), Dr. G. Wayne Clough, Virginia Polytechnic Institute, Mr. J. P. Hartman (SWD), Dr. A. D. Kerr, University of Delaware, Mr. Wayne King (OCE), Mr. R. L. Mosher, Information Technology Laboratory (WES), and Mr. W. R. Stroman. In situ soil tests for analysis of the ribbed mat supporting Building 333, Red River Army Depot, were performed by the following: pressuremeter tests by Briaud Engineers, College Station, TX, cone penetration tests by Fugro Inter, Inc., Houston, TX, and plate load tests by the Fort Worth District (SWD). Messrs. R. H. Floyd and T. Rosamond, Instrumentation Services Division (WES) installed earth pressure cells and strain gages in portions of the mat supporting building 333. The work was performed under the direct supervision of Mr. C. L. McAnear, Chief, SMD, and general supervision of Dr. W. F. Marcuson III, Chief, GL. COL Larry B. Fulton, EN, was Commander and Director of WES during the preparation of this report. Dr. Robert W. Whalin was Technical Director. 2 CONTENTS Page PREFACE..................................1 CONVERSION FACTORS, INCH-POUND TO METRIC (SI) UNITS OF MEASUREMENT PART I: .5 INTRODUCTION..........................6 Background ............................. 6 Description and Applications of Mats ................ 6 Description of Foundation Movements................9 Serviceability .......................... 11 Philosophy of Design ....................... 14 Current Limitations cf Design...................16 Purpose and Scope........................17 PART II: REVIEW OF METHODOLOGY ..................... 19 Introduction...........................19 General Design Procedure.....................19 Soil Profile.......................21 Total Displacements ..................... 24 Initial Mat Thickness .................... 35 Minimum Depth of Foundation. ............... 41 Differential Soil Displacements. ............. 45 Final Design........................52 PART III: CASE HISTORY STUDIES ..................... 61 Introduction..........................61 Soil Parameters ....................... 61 Structural Parameters .................... 62 Ribbed Mat Foundations......................64 Gymnasium, Brooks Air Force BAse ............. 69 Data Processing Facility, Randolph Air Force Base . . .. 77 Maintenance Shop and Warehouse, US Army Reserve Center .85 Dental and Medical Clinics.................93 Pest Management Training Facility .............. 104 Summary and Conclusions. ... .............. 1l Flat Mat Foundations.......................112 113 Wilford Hall Hospital. .................. Fort Cordon Hospital....................123 Fort Polk Hospital.....................131 Summary and Conclusions. ................. 137 PART IV: APPLICATION OF FIELD PERFORMANCE..............140 Introduction..........................140 Description of Soil........................143 Classification Tests....................143 143 Laboratory Strength Tests. ................ 148 Consolidometer Swell Tests ................ In Situ Soil Tests.....................149 3 Page Field Instrumentation.......................154 Piezometers.........................154 Elevation Surveys......................154 Earth Pressure Cells ................... 163 Strain Gages........................169 Analyses............................182 Input Parameters......................182 Plate on Elastic Foundation ................ 193 Beam on Winkler Foundation................196 Frequency Spectrum Model ................. 198 Summary and Conclusions......................200 PART V: GUIDELINES FOR DESIGN AND CONSTRUCTION OF RIBBED MATS . . . 202 Applicability of Mat Foundations................202 Expansive Soil Behavior. .................... 202 Center Lift.........................203 Edge Lift.........................203 Soil Exploration.........................205 Site Characterization ................... 205 Soil Characterization. .................. 206 Design of Ribbed Mats.......................213 Input Parameters......................213 Foundation Plan. ..................... 213 Rib Dimensions.......................220 Construction...........................220 Minimizing Problems. ................... 220 Preparation for Mat Construction..............225 Site Finishing ...................... 234 Followup..........................235 PART V: RECOMMENDATIONS........................238 REFERENCES..............................240 APPENDIX A: EQUIVALENT SOIL ELASTIC MODULUS ............. APPENDIX B: INFLUENCE OF SUPERSTRUCTURE RIGIDITY...........BI APPENDIX C: USER'S MANUAL FOR COMPUTER PROGRAM SLAB2. ......... Cl APPENDIX D: PERFORMANCE ANALYSIS, CENTRALIZED TROOP CLINIC, FORT SAM HOUSTON, TEXAS ................. Dl Al APPENDIX E: INFLUENCE OF SOIL MODEL ON MAT PERFORMANCE. ........ El APPENDIX F: LIGHT TRACK VEHICLE FOUNDATION DESIGN .. .......... APPENDIX G: FIELD TESTS.........................l 4 Fl CONVERSION FACTORS, NON-SI TO SI (METRIC) UNITS OF MEASUREMENT Non-SI units of measurement used in this report can be converted to SI (metric) units as follows: Multiply By To Obtain cubic yards 0.7645549 cubic metres Fahrenheit degrees 5/9 Celsius degrees or Kelvins* feet 0.3048 metres inches 2.54 centimetres 0.1129848 metre-newtons kips (force) 4.448222 kilonewtons miles (US statute) 1.609347 kilometres pounds (force) 4.448222 newtons inch-poundss (force) pounds (force) per inch pounds (force) per square foot pounds (force) per square inch pounds (mass) per cubic foot 175.1268 47.88026 6.894757 16.01846 newtons per metre pascals pascals kilograms per cubic metre pounds (mass) per cubic yard 0.593276 kilograms per cubic metre square feet 0.09290304 square metres square feet squared 0.0086309 square metres squared square inches squared tons 416,231.4256 (2,000 pounds, mass)-feet tons (2,000 pounds, mass)square feet tons 276.5098966 84.280216 8.896444 (torce) tons (2000 pounds, mass) tons (2000 pounds, mass) per cubic foot 907.1847 32,036.92148 square millimetres squared kilogram-metres kilogram-square metres kilonewtons kilograms kilograms per cubic metre tons (2000 pounds, mass) per foot 2,976.327756 kilograms per metre tons (2000 pounds, mass) per square foot 9,764.856 kilograms per square metre * To obtain Celsius (C) temperature readings from Fahrenheit (F) readings, use the following formula: C = (5/9)(F - 32). ings, use K = (5/9)(F - 32) + 273.15 5 To obtain Kelvin (K) read- DESIGN AND CONSTRUCTION OF MAT FOUNDATIONS PART I: INTRODUCTION Background Description and Applications of mats 1. A mat foundation is a large concrete slab that supports column or line loads that are not all in the same straight line. The mat may be (1) thin (less than 1 ft thickness), Figure la, for supporting light structures on firm soil, (2) ribbed or reinforced with cross beams, Figure lb, for supporting light structures on heaving/shrinking and compressible soil, or (3) thick (greater than 1 ft thickness), Figure 1c, for supporting heavy multistory structures. The stiffness of mat foundations may be designed to accommodate or inhibit differential soil movement. The mat foundation is usually preferred instead of spread footings to increase efficiency and economy of excavation and construction when the spread footings are large and closely spaced in one direction and require more than half of the construction area. By combining all individual footings into one mat, mat foundations reduce pressure on the supporting soil thereby reducing total and differential settlement and often increasing total bearing capacity. 2. Mats are especially useful in supporting structures on deep swelling or consolidating soil and fill that cannot be economically supported by pile or drilled shaft foundations. The weight of the superstructure on mats can balance hydrostatic uplift pressure. Mats can also be constructed to float, such as buoyancy or compensated mats, by excavating basement areas so that the weight of the excavated material balances the structural and normal live loads. Mats may be inverted with stiffening cross-beams on top, Figure ld, if the soil is especially soft. Mats may also be placed on top of piles to reduce settlement in soft soil. cellular spaces. Buoyancy rafts are occasionally designed with Numerous permanent military facilities supported by mats have been designed and constructed by the Corps of Engineers. 3. Thick mats. The most common engineered mat foundations for multi- story "heavy" structures consist of flat 2 to 8 ft thick mats with continuous two-way reinforcement top and bottom. A thick mat usually supports structures 6 ~e K *.o" 0. 4~ 0*.;** ~ ~ * 0 . 4"TO 12' L a.THIN MAT ON FIRM SOIL LOAD L BEARING WALL 4 4 O8 O6 16OTO 36" K-. 18" t"TO b. STIFFENED MAT ON HEAVING /SHRINKING c. THICK MAT d. INVERTED MAT Figure 1. Types of mats 7 SOIL with more than 2 stories, but some 1 and 2 story structures could have large column loads causing these structures to be in the heavy category. Post- tensioned slabs of about 1-ft thickness may support light structures and reduce differential movement on soft or heaving soil. Mats may be square or rectangular shaped for supporting buildings or circular shaped for suppcrting chimneys, silos, and water tanks. 4. American practice tends to overdesign thick mats because of uncertainty involved with current analysis methodology. The extra cost of the additional unknown safety against a structural failure is considered relatively small for reasonable overdesign'. Problems with thick mats supporting storage tanks and silos, where foundation economy is essential, have occurred from excessivp tilt and soil shear failures when supported by soft and weak soil 2 . 5. Thin mats. Foundation costs of thin mats 4 to 8 inches thick are a greater proportion of the total cost of the structure than that for thick mats supporting multi-story structures. These foundations usually support light and intermediate structures on and near the ground surface in unstable soil areas such as expansive and collapsible soil. Thin mats are often reinforced with stiffening beams and placed on compacted nonexpansive low plasticity fill to reduce differential movements. These mats may be underdesigned because of inadequate knowledge of the soil profile, lack of design guidance, or to reduce construction costs. Underdesign leads to excessive total and differential movements that interfere with proper function of utilities, machinery, efficiency and comfort of occupants and damage to the superstructure. Overdesign leads to excessive construction time and cost. Ribbed and other mats also occasionally crack during and soon after construction. 6. Inadequate flatness from deficient design, construction or long-term distortion of foundation soils impairs performance of structures and it is costly to repair. Little guidance is available for specifying appropriate floor flatness for specific functional requirements. Long-term repair and maintenance expenses can be substantial exceeding the original cost of the foundation. The cost of repair of damage from heaving soil is typically 'Bowles 1976; refer to REFERENCES for complete listing Burland and Davidson 1976; Tomlinson 1980; Buttling and Wood 1982 2 8 greater than cost of repair of damage in settling soil because structures are generally less able to accommodate heaving. Heave tends to put the superstructure in tension, while settlement puts the superstructure in compression; structures are usually less able to resist tensile than compressive stress. Design guidelines for flexible (thin) mats are not well advanced beyond the relatively costly uniform pressure method applicable to rigid (thick) mats. Description of Foundation Movements 7. Static and dynamic loads cause total and differential movements. Total movement is the magnitude of vertical heave or downward settlement. Vertical heave is caused by wetting and subsequent volume increase of expansive clay soils. Settlement is caused by elastic compression and consolidation of foundation soils under load and the collapse of meta-stable arrangements of particles in some unsaturated soils. Differential movement is the difference in vertical movement between various locations of the structure and distorts the structure. Ribbed mats with stiffening beams and mats subject to the stiffening action of a properly designed and connected superstructure increase stiffness and reduce differential movement caused by nonuniform heave and shrinkage of expansive soil or consolidation and collapse of other foundation soil. 8. Differential movements cause distortion and damage in structures. These are a function of soil moisture change and uniformity, stiffness of the structure and soil, and distribution of loads within the structure. Excessive differential movement may lead to tilting that can interfere with adjacent structures and disrupt the performance of machinery and people. Differential movement can cause cracking in the structure, distorted and jammed doors and windows, uneven floors and stairways, and other damage. Widespread cracking can impair structural integrity and lead to collapse of the structure, particularly during earthquakes. The height that a wall can be constructed on a foundation without cracking is related to the deflection/span length ratio A/L and angular distortion 9. movement 9 The deflection ratio A in the span length of the foundation. A/L is a measure of the maximum differential L, Figure 2. 9 The span length may be between LSAG_ a. COMBINATION L SAG AND L HOG L b RE3ULAR SETTLEMENT c. IRREGULAR SETTLEMENT Figure 2. Schematic illustration of angular distortion ratio 9 - 6/ and deflection ratio A/i. for settling (sagging) and heaving (hogging) profiles 10 two adjacent columns, LSAG or LHOG, Figure 2a. is a measure of differential movement separated by the distance 6 1, Figure 2. Angular distortion 9 - 6/1 between two adjacent points Settlement (sagging) occurs from elastic compression, collapse, and consolidation of the foundation soil. Heave (hogging) occurs from swelling soil, shrinking or subsidence near the edges, downdrag from adjacent structures and movement from nearby excavations. Serviceability 10. Serviceability is an obscure term, partly because it depends on the purpose of the structure, its response to movements, and the reaction of the owner and users of the structure to movement and cracking. Serviceability or performance of structures is especially related to limitations of total and differential movements to within acceptable values. Considerable judgment enters into evaluating whether a structure has performed "adequately" because the definition of adequate is subjective. A simple curtain wall for dividing space that cracks when subject to excessive differential movement can be easily repaired to full serviceability with a plastic joint filler, but the owner of that wall may not be satisfied with the appearance and may consider the wall a failure. 11. Functions of serviceability. Serviceability depends on the flexibility of structural members, joints, and other architectural details. Articulation by inclusion of joints in structures, steel frames, steel and wood studs, interior paneling and wallboard among other features increase structural flexibility. Expansion and crack control joints placed at regular intervals relieve stresses that would otherwise occur in walls and the mat foundation. Expansion joints are commonly placed at 150-ft intervals in ribbed mats, while construction joints in walls may be placed at approximately 25-ft intervals or less. Horizontal and vertical impervious membranes have been successfully used to reduce differential movement from soil moisture changes. Ground modification methods using chemicals or nonexpansive fills are uspful for reducing total heaves to less than 1 inch. 12. Although superstructure stiffness tends to reduce differential movement of the foundation, modeling techniques are not yet able to simulate stiffness of the total structure so that calculated foundation movements agree 11 with field displacement measurements 3 . A contributing factor is that construction materials often display different stiffnesses than those used in design. External and internal loads on the superstructure can lead to distress and damage, even if the foundation performs within specifications, because of a trend toward longer spans between columns, higher permissible stresses, greater brittleness of wall and facing components, and larger structurally independent units. 13. Disturbance of the foundation soil during construction can influence serviceability by altering soil parameters used for design such as strength, elastic modulus and the modulus of subgrade reaction. Many things done to a site during construction such as soil disturbance during clearing, excavation, drainage or wetting of an adjacent area, and environmental effects can lead to greater differential movement. Care should be exercised by the contractor during construction to minimize differential movement by use of proper drainage, compaction control of fills, and grading. 14. Nonstructural damage occurs predominantly by long-term differential movement, while both immediate and long-term movement contribute to structural damage4 . Structures on soil with relatively little long-term movement such as sands tend to show least superficial or cosmetic damage, although structural damage could occur during construction. This is probably related to the later placement of facing materials after most of the immediate settlement had occurred following construction of the structural members. 15. Limitations of total movement. Many structures can tolerate substantial total movement without cracking. Polshin and Tokar (1957) had indicated maximum total settlement of 3 inches for unreinforced masonry walls and 6 inches for reinforced brick and concrete walls; however, total settlement should not exceed 2 inches in practice for most facilities to help maintain differential movements within acceptable levels, minimize damage to connections with outside utilities, maintain adequate drainage, and maintain adequate serviceability of entry ways. for buildings is 1 inch. A typical allowable total settlement Total foundation heave, even without surcharge pressure from the mat foundation, should usually not exceed I to 1.5 inches. 3 4 Focht Jr., Khan, and Gemeinhardt 1978; Bobe, Hertwig, and Seiffert 1981 Skempton and McDonald 1956 12 Limitations of differential movements. 16. Perimeter or center movements beneath mats exceeding I to 1.5 inches can be nearly impractical and Larger differential movements may not economical to accommodate in design. require innovative superstructure designs to increase flexibility such as vertical construction joints in walls, slip joints in interior walls and flexible, watertight utility connections 5 . Differential movements that can cause operation problems occur within some limited lateral distance; therefore these movements are better expressed in terms of angular distortion and Chapter 2 of EM 1110-1-1904 provides guidelines of angular deflection ratio. distortions and deflection ratios for different types of structures. The maximum angular distortion from regular settlement, Figure 2b, 17. m max is 4A/L from geometrical occurs at the corner of a mat foundation. relationships if settlement is in the shape of a circular arc. 6 between the center and corner of a mat is 0.75 The deflection of the center settlement if the Boussinesq stress distribution of a foundation on an elastic soil is applicable; therefore, the maximum angular distortion will be 3 = m max (la) L L where PC = center settlement, ft L - the diagonal length = distance between columns along the diagonal, ft - number of columns on the diagonal N (N-1)1, ft A safe limit of angular distortion for no cracking in buildings is 1/5004.6. Cracking should be anticipated when 9 exceeds 1/300. Considerable cracking in panels and brick walls and structural damage is expected when greater than 1/150. A is Equation la indicates that the differential displacement should be less than 0.5 inch to maintain of 60 to 80 ft. & m max < 1/500 for span lengths Allowable angular distortions in the superstructure should exceed the maximum angular distortion expected in the foundation to avoid structural distress. Tilting can be observed if 5 Technical 6 9 > 1/250 and must be Manual 5-818-7, "Foundations in Expansive Soils" Feld 1965; Wahls 1981 13 L limited to allow clearance between adjacent buildings, particularly in high winds. Underpinning may be necessary if tilt is excessive. The tilt angle W is indicated in Figure 2. 18. Limiting A/L ratios for design is in the range of 1/240 to 1/600. This range is substantially greater than the 1/2500 limit required to avoid all cracking in masonry structures 7 ,8; however, stiffness contributed by components in an assembled brick structure help maintain deflection ratios near 1/2500. The height that a wall can be constructed on a beam without a cracking failure is related to the deflection/span length 7 distortion 6 by A max1 + 3.9 (HL)2(lb) L 3 A/L and the + 2.6 (H2/L) where A - L -span HW - differential displacement, ft length, ft wall height, ft 6max - maximum angular distortion at support, L = 0 Equation lb considers that cracking is initiated at a critical strain 0.075 percent. crit ratio - - was based on field observations of the onset of visible cracking in beams as a function of the wall height/span length ratio. m max Ccrit If 1/500 for initiation of damage the corresponding deflection/span length A/L is about 1/1333 or 6max is about 3 times greater than A/L. Philosophy of Design 19. Mat foundations should be designed and constructed to be safe against a soil shear failure and with loads sufficiently less than the soil bearing capacity to maintain total and differential displacements that optimize the functional purpose and structural (shear and bending moment) capacity of the structure. The maximum pressure applied to foundation soil should be less than the maximum past pressure to avoid virgin consolidation settlements; therefore, heavy structures may be supported by compensated or 7 Burland and Wroth 1978 Polshin and Tokar 1957 8 14 floating mats placed in deep excavations. Thick mats are commonly designed by the uniform (rigid) pressure method described below assuming undrained soil conditions; however, the difference in material and construction expenses saved by using a flexible analysis may be significant. Many structures, especially I or 2 story buildings, are flexible or semi-flexible structures supported on stiffened ribbed mats. 20. Uniform pressure method. Mats designed by this method satisfy two criteria: the centroid of the area in contact with the soil should lie on the line of action of resultant loads applied .o the soil, which promotes a uniform pressure distribution, and the mat dimensions are selected so that the allowable soil pressure is not exceeded. Mats should neither settle or tilt excessively if these two criteria are satisfied. The allowable pressure required to limit foundation settlement to within suitable values may be estimated by applying factors of safety (FS) to the ultimate bearing capacity. If the allowable pressure is less than the applied pressure or initial estimates of total settlement exceed allowable settlement, then a compensated mat or pile supported mat may be considered. 21. The structural design of mats by the American Concrete Institute Ultimate Strength Method (ACI 318-80) usually results in a nonuniform linear soil pressure distribution because column loads are multiplied by load factors and the mat size should be increased to accommodate the larger service loads specified by the building code9 . The uniform pressure method with an illustrative example is described by Peck, Hanson, and Thornburn (1974). 22. Flexible method. design of flexible mats. Wrayl° documented 16 procedures applicable to Of these methods the Post-Tensioning Institute11 and the US Army Engineer Southwestern Division 12 pocedures are more commonly used by designers. Flexible mat foundations may also be designed by soil-structure interaction analysis using finite difference or finite element numerical techniques. During the late 1970's, the Corps of Engineers designed and constructed several military hospital foundations with thick mats such as the Wilford Hall Hospital addition in Lackland Air Force Base, Texas, and the gAmerican Concrete Institute 318-80, Section 17.3 1 Johnson 1988 11 Post-Tensioning Institute 1980 12 Hartman and James 1988 15 hospital in Fort Polk, Louisiana. The design of these mats used a finite element computer program 13 containing a hyperbolic stress-strain soil model to better define foundation movements. This model is applicable to soil for strains not exceeding the strain level at peak strengths. Program SLAB211 is a two-dimensional plate on elastic foundation finite element program modified to accommodate stiffening beams. Beam on Winkler foundation methods 14 ,15 have also been applied to design of flexible mats. Current Limitations of Design 23. Soil input parameters. Advanced design methodology for mat foundations such as plate on elastic foundation, beam on Winkler foundation, and use of finite difference or finite element methods require thorough geotechnical investigations to assist evaluation of reasonable values for soil input parameters. These parameters include the elastic soil modulus and Poisson's ratio for the plate on elastic foundation, coefficient of subgrade reaction for a beam on a Winkler foundation, soil swell pressure, compression and swell indices, depth of the active zone of heaving soil, and edge moisture variation distance. 24. Adequate guidelines for evaluation of elastic soil modulus E S and coefficient of subgrade reaction for a foundation ksf are not yet available. Adequate estimates of kf required in the Winkler foundation is especially difficult to provide because proper modeling of soil behavior requires at least two parameters such as the elastic modulus and Poisson's ratio. Single parameter models cannot properly calculate both displacements and bending moments simultaneously 16 ,17. For example, an appropriate ksf for bending of ribbed mat T-sections (the stiffening beam or web with some width of the flat mat extending on each side of the stiffening beam, Figure lb) may be different than that evaluated for settlement. The American Concrete Institute specifies that for bending an effective T-section width Se e L/4 where L is the span length; the effective overhang distance on each side of the web shall be less than 1/2 the distance to the next web or stiffening beam and not exceed 13Duncan amd Clough 1971 14Godden 1965 15Dawkins 1982 16Vesic 1961 17 Vesic and Saxena 1968 16 8D where D is the thickness of the flat portion of the mat 8 . This implies that the effective support of the soil is provided within the width S . Actual support of ribbed mats by the underlying soil is not known. e Adequate guidelines for other soil parameters such as the active 25. depth for heaving soil Za and the edge moisture variation distance especially incomplete. Za is defined as the depth below which vertical soil movements are insignificant. em are The amount of vertical soil strain that is considered insignificant at depth defined. em Za is unknown, consequently Za is poorly is the lateral distance beneath the mat from the mat perimeter subject to vertical movement from seasonal and long-term soil moisture changes. 26. Advanced facilities. Mat foundations are being used more frequently to support structures with functional requirements that limit the acceptable differential movement. For example, warehouses and service centers are becoming automated with robotic equipment that requires close tolerances on vertical alignment and "superflat" floor slabs. Experience is still limited concerning the toleration of this equipment to differential movement. Facilities containing specialized machinery establish requirements for limited differential movements. Technology does not yet exist that allows the reliable prediction of foundation movements under the given structural loads and soil conditions to the accuracy needed to assure "superflat" conditions. Adequate guidelines do not exist that allow economic design of foundations that can control deformations to within acceptable limits. The serviceability of these new facilities may therefore be restricted by the performance of the foundation. Purpose and Scope 27. This report was prepared to provide guidelines for design and construction of mat foundations with emphasis on ribbed mats in expansive soil. A review of methodology, Part II, was initially completed as an aid in determining useful methodologies and current design limitations. Case histories of the performance of existing construction are discussed in Part III to provide documentation leading to appropriate procedures for design. '8American Concrete Institute 318-80, Section 8.10.2 17 A field study of a partially instrumented stiffened and ribbed mat described in Part IV documents the actual performance of a ribbed mat under service conditions. Guidelines for soil exploration, evaluation of soil input parameters for design of ribbed mat foundations, a procedure developed by the Southwestern Division of the Corps of Engineers for design of ribbed mat foundations in expansive soil using these input parameters12 , and construction methodology are described in Part V. Part VI concludes with recommendations for future work to improve serviceability of permanent military facilities, reduce requirements for design through ground modification or soil moisture stabilization methods, and to reduce maintenance and repair costs. 28. The scope of this report excludes the design of mats on piles. study of methods for reducing foundation soil movements such as ground modification or soil moisture stabilization is also excluded. 18 A PART II: REVIEW OF METHODOLOGY Introduction 29. Design is a multi-discipline area that includes functional, aesthetic, geotechnical, structural, mechanical, and electrical considerations. Consequently, a satisfactory design for a structure is normally accomplished through cooperation between the owner, architect, geotechnical engineer, structural engineer, and others. This review is concerned only with those design functions necessary to analyze the performance of the foundation and supporting soil. 30. Serviceability of the structure is approached in terms of the expected total and differential foundation displacements and comparison with the allowable movements. Ultimate bearing capacities of the foundation soil normally do not control design because structural loads must be limited in order to maintain displacements within allowable total and differential movements. Allowable bearing capacities may be estimated from calculated ultimate bearing capacities using factors of safety that have been shown to maintain displacements within acceptable levels. General Design Procedure 31. Table 1. A general procedure for design of mat foundations is proposed in An initial function of the geotechnical engineer is to evaluate different types of potentially applicable foundations and their relative economy and performance compatible with the soil profile, step 1, and structural requirements, step 2. Soil displacements, step 3, are estimated from given structural loads as an aid in selection of a suitable foundation. The most suitable foundation is subsequently determined in cooperation between the geotechnical engineer, structural engineer, architect, construction engineer, and the owner/operator. A mat may be selected if construction costs compare favorably with other foundation types, expected displacements are within structural limits, and expertise required for construction is locally available. Other items impacting the decision may include construction time, ease of construction, and ability to limit angular deformations or architectural distress. 19 Table 1 General Procedure for Design of Mat Foundations Step Evaluate Remarks 1 Soil profile Characterize the soil profile from in situ field tests, boring logs, and laboratory tests on soil samples; detailed tests performed on the probable foundation bearing stratum; soil parameters for design determined from results of field and laboratory tests. 2 Structural requirements Determine preliminary distribution of loads, location and size of walls and columns based on initial structural design and functional requirements; determine maximum allowable total and differential movements; total settlements usually limited to 2 inches and total heave to 1.5 inches; differential movements depend on serviceability requirements and usually limited to 0.5 inch for normal design or 1 to 1.5 inches for stiffened ribbed mats. 3 Total soil displacements Total displacements for the given structural loads are estimated from empirical relationships, elastic theory, Winkler concept, and consolidation/swell analysis; these movements are checked against allowable total movements. 4 Initial mat thickness Determine minimum initial mat thickness by resistance of the mat to punching shear. 5 Minimum depth of mat base and bearing capacity Base of mat should be below soil influenced by frost heave, soil erosion, and excessive soil moisture changes; design loads may require adjustments if the depth of mat base Db is fixed within a limited range and the allowable bearing capacity exceeded; floating or compensated mats may be used if settlements would otherwise be excessive. 6 Differential soil displacements Estimates of differential displacements may use elastic compression and consolidation or swell in soil-structure interaction analysis for given loads and soil profiles. 7 Final structural design Final design checked for compliance with shear, bending moment, and deflection requirements; uniform pressure method and ACI 336-87, 318-80, 340-77), Strength Design Method usually applied; design of flexible mats may use a soil-structure interaction analysis. 8 Site development plan Construction of additional nearby structures and changes in environment can affect performance of previous construction and must be considered in the site plan. 20 32. An initial estimate of mat thickness required to support the indicated loads is made when a mat foundation is considered, step 4. The minimum or most appropriate depth of the foundation base, step 5, is then selected based on the soil profile and functional requirements of the Soil displacements should be analyzed in detail for the indicated structure. structural loads and distribution of loads, step 6. If the allowable settlements or bearing capacity are exceeded, then adjustments to the design The usual procedure for structural design or foundation depth are indicated. of mat foundations, step 7, is the uniform pressure method assuming linear contact soil pressures. The last step should include a site development plan, step 8, because construction of additional adjacent structures and changes in soil conditions caused by the environment can influence the performance of previous construction. Excavation and loads of the proposed facility may also influence the performance of adjacent existing structures. Soil Profile 33. Evaluation of soil parameters as a function of depth will permit estimation of potential movements and bearing capacities for selected mat dimensions and load distributions leading to an optimum foundation. A surface examination of the sites selected for possible construction of the structure should be conducted first followed by a subsurface soil sampling and testing program to obtain suitable soil parameters required for selection of the design and method of construction. Soil parameters should be plotted with results of visual boring logs as a function of depth to evaluate the soil profile. 34. Depth of exploration. least twice the minimum width B The recommended depth of soil sampling is at of the mat foundation or the depth to incompressible soil, whichever comes first. Greater exploration depths may not be necessary because stress intensities imposed by the structure on the foundation at these depths are about 10 percent or less of the loads applied at the foundation level19 . Existence of soft layers beneath firm strata should be checked since soft layers can lead to excessive displacements under relatively small loads. In practice where primary geological formations, such as those of unweathered and unfissured rock and dense shale, are encountered '9Boussinesq 1885; Westergaard 1938 21 the depth of exploration is often not related to the size of the structure. It may be sufficient to limit exploration to a depth that includes the weathered and fissured materials and depths influenced by the effects of construction. Consideration should be given to obtaining samples near the proposed center, corner, and mid-edge of the structure. Details of surface and subsurface exploration programs are available in EM 1110-2-1804, "Geotechnical Investigations". 35. Field tests. In situ tests may be conducted to evaluate soil strength and deformation behavior. These tests are suitable as an aid to foundation design and construction, especially if undisturbed samples cannot be easily obtained during sampling such as in strata containing cohesionless soil. Field tests are often less costly than soil sampling and laboratory testing programs. An important limitation of field tests is that they are not a direct measure of soil parameters required for design, but are used to estimate soil parameters through correlation factors. Correlation factors vary substantially between types of soil; therefore, laboratory and different types of field tests should be performed whenever possible to verify soil parameters used for design. Some field tests appropriate for evaluation of soil parameters useful to mat foundation design are outlined in Table 2. 36. Laboratory tests. Laboratory tests such as Atterberg limits are initially performed on disturbed samples at relatively frequent depth intervals (within 5 ft) to identify soil suitable as a bearing stratum. Atterberg limits can be used to make a preliminary estimate of the relative potential for soil volume changes 5 . Unconfined compression (UC) and unconsolidated undrained (Q) tests will provide undrained parameters for analysis of bearing capacity and undrained soil elastic modulus for estimates of immediate displacements. UC tests may underestimate strengths because confining pressures are not applied. Confining pressures for be on the order of in situ overburden pressures. Q tests should Consolidated undrained tests with pore pressure measurements (R), although not commonly performed on cohesive soils, provide drained strength parameters for analysis of bearing capacity and drained soil elastic moduli for estimates of long-term displacements. One-dimensional (1D) consolidation and swell tests may be performed to evaluate long-term consolidation and heave. 22 Results of 1D tests Table 2 Field Soil Tests Useful for Analysis of Performance of Mat Foundations Test Application Advantages Disadvantages Standard penetration SPT (ASTM D 1586) Bearing capacity, elastic soil modulus, and settlement Data easily obtained during exploration using standard split spoon sampler; useful in soils difficult to sample such as sands and silts; inexpensive when performed in association with sampling for laboratory classification tests Numerous factors influence blowcount such as variation in drop height, interference with free fall, distorted sampler, and failure to seat sampler on undisturbed soil Cone penetration CPT (ASTM D 3441) Undrained shear strength friction angle elastic modulus and bearing capacity for clays and sands Simulates shape of a pile so tip and side friction some function of same in pile foundations; soil parameters usually multiple of tip resistance Substantial scatter in correlations between different soils; pore pressure buildup during driving may influence readings Pressuremeter PMT (ASTM D 4719) Most soil parameters for clays, silts, and sands Readings theoretically related with soil stiffness useful in design of deep foundations Requires carefully prepared borehole; careful calibration of device; more costly than SPT or CPT; inconsistencies in results common Plate loaddepth (ASTM D 1194) Plate Direct measure of k within twice plate diameter; useful to estimate elastic Costly; must extrapolate to mat dimensions; results depths not useful below twice to plate diamete Dilatometer (Schmertmann 1986) subgrade reaction kp soil modulus up to depths for any soil twice plate diameter Most soil parameters for clays, silts, and sands Uses same pushing equipment as CPT; elastic modulus theoretically related with test data 23 diameter Data depends on small 1.1 mm motion of membrane; soil disturbance from pushing probe may influence data may be corrected to three-dimensional behavior by using the Skempton and Bjerrum procedure 20 , but practical experience using one-dimensional analysis with normally consolidated soil indicates reasonable (± 50 percent) accuracy 7 Total Displacements 37. Settlement of foundations cause by applied loads on underlying soil consists of elastic (immediate) and time dependent components Pt IPi + Ut'Pconj I (2a) '5 jPfj e - e (2b) t 0 eo0- e f where t, ft Pt - total settlement at time Pi = immediate settlement, ft Pcon - consolidation settlement, ft Pf - long-term or final total settiemert, ft Ut - consolidation ratf, at time e - initial void ratio e - void ratio at time ef t t long-term or final void ratio These settlements are negative values, while heave is denoted as positive. Immediate settlement occurs during placement of loads from elastic and inelastic soil deformation without change in water content. Consolidation settlement can be substantial in clays and occurs when pressures applied to the soil exceed the preconsolidation stress in the soil. Consolidation settlement is a result of volume reduction in the soil caused by expulsion of pore water from the soil and may be evaluated by standard consolidation analysis21 . If the stresses beneath the base of the mat do not exceed the preconsolidation stress, then deformation will be limited to recompression settlement. Some heave may occur if stresses in soil beneath the base of the mat are significantly less than the actual swell pressure in the founding soil system and free water is made available to the founding system. 2 °Skempton 21 and Bjerrum 1957 Chapter 3, Engineer Manual 1110-1-1904, "Settlement Analysis" 24 38. Elastic settlement. Experimental data show that the immediate settlement of foundation soil resembles that of an elastic, isotropic solid 17'22 and may be calculated from Young's soil modulus ratio Es and Poisson's Poisson's ratio for soil usually varies from 0.25 to 0.49 with ps' saturated soils approaching 0.49. Reasonable overall values of Poisson's Calculation of elastic settlement is usually much ratio are 0.30 to 0.40. more sensitive to in situ variations in elastic modulus rather than errors in js" estimating a value for Typical values of elastic modulus are shown in Table 3. 39. appropriate measure of Es from laboratory consolidated-undrained triaxial strength tests is the initial tangent modulus model where a An Eti - 1/a of the hyperbolic is the intercept of a plot of the ratio of strain/deviator The elastic modulus may also be taken as stress versus strain, Figure 323. Esec' the mean secant modulus at 1/2 of the undrained soil compression strength, Figure 3a24 . Table 4 summarizes some methods of estimating the elastic modulus from in situ test resultrs. Et, Initial elastic moduli such as or unload-reload moduli such ai from the PMT, Table 4, often better simulate stiffness of su,. usually small. ...ah mat foundations because earth pressures are Soil disturbance may also cause low estimates of elastic modulus from test data. Es should be evaluated by several methods whenever possible such as those described in Table 4, particularly for important structures. 40. The average immediate settlement of a foundation on an elastic soil may be given by the improved Jambu approximation P i 25 "1Ao 'A1 i " qo E* (3) s where Po Ali 22p ickett factor for depth -influence ground surface, Figure 4 D of foundation below influence factor for foundation shape, Figure 4 and Ray 1951 23 Duncan and Chang 1970 24 Skempton 1951 25 Christian and Carrier 1978 25 Table 3 Typical Elastic Moduli Soil Relative Stiffness Young's Soil Elastic Modulus, Es, ksf Clay Very soft Soft Medium Stiff, Silty Sandy Shale 10 - 100 100 - 400 400 - 1000 1000 - 2000 500 - 4000 2000 - 4000 Sand Loose Dense Dense with gravel Silty 200 500 2000 500 26 - 500 2000 4000 4000 ---- ---- ---- - --- * ( GZ- CF ) u Icr-- a. j~ STRESS-STRAIN - -- (C-r l ° + 6( CURVE 6b N ! b. HYPERBOLIC PARAMETERS a,b Figure 3. Elastic moduli from laboratory undrained strength tests 27 Table 4 Methods for Estimating Elastic Modulus From In Situ Soil Tests Source E , ksf Definitions Standard Penetration Test Schultz and Sherif (1973) 0 9.4N . 87 B.[I + 0.4_ ] N - average blow count/ft B - width, ft 0 I BD Bowles (1988) Normally consolidated sand: 10(N+15) Overconsolidated sand: 3600 + 15N Saturated sand 5(N+15) Clayey sand: 6.4(N+6) Silty sand: 6(N+6) Gravelly sand: 24(N+6) - embedment depth, ft N based on actual input drive energy 55 percent of theoretical Cone Penetration Test SMitchell and (I + 's )(l 2j - Gardner (1975) (I correlation factor ) depending on soil, varies "_'q c from I to 8 (see Table AS) - qc - C-4, EM 1110-1-1904 for details on a) cone bearing resistance, ksf A - Soil Poisson's ratio Pressuremeter Test (1 Hughes (1982) + - Unload-reload pressuremeter E ))E p modulus, ksf Plate Load Test 2 (1 8) ) B (1982 Ap B - Iw w - influence factor, w/4 Ap - change in settlement, ft width or plate diameter, ft for rigid circular plate B0.82 for rigid square Aq P -change in pressure on plate, ksf Dilatometer Schmertmann (1986) (1 - 2 As) Ap 34 .7.Ap 28 - change in pressure between inflated/deflated positions of the membrane 0 °0 5 10 15 20 D/B L/B =oo ,_ L/B -- 10 . . ..... L/B 2 . CICL I0 l Ill[ I I I lJ 10 1 101 l l I I ! I I 10 2 I f I lI J i ll lo 3 H/B qo*B Pi - -/ O'l qo - CONTACT PRESSURE, KIPS L B - LENGTH, FT WIDTH, FT = YOUNG'S SOIL MODULUS, KSF " s E* s Figure 4. Chart for estimating immediate settlement in cohesive soil. Reprinted by permission of the National Research Council of Canada from the Canadian Geotechnical Jouirnal, Vol 15, 1978, "Janbu, Bjerrum, and Kjaernsli's Chart Reinterpreted", by J. T. Christian and W. D. Carrier III, p 127 29 q0 E s bearing pressure, ksf equivalent Young's modulus of the soil, ksf - Comparison of test calculations and results of finite element analysis have indicated errors from Equation 3 usually less than 10 percent and always less than 20 percent for H/B between 0.3 and 10, L/B between 1 and 5, and D/B Reasonable results are given in most cases between 0.3 and 3, Figure 425. when p is set equal to unity. An equivalent elastic modulus 41. E* s is required in many settlement analysis methods when stiffness varies with depth. The Briaud (1979) method A E* s - z=n (4a) a. z=l Esi where rIzdZ, A j a. 0 j= area under strain influence factor, Figure 5, for homogeneous soil and type of loading considered, ft lzdz, z. 1 area under strain influence factor, Figure 5, for the ith soil layer and type of loading considered, ft is applicable to a soil profile when stiffness varies with depth and considers edge or center types of loading, but evaluation of the integrals may be laborious. The equivalent radius mat width, ft, and L : 2B. R - LB/r where L = mat length, ft, B - The Kay and Cavagnaro (1983) method simplifies this analysis such that 2qRo(l - u) E* s (4b) -PC where q - uniform pressure on soil, ksf p = center settlement, ft As - soil Poisson's ratio 30 0.0 0.4 0.2 ~.-0.5 0.6 .4 0.8 0.0 1.0 .2 0.4 0.2 .2 p.-0.5 I "IT N <~'U- I L COCD O - CD CO I I/ n r I 0)M 0~ 0.2 Figure 5. a) 0.4 0.6 Influence factors 0.8 1.0' B - width __ 0. _D_0 0.2 0.4 ICfor center and Iefor edge settlement R using data from Ahivin and Ulery (1962). and e of the mat, ps 31 - - {tLB/ where L soil Poisson's ratio. - length The center settlement may be calculated for a uniform pressure discussed later in paragraph 68. q as If the elastic modulus increases linearly with depth, then from Appendix A ) 2kR(I - E* s s (4c) 0.7 + (2 .3 -4 ,S)log n where k - constant relating Es - Young's elastic soil modulus, Eo + kz, ksf E0 - initial elastic soil modulus at the ground surface, ksf n - kR/(E Db - depth of mat below ground surface, ft Es with depth z, ksf/ft + kDb) Equation 4c is applicable to a mat with base at depth depths greater than 2B is incompressible. Db and the soil at The Gibson model (1967) Bk E* S - - (4d) 2 is applicable for elastic moduli increasing linearly with depth from zero at the ;ound surface for the mat base at the ground surface, 42. Winkler settlement, The concept of subgrade reaction was introduced 26 for computation of displacements in soil beneath railroad tracks. This concept has been applied to the analysis of bending moments and deflections in footings, mats, grillage beams, and other foundations that can be represented by a beam resting on an elastic subgrade. pressure q causes a deflection p A soil contact related by a constant of proportionality q k Sf - (5) - p where ksf - coefficient of subgrade reaction applicable to the foundation, 3 kips/ft q - contact pressure on soil, ksf p - settlement, ft 26 Winkler 1967 32 Each point behaves independently of any other as though the supporting soil is a fluid. Stress and strain computations are more easily and economically accomplished using the Winkler hypothesis than elastic theory. Displacements and bending moments in mats may be estimated from influence charts 22 for given loading pressure, mat characteristics, and the coefficient of subgrade reaction. Theoretical and experimental investigations have shown that the Winkler hypothesis is generally not satisfied except for beams of infinite length such as railroad ballast, roads, and embankments resting on a semiinfinite elastic subgrade. Appropriate values of ksf are not easily determined because they are not unique depending on the location in the mat, mat size and depth of base, and whether bending moments or displacements are being determined 17 . 43. Little is known on how k sf varies across the mat. Terzaghi's experience (1955) indicates that for long beams or continuous footings on the ground surface 2 (S+l) Sands: ksfo - k sp* 2S (6a) Clays: ksf ° - k spo5S (6b) where k sf° - coefficient of subgrade reaction at the ground surface beneath the footing, ksf/ft k - coefficient of subgrade reaction of 1-ft by 1-ft plate or beam 1-ft wide at the ground surface, ksf/ft S - spacing of column or line loads on mat, ft Table 5 provides some values of are not performed. ksp for sands and clays if plate load tests If loads are applied to the mat by columns, then the influence of these loads becomes less with increasing distance from the columns. The maximum length of influence is about 7D where D is the mat thickness, ft27 . S is therefore : 7D for locally applied loads. If the 28 footings are in sand with the base below the ground surface, then ksf - ksfo (1 + 2Db/B) 1 / 2 27 Terzaghi 1955 28 Ramasamy, Rao, and Prakash 1982 33 (7a) Table 5 coefficient Empirical Estimates of plate 27 of Subgrade Reaction Clay Sand ksp , ksf/ft ____________Shear Relative Density Medium Dense Undrained Strength, ksf ksp' ksf/ft Submerged Dry/Moist Loose Consistency 80 50 260 1000 160 600 Very Stiff Hard k- k (1+K 0)(1+2D b/B )1/2b 11/2 o sf Stiff kfz [1+2K 1 - 2 2 - 4 > 4 40Dz/B) 150 300 600 7 where ksf z 'Oefficient of subgrade reaction at depth Db embedment depth, ft K0 coefficient of earth pressure at rest B 44. - kf Dz, ksf/ft footing width, ft may also be estimated from elasticity theory by substituting Equation 3 into Equation 5 to give kf where y0 and yi - E* s k0 IB (8a) are found from Figure 4. Vesic and Saxena (1968) had performed parametric analysis that indicated good correlations with bending moments for 3EE* .sfm E k( Eb 2 - ps)D where 34 (8b) E - coefficient of subgrade reaction consistent with bending moments, ksf/ft elastic modulus of concrete, ksf D - mat thickness, ft ksfm c Equation 8b must be divided by 2.4 to obtain good correlation with displacements 17 . The Winkler foundation does not provide unique values of for both calculation of bending moments and displacements for mat 29 foundations. If the coefficient of compressibility is known, then ksf ksf - 1 fm S (9) v where f - factor from 0.5 to 1 m - coefficient of compressibility, ksf 1 The coefficient of compressibility may be estimated from in situ dilatometer DMT tests or laboratory consolidation tests on undisturbed specimens. 45. A comparison of Equations 6b, 8a and 8b for a concrete mat of depth D - I ft on a medium stiff clay with Es - 400 ksf, As - 0.33, Ec - 432,000 ksf, B - spacing of loads - 25 ft is shown as follows: Equation Coefficient of Subgrade Reaction ksf, ksf/ft 14.3 ksf/ft 16.7 ksf/ft 43.8 ksf/ft 6b 8a 8b For Equation 6b, ksf is assumed to be about 150 ksf/ft and S - 7D or 7 ft. L/B is assumed 0.96, Figure 4, and The result of Equation 8b is valid po is assumed unity. for a comparison of bending moments. 2 so that Al For Equation 8a, the length to width ratio Dividing results of Equation 8b by 2.4 is 18.2 ksf/ft, which is consistent with results of Equations 6b and 8a. Initial Mat Thickness 46. - Thickness and reinforced steel requirements of mat foundations depend on applied loads and differential movements in the supporting "Yong 1960 35 foundation soil. Applied loads should be arranged to cause a uniform pressure on thp underlying foundation soil thereby reducing differential movement. uniform distribution of pressure on the soil occurs when corner Qi and interior Qi/4 and Qe - QC A edge Qey column loads are in the ratio of 1 to 2 to 4; e.g., Qc - Corners and edges of structures will nearly always have Qi/2. wall loads added to the floor loads, which can be accommodated to make a uniform pressure distribution, if necessary, by widening the mat beyond the limits of the superstructure. The total edge load Qe at perimeter walls relative to the interior required to maintain uniform soil pressure also depends on the deck framing system. In order to avoid secondary moments in the mat, perimeter wall loads should be about 1/3 of the first interior column load and 3/8 of the next interior column load. 47. The initial mat thickness is evaluated to resist punching shear based on principles of statics. The force on the critical shear section of the concrete is equal to the force on the mat beyond the shear section caused by the soil pressure. The soil reaction pressure is assumed uniform. The critical shear section for diagonal tension failure is assumed to intersect at the base of the slab a distance d d/2 from the face of a column support where is the effective depth measured to the center of gravity of the reinforcement steel. This is the depth required to satisfy shear30 . Perimeter and interior load bearing (shear) walls are checked for wide-beam shear at a distance 48. d from the wall face'. The total mat thickness D required, after steel reinforcement is i added to satisfy bending moments, is D - d + db + Cover (10) where d - depth to satisfy shear, ft db - distance from center of gravity of reinforcing steel to the bottom edge of the reinforcing steel (bar diameter/2), ft 3 inches for reinforced concrete cast against and permanently in contact with ground; otherwise, 2 inches for No. 6 bars or 31 larger and 1.5 inches for No. 5 bars and smaller Cover - 30 ACI Committee 340-77 ACI Committee 318-80, Section 7.7.1 31 36 Reinforcement steel should not be added only to reduce mat thickness because the smaller thickness reduces rigidity. Reduced rigidity tends to localize column and wall loads instead of spreading them as assumed in rigid (conventional) design based on a linear soil pressure distribution. A good initial estimate of mat thickness may be found from Seelye (1956) which contains tables relating soil bearing pressures, column loads, concrete compressive strength, and 20 ksi reinforcement steel with the thickness of square column footings; however, yield strength of reinforcement steel currently used is often 60 ksi. Equations 11 in Table 6 show the required Column shear resistance. 49. to satisfy punching shear requirements for interior, edge, and d thickness corner column and floor loads that cause a uniform soil pressure q'. shear strength The provided by concrete in diagonal tension for ultimate vc 32 strength design USD is vc 4. - f;c .0.144 (12) where v - concrete shear strength, ksf f'c - concrete compressive strength, psi = workmanship factor for shear, 0.85 The factor 0.144 converts from psi to ksf. vc - 26.8 ksf for 3000 psi Steel will be required to satisfy bending in the longitudinal concrete. 33 direction Mu - a' = S.A s .f A s d - a] (13a) 2 f /(0.85.f'c.b') y where Mu - As - bending moment per width of strip, .2 in-lb in area steel per width of strip, d - effective mat thickness, inches fY b' yield strength of steel reinforcement, psi - width of strip, usually 12 inches 32 ACI Committee 318-80, Section 11.10.3 ACI Committee 318-80, Section 7.13 33 37 (13b) Table 6 Required Thickness to Resist Punching Shear Diagram Equations P Plan Location Section Interior For equilibrium: 4v cd(a + d) - q'S d a +d Edge " - -- b -- d d ---f ---- -[2(b+a+ d I c + +a + ~ b + d /22 4 - b - distance column from edge/corner, ft effective depth of mat, ft column width, ft column spacing, ft concrete shear strength, kaf soil pressure resisting punching shear, ksf a* - 2 + q'Iv c 4 + q'/v c f b + (a+S)/2 b 38 d)] -(a+d)(b+a+ 2 + [fb+3)e] 2+ 2q a* vc c f~ - a(a+bl lb -- - ub (0 5 b 5 d/2): - q[safd - (b+a+_)2] -2(a+b)e + 2C4La+b)J2 + q'.*.*2 c_ d = a - q' -- d/21 q' e = ~4f (a+d)]d ------------ For equilibrium d S = Vc - (0 5 b 5 d/2): d-e b+a+d/2 aj 2 (1a) 2 b Notation: + -(b+ 3 )e + Corner -- (a + d) e* For equilibrium b+a+d/2 - = S + - + 2 F2q--S2 (3ea +S 2 -(a+b) 2] (1c) Equations 11 foi typical column widths to 30 ft, and distance b a of 1 to 4 ft, column spacings of 10 from the edge/corner of 1 ft indicate that the thickness of concrete mats may be 7 percent less at the edge and 20 percent less at the corner than in the interior of the mat. 50. Wall punching resistance. The mat thickness required to resist wide-beam shear for reinforced concrete walls and an applied uniform soil pressure q' is q -- (S d - a) - c (14a) q - 1+ v c where vc - 2. fT7F .0.144 ksf 34; note that this is 1/2 the resistance permitted for columns d - effective depth, ft a - wall thickness, ft S - wall spacing, ft ff-workmanship factor for shear, 0.85 For masonry walls, d- c (14b) qI 1+ c The concrete shear strength v - 13.41 ksf for 3000 psi concrete. = Equations 14 were developed similar to those in Table 6 51. Figure 6 illustrates the trend in mat thickness d required to resist punching shear for interior 25-ft column spacings based on Equation llb for applied uniform soil pressures qm' of 0.1, 0.2, and 0.4 ksf/story. is the average pressure per story and equal to q'/Ns of stories. where Ns is the number Figure 6 also shows the distribution of mat thickness 34 Uniform Strength Design method ACI Committee 318-80, Section 35after method of Bowles 1982 39 qm' d 11.10.la 0 Cf)0 ET AL 1978 I-0 KSF / / c M // z / FRS S 0 Oy /** FRAS R 1975 WIN R 1974 &kSTR AN 1978 O 197 / //C COLUMNS WALLS- // -SHEAR I I 0 0 0 /BOBEEL * /"/*198 / FRASER 1975 /HOOF'ER 1981 & WOOD / 1977 / /?OLU LI / / / C) 0 0 EDITOR I CONST 1981 / / NEWS qm' =0.1 0 0 -u) / =0.2 KSF rY' j 0.4 KSF* FOCHT Z 0/)o 10 I I = O/ 8 6 4 2 I 2 I I 4 6 MAT THICKNESS 8 0 10 D, FT Figure 6. Number of stories for buildings versus thickness of mat 40 required to support shear walls as a function of the number of stories from Equation 14a assuming a 1-ft wall thickness, 25-ft wall spacing, and uniform soil pressure qm' of 0.1, 0.2, and 0.4 ksf/story using 3000 psi concrete. About 0.3 ft Thicker walls only slightly reduce the required mat thickness. should be added to the calculated required thickness mat thickness D. The column width d to obtain the total was assumed to increase in proportion a with the number of stories; i.e., a - 1, 2, and 4 ft for - 3, 12, and 50 Ns stories, respectively. 52. Figure 6 illustrates that the thickness of the 8.25-ft thick mat of the One Shell Plaza building with soil pressure of 0.4 ksf/story 36 is only 0.5-ft greater than that calculated for qm' - 0.4 ksf/story. A calculated soil pressure of 0.2 ksf/story is consistent with the observed 0.18 ksf/story given for the 7 story frame structure37 . A calculated soil pressure of 0.3 ksf/story is also consistent with the observed 0.3 to 0.4 ksf/story for an 11 story hospital38 . The 0.24 ksf/story pressure observed on the 3-ft mat of the 22 story residential building39 is a little high for punching resistance only to column loads with a column spacing of 25 ft and indicates that some load may be carried through the walls or column spacing is less than 25 ft. Minimum Depth of Foundation 53. A stratum selected to support the foundation and superstructure depends on functional requirements of the structure, locally existing practice for determining foundation depths necessary to avoid frost heave, soil erosion, soil moisture changes, and depths at which the soil bearing capacity is sufficiently large to support the structure. The depth of thin slabs for light structures is often above grade and on fill, unless a basement is required. Thin mats therefore often have distortion problems from soil foundations with 25-ft column spacing when punching shear controls design movements as a result of seasonal and long-term moisture changes in the soil beneath and near the perimeter of the mat. Mats constructed in excavations are subject to distortions caused by rebound of underlying soil, installation of utilities, and other construction 36 effects. Focht, et al 1978 37 Wardle and Fraser (1975a) 38 3 Stroman 1978 Hooper and Wood 1977 41 Thin mats subject to distortion 9 > 1/500 are often designed with ribs or crossbeams to provide the stiffness necessary to maintain differential displacements within functional requirements. Stresses applied to supporting foundation soil should be limited to 54. maintain settlements within levels tolerated by the structure and to optimize functional usefulness. Soil pressure should therefore be less than the precompression stress to avoid consolidation settlement and commonly limited to a value denoted as the allowable bearing capacity. The allowable bearing capacity is usually given so that settlement is about 1 inch. Evaluation of the allowable bearing capacity requires determination of the ultimate bearing capacity, increase in stress intensity in soil beneath the base of the foundation through any compressible soil layer subject to the applied loads, and guidelines for estimating appropriate factors of safety FS. Stress distributions in soil beneath foundations may be found by methodology in Appendix B, EM 1110-1-1904. 55. Ultimate bearing capacity. Mat foundations are required to be stable against a deep shear failure, which may cause rotation or a vertical punching failure. One of the first equations for estimating the vertical 40 stress required to cause a shear failure is qu 1.3cN + 0.47'B N + qo Nq (15a) where qu - ultimate bearing capacity, ksf c - cohesion or undrained shear strength C Nc - I' - dimensionless bearing capacity factor for cohesion 3 effective unit soil weight, kips/ft B - mat width, ft N - dimensionless bearing capacity factor for surcharge qo N - pressure applied to the soil at the mat base, ksf dimensionless bearing capacity factor for friction , ksf q Improvements to determining ultimate bearing capacity accounting for foundation rigidity and shape, inclined and eccentric loading, base tilt and 41 depth, and slope at the ground surface led to 4°Terzaghi 1943 4 1Hansen 1961, 1970 42 BI'N 7 6 + 7'DbNq 6q Nc 6 c + - (15b) where Db depth of mat base beneath the ground surface, ft - Nc) N , Nq - dimensionless bearing capacity factors 6c, 6 , 6q - dimensionless adjustment factors Data from Milovic (1965) and Muhs (1959) indicate excellent agreiment of bearing capacities with Equation 15b. For cases where bearing capacity may be critical such as in soft, cohesive soil, Equation 15a calculates an ultimate qu bearing capacity - 6.68c, while Equation 15b with modifications to account for soil compressibility 42 calculates q capacity appears to be at least for practical applications where 6C u - 6.36c. The ultimate bearing Cu is the average undrained shear strength in the bearing stratum. Allowable capacity using factors of safety. 56. Limiting soil pressures to the allowable bearing capacity is useful to limit settlements Experience has shown that allowable bearing tolerated by the structure. can often be evaluated using factors of safety applied to the qa pressure ultimate capacity q where -u FS (16a) FS = 2 or 3 are usually used for limiting settlements to less than 2 inches in cohesionless and cohesive soils', respectively. Table 7 illustrates some methods of using results of field tests for estimating allowable bearing capacity and limiting settlement to 1 inch. estimating qa These methods may be applied to of soil beneath stiffening beams of ribbed mats or footings supporting column loads. The plate load test is not included because extrapolation of results to mats is not reliable for B > 3 times the plate width. Factors of safety applicable to applied uniform pressures on mats 57. are variable and usually greater than 3 for limiting elastic settlements to less than I inch. If settlement p is to be limited to about 1 inch, then substituting Equation 16a into Equation 3 of the theory of elasticity and assuming 42 qo " qa and qu - 6Cu leads to Vesic 1975 43 Table 7 Allowable Bearing Capacity From Field Tests q Source Definitions ksf Standard Penetration Test Bowles (1988) K N5 5 4 d B > 4 Db B B K -1+ - 0.33 Db <133 2.5 NBi 2 N 5 5 [B+IIKd - LB - depth of mat, ft - width of mat, ft N55 - blow count, 55 percent efficiency N7 0 -2 N70 - blow count, 70 percent efficiency d NN70[ B+ B> 4 K2d Cone Penetration Test Schmertmann (1978) Sands: * B q 122" D 1+ •L. Clays: F-sNc " 5 I qc bN -B a Nk +av Nk cone resistance, ksf cohesion bearing capacity factor c a, av qc - C- total overburden pressure, ksf - cone factor - Pressuremeter Test Briaud, Tucker, & Coyle (1982) KPM T - pressuremeter bearing capacity factor p*L - equivalent pressuree meter limit pressure, KPMTP*Le+ av FS ksf • Factor of safety equals 3.3 Factors of safety are intended to prevent bearing failure 44 72C B u E FS (16b) s The factors pop, ksf, B - 50 ft, and in Equation 3 are taken as unity. E - 200 ksf, then FS = 18. For example, if Cu - 1 Factors of safety should not usually be used to estimate allowable bearing pressures for mat foundations on the basis of uniform applied pressures; instead, elastic settlements should be estimated for the given applied pressures on the mat to check that settlement will be less than 1 inch or within levels tolerated by the structure. Differential Soil Displacements 58. Most procedures for analysis of soil displacements consider only the influence of loads applied on the soil as discussed in paragraph 37 on total soil displacements. Settlement analyses should also consider structural rigidity and distribution of loads. Foundations to be constructed on expansive or collapsible soil should also consider effects of differential soil movement caused by moisture changes on the long-term serviceability of the foundation and superstructure. Mat foundations that are rigid will not be subject to significant differential movement, although they may tilt. Designs often use a uniform load distribution as much as practical to minimize differential displacements and reduce moments and shears. 59. Differential displacements are used to estimate required for foundation and structural design. deflection A A/L ratios The ratio of the relative (maximum differential movement) to the total settlement varies from zero for rigid mats to as much as 50 percent for many flexible mats, which is directly related with the difference in center and edge settlement influence factors, Figure 5. Deformations in heterogeneous soil beneath rigid mats approach those similar to punching failure as illustrated in Figures 7a and 7c; hence, possible damage to adjacent structures is reduced. Differential movement can be greater in areas near localized changes in soil moisture for mats on swelling soil and can approach the total displacement. Differential movement can exceed the total settlement if portions of the foundation heave on swelling soil. Sophisticated analysis of differential displacements such as taking into consideration changes in structural stiffness and loading during construction are not yet worthwhile because of existing uncertainties in structural stiffness and soil parameters. 45 UNIFORM a. PRESSURE RIGID SMALL FOOTING ON COHESIONLESS SOIL c. FLEXIBLE MAT b. ON q RIGID MAT ON COHESIVE OR COHESIONLESS SOIL J. FLEXIBLE MAT ON COHESIONLESS SOIL COHESIVE SOIL Figure 7. Relative distribution of soil contact pressures and displacements of rigid and flexible mats on cohesionless and cohesive soils 46 60. Deformation patterns. The shape of the deformation pattern beneath mats depends on the flexibility of the foundation and type of soil. The elastic modulus of homogeneous cohesionless soil or sand is a function of confining pressure, while the elastic modulus of homogeneous cohesive soil or clay is essentially constant and independent of confining pressure. Small rigid footings on cohesionless soil cause less soil contact pressure near the edge than near the center, Figure 7a, because this soil is pushed aside at the edges due to the reduced confining pressure. This leads to lower strength and lower elastic modulus near the edge than near the center. The saddle-shaped pressure distribution for large rigid footings and mats occurs because of soil shear at the perimeter 43 , Figure 7b. The overburden pressure pressure under the edge may also confine a cohesionless soil increasing its strength 44 . A uniform pressure applied to a rigid foundation on cohesive soil will also cause a saddle shaped pressure distribution because of greater soil contact pressure near the edge than near the center. This is partly because soil behavior is influenced by stresses in adjacent soil and that additional contract pressure is necessary to provide the stress to shear the soil at the perimeter. 61. The distortion of a uniformly loaded flexible mat on cohesionless soil will be concave downward, Figure 7c, because the soil near the center is stressed under higher confining pressure such that the modulus is higher near A uniform pressure applied to a flexible foundation on cohesive the center. soil, Figure 7d, may cause greater settlement near the center than near the edge because the modulus of elasticity in the soil is constant laterally and cumulative stresses are greater near the center as a result of the pressure bulb stress distribution. A measure of the relative structural rigidity 45 is necessary to assist evaluation of differential displacements 62. OL Structural rigidity. 4 ksfS OL = L. }s : where 43 Burmister 1963 44Kerr 1987 45Hetenyi 1946 47 (17) O - relative rigidity per foot, ft - L - length of member, ft ksf - coefficient of subgrade reaction, ksf/ft S = width of member, ft E - I When - QL rigid. Young's modulus of concrete, ksf 4 moment of inertia, ft is less than or equal to The mat is divided into strips of width between column or shear walls. or soil with a small coefficient OL w/4 or 0.785, the mat is considered 1.75 and semi-flexible for 63. S equal to the spacing A mat is more likely to be rigid on soft soil ksf A mat may be considered flexible if 1.75 > OL > w/4. The soil pressure distribution under flexible mats depends on a variety of nonlinear factors that include (1) immediate settlement caused by loading increments during construction, (2) distribution of loads on the mat, (3) consolidation settlement or heave that overlaps immediate settlement even duting construction, (4) increasing stiffness of the mat during construction, and (5) redistribution of loads and soil pressures on the mat from long-term differential movement. Optimum analysis requires sorting out each of these effects so that each contribution to the resultant soil pressure distribution can be individually analyzed. 64. Numerical analysis using finite element or finite difference computer programs is often used to assist computation of stress and strain because of the above complexity. The problem is simplified some by assuming that soil and structural components are linear elastic materials, which has been justified because of relatively low working loads and displacements usually observed in practice46 . Even with this assumption, the analysis still requires programs and large capacity computers. A further simplification may be made by condensing the stiffness of the superstructure and foundation into an equivalent mat thickness. Differential displacements were reduced by about 1/2 when the stiffness of a 7 story open frame superstructure on a 2.2-ft thick mat was condensed into an equivalent mat of 3.1 ft thickness using Meyerhof's method 37 . This method described in Appendix B also considers 46Hooper 1978 48 additional stiffness from filling of the open frame structure so as to form continuous shear walls. A simple alternative method for estimating the influence of superstructure rigidity on deformation patterns is also proposed in Appendix B. 65. Methodology. Differential displacements may be estimated from the theory of elasticity using soil moduli from results of laboratory strength tests conducted on undisturbed samples from different locations and depths beneath the proposed foundation. Soil-structure interaction analyses that use the theory of elasticity in the solution of differential displacements include plate on elastic foundation programs such as SLAB2"1. SLAB2 also evaluates benaing moments and shears that are required for design. Soil displacements and reaction pressures may be analyzed with variable and nonlinear soil moduli using two-dimensional finite element computer programs such as AXIPLN 47 . The theory of elasticity generally indicates differential displacements from 0 to 50 percent of the total displacement for uniform applied pressures depending on the relative stiffness of the mat and thickness of compressible soil. 66. Mat foundations should be designed to accommodate the maximum angular distortion max* Unfortunately, many observed differential movements are irregular, Figure 2c, making nearly impossible estimation of the maximum Moreover, estimation of angular distortion prior to construction. imax should consider and compare structural loads to heave, heave potential, and loading pressures. la. A rough estimate of Pmax may be obtained from Equation A practical method for quickly estimating the maximum angular distortion when a potential for heave occurs is = max S max -p. i (18) / where Pi = immediate settlement, ft Smax - maximum potential heave,ft 2 - distance between points of maximum and minimum settlement, ft 47 Withiam and Kulhawy 1978 49 The maximum settlement may occur beneath the most heavily loaded part of the structure such as beneath columns and consist only of immediate elastic settlement; consolidation may not occur in a soil with potential for heave in situ. The maximum potential heave is a positive number (settlement is negative) and may occur beneath the most lightly loaded part of the foundation such as midpoint between diagonal columns. the sum of Smax and -pi The total differential movement is Nonuniform soil wetting may be caused by leaking water, sewer, and drain lines. 67. A simple method for estimating differential displacements that considers structural rigidity calculates elastic settlement at a particular 48 location by n Pi = q I..h. Z i=l ' (19) ' Esi where q = soil pressure applied by the foundation, ksf I. I - influence factor for layer h - thickness of layer Esi - i, ft Young's soil modulus of layer The influence factor I. and shown in Figure 8 for diameter ratio L/B i, ksf is given for center and edge settlement in Figure 5 ps - 0.2, 0.3, 0.4, and 0.5. to an equivalent circular raft of radius 68. i should be R - {LB/r The mat is converted in which the length to : 2. Figure 8 shows that the Kay and Cavagnaro (1983) method can be arranged to provide simple estimates of total and differential settlement relative to the center and edge of the mat. Edge settlement appears roughly 1/2 of the center settlement for a completely flexible mat. The differential settlement is found from P - (PC - Pe ) Rs where p - PC - differential settlement, ft center settlement, ft 48Kay and Cavagnaro 1983 50 (20) INFLUENCE FACTOR q. EDG CENTER h.FT 0 N~/~,'/-O3 Io 0 01I SETTLEMENT, FT KSF l KSF, UG CEN7 TE ICJ . = I,\ 4 FT Pc 0510TOTAL 0 p - Rs IFROM CHARTs SLOG'° ' KR RIGIDITY ,oR _ ,,T (c-O RADIUS MAT R __________________________EGUIVALENT FT * MAT THICKNESS D __.___FT - FT POISSON'S RATIO SOIL "P______ 08 MODULUS OF ELASTICITY Ec -MAT z (~J E 04 02 "O - -2 R4 -I Figure 8. Settlement computation (after Kay and Cavagnaro 1983) 51 ' * ____ KSF Pe - edge settlement, ft R = reduction coefficient, dimensionless s R s shown in the chart, Figure 8, is related to the relative stiffness KR pcE cD 3(1 + cc S) s(21) 2qR4 (1 - p S) where Ec = Young's modulus of the mat concrete, ksf q - uniform pressure applied on the mat, ksf D - mat thickness, ft R - equivalent mat radius ps = Soil Poisson's ratio The relative stiffness KR {L7B/, ft is dimensionless. The mat thickness should be an equivalent thickness including superstructure rigidity as evaluated in Appendix B. Final Design 69. Standard procedures for the structural design of mat foundations are documented by American Concrete Institute 49 . These procedures are grouped into the conventional or rigid uniform pressure and flexible or elastic design methods. The flexible method may provide a more economical design if the mat can be considered flexible by Equation 17 where OL > 1.75 and L is the average of two adjacent load or column spacings that vary no more than 20 percent, paragraph 62. Except for unusual problems, the contact pressure q at the base of the mat may be assumed to follow a straight line distribution for the uniform pressure method or a distribution governed by the coefficient of subgrade reaction of the Winkler concept for the flexible method. Some mats are purposely designed with flexibility such as mats for silos or tanks when the primary purpose is containment and the mat should deform rather than crack with differential movement. 70. Uniform pressure method. This method applicable to rigid foundations assumes a uniform pressure or straight line distribution beneath the base of the mat. Eccentric loads with or without overturning moments can 49ACI Committees 318-1980, 336-1987 and 436-66 52 lead to trapezoidal (or nonuniform) pressure distributions and rotation of the foundation. The length of the foundation is made sufficiently large such that the resultant of overturning moments and axial loads from all columns in a line is located in the center of the length of the foundation and the resultant soil pressure distribution will be uniform provided the mat is rigid. 71. The general design procedure is as follows: (1) mat dimensions are selected such that the center of the mat and center of gravity coincide, (2) the mat may be divided into a series of equivalent beams centered on rows of columns, (3) a shear and moment diagram may be constructed assuming that the column loads are point loads, (4) the mat depth is selected to resist the maximum shear without reinforcement, and (5) the amount of reinforcement is subsequently selected to resist the maximum bending moment. for design of rigid mats are provided in the literature49 50 ' Detailed criteria 1 . Concrete floor slabs subject to heavy concentrated loads may be designed by procedures described in TM 5-809-12, "Concrete Floor Slabs on Grades Subjected to Heavy Loads". The uniform method may be recommended for mats on mud, soft clay, peat, organic soils, or even clays of medium stiffness. 72. Winkler foundation. The Winkler foundation may be applicable to mats subject to plane strain such as dry docks with long walls, pavements, or roads. The design of flexible mats commonly use the beam on Winkler foundation concept of to evaluate design parameters from charts 22 or 45 Design parameters take the form ksf computer programs 15 ,52,53. d4 Pressure intensity q': q' - E I d P cdx 4 V E I kips/ft/ft width Shear V: - kips/ft width c 50 Teng 1975 Bowles 1988 52 51 Haliburton 1972 53Chou 1981 53 d P dx 3 (22a) (22b) Bending moment M: kips-ft/ft width M - E I d2 p dx2 (22c) where EC = I = Young's elastic modulus of concrete, ksf 4 moment of inertia, ft p = displacement, ft x = horizontal distance along beam or mat strip of width S, ft A simple solution to Equations 22 is accomplished by equating q' - - ksSp. The solution should be checked against allowable design parameters determined by criteria of the American Concrete Institute 49 . Deflections and bending moments determined by American Concrete Institute 318 and 336 should be consistent with calculated values from computer programs 51 . The solution depends on boundary conditions such as distribution of applied loads, beam length, and distribution of the soil reaction pressure. Soil response curves required for input are found by multiplying appropriate values of by width S. A major disadvantage of this approach is that reliable guidelines are not available for determining appropriate values of how ksf ksf ksf and varies with horizontal locations. 73. The finite element method may be applied to relate forces and displacements of each element by5 3 [F] = [K].(6f) + ksfab.(6 s (23) where - matrix of 3 forces (vertical force, moment about x-axis, moment about y-axis for each node of the element) [K] - stiffness matrix of the foundation element (function of mat dimensions a and b of the element, Young's modulus and Poisson's ratio of the foundation), lb/ft 6 f - displacement array for each node in the foundation element, ft ksf - coefficient of subgrade reaction of foundation soil, ksf/ft 6s - displacements array in the soil, ft The finite element method for the Winkler concept was applied to develop program WESLIQID 53 . 54 74. Elastic foundation. Flexible mats may also be analyzed using the plate on elastic semi-infinite foundation to evaluate design parameters1n 53 5' 4 Boussinesq's solution and Burmister's layered elastic solution are used to compute subgrade surface deflections for homogeneous and layered elastic foundations, respectively. The relationship between forces and displacements of each element can be written similar to Equation 23 (F) (24) ([Kf] + [Ks]).(6 - where (F) - externally applied nodal forces, lb [Kf] - stiffness matrix of the foundation (function of the finite element configuration and flexural rigidity of the mat), lb/ft - stiffness matrix of the subgrade (function of nodal spacing, Young's modulus and Poisson's ratio of the soil), lb/ft - nodal displacement array, consisting of a vertical deflection and two rotations, ft [K (6) J The finite element method for the elastic foundation was applied in programs SLAB2 n , WESLAYER 53 , FOCALS5 5 , SAP- 5 75. 6 and ANSYS 57 . The basic difference between Winkler and elastic foundations is that the Winkler deflections at a given node depend only on the forces at the node, while elastic deflections at a given node depends on the forces at the node and forces or deflections at other nodes. 76. Some specialized simple solutions of thin mats on Applications. swelling/shrinking soils are available and compared in Table 8. An improved design procedure for perimeter loads on ribbed thin mats up to 18 inches thick constructed in swelling soil have also been developed by the Post Tensioning Institute (1980) using program SLAB2 (Appendix C). Many of these simple methods assume some shape of the soil mound Ym CCmm x (25) where Ym - maximum soil heave without surcharge load, ft x - horizontal distance, ft 54 Huang 1974a, 1974b "Wardle and Fraser 1975b 56 Bathe, et al 1978 57 DeSalvo and Swanson 1982 55 Table 8 Summary of Relevant Design Methods DESIGN METHOD BRAB (1968) LYTTON (1972) WALSH (1978) ASSUMED SLAB ACTION Simplified Three Dimensional Simplified Three Dimensional Simplified Three Dimensional L SLAB LOADING q, I -TqL---j -- I WI NKL ER ' k PARRBOLIC I-JJm Empirically Related to Clay Type and Weather --2 - ,e , COUPLED - DETERMINATION OF SLAB SUPPORT AREA COEFFICIENT "c"1 0 qC q qe , MOUND SHAPE O FRASER AND WARDLE (1975) Precise Three Dimensional AND INITIAL ; fIG 58 " TC EL O EsI E[-LS s -Mathematrically Related to e,y k,q m -m-kY 1 [0.05] m 2e L= L -e L Ym CALCULATION OF "II Fully Cracked Section Uncracked Section CALCULATION OF LONG TERM "E" 0.5E 0.5E c Partially Cracked Section Partially Cracked Section Not Specified Use O.75E c c Not Specified Use O.75E c LEGEND: c = support index m = mound exponent e = edge distance, ft qc = E = Long-term modulus of concrete, ksf qe = E based ksf on 28-day modulus =C concrete strength, compressive c mo e fiesrethf4 = mont of imound k = coefficient of subgrade reaction of foundation soil, ksf/ft L = Length of slab, ft center pressure, ksf edge pressure, ksf average foundation pressure, ksf maximum differential heave across the before stab-soil interaction, inches q = Ym = C E = constant characterizing mound shape = soil elastic modulus, ksf soil Poisson's ratio 58 After Holland 1979 56 Cm, m - empirical constants A reasonable value for m is 311,59. that rises too quickly, while m z 4 A value of m : 2 provides a mound appears to flatten out the heave profile too much. 77. The Post Tensioning Institute design procedure is applicable to conventionally reinforced or post-tensioned ribbed mats for light, perimeter loads. Required soil input parameters include Atterberg limits, cation exchange capacity, percent clay less than 2 microns, unconfined compressive strength, elastic soil modulus and Poisson's ratio, edge moisture variation distance, and depth of active zone for soil heave. Required foundation parameters include the concrete compressive strength, elastic modulus and Poisson's ratio and yield strength of reinforcing steel. Development of the design equations used a parametric analysis that assumed the coefficient of subgrade reaction ksf 7 ksf/ft. This method should not be used for perimeter wall loads exceeding 2 kips/ft, stiffening beam depths exceeding 3 ft, beam spacing exceeding 20 ft, differential center lift movements exceeding 4 inches, differential edge movements exceeding 1.5 inches, and mat lengths and widths exceeding 300 ft, or for structures with significant concentrated loads on either the interior or perimeter. The procedure should tend to produce conservative designs because the analysis assumes simultaneous perimeter loads on all four edges, while many practical structures such as houses experience perimeter loads on only two edges. The procedure considers effect of climate on edge moisture variation distance and potential differential soil heave, but other effects such as unusual desiccated soil and rainfall, removal of pre-construction vegetation, and downhill creep are not considered. 78. A simple "untried" method of evaluating the required stiffness Ec I of a mat foundation to maintain differential movements within acceptable levels may be found from an application of the frequency spectrum approach, which was applied to the design of pavements on expansive soil 6 . This model assumes a beam on a Winkler foundation to evaluate El from the relative rigidity OL, Equation 17. The relative rigidity per foot 59 6 Lytton 1972 McKeen and Lytton 1984 57 0 times a model wavelength r may be found from the solution to the pavement model, Figure 9. The model wavelength r is an average length between bumps or depressions along the length of a pavement or mat section of width S. Aa is the acceptable differential movement of the pavement over a length of Ae r/2 and is the expected differential movement of the soil without the pavement on the soil over the same length. 1/1333 such as for 9m max If the allowable deflection ratio A/L is 1/500, a reasonable angular distortion for initiation of damage from paragraph 18, then Aa - (r/2)/1333 or r/2666. The rigidity of the pavement required to flatten or "squeeze the bumps" in the soil to the acceptable differential movement stiffness of the pavement observed range of r Ec I Aa is given by for some pavements is 10 to 35 ft assumes complete contact of the soil with the pavement. ym for a ribbed mat of width B beam width ksf. w - . The The analysis Table 9 illustrates that can be flattened to within = and the may then be found from Equation 17. 6° the differential movement for A/L = 1/1333 12.5 ft (spacing S = 12.5 ft between ribs), 18 inches, and concrete modulus of elasticity The mat thickness may vary from 4 to 8 inches. • Ec - 432,003 For example, if ksf - 7 ksf/ft and P - 20 ft the ribbed mat with stiffening beam depth of 28 inches from the top of the mat will squeeze a soil heave of 5 inches sufficiently to result in a mat deflection ratio A/L - 1/1333. one-dimensional beams and not mat foundations. 58 This model is applicable to 0.0 0.2 0.4 0.6 0.8 1.0 12 110 C4 , 80 Ch 6 FLEXIBLE < -J Fy 2 SEMI-FLEXIBLE RIGID 0.0 0.2 0.4 0.6 0.8 1.0 Aa/Ae a. r Aa Ae - RELATIVE RIGIDITY VERSUS RELATIVE VERTICAL DISPLACEMENT relative rigidity per foot, ft1 wavelength or average length between bumps/depressions, ft acceptable differential movement over length r/2, ft expected differential movement over length r/2, ft b. Figure 9. NOMENCLATURE Relative structural rigidity by the frequency spectrum model 59 Table 9 Examples of Maximum Soil Heave Squeezed to A/L - 1/1333 By a Ribbed Mat 12.5 ft Wide With Beams 18 Inches Wide Maximum soil Heave yml inches Coefficient of Subgrade Reaction ksf ksf/ft sf' Wavelength r, ft Beam Depth Below Top of Mat, inches 20 28 36 4 10 20 30 50 6.0 4.0 2.3 0.8 9.0 7.5 4.5 1.7 11.0 10.0 7.0 3.0 7 10 20 30 50 5.0 3.0 1.5 0.6 7.5 5.0 2.9 1.2 9.0 9.0 4.9 2.1 10 10 20 30 50 4.7 3.0 1.3 0.5 6.4 5.0 2.7 0.9 8.0 9.0 3.6 1.4 14 10 20 30 50 4.0 1.9 0.8 0.4 6.0 3.3 2.1 0.7 7.5 4.0 2.9 1.2 60 CASE HISTORY STUDIES PART III: Introduction 79. Seven ribbed mats supporting moderate loads and three thick flat mats supporting heavy loads from multistory hospital buildings were analyzed to provide design information on soil parameters. These mats are located in San Antonio, TX, except for the thick mats supporting the hospital in Fort Gordon, GA, and Fort Polk, LA. Soil data available from field and laboratory investigations and elevation readings of the mats permit some analyses of the structural performance based on uniform pressure, Winkler, and plate on elastic foundation methods. Representatives of the Corps of Engineers from the Southwestern Division, Fort Worth District, Waterways Experiment Station, and Office, Chief of Engineers, visually examined these facilities in San Antonio in May 1984 to assist evaluation of performance. Results of these analyses are compared with design requirements given by the American Concrete Institute (ACI) and flexure theory. Application of the frequency spectrum method is made in Part IV. Soil Parameters 80. Soil parameters were evaluated from results of laboratory tests performed on soil samples taken from the field before construction. samples were obtained with an 8-inch auger. Disturbed Relatively undisturbed samples were obtained with 6-inch Denison and core barrel samplers. Selected samples were sealed in airtight containers and shipped by truck to laboratories for testing. Boring holes were usually left open about 24 hr to detect perched water levels associated with gravel and other pervious strata, then backfilled with lean cement grout to inhibit seepage of perched water into underlying desiccated soil. 81. Shear strengths of the soil were evaluated from results of unconsolidated-undrained consolidated-undrained Q R triaxial strength tests and occasionally from tests. The elastic soil modulus E s was evaluated from stress-strain data as a function of depth using the hyperbolic model, paragraph 39. Constrained modulus Ed was also evaluated from results of 61 consolidometer tests by 61 Lambe and Whitman 1969 61 E (1 + eo)a = (6 0v(26) Ed 0.435C where e 0 a v C - initial void ratio - vertical overburden pressure on the in situ soil, ksf compression C or swell C index - C s Both compression and swell indices were used to provide a range of Ed ' The constrained modulus from Equation 26 includes the influence of consolidation or plastic strains and will usually be less than strains of Q test results. deformation, while E equal = E when ps Since Ed E5 evaluated from elastic assumes negligible lateral includes lateral deformation, 0.0. Ed > E .E d An equiv.1ent or uniform elastic modulus 5 should E* and 5 coefficient of subgrade reaction required for the analyzes were estimated from results of soil tests using methodology in PART II. Structural Parameters 82. Bending moments and shears were evaluated from methods of the American Concrete Institute6 2 and compared with values calculated from plate on elastic foundation program SLAB211 and beam on Winkler foundation program CBEAMC 5 . Observed displacements were compared with displacements calculated from SLAB2 and CBEAMC. Input parameters for SLAB2 include Young's elastic modulus of the mat concrete ratio of the mat concrete the soil Ec normally assumed to be 432,000 ksf, Poisson's uc - 0.15, an equivalent Young's elastic modulus of E*, and Poisson's ratio of the soil soil was assumed 0.3. Poisson's ratio of the The total moment of inertia cross-section in each of the long L and short to permit computation of the flexure stiffness orientations. u. S Ec I I of the entire mat directions is also input in each of the two Tables Bl and B2 describe evaluation of I for each cross- sections of mat foundations, which may be added together to evaluate the total moment of inertia. Program SLAB2 can be made to simulate soil center heave patterns by imposing edge gaps and edge heave by imposing center gaps. 83. Program SLAB2 requires input of a uniform Young's elastic soil modulus that is applicable for the entire mat E*. s 62 Eshbach 1954 62 However, mats placed on the ground surface and on expansive soil characteristic of this study are subject to soil deformation caused by moisture changes in the active zone of soil heave. This active zone of heave may include 20 or more feet of soil beneath the mat. The effective soil modulus representing heave beneath ribbed mats is therefore assumed in this study to be the average modulus within 50 ft beneath the ground surface. E* may be evaluated from Equations 4. s Beam on Winkler foundation program CBEAMC 15 was also applied because 84. beam programs are often used for design and they are simpler and more economical to operate than plate on elastic foundation programs. Input parameters of CBEAMC include the moment of inertia of the section (Tables BI and B2). Program CBEAMC can simulate heave patterns by specifying displacements. Results of a CBEAMC analysis for uniform pressure applied on a soil of uniform stiffness will cause zero bending moments and shears in the mat section. The soil stiffness k' input into CBEAMC is in units of ksf and found from the coefficient of subgrade reaction of the mat k' where ksf S ksf by kksf" S - (27) is assumed the spacing between columns or T-sections of ribbed mats. may be calculated from known soil pressure/settlement ratios, Equation 5 or estimated from Equations 6 to 9. The values of ksf are consistent for displacements; therefore, bending moments calculated with these Winkler foundation may not be correct because foundations. ksf ksf for the are not unique for mat Winkler analysis is further handicapped because the extent of soil support under the flat portion of the ribbed mat is not known. Paragraph 24, PART I, describes the American Concrete Institute specification for bending of an effective T-section width that can be substantially less than the spacing S larger required to compute bending moments than that required for ksf between ribs, which may partly compensate for the 2.4 times displacements described in paragraph 44. corrections for evaluating Equation 27 with k sf ksf , Because of these uncertain the stiffness k' is calculated from evaluated from given applied pressures and displacements calculated from SLAB2 analysis. 63 Ribbed Mat Foundations 85. Ribbed mats are composed of cross-beams supporting a flat floor slab, Figure 10. Mats selected for analysis and identified in Table 10 were constructed on about 4 ft of nonexpansive, low plasticity compacted fill overlying expansive soil strata. This fill is compacted to not less than 92 percent of maximum density after ASTM D1557. Trenches of about 3 ft in depth were excavated in the fill for placement of reinforcing steel and concrete for stiffening beams. Stiffness parameters of the compacted fill were not determined, but were assumed similar to those of the underlying soil. Six inches of granular material were placed on the prepared surface of the compacted fill between stiffening beams of all the mats. A polyethylene vapor barrier was placed on the granular fill beneath the flat portions of the mat prior to concrete placement and snugly fitted against the walls of the trenches for the stiffening beams. 86. Reliable benchmarks for level surveys were not available for any of these mat foundations. Reference benchmarks consisted of 2 or 3 manholes used for drainage located in the immediate vicinity of the ribbed mats. These benchmarks are identical to those used by the contractor during construction. Differences in displacements relative to the original elevations measured by the contractor therefore include both differences in elevation readings, elevation changes in these benchmarks, and contractor error. Consequently, only rough comparisons may be made between these measured displacements and those calculated from the analyses. 87. Table 10 illustrates the structural capacity of the T-beams of the selected ribbed mat foundations 62 . Letters A and B in the left column of Table 10 indicate T-sections described later in plan views of each mat. Numbers 1 to 6, U. S. Army Reserve Center Warehouse, indicate each of the six stiffening beams parallel with the short direction. flexible with All of these mats are OL >> 1.75 (see paragraph 62) as shown in Table lla. differential displacement A Maximum between the center and edge of these mats will be at least 80 percent of the difference between center and edge settlement of a fully flexible mat as shown in Table llb. Table 12 illustrates bending moments developed in these mats for the given maximum differential soil heave Ym using the Walsh (1978) method for a beam on a Winkler foundation, Table 8. 64 7;9 LNGIUIN . .. .............. . .... ..... w I Figure 10. S Schematic diagram of ribbed mat section of width for soil-structure interaction analysis 65 Table 10 Structural Parameters for T-Beams a. A , 2 Mat Mat d, in. W, in.in. Gymnasium Brooks AFB Data Processing Randolph AFB US Army Reserve Fort Sam Houston 3.12 A 3.12 B Facility 3.27 A 4.00 B Center Warehouse 3.12 1 3.12 2 3 3.12 4 3.12 5 3.12 3.12 6 Maintenance Building A 1.20 3.12 B Dental Clinic 3.00 A Fort Sam 3.00 B Houston Medical Clinic 3.00 A Fort Sam 3.00 B Houston Facility Training Management Pest 2.00 A Fort Sam B 2.00 Houston j M, ft-kips V, kips Flexure Rigidity,2 2 , kips-ft E I E~cloormkp 18 18 33 33 0.91 0.91 ± 468 ± 468 71 71 3,915,600 3,776,502 12 12 33 33 0.91 0.91 - 490 + 600 47 47 3.062,108 3,062,108 18 18 18 18 18 18 27 36 44 53 61 69 0.90 0.91 0.92 0.93 0.93 0.93 ± 380 ± 513 ± 631 ± 765 ± 885 ±1005 59 76 92 108 126 142 2,485,398 4,940,494 8,541,116 13,453,350 21,649,488 30,037,626 18 18 33 33 0.94 0.91 ± 186 ± 468 71 71 3,951,668 4,085,270 16 16 29 29 0.90 0.90 ± 392 ± 392 56 56 2,367,360 2,336,562 16 16 29 29 0.90 0.90 ± 267 ± 267 71 71 3,818,284 3,540,180 12 12 27 27 0.90 0.90 ± 243 ± 243 39 39 1,567,097 1,600,245 + indicates compression and - indicates tension in top fibers Includes steel ***Refers to the T-section analyzed in the mat described later * ** b. S M _- f - Dbin L2 W2 - spacing, in. beam width, in. D A " slab thickness, in. beam cross-section, W(3+d) in.2 d - beam depth plus slab thickness minus 3 in. 2 area steel, in. A ------ AsfsJd, maximum bending moment resisted by steel, lb-in, n v = = - - section, lb teel tensile strength, 60,000 psi f'c fs - I - k/3 I oor= k VcA, allowable vertical resisted by beam10.ps - r 2 [ pn + - A/Wd 211/2 - pn (pn)J 6- 66 - Est/Ec allowable shearing stress resi ted by V in.shear - secton S spacng, W Nomenclature concrete, 2 - fc ultimate concrete c8sdaystrensafter composite moment of mat inertia of ribbed 4 T-section, in. (Equation B13) Table 11 Relative Flexibility of Mats a. Hetenyi (1946) Method Mat B, ft Gymnasium, Brooks AFB Section Bl Data Processing Facility, Randolph AFB, Section A Maintenance Bldg, Section A Troop Dental Clinic, Fort Sam Houston, Section A Troop Medical Clinic, Fort Sam Houston, Section A Pest Management Facility, Fort Sam Houston, Section A Ek (1- kof kaf/ft Ec1, ft 5.2 17.3 3,776,502 0.050 85.3 4.20 149.8 3.0 18.5 3,062,108 0.047 149.8 6.90 72.7 6.1 27.0 3,951,668 0.058 72.7 4.14 109.7 4.0 13.8 2,367,360 0.050 109.7 5.38 164.0 2.7 15.0 3,818,284 0.041 164.0 6.59 58.7 7.5 15.0 1,567,097 0.066 98.7 6.42 ** f, S 4 4 = 0.3 - 1.0 - JA2s )BI U L, 1 ft-f C 2 kips-ft 85.3 - 400 5 ksf ES ksf S, ft * U >1.75 1.75 ieldsa flexible mat I c w b. Kay and Cavagnaro (1983) Method Mat S, ft Gymnasium, Brooks AFB Section Bi Data Processing Facility, Randolph AFB, Section A Maintenance Bldg, Section A Troop Dental Clinic, Fort Sam Houston, Section A Troop Medical Clinic, Fort Sam Houston, Section A Pest Management Facility, Fort Sam Houston, Section A *3 D rF-21 R - I, EcI, 4 D, L, kipsct2 ft ft B, Ri ft ** ft R LogK R R5 17.3 8.74 3,776,502 1.82 89.3 85.3 49.2 -1.03 0.80 18.5 7.09 3,062,108 1.66 199.8 149.8 97.6 -2.05 0.95 27.0 9.15 3,951,668 1.60 204.0 72.7 68.7 -1.64 0.90 13.7 5.48 2,367,360 1.68 143.3 109.7 70.7 -1.61 0.90 15.0 8.84 3,818,284 1.92 190.0 164.0 99.6 -1.88 0.92 15.0 3.63 1,567,097 1.43 98.7 58.7 42.9 -1.17 0.80 Ec - p E - 432,000 a E = KR = c + 2[ 13 D 67 . 400 ksf ksf Table 12 Maximum Bending Moments by Walsh (1978) Method Mat L, ft Gymnasium, Brooks AFB 85.33 Section B1 Data Processing Facility, 150.00 Fort Sam Houston Section A Maintenance Building, Fort 72.67 Sam Houston, Section A Dental Clinic, Fort Sam 109.67 Houston, Section A Medical Clinic, Fort Sam 164.00 Houston, Section A Pest Management Facility, 58.67 Fort Sam Houston, e /L w, kips/ft 0.2 2.3 Edge 0.2 4.8 0.4 Lift Mode Ym' inches C1 M kips-ft Center 0.25 1.00 0.40 0.5 4.0 2.0 0.98 0.94 0.98 42 124 270 4.6 Center 2.00 0.10 4.0 0.86 429 0.2 3.0 Center 1.00 0.20 1.0 0.96 180 0.4 2.7 Center 0.60 0.20 2.0 0.98 182 0.4 2.5 Edge 2.00 0.10 2.0 0.79 226 L = am - A ym = w k' = length of section, ft edge moisture penetration distance, ft maximum tolerable differential movement, in. maximum differential heave, in. applied load/length of section, kips/ft stiffness, k fS, kips/ft length/ft displacement C1 = constant obtained from Table 1 of Walsh (1978) M - maximum bending moment, kip-ft, (1 - C1 )WL2/8 = w/(k'y m ) 0.25 1.00 0.60 Section B Notation: A/Ym 68 A/L The deflection requirement 9max - 1/500 where L is taken as 1/1333 from Equation lb assuming is the spacing S The Walsh between adjacent beams. method can calculate large changes in bending moments for small change in the C1 when constant C1 approaches 1.0, Table 12. Gymnasium, Brooks Air Force Base The gymnasium is an L-shaped building located in the south portion 88. of Brooks Air Force Base near San Antonio, Texas, at the intersection of West Gate and Inner Circle Roads. Construction was initiated in the fall of 1981. Superstructure framing consists of a steel roof deck on open web steel joists supported by steel trusses and concrete columns in the gym area and load bearing masonry walls and steel beams in the locker room areas. Stiffening beams, Figure 11, are 18 inches wide by 3 ft depth below the mat top. spacing is variable from 8 to 34 ft. S beams is 5 inches. Mat thickness D Beam between stiffening The building was equipped with downspouts and 2-ft long splash blocks directing rainfall away from the mat foundation. The grade was nearly flat around the building. 89. Soil parameters from results of laboratory tests Soil parameters. on soil samples from five borings taken in June 1977 are shown in Figure 12. Overburden soil consists of lean clay, sands, and silts of generally alluvial A perched water table was found about origin down to a depth of about 15 ft. 8 ft below ground surface in the gravel GC stratum. Below the overburden soil is 4 to 7 ft of yellow-brown medium plastic CH-CL clay with caliche weathered from the underlying primary formation. The primary stratum consists of about 75 ft of noncalcareous, bentonitic clay shales of the Midway formation of Tertiary age. 90. The results of Q triaxial strength tests on specimens from relatively undisturbed boring samples indicated an undrained shear strength Cu of about 1.6 ksf that increases at a rate of about 0.04 ksf/ft of depth, Figure 12. The ultimate bearing capacity of this soil is at least 10 ksf providing an allowable bearing capacity for pressures on the stiffening beams of more than 3 ksf assuming a factor of safety of 3. E The elastic soil modulus appears to be about 400 ksf, while the constrained modulus less at about 80 ksf based on swell indices. 69 Ed is much Swell pressure tests (Method C, B2 1"1[ 11 UPPER RIGHT QUADRANT SLAR 1ANALYSIS,, I L -4 1 SL - f r L - lij - - 4_ 2J ]FJ -J, IL - -I -I-I- -L--- ?J I . L,'' I I I 1' -- , r ---- ---. --.-.. -. ILI p~ N I L -iJ--J ~ ~ N H B SSECTION 7I- Figur Fonainpa II~ H L 11. 2-N 4 rosArFreBs5ynsu 70i Z 4r GU O 0 0 0 UU 000 U- a I, 50. x52 at, ] >- a 13* al C cc T 3t ST 7'! 0 7- 0 0 P - 0 a 0 0 00 ~U NN I N00 I I IA NHLd3O Figure 12. Soil parameters Brooks Air Force Base gymnasium 71 ASTM D 4546) indicate a desiccated zone with potential for swell above and below the perched water table. 91. Level survey. A level survey of the gymnasium taken November 1983, Figure 13, relative to the original contractor survey shows small and uniform settlements up to 0.3 inch in the gymnasium area and up to 0.8 inch in the adjacent locker room and administrative facilities. Slight heave or apparent center lift was observed near point 5 of the gymnasium. A level survey repeated in April 1985 indicated a slight (0.05 inch) decrease in heave near point 5 and slight (0.05 inch) increase in heave near points 25, 31, and 32 relative to the November 1983 survey. The maximum observed A/L ratio is on the order of 1/900 near points 1-2 and 4-5 in the gymnasium (section A) near the exterior beam and points 24-30 and 24-25 in the locker room area (section B). A 1/8-inch diagonal crack was observed during the May 1984 field trip in the concrete masonry units in the locker room area on the second floor inside the stairwell on the northwest side near point 25. Vertical control joints were not observed in the superstructure except between the two distinct parts of the building. Water was observed to be leaking out beneath the south wall of the gymnasium over the exterior stiffening beam near points 2 and 3. Heave measured at point 5 could be a direct consequence of this leaking water. 92. Analysis. Program SLAB2 was used to analyze the soil-structure interactian behavior of the locker room for uniform beam loads of 2 ksf and 1 ksf, Figire 14, assuming E* - 400 ksf. A uniform pressure S q - 1 ksf on the stiffening beams appears to cause displacements reasonably representative of the observed displacements in the locker room. Negative displacements refer to settlement and positive displacements heave. Calculated bending moments ind shears for no soil heave (Ym - 0.0) for sections B and B 1 2 (y -00)fo ecios are well within structural capacities of the mats. The calculated A/L ratio for no h!ave is about 1/3000 for points 1-2, 4-5, 24-25, and 24-30. induced -dge lift ym - 0.25 An inch penetrating 10 ft beneath the perimeter of the mat is representative of the maximum observed and displacement pattern, Figures 13 and 14. A/L ratio of about 1/900 This edge lift increases the maximum calculated bending moments to about 100 kips-ft and maximum shears to about 10 kips, Figure 14. A maximum induced edge lift of 1 inch, much greater than currently impressed on the building, would begin to mobilize the full 72 Ll. NN (D \ e)C IIY CO / X~ CD/ CY/ S3HONI'3AV/ - el,0A, 4C"' FigueNovmbe 13 Broos Ar Foce 198 ase 73/ levl suvey ymnsiu 0 LENGTH, FT 20 10 30 I I 40 0 LENGTH, FT 20 30 0 40 I FI fI I 11 _ 400 400 i/1ILo .. ' . ... .°" °... ................. f. ........ ............... £200 2 200 0 0 z !p LEGEND - -200 2 KSF, Y.=0 INCH c= I KSF, Y. = 0 INCH ...- '= I KSF, YM = 0.25 INCH = .............. I KSF, Y. 50 ; = 1,0 INCH ..........Z 50 .".. .--.. '..... "..........-.. 0 . ° ......... °°°".......... I*J -- -50 ." °.... 50 075 0.75 Q OBSERVED 0.50 0.25 ,. .... -- -200 DISPLACEMENT , 0.50 0.25 - 0 0 - 0-025 -025 -0.50 -0 50 * -----......... - - - - - -0.75 -0.7S -1.00 -1.00 -1.25 -1.25 a. SECTION Figure 14. .. -07 -- - - - 0 b. SECTION B2 B Soil-structure interaction analysis of section B, Brooks Air Force Base gymnasium, using SLAB2 74 structural capacity. assumed The effective concrete modulus is probably less than the Ec - 432,000 ksf, which would decrease moments and shears. The Walsh (1978) method predicts maximum bending moments less than results of SLAB2 for similar edge lift conditions, Table 12. 93. The displacements pi calculated by SLAB2 in the center (point 1), edges (points 2 and 3), and corner (point 4), Figure 11, are 0.636, 0.541, 0.490, and 0.408 inch, respectively, indicating a dishing action characteristic of a flexible, uniformly loaded mat on a deep elastic, compressible cohesive soil, Figure 7d. A beam on a Winkler foundation analysis that simulates the SLAB2 displacements requires that the coefficient of subgrade reaction ksf should vary across the mat as follows for an average pressure on the mat q - 0.21 ksf (or 1 ksf only on stiffening beams) Point Location p, inch 1 2 3 4 C.nter Middle lomg Middle short Corner 0.636 0.541 0.490 0.408 ksf, ksf/ft A0 i 1.18 1.01 0.91 0.76 3.96 4.66 5.14 6.18 The above table also shows how the influence factor poi calculated from Equation 8a (paragraph 44) required to vary in order to match displacements for E* - 400 ksf and S = 85.33 ft. This shows that kf is not unique for s mat foundations. This trend in ksf determined as a function of location are used as described below to calculate influence factors applied in Equation 8a to evaluate appropriate p0 i that may be ksf depending on location in mat foundations. 94. A CPEAMC analysis was performed for section B1 , Figure 11, using a linear distribution of coefficients and ksf between points 1 and 2 bounded by the above q - 1 ksf on the stiffening beams of the T-section or 0.21 ksf over the full T-section with width equal to beam spacing. stiffness q - The soil k' required for input into CBEAMC was found from Equation 27. These results from CBEAMC provide displacements on the order of those using SLAB2, Figure 15. Three cases were performed using CBEAMC to compare SLAB2 results: 75 LENGTH.L, FT 0 10 20 30 40 50 00 LEGEND 0 (3 -50 z e 0% 00 -100 0000 VARIABLE I FULL SUPPORT (CASE ---- CONSTANT I FULL SUPPORT (CASE 21 VARIABLE I BEAM SUPPORT (CASE 3) os!00 0.02 8- DISPLACEMENT C3 ACTUAL DISPLACEMENT 10 00 -(0 0 U) z z -05 Uj -j -0 CASE 3 1) AT 2 8 INCHES Figure 15. Comparison of results between SLAB2 and CBEAMC for section B 1,Brooks Air Force Base gymnasium 76 Case 1. Variable I, full support Description The moment of inertia is that of the T-beam section indicated in Table 10b between crossbeams, but equal to 3 S(t + D) 12 at each cross-beam, Figure 10. Soil support was used under the entire T-beam section. All stiffening beams loaded q - 1 ksf. 2. Constant I, 3. Moment of inertia represented only by the full support T-beam section, Table lob. Cross-beam I excluded. Soil support provided under the full T-section Variable I, beam support Moment of inertia same as case 1, but soil supports only the stiffening beams. Case 2 simulates SLAB2 results best, but moments at each cross-beam are not simulated because loads were not applied on the cross-beams. Case 1 where loads were applied on the portion of the mat supported by stiffening beams caused large edge settlements and negative bending moments (tension in the top fibers) that contrasted with the positive moments from SLAB2 (compression in top fibers). Results of case 3 show that the flat portion of the mat contributes substantial support since actual displacements are much less than 2.8 inches. Data Processing Facility, Randolph Air Force Base 95. The data processing facility, located on Randolph Air Force Base near San Antonio, Texas, between First Street East and First Street West adjacent to J street, was completed in 1975. The facility is a rectangular 200 by 150-ft single story masonry building constructed on a ribbed mat with fairly regular beam spacings from 13 to 19 ft, Figure 16. Beam width is normally 12 inches and beam depth below the mat top is 36 inches. Mat thickness between stiffening beams is 6 inches. 96. Soil parameters. Soil parameters from results of laboratory tests on soil samples from five borngs taken in May 1972 are shown in Figure 17. 77 .. 0-, a U) ~~0<zm 0I U) ...-. 91 .9-.91 I I ) I o' I 1fOI,-.6tr, ,9-,9I - .9-.9 .0- , , -J L.J L.---JL.rJ ,jII z ! " .. , i I - IIi Ii I , r-i-]r !Io -,g i Ii I II 1 VJ <O - iI Ii N cc < z 0 z' b 0 I--~~Z~:LJ ,, -., . II I , j IJ .-- I----IF - 7 <m i -- - -- If---7 ' -- - L I - -- +1 D L r 1 i - - -r- AL L J..J L JL. I- - rJ 'K4L-I--III I 7 I 1 - - ------- L L -- 11---J _L Figure 16. .1 I I' . - II r-r ' L. I I I in I- I - II r-1 ir Ir - -- _ I j bD -A ___L___ ___J___ Foundation plan for the Data Processing Facility, Randolph Air Force Base 78 0 I _ I I I I I I I u. 0o 0a w _.00 0 I N I I 0 I 0 ~'0 z j -C I QuO 0 0 0* 0. zu II 0 - Z Cc 01 00 o 0 0 cc 0 o z8 0 0 0 00 I- , 0 7o 0 0 0 (3 0 0 0 0 I I Figure 17. I Soil parameters for the Data Processing Facility, Randolph Air Force Base 79 The overburden soil consists of about 8 to 10 ft of plastic CH dark gray to black, noncalcareous, stiff clay containing some scattered, discontinuous zones of clayey gravel. About 7 to 9 ft of tan to light gray, low to medium plastic CL clay containing calcareous particles up to cobble size was Two to 3 ft of clayey and encountered beneath the surface overburden soil. silty gravel overlying the primary formation was encountered about 18 ft below A perched water table was observed 12 to 15 ft below the ground surface. ground surface, which probably collected in the permeable gravel layer overlying the relatively impervious tan to gray clay shale of the primary The primary formation is Taylor marl of Cretaceous age. formation. 97. Results of several undrained triaxial Q tests shown in Figure 17 indicate that the allowable bearing capacity should be at least 2 ksf assuming a safety factor of about 3. Young's soil modulus evaluated from results of tests is about 600 ksf, .,hile the constrained modulus ksf based on swell indices and Equation 26. Ed Q is only about 60 Swell pressure from a consolidometer/swell test (Method C, ASTM D 4546) on an undisturbed specimen taken 7 ft below ground surface in the overburden soil was 4 ksf indicating desiccation. 98. Level survey. A level survey conducted in November 1983 indicated center lift up to 0.5 inch toward the southwest portion of the mat, Figure 18. Settlement is about 0.3 inch in the West corner increasing to about 0.6 inch at the south and north corners. of about 1.1 inches. A 20-ft addition had been added to the northeast side and east corner during 1979. existing building. The east corner shows substantial settlement This addition was secured with dowels into the A level survey conducted in April 1985 indicated a general heave increasing to 0.25 inch at the east corner relative to the November 1983 survey. 99. Distress was not observed prior to 1979 before the addition. A long fracture was observed in the mat in May 1984, Figure 18, inside the building near the east corner. The ceiling and floor tiles were showing several inches of lateral distortion near the center of the original building. Excessive settlement caused by the addition appears to be contributing to the interior distress in the superstructure; therefore, consideration should be given to 80 //\ \\\ / \ /// / '\ \I ,, \I !V3R\\ ,, 4/,'/. , i// \ I I i / / \/ //\ / 0 \/ / \ \/\ ) /.. '//", / :\,/ \ / 4. /, \/ ,, /\ , / / / I \ ' / '4\,/ \ /\\ ! .. I /., 4. '44. / / /\ . \ /II' \\ /\I Fiue1 / Le./sre Randolp fo/h A/ t Foc 81 Pr singFciiy Bs '~I '4 providing flexible connections with new additions. perimeter was about 1 percent or more. The grade around the The maximum observed A/L ratio was 1/400 near points 19-22. 100. Soil-structure interaction analyses were performed for Analysis. sections A and B shown in Figure 16 using program CBEAMC and for the south quadrant using program SLAB2. Option NSYM - 4 in SLAB2, Table C3, requires analysis of only 1/4 of the mat with symmetry about the X and Y axes. soil elastic modulus was taken as 600 ksf. beams was assumed 2 ksf. The Loading pressure on the stiffening For section A, the beam width is 18.5 ft with length 150 ft and for section B, the beam width is 16.5 ft with half length of 100 ft. The mat coefficient to a soil stiffness k' ksf = for the CBEAMC analysis is 3.1 ksf/ft leading 56.4 ksf for section A and 50.3 ksf for section B. The finite element mesh for program SLAB2 is illustrated in Figure 19. 101. Results of program SLAB2 for the south quadrant sections A and B, Figure 16, are shown in Figure 20. Calculated moments and shears for no imposed heave are small with a maximum center settlement of 1.1 inches. Settlement calculated by CBEAMC for sections A and B for loads consistent with the SLAB2 analysis are 0.92 and 1.0 inches, respectively. While settlements calculated by CBEAMC are flat, SLAB2 settlements resemble a shallow bowl. distribution of ksf required to duplicate SLAB2 displacements using program CBEAMC for points 1 to 4, Figure 18, for an average pressure E* - 600 ksf, and B The - q - 0.264 ksf, 149.8 ft is s Point Location p, inch 1 2 3 4 Center Middle short Middle long Corner 1.073 0.789 0.814 0.610 ksf , ksf/ft 2.82 3.96 3.76 5.13 0/i 1.42 1.01 1.07 0.78 The above -able also shows the distribution for the influence factor Equation 8a. The A/L Popi, ratio between center and edge is a maximum of 1/1800 such that cracking is not expected if heave is not imposed on the foundation. 102. (-) Figure 20 shows that the locations of the maximum (+) and minimum moments and shears for no imposed heave are located near the midedge and 82 10 9 20 30 40 Q- 50 60 70 80 90 100 1 10 120 - ___..I 130 - I39 140 139 -+x _138 8 7 137 6 136 5135 4 134 @ +x 133 __ y 2- 0® _ 132 ----------------- 00 11 -Y09 21 31 41 51 61 71 81 91 101 111 121 LEGEND -x A +x A -y A +y A - 0 + 0 MINIMUM MAXIMUM MINIMUM MAXIMUM MOMENT x DIRECTION MOMENT x DIRECTION MOMENT y DIRECTION MOMENT y DIRECTION MINIMUM SHEAR MAXIMUM SHEAR Figure 19. Finite element mesh for SLAB2 analysis, Data Processing Facility, Randolph Air Force Base 83 131 LENGTH L, FT 0 40 20 120 100 60 60 140 100 120 ISO 160 140 ~- 200 Q. -' 0 2 A ~/ I -200 A m !" j -OSEVE 50 A/ A- -400 0 > 'A At A N DISLAEM UPPE A. A A -OBSERVED DISPLCCE z RIGH SECTIONAA [LB2 NTIL L 8 2 025E I 2 A A A wA ~ A I I , ,A A. A-i.. A wA~ -00LENTER SLAB2. UPPER RIGHT SECTION A HEAVE 0 6 A A A A A 0-AA B SECTION B A SECTION A Figure 20. Soil-structure interaction analysis, Data Processing Facility, Randolph Air Force Base. 84 q - 2 ksf 200 corner, respectively. Distances from the edge and corner are approximately the same or less than the relative stiffness length11 4Ec - (28) where 9' = relative stiffness length, ft Ec = Young's concrete modulus, 432,000 ksf E - Young's soil modulus, 600 ksf I - moment of inertia of the mat cross-section, ft4 103. Imposing zero center displacement for sections A and B using CBEAMC and edge-down gaps in the south quadrant using SLAB2 roughly simulated the observed displacements, Figure 20. Displacements calculated by SLAB2 were realigned to simulate zero displacement near the mat center. Calculated moments and shears from both programs CBEAMC and SLAB2 appear to be similar and approach the capacity of the T-beams, Table 10 The maximum and minimum moments and shears calculated by SLAB2 were located near the mat corners within distance 9', Equation 28, and approximated the mat capacity. The Walsh method, Table 12 predicts high bending moments of 270 kip-ft, but still within the mat capacity. Maintenance Shop and Warehouse US Army Reserve Center 104 The maintenance s!'op and warehouse of the US Army Reserve Center were constructed in 1980 and are located between Sultan and Winans Road near Harry Wurzback Road in Fort Sam Houston, Texas. They are steel frame rectangular buildings with metal siding and concrete masonry unit walls. layout and size of the foundations are illustrated in Figure 21. spacings vary from 17 to 27 ft. The Beam Beam depth for the maintenance shop is 3 ft including the 5 inch thickness of the flat portion of the mat between stiffening beams. The depth of each of the six beams for the warehouse mat from left to right varies from 2.5 to 6 ft (numbers 1 to 6, Table 10) including the 5-inch thick flat slab between stiffening beams. Beam width varies from I ft at the bottom to 2.5 ft near the top; analyses assumed an average width of 1.5 ft. Steel reinforcement consists of two number 11 bars 85 A E. - ,--, .. .- .. I _L. . . -- -- -r ---T } i II _-LL . III L.. J,-_ -~---------LIL-- - . . . ii . . . Il II A[ [ r - -- i ...-[ - _ _ _ IL 24-8- -r I '. ~ -r ... 20i-0- .20'0 ... I / II t, I I i II ---. 1$ i .J1,L..__ :I - - - - - ---- - -r 27-0 ,I Ir-. -.. 27-0 I I - - - r I/I . L '-I 27-0 I --,J - IL - -- 204'-0" i i Ii/ II iL II - 2 I i II . - -,'J II JL I - ---- -- - --I --' --" -r --I -r-~ ,i "t r---- -- . -J ... I' -- ...--- .-7 II -- --- 21-6 I !I . ... 6-10 I \ \ MAINTENANCE BUILDING I I I ! I II II II - -.- - - - - -. - -.'- -_. L _ ",_ Si: I 25- 250 I 2- I 250 I ._25*-'-o . 25 -'. US Figure 21. __25'-o; rm WAREHOUSE Reev 28 .. 25'-o- - 25-o" Cetr ot! a oso Foundation plan Maintenance Shop and Warehouse, US Army Reserve Center, Fort Sam Houston 86 top and bottom in each beam, except beams in the short direction of the maintenance shop contain two number 7 bars top and bottom. 105. Soil parameters. Soil parameters evaluated from results of laboratory tests on soil samples of 34 core borings obtained October and Overburden materials consist of about 2 November 1978 are shown in Figure 22. ft of medium plasticity (CL) black clay, 3 or 4 ft of high plasticity (CH) brown clay, about 7 ft of white, calcareous medium plastic (CL) clay, and about 3 ft of clayey gravel. The gravel contains a perched water table with water level beginning about 14 ft below ground surface. The primary material underlying the overburden is a tan to gray, weathered and jointed clay shale of the Anacacho formation of Cretaceous age. This material is about 200 ft thick and consists predominantly of moderately hard calcareous shale with occasional hard limestone interbeds up to 20 ft thick. Weathered shale is found down to about 49 ft below ground surface and the unweathered, hard, blue shale is found below this depth. 106. Results of triaxial undrained strength Q tests indicate that the soil has an undrained shear strength of 2 ksf near the ground surface increasing linearly with depth at the rate of 2 ksf/15 ft of depth. The allowable bearing capacity of soil beneath the stiffening beams is at least 4 ksf. The elastic Young's soil modulus is about 400 ksf down to 30 ft and 800 ksf or more below this depth. The constrained modulus is about 200 ksf or less down to 30 ft and more than 400 ksf below this depth. Consolidometer/swell test results indicate swell pressures of about 2 ksf and significant swell potential above 14 ft of depth. 107. Level survey. A survey conducted on the mat surface of the maintenance building in November 1983, Figure 23, shows a general settlement increasing toward the north from 0.5 to 1.2 inches. dual-shaped differential heave in the n An unusual, symmetrical hern part of the mat appears, which could be a construction error in the mat elevation. The northern half of the mat was designed with a slope that caused the east and west perimeters to be 4 inches lower than the center to permit drainage of runoff water from washing operations. A 1-inch error in the slope at points 19-13-9 and 17-11-7 will account for this unusual displacement pattern. Visual observations in May 1984 indicate no distress, except for a small crack in the concrete masonry 87 8 0 0 0 0 o.. 0 0 0 ] I 8T 0 J 008 0 0 8o 0 00 00o o~ 0 0 0 0 8o 0000 00 0 '1 00 040b 0 0 Figure 22. Soil parameters Maintenance Shop and Warehouse, US Army Reserve Center, Fort Sam Houston 88 I N I\0 ~ In N IIj S3HONI '3AV3H N / / S3~I3'~ / ICD / /, / 0 , / , n ~/ In' Fiue2. Noeme 198 lee suve Maneac/hp \ / / 0) / / S/ Fiur ~ / /~ / 89 Noe/3 o SAm / \e198 eev \/0) lee eteFr \ 89 uvyMineac a hp oso units of the wall near point 10 at ground level, Figure 23. If mat distortion recorded in Figure 23 is correct, the maximum observed ratio is 1/200 near points 8-9; otherwise, the maximum observed about 1/400 near points 12-8. A/L A/L ratio will probably be Level readings taken in April 1985 are not significantly different than those of November 1983. 108. Analyses. program SLAB2 for Results of the soil-structure interaction analysis using E5 - 400 ksf and q - I ksf, Figure 24, indicate relatively low bending moments and shears for no soil heave. The maximum calculated A/L ratio is about 1/2000 so that distress is not expected in the mat or superstructure. The SLAB2 analysis indicates bending moments and shears that are larger in the short direction than in the long direction; specifications indicate less steel in the short direction. 109. The finite element mesh for the maintenance shop shown in Figure 25, assuming mat symmetry about the X or long axis, shows the location of maximum moments and shears near the northwest corner and mat center. Calculated settlements near the center are greater than near the edge, in contrast to flat displacements from Winkler solutions. The observed dish- shaped pattern of displacements appears consistent with the SLAB2 elastic foundation analysis, Figure 23. 110. Displacements input into SLAB2 in an attempt to simulate the distortion pattern observed in Figure 23 led to excessive bending moments and shears that would fracture the mat, but such damage was not observed. The mat stiffness is too large to simulate this distortion pattern in the north part of the mat indicating gaps should appear beneath the ipat. Results of the Walsh method, Table 12 predict bending moments exceeding the structural capacity, Table 10. A construction error therefore appears to cause the slope to be about an inch less than intended. The distribution of ksf and P0 i required to simulate SLAB2 displacements for points shown in Figure 22 using the Winkler found,-ion with no heave and a uniform pressure - 400 ksf, and B - 72.7 ft is 90 q - 0.17 ksf, E* s LENGTH L, FT 0 20 40 60 80 I I 1 100 140 120 I 160 I 8SO _ _ _ 200 0 20 40 _ _ I1 - 400 .(L 200 w 0 200 >E 0 -400 50 \ I - Z 0 __ -50 L.J zw \ -- -- SLAB2. NO HEAVE SLAB2 CENTER HEAVE i J" "2- - - - [ - / 0 o\ SECTION 8 1/2 SECTION A Figure 24. Soil-structure interaction analysis Maintenance Shop, US Army Reserve Center, Fort Sam Houston using SLAB2 91 1 0 HOIM J4VH 0 I 0 I - I -®N 0 - X>>- - - 0 > xx xx 00 S0 Figure 25. Finite element mesh of the mat supporting the Maintenance Shop, US Army Reserve Center 92 Point Location p, inch I 2 3 4 Center Middle short Middle long Corner 0.737 0.541. 0.628 0.450 ksf , ksf/ft 2.77 3.77 3.25 4.53 0 pi 1.99 1.46 1.69 1.21 Dental and Medical Clinics 111. The dental and medical clinics, located in northeastern Fort Sam Houston near Garden Avenue and Harvey Road, were constructed in 1980 and 1981. The clinics are single story, rectangular brick and concrete masonry structures supported on ribbed mats, Figure 26. Vertical construction joints were closely placed in the superstructure at approximately 4-ft intervals to The site slopes downward from northwest to southeast at increase flexibility. a slope of about 3 percent leading to a grade differential close to 8 ft across the diagonal of both structures. Beam spacings vary from 10 to 15 't in the dental clinic and 11 to 30 ft in the medical clinic. Beam depth of the dental clinic mat is 2 ft 8 inches from the mat top with beam width of 1 ft 4 inches. Beam depth of the medical clinic is 3 ft from the mat top with beam width of I ft 6 inches. Thickness of the flat part of the mat is 6 inches. Reinforcement steel consists of three number 9 bars placed both top and bottom in the stiffening beams supporting the medical clinic. 112. Soil parameters. Results of laboratory tests on soil samples from borings taken at the dental clinic site in December 1977 and January 1978 are shown in Figure 27a. Results of laboratory tests on soil samples from five additional borings obtained at the medical clinic site in January 1979 are shown in Figure 27b. Overburden material varies from 6 to 16 ft thick and consists of dark brown to black, gravelly, medium CL to high CH plasticity clay and clayey gravel GC. Figure 27a shows about 10 ft of black CH clay overlying about 6 ft of clayey gravel beneath the dental clinic site. Figure 27b shows about 6 ft of black CL to CH gravelly clay overlying about 2 ft of sandy gravel beneath the medical clinic site. The clayey gravel contains a perched water table with water level 7 to 12 ft below ground surface. The primary material below the overburden is the Taylor formation of upper Cretaceous age. This material is yellow-brown, calcareous, slightly silty, 93 AA 3T I ' LJ r L JffIr1f - - - - L JL JL 311 - L_ L- L _J ... -_ J _ JL L --- L- - __1 jL. J = J L L J" F -- -1-1 i -- --Ir \--- L__ /--- - J 1 1- _11 -r- L r , -- J Ir :- --- -; - -L- -'- II J__ -- ; I I I- - L-L__LJL_ J__I .. L al _jN L- I, I , n JLJJ ii ' L ..-. ',i- I ! l r~- ' LL. I I-'oI - II LrL* -, L : _- I! - I-- -- ' -4 II 4 3 l:' ' Lr-T I ii 4 .'d ] ADPANT SLAB2 ANAL A CLINIC MENTAL A TROOP __J__ _, -I__ _ , L-_ '--- ,-- ---------I'----- " 1 i ---- ''------''-----' __ i__ ,---,,--..J-, .--. ---, ' I '------'------'--------- " 'i'F--, L- I r I * I I ' I I i - - I II i 1* I 1 III I II - -- II I if[ 06 4 ..... 11L L( L _.. - -i- -b'-O Figure 26. J _ _l J q -. AI L,_ .... . .. . .... - Foundation plan Troop and Medical Clinics, Fort Sam Houston 94 00 g _ I__ 0 __ _ _ __ __ _ _ 00 C l II-I 00 FP .0 0 0C 0 - E0 0 0 zz o o 00 00 00 C / ,"" 'P "~~~~0r j 0 0 0 0 0 0 I I 0 0 0 ow,. o4oo "ioo--.00 00 1 ?PL 00000 - 0 Figure 27. QIo Soil parameters Troop and Medical Clinics, Fort Sam Houston 95 soft to moderately hard (Rock classification) clay shale containing occasional The shale is expansive CH jointed and weathered hard marl up to 3 ft thick. clay up to 50 or 60 ft below ground surface. 113. Results of triaxial undrained Q strength tests indicated an undrained shear strength of 1.6 ksf about 9 ft below ground surface with substantially greater strengths below this depth. capacity is at least 3 ksf. The allowable bearing The soil elastic modulus Es varies from 200 to 400 ksf within the top 15 ft of soil and 600 to 1000 ksf below 15 ft from the ground surface. Results of consolidometer/swell tests indicate a potential for swell and swell pressures exceeding calculated vertical overburden pressures above 7 ft and below 17 ft, Figure 27. 114. Level survey, dental clinic. A level survey of the dental clinic conducted in November 1983, Figure 28, indicates a tendency toward center heave up to about I inch. east edge. Settlement of about 0.5 inch was measured near the The April 1985 survey indicated about 0.3 inch reduction in settlement (or heave) near the east edge relative to the November 1983 survey and about 0.1 inch more heave near the mat center. Visual observations of the building in May 1984 indicated no cracks in the exterior brick panels; these panels include vertical construction joints at 4-ft intervals. Cracks were observed in the exterior stiffening beams on both east and west sides of the dental clinic mat. The maximum observed A/L ratio was about 1/250 near points 6-16, 9-20, and 27-28, Figure 28, running east to west. 115. Analysis. dental clinic. Results of soil-structure interaction analysis of the dental clinic mat, Figure 29, were completed for sections A and B in Figure 26a using CBEAMC and for the northeast quadrant of Figure 28 using SLAB2. The soil modulus E* was taken as 400 ksf. s Mat settlement for a uniform pressure of 1 ksf on the stiffening beams of section A was 0.83 inch using CBEAMC. SLAB2 calculated about 1.0 inch of center settlement and 0.8 inch edge settlement. The distribution of ksf for points 1 to 4, Figure 26a required to simulate SLAB2 displacements using the Winkler foundation, q 0.22 ksf uniform pressure, E* - 400 ksf and B - 109.7 ft is s 96 IA 0 S3H:)NI '3AV3H 'S D I.,In 0~0 w 0 'CY CYC 0' 0 CV' 'C w~ A / 0INDC oO 0 'S Figue Novmbe 28 198 For ~ "C N 00 levl Na suveyDentl oso 97 Clnic LENGTH L. FT 0 20 40 60 80 0 100 ! SII 20 40 I 60 I 200 " ~ od /0 0IV 0 01 -200 ",-' 0"" 0".; * --- "'-\ 1 0 0i 0 0 0 0 O 0 LEGEND CBEAMC, NO HEAVE -- CREAMC. CENTER HEAVE 0 9 CBEA'4C. PERIMETER LOAD I KSF ---- -400 50 0 000 SLAB2, NO HEAVE 0 0 SLAB2, CENTER HEAVE I oOI 000 0 0 NJ0 0 / 0 000 00 O00RE 0 0 0 00MNTN00 DSP 0 0 0 . 0 r -50 ~~~OBSERVED DISPLACEMENT-, 0% 10 000 0 0 0 0 0 " - -- --- --- -- - - - ,0 .. J*000 E-WO000000000. A. DENTAL CLINIC Figure 29. - SECTION A S. DENTAL CLINIC - SECTION S Soil-structure interaction analysis Dental Clinic, Fort Sam Houston 98 116. Point Location p, inch ksf, ksf/ft 1 2 3 4 Center Middle short Middle long Corner 1.073 0.789 0.814 0.610 2.45 3.33 3.23 4.31 Po0i 1.49 1.09 1.13 0.85 Imposing center heave and perimeter loads increased moments and shears toward the structural capacity of the mat, Table 10. This was particularly evident from results of CBEAMC for center heave which caused moments to exceed the structural capacity. The corresponding calculated displacements shown in Figure 29 imposing a I ksf perimeter load for the CBEAMC analysis and edge gaps for the SLAB2 analysis to simulate heave illustrates the center doming pattern that can be obtained. Gaps imposed for SLAB2 analysis to simulate displacements of section B appear to compare better along lines 2 and 3, Figure 28, than along lines 4 and 5. displacements simulate those along lines 4 and 5 well. CBEAMC calculated The gap procedure required to simulate soil heave using SLAB2 is restrictive and cannot be used if areas affected by soil heave are relatively small. A three-dimensional view of displacements calculated by SLAB2 in the northeast quadrant for center heave, Figure 30, shows a ripple near the corner causing unusually large moments and shears that may exceed maximum permissible limits in this area. Since some fractures were observed in the exterior stiffening beams on east and west sides parallel with section A, results calculated by CBEAMC and SLAB2 appear realistic. Shears calculated by CBEAMC show spikes caused by fixing vertical input displacements. Maximum bending moments predicted by the Walsh method, Table 12, are about 180 kips-ft and within mat capacity, Table 10. 117. Level survey, medical clinic. The November 1983 level survey of the medical clinic, Figure 31, indicates a cylindrical center heave pattern of about 1 inch toward the south with settlement up to 0.5 inch toward the northwest corner of the mat. The April 1985 survey indicates up to an additional 0.3 inch heave toward the south end and slight settlement up to 0.1 inch along the east and north perimeters relative to November 1983. appears to be wetting toward the south. The soil Visual observation of the medical clinic in May 1984 indicated a diagonal crack in the east half of the south 99 InI N 0 NN '0 C w w CO 0 0 -z Figure 30. Displacement pattern of the Dental Clinic for E* - 400 ksf and q - 1 ksf on stiffening beams s 100 S' , /\ \ (1 / \ / \ / / \ \/ / \ / \ I " \ N ' / I\, " / X-- / \0 \ ur - IX \I X- \ /i\ N /\ /\ \ \ \ N /\/ \ / / \\ \/ / ( / / x IU \31. 0 Fort Sam Hout \/ / / \ / \ \? I o1I/ / \ /// ,3HON / '3,3 N ,//1 \\i \\/ / \ / \O . , / x'. / \ / -o 3 ', " '3/3 £igre 1. oveberlg8 Fot lee su9yA>o' aN Huso 101 edclClnc exterior wall. A vertical crack over the door of the main entrance in the Cracks were observed on the inside wall east wall existed since construction. partitions near the south wall directly opposite the exterior diagonal crack. Vertical control joints had not been placed in the brick exterior wall. maximum observed A/L The ratio is 1/250 near points 27-25 of Figure 31 in the area of the observed cracks near the south walls of the medical clinic. 118. Settlement of section A calculated by Analysis, medical clinic. CBEAMC for loads on the stiffening beam of 1 ksf is 1.1 inches, Figure 32, which compares well with settlements calculated by SLAB2. ksf The distribution of to simulate SLAB2 displacements using a Winkler foundation, average pressure on the mat q - 0.18 ksf, E* - 400 ksf, and B - 164 ft for points 1 s to 4, Figure 26b, is 119. Point Location p, inch 1 2 3 4 Center Middle short Middle long Corner 1.301 0.944 0.957 0.715 ksf, ksf/ft 1.67 2.30 2.27 3.04 Ao'01 1.46 1.06 1.07 0.80 Observed displacements were reasonably simulated by imposing center heave (i.e., perimeter gaps) using SLAB2 or perimeter loading using CBEAMC and translating calculated displacements as shown in Figure 32. Moments and shears calculated for these displacements approach the maximum capacity, Table 10. A rough estimate of maximum bending moment by the Walsh method, Table 12, is about 2/3 of the maximum capacity. A/L The maximum calculated and observed ratios are about 1/500 which should not cause damage in the mat, but some superstructure damage is possible. south brick exterior wall. Fractures were observed in May 1984 in the The exterior walls of the medical clinic did not have vertical control joints. Upper portions of a nearby interior wall made of concrete masonry units parallel with the south exterior wall also exhibited cracking. Appendix D describes results of a movement study of the medical clinic completed by the Fort Worth District, which is in general agreement with this analysis. 102 LENGTH L, FT 0 20 40 60 I I I 80 0 20 40 60 80 0 I I I I I I I U 'uU U U 200 It 0000 0 -- , z 0000 0oOooo Oooo oosee -oO LEGEND 0 CBEAMC. NO HEAVE 0 CBEAMC. CENTER HEAVE I -200 00000 SLAB2, PERIMETER LOAD q 00000 SLAB2. NO HEAVE 0 -400 I -F OBSERVED DISPLACEMENT 50 a-~ ~~~0 10o0ca~O~~~ 0 50 9000 ~0 '"CBEAMCADJUSTED UP 0 6 0000000000000000000000000000000000 0000002000000 5 SECTION B SECTION A Figure 32. Soil-structure interaction analysis Medical Clinic, Fort Sam Houston, for E* - 400 ksf and q - 1 ksf on stiffening beams s 103 Pest Management Training Facility 120. This facility was constructed from 1978 to 1979 and it is located off W. W. White Road on the east edge of Fort Sam Houston, Texas. The foundation, Figure 33, supports a single story structure of load bearing concrete masonry units with a metal roof deck. The load distribution shown in Figure 33 simulates the actual force/ft applied by the load bearing walls. Beam spacing varies from 7 to 23 ft, beam depth is 30 inches from the mat top, beam width is 12 inches and mat thickness between stiffening beams is 5 inches. Steel reinforcement in the stiffening beams consists of two number 9 bars placed both top and bottom. The top 18 inches of natural soil was replaced with compacted low plasticity fill. 121. Soil parameters. The soil at this site consists of about 9 ft of CH clay overburden overlying a thin layer of clayey gravel deposited on the primary formation, Figure 34. Cretaceous age. The primary formation is Taylor marl of upper Strength parameters of this soil are considered similar to those of the US Army Reserve Center and the dental and medical clinics. Additional soils data are not available. The allowable bearing capacity of this soil is estimated at 2 ksf beneth stiffening beams and the soil Young's modulus is considered to be about 400 ksf. 122. Level survey. Level observations of the Pest Management facility soon after construction indicated differential movement had increased through November 1983, Figure 35. Heave approached 4 inches on the east side and settlement of 0.5 inch near the south side and southwest corner by November 1983. Heave had decreased some on the east side and settlement slightly increased toward the west side by April 1985. Water has been observed to seep from fractures in portions of the exterior stiffening beams on the north and east bearing walls. 123. Analysis. Sewer and water lines are located out from the east wall where most heave has been observed. Figure 36 illustrates the water content and soil suction profiles (refer to TM 5-818-7 for the measurement procedure) near point 7, Figure 33, inside the walkway and outside the east wall. Suctions were almost zero about 5-ft below ground surface outside the east perimeter where most structural distress and water lines are located. Extensive fractures were observed in the exterior concrete masonry walls of 104 0 4v. oz __ _I: b S I I , I I _________ __ II , _ i r I - I 1.63 KIPS FT o rL_ ------ N--1---ij-/ L II L Ju__ - I Hi Figui 33. Foundation plan Pest Management Training Facility, Fort Sam Houston 105 CrU) a- za: wb /~ CO > U 0 M 0: z -z a:-1- 0 U) >V) -Hj~ 22 Z 0U0U 2 - x U z z Ir UHH -j 0 4 ) z- -00 D U 0 U Cr ZO F: 0 3. z oi 44; 00 LU00 0- a:- 0 0 0 13J Hid3O Figure 34. Soil parameters Pest Management Training Facility, Fort Sam Houston 106 Q' (- C OC S3H:)NI '3AV3H Figure 35. Level surveys Pest Management Training Facility, Fort Sam Houston 107 0 oJ _j O C') 0 u. w O w LL W V) 0 r- U F o U) f to q O 0* , J I-I U) IDODC IO ¢nj z Cc) w -- 0 Z4O- I-- 0 "m 0 1.='Hid3a Figure 36. Water content and soil suction profiles in February 1982, Pest Management Training Facility, Fort Sam Houston 108 this facility with cracks up to an inch in width. The maximum A/L ratio is about 1/120, which should lead to structural damage in single story buildings. Vertical control joints were not used in this structure, which contributed to the observed superstructure damage. Parts of the mat that could be observed inside the facility did not indicate unusual distress and the interior floor tile was found in a satisfactory condition. The grade around the facility provided positive drainage. 124. Results of the soil-structure interaction analysis for uniform pressure on the stiffening beams of Figure 37. q - 1 ksf and E* s - 400 ksf are shown in Settlement of section B calculated by CBEAMC was 0.4 inch and in close agreement with results of SLAB2. The distribution of ksf required to simulate the settlements of an elastic foundation using the Winkler foundation based on an average pressure q - 0.15 ksf, E* - 400 ksf, and B - 58.7 ft for points 1 to 4, Figure 33, is Point Location p, inch I 2 3 4 Center Middle short Middle long Corner 0.465 0.338 0.358 0.263 ksf , ksf/ft 3.87 5.33 5.03 6.85 P0Ai 1.76 1.28 1.35 0.99 An additional analysis performed using SLAB2 for the more realistic load distribution of 1.63 kips/ft on internal beams and 0.815 kip/ft on exterior beams indicate maximum moments of 48 kips-ft located near point 5 on section A and 72 kips-ft near point 6 on section B, Figure 33. Maximum settlement was 0.3 inch at point 7 and minimum settlement was 0.15 inch at the southeast corner. 125. A 2-inch center heave was simulated using SLAB2 and 2-inch gaps around the edges. This gap simulation for heave approximated movement along section A, but not along section B. A 2-inch edge heave was simulated in CBEAMC for section B and the calculated settlement translated up 1.7 inches. Calculated moments from both programs CBEAMC and SLAB2 greatly exceeded structural capacity, Table 10. The Walsh method, Table 12, indicates maximum moments near the structural capacity of the mat. therefore expected from these calculations. 109 Structural distress is WIDTH. FT LENGTH. FT U U 100 80 60 40 20 0 U U U U 40 20 0 U U 400 S200 ~~0000000 000Wg 0 0 M0 0 00 z 0LEGEND00 Q -200 w0 Z * -400 - 100 -0 CBEAMC, NO HEAVE CBEAMC, 2" HEAVE 0000 SLAB2, NO HEAVE 0000 SLAB2, 2' HEAVE OBSERVED DISPLACEMENT S - 0 on_- 50 00 -50 00 L -i * __ z % -- 0 -50o 00 o00000 0 UP110 -1000 60 Summary and Conclusions 126. Observed long-term displacement patterns of these mats are influenced by heave in addition to settlement and cannot be readily predicted from the available data. Reliable predictions of displacements require reasonable estimates of soil moisture changes and distribution of applied loads. Some moisture changes that caused heaves such as those observed in the Gymnasium, Brooks Air Force Base and Pest Management Training Facility are attributed to leaks in plumbing and poor drainage that cannot be readily predicted. Observed distress is in general agreement with calculated deflection ratios A/L. 127. All of these ribbed mats are flexible and require consideration of soil-structure interaction effects for proper analysis of mat performance. Programs SLAB2 and CBEAMC appear to provide comparable and realistic bending moments for similar given displacement patterns. Plate program SLAB2 considers two-dimensional lateral restraint of ribbed mats, which strongly influences mat performance. One-dimensional Winkler foundation program CBEAMC will calculate bending moments and shears similar to SLAB2 if soil movements can be anticipated and input into CBEAMC. Larger bending moments were observed in the short direction than the long direction of the Maintenance Shop, US Army Reserve Center. 128. The Winkler foundation requires evaluation of a coefficient of subgrade reaction ksf that varies with location beneath the mat in order to simulate displacements of an elastic foundation. Equation 8a where the influence factor length/width ratio L/B Center 1.0 1.5 2.0 2.5 3.0 1.3 1.6 1.8 1.9 2.0 may be evaluated from as a function of the is L B pop, ksf Short Edge (B/2 from center) 1.0 1.3 1.5 1.6 1.8 Long Edge (L/2 from center) 0.9 1.1 1.3 1.4 1.6 i11 Corner 0.7 0.9 1.1 1.2 1.3 The Pbove factors illustrate the dishing action of mats on the surface of compressible, cohesive soils with a variation of about 30 percent settlement between the center and edge and about 45 percent between the center and corner. 129. Soil stiffness and movements within the top 50 ft of soil beneath the mat appeared to determine the effective soil modulus. The effective soil modulus for SLAB2 analysis is approximately 400 ksf and may be given by the initial tangent modulus of soil from UU test results on undisturbed soil samples. 130. The flat portion of the mat provides some support. The American Concrete Institute considers this by recommending a standard effective Tsection width (ACI 318, art. 8.10.2). Additional analyses of ribbed mats instrumented to allow estimates of bending moments from strains and measurements of soil pressures exerted by the mat are necessary to provide data to improve guidelines for estimating effective T-section widths. Plate load tests may provide reasonable values of the coefficient of subgrade reaction ksf that simulate loading pressures on stiffening beams. Flat Mat Foundations 131. Thick mats of uniform thickness supporting three hospitals were analyzed using a rigid beam with Godden's (1965) Winkler foundation method, plate on elastic foundation program SLAB2 11 , beam on Winkler foundation program CBEAMC 15 , and plate on Winkler foundation program WESLIQID5 3 . Godden's method using a rigid beam is similar to the uniform pressure method and designated below as the uniform pressure method. WESLIQID was modified to calculate bending moments and shears in addition to displacements. Hand methods of calculating soil-structure interaction behavior of a plate on a Winkler foundation based on results of parametric analyses 50 are beyond practical application for this size of problem. The results of a single series of correct hand calculations should provide results similar to WESLIQID for a single point on the mat. 132. The three mats support Wilford Hall hospital, Lackland Air Force Base, Texas; Fort Gordon hospital, Georgia; and Fort Polk hospital, Louisiana. Level elevations were referenced to the elevations of permanent deep 112 Displacements are elastic, recompression benchmarks near these hospitals. settlements because applied loads are compensated by construction of the mats in excavations. 133. These mats excluding the stiffness of the superstructure are flexible after Equation 17. The superstructure, however, increases the effective flexural stiffness of the mat by an unknown amount. Increases in stiffness from the superstructures of these hospitals were estimated using Equation B6 to calculate a composite moment of inertia of the combined mat and superstructure Ioofm* The equivalent thickness of each mat was subsequently determined using Equation Bll. Wilford Hall Hospital 134. The mat addition to the hospital complex supports an 11 story tower located in the northwest sector of Lackland Air Force Base near San Antonio, Texas. The mat, constructed in 1977, is 3.5 ft thick by 108.33 ft wide by 209.83 ft long and it was placed in an excavation 27 ft below the existing ground surface. This mat is adjacent to and east of the existing hospital complex supported on drilled shafts. Steel reinforcement in the mat constitutes 5 percent of the cross-section and it is located in both top and bottom parts of the mat. The superstructure is built of a structural steel frame supporting a masonry facing. 135. Load pattern. The dead and live column load distribution, Figure 38, leads to a weight of about 55,000 kips plus 12,000 kips contributed by the mat weight or a total building weight of about 67,000 kips. uniform pressure excluding weight of the mat concrete q = The applied 2.415 ksf. Weight of soil displaced by the building is about 74,000 kips so that there may be a small net loss of weight on the foundation soil beneath the mat. 136. The mat is designed for bending moments of 36,000 kips-ft per 26-ft wide section from Equation 13a. The required thickness for the maximum applied column loads is about 2.5 ft from Equation lla, which is about 1 ft less than the actual thickness. The effective structural stiffness that includes stiffness contributed by the tower for an average ceiling height of 10 ft leads to an equivalent mat thickess of 36.8 ft from Equation Bll, excluding stiffness from steel reinforcement. Significant stiffness is also contributed by the reinforced concrete walls of the basement. 113 0 O0 __ 0 _ - T-- zz II (T, I I q 0~ 0f O0D -- 0 0 P ~ I 0 ~ ~ I 0 LLI I D W Figre ounaton 8. lanWilor Hal Hspial LakadArFreBswihclmjod nkp -. 114 137. Soil parameters. Soil parameters, Figure 39, indicate an expansive plastic CH clay overburden and shale with a perched water table about 23 ft The soil profile consists of overburden, Lower Midway, below ground surface. and Navarro formations with an occasional stratum of clayey gravel in the Consolidometer/swell tests indicate vicinity of the perched water table. potential for swell in the overburden down to about 17 ft below ground surface and within a 10-ft thickness of soil immediately beneath the mat. 138. Results of undrained triaxial shear strength tests indicate relatively large shear strengths and adequate bearing capacity. The soil elastic modulus can be approximated as increasing linearly with depth Es where Es - Figure 40 where reaction analysis. E0 is in feet. The elastic modulus An upper range is also shown in k = 32 ksf/ft. E* s and coefficient of subgrade must be evaluated to complete the soil-structure interaction Figure 8 was used to obtain a center settlement for a loading pressure of Figure 40. z is taken as zero. The equivalent soil modulus k sf (29) 25z - is in units of ksf and depth at the ground surface 139. kz pc - 0.127 ft q - 2.415 excluding the mat weight as shown in From Equation 4b, the equivalent soil modulus is E* 2.2.415.85.06.(l - 0.32) - s - 2943 ksf 0.127 The compressible soil depth beneath the mat was taken as 320 ft or nearly 4 R - 85.06 ft. times the equivalent mat radius 0.3. Poisson's ratio was assumed E* = 3100 ksf from Equation 4c assuming an infinite depth of elastic s soil beneath the mat and using k = 25 ksf/ft from Equation 29. Equation 4a should provide similar results to Equations 4b and 4c. 140. Assuming E* - 2943 ksf is reasonable, the settlement from Equation s 3 is p - or 1 inch, where 0.96. 2.415-108.33 2943 - - 0.085 ft 0.96 (L/B - 2) and p0 - 1.0. The effective coefficient of subgrade reaction from Equation 5 should be approximately 115 i o I I I I 0: 0,00 0 0 o 00 0 I 1 ~ 0 0. 20 0 6Q b0 I' _oI 0~ =, .- I I 0000 0 <z1 I u I ~Lip Cb 0 O I I 0 0 000 L0 Oo a w 00 00 00 0 20 I I o 00 0 00 I t 0 CD ~ 00 60 0 o 1. o o 00 o o 0 o[ 8I I 0 0I ii 0 0n~ 40 I 0 I 0 I Figure 39. 2 o I000 I I ZIdt Soil parameters, Wilford Hall Hospital, Lackland Air Force Base, Texas 116 INFLUENCE FACTOR q.2. h, FT Re 0 0 05 100 P qh c/E qhle/Es 20 1875 .75 .01932 .31 .00799 20 20 2375 2875 .30 .00610 20 20 3125 3875 .70 .01424 .60 .0100 .52 .00804 .44 .00548 - 20 4375 .36 .00397 .22 .00243 4875 5375 5875 6375 6875 7375 787 8 1 .30 .25 .20 .17 .15 .13 .11 .10 .00297 .00225 .00164 .00129 .00105 .00085 .00067 1 20 20 20 20 20 20 20 20 .20 .18 .16 .14 .12 .11 .10 in I -02 4 = .26 .30 02 2 Pe .55 .03036 .68 .02389 05lI r O=• 875 1375 I 0511/ 1 SETTLEMENT. FT e 20 20 -I KSF E" KSF lTE - I 4 05 TOTALpc- n-J127 LOGIo KR " LOGIo .01435 .01054 .29 .00487 .27 .00417 .25 .00312 FT p(-._( -1 ,!c Ec D '" IR' 12 q RsIFROM CHART) 0.92 --Q6 F EQUIVALENT RADIUS MAT R 85.06 FT POISSON'S RATIO SOIL MAT MODULUS OF ELASTICITY E c - 3 432, 000S F 06 z 04 0 2- 0 -2 - Figure 40. 2 Settlement computation for Wilford Hall Hospital, Lackland Air Force Base, after Figure 8 117 FT 0C I- I- 76 .o0_06.FT MAT THICKNESS D 0 . 2FT A,- Rsl,Oc-O) A/I lc-p [LOG,,oK,. RIGIDITY .00198 .00162 .00132 .00106 .00084 .00072 .00061 .00nmR k ksf sf - q 2.415 p 0.085 - 28 ksf/ft. from the Kay and Cavagnaro method. Figure 40, for center and edge settlement is 19 and 36 uniform conservative value foundation analysis and foundation analysis. ksf/ft, respectively, for q - 2.415 ksf. A ksf - 24 ksf/ft was selected for the Winkler E* - 2943 ksf was selected for the elastic s As a point of interest, similar to k - 25 ksf/ft from Equation 29. k ksf ksf of 24 to 28 ksf/ft is should be approximately from Equations A6 and A7. 141. Level survey. Level surveys were performed on the mat surface relative to the initial survey taken in December 1977, Figure 41, following mat construction; thus, this initial survey excludes settlement from the mat weight. The August 1978 survey indicated most settlement of about 1 inch in the center decreasing to about 0.8 inch along the east and west edges in the long direction. The mat was relatively flat from north to south, except along the eastern edge, indicating relatively large rigidity along the short direction. The general deformation pattern is consistent with a semi-flexible mat on a semi-infinite elastic soil. 142. The November 1983 survey indicates about 0.2 inch heave toward the western edge since August 1978. The older hospital complex is adjacent to this western edge of the mat where soil had been observed to heave into the void space beneath grade beams supported on drilled shafts. The May 1985 survey indicates a continuation of about 0.2 inch settlement uniformly distributed beneath the mat since November 1983. 143. Visual observation of the building in May 1984 indicated minimal distress in the mat and superstructure. August 1978 between points corner. Q-35 and The A/L ratio was about 1/1000 in S-35, Figure 41, in the northeast Some hairline to 1/16 inch cracks were observed May 1984 in the exterior stiffening beams on the northeast side of the adjacent ribbed mat supporting a cafeteria. in May 1985. These crack widths had increased to 1/8 to 1/4 inch An underground tunnel is located in this area below the north side of the ribbed mat. Distress observed in this mat is above the tunnel area that is placed over compacted, low plasticity fill without an impervious moisture barrier. Further west, distress was not observed in the mat where 118 I,, / zz .// /, \c " , / X\X ,, 4\\ z 34 7 / / 0 'I' Figure 41. Level surveys, Wilford Hall Hospital, Lackland Air Force Base 119 the tunnel was constructed over a chlorinated polyethylene impervious moisture barrier placed directly on the natural expansive soil. 144. Analysis. Results of soil-structure interaction analyses of sections A and B of Figure 38 are shown in Figure 42. Winkler soil programs CBEAMC and WESLIQID using high mat stiffness (an effective concrete modulus of 500,000,000 ksf or mat thickness 36.8 ft to include superstructure stiffness) and the uniform pressure method (Godden's procedure for a rigid beam 1 4 ) all provide similar results for section A, Figure 42a. The magnitudes of negative bending moments are greatest for the plate on the Winkler foundation calculated by WESLIQID. These bending moments are well within the mat structural capacity of 36,000 kips-ft from Equation 13a. Negative bending moments indicate tension in the mat top or an edge down displacement pattern. 145. Bending moments calculated by SLAB2 for the 35-ft thick mat are relatively small, Figure 42b, and well within mat bending resistance calculated by Equation 13a. Bending moments calculated by SLAB2 for the complete structure using an equivalent mat thickness De of 36.8 ft (from Equation Bll) were positive and substantially larger than those calculated for the mat on a Winkler soil. The bending resistance of the composite structure including stiffness of the superstructure is about 8 times that calculated by Equation lla using Equation B15; therefore, calculated bending moments of the structure are still well within capacity. 146. Observed displacements shown in Figure 41 for May 1985 are generally consistent with the dish-shaped or center down displacement pattern calculated from SLAB2. The flexible mat of 3.5-ft thickness ignoring rigidity contributed by the superstructure is generally consistent with the observed displacement pattern. Observed displacements in May 1985 tend to be slightly less than those calculated, but observed displacements do not include the unmeasured settlement caused by the mat weight. Overall, the assumed soil modulus and coefficient of subgrade reaction are reasonable. 147. A finite element soil-structure plane strain analysis performed in 1977 on the Wilford Hall 3.5-ft thick mat used similar loads 38 . was made using the hyperbolic soil model 23 . The analysis Calculated settlements of about 0.7 inch were determined using a representative soil modulus of about 1600 ksf and 80 ft of foundation soil beneath the mat underlain by an incompressible 120 LENGTH, FT 0 20 7266K 40 14306K 60 80 100 457 K 1495 K ~ -1010- 120 140 160 180 5K 545 41414 K 1 0 200 179 Vj 1 K 86 WIDTH, FT 40 60 20 37 K 41099 K 1424 K 1453 K 80 100 1421 K -0-UNIFORM PRESSUREMETHOD CBEAMC.HIGH STIFFNESS -- 0-- WESLIQIG.HIGH STIFFNESS 1D.3676 FT) -0-IWESLIOID. LOW STIFFNESS (D-3 5 FTI -20.000-6- OB8SERVEDDISPLACEMENTMAY 0 985 SECTION 8 SECT CN A a a. Figure 42. NIl.KLER FOUNDATICN Winkler SOIL. IK,=24 KSF/FT foundation, k sf 24 ksf/ft Soil-structure interaction analysis of Lackland Air Force Base Hall Hospital, 121 Wilford 1 125 K 0 40 20 72 40K 60 14576K 60 HALF LENGTH. FT 120 100 1495 K J1455 K 140 J1453 K 180 160 J1414 K 0 200 i 4 79 KW 16K 33? K HALF WIDTH' FT 60 40 20 +I099 K J1424 K J15 80.000 +1421 K 1 25 K HIGH STIFFNESS. D.36 76 FT LOW STIFFNESS. D-3 5 FT SLAB2. E, 2943 6SF. 0. :35 FT E, -2943 KSF. 0. .36 76 FT 60.00 ____SLA62. 20.000 4.000 - 100 LEGEND 0 z 80 2.000 ZOBSERVED DISPLACEMENTMAY 1985I SECTION b b. SECTION A SEMI-INFINITE ELASTIC SOIL. C, =2943 KSF Semi-infinite elastic soil, Figure 42. E* S (Concluded) 122 - 2943 ksf B base. These results indicate a more stiff soil profile than the results of the analysis described in Figure 42. The settlement of large mats is influenced by the stiffness of the soil profile for considerable distances beneath the mat. Fort Gordon Hospital 148. The l-story tower of Fort Gordon Hospital in Georgia, constructed in 1971, is supported by a 5-ft thick flat mat 331 ft long by 106 ft wide. This mat is placed in an excavation approximately 35 ft deep. Much of the steel reinforcement is composed of number 11 bars placed top and bottom providing about 0.3 percent of the cross-section area. Steel is preferentially placed, either top or bottom of the mat, to take the positive and negative bending moments that may occur. The column load distribution is symmetrical, Figure 43, leading to 119,110 kips or bearing pressure of 3.4 ksf excluding the mat weight. Total bearing pressure on the supporting soil is 4.1 kst 149. Soil parameters. Soil parameters, Figure 44, indicate silty and clayey sands with some plastic CH clay layers. At the bottom of the mat the soil overburden pressure had been approximately 4 ksf, which fully compensates for the weight of the hospital. All observed displacements should be elastic, recompression settlements with insignificant long-term consolidation of the clays. Bearing capacity of this soil is adequate. Groundwater elevations were not determined, but results of consolidometer/swell tests indicate swell pressures consistent with overburden pressures and any potential for heave should not exist. 150. Shear strength data from R triaxial tests of the sands above the mat elevation, Figure 44, indicate soil elastic moduli of at least 3200 ksf. The soil modulus should be substantially greater at deeper depths because the blow count increases substantially with increasing depth, Figure 44. Settlement from Equation 3 is p= 1.1. .1106 = 0.149 ft 3200 where reaction = 1 ksf 1. . for L/B = 3 and p0 from Equation 5 is = 1.0. 4.1/0.149 The coefficient of subgrade = 27 ksf/ft. The maximum bending resistance of the mat for a 24-ft wide section is on the order of 6000 kips-ft 123 _ife0-a'4_ tecl b -O 1* W) at to ~ ~a C) ~P3 t CYt Id V - If)- fn v 0- -0 0 0 w N t N Utff 0 2e -7: - -4 at - 1 - NO N -v - N N o to nt W) N N 0 -04- a C) C3 It a WCN yt IT IT 1 7- ~ ~ o W) N N 3 Fo Jt I? 1 124~t t .090 N3 1 N - - It v V) NlN N to Figure m to Nonato Nlnadla itiuin t o Hospita aodo a = .I *-"/. . . . . .. ., O|_ *. e |* *s *o I or I *.,*o j 14- C, I_ _ 1 0 zI I L I I I I I I L I I F I I I H 0~0 o ao I SI I I o T I 0 0 C' I I I So Figure 44. I a I o Soil parameters, Fort Gordon Hospital 125 from Equation 13a and the required mat thickness to satisfy punching shear is 3.3 ft, Equation lla. The stiffness that may be contributed by the 11 story tower may lead to an effective mat thickness of about 36 ft from Equation B6. 151. Level survey. Displacements of the mat observed in February 1974, 3 years after construction, are fairly uniform at about 0.5 inch settlement, Figure 45. The southwest corner indicates no settlement in 1974. These observed displacements of about 0.3 inch exclude settlement due to mat weight. The maximum A/L ratio in 1974 was less than 1/1300. New surveys conducted in 1984 indicate increased settlement in the northwest to 0.5 inch, but the eastern half of the mat appears to have moved up for a net heave of 0.2 inch at the east end. The maximum A/L ratio is still less than 1/1300 in 1984. Differential movement is less in the short direction than in the long direction. 152. The soil profile, Figure 46, does not indicate any greater presence of clay soils near the west end compared to the east, or any significant unsyummetrical slope of the original ground surface. the mat vicinity are symmetrical. pressures were not observed. Loads applied on and in Soil swell pressures exceeding applied The soil, particularly clay beneath the west end, appears to be compressing more than the soil beneath the east end. entire mat is slightly tilting toward the west. The The blow counts of some of the soils immediately beneath the west end are relatively low compared to those beneath the east end and indicates a greater potential for compression. 153. Analysis. Soil-structure interaction analyses performed using the Winkler foundation program WESLIQID and elastic program SLAB2 excluding mat weight, Figure 47, calculated settlements substantially greater than those observed for and E* s kf - 27 ksf/ft and E* - 3600 ksf. The actual effective kf may be up to 4 times greater than those indicated in the soil above the mat elevation, Figure 44, based on the record of larger blow counts observed at deeper depths beneath the mat. The relatively flat displacement observed in 1974 and apparent uniform tilt toward the west observed in 1984 indicate that the Winkler foundation using a constant appears appropriate for these sandy friction soils. ksf - 100 ksf/ft Calculated bending moments for the 5-ft thick mat excluding superstructure stiffness from results of both programs WESLIQID and SLAB2 are well within the bending moment 126 %% 0,0/ 0 i N \ / 0 %% \ a .o,. ^- 0 7 / °U o '' iiIVH~ i/IN I/ II / / / I! \,,\i ,II ! !i / /u I / \\ / /12 I /t / \I Figure 45. / \/ I I Level surveys, Fort Cordon Htospital 127 x:0001 I 00CWV: x-02 *04X v Coj I U) I= : 0f.! N o : w:a zz 00 0 _ U)) 00 'I.,, IIn I I a; CD~~ - c ON ON"a 0 ,, IN 0 a1 0 0CN IJ 'NOIIVA3-13 Figure 46. Soil profile, Fort Gordon Hospital 128 60 40 20 0 140 +2135K +2135K HALF WIDTH, FT 40 20 0 160 I068BKJ ,957K E DG E i 1968 K I I I +2135K J2135K 12135K 12135K __G 120 I I I CENTER HALF LENGTH, FT 100 80 2 135 K EDGE m CENTER 20,000 00 z w - 0,000 LEGEND 0 HIGH STIFFNESS. D-36 FT m LOW STIFFNESS, 0=5 FT K s =27 KSF/FT - K s -IO0 KSF/FT AA AA AAA 0" -1.000 OBSERVED DISPLACEMENT 0 A A CENTER FEB f974 JAN 1984 NOV 1984 EDGE I AEAST - 0 zA -0 -_-.B~--_i--0~ _, . T, ST -2 SECTION a. Figure 47. SECTION A Winkler soil, WESLIQID Soil-structure interaction analysis, Fort Gordon Hospital 129 B O 20 40 HALF LENGTH. FT 100 60 80 140 120 0 160 HALF WIDTH, FT 20 40 120,000 LEGEND 100.000 -0 HIGH STIFFNESS. 0=36 FT m 80.000 LOW STIFFNESS, D=5 FT E,=3,600 KSF 14,400 KSF -Esz 60.000 z 0 - 20,000 0 -1.000 - 2,000 CENTER EAST -'WEST -3 SECTION 8 SECTION A b. Elastic soil, SLAB2 Figure 47. (Concluded) 130 60 resistance of 6000 kips-ft. The structure is performing in a satisfactory manner. Fort Polk Hospital 154. This hospital, constructed in 1978-1979, is located south of 3rd street, west of Mississippi Avenue on South Fort Polk, Louisiana. The topography is hilly and slopes down to the south and southwest at The 242.5-ft by 259-ft rectangular approximately an 8 percent grade. multistory structure consists of a 7 story central tower section with adjacent 2 story elements. The mat supporting the hospital is 3 ft thick beneath the tower section and 2 ft thick beneath the low rise sections as illustrated in the west half of the foundation plan, Figure 48. Minimum bottom reinforcement in the 3-ft thick portion of the mat consists of number 10 bars at 12-inch centers eac', way, whlich contributes a positive (tension in bottom fibers) bending moment resistance of 171.4 kips-ft/ft width of mat from Equation Ila. The superstructure is relatively flexible consisting of precast concrete panels on a structural steel frame. average pressure of 1.4 ksf. Column loads, Figure 48, lead to an The mat weight contributes an additional 0.5 ksf q - 1.9 ksf. for a total average applied pressure 155. Soil parameters. Thirty-two borings were made from December 1976 through March 1977 for the purpose of obtaining information for foundation design and to select the optimum site. Surface soil consists of loose, silty sands (SM, SC) from a few inches to about 2 ft in thickness underlain by beds of high CH to medium CL plasticity clays of the Blount Creek member of the Fisk formation, Figure 49. percent. Water content of the clays is approximately 20 A perched water table is indicated within 10 ft beneath the mat base. 156. Consolidometer/swell tests indicate swell pressures in excess of the overburden pressure with possible potential for soil swell at depths exceeding 10 ft beneath the mat. The pressure exerted by the structure and overlying soil is less than the swell pressure so that the soil can heave on wetting and some uplift of the structure may occur. The soil elastic modulus within 30 ft beneath the mat base appears highly variable and may be as large as 3300 ksf. 131 al 4- -T 0) o 0 N N ) 0 v r4 40 0 0 0 40 ~ 1 col NNj C' - C Na . ) 1 0 0 I ' I~ In0 0- 'n 0l o'Z' - N o Ch ®I 01 6) n, C , 0 I D 10 0t' cov 0 6 re.0 0 - ' U U 0Y a~0 )i For Pol U132 0 ' 0 IOINN LO a ci 0 NI W) (D N . .. .0 1 o ( 0 NIOD o o -oN 0 6 0 0 q1 0 .0 ~ O0 OI I~ 0DV f'YIN v) - V0 ) ) 01 r-0 !-Y. CU) 0 - N1 v * N '- D 6) 0~ NOU 0 c Ui U ()0 C, 0) 10 0w No ULO --E- - 0 'a I Hopia, NIn~ j (a a a)I Loisan N N N, 0I ~N 0 0 0 0 0 0 ' - 00 0 0~ 0 0 0o0 .0o 0n 0 0 Soo 00 0 00 O0 0 0 w 0 0 8o 0i 00 ®1 b 88T w. 00 z- 0 00 0 00 0 I '- T 0 01I T" 0 0 0 0 0 20 oi- 00 0 Figure 49. Soil parameters, Fort Polk Hospital 133 157. Level survey. Level surveys conducted following construction of the mat in September 1979, Figure 50, indicate an initial slight rebound in November 1979 to a maximum of 0.35 inch near the northeast corner where the depth of excavation of about 15 ft is greatest. At that time the center west edge appeared to experience the greatest differential movement of about 1/500 and settlement of about 0.4 inch. During further construction and placement of the superstructure to April 1980, the entire mat settled and reached a maximum settlement near the north perimeter. inch. Average settlement was about 0.3 0.5 inch was taken as the actual settlement to compensate for some swell. The effective modulus E* is 11,000 ksf from Equation 3 assuming p - s 0.5 inch, q - 1.9 ksf, p, - 0.7 and y 0 - 1.0. This modulus is substantially larger than those from soil tests. 158. A level survey conducted in February 1981, about 1.5 years following completion of construction, indicated a small heave of about 0.5 inch relative to April 1980 distributed fairly evenly over the mat except in the southeast corner. The basis for this heave is presumably the potential for swell, Figure 49. Level readings taken in March 1982 indicate a fairly uniform settlement relative to February 1981. The overall displacement by March 1982 relative to the initial readings in September 1979 was only about 0.1 inch of settlement. The maximum recorded settlement in March 1982 was 0.4 inch near the southeast corner and maximum recorded heave of about 0.5 inch was near the northeast corner. the hospital. Structural distress had not been observed in The dishing action characteristic of uniformly loaded flexible mats on deep, compressible, cohesive soil is not readily apparent. 159. Analysis. Results of soil-structure interaction analyses performed using programs WESLIQID, CBEAMC, and SLAB2 are shown in Figure 51. denoted as Run 1 used a constant mat thickness of subgrade reaction ksf - 27.6 ksf/ft, and ksf/ft is approximately equivalent to D Ec - Analysis 3 ft, constant coefficient 432,000 ksf. ksf - 27.6 E* - 5500 ksf for an elastic analyis s when simulating displacements. Analysis denoted as Run 2 used a variable calculated from Equation 8a using E* derived from the ribbed mat analyses. - 11,000 ksf and influence factor ksf POP, These influence factors are in part justified by noting that the stiffness of this mat should approximately be the same stiffness as thp ribbed mats. Results show that bending moments and 134 / ~\ I' / / / \ ~\ / ,\ / ~ ~' ' / , ' ,/ ./ \\ ~'\ \ '- ,/ / \\ \ ,/ 'I' ~-V / // \ / 4/A \ x \ // I \ / / ' Al / ~ / /\~ \ \ ,// I ~A *~i ,/ ,' ' ~ , /~\ ~<'\ ~ / / C' \ / / I /\\ A' A~ \ ,/ / ~\ \,/ A\ ,2/ v, / ,/ /21 / <V / \ ~/ ~ // \)(// / /1 / V / \ Figure 50. Level surveys, Fort Polk Hospital 135 WIDTH, 8. FT 0 400 K 30 1 18K 60 598 K 90 120 150 180 11426 K7 1476 K 1396 K i1436 K _ 640 K 210 F t612 K 240 i 474 K 5.000 z 0 w 0,000 .000 > i'- -50 I - I II/I 1,000 -I N 0~- 0 BAC z.7 S/T C-3,0 K0.03FT U 1363 0 HALF LENGTH. L/2, FT 30 60 90 1231 K' 698 K 89 1 K 14,39K 906 K1310 K 120 1512 K shears from SLAB2 are least, while those from CBEAMC are greatest. All bending resistances are within capacity. 160. Calculated displacements for the Winkler foundation indicate maximum settlement near the center section A with edge down behavior. Calculated displacements at the edge of section B had substantial edge down movement. CBEAMC results indicated slightly smaller settlements than W#ESLIQID results from Runs I and 2. Results from SLAB2 indicate center down displacements relative to the edges and appear most representative of the observed mat performance. better given in Figure 52. varying ksf A comparison of WESLIQID and SLAB2 displacements is Modeling the variations in mat thickness and across the mat dimensions appear to have limited influence on the calculated performance. Actual displacements are less than calculated because the soil stiffness may be greater than that assumed and some soil heave had occurred. The SLAB2 analysis indicates less differential movement in the short direction than in the long direction. 161. A two-dimensional finite element plane strain program using the hyperbolic model soil model was performed in 1977 (data furnished by the Fort Worth District) that simulated excavation and construction loading increments. The soil elastic modulus was similar to E* - 5500 ksf. s The maximum depth of the finite element mesh was about 60 ft beneath the mat base. Calculated mat displacements for section A was a maximum of 1 inch settlement in the center with a net heave of about 0.4 inch near the north end. Actual movements observed in 1982, Figure 50d, indicate heave in the north corner of about 0.4 inch and maximum settlement of about 0.5 inch in the center. Summary and Conclusions 162. Settlement of these multistory structures is primarily from recompression of the soil. The influence of environmental changes such as moisture flow and heave could be observed on differential movements, but these differential movements did not significantly reduce performance. Differential movement in the short direction was less than in the long direction. 163. flexible. The stiffness of these complete structures on flat mats is semiPlate on elastic foundation computer program SLAB2 appeared to provide an adequate correlation of calculated deformation of flat mats in cohesive soil, while the Winkler foundation using a constant 137 ksf appeared 6 154 143, 132 B N ~ .. , . - ''f , 66 44 " --- 366 144 - 122, - 'A)'~-, 'N 00 .~ > '.23 << a WINKLER FOUNDATION, 35 65K S'2 4 KSF/FT, 2SO63 FT t:-72,0 s£ - A .2 '1'5 55 5 < 1 0' A b SEMI-INFINITE ELASTIC FOUNDATION, S-1 1.000 KSF. Af- 3. 0-3 FT Figure 52. Displacement patterns of Fort Polk Hospital mat, E - 720,000 ksf 138 superior in cohesionless soil. ksf may be evaluated from elasticity theory using Equation 8a when simulating displacements. ksf is also similar to the constant k relating the Young's soil modulus with depth z, Equation 29. This observation is consistent with the correlation between given in Appendix A. ksf and k Young's soil modulus is taken as the initial tangent modulus evaluated by the hyperbolic soil model from results of triaxial strength Q tests. A representative elastic modulus may be calculated from Equations 4 for nonuniform soil and depends on the soil stiffness for substantial depths beneath the mat. The depth of soil testing should be about twice the minimum width of uniformly loaded flat mats. 164. Stresses in mat foundations developed by heaving soil as a result of changes in soil moisture are often significantly more severe than stresses caused by normal displacements under structural loads. Appendix E shows that bending moments substantially increase in mats supported by soil of greater stiffness for given soil heave patterns. The soil heave pattern is typically random for these studies and not easily predictable for any of these structures. If differential movements caused by changes in soil volume do not occur, increasing soil stiffness decreases bending moments because of imnproved soil support, reduced settlement and distortion. 139 PART IV: APPLICATION OF FIELD PERFORMANCE Introduction 165. A field study of building 333 at the Red River Army Depot (RRAD), "Light Track Vehicle Shop" of the Maintenance modernization Project was initiated to provide improved understanding of the performance of ribbed mats constructed in cohesive/expansive soil. The site is located on the eastern edge of the RRAD west of Texarkana, TX, bounded by Texas Avenue on the north, K avenue on the east, 8th street on the south, and C Avenue on the west. 166. Building 333, under construction from 1983 to 1985, is a flexible, steel framed structure on a ribbed mat spanning 678 ft by 304 ft and includes two expansion joints dividing the mat into three monolithic units, Figure 53a. Stiffening beams are placed on 12.5-ft centers near the perimeter with interior beams on 25-ft centers as indicated by an enlarged view of the Southeast corner of the mat plan, Figure 53b. All stiffening beams are 1.5-ft wide by 3-ft in depth below the top surface of the mat. Column loads are placed on enlarged sections of the stiffening beams up to 10.5 ft on a side as illustrated in Figure 53b by the squares for interior columns and triangles for the perimeter or corner columns. Reinforcement steel consists of two No. 11 bars placed top and bottom with 4 inches of concrete cover below the top surface of the mat and above the bottom of each stiffening beam. Steel was not continuous between each monolithic unit at the expansion joints. 167. Excavation of from 5 to 8 ft of overburden and placement of compacted cohesive, nonexpansive, low plasticity fill was initiated on the north end of the site during 1983 and completed on the south end by August 1984. A 6-inch gravel layer and a plastic polyethylene vapor barrier were placed on the fill. A vapor barrier was also placed in the bottom of the stiffening beam excavation trenches and seated snugly against the walls of the trenches. perimeter. The limits of the fill extend 5 ft outside of the ribbed mat The construction site also includes an old drainage ditch aligned along the east-west direction near line 23 (shown later in Figure 55a). Appendix F provides the foundation design by the Facilities System Engineering Corporation using the Post-Tensioning Institute method1 1 and foundation design analysis by the US Army Engineer District, Fort Worth. 140 m w Ld( r00 Z 0 00 D0000 (fl -4 DM0000 I0- 0 Dz 0 0 zo 0 1-U ~Ld 0 0 0 0 0 0 0 )000 0 0 0 c 0 0 V 00 o. 0 0 Figure 53a. - 0 .-- ,,hO 0 0 Q 0 0 0 0 I.- Lii 0 0 0C Plan view of mat for building 333 141 0@ 00@0000@ w 7~~ II IIIt CIF-17~ GDDD GDLZDE I-ILa 0 0Wcc 1:1E1-1E N' C CLwC)aa wCea_ I: sCU 0 we 0 am 0a 4 Figure 53b. '- gy Uw EI 3 CU 0 Southeast corner of the mat plan 142 Description of Soil 168. Twenty-two borings were made during April and May 1979 to determine subsurface soil conditions and to obtain samples for laboratory testing. Undisturbed boring samples were obtained by 6-inch diameter Denison and core barrel samplers and disturbed samples were obtained by an 8-inch auger. Boring holes left open for various time periods indicated a possible perched water table about 9 ft below ground surface. An additional 6-inch diameter undisturbed boring sample was obtained in June 1985, 15 ft east of column A-23 at the location of piezometer 1 with tip elevation 80 ft below ground surface. Classification Tests 169. Classification of soil from the boring samples indicated that much of the area had been covered with a variable earth fill up to 8 ft thick consisting of medium CL to high plasticity CH clays, clayey SC sands, clayey sandy GC gravel, sandy silty ML-CL clays and silty SM sands with some organic material. Much of this existing fill was excavated and replaced with nonexpansive red and brown cohesive granular material of adequate bearing capacity to support the mat foundation. This fill of low plasticity index <12, was compacted by sheeps foot and rubber tired rollers to exceed 92 percent of optimum density determined by ASTM D1557. 170. Material underlying the fill consists of a high plastic CH clay shale identified as the Midway group of Tertiary age, Figure 54a. The natural water content in the clay shale is highly variable 8 to 12 ft below ground surface from a low of 20 to over 40 percent. Additional classification data from soil of boring 6DC-425 taken June 1985, Figure 55a, is consistent with these results from soil of the 1979 boring samples. Laboratory Strength Tests 171. strength Soil strength parameters were evaluated from triaxial undrained Q tests performed on 1.4-inch diameter undisturbed specimens at a confining pressure similar to the total vertical overburden pressure on the in situ soil. The results of undrained Q tests performed on specimens from the earlier boring samples taken in 1979, solid circles in Figure 54b, indicate least soil strength 5 to 12 ft below ground surface. The ground surface coincides with the elevation of the bottom surface of the flat portion of the 143 .0 Z CO ~0 00 0 0 0 M CD0 ED 0 L.J1: z CLi 0 0 w~0 0 .4 ~~0 0 01 0 L.) QC- 00 F,. a. Figure 54. CLASSIFICATION DATA Soil parameters from 1979 boring samples 144 F- c W CL -i a.44 wU x >-k 0 0 WC 0 0 F-N 0 c1 r N (L -j .00 -J C1 C -. 0 0 00 0 C,, LL w 0N -I 0 *0 LdW 0U W > 0 LO Y,0 00 zJ z MEHNIA PARAETER 54ICocudd Fiur 145 0 01 Ij 0 O') Q3 0 I 0 LLJ~C1 a-, w I) C0 O_- OZ- OC- Ii a. Figure 55. Ot- 09- 09- OL- 08- 'Hid]G CLASSIFICATION DATA Soil parameters from boring 6DC-425, June 1985 146 iA 'Z .Hid3CI Q ~ e. 01- Oz- aV- Ot- Os- 09- OL- 09- 0 NN 0- 00 U- 0 in C4 0 0 0:0 LJ 100 0 D 00 ~ 0- C ~ ~ UZ 9 iJ 'Z 'Hid3G b. MECHANICAL PARAMETERS Figure 55. (Concluded) 147 L 9 The nominal elevation of the finish mat, elevation 365.33 ft above sea level. floor surface is 366.00 ft. The undrained strength may increase linearly with depth below 5 ft of depth by C 0.2z, - z > 5 ft (30) u where Cu = undrained strength, ksf z - depth, ft Additional strength tests performed on specimens from boring sample 6DC-425 taken June 1985 confirm earlier results, Figure 55b. 172. The elastic soil moduli Es determined from laboratory tests, solid symbols in Figures 54b and 55b, are the initial moduli calculated by the hyperbolic model 23 . The elastic modulus approaches a minimum of 200 ksf from 6 to 10 ft below the ground surface and appears to increase with depth below 10 ft approximately by Es where Es - 30z, (31) z > 5 ft is the soil elastic Young's modulus, ksf. and 31 indicate that E s is about 150 times Combining equations 30 C u Consolidometer Swell Tests 173. Two consolidometer swell tests were performed on undisturbed specimens from soil samples obtained in 1979 after ASTM D4546 method C (labeled SWELL-C in Figure 54b) and an additional three tests were performed on undisturbed specimens from boring sample 6DC-425 after ASTM D 4546 method A (labeled SWELL-A in Figure 54b). The results of method C on the 1979 soil specimens indicate that swell pressures pressure above 20 ft of depth. indicate a a a exceed the vertical overburden Results of method A on the 1985 soil specimens on the order of the vertical overburden pressure above 20 ft and - 1.95 tsf or about 1/2 of the total vertical overburden pressure at 32 ft of depth. The soil is overconsolidated with an overconsolidation ratio (OCR) of about 4 above 20 ft and an OCR of 10 at 32 ft of depth. index C c 174. is 0.20 ± 0.05 and the swell index The compression C is about 0.07 ± 0.1. s A shallow water table may exist at this site based on comparison of the overburden pressures with swell pressure results from the 1985 soil 148 specimens using method A. Removal of these specimens from the field had relieved the vertical and lateral confining pressures and caused the pore pressures in these specimens to decrease by approximately the mean normal confining pressure a am (1 + 2K0) v (32) 3 where a - mean normal confining pressure, ksf a - total vertical overburden pressure, ksf K0 - coefficient of earth pressure at rest For OCR of 4 to 10, Ko where a is about 1.2 to 1.563. is about 3.8 ksf and K At 32 ft is about 1.5. a m is about 5.2 ksf Assuming the effective stress remains constant following removal of the soil samples from the field, the in situ positive pore water pressure ksf. u -w am - a s or 5.2 - 3.8 - 1.4 This translates to a pressure head of 23 ft at 32 ft of depth. The groundwater level should be about 9 ft below ground surface assuming that the pore water pressure is hydrostatic. This is consistent with the actual observed groundwater level of 9 ft below ground surface in open boreholes during soil sampling. Piezometric data described later as part of the field instrumentation program show that a shallow perched water table exists following construction above 50 ft of depth with groundwater level approximately 5 ft below ground surface. In Situ Soil Tests 175. Pressuremeter, cone penetration, and plate bearing tests were performed to complement results of the laboratory tests. illustrates the relative location of these field tests. Figure 56 Details of these tests are provided in Appendix G. 176. Pressuremeter. Eight tests, besides calibration tests to compensate for volume losses and membrane resistances, were performed 26 November 1983 in two hand augered holes. 10 ft west of column A on line 26 One test was conducted in a borehole of the planned location of building 333, Figure 56, in the bottom of the open excavation prior to placement of the 63 Brooker and Ireland 1965 149 PB4 1 80 SCALE, FT 0 '1, 0 40 so 0 E 0 ZS PRESSUREMETER (PMT) PLATE BEARING (PB)0 CONE PENETRATION (CPT) P B 2 PB6 2 0 A L Figure 56. Location of field tests 150 The remaining tests were conducted 16 ft west and 6 ft south compacted fill. of location A-26, at the bottom of the excavation. Results of the pressuremeter tests were used to estimate the undrained shear strength and Young's elastic soil modulus. The undrained shear strength evaluated from the pressuremeter 177. limit pressure by C - L 10 + (33) 0.5 where C - undrained shear strength, ksf u PL* - limit pressure, ksf compares well with results of the laboratory undrained strength data, except between 330 to 345 ft, Figure 54b. local variations in soil stiffness. An anomaly such as this may be due to Equation 33 provides estimates of soil shear strength that are least among several methods64 . The pressuremeter modulus may be evaluated by 178. E (1 + s) AP (R + ARm ) (34) =- AR where As - Poisson's ratio of soil, 0.33 AP - change in pressure measured by the pressuremeter, ksf R0 - probe radius, 2.28 inches ARm = change in radius from Ro at midpoint of straight portion of pressuremeter curve, inches AR - change in radius between selected straight portions of pressuremeter curve, inches The first load pressuremeter modulus calculated from Equation 34 was evaluated from the slope of the straight portion of the pressuremeter curves on loading. This pressuremeter modulus, Figure 54b, is consistent with the initial soil modulus evaluated from the undrained triaxial strength test results for soil above 20 ft of depth, but substantially greater than laboratory data between 64Baguelin, Jezequel, and Shields 1978 151 20 and 30 ft. Table 4 indicates that the elastic modulus is (I + s),Ep; this is consistent with the initial soil modulus from laboratory strength tests. 179. Cone penetration. The cone penetration test (CPT) was conducted 15 ft east of location A-26, Figure 56, on 17 August 1984 in accordance with ASTM D3441 with the exception of the rate of penetration. This test was conducted outside the limits of the compacted fill, Figure 56. The cone is a Fugro electronic friction sleeve type hydraulically pushed into the ground at a constant rate of 4.72 inches/sec. The CPT sounding was conducted to a depth of 40 ft before the test was terminated due to friction buildup on the cone rods that exceeded the 20-ton capacity of the truck. 180. The CPT data indicated a soil classification consistent with that observed from laboratory classification tests on soil specimens, Figure 54a. Estimates of the undrained shear strength may be made from the tip resistance by C c = u v (35) Nk where qc - tip resistance, ksf a - vertical overburden pressure, ksf Nk = tip cone factor Figure 54b shows estimates of Nk equal to 20. Cu determined from qc at 1-ft increments for These cone derived strengths are initially high exceeding 12 ksf in the natural subgrade and decreasing rapidly to about 1.5 ksf in the Midway clay. An exceptionally low value of 0.4 ksf was observed in the Midway clay 9 ft below grade indicating a soft material. Results from other tests were not available to check the cone strength at 9 ft. The CPT is able to provide a continuous log of soil parameters in the profile and can detect the existence of thin strata that might otherwise be missed. Undrained strengths below 9 ft increase at approximately a constant rate slightly greater than 0.2 ksf/ft as the depth increases. 181. The constrained soil moduli may be roughly estimated from Ed where a - a.qc qc by (36) is an empirical constant that often varies from 3 to 8 for lean 152 clays when q is less than 14 ksf. - 8 is shown in Figure 54b. Ed estimated from Equation 36 for Young's soil elastic modulus will be roughly 30 percent of the constrained modulus for ps - 0.4; these moduli are reasonably consistent with results of the other tests. 182. Plate bearing. A series of plate bearing tests was performed 16 to 20 July 1984 in general accordance with ASTM Standard Test Method D1194 at six different locations on prepared surfaces, Figure 56. The soil surface at each location was initially leveled by scraping away loose material within a 3-ft diameter. Clean, fine sand was subsequtently sprinkled on the prepared Three circular steel bearing soil surface to assist leveling of the plates. plates at least 1 inch thick each with diameters of 12, 18, and 30 inches were concentrically positioned at each location with the 30-inch plate on the bottom. The maximum pressure applied through the 12 and 18-inch plates to the 30 inch plate by the truck and water tank loading system was 30 psi. 183. The plate coefficient of subgrade reaction ksp measured from these tests was converted to an elastic soil modulus by the elastic equation 8a Es - popiksp (37) Bp where A0 = depth influence factor, Figure 3 Ai = shape influence factor, 0.62 (Figure 3) ksp = plate coefficient of subgrade reaction, ksf/ft B P - plate diameter, 2.5 ft The depth influence factor p was normally 1.0 for tests conducted at the ground surface except for test PB-4 where p was taken as 0.9 because the test was conducted 6.7 ft below ground surface. surface. The elastic soil modulus The elastic soil modulus evaluated by Equation 37 from results of the plate bearing test, Appendix G, shows values from 700 to 1300 ksf in the compacted fill or natural grade. 184. After plate bearing test PB-2, a 6-inch diameter mold was pushed into the compacted red fill by the hydraulic jack reacting against the truck weight at this same location, Figure 56, to obtain a soil sample for laboratory tests. Results of an unconsolidated-undrained triaxial test of a 153 specimen cut from this soil sample indicated an elastic modulus of 2600 ksf. The elastic moduli evaluated from results of the plate bearing test are influenced by the soil stiffness down to about twice the plate diameter or about 5 ft below the plate. Therefore, the average elastic soil modulus in the fill may be substantially less than the 260C ksf that was measured within the fill near the ground surface. Result of plate bearing test PB-4 conducted 6.7 ft below grade is consistent with results of laboratory strength tests, but more than twice E5 E P evaluated from evaluated from Equation 34 for the pressuremeter first load modulus, Figure 54b. Field Instrumentation Piezometers 185. Six Casagrande type porous stone piezometers I through 6 were installed with tips at depths of 80, 50, 40, 26, 8, and 5 ft, respectively, below ground surface in front of building 333 in June 1985 near column A-26, Figure 53b. Detail of the tip installation is shown in Figure 57. Tip locations of piezometers 5 (8 ft) and 6 (5 ft) were selected to determine the ground water level just below the base of the fill and within the fill. Piezometers 2 (50 ft), 3 (40 ft) and 4 (26 ft) were selected to evaluate the hydraulic head in the clay shale. The piezometer tip at 80 ft is used to detect any deep water level within 80 ft of the ground surface. 186. Piezometric readilngs from August 1985 through June 1988 indicate a shallow permanent perched water table with water level about 5 ft below ground surface, Figure 58. The piezometric head from this shallow water table decreases below 40 ft; however, pore pressures are increasing 50 ft below ground surface. Falling head tests in these piezometers indicated -8 permeability of about 10 about 10 cm/sec, while permeability of the shallow clay is -5 cm/sec. equilibrium. The piezometer at 50 ft may not yet have reached The dry piezometer at 80 ft indicates no deep water table within 80 ft of the ground surface. Elevation Surveys 187. Elevation surveys were periodically performed on at least 114 locations on the mat surface, Figure 53a. These locations are fixed with brass boltheads set in the concrete floor during mat construction in August 154 5" DIAfl SCREW-ON PIPE 3/8"0. PVC PIPE CAP W/ 1/8" VENT HOLE CAP (W/I/80 VENT HOLE) 5" DIAM PVC PROTECTIVE 4' MIN ~ PIPE THREADED ON TOP 3/8"1 01MM PIPE GROUT TORIE GROUND S URF AC E 9~NTN!TEBENTONITE CONCRETE SANDSESN 1. 5" Y. 24'ZN POROUS PLASTIC TIP *R!SER SH,-,U!L[ EXTEND I" TO~ 2" ABOVE PROTECTIVE ,2r'E WJHEN PR31wTi 'E P'IPE Figure 57. CR1P IS REr10- t, Piezometer installation detail 155 JA 'Hld3G 01- Oz- 0c- 0*- 09- 09Z I 11 C L -0 mr~m '.44 xn I 00 Figue Pizomeric 58 156n ead 1984. Additional elevations were determined along line 26 at 12.5-ft increments from Column A to Column N. 188. Temporary benchmarks were established at six different locations by the contractor during construction. These temporary benchmarks include rims of two concrete manholes for sewer lines, a concrete foundation for a pump station adjacent to a sludge pond, concrete docks of buildings 345 and 315, and a railroad rail. The initial elevation survey made 6 September 1984, 31 October 1984 survey and the 28 Jan 1985 survey used these temporary benchmarks. A permanent deep benchmark with tip elevation 80 ft below ground surface was installed about 100 ft NW of the NW corner of building 333 in June 1985 with details shown in Figure 59. Tabulated elevations from all surveys are provided in Appendix G. 189. Figure 60 illustrates three dimensional views of the displacement of this mat from results of the surveys relative to 6 September 1984. Settlement through May 1987 is approximately 0.1 to 0.3 inch with most settlement near the center. along line 26. A slight heave was observed in the south end One distinctive feature observed from these plots is the unusual V-shaped settlement approximately 1/3 of the way from the south end of the mat. This settlement, which exceeded 1 inch after August 1985, coincides with an old drainage ditch that passed through the construction site, Figure 56. Softening of the subsoil below this drainage ditch from long-term wetting, possible reduction of compaction efficiency above this soft soil, deeper fill depth at this location, and the expansion joint at this location may have contributed to this settlement. operations. This settlement has not hindered A second feature is the appearance of the dish-shaped pattern characteristic of flexible plates on a semi-infinite elastic foundation. The mat appears stiffer in the east-west or short direction consistent with results of plate on elastic foundation analysis in the short direction in Part III. The mat appeared to have reduced edge-down distortion in the south end after August 1985 to June 1986. This correlates well with the removal of heavy equipment temporarily stored on the south end prior to installation. 190. Two-dimensional views of the deformation patterns in the long (line G) and short (line 26) directions of the mat are shown in Figure 61. The length is taken from line 1 to line 157 30 (0 to 678 ft) and the width is GROUND SURFACE BOX RECESSED IN PAVEMENT 2' SQUARE X ' DEEP 4" DIAM 2 3/8" DIAM DRILL PIPE SET 80' PIPE X 20' BELOW GROUND SURFACE 80' CEMENT GROUT Figure 59. - Deep benchmark detail 158 28 JANUARY 1985 31 OCTOBER 1984 a,. I- 28 AUGUST 5 JUNE 1985 Figure 60. 1986 Three-dimensional view of mat movement 159 12 MAY 1987 Figure 60. (Concluded) 160 COLUMN (D G) @ G I I I n0 100 200 I 9@ I 300 400 I II 500 600 If 0 LONG DIRECTION LINE G z WII L.J s 0 < __j x " _ Iry > 10/31/84 -• " o 0 01/28/85 08/28/85,06/06/86 05/12/87t 100 200 - 300 LENGTH, a. Figure 61. 400 5oo FT LONG DIRECTION LINE G Two-dimension deformation patterns 161 600 COLUMN i II I 200 150 100 50 0 250 30% " LU' 0 ,i * SHORT DIRECTION LINE 26 10/31/84 .08/28/.85 :. . 08/28/85 o U> - 06/06/86 05/12/87 In In 0 WIDTH, b. 200 150 100 50 FT SHORT DIRECTION LINE 26 Figure 61. (Concluded) 162 250 306" taken from line A to line N (0 to 304 ft), Figure 53. The deformation in the long direction, Figure 61a, tends to show a dishing shape characteristic of a flexible plate on an elastic foundation, particularly by June 1986. The deformation in the short direction, Figure 61b, tends to show a rigid pattern. Differential moment A/L is about 1/600 and greatest in the short direction near column A at lines 20/21 significant. where settlement into the old drainage ditch is Settlement increases toward column N or the west. Earth Pressure Cells 191. Installation. Thirteen Carlson soil earth pressure cells labeled M-1 to M-12 were placed on the bottom of the trench for the stiffening beam located along line 26 from Column A to Column G, Figure 53b, on 24 July 1984. These cells are 7.25 inches in diameter with a stem 4.35 inches high by 1 inch in diameter, Figure 62, and have a maximum pressure range of 50 psi. Details of the installation procedure are described in Instruction Report 365 192. The moisture barrier was cut away at the bottom of the stiffening beam trench in each area where a pressure cell was to be placed and the subgrade surface scraped smooth. A thin layer of masonry sand was placed on the prepared subgrade surface to level each earth pressure cell. Each cell was held in place by a 2-inch layer of masonry sand/cement (3:1 ratio) mortar and allowed to set 24 hr prior to placement of concrete for the beam. Several shovels of concrete were manually placed around and on each cell immediately before concrete was placed in the grade beam trench on 25 July 1984. The minimum compressive strength of the concrete was 3000 psi. 193. Readings. Initial readings 20 hours (07/26/84) after placement of concrete in the stiffening beam trench indicates initial earth pressures of about 3 psi, Figure 63, consistent with the weight of the concrete in the beam trench. Earth pressures were larger near Column F consistent with the weight of a concrete pump truck providing concrete for placement of the flat portion of the mat south of line 26. The 40 hour readings appear erratic with greatest pressure near column G and zero pressure near Column E. Readings I day (08/03/84) after placement of the flat portion of the mat indicate some redistribution of earth pressures with maximum near colunn B. 65 Sherman 1957 163 TAE TO METE A. W.>1,Z ' NDSTU BE .17 " I A D L FOUNDATIO CALO SOILE METER TOES Figure 62. Diagram of earth pressure cell installation (after Figure 16, Sherman and Trahart 1968) 164 W 41 N U') * 0... x + .~ 07/26/84 07/26/84 08/03/84 N4 20 HRS AFTER BEAM 40 HRS AFTER BEAM U) CL. 1 DAY AFTER MAT C. rCr Lii V) F G C) LL EDCBA *08/17/84 S+ x 09/07/84 11/08/84 15 DAYS AFTER MAT 36 DAYS AFTER MAT 2 MONTHS AFTER MATW Cr) 0 Cr) U') Li Li G F E _N U5 02/12/85 x 06/05/85 +o-i08/23/85 CL D C A N ALL ROOF DL ROOF AND CRANE DL ALL DL o CL01.. F Figure 63. E D C BA Earth pressures during construction 165 ) 0. a:D G _ 194. Readings taken 15 days (08/17/84) to 2 months (11/08/84) after mat placement, Figure 63, indicate earth pressures had decreased to zero or near zero between Columns F and A. Concrete shrinkage during cure appears to be transferring weight of the overlying beam and mat from the soil beneath the beam to adjacent soil beneath the flat portion of the mat to let the beam "hang" in the trench. This may increase the probability of cracking in the mat as loads are applied to the stiffening beams during construction until the stiffening beams are firmly seated on the underlying soil. 195. Permanent loads such as the roof dead load, roof live load, crane dead load, and wall loads for building 333 lead to axial loads of approximately 32, 64, and 128 kips for corners, edges, and interior columns (see paragraph 216). These loads are placed on widened beam sections of side 10.5 ft beneath each column, Figure 53b: squares for interior columns and triangles for perimeter or corner columns. The pressure applied on these widened sections assuming that all of the column load is concentrated only on these sections is about 8 psi. This pressure drops to about 4 psi assuming loads are actually distributed to a soil area twice the area of the widened beams. Maximum pressure on the foundation soil is designed to be less than 2 ksf or 14 psi. 196. Permanent dead loads from construction of the superstructure were in place by 23 August 1985. Earth pressures in 1985, Figure 63, vary from 4 to 6 psi near columns G and D. Earth pressures near the perimeter column A appear to be increasing substantially to at least 16 psi by 23 August 1985. Pressures between the column loads such as FE and CB are negligible. 197. Installation of equipment within the building continued from August 1985 through 1987. Earth pressures increased to about 9 psi at column G, remained stable at about 4 psi near column D and had increased substantially near column A exceeding 40 psi by 23 February 1987, Figure 64. Earth pressures at column G during operations of 25 May 1988, Figure 65, decreased to about 8 psi. 198. The extremely large perimeter earth pressure is consistent with the behavior in the short direction of a rigid mat on a semi-infinite elastic foundation cohesive (or cohesiunless) soil and attributed to shear43 . The relative displacement diagrams in Figures 60 and 61 tend to show rigidity in 166 * x + 11/15/86 02/13/86 06/02/86 cn ~U) Li Ld ND DN Cl) LI) 40 to F G E D A CB *08/25/86 + 05/2/& Cr DN ND Cr) CI) of0 G F Figure 64. E D C B A Earth pressures during equipment installation 167 0 o 0-4 * 05/25/88 w - Ld Li D N CKo LJ W cco 0 0 G F Figure 65. E D C B Earth pressures during operation 168 A the short direction parallel with line 26 of the instrumented beam and the characteristic dish-shaped flexible behavior in the long direction. The distribution of earth pressures on both sides of column D shows the effect of beam stiffness on spreading the column loads to the underlying soil. Higher earth pressures at column G than at D may indicate less distribution of pressures from the footing to the soil beneath column G and possible fracture Visual observations indicate in the stiffening beam of the mat near column G. cracks in the mat betweem columns G and F. These observed earth pressures along line 26 appear consistent with observed deformation of the mat. Strain Gages 199. Installation. Ten SR-4 type temperature compensated strain gages labeled SG-I to SG-10 were mounted with epoxy cement to 3-ft lengths of No. 4 reinforcement bars at the Waterways Experiment Station by the Instrumentatiom Services Division. Strain gage assemblies SG-6 to SG-10 were tied to the inside of the bottom left No. 11 reinforcement bars looking west from Column A-26, Figure 53b. Strain gage assemblies SG-I to SG-5 were tied to one of the two top No. 11 reinforcement bars. SG-I and SG-2 were tied beneath the top left No. 11 bar (looking west from Column A-26) and SG-3, SG-4, and SG-5 were The top No. 11 bars are placed on the right side of the top left No. 11 bar. separated by 28 inches from the bottom reinforcement bars. Locations of these strain gages are illustrated in Figure 53b. 200. Cables from both earth pressure cells and strain gages were threaded through 2-inch diameter plastic electrical conduit placed on the existing ground surface 20 inches above the bottom of the stiffening beam adjacent to the stiffening beam on line 26. The electrical conduit and cables at Column A-26 were conducted ouside the mat perimeter through a 6-inch diameter opening made in the exterior stiffening beam. This opening is located about 18 inches above the bottom of the beam and 5 ft left of the center of Column A-26 viewing toward the west. The cable ends were coiled and placed in two concrete street light ground boxes located adjacent to the mat perimeter and level with the surface of the concrete ramp used by robot operated cargo containers. 201. Readings. Twenty hours (07/26/84) after the concrete was placed in the beam trench the initial readings of the five bottom gages indicated 169 about 90 microinches/inch of tension, Figure 66a. to natural drying shrinkage of concrete6. This tension is attributed Forty hours (07/27/84) after concrete placement the readings of the bottom gages indicated over 100 microinches/inch of compression beneath Column G. The stiffening beam near column G appears to be curling down consistent with the increased earth pressure observed near column G at this same time, Figure 63 (07/26/84). The compression continues to increase in the bottom strain gage beneath column G at 1 day (08/03/84) and 15 days (08/17/84) following placement of the concrete for the mat, Figure 66a. All of the bottom strain gages indicate some reduction in the initial tensile strains by 15 days after the mat concrete was placed indicative of an edge-down (or center heave) behavior. The top strain gages at this time are covered with concrete of the flat portion of the mat and indicate about 100 microinches/inch of tensile strain again attributed to natural drying shrinkage of concrete. Except for strains beneath and near column G, strains appear fairly uniform. The mat may be heaving slightly on line 26, which appears confirmed by the level survey along line 26 conducted 31 October 1984, Figure 60. This apparent heave may be attributed to arching from settlement exceeding 1 inch observed near lines 20/21 and settlement of about 0.2 inch observed at the perimeter on line 30, Figure 60. Heavy equipment stored in the south end of the building prior to installation may have contributed to settlement near the perimeter, Figure 60. 202. Continued construction of the superstructure with increased column lo-is cause substantial increases in compressive strains in the bottom strain gages beneath and near column G, Figure 66b. Some tensile strain still remains in the bottom gage beneath column G and near column A. The top strain gages indicate about -100 microinches/inch of tensile strain except beneath column G where compression is building up 2 months (11/08/84) after placement of the mat. By 12 February 1985, Figure 66b, compressive strain in the bottom gage beneath column G had peaked at about 800 microinches/inch and dropped back to about 400 microinches/inch by 5 June 1985. Tensile strains seem to be increasing in the top strain gages to about -150 microinches/inch by 5 June 1985, except beneath column G where compression had increased to about 250 66Ytterberg 1987 170 o o o o 00 , Z 07/26/84 20 HRS AFTER BEAM 07/27/84 40 HRS AFTER BEAM "o" BOTTOM STRAIN GAGES • 0 (' 0 o " (o o V) 0C.) 1 G E F D C B A H00 "T" 0 (._)08/17/84 o (o o -- o 0 I oZ Zo x * ,, :£ 'C 08/03/84 E D C 0 0 B Z ~0 BEFORE SUPERSTRUCTURE CONSTRUCTION Figure 66. A o~f ' z C-) a. o 1 TOP STRAIN GAGES BOTTrOM STRAIN GAGEST o F 1 DAY AFTER MAT 15 DAYS AFTER MAT j 0 Strains during construction 171 o Cn - 09/07/84 36 DAYS AFTER MAT - - - -11/08/84 2 MONTHS AFTER MAT' x TOP STRAIN GAGES * BOTTOM STRAIN GAGES U o 0 V) co <I 14 H05 u 4 06/05/85 U U ALL DL 00 T0 ~0 CT oZ 85A H0 0 0 G F b. ED C B DURING SUPERSTRUCTURE CONSTRUCTION Figure 66. (Concluded) 172 microinches/inch in the top strain gage. Continued drying shrinkage may have contributed to the greater tensile strains in the top gages. These strains indicate a concentration of strains (and stress) in the footing of column G. The level survey conducted 28 January 1985 indicate an increased center hump that diminished by 28 August 1985, Figure 60. Upward curling near edges or the perimeter attributed to moisture loss from the upper surface of the mat and drying shrinkage does not appear significant. Earth pressure cells indicate increased soil pressures beneath the columns, Figure 63, during superstructure construction. 203. The top strain gages are generally subject to more tensile strain than the bottom gages during equipment installation from 23 August 1985 to 2 June 1986, Figure 67. The plastic vapor barrier beneath the stiffening beams appears to have restricted evaporation of moisture from near the bottom of the stiffening beams, while evaporation and drying shrinkage continued from the mat surface. The level surveys of 28 August 1985 and 28 January 1986 confirm a humped distortion pattern along line 26, Figure 60. Compressive strains were increasing in the bottom strain gage beneath column G from 23 August 1985 through 13 February 1986, then dropped substantially indicating a large tensile strain of about 300 microinches/inch by 2 June 1986. 204. By 25 August 1986 tensile strain in the bottom strain gage near column G had increased in tension much further to -3000 microinches/inch suggesting a possible fracture in the bottom of the beam beneath or near column G, Figure 67. The compressive strain in the bottom gage near column F dropped nearly to zero by 25 August 1986. From 25 August 1986 through 23 February 1987 the strains in the two bottom gages near columns G and F appear to have rebounded and become positive; strains in the bottom gages indicate increasing tension near columns G, F, and A by 25 May 1988. Tensile strains in the top gages appear fairly steady from 23 February 1987 through 25 May 1988. Additional drying shrinkage appears insignificant since August 1986. The level survey conducted 6 June 1986, Figure 61b, shows a reversal of curvature near column C compared to the earlier level survey of 28 August 1985. Column G appears to have risen some from 6 June 1986 to 12 Moy 1987 consistent with increased compression in the bottom gages near G and 25 August 1986 to 23 February 1987, Figure 67. 173 F from 0o 0 08/23/85 20 tox * TOP STRAIN GAGES BOTTOM STRAIN GAGES 02 00 Z0 -0 00- Zo 0Of 0o C:) F E D C 0 0 I 0-w x * 02/13/86 06/02/860 ~TOP STRAIN GAGESw BOTTOM STRAIN GAGES B A' 0 0 02 0 0 0: 0 0V0 00 coZ 174 0 08/25/86 --- 02/23/87 x TOP STRAIN GAGES BOTTOM STRAIN GAGES * 0 0 0 0 E CFj o-- D C B A' 05/12/87 05/25/88 _ x TOP STRAIN GAGES BOTTOM STRAIN GAGES * 0 0 Cfo oS .. 0F >G F E Figure 67. C D (Concluded) 175 B A &D The strain data may be sorted into Stress and bending moments. 205. axial and bending strains and then converted to stresses and bending moments by compound stress theory 7 . This analysis ignores tensile strains from drying shrinkage and assumes no slip between the re-bar steel and the concrete. For the assumption of a rectangular section consisting of a typical stiffening beam, strains at the top et and bottom D * Eb of the beam, Figure 68, may be found from d.e C tmeas cov Cbmeas d t (38a) D cov dC bmeas b Dcov 4tmeas (38b) d -D cov where ft = total strain top of section, Ain./in. Eb = total strain bottom of section, Ain./in. 4tmeas = fbmeas = strain measured in a gage mounted on the top reinforcement steel, Ain./in. strain measured in a gage mounted on the bottom reinforcement steel, pin./in. d = Hb - Dcov, 31.33 in. Hb = height of beam, 36 in. D = distance from beam surface to center of reinforcement steel, 4.67 in. coy For the stiffening beam of building 333 where d = 31.33 inches and D c = 4.67 inches, top and bottom total strains are 206. found from ft = l.175c tmeas - 0175cbmeas (39a) fb = l.175cbmeas - 0,175ctmeas (39b) Axial ct and bending strains top ca and cb by CbCt a b t - Ct~b t b(40a) C t + Cb 67 popov 1968 176 cmt and bottom cmb may be 0 Hb AXIS OF ZERO BENDING STRAIN Cb to ta I top strain to ta l bot tom s tra (tmeaS bmeaS Hb Ct Cb EbmeaS in 2 measured stra in on top re ;nforcement bar measured strain on bottom re ; nfor emen t bar = height of beam above axis of zero = distance bending strain be low axis of zero = d ;stance bend;ng Strain a. DIAGRAM OF STRAIN oDc ov .DI AM -- LL LL -0~ 2: 0 10 b. Figure 68. - BEAM DIMENSIONS Schematic of strain distribution in beam 177 Ct Ct+C Cb) - (Ct fmt (40b) Ct + C b fmb (Cb = b Ct + C b t b Ct - (40c) where Ca axial strain, pin./in. fmt - top bending strain, pin./in. Emb - bottom bending strain, pin./in. Ct = distance from top to axis of zero bending strain, in. Cb - distance from bottom to axis of zero bending strain, in. The neutral axis is the axis of zero bending strain and has been taken as the distance kd below the top of the mat where kd is defined in Table 10. The actual depth of the neutral axis in the T-section will probably be in the upper half of the beam below the bottom of the slab or the T-section flange. 207. The axis of zero bending in the rectangular section of interest in this analysis is assumed for simplicity to be in the centroid. Then, C t -Cb and a a2 mt2 mb - b - mb 208. Axial stress a b (41a) Eb (41b) t (41c) 2 aa may be evaluated from Eeff fa (42) where aa - Eeff - axial stress, ksf effective modulus of elasticity of the section, ksf 178 The effective modulus of the rectangle section may be found from ElI Eef f + E( I cc s - - I) (43a) S I c %3 WHb 3 (43b) 12 c I 41 5 so + 4Asd 2 sl (43c) where Ess modulus of elasticity of steel, 4,320,000 ksf Ec modulus of elaticity of concrete, 432,000 ksf 4 steel moment of iertia, .054 ft I I - 4 concrete moment of iertia, 3.375 ft W - width of beam, 1.5 ft It b - Is so r = height of beam, 3 ft 4 4 (/4)r , ft radius of reinforcement steel, .059 ft = 2 cross-section area of steel bar, .0108 ft c As dI distance from center of beam to center of reinforcement steel, 1.1108 ft Substituting the above values into Equation 43a leads to 209. Eef f - 489,600 ksf. Figure 69a shows the distribution of axial stress on line 26 including drying shrinkage from A to G calculated using Equation 42 from the strain measurements for 12 May 1987 and 25 May 1988 assuming ksf. Eeff - 489,600 Figure 69b shows the axial stress distribution with the initial tensile strain of at least -90 pin./in. subtracted from the measured strains. stiffening beam is still in tension except near indicate a slight hump, Figure 60. B The where level measurements The initial tensile strains may be associated with the drying shrinkage. 210. The bending moment M - M may be evaluated from c -beff Cb where 179 (44) o 0 010 i 0 ------ 05/12/87 05/25/88 0 0 a LUI 180 ADJUSTED MO WMIAGE SRAJS -90 - 0523 U ___NH/W 01 f)o co4 0 GC F D C b. 'VITHOUT DRYING SHRINKAGE STRAINS Figure 69. (Concluded) 181 B A' M - bending moment, kip-ft/ft Eeffl c = 2 stiffness of composite section, ksf-ft Cb = 1.5 ft Figure 70a shows the distribution of bending moments in the instrumented beam on line 26 for 12 May 1987 and 25 May 1988 including drying shrinkage. Figure 70b shows the bending moment distribution when excluding drying shrinkage. A positive bending moment indicates a depression and a negative bending moment indicates a ..... p in the surface, Figure 68a. Bending moments tend to be negative indicating an edge down pattern or hump, which is consistent with displacements on line 26 in Figure 61b. Bending moments near G are positive indicating a dish-shaped (center down) pattern consistent with Figure 61b at this location (150 ft on line 26). A large negative bending moment of about 30 kip-ft/ft existed near F, 12 May 1987. - The resisting bending moment for the steel reinforcement of two No. 11 bars top and bottom is 435 kip-ft or 35 kip-ft/ft assuming a 12.5-ft spacing between stiffening beams after the calculation for moments given in Table 10. Observations of fractures near columns F and G indicate some distress in the mat. The distortion pattern on line 26, Figure 61b, for 12 May 1987 is consistent with these bending moment signs: a depression near G and a hump near F (150 to 200 ft). Analyses 211. Analyses selected to determine the performance of the mat foundation supporting building 333 include plate on elastic foundation using program SLAB2, beam on Winkler foundation using CBEAMC, and the frequency spectrum model. The distortion pattern observed through May 1987 indicates primarily elastic compression. Accomplishment of the proposed analyses requires that (1) pertinent soil input parameters simulating the in situ environment should be determined, (2) the size, depth, and stiffness of the mat foundation should be characterized, and (3) a reasonable magnitude and distribution of structural loads should be estimated. Input Parameters 212. Soil. Input parameters of these soils required for analyses of mat performance includes values for the soil Poisson's ratio, effective soil elastic modulus, and the effective coefficient of subgrade reaction. 182 05/12/87 05/25/88 - -- o L c'J \ \ 0 "" 0 0 o i° , 42Ld 'GF C D a. Figure 70. 8 WITH DRYING SHRINKAGE STRAIN Bending moments from strain data 183 AT co-90 L ADJ1JST 0 FOR SHRNCAX TRN4S 03'/2U macR1i4}C4O 3OTum-150 1MONCX/1CS4 TOP 0 r L.Ii C1.8 Piezometric data indicate that a perched water table exists at this site near Variations of the groundwater level of the bottom of the nonexpansive fill. this water table are assumed to have negligible effect on soil volume changes. The overall Poisson's ratio of the soil at this site is assumed 0.4. The strength and stiffness of the soil may be approximated as 213. The effective elastic increasing linearly with depth, Figures 54b and 55b. soil modulus may therefore be estimated from Equation 4c for a soil with an elastic modulus that increases linearly with depth down to an essentially infinite depth 2kR(l E* s E* 0.7 + (2.3 = s - p) (4c) j_ - s E* - - 4 s)loglon 2.30.255.93.(l - 0.16) 0.7 + (2.3 - 1.2)log 85.31 4,567 ksf (31,718 psi) where k - constant relating elastic soil modulus with depth, 30 ksf/ft from Equation 31 R - equivalent mat radius, L - mat length, 677.8 ft B - mat width, 303.6 ft = Poisson's ratio of soil, 0.4 n = R/Db, 85.31 Db = depth of mat below ground surface, 3 ft s f-EB2, 255.93 ft The soil elastic modulus at the ground surface Eo is taken as zero. An effective modulus of 4,567 ksf or 31,718 psi is substantially larger than that evaluated from any of the soil samples above 80 ft of depth below ground surface. E* s The Gibson model, Equation 4d, calculates a nearly identical modulus - 304.30/2 214. - 4560 ksf. A coefficient of subgrade reaction may be estim. ted after Equation 8a 185 k applicable to this mat E* ksf ksf = 4567 pop, 303.6 sf0* 15 15 P0 pi ks f where (8a) sB Y0pi 8.7 ksf/ft pii psi/in or A0 pI is the influence factor. For L/B = 2 similar to this mat supporting building 333 (L/B - 677.8/303.6 - 2.23), pop, = 1.8, 1.5, 1.3, and 1.10 at the center, at the edge along the short direction at the edge along the long direction L/2 B/2 from center, from center, and at the corner, respectively, based on the case history analyses for ribbed mats given in paragraph 128, Part III. ksf is therefore 8.3, 10.0, 11.5, and 13.6 ksf/ft (4.8, 5.8, 6.7, and 7.9 psi/in) from center to corner. A to G, pop, varies from 1.20 to 1.50; therefore, ksf varies from 12.5 to 10.5 ksf/ft (7.3 to 5.8 psi/in.), respectively. ksf At line 26 from Column are less than half of the constant paragraph 171. ksf Note that these values of k = 30 ksf/ft of Equation 31, will be less than half of k when n > 100, Equation A7 which is consistent with the observed soil stiffness and location of this mat on the ground surface. The modulus of subgrade reaction program CBEAMC is found by multiplying ksf by k' input into S, the width of the beam section. 215. Mat. The ribbed mat is 678 ft long by 304 ft wide with a cross grid of internal stiffening beams at a spacing of 12.5 ft within 50 ft of the perimeter and expansion joints located at lines 10-11 and 20-21, Figure 53. Each stiffening beam has d~mensions indicated in Figure 71. 216. A computer program MOM.BAS was developed, Table 13, to evaluate the center of gravity and moments of inertia (M.O.I.) after Table B2. This program calculates T-section M.O.I. for uncracked, top cracked (cracked above the center of gravity) and bottom cracked (cracked below the center of gravity) T-sections. A description of input parameters is provided in the comment (REM) statements of the program in Table 13. Table 14 provides the center of gravity and M.O.I. in the long and short directions for the mat supporting building 333. For example, the total uncracked moment of inertia 186 - SS = 12.5' - 22 -2.33' No 11 bars, W a. , 3' • 00v 1.5' INTERIOR T-SECTION 1 7.67' LONG DIRECTION S 8.8' SHORT DIRECTION ocv a 0.89' S S B top and bottom 0.6?71L . _ 0 - 2. 33' b. Figure 71. END SECTION 2 T- and End-section dimensions for stitfering beams supporting building 3^' 187 Table 13 Listing of Computer Program MOMBAS PPROGPAM M13M.BAS FOR MOMENT OFCROSS-SECTION INERTIA NCP I1IFUNEPACKED; =2 IFTOP CRACKED; =3 IFBOTTOM CRACKED A$ iDESCRIPTION OF CROSS-SECTION' NISEC =NUMBER OF T-SECTIONS OF DIFFERENT DESIGN INTHE SECTION EC CONCPETE ELASTIC MODULUS, PSI; EST = STEEL ELASTIC MODULUS W BEAM WIDTH, INCHES; T =BEAM HEIGHT EXCLUDING MAT THICKNESS. INCHEs S FLANGE WIDTH ON T-SECTION. INCHES 17'tREM D IHICKNESS OF FLAT PORTION OF MAT, INCHES 180 REM D1kM' = DIAMETER STEEL, INCHES 191.REM NB NUMBER GF BARS INBEAM BOTTOM; MT = NUMBER OF BARS INBEAM TOP' 20u' REM CuOV CONCRETE C3VER OYER STEEL PLUS DIAMS12, INCHES 10 *REM M = NUMBER OF T-SECTIONS OF IDENTICAL DESIGN 22v' PI=3.1415 92b5 22r FOR NCR=I TO 3 REM h~ 110 REM 120 REM 131"REM i±l REM i50 REM 160 PEM 230 OPEN "C:RIB,D)AT" FOR INPUT AS #1 24 INPUT #WA$,NI3EC!EC,Er3 24r~LPRINT As FOR 1=1 TO NISEC ,.INPUT 11W,TS,,DDIAMS,NB,NT.COV.M AB REAST = Pi *DIAMS*2.)-2. 2g, XO'ST = PI*(DIMS/2.)"*.1;4. 300 HC=fW*T-'2. + S*D',2. + 2.*S*D*Tii(2.*(W*T + S*Dfl 310 LPRiNT 320 LPRINT 'CENTER OF GRAVITY =';HC;" INCHES";" FOR T-SECTION "; 33() LPRiNT 4, 1F NCR=I THEN GO10 510 350 IFNCR=2 THEN GO10 610 360: HCB=iV*T+D-HC)*(D+T+HCU/2. + (G-WJ#*T+Di2.) + NB*AREAST.COV)i(W*U4+D-HE) + (S-WI#D + NB*AREAST 30LPRINT CRACKED BOTTOM CENTER OF GRAVITY = ';HCB;' INCHES^4' 380 XOGRMCB=kS*D 3. + W*(T-HC)3.)/12. + S*D*iD/2. + HCB). + W#(T-HC )*kHCB-(HC+T)i2.)"2. CRACKED BOTTOM T-SECTION M.O.I. EXCLUDING STEEL = ;XDORMCB;7 INCHES-4' 390 LPRINT ' 4~06XIOSTB=NB#*UOST + AREAST*(HCB-CDV)A2.) o' 410 X1ITT =NT*UO3GT + AREAST*(U4D-COV-HCBv- 2.) 420 LPR INT . BOTTOM STEEL M.O.I. = ";XIGSTB;K INCHES 4' 430" LRIHT TOP STEEL M.O.I. = ;ISTT;' INCHES'Y,4 44-VEI=EC*(XGOPMCB - XIOGTT) + ES*(XIOSTB + XIOSTT! j(, 45 I=EitEC 460 LPRINT EFFECTIVE BOTTOM CRACKED M.O.I. = ";XI;" 462 LPRiNT 464 IF I=NISEC THEN LPRINT *BOTTOM CRACKED' q'jGOTO INCHES.4' goo 510 XOIORM=(W#T A3. + S*D .)12. + W*(HC - T/2.)'2. +S*D*iHC - T - D/2.)A2. .r,2" LPRINT UNCRACKED T-SECTION M.O.I. EXCLUDING STEEL = ';XOORM;o INCHESA4" '3 .ES_NB*(XOST4AREAST.(HC-COV)P2.) + NT#I(XST.AREAST.(D+T-HC-COV)",2.) '.40 LPRINT 11 STEEL M.O.I. = ;AST;' INCHES",' EI=EC#1XOORM + ES*XST 56 XI=EIEC 51,LPP.INT EFFECTIVE M.G.]. = ;XI; INCHES"'4 572 LPRINT 574, IFI =NISOEC THEN LPRINT UNCRACKED" A -XST) 53ci GO010900 o0HCT=)W*HC#HCI2. 4 NT.AREAST*(T+D-COV))/)U;HC + NT*AREAST) 62e LPRI NT CRAC ED TOP CENTER OF GRAVITY =';HCT;l INCHES" b30 XOGRMCT=W#HC 3,/12. +W*HC* HCT-HCQ2.)2. CRACKED TOP T-SECTION M.O.i. EXCLUDING STEEL = ;XOORMCT;' 646 LPRINT " 6r IOSTBtNB*(XOST + AREAST'HCT-CO)V2. 660 XIOSTT=NT*(XOST + AREAST*(T+D-COV-HCTI 2.) 188 INCPES 4 Table 13 (Concluded) 610 680 b90 00 710 720 730 LPRIN!I BOTTOM STEEL M.O.I. =";XIOSTB;" INCHES -4' LFRINT " TOP STEEL M.O.I. =';XIOSTT;l INCHES-4° EI=EC*(XOORMCT-XIOSTB) + ES*iXIOSTB + XIOSTTi Xi=EIiEC LPRINT ' EFFECTIVE TOP CRACKED H.O.I. = ';XI;" INCHESA41 LPRINT IF I =NISEC THEN LPRINT TOP CRACKED' 900 XMOI=XMOI + M*XI 91( 930 940 9V5 90 962 964 965 966 999 NEXT I B$= ' TOTAL MOMENT OF INERTIA OF CROSS-SECTION LPRINT WS; LPRINT USING 'W#####I .#14;XMOI; LPRINT ' INCHES '.4 LPRINT LPRINT CLOSE #1 NEXT NCR END 189 Table 14 Calculations of Moments of Inertia for building 333 a. Long Direction LUNG DIMENSION BUILDING 333 CENTER OF GRAVITY = 26.67606 INCHES FOR T-SECTION UNCRACKED T-SECTION M.O.I. EXCLUDING STEEL = STEEL M.O.I. 1695.099 INCHES-4 EFFECTIVE MO.I. = 169016.1 INCHES'4 CENTER OF GRAVITY = 24.68387 1 154325.2 INCHES FOR T-SECTION UNCRACKED T-SECTION M.O.I. EXCLUDING STEEL = STEEL M.O.I. = 1503.979 INCHES"4 EFFECTIVE M.O.I. = 146811.9 INCHES 4 UNCRACKED TOTAL MOMENT OF INERTIA OF CROSS-SECTION INCHESA4 2 133777.4 INCHES 4 9251474.00 = INCHESA4 LONG DIMENSION BUILDING 333 CENTER OF GRAVITY = 26.67606 INCHES FOR T-SECTION 1 CRACKED TOP CENTER OF GRAVITY = 13.45862 INCHES CRACKED TOP T-SECTION M.O.I. EXCLUDING STEEL = 28481.48 BOTTOM STEEL M.O.I. = 279.7796 INCHES4 TOP STEEL M.O.I. = 1073.988 INCHESA4 EFFECTIVE TOP CRACKED M.O.I. = 41288.12 INCHESA4 CENTER OF GRAVITY = 24.68387 INCHES FOR T-SECTION = INCHESA4 2 CRACKED TOP CENTER OF GRAVITY = 12.47914 INCHES CRACKED TOP T-SECTION M.O.I. EXCLUDING STEEL = 22567.94 BOTTOM STEEL M.O.I. = 224.9115 INCHES^4 TOP STEEL M.O.I. = 1190.413 INCHESA4 EFFECTIVE TOP CRACKED M.O.I. = 36024.5 INCHES^4 TOP CRACKED TOTAL MOMENT OF INERTIA OF CROSS-SECTION INCHES'4 2260320.00 INCHES'4 LONG DIMENSION BUILDING 333 CENTER OF GRAVITY = 26.67606 INCHES FOR T-SECTION 1 CRACKED BOTTOM CENTER OF GRAVITY = 31.83818 INCHES"4 CRACKED BOTTOM T-SECTION M.O.I. EXCLUDING STEEL = 6917.514 BOTTOM STEEL M.G.I. = 2420.525 INCHESA4 TOP STEEL M.O.I. = .460G128 INCHES 4 EFFECTIVE BOTTOM CRACKED M.O.I. = 30313.99 INCHES4 190 Table 14 CENTER OF GRAVITY = 24.68387 (Continued) INCHES FOR T-SECTION = 2 CRACKED BOTTOM CENTER OF GRAVITY = 31.46775 INCHES'4 CRACKED BOTTOM T-SECTION M.O.I. EXCLUDING STEEL = 5756.839 BOTTOM STEEL MO.I. = 2356.544 INCHESA4 STEEL M.O.I. z 1.272744 INCHES^4 TOP EFFECTIVE BOTTOM CRACKED M.O.I. = 28547.8 INCHES'4 BOTTOM CRACKED TOTAL MOMENT OF INERTIA OF CROSS-SECTION 1664055.00 INCHES^4 DATA FOR LONG DIRECTION 'LONG DIMENSION BUILDING 333",2,3.EO6,29.OE06 lB.,28.,150.0,8.,1.410,2,2,4.0,53 IB.,28.,92.0,8.,1.410,2,2,4.0,2 b. Short Direction SHORT DIMENSION BUILDING 333 CENTER OF GRAVITY = 26.67606 UNCRACKED T-SECTION M.O.I. EXCLUDING STEEL = STEEL M.O.I. = 1695.099 INCHES 4 EFFECTIVE M.O.I. = 169016.1 INCHES"4 CENTER OF GRAVITY = 24.9125 I INCHES FOR T-SECTION 2 INCHES FOR T-SECTION UNCRACKED T-SECTION M.O.I. ExCLUDING STEEL = STEEL M.O.I. = 1523.394 INCHES 4 EFFECTIVE M.O.I. = 149267.6 INCHES-4 INCHES 4 154325.2 INCHES 4 136064.9 UNCRACKED TOTAL MOMENT OF INERTIA OF CROSS-SECTION 418590 4 .06 INCHES 4 SHORT DIMENSION BUILDING 333 CENTER OF GRAVITV = 26.67606 INCHES FOR T-SECTION CRACKED TOP CENTER OF GRAVITY = 13.45862 INCHES CRAC ED TOP T-SECTION M.O.I. EXCLUDING STEEL = 28481.4B INCHES'. BOTTOM STEEL MO.I. = 279.77% STEEL M.O.I. = 1073,988 INCHES'4 TOP EFFECTIVE TOP CRACKED MO.I. = 4128.12 INCHES 4 191 I INCHES'4 (Concluded) Table 14 CENTER OF GRAVITY = 24.9125 2 INCHES FOR T-SECTION CRACKED TOP CENTER OF GRAVITY = 12.59142 INCHES CRACKED TOP T-SECTION M.O.I. EXCLUDING STEEL = 23200.46 BOTTOM STEEL M.O.I. = 230.8968 INCHESA4 STEEL M.O.I. = 1176.763 INCHESA4 TOP EFFECTIVE TOP CRACKED M.O.i. = 36576.95 INCHES'4 TOP CRACKED TOTAL MOMENT OF INERTIA OF CROSS-SECTION INCHESA4 1022781.00 INCHES 4 SHORT DIMENSION BUILDING 333 CENTER OF GRAVITY = 26.67606 I INCHES FOR T-SECTION CRACKED BOTTOM CENTER OF GRAVITY = 31.83818 INCHES'4 = 6917.514 CRACKED BOTTOM T-SECTION M.O.I. EXCLUDING STEEL BOTTOM STEEL M.O.I. = 2420.525 INCHES '4 .4698I28 INCHES-4 STEEL M.O.i. TOP EFFECTIVE BOTTOM CRACKED M.O.I. = 30319.99 INCHES'4 CENTER OF 3RAVITY = 24.9125 2 INCHES FOR T-SECTION = CRACKED BOTTOM CENTER OF GRAVITY = 31.52613 INCHES 4 CRACKED BOTTOM T-SECTION M.O.I. EXCLUDING STEEL = 5785.551 iOTTOM STEEL M.O.I. = 2366.572 INCHES"4 STEEL M.O.I. = 1.089294 INCHES"4 TOP EFFECTIVE BOTTOM CRACKED M.O.I. = 28671.85 INCHESA4 BOTTOM CRACKED TOTAL MOMENT OF INERTIA OF CROSS-SECTION 754703.50 INCHESA4 DATA FOR SHORT DIRECTION ;'SHORT DIMENSION BUILDING 333',W 06,29.OE06 1828. .0,p8.,1.410,2,24 .0,2 192 inches 4 of the mat cross-section parallel with the long direction is 9,251,474 and the total mat uncracked M.O.I. parallel with thr short direction is 4,185,904 inches. This calculation assumes T-section dimensions indicated in Figure 71 with stiffening beams uniformly placed with spacing at 12.5-ft Table 14 also shows the input data listing for program MOM.BAS. A centers. simplified arrangement of vertical loads applied only at the columns is assumed for these analyses. A reasonable assumption of structural dead loads excluding wind and snow loads is approximately 32, 64, and 128 kips on the corner, edge, and interior columns. A 32, 64, and 128 kip load distribution will cause approximately 8 psi pressure on the widened beams or footings beneath each column. Plate on Elastic Foundation 217. A finite element mesh, Figure 72, describes the dimensions and load distribution. Loads were assumed to be uniformly distributed within the rectangle at each column area indicated in Figure 72. The area of these rectangles is about twice the actual footing size beneath each column leading to an applied pressure of 4 psi consistent with the earth pressures measured near column D. The total load applied at each column is assumed to spill on to some of the soil adjacent to that beneath each column. 218. Soil input parameters include an equivalent soil elastic modulus E* - 30,000 psi (4320 ksf) and soil Poisson's ratio S parameters include an elastic modulus of concrete ksf) with a concrete Poisson's ratio yc = 0.15. us - 0.4. Mat input Ec - 1,500,000 psi (216,000 A partial gap beneath line 20-21 at the expansion joint was also input to simulate the loss of support in the softened soil in this area. The computer analyses also assumed a joint at line 20-21 to simulate the expansion joint, Figure 53a. Analyses were performed with and without the weight of the mat. 219. Analysis for the southeast quadrant, Figure 73, indicate displacements of 0.05 ft without the mat weight and 0.15 ft with the mat weight. These displacements bound the 0.1 ft measured in the southeast quadrant 12 May 1987, Figure 74. The calculated V-shaped settlement, Figure 73, also reasonably matches the measured settlement, Figure 74. The results of additional computez aiialyses performed without the expansion joint were similar to those in Figure 73. 193 CYu GD- z Lr DLJ cD ' In Figure 72. I. all IfO Finite element mesh for building 333 194 a: JOINT 0.00 1 INCH GAP 42.36 84.72 127.09 Q=4 PSI 169.45 211.81 ES=30000 PSI 254.18 296.54 338.90 124.22 124.22 82.82 82.82 41.41 41.41 0.00 0.00 42.36 a. JOINT 0.00 84.72 127.09 211.81 254.18 296.54 338.90 0.7 PSI UNIFORM PRESSURE FROM MAT WEIGHT 1 INCH GAP 42.36 10.00 169.45 84.72 127.09 Q=4 PSI 169.45 211.81 ES=30000 PSI 254.18 296.54 338.90 124.22 124.22 82.82 82.82 41.41 - 0.00 0.00 - 41.41 42.36 84.72 b. Figure 73. 1 127.09 169.45 211.81 254.18 296.54 WITHOUT PRESSURE FROM MAT WEIGHT Deformation pattern calculated for building 333 using program SLAB2 195 0.00 338.90 12 MAY 1987 0 100 200 300 400 300 500 1300 V 600 200 200 100 /100 o - 0 100 Figure 74. 0 200 300 400 500 600 Measured displacement pattern in the southeast quadrant Beam on Winkler Foundation 220. A beam on Winkler foundation analysis was completed for line 26 from Column A to Column G using ksf The modulus of subgrade reaction where S k' from 7.3 to 5.6 psi/in., respectively. input into program CBEAMC is is the width of the section in inches. (20 ft), then k' varies from 1710 to 1365 psi. If S Spacing ksf.S is assumed 260 inches S - 20 ft is a little less than the interior beam spacing of 25 ft. 221. A plot of the deformation pattern using program CBEAMC for an applied pressure of 4 psi or loads of 64 kips at the perimeter Column A and 128 kips at the interior columns D and G indicate maximum settlements of nearly 0.2 inch at the perimeter and about 0.1 inch at the interior columns, Figure 75. Doubling these loads will approximately simulate the maximum observed settlements by 6 June 1986 along line 26, Figure 61b (about 1/3 of the distance from the south perimeter). Negative bending moments in Figure 75 denote compression in the top and tel,3ion in the bottom fibers. 222. Beam programs similar to CBEAMC do not consider stiffness contributed by adjacent portions of the stiffened mat (two-dimensional stiffness) and they do not consider the cohesive or interactive particulate 196 I - % % , , / <3= . __- C ..- .. - .I ,I -\ I " 1' I I -,,J-- I' rj- I II I r II INC TH, I-I I o E I . CO0LU ii Figure 75. Calculated performance of mat supprorting building 333 using program CBEAMC on line 26 from column C to A. (Note that the lateral deflection of this section is the vertical movement on line 26) 197 nature of soil; that is, soil does not behave as an independent bed of springs simulated by the Winkler foundation. Calculated perimeter settlements are therefore greater than interior settlements for this type of loading pattern. Vertical deformations predicted by an independent method must be input into beam on Winkler foundation models to calculate proper stresses and bending moments. The Winkler procedure for design of ribbed mats developed by the Southwestern Division of the US Army Corps of Engineers 12 uses movement data. Frequency Spectrum Model 223. An application of the pavement frequency spectrum model described in paragraph 78 to this mat foundation is provided in Table 15. ignores the two-dimensional stiffness of the mat. This model The relative rigidity/ft is evaluated from Equation 17, paragraph 62, for the given stiffness the mat. of Minimum and maximum values for the foundation coefficients of subgrade reaction ksf are assumed 4 and 14 ksf/ft. this range is multiplied by the wavelength the relative rigidity. A r The n evaluated for of 10, 20, and 30 ft to obtain Figure 9 is subsequently used to evaluate the ratio of the acceptable to the expected amplitude deflection Ec I 0 Aa/Ae. The accepted amplitude or of the mat is r/2666 from paragraph 84 for an allowable deflection ratio Fm max - 1/500. The maximum amplitude or displacement of the soil without the mat in feet for the given mat stiffness Ec I is shown in the last column on the right, Table 15. 224. Table 15 shows that the uncracked T-section with spacing S ft can squeeze soil with ksf - 4 ksf/ft down to - 12.5 A/L < 1/1333 for heaves without the mat > 8 inches and soil wavelengths of 10 to 30 ft. If the section is cracked, then the maximum heave is reduced to about 3 inches. If the section contains only steel, then the maximum heave is reduced further. The maximum heave tolerated for harder soil, ksf - 14 ksf/ft, is substantially less than for the softer soil. The observed deformation of the mat at the expansion joint (line 20/21) lying over the old drainage area appears consistent with this model. Although these computations only indicate trends in performance because loads are not considered, the model is limited to one dimension and soil wavelengths and amplitudes beneath facilities are not known, this application illustrates the simplicity and potential power of frequency spectrum models when developed for mat applications. 198 Table 15 Frequency Spectrum ADplication of Interior T-section. Figure 71a Case 2 3 4 Moment of Inertia I, E I, ksf ft4 Uncracked Top Cracked Bottom Cracked Only Steel 8.15 1.99 1.46 0.57 kip-ft 2 3,521,200 859,750 631,666 246,500 5 ft ksf/ft 7 , r, or "I ft 8 Aa/Ae 9 Ae, ft 4 0.0434 10 20 30 0.434 0.868 1.302 0.004 0.009 0.017 0.95 0.83 0.67 14 0.0594 10 20 30 0.594 1.188 1.782 0.006 0.014 0.038 0.63 0.54 0.30 4 0.0617 10 20 30 0.617 1.234 1.851 0.006 0.015 0.042 0.63 0.50 0.27 14 0.0850 10 20 30 0.850 1.700 2.550 0.009 0.035 0.109 0.42 0.21 0.10 4 0.0667 10 20 30 0.667 1.334 2.001 0.007 0.018 0.048 0.54 0.42 0.24 14 0.0912 10 20 30 0.912 1.824 2.736 0.009 0.041 0.140 0.42 0.18 0.08 4 0.0844 10 20 30 0.844 1.688 2.532 0.008 0.034 0.106 0.48 0.22 0.11 14 0.1154 10 20 30 1.154 2.308 3.462 0.013 0.075 0.270 0.29 0.10 0.04 --------------------Column 2: Moment of Inertia from Table 14 Column 3: E - 432,000 ksf 4 k s Column 5: 0 calculated from Equation 17, --- Column 8: Column 9: 6 --- -------- ----- 4E I c From Figure 9 Expected soil movement without mat section 199 Ae - (r/2666)/Column 8 Summary and Conclusions 225. The soil supporting building 333 is of an expansive nature, but the placement of an engineered nonexpansive fill to depths of 5 to 8 ft and the existence of a perched water table with groundwater level about 5 ft below ground surface have essentially eliminated any potential for swell or shrinkage at this site. Soil swell may have been realized if a perched water table had not existed prior to construction, but developed later in the life of the project. This site was cleared of trees and vegetation and supported earlier facilities. Construction in a previously forested site may not contain a perched water table because trees take moisture out of the soil. 226. Data from field instruments show that the mat performance is similar to a plate on an elastic foundation. Elevation surveys show that loads applied through August 1987 have led to relatively small settlements from 0.1 to 0.3 inch, except where a drainage ditch had previously existed. Settlement in this area exceeds 1 inch perhaps because of settlement of an increased fill thickness and softening of the subsurface soil; less efficient compaction of fill is possible above softened soil. Observed distortions are consistent with data from earth pressure cells and strain gages. The distortion pattern shows rigid behavior in the short direction consistent with the exceptionally large earth pressures observed near the perimeter simulating a plate on an elastic soil. The observed tensile and compressive strains are consistent with the depression and hump observed on line 26. The hump may have developed because of arching in the mat from (1) temporary heavy loads placed near line 30 from A to N leading to additional settlement and (2) settlement approaching 1.5 inch near line 20-21. The stiffening beam on line 26 near column G appears to have fractured based on the unusually large strains measured near G; fractures were observed on the mat during construction between columns G and F near line 26. Stiffening beams hanging in the trenches without soil support following shrinkage from concrete cure or arching of the mat may aggravate fracture in the mat following beam loading during construction of the superstructure. Axial stress and bending moments calculated from the strain gages assuming a rectangular beam are generally reasonable. 200 227. Analyses show that an equivalent elastic modulus may be evaluated leading to good comparisons of calculated with measured settlement using plate on eastic program SLAB2. provide realistic results. Beam on Winkler foundation program CBEAMC did not One-dimension, single parameter models such as the Winkler concept will not calculate reliable stresses and bending moments unless displacements can be accurately predicted and input into the analysis such as observed in Part III. The frequency spectrum model indicates consistent distortions for the given mat stiffness. The mat may be overdesigned, except where the old drainage ditch was located, because the design was based on a potential heave ym of the actual heave potential may be negligible. 1.5 inches (Appendix F), while Field measurements of wavelengths and amplitudes of soil movements beneath and adjacent to facilities and correlations with distress of facilities are recommended to calibrate the frequency spectrum model to foundations. 201 PART V: GUIDELINES FOR DESIGN AND CONSTRUCTION Applicability of Mat Foundations 228. Mats are an appropriate, economical foundation system, particularly where a stable bearing stratum not subject to significant volume change is more than 30 ft below the ground surface. Ribbed mats useful for supporting light (family housing) and intermediate (warehouses, operational and maintenance facilities) consist of a thin slab on grade monolithic with a grid of stiffening beams beneath the slab. The stiffening beams or ribs may be cast into trenches excavated in the foundation soil. Flat mats useful for supporting heavy multi-story structures such as hospitals are usually 3 to 5 ft thick and often constructed 25 to 30 ft below grade such that the net increase in pressure on the bearing stratum is insignificant. Settlement of such floating foundations is limited to elastic recompression. supporting heavy structures designed by conventional techniques 49 performed adequately. Mats 50 51 , have Mats supporting light and intermediate structures in expansive soil have been subject to distress and therefore design of these mats is the subject of this part. Expansive Soil Behavior 229. Expansive soil exhibits volume changes caused by changes in soil moisture that occur predominantly in the vertical direction. The plastic CH cohesive soils containing montmorillonitic clay minerals are most susceptible to volume changes, although lean CL clays can also lead to structural damage if soil water content changes are sufficiently large. These soils when exposed to the natural environment swell and shrink during wet and dry seasons. The natural fissure system inherent in these soils influences the amount of volume change that occurs within a given time frame or season. Numerous fissures, for example, promotes flow of free water from surface runoff through the soil into deeper, possibly desiccated zones increasing the depth of active soil volume change Za , while fewer fissures restrict the flow of free water limiting the depth of penetration and volume change that can occur within a single season. Soil movement for analysis of foundation performance is characterized by center and edge lift deformation modes. 202 Center Lift 230. Center lift is upward movement of the mat relative to the edge, Figure 76, caused by increases in soil water content and heave toward the center relative to the perimeter or decreases in water content and shrinkage Placement of the foundation on toward the perimeter relative to the center. the ground surface inhibits evaporation of moisture from the ground surface and eliminates transpiration of moisture from previously existing vegetation. The soil therefore tends to increase in water content, particularly toward the center of the mat where environmental conditions at the perimeter have least influence. Soil outside the perimeter may also dry out during drought causing the perimeter to settle relative to the center. Figure 76a illustrates the center lift deformation assumed for design where the mat acts as a cantilever. 231. eM Two important input parameters required for design Figure 78. ym are Ym and is the maximum soil surface heave relative to the edge under no foundation load and depends on the type of soil and water content change within the depth of the active zone for heave Za . em is the maximum edge moisture variation distance or lateral distance into the interior from the perimeter where seasonal moisture changes cause the mat to lift off of the soil. V The maximum deflection 6, bending moment M, and shear stress will be determined by the design analysis. Edge Lift 232. Edge lift is upward movement of the edge relative to the center, Figure 78b, caused by increases in soil water content and heave near the perimeter or decreases in soil water content and shrinkage toward the center. Seasonal rainfall or summer irrigation in arid and semi-arid climates commonly cause edge lift. Edge lift may also occur from drying out of soil beneath interior portions of the mat when moisture flows away from heated areas. Figure 76b illustrates edge lift assumed for design where the mat is supported at the edge and at some interior location. sag and contact the soil as shown. Interior loads cause the mat to The mat acts as a beam simply supported by soil at the edge and at some interior point. 203 --- -- HERVE BENEATH FLEXIBLE WEICHTLESS SLAB Le a. CENTER LIFT OR DOWNWARPING em b. Figure 76. EDGE UPLIFT Soil-slab displacements on heaving soil 204 Soil Exploration A thorough field investigation must be conducted of the proposed 233. construction site to determine site characteristics for construction and soil input parameters to accomplish the design. Site Characterization Foundation soil and groundwater characteristics should be 234. determined early in the design process to avoid unexpected obstacles to construction such as underground streams, sink holes, boulders, poor site trafficability, poor drainage, unstable excavation slopes, excessive heave of excavation bottoms, and loss of ground adjacent to excavations. 235. Surface soil. Surface soils within and near the potential construction site should be identified to determine trafficability of construction equipment and suitability of the soil to support the structure or use as fill. Plastic soils can reduce site trafficability and may be potentially expansive. Expansive and plastic surface soils are easily identified following dry periods by a polygon network of fissures appearing on the ground surface; otherwise, they may be identified by their slick and sticky texture when wet. Expansive soil often contains montmorillonite and it is associated with high plasticity CH cohesive clay with plasticity index PI > 40 and liquid limit > 50. Lean CL soil with PI Z 15 can cause structural damage to the foundation and superstructure if water content changes and subsequent differential movements are sufficiently large. 236. Collapsible soil is also an undesirable foundation material. It has a loose structure often associated with mudflows and partly saturated windblown colluvial, cohesive silty sands found in arid and semi-arid climates. Cohesion is often imparted by precipitation of soluble compounds such as calcium carbonates, gypsum, or ferrous iron that dissolve when wet leading to rapid volume decreases and substantial nonuniform settlement. 237. Topography. Topography of the site should be checked for adequate drainage of surface water away from the site and a suitable level location for the foundation. Cuts or excavations to level sites are undesirable, especially in low permeable, cohesive soil because long-term rebound can cause substantial heave. Combination cut and fill earth work to level sites aggravate differential movement from settlement of the fill and rebound of the 205 cut. Sites requiring cuts should be overcut and a minimum depth of 2 ft of fill placed beneath the full area of the proposed foundation. Soil Characterization Soil strength and stiffness parameters such as the allowable 238. bearing pressure qal elastic soil Modulus subgrade reaction ksf (nonexpansive) soil. zone for heave Za ,' ES, and the coefficient of are required for design of mats on stable Additional parameters such as the depth of the active edge moisture variation distance and maximum potential swell ym em, swell pressure a are required for design in expansive soil. Soil parameters are evaluated from a combination of in situ and laboratory soil tests. Results of in situ tests will be a primary source of data for soil that cannot be easily sampled such as cohesionless sands. In situ tests and soil sampling should be conducted on each strata down to depths of twice the least width of the proposed foundation or to the depth of incompressible strata, whichever comes first. A minimum of three cone penetration tests, for example, may be conducted initially for economically significant structures to determine a preliminary classification of the soil and to provide a basis for judging lateral variations in soil parameters. These tests should be located at the center, corner and middle edge of the longest dimension of the proposed structure. Other types of field tests such as standard penetration, pressuremeter, and dilatometer tests may also assist the reasonable estimation of soil parameters. 239. Several disturbed and undisturbed boring samples should be obtained from each strata at locations of potential soil weakness such as softened, loose, expansive, or collapsible soil depending on results of field tests. Disturbed boring samples should be used to classify the soil in each stratum. At least one consolidometer swell test described in EM 1110-2-1906 or ASTM D 4546 should be performed on soil from each strata with plasticity indices PI greater than 15 and Liquid Limits greater than 35 to determine the potential swell. Soil sampling should be conducted near the end of dry periods to provide maximum estimates of swell pressure and potential heave. 240. Strength and stiffness. Field tests illustrated in Appendix G may be used to estimate the soil shear strength, elastic modulus, and coefficient 206 of subgrade reaction for a plate. Refer to Part II for further details on estimating the soil stiffness and strength required for design. The depth of the active zone Depth of active zone for heave. 241. for heave is defined as the least soil depth above which soil heave may (Za) occur because of change in environmental conditions or climate following construction. below Za Climate is defined in terms of the maximum amplitude of surface suction range occurs. may be approximated by guidelines in Past experience indicates Za . Table 16. The water content distribution should not change with time 2Uo that this maximum amplitude n and the cycles/year For example, severe extreme may be an arid or desert climate subject to a heavy rainfall every other year. Piezometers should be placed in construction sites to determine groundwater levels, which assist in determining reasonable estimates of Preliminary criteria for 242. Z a based on soil suction principles are Za shown in Table 17 as a function of the severity of the climate. Za may be derived from maximum and minimum suction envelopes for cyclic surface suction changes 68 such as illustrated in Figure 77 In Au (45) 2Uo Z a where Au - maximum acceptible change in suction at depth Z , 0.4 pF; a' Suction in pF units is the logarithm to the base 10 of suction 3 + logarithm to the base in units of centimeters of water or 10 of suction in tons/square foot (tsf) Uo = 1/2 of the maximum range in suction at the ground surface from the climate, pF n = number of cycles per year that the climate oscillates from peak to peak range a = diffusion coefficient, ft 2/year Au = 0.4 pF is recommended at this time because calculated 5 value is comparable with past experience , Table 16. 68 McKeen and Eliassi 1988 207 Za using this The diffusion Table 16 Guidelines For Estimating Depth of the Active Zone Z a Relative To Guideline Water table Za will extend to depths of shallow groundwater levels : 20 ft (see Figure 77) Swell pressure Za > will be located within depths where asj asj - average swell pressure of stratum 0 where afj - total average vertical overburden and j pressure prior to construction in stratum Fissures afj will be within the depth of the natural fissure Za system caused by seasonal swell/shrinkage Climate TMI humid semi-arid arid > 20 -20 to 20 < -20 Z ft a' 10 15 20 69 TMI - Thornthwaite Moisture Index 69 Thornthwaite 1948 Table 17 Preliminary Criteria for Depth of Seasonal Active Zone Climate Cycles/year, n Maximum Suction Range 2Uo, pF Depth of Seasonal Active Zone Zat ft Severe Extreme 5 0.5 15 - 22 Severe Moderate 4 1.0 10 - 14 Normal 3 1.5 7 - 10 Moderate 2 2.0 5 - 7 Mild 1 2.5 208 < 5 j FOUNDATION I WET PROFILE METHOD 1: Uf' 0 -- 10 - = CL \ 0 20 FT DRY PROFILE ! 2 0 METHOD 2: U f y( z - Za) 30L -2 -1 1 0 PORE WATER PRESSURE 2 U ,, TSF SHALLOW GROUNDWATER LEVEL a. FOUNDATION 04 /<WET PROFILE Zo < 20 FT 10/ 28 0 DRY METHOD 31 PROFILE U zU -2 + -1 Y z Figure 77. 1 0 PORE WATER PRESSURE b. ), - 2 U. , TSF DEEP GROUNDWATER LEVEL Anticipated equilibrium pore water pressure profiles 209 coefficient 2 ip a measure of the rate of moisture flow through soil and related with the permeability by au - (46a) k- where au - rate of change of suction head in feet with respect to fraction of volumetric water content, wG s/(100(l+e) aO = rate of change of volumetric water content w = water content, percent Gs - specific gravity e = void ratio A selected range of observation6 8 . a 8, the from 60 to 120 2ft /year is consistent with The results of Table 17 are plotted in Figure 78a to show how the seasonal active zone fluctuates with the severity of the range in suction. In situ diffusion coefficients a < 60 ft2/year will reduce Z and be above a 2 a > 120 ft 2/year will increase Za and be Table 17 must be confirmed from results of field the solid line in Figure 78a and below the dotted line. tests; this does not consider long-term wetting or drying of the soil profile. 243. distance Edge moisture variation distance. em The edge moisture variation is the distance inside the mat from the perimeter that soil is subject to variations in moisture. This parameter is not well known, but experience appears to show that it may vary from 2 to 8 ft"l and become larger with more severe climates. A more severe climate is associated with a dryer environment thit occurs over longer periods of time before a heavy rainfall. Larger fissures caused by greater drying (droughts) reduce the diffusion coefficient a and increase the active zone depth Za . Parametric analysis of two-dimensional moisture flow beneath a ribbed mat 70 shows that the edge moisture variation distance is a function of perimeter stiffening beam D, Figure 78b, and Za and the depth of the approximately Z e m2 - a - D Figure 78b must be confirmed from results of field tests. 70 Vallabhan and Sathiyakumar 210 (46b) 0 0 LU LUJ 0 N F- -N I N 1 I0 EDGE 4 1o 8 / MOISTURE VARIATION DISTANCE em, FT 12 U FFI"SURE WFE b. EDGE MOISTURE VARIATION DISTANCE -- n 0 FEW FISSURES I - ETIGHT -r O= 120 LU SOIL FT2/YEAR a-_ "60 F-rYFR 4 Z oIA LU I- N , 2 R MANY FISSURES LOOSE SOIL D " I (T . ('4 I 1 * 2 CLIMATE I I 3 4 * 56 SUCTION RANGE 2Uo, pF ACTIVE ZONE DEPTH a. (Data from Table 17) Figure 78. Preliminary relationships for active zone depth and edge moisture variation distance 211 244. Swell Pressure. Swell pressure a s, evaluated from results of consolidometer swell tests71 '72 , should be determined down to the depth of the active zone for heave 245. Z a Potential Swell. Useful estimates of the anticipated heave based on results from consolidometer swell tests can often be made. program HEAVE 73 m / Computer is useful for calculating potential heave beneath mat foundations in multi-layered expansive soil. The anticipated heave is (47a) h. e n ef. j-1 1 + eoj 3 where Y = maximum potential vertical heave, ft h. J ef. = thickness of stratum = final void ratio of stratum eoj = initial void ratio of stratum n j, ft j j number of strata within the depth of heaving soil Z a The initial void ratio, which depends on a number of factors such as the maximum past pressure, type of soil, and environmental conditions, may be measured by standard consolidometer test procedures. 246. The final void ratio depends on changes in soil confinement pressure and water content following construction of the structure; it may be anticipated from reasonable estimates of the equilibrium pore water pressure uwf, depth of active zone Za', and edge effects by rewriting Equation 47a in terms of swell pressure n Ym Z j-1 C a. sj . 1og 1 0 1 + eoj sj • h 7fj where I Csj - swell index of stratum as j - swell pressure of stratum j, tsf 7Engineer Manual 1110-2-1906, "Laboratory Soils Testing" 72ASTM D4546 73 Johnson 1982 212 (47b) at. f] - final or equilibrium average effective vertical pressure of stratum j, afj - Uwfj, tsf afj - final average total vertical pressure of stratum Uwfj - equilibrium pore water pressure in stratum J, tsf J, tsf The swell index and swell pressure of the soil in each stratum may be determined from results of consolidometer swell tests. Table 18 illustrates the evaluation of the equilibrium pore water pressure. The equilibrium pore water pressure is independent of the type of strata in the soil profile. An application of the heave prediction method is provided in Chapter 5, EM 11101-1904. Design of Ribbed Mats 247. A useful procedure for design of stiffened ribbed mats in expansive soil areas 12 adopted in this report, Table 19, is a conservative and simple methodology applicable to the beam on Winkler foundation concept. This procedure inputs displacement values based on estimates of maximum differential heave ymI and can provide useful calculations of bending moments and shears based on reasonable input data. A computer program RIBMAT is available from the Southwestern Division to assist analysis. The Post 1 Tensioning Institute method ' illustrated in Appendix F for building 333 is recommended when conditions are satisfied, paragraph 77. Input Parameters 248. Step 1 to determine input parameters may be accomplished using Table 20 and results of laboratory and field soils tests with consideration of past experience. Foundation Plan 249. Step 2 to determine foundation plan dimensions and loads is initially accomplished by knowledge of structural functional requirements and minimun requirements described in Table 21. Some rules of thumb for line and column loads described in Table 22 are based on a survey of engineering firms. Tall multistory structures may have column loads exceeding 1000 tons. spacings are often 20 to 25 ft or more. The average pressure per story of a building often varies from 0.2 to 0.4 ksf. 213 Column Table 18 Equilibrium Pore Water Pressure (Figure 77) Profile Equation Saturated (Method 1) u = 0 Hydrostatic with shallow water table (Method 2) uwf = -w(Z Hydrostatic without shallow water table (Method 3) Note: 1w z Z a Uwf Uwa + Remarks Realistic for most practical cases: houses or buildings exposed to watering of perimeter vegetation and possible leaking of underground water and sewer lines. Water may also condense or collect in permeable roil beneath slabs and penetrate into underlying expansive soil unless drained away or protected by a moisture barrier. This profile should be used if other information on the equilibrium pore water pressure profile is not available. - Z ) -w(z Realistic beneath highways and pavements where surface water is drained from the pavement and where underground sources of water such as leaking pipes or drains do not exist. This assumption leads to smaller anticipated heave than Method 1. - Za) Similar as Method 2 but without shallow water table. - unit weight of water, 0.031 tsf - depth below the foundation, ft depth of active zone for heave, ft Uwa - value of negative pore water pressure at depth methodology described in TM 5-818-7. 214 Za; evaluated by Table 19 Southwestern Division Structural Design of Ribbed Mats Step Description 1. Determine input parameters for design from Table 20. E OlRGONRL 2. Determine foundation plan dimensions and initial geometry and spacing of ribs S from functional TRRNSVERSE RIB RIB _ and minimum requirements, Table 21. C 3. Calculate interior P, and perimeter Pp loads, U - I* lb/ft. Interior or perimeter column loads may be converted to Pi or P by dividing by spacing S. A or SI in feet. Calculate uniform pressure q in A psf on the T-section being analyzed. Loads should consist of full dead (DL) and live (LL) loads including DL of slab and ribs. L equals Ss or S1 . 1 2 3 PERIMETER RIB 4. Estimate rib width w in inches from applied loads and allowable bearing capacity qa where psf. q = P 12"PL or 12.- w s 5 5 '4 qa q , allowable bearing capacity (Table 20), PSF , , 4, i j 5. Estimate effective T-section width S in inches e after ACI 318, Section 8.10.2 by S e ' 1/4 beam span length L and the effective overhang (OH) distance on each side of the web shall not exceed S. -. i-'i OH 5 8D OH 5 1/2 clear distance to next web. D DH - Span Length L: L initially S or SI Center Lift: L = 4L c (step 8) Edge Lift: L = Le (step 10) e e- -_-- - 6. Estimate effective moment of inertia of mat cross- -0 section Ie, in., after ACI 318, Section 9.5.2.3 d TF T for center and edge lift ra=[Z]g 3, 1 [Mc r]3] L. L!T _] Since M is initially unnow r2 M -A r use Mr = calculated maximum moment, in.-lb = gross beam area gfy = 240A *d for ASTM60 grade steel g OR Estimate I as:g CENTER LIFT: Ia = EDGE LIFT: Ie 0 1 .7 g 0.41 1 y CE TER w(t + D), in. f - tensile yield strength of reinforcement y steel, psi Initially estimate 20 5 t 5 36 in. d D + t - 3 in. (3 in. = concrete cover) Is gross moment of inertia, in. I 3 + wt 2 BD 3 + Ig9c- . h wt 2 + 2DtS + SaD2 2(wt + Se ) 215 Dt2 t]wt+SeD t+ - hc __ Table 19 (Concluded) Description Step - cracked moment of inertia, in4 Icr -cakdmmn fieta n M = cracked moment, in.-lb 7. Calculate moment of inertia I in in4/ft byi I S I e/S - S1 or S e in feet CENTER LIFT: * wh 3 * M maximum deflection at perimeter A, and maximum angular distortion 3max, m max M W (t 9. Calculate minimum top reinforcement steel area A s in transverse rib to accommodate maximum moment M for center lift. Select size and number of . = cr 5 limits of Table 24. - h ) SIe D3+ D M A - D M - Grade 60 *fyeje(d A- _ ) 50,700(d - _D) area of stirrup, in2 (Vr- vc°w-j-d).s Ar = '. ySOjd vc 11. Calculate minimum bottom reinforcement steel to accommodate maximum moment in transverse rib for edge lift similar to step 9. Check required area of stirrups to resist maximum shear. + c f'c concrete compressive strength, 3000 psi *Neglects steel reinforcement 2 A = area of reinforcement steel, in. g = 0.90 required area of stirrups A r to accommodate maximum f 000 s 60,000 psi shear V r and determine size of stirrups for spacing fy r 0.939 10. Calculate maximum deflection at perimeter Ap, angular distortion max, moment Mr, and shear Vr h D 1I - t + D - h reinforcement bars with total area ! A s . Calculate for transverse rib subject to edge lift, Table 23c. Check Bma x 5 limits of Table oI = EDGE LIFT: (step 7), using Mr" Then calculate maximum Check Mrc. c transverse rib subject to center lift. Recalculate S (step 5), Ie (step 6), and I hear V 2 b-5 c + wh c [ 8. Calculate maximum Mr from Table 23b forICr a " stirrup spacing, 5 24 in. 12. Calculate maximum moment and shear of perimeter ribs by conventional methods: center lift, ribs support perimeter Pp and span between transverse ribs assuming no soil support; edge lift, perimeter ribs span between transverse ribs and subject to net uplift R - R where R is soil P reaction from step 10. 13. Calculate moment and shear capacity of diagonal ribs as larger of two adjacent transverse ribs. Diagonal ribs support corners for center lift if soil support lost beneath both perimeter ribs. 14. Calculate maximum moment, shear, deflection interior ribs (not subject to soil heave) by conventional beam on Winkler foundation methods. Interior ribs and rib intersections should be located at wall and column loads. Design should be consistent with minimum requirements, Table 21. 216 steel Table 20 Input Parameters For Design Description Equation Parameter T-r Allowable soil bearing pressure qa, psf See Table 7 Factor of safety should be at least 3 or settlement limited to less than 1 inch From Q Test: 2C C = u u soil overburden pressure prior to construction, psf a Coefficient of subgrade reaction k pci , soil modulus of elasticity, psi; initial tangent or hyperbolic modulus determined from triaxial Q test with confining pressure at ao . E E s S e S = equivalent width of T-section, in., e k B s ps 1.5S e average undrained shear strength of undisturbed soil sampled from base of rib; determined from undrained triaxial Q test with confining pressure at ao, psf from step 5, Table 19. - coefficient of subgrade reaction from plate load test, pci (see Appendix G) = diameter of plate, in. k B p Es, psi Clay ks, pci 40-90 Soft 700-3500 Medium 2000-7000 90-170 jard 7000-14000 > 170 Permissible range: Climate Edge Moisture Variation Distance em, ft Soil swell pressure Psw' psf a - a0 s 0 Sand E, psi Silty 1000-3000 Loose 1400-3500 Medium Densey 7000-12000 Clayey ks, pci 90-170 20-60 35-290 230-460 110-290 50 5 ks 5 200 pci am, ft The permissible range of the edge moisture variation Arid 8 distance is 2 to 8 ft; see _Semi-arid Humid 6 4 Figure 78b for further guidance on evaluating S e -average soil swell pressure from results of consolidometer swell test determined at the initial void ratio by ASTM D4546 on soil within the active zone Z a beneath the mat, psf = soil overburden pressure prior to construction, psf Permissible range of Psw : 1000 to 8000 psf Soil heave Ym' in. Za E Ah 0 Ah = heave of 1 ft thickness of soil at depth z beneath mat down to active depth Za, in.; soil subject to a prior to construction; Equation 47 may be used to calculate ym; Z. may be estimated from Table 16 and Figure 78a; refer to ASTM D4546 or EM1110-2-1906 to estimate Ah from results of consolidometer swell tests; assume saturated active zone (Method 1, Table 17 and Figure 77) where long term pore water pressure is zero; refer to MP GL-82-7 for calculation by program HEAVE; Ym may differ for center and edge lift conditions; permissible range is 0.5 to 3.0 inches 217 Table 21 Minimum Requirements Item Component T- Subgrade preparation Description - T - Vapor barrier Capillary water barrier Fill 6 mil (preferably 10 mil) PVC membrane 6 inches gravel beneath membrane Slab 4 inches thick 5 inches thick Reinforcing Vehicular loading Family housing; small, lightly loaded buildings Other buildings 0.2 percent Design for maximum wheel load similar to paving; use 650 psi flexural strength concrete Grid geometry of ribs in mat Grid Spacing Continuous S 20 ft in expansive soil; < 25 ft in nonexpansive soil Support wall, column loads; resist thrust from rigid reactions; adjacent large openings in slab 250 ft intervals; break irregular shapes into rectangular elements except not required for family housing Location Expansion joints Rib dimensions Depth, t Width, w 18 inches cohesive, granular, nonexpansive a 20 inches; : 3 ft a 12 inches; 10 inches family housing; allowable soil bearing capacity q a may not be exceeded based on total width - w + 2D where D - slab thickness or provide fillets at rib intersections acting as spot footings to support column loads Rib capacity Concrete Steel Area ratio Compressive strength f'c - 3000 psi at 28 days ASTM Grade 60; use No. 3 ties Grade 40 at 24 in. Cross-section area steel/concrete - 0.005 top and bottom Construction joint detail Conventional Spacing S 50 ft either direction; horizontal joint may be provided in ribs at base elevation of the capillary water barrier where unstable trench walls may cause construction problems Post-tensioned Spacing 75 ft either direction; tendons within each placement shall be stressed to 15% final post-tensioned stress : 24 hr after concrete has attained sufficient strength to withstand partial post-tensioning 218 Table 22 Some Typical Loads on Foundations* Structure Line Load, kips/ft Column Load, kips Apartments 1 to 2 60 Individual housing 1 to 2 < 10 Warehouses 2 to 4 100 Retail Spaces 2 to 4 80 Two-story buildings 2 to 4 80 Multistory 4 to 10 200 Schools 2 to 6 100 Administration buildings 2 to 6 100 buildings Industrial facilities 100 *Uniform total pressures are about 0.2 to 0.4 ksf/story, except housing and apartments where pressures may be less. 219 Rib Dimensions 250. Rib dimensions are determined by steps 3 to 5 with the assistance of Table 23. Reinforcement steel required to resist the calculated moments and shears may be determined by steps 6 to 11. The calculated maximum deflection should be checked to maintain angular distortions acceptable to the functional requirements and compatible with the flexibility of the superstructure, Table 24. Additional information on allowable deflections is provided by ACI Committee 435 (1980). Perimeter, diagonal, and interior ribs may be designed last, steps 12 to 14. An example application is provided in Technical Report ITL-88-1. Construction 251. A properly designed foundation can be expected to perform as intended if the construction methodology avoids significant disturbance of the foundation soil, the soil is of adequate bearing capacity, soil heave potential is either reduced to tolerable levels or the effects are accounted for in the structural/architectural details, and the foundation exceeds flexural rigidity and strength requirements. The foundation soil and groundwater characteristics should be adequately investigated to avoid unexpected obstacles to construction such as underground streams, sinkholes, boulders, poor site trafficability and drainage, unstable excavation slopes, excessive heave of excavation bottoms, and loss ot ground adjacent to excavations. Unforeseen problems caused by lack of prior subsurface investigations of soil and groundwater conditions will increase the cost of construction and may reduce quality of the foundation. Construction should be located where the foundation is supported by a uniform soil of adequate bearing capacity and resistant to differential movement on change in soil water content. Foundation soils that are not laterally uniform aggravate differential movement. Minimizing Problems 252. Many problems with foundations of structures can be avoided by using proper construction practice and adequate quality control of materials and workmanship. Adequate field records are essential to confirm that contract specifications are met. Specifications must be explicit and concise 220 Table 23 Analysis of Transverse Ribs a. Nomenclature TT Term Units Definition • ft Edge moisture variation distance, Table 20 I in 4/ft Moment of inertia per foot, I /S I in. Moment of inertia of rib ks Lb Lc Le lbs/in ft ft ft Li ft Distance from perimeter to location of interior load L L. 1 ft ft in. Basic length of cantilever Location of maximum moment from perimeter, edge lift Length between maximum difference in deflection A; 48L C for center lift; 12L a for edge lift M Mr ft-lb/ft ft-lb ft-lb/ft lb/ft Bending moment per foot Maximum moment for a given rib, Mmax S Maximum bending moment per foot Interior load per foot lb/ft Perimeter load per foot Mmax Pi PP 2 (pci) Coefficient of subgrade reaction, Table 20 Width of bearing soil at perimeter, edge lift Equivalent length of cantilever, center lift Equivalent length of simple beam, edge lift P lb/ft q R S lb/ft 2 (psf) lb ft V Vmax Vr lb/ft lb/ft lb Uniform applied pressure End reaction at perimeter for equivalent simple beam Rib spacing; - S short direction; - SI long direction Shear per foot Maximum shear per foot Maximum shear for a given rib, Vmax S Ym in. in. in. Soil heave without foundation load, Table 20 Deflection Deflection at perimeter radians in./in. Rotation of support of equivalent cantilever Maximum angular distortion A AP 8 3 (psf) Soil swell pressure, Table 20 max b. Center Lift Beneath Transverse Rib Calculation Equation Comment r -------- ----------C = 0.8 T----------- Maximum Lc = LoC moment for - ------- 0.12 .I L=23m a given rib 2 Mr, ft-lbs2...TMm =PpL PLa + q P c max H Ma Diagram 0 16 . ----- 0 12 T --- /P p + 0.4e Maximum shear for a given lbs rib V rV maxS Vma max and assumed.j,,, P = zero fat the perimeter and 5Lc from the perimeter + wL P VmaxS c -------- -- ------ ----- -- ------ .~ located distance L c from perimeter to vary linearly from M r to Mr - V located distance L max from the perimetr and assumed to vary linearly to P at the perimeter and and approach zero 5Lc from___1 the perimeter 221 'ha,,. (Concluded) Table 23 Equation Calculation T - Diagram Comment - 0.11 + 12L 8 Maximum deflection at perimeter A . in. p Ap PC Maximum angular distortion a max 0 A /1 max 1 - 4(12L ) 1 4 M . max 0 "5 9800I-k a 0.11 in. is an approximation for support translation plus cantilever bending and 12 converts L to inches c a s allowable angular max distortion (Table 24) c. Edge Lift Beneath Transverse Rib Calculation Equation Comment Diagram 7.51'L Maximum 0.17 0.3 0.12 Annscees iteration scheme is i deflection L = L p required to calculate Le Ap, in. e 0.11 because Ap is unknown. q 0.07 P* i Initially assume Ap< Ym Pi(Le- Li) then calculate Le, R, R qL Lb., a RP+ + and A . Repeat calculation Le 2 p until last A 1.1R L.-R0.01 --_ _ _ _ _ L Lb-e is within A inch of previou P, qpsf PP s/ If Pi- 0 or Li> Le , then ApMaximum angular distortion Ym(em 0 max Lb)e - 2 L ma 0 0 allowable angular 1 m max distortion (see Table 24) =A/L e max -, ,, lbs/, L 10.510.17 A .121q0.07 P M ob M 0;$S Iq I ;6. i Moment calculated by moment for M miven rib - M ,ft-lb L(R-Pp) - -2 gie p i ~Sheor M " M* statics. Location Mmax, L - R -P __P M Maximum shear for given rib Vr , r V - _ (R Mmax =M -IP Pi(L-Li) O'S"' If L ?:Li -; ... pp)2 q(Li - Le) " VmS max - P ' + , VIbs 2q S max max V EI If L < Lq i M - M* robo Distributed support from soil reduces shear calculated near interior hence, limit Vsupport; as given 222 Table 24 6 8 74 Limiting Angular Distortions to Avoid Potential Damages5 ' Length Height Limits to Avoid Damage Hogging of unreinforced load-bearing walls Allowable Angular Distortion, / 1 1/2000 2 5 s 3 Load bearing brick, tile, or concrete block walls 1/1250 1/2500 Sagging of unreinforced load-bearing walls 1/1000 Machinery sensitive to settlement 1/750 Frames with diagonals 1/600 No cracking in buildings; tilt of bridge 1/500 abutments; tall slender structures such as stacks, silos, and water tanks on a rigid mat Steel or reinforced concrete frame with brick, block, plaster or stucco finish Circular steel tanks on flexible base with floating top; steel or reinforced concrete frames with insensitive finish such as dry wall, glass, panels 5 : 3 > 1/500 1/1000 1/300 Cracking in panel walls; problems with overhead cranes 1/300 Tilting of high rigid buildings observed 1/250 Structural damage in buildings;, flexible brick walls with length/height ratio > 4 1/150 Circular steel tanks on flexible base with fixed top; steel framing with flexible siding; 1/125 74 - 1/500 Technical Manual 5-818-1, "Procedures for Foundation Design of Buildings and Other Structures (Except Hydraulic Structures) 223 spelling out exactly what the contractor or construction engineer is expected to accomplish. Records will also be an important source of factual data in case lawsuits are filed seeking compensation for losses incurred by contractors or by owners of the construction. Lack of explicit specifications reduces quality and may leave the owner open to claims. Records will also be useful if the structure becomes damaged at some future time to assist determination of the cause of damages and appropriate remedial measures. 253. Preparation of foundation soil, engineered fill placement and mat construction should be closely monitored by a responsible inspector, geotechnical engineer, and/or representative of the owner/operator to confirm that assumptions used by the designers actually occur in the field. Parameters of the load bearing soils should be checked to be sure they are similar to those used in the design, have sufficient bearing capacity, and located at the expected depth. The unexpected detection of unstable soils such as expansive, collapsible and soft materials should be brought to the attention of the designers and owners of the project so proper adjustments may be made to the structure. Construction materials should meet or exceed design sp-cifications such as use of proper fill plasticity and density, reinforcing steel of proper size and strength, and concrete of adequate strength and workability. 254. Identification of soil. Foundation soils encountered during construction should be identified, particularly if the soils are expansive or collapsible, paragraphs 235 and 236. Observations of soils actually encountered during construction will be used to confirm the assumptions made by the designers and to check that the intent of the foundation design will be accomplished during construction. Actual soil conditions that do not match design assumptions will require modifications to the design to assure that the foundation will perform adequately on the supporting soil over the projected life of the facility. Examination of the condition and types of structures adjacent to the construction site can provide additional information on the foundation soils. 255. Maintenance of constant water content. Every practical procedure should be taken to promote constant soil moisture and therefore maintain adequate soil strength and bearing capacity. 224 Deformation that occurs will therefore be limited to the normal elastic recompression settlement. Changes in water content can be minimized by promoting drainage, dewatering, and construction efficiency. Adequate drainage will eliminate ponding of surface water and reduce percolation of runoff into the foundation soil. 256. Rapid construction reduces time available for rainfall to occur and collect in the foundation soil and reduces evaporation from prepared soil bearing surfaces before the foundation can be placed. Construction efficiency may be improved by having equipment and materials required for a particular task at a convenient location adjacent to the site. All unnecessary items should be removed from the construction site to reduce clutter and increase mobility. Materials required for a particular construction sequence should be ordered sufficiently in advance to be available on site prior to the time of construction. Quality control and quality assurance must be maintained while rapid construction is facilitated. Construction errors should be corrected as soon as possible after they are made to reduce delay and cost. Delays can be minimized by careful management including frequent checking for adequate quality and frequent communication with subcontractors, construction workers, and suppliers of equipment and material. Delays early in construction should especially be avoided to prevent soil preparation work from "slipping" into wet or adverse weather seasons. Preparation for Mat Construction 257. The site should always be provided with adequate drainage to promote runoff of rainfall and minimize change in soil moisture and subsequent differential movement. firm soil surfaces. mechanized equipment. Site drainage should provide dry working conditions on Trafficability should be adequate to promote mobility of A granular fill layer up to 1 ft thick provides temporary roads for rapid movement of equipment and materials into and out of the site. This fill can also improve the grade to promote drainage and can also exert a surcharge pressure on underlying foundation soil that can help suppress swell pressures in the soil that develop on long-term wetting. Lime and/or cement mixed into surface soil of low trafficability often increases bearing capacity and site mobility. Site preparation work should be completed prior to the wet season, without delay and with adequate quality control to 225 optimize performance of the foundation soil. Soil preparation work should occur continuously until protected by the foundation of the structure to reduce detrimental effects of rainfall and drying on the foundation soil. 258. Clearing the site. Existing trees and other vegetation removed from the site may leave depressions. Depressions, holes, and trenches may often be filled with the natural soil compacted at the natural water content and density of the in situ soil to initially level the ground surface. Soil removed in cuts should be minimized because cut areas reduce the overburden pressure on underlying foundation soil, which also reduces the pore water pressure in the soil. If the soil is relatively impervious such as for cohesive materials, considerable time is required for these pore pressures to increase to an equilibrium consistent with the surrounding area. Rebound and a long-term time dependent heave may occur that will aggravate differential movement over many years, particularly if the soil is expansive. A perched water table may even develrp, if not already present, because previously existing vegetation naav have desiccated the soil. depths exceeding 5J 259. rc60 ft. Excavation. Trees can desiccate soil to 75 Prior to initiation of any excavation work, maps of subsurface utilities should be investigated to determine the location and types of utilities that will be encountered so accommodations may be made to continue service and prevent damage to the utilities. During excavation work unexpected as well as expected problems must be identified and dealt with such as loss of slope stability, loss of ground, bottom heave, and groundwater. Excavations should be completed to the design depth as rapidly as possible and exposed soil protected from both wetting and drying. Equipment should be selected to optimize removal of overburden soil depending on the size and depth of the final excavation. Transportation equipment to remove overburden to appropriate disposal areas should be selected depending on the rate of excavation and haul distance. Table 25 provides an example of excavation specifications. 260. The bearing soil at the design depth should be checked prior to excavating to the design depth to be sure that this soil is satisfactory and will support the foundation within allowable displacements. 75 Blight 1987 226 If this soil is Table 25 Example Excavation Reouirements Excavations conformed to the dimensions and elevation of each structure. Excavations include trenching for utility and foundation drainage systems to a point 5 ft beyond the building line. Excavations extend sufficient distance from walls and footings to allow for placing and removing forms. Excavation below indicated depths are not permitted except to remove unsatisfactory material. Satisfactory material removed below depths indicated shall be replaced with satisfactory material at no additional cost to the government. The thickness of concrete footings shall be increased in thickness to the bottom of the overdepth excavations and overbreak in rock excavations. Excavation shall be performed so that the area will be continually and effectively dewatered* and surface drained**. Water from any source shall not be permitted to accumulate in crawl space areas and in the excavation. The excavation shall be drained by pumping or other satisfactory methods to prevent softening of the foundation bottom, undercutting of footings, or other actions detrimental to proper construction. Shoring including sheet piling shall be furnished and installed as necessary to protect workmen, banks, adjacent paving, structures, and utilities. *dewater refers to the elimination of any ground water in the excavation **surface drained refers to the elimination of any surface water 227 not satisfactory, then this weak or soft soil must be excavated to a sufficient depth beneath the proposed foundation depth and replaced with fill compacted to a satisfactory density and bearing capacity. The depth of overexcavation depends on the extent of unsatisfactory material and economics of this situation. Some redesign of the foundation may be required if unsuitable bearing soils are found and some delay and additional cost may occur. A thorough soil investigation prior to construction should minimize encountering this kind of problem. 261. After the final layer of soil to be excavated is removed, the exposed surface of the load bearing soil should be immediately protected from disturbance such as wetting or drying. This is especially critical with clays and shales that may flake, spall, shrink, swell or otherwise deteriorate from exposure to the atmosphere. A layer of concrete called a "mudslab" or a permanent membrane may be placed on the exposed bottom of the excavation to protect the soil. A chlorinated polyethylene membrane of about 10-mil thickness may also adequately protect the soil surface. Asphalt coatings may also be applied to protect the excavation bottom, but these may be sticky and difficult to use. 262. The foundation and superstructure should be constructed as soon as possible on the prepared surface of the excavation bottom to replace the loss in pressure applied to the underlying soil from the excavated overburden. Rapid construction and placement of the structural loads replace the original soil weight and therefore reduce heave from rebound and subsequent settlement and differential movement caused by recompression of the underlying soil. 263. Surface runoff from rainfall, groundwater seeping into the excavation, and other sources of water must be drained from the site and excavation. Ponded water must not be permitted to collect in open excavations because this water will seep into the underlying soil and reduce its shear strength. The soil may also expand with some or most expansion taking place following construction of the foundation. Pumping equipment may be required to dewater the excavation. 264. The excavation perimeter must be stable against a slope failure. An open excavation in normally consolidated clay will stand vertically without support for heights up to 4 times the undrained shear strength divided by the 228 wet density of the soil until drying and/or pore pressure recovery reduces the Loess and stiff glacial tills will stand vertically over long mass strength. periods. Moist sands and sandy gravels can stand vertically from cohesion Dry sands and gravels will stand at caused by negative pore water pressure. slopes equal to their angle of repose. Removal of lateral pressure, however, may open fissures and exposure to the environment will cause deterioration and may increase pore water pressure near the surface of the perimeter soil of the excavation; slides may subsequently occur. Consideration should be given to placement of a temporary impervious membrane or sprayed bituminous coating on the exposed perimeter soil. 265. Pavements, facilities and other property near the excavation must be protected. Property must be checked and their condition recorded prior to any excavation. Periodic level readings of temporary benchmarks or stakes placed around the perimeter and near existing structures and pavements should Loss of ground or vertical settlement be recorded to monitor loss of ground. on the ground surface outside the perimeter of an excavation exceeding 1/4 inch may indicate lateral deformation and creep of the perimeter into the excavation, seepage of groundwater into the excavation, or heave of the excavation bottom. Loss of ground should not exceed 1/2 inch or lateral creep should not exceed 2 inches to avoid any damage to adjacent facilities. 266. Excavation slopes may be supported by inclined or horizontal braces against vertical piles and sheet walls, closely-spaced cast-in-place concrete drilled shafts, sheet pile walls with ground anchors, or reinforcing the earth with steel rods driven through a facing material such as wood planks or metal sheets. Excessive rebound of the excavation bottom may be reduced by limiting the size of the excavation and constructing the foundation and superstructure in several sections. 267. Fill placement. Cohesive, low plasticity fills compacted to a density with adequate bearing capacity are commonly used to replace unsatisfactory soil of low bearing capacity or soil of a swelling/collapsible nature to depths of about 4 to 8 ft beneath the mat, raise the existing ground surface to the final grade elevation, and place around the perimeter of structures constructed in excavations. Materials selected for fills should be sands and gravels containing a less than Number 40 mesh fraction of fines with 229 plasticity index less than 12 and liquid limit less than 35. Peats, organic materials, silty sands and silts of high plasticity are not acceptable fill materials. 268. The fill should have cohesion to allow construction of trenches for ribs and utility lines with minimal form work. The cohesion also reduces permeability of the fill and minimizes seepage of surface water down into the natural stratum beneath the fill. Seepage into a pervious fill overlying a relatively impervious natural stratum can contribute to a perched water table in the fill and may lead to long-term differential movement if the underlying stratum is desiccated expansive or collapsible soil. Table 26 provides an example fill specification. 269. Sufficient laboratory classification and compaction tests should be performed during the site and soil exploration program to identify potential fill materials, to assure adequate quantities and to determine compaction characteristics of the various materials available in the borrow areas. Accurate identification by Atterberg limit and gradation tests assist selection of appropriate fill material and water content limits required to achieve adequate density and bearing capacity of a particular fill. The fill should be uniform in the horizontal direction to minimize differential movement of the mat foundation. Compaction effort normally required for cohesive fill is at least 90 percent of optimum density determined by the compactive effort described in ASTM D 1557. comparable with modified AASHTO. This high compactive effort is For the low plasticity fills of plasticity index < 12 often reconmended beneath structures compaction should be at least 92 percent of optimum density. Laboratory tests should be performed prior to construction on the proposed fill material to be sure that the plasticity, stiffness and strength of the compacted fill will provide optimum performance of the foundation. 270. The first fill layer following compaction should be checked to meet density and material specifications such as those in Table 26. Substantial delays can and will occur if unsatisfactory compacted material must be removed and replaced with satisfactory material. In situ density tests such as ASTM D 1556 should be performed to check the density and used to calibrate surface moisture nuclear gages. 230 Numerous surface moisture gage Table 26 Example Fill Reguirements Type of materials permitted in fill include GW, GM, GC, GP, SW, SP, SM, SC, and CL of the Unified Soil Classification System. The plasticity index should be less than 12 and the liquid limit less than 35. Such material may be cohesive and should be compacted to not less than 92 percent of optimum density. Unsatisfactory materials include PT, OH, OL, ML, MH, and CH of the Unified Soil Classification System. When subgrade surfaces are less than the specified density, the surface shall be broken up to a minimum depth of 6 inches, pulvrized and compacted to the specified density. The excavated surface shall be scarified to a depth of 6 inches before fill placement is begun. Satisfactory unfrozen material shall be placed in horizontal layers not exceeding 8 inches in loose depth and then compacted. Materials shall not be placed on surfaces that are muddy, frozen, or contain frost. Compaction shall be accomplished by sheepsfoot rollers, pneumatic-tired rollers, steel-wheeled rollers, or other approved equipment well suited to the soil being prepared. Materials shall be moistened or aerated as necessary to provide proper water content that will readily facilitate obtaining the specified compaction with equipment used. Fill materials shall be compacted to densities after ASTM Standard D 1557: Cohesive Cohesionless Under structures 92 95 Under sidewalks and grassed areas 85 90 231 readings can subsequently be made following compaction of additional layers of fill. Nuclear gages should be periodically checked with results of ASTM D 1556 or other appropriate density measurement method performed on compacted fill. If inclement weather stops the fill operation, then upon resuming work the top layer of compacted fill affected by rainfall should be scarified until the correct range of water content is achieved before recompacting and continuing with fill placement. 271. Construction of stiffening beams. Trenches for construL Ion of stiffening beams and utilities may be excavated in the cohesive granular fill using a trenching machine capable of a minimum width of 12 inches and depths up to at least 3 ft below grade. Widths of 18 inches or more are usually required to accommodate placement of steel reinforcement in the beams. 272. Vapor barriers. Vapor barriers such as plastic films may be placed in trenches and beneath slabs. These barriers prohibit accumulation of moisture into the concrete with possible sweating of this moisture up through the concrete to the surface of the floor. This is especially important where compacted fills of relatively high permeability have been placed over relatively impervious natural soil. fills. Groundwater tends to accumulate in these Plastic films should be checked to be free of punctures, holes, and other leaks before placing the concrete. 273. Plastic films also prevent loss of moisture into underlying soil from the concrete mix; therefore, the concrete mix should not contain excess water to minimize drying shrinkage. Drying shrinkage occurs at the surface of the mat and may cause some upward curling at the edges or joints. Stiffening beams at the perimeter and expansion joints of the mat foundation can effectively reduce curling. Vapor barriers should be placed snugly against trench walls to avoid any gaps between the trench walls and the membrane; the concrete stiffening beams otherwise will not have the correct shape and dimensions required to resist bending moments. Incorrectly placed vapor barriers must be removed or corrected to allow stiffening beams to form with the correct dimensions. 274. Reinforcement steel. Steel reinforcement should be placed in the proper location to provide adequate concrete cover and optimum bending moment resistance. Reinforcement steel should be ASTM Grade 60, except Grade 40 may 232 be used for ties. Refer to Chapter 4.7, ACI 302 (1980) for further details on Steel tendons and anchors for post-tensioned concrete reinforcement steel. must be properly supported and means provided for holding post-tensioning anchorage assemblies in place. Concrete near anchors should be reinforced The post-tensioning stress should be applied as soon with additional steel. as the concrete reaches its design strength. Columns should have sufficient freedom to move laterally when the post-tensioning stress is applied. Proper post-tensioning requires careful control of construction under expert supervision. 275. Concrete. Concrete should be of the correct composition to provide the design strength, which is usually 3000 psi after 28 days. The slump should be 4 to 6 inches and no water should be added to the mix after leaving the batch plant. Further details on concrete for building construction are in the literature76 . 276. Excess water cannot drain out of concrete placed on impervious membranes. Water reducing admixtures (ASTM C494) may be added to increase workability, reduce water required to obtain the desired slump, and thereby increase strength of the finished concrete. Concrete shrinkage may be reduced by using cement with lower water demand such as Type I and coarse aggregates that do not shrink when dried66 . High range water reducers or Mats superplasticizers are prohibited in guide specification CEGS 03300. supporting large structures are commonly constructed in sections where concrete is placed on portions of the foundation area, while excavation and preparation of the bearing soil surface proceeds in other areas. Concrete should be adequately cured before removal of forms and before permitting traffic on the mat. Refer to TM 5-818-7 for further construction details on expansive soil. 277. Concrete for large ribbed mats may be placed in one or two stages. If placed in two stages, the first stage is to place concrete for the stiffening beams followed a few days later with concrete for the remaining mat. The exposed concrete surface on the stiffening beams must be kept clean to allow the fresh concrete to adhere to concrete placed earlier. The 76Corps of Engineers Guide Specification (CECS) 03300, ACI 302 (1980), Technical Manuals 5-809-2 and 5-809-12 233 finishing of concrete is important in obtaining sufficient levelness and flatness of the floor to optimize operational efficiency. Guidelines for the degree of floor flatness/levelness required to achieve adequate operational efficiency, however, are not complete. A standard recommended for specifying floor flatness/levelness is the F-number system77 . Site Finishing 278. Site finishing involves connection of utility lines, backfill of open excavations, installation of drainage systems, and landscaping. connections to outside lines should be flexible and watertight. Utility Backfill materials should be nonexpansive with low permeability to inhibit migration of surface moisture down to soil with potential for volume change. 279. The site should be graded to provide at least a 1 percent slope from the perimeter of the structure for positive drainage. A 5 percent slope should be provided for at least 10 ft from the perimeter of the structure for foundations on potentially expansive soil to promote rapid runoff of surface water. Fill placed to raise structures above the original ground surface contributes to a positive grade for drainage and reduces differential movements from volume changes in nonuniform foundation soils. The structure should be provided with gutters and downspouts to collect rainfall. Runoff from downspouts should be directed on to splash blocks at least 5 ft long and sloped for positive drainage from the structure. Impervious horizontal moisture barriers or membranes about 10 ft wide placed around the perimeter and protected by 6 inches of fill helps to promote uniform changes beneath the mat and moves the edge moisture variation distance out from beneath the foundation. These should be placed at the end of the wet season. Underground perforated drain lines adjacent to mats placed in excavations to collect seepage should be constructed with a 1 percent slope to avoid water ponding in the line. The drain must be connected to an outlet to drain seepage collected around the foundation. An impervious membrane placed beneath the drain will minimize seepage into desiccated subsoil. Underground drains, however, are usually not recommended because they have been a source of moisture into expansive/collapsible subsoils aggravating differential foundation movements. 77Face 1987, ASTM E 1155 234 Followup 280. The foundation and superstructure should be observed periodically to evaluate performance of the structure. Table 27 illustrates a preliminary systematic record system for rating performance of foundations. Table 27a defines the type of movement, whether center mound (center heave) or center dish (edge heave or center settlement) expected depending on the type of observed cracks. distortion I Table 27b allows the observer to evaluate the angular from the measured crack dimensions and to rate the distress. Cracks, distortions, and other structural deterioration should be recorded similar to that illustrated in Table 27c. The type of movement, £ estimate, and level of distress may also be entered in Table 27c. A floor and wall plan of the facility should also be attached to Table 27 to complete the damage record. The grade around the perimeter should be checked for adequate slope and control of erosion. The grade may become impaired with time around the perimeter from settlement of backfill or heave of in situ expansive soil. An expansive soil is not restrained from heave outside the perimeter and may destroy the grade. Eventually, rainfall may be directed toward the foundation until positive drainage is restored. 235 Table 29 Preliminary SYSTEMATIC DAMAGE RECORD SYSTEM For Record of Differential Movement in Foundation Soils a. Component Exterior Walls Type of Movement Distress Horizontal Cracks Vertical Cracks Center Mound - near top (roof restraint) - wall bulging out - wall bulging in X X - larger near top, more frequent near top X Center Dish X - larger near bottom, start X near bottom Diagonal Cracks - up toward corner from bottom of wall X - up toward corner from top of window X - down away from window X X X - up from corner - radiate up toward interior Slabs Deep Foundation Tilting up toward center of facility Tilting up toward perimeter Cracks parallel with wall, larger at top surface X Fractured - near center of facility Plinths - near edge of facility X b. X X X Damage Rating Hand Level Readings 6, Vertical Change Crack Widths Width, in. Degree of Damage < 1/8 Slight Distress Level Length 1/8 > 1/150 > 1/250 > 1/500 Structural damage Inconvenience to occupants Cracking - 1/4 1/4 - 1/2 1/2 - 3/4 > 3/4 236 Minor Mild Moderate Severe c. Site Assessment Facility Age (yrs) Location Date Inspector Check Climate: Humid Semi-arid Check Ribbed mat Foundation: Flat mat Drilled shaft __ Driven pile_ Shallow footings Strip footings Arid___ Depth of Foundation Base Below Ground Surface, ft Downspouts Splash blocks Gutters Slope from perimeter: Check Drainage: Soil Description: Utility Water Loss: Crack Distress Record Level Record T Location Location Vertical Change, in. - Occupant Comments: Dish Settlement Inspector Comments: Maximum 9 Distress Degree of Damage 237 T Length, Maximum in. Width,in. Visible Moisture Source to Soil Performance Rating Maximum Crack Width, in. Shape of Movement: Mound Check probable Movement: Heave Orientation ± - Level length, in. T T T PART VI. 281. RECOMMENDATIONS A systematic damage record system to document foundation distortion, distress in facilities, and maintenance requirements should be fully developed in preparation of field surveys of constructed facilities to catalog damages to structures and therefore make possible progress in identifying the cause of damage, requirements for repair and efficiency of operations, particularly the impact of foundation movement on machinery and robotic equipment. Field surveys should subsequently be performed to measure surface displacements inside and outside of existing structures and to rate the performance of structures using the frequency spectrum method with the systematic performance record system. The specific floor flatness/levelness requirements to provide optimum performance of facilities should be determined. Guidelines may then be implemented to minimize these damages and their effects on short and long-term structural performance and aid in reducing repair and long-term maintenance. 282. Research is recommended to determine methods for reducing soil movement by ground modification or soil moisture stabilization and therefore, to reduce requirements of designing foundations to resist soil movements. Research and development efforts are necessary to verify the effectiveness of soil moisture stabilization, establish criteria for stabilization, establish structural criteria for mats on moisture-stabilized soils, and develop construction details for perimeter moisture barriers. 283. Research is recommended to investigate the problem of cracking during construction of ribbed mats. Drying shrinkage in stiffening beams, which may let the ribs hang in the trenches, may be a factor in cracking. Research may be useful to recommend spacing of construction joints, acceptability of joints between stiffening beam ribs and slabs, location of the membrane vapor barrier, concrete strength and mix design, percent and location of reinforcement, and curing methods. 284. Research is recommended to determine proper specifications for preparation and compaction of low plasticity, nonexpansive, cohesive fills commonly placed to support ribbed mats and other shallow foundation systems. Current specifications for compaction of cohesive clays and cohesionless sands may not be appropriate for these engineered fills. 238 285. A field survey of Corps of Engineers division and district offices, real estate developers, contractor organizations, casualty insurance writers, private consultants, and educational institutions is recommended to collect a detailed list of all design/construction procedures and local practices for ground modification and soil moisture stabilization in unstable (expansive/collapsible,soft) soil areas. These practices should be rated to determine their relative usefulness in providing economical and adequate guidelines for design and construction of foundations in unstable soils. 286. Centrifuge and/or field tests should be performed with unstable soil to confirm and improve appropriate soil input parameters for design such as the active depth of heave, edge moisture variation distance, potential soil heave and to obtain information on a fundamental new parameter, the maximum acceptable change in suction at the lower boundary of the depth of soil subject to heave. The centrifuge can simulate a full scale field test by subjecting a small model to acceleration such that the field situation is simulated. A sequence of events such as placement of loads and diffusion of moisture of a full scale test can be simulated rapidly in the centrifuge so that the distribution of volume changes and vertical displacements from applied loads and moisture changes can be observed in just a few days rather than months or years required in the field. Costs can be substantially reduced by eliminating many full scale field test sections with associated instrumentation and monitoring and analysis of data over a long period of time. Field test sections in different climates will validate design guidelines for general applications. These tests may be used to analyze the effectiveness of ground modification techniques and the ability of design methodology to predict behavior of the foundation in the soil. Guidelines for ground modification techniques that reduce potential volume changes leading to the design and construction of more economical foundation systems may subsequently be developed. 287. Two- or three-dimensional soil-structure interaction models such as the plate on elastic foundation, frequency spectrum model for mats or other model shown to reasonably simnulate field behavior may be improved to aid the analysis and design of mat foundations in unstable soil. Foundary elements, which are particularly appropriate for moisture diffusion problems, as well as the finite element method may be considered in analyses. 239 REFERENCES ACI Committee 302. 1980. "Guide for Concrete Floor and Slab Construction", Construction Practice and Inspection Pavements, Part 2, ACI Manual of Concrete Practice, American Concrete Institute, Detroit, MI ACI Committee 318. 1980. "Part 4-General Requirements", Use of Concrete in Buildings: Design, Specifications, and Related Topics, Part 3, ACI Manual of Concrete Practice, American Concrete Institute, Detroit, MI ACI Committee 336. 1987. "Suggested Design Procedures for Combined Footings and Mats", American Concrete Institute Committee 336, American Concrete Institute, Detroit, MI ACI Committee 340. 1977. "Slab Design In Accordance With ACI 318-77", Supplement To Design Handbook In Accordance With The Strength Design Method, ACI Publication SP-17 (73)(S), American Concrete Institute, Detroit, MI ACI Committee 435. 1980. "Allowable Deflections," Use of Concrete in Buildings: Design. Specifications, and Related Topics, Part 3, ACI Manual of Concrete Practice, American Concrete Institute, Detroit, MI ACI Committee 436. 1966. "Suggested Design Procedures for Combined Footings and Mats," Journal of the American Concrete Institute, Reported by S. V. DeSimone, Vol 63, Detroit, MI, pp 1041-1056 Ahlvin, R. G. and Ulery, H. H. 1962. "Tabulated Values for Determining the Complete Pattern of Stresses, Strains, and Deflections Beneath a Uniform Circular Load on a Homogeneous Half Space," Stress Distribution in Earth Masses, Highway Research Board Bulletin 342, NAS-NRC, Washington, D. C., pp 113 "Chemical Admixtures For Concrete," 1988. Annual Book of ASTM Standards. ASTM Standard Specification C494-86, Concrete and Aggregates, Part 04.02, American Society for Testing and Materials, Philadelphia, PA ' 1988. "Bearing Capacity of Soil for Static Load on Spread Footings," ASTM Standard D1194-72, Soil and Rock Building Stones; Geotextiles, Volume 04.08, American Society for Testing and Materials, Philadelphia, PA 1988. "Density of Soil in Place by the SandCone Method," ASTM Standard Test Method D1556-82, Soil and Rock: Building Stones: Geotextiles, Volume 04.08, American Society for Testing and Materials, Philadelphia, PA 1988. "Moisture-Density Relations of Soils and Soil-Aggregate Mixtures Using 10-lb (4.54-kg) Rammer and 18-in. (457-mm) Drop." ASTM Standard D1557-78, Soil and Rock: Building Stones: Geotextiles, Volume 04.08, American Society for Testing and Materials, Philadelphia, PA 240 . 1988. "Penetration Test and Split-Barrel Sampling of Soils," ASTM Standard D1586-84, Soil and Rock: Building Stones: Geotextiles, Volume 04.08, American Society for Testing and Materials, Philadelphia, PA 1988. "Deep, Quasi-Static, Cone and Friction- Cone Penetration Tests of Soil," ASTM Standard D3441-79, Soil and Rock: Building Stones: Geotextiles, Vol 04.08, American Society for Testing and Materials, Philadelphia, PA . 1988. "One-Dimensional Swell or Settlement Potential of Cohesive Soils," ASTM Standard D4546-85, Soil and Rock: Building Stones: Geotextiles, Vol 04.08, American Society for Testing Materials, Philadelphia, PA 1988. "Pressuremeter Testing -f Soils," ASTM Standard D4719-87, Soil and Rock: Building Stones: Geotextiles, Vol 04.08, American Society for Testing Materials, Philadelphia, PA .. 1988. "Standard Test Method for Determining Floor Flatness and Levelness Using the F-number System", E1155-87, Building Seals and Sealants: Fire Standards: Building Constsructions, Vol 04.07, American Society for Testing and Materials, Philadelphia, PA Baquelin, F., Jezaquel, J.-F., and Shields, D. H. 1978. The Pressuremeter and Foundation Engineering, Trans-Tech Publications, Rockport, MA Bathe, K., Peterson, F., and Wilson, E. 1978. "SAP5-WES Structural Analysis Program," Program No. 713-F3-R0012, U. S. Army Engineer Waterways Experiment Station, Vicksburg, MS Blight, G. E. 1987. "Lowering of the Groundwater Table by Deep-Rooted Vegetation - The Geotechnical Effect of Water Table Recovery", Groundwater Effects in Geotechnical Engineering, Proceedings Ninth European Conference on Soil Mechanics and Foundation Engineering, Dublin, pp 285-288 Bobe, R., Hertwig, G., and Seiffert, H. 1981. "Computing Foundation Slabs With Building Rigidity," Proceedings of the 10th International Conference on Soil Mechanics and Foundation Engineering, Vol 2, Stockholm, Sweden, pp 53-56 Boussinesq, J. 1885. Application of Potential to the Study of the Equilibrium and Movements in Elastic Soils, Gauthia-Villard, Paris . 1976. "Mat Foundations," Analysis and Design of Building Foundations, Chapter 8, editor H. Y. Fang, Envo Publishing Company, Lehigh Valley, Pa, pp 209-231 . 1982. Foundation Analysis and Design, 3rd Edition, McGraw-Hill Book Company, New York, NY, pp 187-188, 240-258 . 1988. Foundation Analysis and Design 4th Edition, McGraw-Hill Book Company, pp 219-222, 266 241 Briaud, Jean-Louis. 1979. "The Pressuremeter: Application to Pavement Design," Ph.D. Thesis, Department of Civil Engineering, School of Graduate Studies, University of Ottawa, Ottawa, Canada, pg 184-188. Briaud, J.-L., Tucker, L., and Coyle, H. M. 1982. "Pressuremeter, Cone Penetrometer, and Foundation Design," Civil Engineering Department, Texas A&M University, College Station, TX Brooker, E. W. and Ireland, H. 0. 1965. "Earth Pressures at Rest Related to Stress History", Canadian Geotechnical Journal, Vol 11, pp 1-15 Building Research Advisory Board (BRAB). 1968. "Criteria for Selection and Design of Residential Slabs-on-Ground," Publication No. 1571, National Academy of Sciences-National Research Council, Washington, D. C. Burland, J. B. and Davidson, W. 1976. "A Case Study of Cracking of Columns Supporting A Silo Due to Differential Foundation Settlement," No. CP42/76, Building Research Station, Building Research Establishment, London, England Burland, J. B. and Wroth, C. P. 1978. "Settlement of Buildings and Associated Damage," Foundations and Soil Technology, The Construction Press, Lancaster, England, pp 287-329 Burmister, D. M. 1963. "Prototype Load-Bearing tests for Foundations of Structures and Pavements", Field Testing of S~ils, American Society for Testing and Materials Standard Technical PublicationNo. 322, pp 98-119, Philadelphia, PA Buttling, S. and Wood, L. A. 1982. "A Failed Raft Foundation on Soft Clays," Ground Engineering, Vol 15, No 5, pp 40-44 Chou, Y. T. 1981. "Structural Analysis Computer Programs for Rigid Multicomponent Pavement Structures With Discontinuities - WESLIQUID and WESLAYER," Technical Report GL-81-6 (3 Reports), U. S. Army Engineer Waterways Experiment Station, Vicksburg, MS Christian, J. T. and Carrier III, W. D. 1978. "Janbu, Bjerrum, and Kjaernsli's Chart Reinterpreted," Canadian Geotechnical Journal, Vol 15, pp 123-128 Dawkins, W. P. 1982. "User's Guide: Computer Program for Analysis of BeamColumn Structures With Nonlinear Supports (CBEAMC),' Instruction Report K-826, U. S. Army Engineer Waterways Experiment Station, Vicksburg, MS Department of the Army. Corps of Engineers, Office of the Chief of Engineers, 1984. "Geotechnical Investigations," Engineer Manual EM 1110-2-1804, Washington, D. C. (To Be Published). Manual EM 1110-1-1904, Washington, D. C. 242 "Settlement Analysis," Engineer 1970. "Laboratory Soils Testing," Engineer Manual EM 1110-2-1906, Washington, D. C. Engineer Mar-al EM iLiO-2- 1972. "Soil Sampling," 1987. "Concrete for Building Construction", Corps of 1907, Washington, D. C. Engineers Guide Specification 03300, Washington, D. C. Desai, C. S., Johnson, L. D., and Hargett, C. M. 1974. "Analysis of PileSupported Gravity Lock", Journal of the Geotechnical Engineering Division, Proceedings of the American Society of Civil Engineers, Vol 100, pp 1009-1029 DeSalvo, G. J. and Swanson, J. A. 1982. ANSYS Engineering Analysis System User's Manual, Swanson Analysis System, Inc. Houston, PA Duncan, J. M. and Chang, C. Y. 1970. "Nonlinear Analysis of Stress and Strain in Soils," Journal of the Soil Mechanics and Foundations Division, Proceedings of the American Society of Civil LEngineers, Vol 97, pp 1629-1653 Duncan, J. M. and Clough, G. W. 1971. "Finite Element Analysis of Port Allen Lock," Journal of the Soil Mechanics and Foundations Division. Proceedings of the American Society of Civil Engineers, Vol 97, pp 1053-1068 Editor, 1982. 19, 21-22 "Structural Foundations," Construction News, June 11, pp 18- Eshbach, 0. V. 1954. Handbook of Engineering Fundamentals, 2nd Edition, John Wiley & Sons, pp 5-64 to 5-68 Face, A. 1987. "Specifying Floor Flatness and Levelness: The F-Number System", The Constrsuction Specifier, Alexandria, VA Feld, J. 1965. "Tolerance of Structures to Settlement," Journal of the Soil Mechanics and Foundations Division, American Society of Civil Engineers, Vol 91, No SM3, pp 63-77 Focht, Jr., J. A., Khan, F. R., and Gemeinhardt, J. P. 1978. "Performance of One Shell Plaza Deep Mat Foundation," Journal of the Geotechnical Engineering Division, American Society of Civil Engineers, Vol 104, No GT5, pp 593-608 Fraser, R. A. 1975. "Review of Investigation on Raft Foundations for Major Buildings on Deep Soils, Perth Area," Paper III, Proceedings of Symposium on Raft Foundations, Perth, Western Australia, pp 23-40 Fraser, R. A. and Wardle, L. J. 1975. "The Analysis of Stiffened Raft Foundations on Expansive Soils," Symposium on Recent Developments in the Analysis of Soil Behavior and Their Application to Geotechnical Structures, Vol 2, Department of Civil Engineering Materials, University of New South Wales,m Kensington, N.S.W., Australia, pp 89-98 243 Gibson, R. E 1967. "Some Results Concerning Displacements and Stresses in a Nonhomogeneous Elastic Half-Space," Geotechnique, Vol 17, pp 58-67 Godden, W. G. 1965. Numerical Analysis of Beam and Column Structures, Prentice-Hall, Inc., Englewood Cliffs, NJ Golubkov, V. N., Tugaenko, Y. F., Matus, Y. V., Sinyavskii, S. D., and Varenik, P. F. 1980. "Investigation of Deformations in Soil Beneath Foundation Mat of 16-Story Residential Building," Translated from Osnovaniya, Fundamenty i Mekhanika Gruntov, No. 6, Odessa Civil Engineering Institute, Russia, pp 232-235 Haliburton, T. A. 1972. "Soil Structure Interaction: Numerical Analysis of Beams and Beam-Columns," Technical Publication No. 14, School of Civil Engineering, Iklahoma State University, Stillwater, OK Hansen, J. B. 1961. "A General Formula For Bearing Capacity," Bulletin No. 11, Danish Geotechnical Institute, Copenhagen, pp 38-46 . 1970. "A Revised and Extended Formula For Bearing Capacity," Bulletin No. 28, Danish Geotechnical Institute, Copenhagen, pp 5-11 Hartman, J. P. and James, B. H. 1988. "Development of Design Formulas for Ribbed Mat Foundations on Expansive Soils," Technical Report ITL-88-1, U. S. Army Engineer Waterways Experiment Station, Vicksburg, MS Headquarters, Department of the Army. 1984. "Concrete Structural Design for Buildings", Technical Manual 5-809-2, Washington, D. C. _ 1979. "Concrete Floor Slabs On Grades Subjected to Heavy Loads," Technical Manual 5-809-12, Washington, D. C. _ 1983. "Soils and Geology Procedures for Foundation Design of Buildings and Other Structures (Except Hydraulic Structures)", Technical Manual 5-818-1, Washington, D. C. _ Soils," 1983. "Foundations in Expansive Technical Manual 5-818-7, Washington, D. C. Hetenyi, M. 1946. Beams on Elastic Foundation, The University of Michigan Press, Ann Arbor, MI, p 46 Holland, J. E. 1979. "Behavior of Experimental Housing Slabs on Expansive Clays," 7th Asian Regional Conference on Soil Mechanics and Foundation Engineering, Singapore Hooper, J. A. 1978. "Foundation Interaction Analysis," Chapter 5, Developments in Soil SMechanics-l, C. R. Scott, editor, Applied Science Publishers LTD, London, England, pp 149-211 244 Hooper, J. A. and Wood, L. A. 1977. "Comparative Behavior of Raft and Piled Foundations," Proceedings of the Ninth International Conference on Soil Mechanics and Foundation Engineering, Vol 1, Tokyo, pp 545-549 Huang, H. H. 1974a. "Analysis of Symmetrically Loaded Slab on Elastic Solid," Technical Note, Journal of Transportation Engineering, American Society of Civil Engineers, Vol 100, No TE2 Huang, Y. H. 1974b. "Finite Element Analysis of Concrete Pavements With Partial Subgrade Contact," Transportation Research Record 483, Transportation Research Board, Washington, D. C. Hughes, J. M. 0. 1982. "Interpretation of Pressuremeter Tests for the Determination of Elastic Shear Modulus," Proceerdings of Engineering Foundation Conference on Updating Subsurface Sampling of Soils and Rocks and Their In Situ Tests, Santa Barbara, CA Johnson, L. D. 1982. "Users Guide for Computer Program Heave", Miscellaneous Paper GL-82-7, U. S. Army Engineer Waterways Experiment Station, Vicksburg, MS Johnson, L. D. 1988. "Proceedings of the Workshop on Design, Construction, and Research for Ribbed Mat Foundations," Miscellaneous Paper GL-88-6, U. S. Army Engineer Waterways Experiment Station, Vicksburg, MS Kay, J. N. and Cavagnaro, R. L. 1983. "Settlement of Raft Foundations," Journal of Geotechnical Engineering, American Society of Civil Engineers, Vol 109, No 11, pp 1367-1382 Kerr, A. D. 1987. "Analysis of Footings on a Sand Base", Interim Progress Report for Contract CE DACW39-86-M-1358, Submitted to U. S. Army Engineer Waterways Experiment Station, Vicksburg, MS Lambe, T. W. and Whitman, R. V. York, NY, p 153, 202 1969. Soil Mechanics, John Wiley & Sons, New Lytton, R. L. 1972. "Design Methods for Concrete Mats on Unstable Soils," Proceedings of the 3rd Inter-American Conference on Materials Technology, Riode-Janeiro, Brazil, pp 171-177 McKeen, R. G. and Eliassi, M. 1988. "Selection of Design Parameters For Foundations on Expansive Soils," Prepared for U. S. Army Engineer Waterways Experiment Station, Vicksburg, MS, under Contract DACA39-87-M-0754 McKeen, R. G. and Lytton, R. L. 1984. "Expansive Soil Pavement Design Using Case Studies," International Conference on CAse Histories in Geotechnical Engineering, editor Shamsher Prakash, Vol III, St. Louis, MO, pp 1421-1427 Meyerhof, G. G. 1953. "Some Recent Foundation Research and Its Application to Design," Structural Engineer, London, England, Vol 31, ?p 151-167 245 Milovic', D. M. 1959. "Comparison Between the Calculated and Experimental Values of the Ultimate Bearing Capacity," Proceedings of the 6th International Conference on Soil Mechanics and Foundation Engineering, Vol 2, Montreal, Canada, pp 142-144 Mitchell, J. K. and Gardner, W. S. 1975. "In Situ Measurement of Volume Change Characteristics," SOA Report, Proceedings uf the American Society of Civil Engineers Special Conference on the In Sitsu Measurement of Soil Properties, Raleigh, N. C. Mitchell, P. W. 1980. "The Structural Analysis of Footings on Expansive Soils," Kenneth W. G. Smith & Associaters Research Report No. 1, Webb & Son, 16 Fenn Place, Adelaide, Australia Muhs, H. J. 1959. "Neuere Entwicklung der Untersuchung in Berechnung von Flachfundationer," Schweiz. Bauzeitung, Germany, Vol 19, p 11 Peck, R. B., Hanson, W. E., and Thornburn, T. H. 1974. Foundation Engineering, 2nd Edition, John Wiley & Sons, New York, NY Pickett, G. and Ray, G. K. 1951. "Influence Charts for Concrete Pavements," Transactions, American Society of Civil Engineers, Vol 116, pp 49-73 Polshin, D. E. and Tokar, R. A. 1957. "Maximum Allowable Non-uniform Settlement of Structures," Proceedings of the 4th International Conference on Soil Mechanics and Foundation Engineering, Vol 1, London, England, pp 402-406 Popov, E. P. 1968. Introduction to Mechanics of Solids, Prentice-Hall, Inc. Englewood, CA, pp 378-389 Post-Tensioning Institute (PTI). 1980. Design and Construction of PostTensioned Slabs on Ground, 1st Edition, Post-Tensioning Institute, Phoenix, AZ Ramasamy, G., Rao, A. S. R., and Prakash, C. 1982. "Effect of Embedment on Settlement of Footings on Sand," Indian Geotechnical Journal, Vol 12, No 2, pp 112-131 Schmertmann, J. H. 1978. "Guidelines for Cone Penetration Test Performance and Design," Report No. FHWA-TS-78-209, U. S. Department of Transportation, Federal Highway Administration, Office of Research and Development, Washington, D. C. Schmertmann, J. H. 1986. "Dilatometer to Compute Foundation Settlement," Use of Insitu Tests in Geotechnical Engineering, Geotechnical Special Publication No. 6, American Society of Civil Engineers, New YOrk, NY 10017, pp 303-321 Schultze, E. and Sherif, G. 1973. "Prediction of Settlements From Evaluated Settlement Observations for Sand," Proceedings 8th International Conference on Soil Mechanics and Foundation Engineering, Moscow, Vol 1.3, pp 225-230 Seelye, E. E. 1956. Foundations Design and Practice, John Wiley and Sons, Inc., New York, NY, pp 2-2 to 2-5 246 Sherman, W. C. 1957. "Instructions for Installation and Observations of Engineering Measurement Devices; Port Allen Lock, Gulf Intracoastal Waterway, Plaquemine-Morgan City Route", Instruction Report 3, U. S. Army Engineer Waterways Experiment Station, Vicksburg, MS Sherman, W. C. and Trahan, C. C. 1968. "Analysis of Data From Instrumentation Program, Port Allen Lock", Technical Report S-68-7, U. S. Army Engineer Waterways Experiment Station, Vicksburg, MS Skempton, A. W. 1951. "The Bearing Capacity of Clays," Proceedings of the Building Research Congress, Division I, Part III, London, England, pp 180-189 Skempton, A. W. and Bjerrum, L. 1957. "A Contribution to the Settlement Analysis of Foundations on Clay," Geotechnique, Vol 7, No 4, pp 168-178 Skempton, A. W. and MacDonald, D. H. 1956. "Allowable Settlement of Buildings," Proceedings of the Institute of Civil Engineers, Part III, Vol 5, pp 727-768 Sowers, G. B. and Sowers, G. F. 1972. Introductory Soil Mechanics and Foundations, 3rd Edition, The MacMillan Company, New York, NY Stroman, W. R. 1978. "Design and Performance of a Mat Slab Foundation in Expansive Soils," Preprint 3317, American Society of Civil Engineers Convention and Exposition, Chicago, IL Teng, W. C. 1975. "Mat Foundations," Foundation Engineering Handbook, editors, Winterkorn and Fang, Van Nostrand-Reinhold, New York, NY, pp 528-536 Terzaghi, K. 1943. New York, NY Theoretical Soil Mechanics, Chapter 8, John Wiley & Sons, Terzaghi, K. 1955. "Evaluation of Coefficient of Subgrade Reaction," Geotechnique, Vol 5, pp 297-326 Thornthwaite, C. W. 1948. "An Approach Toward a Rational Classification of Climate", Geographical Review, Vol 38, pp 55-94 Tomlinson, M. J. 1980. Foundation Design and Construction, 4th Edition, Pitman Publishing Limited, London, England "A Computer Program For Analysis Vallabhan, C. V. and Sathiyakumar, N. 1987. of Transient Suction Potential in Clays," Prepared for U. S. Army Engineer Waterways Experiment Station, Vicksburg, MS, under Contract DACA39-87-M-0835 Vesic, A. S. 1961. "Bending of Beams Resting on Isotropic Elastic Solid," Journal of the Engineering Mechanics Division, American Society of Civil Engineers, Vol 87, No EM2, pp 35-51 Vesic, A. S. 1975. "Bearing Capacity of Shallow Foundations," Foundation Engineering Handbook, Chapter 3, editors, H. F. Winterkorn and H. Y. Fang, Van Nostrand-Reinhold Company, New York, NY, pp 121-147 247 Vesic, A. S. and Saxena, S. K. 1968. "Analysis of Structural Behavior of Road Test Rigid Pavements," Soil Mechanics Series No. 13, School of Engineering, Duke University, Durham, NC Wahls, H. E. 1981. "Tolerable Settlement of Buildings," Journal of the Geotechnical Engineering Division, American Society of Civil Engineers, Vol 107, No GTlI, pp 1489-1504 "The Analysis of Stiffened Rafts on Expansive Clays," Walsh, P. F. 1978. Technical Paper No. 23 (2nd Series), Division of Building Research, Commonwealth Scientific and Industrial Research Organization, Australia Wardle, L. J. and Fraser, R. A. 1975a. "Methods for Raft Foundation Design Including Soil Structure Interaction," Paper I. Proceedings of the Symposium on Raft Foundations, Perth, Western Australia, pp 1-12 _ 1975b. "Program FOCALS-Foundation on Cross Anisotropic Layered System: User's Manual," Geomechanics Computer Program No 4, Commonwealth Scientific and Industrial Research Organization, Division of Applied Geomechanics, Australia Westergaard, H. M. 1938. "A Problem of Elasticity Suggested by a Problem in Soil Mechanics: Soft Material Reinforced by Numerous Strong Horizontal Sheets," Contributions to the Mechanics of Solids, Stephen Timoshenko 60th Anniversary Volume, The Macmillan Company, New York, NY, pp 268-277 Winkler, E. 1867. Die Lehre von Elastizitat und Festigkeit (On Elasticity and Fixity), Prague, p. 182 Winter, E. 1974. "Calculated and Measured Settlements of a Mat Foundation in Arlington, Virginia, USA," Settlement of Structures, British Technical Society, John Wiley & Sons, New York, NY, pp 451-459 Withiam, J. L. and Kulhawy, F. H. 1978. "Analytical Modeling of the Uplift Behavior of Drilled Shaft Foundations," Geotechnical Engineering Report 78-1, School of Civil and Environmental Engineering, Cornell University, Ithaca, NY Woodburn, J. A. 1979. Footings and Foundations for Small Buildings in Arid Climates, Institute of Engineers, Australia Yong, R. N. Y. 1960. "A Study of Settlement Characteristics of Model Footings on Silt," Proceedings of the 1st Pan-American Conference on Soil Mechanics and Foundation Engineering, Mexico, D. F., pp 492-513 Ytterberg, R. F. 1987. "Shrinkage and Curling of Slabs on Grade, Part IDrying Shrinkage," Concrete International Design and Construction, American Concrete Institute, Vol 9, pp 22-31 248 APPENDIX A: EQUIVALENT ELASTIC SOIL MODULUS Modulus Increasing Linearly With Depth The Kay and Cavagnaro (1983) model may be used to derive an 1. equivalent soil modulus linearly with depth E* s from elastic soil moduli that increase E s z E - (Al) + kz E s 0 where E0 - Young's soil modulus at the ground surface, ksf k - constant relating The functions of Al. z in units of ksf/ft. in Figure 5 may be approximated as shown in Table Ic The influence factor with E5 Ic with depth z in Table Al and Equation Al may be integrated to evaluate the center displacement in units of feet I c PC - q (A2) T- dz s where is the pressure applied on the soil in units of ksf. q Integration of Equation A2 leads to the following settlement 2. function for q[ = z* - 0.0 to 4.0 [l+2n (a-b/n)ln(l+0.5n)+(c+d/n)inLl+-.n 1 j [l+4n]1 + (e+f/n)l-- nJ- g (A3) where z*= (z n kR/(E R = D = - Db)/R + kDb) LB/ir depth of mat base below ground surface, ft If the elastic soil modulus at the ground surface Db - 0 Eo 0, then = for the base of the mat on the ground surface, then shown in Table A3. z*- 4.0 p n n = kR/E . results in the parametric equations for may therefore be given for or soil of approximately infinite depth by AI z* If The The solution of constants in the above equation are given in Table A2. Equation A3 as a function of n = R/Db. = (z - Db)/R - C 0.0 to Table Al Variation of Influence Factor I With Depth C Soil Poisson's Ratio, Range of Depth, z* AS z* - (z-Db)/R 0.0 - 0.5 Ic 0.700 + 0.300z* 0.5 - 2.0 2.0 - 4.0 1.050 0.400 0.3 0.0 - 0.5 0.5 - 2.0 2.0 - 4.0 0.500 + 0.500z* 0.917 - 0.333z* 0.400 - 0.075z* 0.4 0.0 - 0.5 0.5 - 2.0 2.0 - 4.0 0.250 + 0.900z* 0.850 - 0.300z* 0.400 - 0.075z* 0.5 0.0 - 0.5 0.5 - 2.0 2.0 - 4.0 0.717 0.400 0.2 z Db - Influence Factor 0.400z* 0.075z* - 1.200z* 0.233z* 0.075z* - depth below ground surface, ft depth of mat base below ground surface, ft R - equivalent mat radius, LB/w, ft where L : 2B L - length of mat, ft B - width of mat, ft Table A2 Constants for Equation A3 Poisson's Ratio Constant 0.2 a b c d e f g 0.700 0.300 1.050 0.400 0.400 0.075 0.600 ys 0.3 0.4 0.500 0.500 0.917 0.333 0.400 0.075 0.400 0.250 0.900 0.850 0.300 0.400 0.075 0.150 A2 0.5 0.000 1.200 0.717 0.233 0.400 0.075 -0.100 Table A3 Settlement as a Function of Poisson's Ratio Soil Poisson's Ratio, AS Dimensionless Settlement, pc.(k/q) 0.2 0.70 + 1.561oglon 0.3 0.70 + 1.181ogiOn 0.4 0.70 + 0.731oglOn 0.5 0.65 + 0.301oglon n - kR/E ° + kDb ) k - constant relating Es with depth z, ksf/ft q - pressure applied on soil, ksf Table A4 Relationship of n with k/k sf, Equation A7 k n ksf 1 2 3 5 0.70 0.90 1.03 1.19 10 100 1.40 2.10 1000 2.80 Note: n - kR/(E A3 + kDb) Below z* - 4.0 (A4a) (q/k)[0.7 + (2.3 - 4.0us)logl0 n] PC- the soil is assumed incompressible. settlement is given from z* - 0.0 For more shallow soil by z* = 2 PC - (q/k) z* = 0.5 PC - (q/k) E0.46 + 1.44s .55 + (2.507 - 4.533us)log1 0 n + (2.42 - 4.6p slOg 1 0 n Settlement is especially sensitive to soil stiffness for 3. The equivalent soil modulus Equation A4a for z* - 4.0 4c shows that increasing decreasing the ratio 4. S (A4c) z* - 0.5. may be found by substituting into Equation 4b to obtain Equation 4c. Equation ps toward the undrained state of 0.5 and n increases E*. s Substituting Equation A4a into ksf (A5) q/ksf Pc - where E* (A4b) is the coefficient of subgrade reaction of the foundation, leads to k k sf If 's - 0.7 + (2.3 - 4 p )loglon (A6) 0.4, a reasonable value for many clays, k sf 5. - 0.7 + 0.7log10 n Table A4 illustrates values of is approximately k when in Part III have n values (R/Db this range. mats. ksf Therefore, n ksf (A7) k/ksf is from 2 to 3. ratios when for given values of k when E0 - 0) n > 100. approximately in k for these thick n can be greater than 100, for example, if the mat is placed on the ground surface and ksf The flat thick mats described should approximately equal will be less than half of n. (Db - 0) kR > 100E 0 . This was observed for the large mat on the ground surface described in Part IV. A4 Constant Elastic Modulus 6. Graphical integration of the influence factor Ic settlement, Figure 5, for a constant elastic soil modulus center settlements as a function of soil Poisson's ratio Solution of Equation A2 when soil z* Es - E0 is given in Table A6. soils greater than for center E5 - E0 p Table A5. for some depth ranges of compressible Settlements are only slightly influenced by z* - 4.0. Table A5 Center Settlement for Constant Elastic Modulus Pc' E/qR 'US 0.2 0.81 + 1.31.1ogi 0 z* 0.3 0.71 + 1.28-iogi 0 z* 0.4 0.62 + 1.26.1ogi 0 z* 0.5 0.50 + 1.16.1og 10 z* Note: z* - indicates (z - Db)/R Table A6 Center Settlement for Various Depth Ranges z* p.E /qR 8 ps 0.5 0.55 - 0. 2.0 1.50 - 1.4p s 4.0 1.85 - 1.4ps A5 z* APPENDIX B: INFLUENCE OF SUPERSTRUCTURE RIGIDITY Meyerhof's Method 1. Meyerhof (1953) developed a simple analysis to compensate for superstructure rigidity Ns (lsu EppiL2] -i-1Eib z (El) 2h2 +A ILi (Bi) Iui hi+hi I' - bi i 1+ Ibi (B2) I I + lui i where (EI)s u - 2 superstructure stiffness, kips-ft Eb - elastic modulus of beam, ksf EP - elastic modulus of wall panels, ksf L - length of building, ft h. - height of story 1 - Ipi - span length between columns or beam length, ft 4 panel moment of inertia, ft Ibi ILi I . = Ns = i, ft beam moment of inertia, ft4 - lower half of column moment of inertia, ft4 - upper half of column moment of inertia, ft4 number of stories The rigidity from Equation BI should be added to the foundation rigidity to obtain the composite structure rigidity or stiffness. Meyerhof assumed that the rigidity contributed by the foundation is much less than that of the superstructure and may often be ignored in practice. Bi Proposed Method The following method calculates a composite moment of inertia for 2. the structure that includes the effect of a simple framed building or shear wall on the mat foundation. The moment of inertia with respect to the I00 centroid of a composite structure may be given by the parallel axis 7 theory = I N Es (I + Aih ) (B3) where moment of inertia of the axis passing through the centroid axis 4 of story i, ft Ioi = A.1 - area of cross-section of story hcci = distance between center of story The centroid axis h Ns where hci i and centroid axis, ft is found from c hc i, ft 2 Aihci - il z i-1 (B4) A. 1 is the centroid of each section or story from the bottom of the mat. Flat Mats 3. The centroid for a structure on a flat mat with a simple shear wall as schematically shown in Table B1 is h c - ah w 2 2 hDN + BD s w s 2(BD + awhN s) N 2 +2a where aw - wall thickness, ft D - thickness of mat foundation, ft h - height of each story, ft - number of stories - width of foundation or spacing N s B Each story is assumed to be equal in height. B2 S, ft (B5) Table Bi Centroid and Moment of Inertia of Composite Structure With a Flat Mat Centroid h If h, = h . 2 Ns = h, = Then BD2 Na 21-1 Z (a h,hi ) + c eD + -- N BD + i awhi L i-I ] 1 h2 2 E (21-1) - Ns i-I Since 2 2 Then ah N a aw h h - 1 1-1 2 + 2a hN D + BD w mC 2(BD + awhN s) Moment of Inertia hc h a _ loofmD B I " BD3 -2+ [ D] 2 BD hc Ns 2 + E (I.t Aihccl) Aih 2ci Ioi ah a 2 w2 12 [ 2 -[ ah w 2 2 2 a h3 + [i1 F2 12 w - [hLc L2 Nsawh3 Sum IC2 12 I* 2 - awh [ BD3 + Nsawh Ioofm - 2 shc + BD c - N (Ns5 Nsh hc- 2hcNsD + 2 + I* B3 2 _ 12 1 )h2 -- 2 +N 21] Dh+ ND 4. The composite moment of inertia for a flat mat from Table BI is 2 3 BD3 + N a h loofm + BD[h 12 - Nshch + Nsh 5. + - (B6a) I* N (4N 2 _l)h 2 12 - 2h NsD + N 2Dh + A parametric analysis was performed to calculate the composite moment of inertia Ioofm for a flat mat from Equation B6 with from Equation B5 and mat thickness D h evaluated evaluated from Equation Ila plus 0.3 ft. The wall thickness a was evaluated as an equivalent thickness for w 78 columns of width a and spacing S by a - aw If a 2 (B7) -S is assumed to vary in proportion with the number of stories a - 1, 2, and 4 ft for Ns i.e., N5 - 3, 12, and 50 stories, respectively, then the composite moment of inertia is approximately loofm - (17.3 0.4S).N (3.42 + 0.011S) - The height of each story 6. h (B8) was assumed 10 ft. The moment of inertia of a continuous shear wall Isw excluding the mat foundation is a (N s w s sw If h - 10 ft and aw (B9a) -12 is found from Equation B7 with a varying with Ns above, then 4 27.77N I sw where 3 : NS 5 - 50 stories and s (B9b) S 15 : S : 3( 78Desai, Johnson, and Hargett 1974 B4 t. Comparison of Equations B8 as and B9b shows that the composite Ioofm is significantly greater than Isw for the same number of stories without the mat, especially for fewer stories when the mat is less thick; therefore, the mat rigidity should be included in the overall stiffness of the structure if this analysis is a realistic interpretation of structural stiffness. 7. The effect of superstructure rigidity on a mat foundation was estimated for a wall spacing pressure s 3 12 50 qm S - 25 ft, story height h - 10 ft, and soil 0.2 ksf/story is - it 1.0 2.0 4.0 The mat thickness D D 't (4) ft oofm, 1.8 3.3 5.6 412 69,663 13,684,290 7 mat De I ft 34 930 37,402 5.8 32.2 187.2 oofm (7ft Lmax' was estimated from Equation lla plus 0.3 ft. column 4 was estimated from Equation B8. 25 91 341 Ioofm in The ratio of the structure moment of inertia to that of the mat shown in column 5 is loofm 00ofm 12-.... = (BlO) BD3 Imat Column 6 shows the equivalent mat thickness De if the stiffness of the entire structure is collapsed into the mat 3 12"I1f D e = - (Bll) 00 S De shown above, although large, may not be unreasonable because Hooper and e Wood (1977) calculated an equivalent thickness of at least 6 times that of the actual mat thickness in order to calculate differential displacements in agreement with observed displacements. The superstructure exerts a large influence on the mat rigidity consistent with previous observations of soilstructure interactioit nalysis7 . The concrete elastic modulus be increased to give the same equivalent rigidity calculated using De or Ioofm substituted for QL I E c may also that would be in Equation 17. 79 Wardle and Fraser 1975a; Focht, et al 1978; Stroman 1978; B5 Bobe, et al 1981 Lmax such that Column 7 above illustrates the maximum mat length 8. the mat appears rigid from the criterion of Equation 17. subgrade reaction ksf The coefficient of was calculated from Equation 6b as 27 ksf/ft assuming and k sp - 1000 ksf/ft, an upperbound value simulating hard clay27 . The PTI (1980) used ksf - 7 ksf/ft for a long-term coeffi-ient to determine S = 25 ft the PTI design equations, which leads to column 7. If Lmax 1.4 times those shown in k sp - 150 ksf/ft simulating a stiff clay, then twice those shown in column 7. Ec was assumed 432,000 ksf. Lmax will be A multi-story structure with 11 or more stories may therefore appear rigid as had been observed from records of uniform displacements80 . Superstructure stiffness may be neglected for cases such as steel storage tanks or low-rise buildings with open floor plans and large areas 46 Ribbed Mats 9. The centroid for a structure on a ribbed mat with a simple shear wall schematically shown in Table B2 is hc - 2 2 wt 2 + BD + 2BDt + 2a h(t+D)N + a h2N w S w s 2(wt + BD + Nsawh) (BI2) where aw = wall thickness, ft w = thickness of stiffening beam, ft t = depth of stiffening beam, ft B - width of foundation or spacing D - mat thickness, ft h - height of each story, ft - number of stories N S, ft s 10. oo oorm 8 - The composite moment of inertia is given from Table B2 wt3 + BD31 + N a 2+ BD[h c wt[hc - t - Hooper and Wood 1977, Stroman 1978, Focht, et al 1978 B6 + I** (Bl3a) Table B2 Centroid and Moment of Inertia of Composite Structure With a Ribbed Mat Centroid h If c . - h hNs- B h, Then Ns 2i-1 S wt2 + BD 2 -2 h+ N g (t+D) + BDt + Zai-I hc N Z awh i + BD + wt h Therefore, wt 2 2 + BD + 2BDt + 2awhNs(t+D) + ah N2 h 2(wt + BD + NNawh) c Moment of Inertia I h ~~ 'oorm h t + BD[ W Io 2 -t h• h [(I .+A + w Ajhj oi i awhl[h c - t 1- + D + 2 12 3 Sum h Nsa wh 3 12 loorm = 2 N2 1** - awhNsh 2 L12 wt3 + BD3 + 12 w - 2(t+D)Nshc - hhc s + wth Icc- BD[h + N (t+D) 2 + (t+D)hN + - t + 7 B7 I** 2 + N (4N -1)h2 ID I** t 2 ahNh D h2 sc 2 2 N(4N -l)h 2 s + N(t+D) + s(t+D)hN hhN 12 A parametric analysis was performed to calculate Equations B13 for column width a - 1 ft where B7, h - 10 ft, and stiffening beam width aw of ribbed mats from was found from Equation w - I ft Ioorm = N5 - number of stories, t = thickness of stiffening beam, S - column or wall spacing, ft (28 + 5t I00orm 0.72S)N s(3 - 0.13t) - (B14) where < 3 < 3 ft The mat thickness was 0.5, 0.75, and 1.0 ft for respectively. Ioofm A comparison of I00orm from Equation B14 for a ribbed mat and from Equation B8 for a flat mat with moments of inertia for each case. a flat mat and I oorm N - 3 Comparison of stories indicates similar Ioofm from Equation B6 for from Equation B13 for a ribbed mat shows that the stiffening beam increases 3 ft, respectively, when percent with N s - 1, 2, and 3 stories, I00 N about 2, 7, and 14 percent with - 2. I t - 1, 2, and is similarly increased 6, 23, and 56 t - 1, 2, and 3 ft, respectively, when N - 1. The additional stiffness from a stiffening beam in a ribbed mat becomes increasingly significant as the number of stories in the superstructure decreases. Resisting Bending Moment 11. The resisting moment after the flexure formula (Popov 1968) is M - A sf (hc - 3.0) (B15) where M - resisting moment of steel, lbs-in As - area of reinforcement steel, in2 fs - steel tensile strength, psi hc - centroid of structure, in. If the steel is placed in the bottom of the mat with 3.0 inches of cover, the bending moment resistance will be increased about 4 and 10 times for 3 and 5B8 ft thick mats, respectively, supporting 11 stories using the parameters in paragraph 5 above. The increase in bending moment resistance from the superstructure can be substantial. Limitations of Model 12. Although this framed building or shear wall model appears similar to that illustrated in Figure 3.1 of ACI 435 (1980), "Allowable Deflections", the above model requires confirmation. or spacing S For example, the effective width B is not known and may be less than the actual width or spacing such that the composite moment of inertia of the structure may be less than that calculated by this model. Moreover, only a portion of the structure may be constructed with a shear wall further complicating selection of an appropriate value for B. Cross-frames, struts, and other structural components also complicates calculation of the composite moment of inertia of the structure. B9 APPENDIX C: USER'S MANUAL FOR COMPUTER PROGRAM SLAB2 Introduction 1. SLAB2 is a fortran finite element program originally developed by Huang 54 and modified by W. K. Wray and R. L. Lytton for ribbed mats in expansive soil11 . This program is available from the Soil Mechanics Branch, Soil and Rock Mechanics Division, Geotechnical Laboratory of the US Army Engineer Waterways Experiment Station. The stiffness of the ribs is considered by calculating the total stiffness of the sum of the ribs in each of the X and Y orientations. SLAB2 provide- solutions in the X and Y orientations for stresses, deflections, bending moments, and shear forces due to loading and/or warping in a single rectangular mat, or two mats connected by dowel bars at the joint, resting on a foundation of the elastic solid type. The program was written on a permanent file SLAB2.FOR for IBM PC compatible microcomputers and it is available from the Soil Mechanics Division, Geotechnical Laboratory of the US Army Engineer Waterways Experiment Station. The program requires 640K of memory to execute. DASLAB.TXT. Input data is saved on a file Output data is sent to a file SLAOUT.TXT. In addition, deflection, X-direction and y-direction bending moments are sent to plot files CAL.DEF, CALX.MOM, and CALY.MOM. 2. The program is composed of the main routine and eight subroutines. Subroutine SOLID calculates stresses for mats of constant thickness. Subroutine TEE calculates stresses for mats with stiffening beams. Subroutine MFSD is the algorithm to factor a symmetrical positive definite matrix. Subroutine TRIG applies the Gauss elimination method to form an upper triangle banded matrix for a given contact condition which can be used repeatedly. Subroutine LOADM uses the triangularized matrix from Subroutine TRIG to compute mat deflections. matrix. Subroutine SINV inverts a symmetrical positive Subroutine QSF computes the vector of integral values for a given equidistant table of function values. force Subroutine SHEAR calculates the shear in units of ]bs/in. 3. The mat foundation is divided into rectangular finite elements of various sizes. to top along the The elements and nodes are numbered consecutively from bottom Y axis and from left to right along the X axis. If two slabs are connected by dowel bars at the joint, each node at the doweled joint CI must be numbered twice, one for the left and the other for the right mat. The dowels are assumed 100 percent efficient, so that the deflections at the joint are the same for both mats. Loads may be applied to either or both mats, and the stresses at any node in either mat may be computed. The program can determine the stresses and deflections due to dead load, temperature warping, or live load, either combined or separately. Options are as follows: Option 1: Mat and subgrade are in ful] contact: 0, NWT - 0, and NCYCLE - 1 Set NOTCON - Option 2: Mat and subgrade are in full contact at some points but completely out of contact at the remaining points because of large gaps between the mat and subgrade. Set NOTCON - number of points not in contact, NGAP = 0, NWT 0, and NCYCLE = 1 = Option 3: Mat and subgrade may or may not be in contact because of warping of the slab. When the slab is removed, the subgrade will form a smooth surface with no depressions or initial gaps. Set NOTCON = 0, NGAP - 0, NCYCLE - maximum number of cycles for checking contact O-tion 4: When mat is removed, the subgrade will not form a smooth surface, but shows irregular deformation. Set NOTCON = 0, NGAP - number of nodes with initial gaps, NCYCLE - maximum number of cycles for checking contact Application 4. Table Cl illustrates the organization of the input parameters for program SLAB2, while Table C2 defines the input parameters. normally consistent with units of pounds and inches. Mat width and length and their respective nodal distances are input in units of feet. omitted if the option is not selected. Input data is Input lines are Data must be placed in the correct format sl wn in Table C2 for proper operation of the program. An example of input data is shown in Table C3 for analysis of the ribbed mat described in PART IV. Output data for this problem is shown in Table C4. Deflections are in inches, moments in lbs-in./in. of width, and shears are in lbs/in, of width. C2 Table C1 Organization of Input Data I5 1 NPROB 2 XXL 3 BEAMLW 4 Format Statement Input Parameters Line MOIX XXS XEC BEAMSW XYMX MMM ISOTRY LIFT BEAMSL ASPACE BEAMLL (Line 3 omitted if ISOTRY 4FlO.4,3I5 BSPACE 0) - 9F8.3 2E13.6 MOIY (Line 4 omitted if ISOTRY - 0) 5 NSLAB PR NSYM PRS NX2 T YM NOTGON 6 NXl NY 7 X(1) .. .X(I) 8 NZ(1) .. .NZ(I) YMS NREAD NCYCLE I5,2F8.4,2E10.3, F8 .4,515 NB NPUNCH NP(l)... .NP(I) NPRINT 1415 9F8.3 Y(l) ...Y(I) 1415 (Line 8 omitted if NOTCON - 0) 9 10 11 12 13 14 NGAP DEL NTEMP NLOAD ICL RFJ ICLF DELF NOK NWT NODCK(1) ...NODCK(I) (Line 10 omitted if NOK CURL(l) ...GURL(I) (Line 11 omitted if NREAD Q 615,2F8.3, 2F8.5,F5.2,I5 1415 - 0) 6E13.6 - 0 or 2) NG(1) ...NG(I) (Line 12 omitted if NREAD - 1415 1 or 2, NOAP not used) CURL(NG(1)). ...CURL(NG(l)) (Line 13 omitted if NREAD - MA8. 1 or 2, NOAP not used) F7.3 QSLAB (Line 14 omitted if NREAD 15 TEMP NL(I) - 1 or NWT - 0) XDA(I,2) YDA(I,l) YDA(I,2) XDA(I,1) (Line 15 repeated for each I - 1,NLOAD) CG3 15,4F10.5 Table C2 Definition of Input Parameters Line Parameter Definition 1 NPROB Number of problems to be solved; new input data for each problem 2 XXL XXS XEC XYMX Length of mat, ft Width of mat, ft Edge penetration distance, ft Amount of differential shrink or swell ym MMM ISOTRY LIFT Exponent "m" of Equation 25 = 0 for flat mat; - 1 for stiffened mat = 0 for no swell; = 1 for center lift; - 2 for edge lift BEAMLW BEAMSW BEAMLL BEAMSL ASPACE BSPACE Depth below flat portion of mat in short direction, inches Width in short directioi, inches Depth below flat portion of mat in long direction, inches Width in long direction, inches Beam spacing in long direction, inches Beam spacing in short direction, inches 3 Beam dimensions 4 5 Moment of inertia - - inches omitted if ISOTRY = 0 omitted if ISOTRY = 0; MOIX MOIY MOIX 4 Total moment of inertia of mat section along length, inches MOIY 4 Total moment of inertia of mat section along width, inches NSLAB PR T YM YMS PRS NSYM NOTCON NREAD Number of mats in problem, either 1 or 2 Poisson's ratio of concrete in mat Thickness of flat portion of mat, inches Young's modulus of concrete, psi Young's modulus of soil, psi Poisson's ratio of soil -1 for no symetry; - 2 for symmetry with respect to Y (vertical) axis; - 3 for symmetry with respect to X (horizontal) axis; - 4 for symmetry with respect to Y and X axis; - 5 for four mats symmetrically loaded Total number of nodes with reactive pressure - 0; if NCYCLE I, these nodes will never be in contact; if NCYCLE > 1, these nodes may or may not be in contact depending on calculated results Gaps or precompression to be read in - 0 for line 11 omitted., CURL(I) - 0.0, I = I,NX NY - I for lines 12, 13, and 14 omitted, CURL(I) read in for I I,NX NY, NGAP not used - 2 for lines 11, 12, and 13 omitted; use gaps and precompressions from previous problem, NGAP not used C4 Table C2 Line 6 Definition Parameter NPUNCH NB Not used. Put 0 Half band width, (NY + 2) 3 NXl NX2 NY Number of nodes in X-direction (left to right) for mat 1 Number of nodes in X-direction for mat 2 Number of nodes in Y-direction (bottom to top); nodes numbered from bottom to top and toward the right Naximum number of cycles for checking subgrade contact; use 10 Number of nodes at which stresses are to be printed; if - 0 stresses at all nodes are printed Node number I to be printed; leave blank if NPRINT - 0; continue until I - 1, NPRINT NCYCLE NPRINT NP(I) 7 (Continued) X(I) Y(I) X coordinate starting from zero and increasing from left to right, ft; read X twice at joint if NSLAB - 2; continue u Lti! I = NX - NXI + NX2 I coordinate starting from zero and increasing to top, ft; continue until I - NY; follows immediately after the last X coordinate 8 NZ(I) Number of node at which reactive pressure is initially zero; continue until I - NOTCON\ omitted if NOTCON - 0 9 NGAP DEL DELF RFJ IGLF Total number of nodes at which a gap exists between mat and subgrade; - 0 if no gap or very large gap Warping condition; - 0 no temperature gradient; - 1 for temperature gradient Number of loads applied to mat Maximum number of permitted iterations for coarse control; use 1.0 Number of nodal points for checking convergence Consideration of mat weight; - 0 weight not considered; - 1 weight considered for non-constant cross-section; - -1 weight considered for flat rectangular cross-section Difference in temperature between top and bottom of mat, °C Pressure from loads on mat, psi Coarse tolerance to control convergence; use 0.001 Fine tolerance to control convergence; use 0.0001 Joint relaxation factor; use 0.5 Maximum number of iterations for fine control; use 30 NODCK(I) Number of nodal point for checking convergence; continue NTEMP NLOAD ICL NCK NWT TEMP Q 10 until I - NCK; omitted if NCK - 0 C5 Table C2 Line 11 (Concluded) Parameter CURL(I) Definition Amount of gap between mat and subgrade for each nodal point I if NREAD - 1; continue on additional lines until I - NX NY omitted if NREAD - 0 or 2 12 NG(I) Number of node at which gap is specified between mat and subgrade; continue on additional lines until I - NGAP; omitted if NREAD - I or 2, NGAP - 0 13 CURL(NG(I)) Amount of gap between mat and subgrade for nodal point NG(I), inches; continue on additional lines until I - NGAP; omitted if NGAP - 0, NREAD - 1 or 2 14 QSLAB Pressure from weight of mat as uniformly distributed load, psi; omitted if NREAD - 1 or NWT = 0 or -1 15 NL(I) XDA(II) XDA(I,2) YDA(I,I) YDA(I,2) Placement of loading pressure Q of line 9 on portions of element I; use -1 for lower bound of element and +1 for upper bound of element; continue until I = NLOAD; an element may be loaded more than once Number of element subject to loading q; elements numbered bottom to top, left to right Left limit of loaded area in X-direction Right limit of loaded area in X-direction Lower limit of loaded area in Y-direction Upper limit of loaded area in Y-direction C6 Table C3 Input Parameters for Ribbed Mat, PART IV i.3,6,67 .0 28. 13. 23. 18. 9.251474E 06 4.185904E 06 i .15 8. 1.500E 06 15 0 7 10 0 0 A10 12.5 37.5 62.5 2i2.5 237.5 262.5 287.J 75 100. 0 125.0 151.83 29 30 31 32 33 34 43 44 45 46 47 48 21 v 116 10 8 1 15 27 45 56 65 75 27 30 31 32 33 34 43 44 45 46 47 48 0.5 0.5 0.5 1. i. 1. 0. 1.0 1 8 3 -.0i8 1. 1. -1. .46 0.0 150. 1 150. 3.OOOE 04 0.4 87.5 312.5 35 112.5 338.9 36 37 0.0 0. 0.0 0.5 -1. -. I.46 -.40 6 -.06 -I. 1. -.40 .442 -1. -1. 1. -. 46 -.46 9 -1. -.46 1. -.46 .46 .46 -1. 1. 1. -. 46 .6 1. -I. -.46 -1. .46 -1. Ib ,. .442 .442 -1. -1. 1. 15 -.46 1. -.46 1. -.46 .46 1 1 1. i3 -1. 13 .,6 -.46 1? -11. -.46 .442 .442 -1. P; .40 1. -1. -.46 I. 46 .46 i 1 -1. 12 -1. 12 .16 13 -1. 13 .4 E1 2A 22 22 -1. .46 -.-. .46 24 -I. 24 25 25 2 27 .11 -1. .4b -.46 1. 1. 1. -.46 1 .46 .46 -1. -1. .46 -1. -1. .442 .442 1. -.46 -.46 1. 1. -.46 -1. ,i.42 30 1I o$ 31 31 -. -.46 1. -1. -.46 1. 1 -. o -1. .442 -1. 0 162.5 25.0 40 1. 0.5 -.46 1. 28 -i. 0. 0.5 1. 1. -.46 .46 .46 39 1. -1. -. 46 ±, 38 -.46 -.46 1. 1. -. 46 -.6 -.46 -. 137.5 .0 21 0 27 187.5 50.0 41 42 49 1, 9 4 0.0 4.0 0.001 .0001 0.5 30 93 104 35 36 37 38 39 40 41 42 -.08 1. 0 49 4 7. 1 1. 1. -.46 . 1. -. 46 C7 1. 0.5 Table C3 33 -1. 33 .46 34 34 -1. .46 -. 46 36 -1. 36 .46 -.46 1. 37 -1. -. 46 -1. 37 1 -. .46 1. -.1. 46 .46 .46 -1. -1. .442 .442 1. I. -. 46 -. 46 1. I. -.46 39 -1. 39 .46 40 -1. 40 .46 42 -1. -.46 1I .46 .46 -.46 -1. -.46 1. -.46 -1. .442 -.46 42 43 43 45 45 46 46 48 48 49 49 51 51 52 52 54 54 55 1. -.46 1. -.46 1. -.46 1. -.46 1. -.46 1. -.46 1. -.46 1. -.46 1. -.46 .442 -1. -1. .46 -1. -1. .46 .46 -1. -1. .442 .442 -1. 1. 1. -.46 -.46 1. 1. -.46 -.46 1. 1. -.46 -.46 1. 1. -.46 -.46 1. 1. -.46 .46 -1. .46 .46 -1. .46 -1. .46 -1. .46 -1. .46 -1. .46 -1. .46 -1. .46 -1. -1. .442 .442 1. 1. j .46 1. -1. 57 57 58 58 60 60 61 -1. .46 -1. .46 -1. .46 -1. -. 46 .46 .46 -1. -1. .442 .442 -1. 1. 1. -.46 -.46 1. 1. -.46 61 .46 -.46 1. -.46 1. -.46 1. -.46 1. -.46 1. -.46 1. -.46 1. -.46 1. -.46 1. -.46 1. -.46 I. -.46 1. -.46 1. -.46 1. 63 -1. 63 .46 64 -1. 64 .46 66 -1. 66 .46 67 -1. 67 .46 69 -1. 69 .46 70 -1. 70 .46 72 -1. 72 .46 73 -1. 73 .46 75 -1. 75 .46 76 -I. 76 .46 (Continued) -1. -.4b .46 .46 -1. -1. .442 .442 -1. -1. .46 .46 -1. -1. .442 .442 -1. -1. .46 .46 -1. 1. 1. -.46 -.46 1. 1. -.46 -.46 1. 1. -.46 -.46 1. 1. -.46 -.46 1. 1. -.46 -1. -.46 C8. Table C3 78 78 79 79 79 80 -1. .46 -1. .433 .433 .433 -.46 1. -. 488 1. 1. 1. .442 .442 -1. -1. .46 -1. 81 81 81 82 82 82 83 83 B4 84 84 .433 -1. .433 -1. .433 .433 .433 .433 .433 -1. .433 1. -.488 1. -.488 1. 1. 1. 1. I. -.488 1. -1. .46 .46 -1. -1. .46 -1. .46 -1. .442 .442 80 .433 1. .46 1. 1. -. 46 -.46 1. -.46 1. -.46 1. 1. -.46 -.46 1. -.46 1. -.46 1. 1. C9 (Concluded) Table C4 Output Data for Ribbed Mat, PART IV - ! ; ELEMENT INALiSiS OF CCNCRETE SLABS N:. OF SLA : F'ISSON RATIO OF CONCFETE= ICOREE:EjC L. i57Et,2 ...... i0CULu3 OF MO'LUl NFRTB= 4 ).54E,{7 0 NREAD= SLAB LENLGTH = c76,8 FT ELGE EFFECT = .,)0 FT LAB WIDTH = 3,3.&" FT BEAM DEPTH = .00 IN FAFBLiC EwUATIO!4 EXPONENT M" I MEMENT OF iNEFfI . 0.1500 nF SUE, OFO+6 ... .MODGOLUE '"Gq -E . hE+5 THICKNESS OF CONCRETE: .0000 POISSON RATIO OF SUGADE '.000 NPUNCH= YM 0.00 IN ,.I41S54E+ OF GRADE BE MS . ,,i-ON SHORT DIMENSION LONG DIMENSION SPACING TPANSVERSE GRADE BEAM 22. 00000 18. 00000 150. LONG TUD I NAL GADE ;EAM 28. 0000 I. 0000 15. Ni= 15 VALUES OF 1 APE: 0.0 2,500 2-5262.5:: NX2= AE: VALUES OF 250 5.00 7 NY= 112. -_ 237.500 50 312.500 338.900 5.0 75.000 160.001 87,J00 NCYLE= 112. 500 137.5(0 125.00 151.830 10 .0000 21 NOTCON= 187.50 12. NB= 212.50 REACTI,-NS AT THE FOLLOWING NODES ArE ASSUMED INITIALLY ZERO: 23 30 31 32 33 34 35 36 3 49 40 41 42 4+3 44 45 46 iER= NGAP= TEIP= 37 47 3B 48 0 21 NTEMP= 0.00:00 = 0 4.0000 NLOAD= 116 RFJ= 0.50000 THE FOLLOWING NODES ARE USED TO CHECK CONVERGENCE: 15 27 45 56 65 NODAL NUMBERS AND INITIAL GAPS ARE 29 0.50000 30 0.5(000 31 36 1.00000 37 1.00000 38 43 0.50000 44 0,50000 45 ICL= DEL: 75 TABULATED AS FOLLOWS: 0.50000 32 0.50000 1.00000 .00000 39 1.00000 0.50000 46 O.50000 '0 0.0(100 93 NCK: DELF= NWT= ICLF= 104 33 0.00000 34 40 1. 41 47 0.0:060 48 CIO 8 (.000010 0.00000 0.00000 0.00000 35 0.00000 42 0.00000 49 0.00000 I 3.0 2 Table C4 NODE I 5 9 13 17 21 25 29 33 37 41 45 49 53 , bM 65 9 73 77 81 85 89 93 DEFLECTION 0.232646Et00 0.205883E+00 0.224288E+O0 0.150456E+00 0.217054E+00 0.170236E+00 0.219361E+00 0.729930E+00 0.211426E+00 0.121167E+01 0.185905E+00 0.715410E+00 0.165448E+00 0.211569E+00 0.21545E+00 0.192112E+00 0.204891E+00 0.174275E+00 0.195895E+00 0.153023E+00 0.191064E+00 0.190473Et00 0.168451E+00 .1,?I!E+O0 0.147862E+00 9.1q9504E+00 1 105 01.119995E+00 NODE MOMNT x I ).267014E+03 1.6282' E+03 H",63-31E+03 o u.36q57E+03 5- ,4qgOE+, 0 i2 r+"-2 i ,34 E :4 0.5?1 5E 34cE+'5 -: 4 2';j24 - 7 -*' 0.5 79237E+63 -o. 22229E+03 -0.221233E+03 0.598303E+03 NODE 3 7 11 15 19 23 27 31 35 39 43 47 51 55 59 63 67 71 75 79 .4 91 95 99 103 MOMENT xi 0.137648E+01 -0,64103E+0 0.959937E+00 -0.422608E+00 -0.Ij3696E+00 0.) ( 1509E+,3 E+ 0.766238E+00 ().'iOh'w00E+0 .(I00008 E,0 3 '.6645 tr+ '3 -. 843615E+f'0 0.+26 2 E - ..$ 148S E+'00 A267;47+3 0.592383E+m0 . 14352E+03 -',5609d E*01 -0.231Q90E+03 - 23E+ 2 -0.2503 %-, , Ia -. 2E+'4 '16,I"I": .,, =+,,.. ,. i .I i i" +02t' - DEFLECTION 0.224480E+00 0.191427E+00 0.220759E+00 0.172267E+00 6.218212E+00 0.232695E+00 0,200683E00 0.721414E+00 0.188873E+00 0.120824E+01 0.165385E+00 0.714838E+00 0.224305E+00 0.193436E+00 0.207860E+00 0.178263E+00 0.201763E+00 0.157205E+00 0.197673E+00 0.199742E+00 0.176312E+00 0.182682E+00 0.156883E+00 0.168428E+00 0.133401E+00 v.14691BE+00 MOMENT Y 2 a NODE 2 6 10 14 18 22 26 30 34 38 42 46 50 54 58 62 66 70 74 78 82 86 90 94 98 102 (Continued) 4 +464E+ I Kci -,2 !05b3+o1E'5 .I 3%.EK 5 14I2 4E+':5 -,1 E .+ Lt., T775,:.3 9 . E+,2 -).j~ 32,3i+03 0.152874E+03 ,.r94847 +-'3 -.:;.32?740 63 •.±c,156S58.0j 0',562672E+3 -t. 18361 E+'3 '. 1'.)65E+03 0() 6(1E+C)0 8.5jB958E+03 -0.243i4E+03 -" 131575E+0 f .557"83E+63 -. 26 926E+63 I.P5803E,03 0.,", 0 -0 4 018;IE+ 0.3'15452E+1 0. 636683E+06 0 40%5Eti0 - .Ifl46E+-it v.2002QE+02 I 7I 50E+.: -,).152247E+02 0 )000(00E+,: -0. 45225E+'.i -'.i563206E+01 0.2 4296iE+02 -0.148744E+03 -0.864176E+02 0. 879175E+02 [".000E+(0 ll DEFLECTION 0.220939E+00 0.172275E+00 0.222583E+00 0.228773E+00 0.203453E+00 0.224429E+00 0.166645E+00 0.719416E+00 0.165460E+00 0.120730E+01 0.725792E+00 0.207963E+00 0.216095E+00 0.180355E+00 0.204584E+00 0.160637E+00 0.203205E+00 0.206874E+00 0.182593E+00 0.191912E+00 0.163964E+00 O,1tO7./E+00 0.141701E+00 0.170395E+00 0.152905E+00 0.140925E+00 NODE 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 8o 84 88 92 96 100 104 DEFLECTION 0.221860E+00 0.233566E+00 0.204624E+00 0.220621E+00 O.18757E.+00 0.221221E+00 0.169323E+00 0.718660E+00 0,12197BE+0 0.118109E+01 O.717308E+00 0.186462E+00 0.213082E+00 0.163485E+00 0.206250E+00 0.212937E+00 0.187436E+00 0.198878E+00 0,169687E+00 0.189015E+00 0.147947E+00 O.B2515E+00 0.177466E+00 0.1B105E+00 0.151450E+00 0.132955E+00 Table 29 30 3 32 -0,3766EM -,536E 2 -0.379636E+04 U 119795E+04 E3675"EO4 -0.55"+49E (4 -0.35245E+04 A2i125E+05 43 34 (n M6 ME+03 1h. 37 -0, 3; 3? 40 441- -0,+,! 6!3E+ "5 0.5M M0+0 4 (Continued) O242328E+00 0.275227E+0i 0 -i6257E02 O.7895E+02 -0.247480E+03 -13.0_42H43 E+,"0 + 0 i.9?E+5 0.935447E+03 -0.14986E-01 .2?33E+05 -),755AE'3 0 25!3;E-01 l 0 '.29765E- .,,5 o.258 1.46E+,:;4+ 0.5i7062E-01 0.290 14E+05 -. 48554E+(4 0,81037SE-01 0i.8042E+ ;5 0.3922E+05 .2320!4E+00 -A.35S0MA -(. 36731,'E-05 0.,690979E+00 0.634940E+02 0.4 *ioi0OE+ 04 000000E+00 i3 -6.375563E+04 -0 -' 5 #4 4, -..373515E+04 -0.67395E+ 01,i977E+i4 -0.552E0 -0.268276E+01 E1 A 4b 47 -0.351696E+04 -0.57775E+05 0.211109E+05 --.205739E+05 -0.788235E+32 0.2477.)E+0 48 0.360527E+03 .499331E+04 0.302355E+03 4c E+02 -'. 170 0o26464?E+02 0,0 0000E+01 0.0 000iE+0 5;v -0. 139725E+05 6,586579+63 0,231400E+00 51 52 53 -0.13?0IE+05 -0.140178Et,5 -0,14 1937E+05 -' .245974E+03 -0.134600E+03 0.55531.. n- 051 1 -,.2410'2E+02 149003E+O,3 54 (1.131273E+05 188259E+03 -0.57043E+0I 0.355819E+04 0.355437E+04 -0.269992E+03 0.1i70'5E+03 55 5 57 58 5; 6 61 62 0.356763E+04 .... E+04 -0 5946E504 0.679328E+02 S6 .3274E+02 0.983726E+02 0,00000E+00 0.532733E+03 -0.2705E+3 -0,884242E+(2 0.00000E+00 -0.133991E+00 0. 32692E+00 -0,22080E+0i -0.184676E+00 0.566*.,. -0.19041iE+03 -0.32505E+(2 -61.72305E+02 0.12249(E+03 0.153405E+02 O. E0005M +i0 "."0(E+O t4 ,5 66 6 -0.865662E+03 -,.863275E+03 -0.d3i21EI03 -0 .8d33E+03 0.57.95E+03 -0.226646E+03 -i,229P49E+,3 0,0151E+03 -, 359. E-,.1 0.23533E+00 0. YE+-1 to 6q 70 0%53D03 1 M..K6EOM 0.30.M.EMOi 72 0.21906ES03 -0,26038 +03 j.1375,fkjE+0;3 0,c0 '0 E+0 0'.574613E+03 -0.230 E+0B 0.4,55E+01 -0.358793EKfM 0.0000 0E +0 i( -0,211262E-O1 0, 11750E-01 d0,24'5E+:3 73 74 75 7b U.. 78 79 80 0.251994E+03 -0.229802E+03 I BO08E+00 ,,.255591E+03 0.60373E*03 -0.B8498E+01 -0. ,?761E+03 -0,24719E+03 -0.844684E+u0 0,205512E+02 0.132559E+03 0.126513E+01 0.2,00!0E+02 0.Ol,00 EO 0 .000 000E+O0 -0.120873E+02 0.571493E+03 0.103412E-01 -0.13591E+02 -0.232165E+03 0.997958E-01 -O.!A5780E+A? -0,232132E+03 0.154263E+00 ;I -,.. -877E+02 777 S2 83 84 85 86 87 38 6 0.903839E+02 0.309476E+02 0.2378 19E+02 0.407q4E+02 0,43'i177E+02 0.431340E+02 0.378400E+02 0.802973E+01 0.603685E+03 0.788741E+O0 -0.252872E+03 0.132266E+03 0.000000E+00 0.654236EPOO 0.172420E+0 0.563746E+03 -0.23273SE+03 -0.232876E+03 0.594267E+(3 -0,253394E+03 0.00000E+00 -i.29006A+f,0 0,280745E+'.0 .,406971E-01 i.22541E+00 0.01616E.)00 C12 Table C4 (Concluded) 9 91 92 93 94 95 96 "7 98 99 100 I1 102 6.127694E+02 0.166444E+02 0.274027E+03 0.162560E+03 0.161690E+03 0.270946E+03 0.161567E+03 0.137890E+03 0.143694E+03 O.O00000E+00 0.000000E+00 O0OOOE+00 0.060000E+00 0.132555E+03 O.O00000E+00 0.498931E+03 -0.200647E+03 -0.201281E+03 0.516256E+03 -0.223823E+03 0.143332E+03 O.OOOOOOE+00 0,850791E+02 -0.543437E+01 -0,439218E+01 (1,986481E+02 0.566208E+00 0.000000E+00 -0.375000E-01 0.190581E+01 -0.153205E+01 0.53626?E+00 0.23BBOBE+01 0.382425E+00 0.O00000E+0O.O00000E+00 O.O00000E+00 O.O00000E+00 0.(00OOOE+00 103 1(04 0.O00000E+00 0.00000E+60 -0,280563E+01 0.140605E+03 0.O00000E+00 O.OOOOOOE+00 1K5 0.060000E+00 ,.O000f60E+00 O.OOOOOOE+00 CALCULATED SHEAR INLONG DIRECTION (LBS/IN) INCP SHEAR X INCR INCR SHEAR X I -,.453551EtK0 SHEAR X S -0.50q997?E+00 9 0.401638E+,0 15-0 .0'7IhE- i 21 0.165*32E+0 27 -0.831826E+O0 33 0.354861E+01 39 -0.144864E+02 45 -0.526926E+02 2 -0.435260E+00 8 ,).402230E+00 14 0.72972iE+0 I VV368718-+0 20 (.181421E+00 19 1.'25E+O 25-8 7 ,7E+O 26 -0.847947E+60 32 6.364924r+01 31 -.33375E+01 37 -".4654E+'0 38 0.133728E+02 44 .01 1BE+0 43 ).16935+0 -0.360E+00 1 9.,S33"E+SC 56 -0.322552E+02 05-v.3213572+02 62 -0.1062B4E+03 1-.I5E+K3 68 (.15551E+03 0.I(595E+03 u0 5Et3 -4 0.q33345E+02 i3-0i25714E+01 8 522%0E+02 ?G -'.8'1 .354933E+00 3K.383247E+1" t 139,76E+(i92 93 -O.385297E+6l ? -. 581E+01 4-.'C64986E+O(' 5i 1.142%E+01 57 0.822255E+00 3 -0 106113E+03 69 106296E+03 7C 0.327255E+02 81 -M.55944E+,2 E-O.1444BOE+02 93 -r 914847E+O0 iFCR INCR SHEAR X SHEAR X INCR SHEAR X 4 -0.855259E+00 1K 0.478478E+00 16-0.572629E-01 22 0.124702E-01 28 -0.827548E+00 34 0.351081E+01 40 -0.140158E+02 46 0.565347E+02 5 11 17 23 29 35 41 47 -0.510385E+40 0.728920E+00 -0.261209E+00 0.344232E-01 0.575178E-01 0.352129E+01 -0.139443E+02 0.555112E+02 6 -0.513193E+00 12 0.385689E+00 18 0.173397E+00 24 0.900527E+00 30 0.408360E-01 36 -0.105030E+00 42 -0.139640E+02 48 0.552844E+02 52 53 -0.342788E+02 5f -0.325522E+02 59 65 71 77 83 89 95 60 66 72 78 84 90 96 0.201922E+03 58 0.208530E+01 64 0.593045E+00 70 0i.106144E+03 76 0.321349E+02 82 -. c,945E+02 88 0.i45C50E+02 94 0.435818E+01 -0.416246E+03 -0.212910E+01 -0.147501E+01 0.321574E+02 -0.553474E+02 0.150444E+02 -0.424602E+01 -0.104270E+03 0.415204E+03 0.174104E+01 0.479515E+00 -0.55 7E2572E 0.149602E+02 -0.572724E +01 Lu', TE SHEP IN SHO;T DIRECTi0ii 'LBS/IN. PC rcp SHEAR E y S4EAR y INCR + ).345160E+(0 0.47-.243E , 1 . 23 0BIE+01 -. ,-4..12244,E+'2 .!L .275892E+01 ' i4 C,. 128525EtOI 15 -. 282537E+(,i -,E+O E2 T.K7762E+0'1 '.SB5992E+Ci 0(.12S?24E+,)I .. ' -'.41'3 28 '.23I664E+01 2 -0.281973E+01 26 0,125(152E+01 .ISE) 3 ',2696E+01 33 -.2Q87,E (I 1-.I8616E+i*1 31i- ,*4E")5EO 32 -_ :5:-,-)..4 3 K, ' .215462E+0 i 4 0.51@417EtOl -.3-:.3C3-95 , 4 0.25234t+, 5- 224N7E+01 i),17q95E+1 I 2 6..92064E+02 5 -. 13973-+03 E..- 50 .4 2,,eEE+.2 . . 53 29E+02 5 .Ib414bE+:3 5.-0,25 2+ 4,P2 4G3E+02 13 8412E03 3 62 ",6514E+,'. 1E +0 I. 7' U2668'0EK'1 -";,2^-;464E+01 K.963521E+' . ' -i).374EE+( 73-0.375E ,' .1)472291 - 2. 55441E+11 t 0,24570E+01 7) -,'t.'22, K',57592+01 " -. 4-,12,i 6 29K4?2E+1 rj-6,;E,'EI S 81E ?48162+112 E+'±I d-'3,275815E+K'I* 1 ,1S S-K .4971- y.+--i0(, .. "4. " 2 E 8 1 ', C13 INCR SHEAFR y INLF SHEAR Y 5 -0. 1362C6E-02 11 0.2651"5E-'2 17-C.I102032E-03 23 - .339440E-04 29 0.253253E-02 35 -0.liC)i3E-O i SHEAP Y 6 -0.295696E+00 12 18 24 30 -0.230372E+01 -0.26552,E+(01 -. 61888E+( I -0.26832Et:I .O. J-.' 47 0.484215EO" 53 -0.226134E+02 ^0b ,2 I1E+K1 422 7 48 -0,280116E+01 54 '.431634E-01 5q O.11819E+Of' 64'- 41 65-I.224614E+2 71 (,29456E+ 17 0,431 75E-01 83 -0.144386-01 82 'O1446- .63613E+iI 66 6.428i14E+ I '20.2753.E+ ! 8- ,27J"4E + 84 90 (.3,E9275E+0: ... 1 E,1 APPENDIX D: PERFORMANCE ANALYSIS, CENTRALIZED TROOP CLINIC, FORT SAM HOUSTON, TEXAS Purpose 1. On 4 November 1983 it was reported that the subject structure was apparently moving. This assessment was based on cracking of interior plaster board and exterior brick walls. The structure was inspected on 10 November 1983 by geotechnical and structural personnel. In conjunction with a cooperative research project being conducted by Fort Worth District and the Waterways Experiment Station, a vertical survey of the structure was conducted on 14 November 1983. This report presents a summary of foundation design and construction, results of the visual inspection and the vertical survey. Recommendations for monitoring the structure and potential remedial procedures is also made. Design 2. The structure was designed by Harwood K. Smith and Partners, Dallas, Texas, under contract to the Fort Worth District. The structure consists of precast concrete exterior panels with face-brick fillers. supported on steel frames with interior pipe columns. The roof is Column bays are generally 30 by 41 feet. The structural foundation consists of a reinforced concrete ribbed mat slab. The ribs are placed on 15 by 20.5-ft centers and coincide with the superstructure framing system. Beams are widened at column locations so that the resultant soil pressure does not exceed 2.0 ksf. The foundation materials consist principally of 5 to 10 ft of CH clays overlying clay shale. From 2.0 to 5.5 ft of the CH materials were removed and replaced with nonexpansive fill compacted to at least 92 percent maximum density. Typical profiles through the structure are shown on Figure Dl. During design it was predicted that the subgrade materials would move to the point that the perimeter of the foundation would cantilever 7.5 ft. Based on this, the exterior beams were reinforced with four No. 11 T&B. Construction 3. Co., Cunstruction of the building, accomplished by Fortec Construction San Antonio, Texas, proceeded from February 1981 to September 1982. Dl V.(5 1 zt ° -4 ' , I. Na ~1 -j J - I' 1 -o,,,-.-= Figure Dl. Subsurface profiles, Troop Medical Clinic Fort Sam Houston D2 During latter stages of construction of the foundation, it was noticed that the horizontal reinforcing steel in the interior ribs was not being satisfactorily anchored into the perimeter foundation beams. To remedy this mistake, the contractor broke out part of the concrete ip the floor and beam system and grouted in additional transverse steel. Performance 4. General. Performance of the structure to date (November 1983) appears to be satisfactory with the few exceptions listed below. (1) A small hairline crack has developed in the brick below the window frame in the exterior south wall. (2) A small crack has appeared in the exterior precast panel of the east wall. The crack is 0.02-inch wide at the bottom and fades out where the smooth concrete meets the exposed aggregate concrete. (3) A noticeable crack has developed in the precast concrete above the front entrance door. The crack is 0.07 inch wide at the bottom and 0.03 inch wide at the top. (4) A significant erosion channel has developed adjacent to the foundation at the southeast corner of the building. Tests have indicated that the roof drain at this location is partially blocked and water pouring through the roof scupper has eroded the foundation soils. (5) Several cracks, generally at the top of door frames, have developed in the south wall of the south corridor. (6) Roof and window frame leaks were noted in the office in the southeast corner of the building (Room 116). 5. Survey. The performance of the foundation was determined by running a level through 30 points on the floor slab, Figure 31 of PART III. The floor slab shows a typical center lift (heave) mode movement with a slight skew toward the northeast corner of the building. Generally the differential movement of the structure is well within tolerance limits. Typical and "worse case" differential movement between adjacent points are given in Table Dla. All other points show less deflection ratios. According to Skempton and MacDonald (1956), wall panels and sheet rock walls should be able to tolerate differential movements on the order of 1/300. D3 Consequently, it is inferred Table DI Differential Displacements Troop Medical Clinic a. Survey Points 118 21 22 27 - Adjacent points Differential Settlement 5 1/400 24 22 23 25 1/480 1/427 1/458 1/230 b. Three adjacent points Survey Points Differential Settlement 26-27-28 20-21-22 21-22-23 27-28-average 18,19 1/1400 1/976 1/850 1/820 D4 that except in the area of survey points 27 - 25, the structure is performing satisfactorily. 6. Woodburn (1979) has developed performance criteria based on the differential movement of three adjacent points. Typical and "worse case" deflections using three adjacent points are shown in Table Dlb. According to Woodburn, masonry wall panels and sheet rock walls should be able to tolerate differential movements on the order of 1/800. As shown by the above table, the movement at the southeast corner of the building is approximating the tolerance limit. Recommendations 7. It is recommended that the roof drains in the southeast corner of the building be repaired to a functional condition. Although it may be only accidental, it is noted that the poorest foundation performance coincides with the malfunctioning roof drain. 8. The progression of cracks in the precast concrete panels should be monitored on a bi-weekly basis. The resident office personnel have placed small dental plaster patches across the crack to make a quick determination of additional movement. 9. Should movement progress to any significant extent, the foundation should be stabilized before the building moves to the extent that the Pest Management Facility has moved. It is considered that some form of intrusion groutng will be used, such as was done for the Night Lighting Vault, Fort Polk, should it become necessary to affect foundation repairs. 1,5 APPENDIX E: INFLUENCE OF SOIL MODEL ON MAT PERFORMANCE Introduction 1. Parametric analyses were completed using plate on semi-infinite elastic program SLAB2 and plate on Winkler foundation program WESLIQID to determine the influence of soil behavior on mat performance. Influence of soil type was determined by a comparison of mat performance calculated by SLAB2 and WESLIQID. Influence of soil stiffness was determined by calculations of bending moments using program SLAB2 for mats subject to imposed heave. 2. Programs SLAB2 and WESLIQID were used to analyze the bending moments and displacements of a 200-ft square, flat concrete mat with a Young's modulus of 432,000 ksf and Poisson's ratio assumed 0.3. 0.15. The soil Poisson's ratio was Symmetrical loads were applied so that only 1/4 of the mat need be modeled by the finite element mesh. This mesh was divided into 100 square elements of equal size of 10 ft on each side. Influence of Soil Model 3. Bending moments calculated by programs SLAB2 and WESLIQID for similar displacement patterns caused by imposed loads and heaves may be compared to determine influence of the soil model. An analysis of the 200-ft square mat of 12-inch thickness was performed first using SLAB2. parameters included a uniform applied pressure modulus Es - 400 ksf. Input q - 2 psi and Young's soil Bending moments and displacements distributed from the center to middle edge calculated by this initial run using program SLAB2 are shown in Figure El. The coefficient of subgrade reaction for each nodal point of the mesh was subsequently determined by ksf where p = q/p (El) is the settlement calculated from SLAB2 at each nodal point. Program WESLIQID was then applied using these 2 psi. pressure ksf for the imposed load Displacements calculated by both programs SLAB2 and WESLIQID q - for q - 2 psi in Figure El are essentially idential as expected. The bending moments calculated by these programs differ near the edge where results from SLAB2 indicate larger bending moments than rest Its from WESLIQID. El 0 oz9 I-- OI-~nio Z-t- 9-a- 0 o 0 * o C a0 tw cc 0W@ Z- 0 00 0o 0 0 N (n I-C 04 9 a - t - -I-z 9 go ~ 4 COJa 0~ 0- 0 0r9 0- - t9 9 0 0- (0 0 10 2 00 0 z W 0 aE Z SOaI33O a3ON oo 9~~C'~ t 0 ONON1 AVO oJi-I C4 0 4. Programs SLAB2 and WESLIQID were applied in a second analysis using and an imposed identical 1 inch edge gap around the perimeter of q - 2 psi the mat, Figure El. Displacements calculated from this second analysis indicate edge-down displacements, but the mat on elastic soil appears more flexible with greater edge down displacement than the mat on Winkler soil. Bending moments are substantially more negative near the edge for the mat on elastic soil of program SLAB2 than the mat on Winkler soil of program WESLIQID. 5. A third analysis imposci a center load of 115,200 pounds on the mat, the weight of the mat, and the same edge gap as the second analysis, Figure El. Displacements calculated for this third analysis are less than those for the previous two analyses because of the smaller applied loads. The displacement pattern calculated by SLAB2 does not show as much settlement in The elastic material shares the load the center as calculated by WESLIQID. with adjacent soil elements, while the Winkler soil does not. The positive bending moments calculated by WESLIQID are subsequently much larger near the mat center than those calculated by SLAB2. Influence of Soil Stiffness 6. Program SLAB2 was applied to determine the influence of the stiffness of an elastic soil on the maximum bending moment. An imposed center heave was simulated by applying a I inch gap at the mat perimeter. was simulated by applying a 0.4 inch gap beneath the mat center. Edge lift The mat is sufficiently flexible such that the mat is fully supported by the soil. The m-ximum negative bending moments due to center lift, Figure E2a, occurs approximately 10 ft from the mat perimeter and maximum positive bending moment imposed by edge lift, Figure E2b, occurs at the center. Figure E2 shows that increasing the soil elastic modulus causes significant increases in the magnitude of the maximum bending moments when heave is imposed. If heave is not imposed, an increasing elastic soil modulus tends to decrease bending moments because of improved soil support and reduced settlement and mat distortion. E3 0 CL 100 200 300 400 500 600 700 800 o 0 8 8 0 0 I L I C'4 (I) 12 INCHES THICK Z 24 INCHES THICK --10 100 200 300 400 500 600 " SOIL ELASTIC MODULUS, 00 o0 100 a. 200 700 So KSF CENTER HEAVE 300 400 500 600 700 80% 11 160'260 360 460 560 60 7EoOf0 SOIL ELASTIC MODULUS, b. KSF EDGE HEAVE, 12 INCHES THICK Maximum bending moments of a lO-ft wide strip of Figure E2. 200-ft by 200-ft mat 12 or 24 inches thick subject to heave E4 APPENDIX F LIGHT TRACK VEHICLE FOUNDATION DESIGN U 6. PROJECT TITLE AJT -- ThNA-CK t Ak7M0 \ToV0 F VYf'CCLS k.ASA SOL~~C4 TA 1LtL~pjq&-P UVTt -- -Gt C~~ C14- Az4CAu~k-rlzUT -- r -P, cGI+ T&AJCavs NG . LZ "L4T- C~ c sT TIk.-gA-U iJ7 7oT PZ -- X IImLN WAcP-r- v w' czuLC-W - /A z~ A-'P-Q b-T At -gznl-i4 oLC-0ZAMC A,~~ SUWJ-f 3OLA-C - 10D LOS(: ANt L ,A Q OF-TCZJAT RLAND WA DBL. 'TEAN PROJECT TITLE 'iA-JDr P-1.4I ,2 P~-~c ~ 9k C5,J J41ro-1(~I A - 4- Ad.-U~1)OW6A%- A-L Toa COMPONENT __ _ _ _ _ _ V &.-TL-46N -o5AV y _ _ ________________ _ _ _ ____ _ 5v ToK *--- -ST c _ 0u~470 L "Fr N-UVJ7O OL-tI7JQ -SPD-- 4 SYSTEM ~~ AktJD0 9A-f > (rr To- * T ~?i~ ppVt~ -~~~I 6r. H 4c-{A ~ ~ -Si -$[ DT cj- HS t4o!-tr, ~i- k _ JOB NO. DATE ~-~FACILITIES SYSTEMS ENGINEERING CORPORATION DESIGNER U- LOS ANGELES. CA. RIC LAND. WA DUBLIN. IRELAND PROJECT TITLE " , C. 4 B \yL.Y A,-4. -U. 0%Q 1 -krt4 oo )) f4A-). Ar- -.vt= s [ . - F-"-M TO .,Te -a isE T. C "PA A-T Ae- F-3 ' rA J- V A7 SA-A S T%) iLi SYSTEM _ _ _ _ _ _ _ _ _ _ _ _ _ DATE JOB NO. COMPONENT EFACILITIES S A-x- -t 8, Q --SL- DESIGNER SYSTEMS ENGINEERING CORPORATION LOS ANGELES. CA. RICHLAND. WA DUBLIN, IRELAND PROJECT U- L Cj9d) C.r- ;;u=-c,'.Wtt 1 '3 P e, 13L4. A 1) TITLE-- Tx_ - 13T8 S SYSTEM __ _ _ _ _ _ _ _ _ -- TLA-,i 'r, t~70:: Z- 19'.j -- C -SM -T _ _ i -1-l 5 _ _ _ DATE JOB NO. COMPONENT ____ ____ ____ ____ U-FACILITIES ____ ____ ____ ____ DESIGNER _ _ _ _ _ SYSTEMS ENGI NEERING CORPORATION LOS ANGELES. CA. /g 2/ _ RICHLAND. WA DUBLIN. IRELAND _ _ _ _ _ . 44) PROJECT TITLE T_-._ x- .tx.\ r ~~~~u~ r-7L~ =- ._I.- G7 .. COJ, IIA k7 3- 1/~4 _ .__-.5 4 - __ .. __)C1 ~( (-7 " --- ._______________ = . C-- gh . -- -. /, / =. SYSTEMA COMPONENT JOB NO. EFACILITIES ZDAT DESIGNER__.__-_-, SYSTEMS ENGINEERING CORPORATION LOS ANGELES. CA. RICHLAND. WA DUBLIN. IRELAND - . = PROJECT TITLE -i.- '- -- - - -- I L2 3 - - L ',- "-L ' - . 4 .... ]) _ JOB NO.DATE ... (-~~ = -.- .... . ACiLIIE YTMSEGNEIG-OPRTO ~ACLTE SYSTEMS LOS.ANGELES.C. LOS ANGELES. CA. CPORATIONA~k A TE- RICHLAND. ENGINEERING________ WADUBLIN. RICHLAND. WA DUBLIN. IRELA~ND PROJECT TITLE -'"0 - B ( u, -I]/ = C D-- .. . - ' - -z .r--- .- -) - Ust) c-' -t ~%r(4&.- (-- e - o>y<.< y ,, :-: COMPONENT 4C'a<:>:)''"B'' )" -- ':¢Y _(i "-C I . L) L - "A JOB NO. _____________________ E D ) - DESIGNER DATE <, - FACILITIES SYSTEMS ENGINEERING CORPORATION LOS ANGELES. CA. RICHLAND. WA DUBUN. iRELAND . 'N, ..- PROJECT TITLE __ -- a. -4T , .-.. ..- .. .¢ 4 _ _ - . ,l I )e 3_ 3_ _- _ __ ,C, S*- ,: t .) .... C -. • f'c >.. " } L(--)s ti~ I-L7~ ~~~t QSYSTEM COMPONENT 3{a44'~./6 ___________________JOB .FACILITIES NO. DESIGNER DATE _-_-_ SYSTEMS ENGINEERING CORPORATION LOS ANGELES. CA. RICHLAND. WA DUBLIN. IRELAND __ "'., PROJECT TITLE .Is -:, oQ 7.-"'(. 1 S)8, ' '' C-' )"' -1 t( . -l>-tt.(- ... . . -- - COMPONENT q- -.o C . .L " l -, ________________ E C 1 .. = - ____ JOB NO. DESIGNER DATE ' -- FACILITIES SYSTEMS ENGINEERING CORPORATION LOS ANGELES. CA. RICHIAND. WA DUBLIN. IRELAND BX .- PROJECT TITLE 3k) • - - kk~ ~-~Aq-~ IL 0 ~ a TIr; -_.._4. r"oft t-~ps ~ . - ST~ - A - ... .... .... 5rQ- 3o) -~ SSYSTEM COMPONENT a _ _ ___ _ _ ",_____ _ _ ,o___ _ __ _ _ _ % JJc _ _.JOB NO. -. -~//DATE :_"___"_'___-______,_-__DESIGNER ~EC FACILITIESSYSTEMS ENGINEERING COJRPORATION -LOS ANGELES. CA. RICH-LAND, WA DUBLIN. IRELAND A.............~k~ - 3 4r" PROJECT TITLE ''"( ,>@-. -- .;-T~ -x. -.--1. k - 's9 .. =-o x2!-n o k-i+ --..-- _- . . J I .....:- - '-4 L.. " .- ... , - .. . .. .- _ ___ __.... -- __ .. ...U e. ~. 7- c-r-M C*'- T A- SYSTEM ,A--T ;L4-&N ~o . ... ___ ...... . CZ2, J. . __-__-_"_-- .i T _---"T . F -l - * SLA Sc-&a - AS B-A {-f - L-,-S \ :-~ __________._-__ COMPONENT JOB NO. . DESIGNER EFACILITIES "' DATE ' SYSTEMS ENGINEERING CORPORATION LOS ANGELES, CA. RICHLAND. WA DUBLIN. IRELAND - " - to SLAB SIZE: 48 ft x 40 ft 14 = 30 12d in em= 5fIt 10 (MOMENTS IN FT-KIPS/FTj (MOMNTSIN HORTDIRCTIN) (OMETS N LOG DRECION 144P -- 0- U. 2. F;...5.3 Typical var iation of moment along the longotudinal axis as slab length incress 1108) 11 PJ2- PROJECT TITLE .3-- _ b 1. .'c; O.-Jr-- EO S 'ktO -k7 -_u_/ g ..- t - S _ z --- Ti-Gc7 -b AA".LK1 . e__.'T \.J ZT.1 < l q -.- 1 ;-CTc t It.r t - c -' (j- , :? - _.. us 7§0k CSYSTEM VVLr -:: -- C-1, -5 :41 PMI -. h_____ 5..Jp1~~ ___________ JO COMPONENT __ NO. . DESIGNER FACILITIES SYSTEMS ENGINEERING CORPORATION E~ _ ,- .. LOS ANGELES. CA. RICHLAND. WA DUBLIN. IRELAND PROJECT TITLE______ ______ 3o .z' .... A- d(l:] c- JOBN .A COMPONENT i=i[ .... COMPONENT o~ it%.4 _ ""I" ,, --. 8__._-.._ - _/ ___0_____._________________ UFACILITIES ___ OB N - / ' -DESIGNER SYSTEMS ENGINEERING CORPORATION LOS ANGELES. CA. RICHLAND. WA DUBLIN. IRELAND %" . . Summary FOUNDATION DESIGN ANALYSIS RED RIVER ARMY DEPOT MAINTENANCE MODERNIZATION The following summarizes the foundations report prepared March 1981 by the Foundations and Materials Branch, U. S. Army Engineer District Fort Worth. The original report and additional reference material including boring logs, locations of boring logs and soil samples, and results of laboratory soil tests may be obtained from this district office. General 1. This project will provide an efficient modernized maintenance facility for the overhaul and dieselization of the light track family of vehicles. The project will consist of three buildings, a Light Track Vehicle Shop (Building 333), a Material Staging and Control Facility (Building 312) and a Heat Treating Facility (Building 328). The Light Track Vehicle Shop Building will be approximately 197,610 square feet in area, Material Staging and Control Facility will be approximately 125,000 square feet, and the Heat Treating Facility will be approximately 500 square feet. At this stage of planning, all structurcs are thought to be steel frame structures with concrete masonry unit walls. 2. The proposed site is located on the eastern edge of the Red River Army Depot in an area bounded by Texas Avenue on the north, Avenue K on the east, Eigth Street on the south and Avenue G on the west. The site is generlly level; however, some drainage ditches are in the area. Subs'irface Investigations 3. During April and May 1979, 22 borings were drilled in the areas of the three proposed structures. These borings were drilled to determine the subsurface conditions and to obtain samples for testing. Samples of the subsurface materials were obtained with an 8-inch earth auger, a 6-inch Denlison barrel sampler and a 6-inch core barrel sampler. Samples recovered from the borings were sealed in airtight containers and shipped to the laboratories for testing. 4. General Geology. Red River Army Depot lies in the north central portion of Bowie County, Texas, and is situated within the West Gulf Coastal Plains physiographic province. topography. This area is characterized by very gentle The region is underlain by sedimentary deposits of Tertiary Age. F15 The primary geologic strata are assigned to the Midway and Wilcox groups and dip to the south at a rate slightly steeper than the change in surface elevation. The Midway group has a thickness of approximately 400 feet and consists chiefly of clay shale. clay shale. The Wilcox is predominantly sandy and silty These primary strata are generally masked by a thin soil stratum, consisting of both residual and transported materials. Overburden generally consists of silts and clays with varying amounts of sand. 5. Site Conditions. Boring logs revealed that much of the area has been covered with earth fill materials. The fill materials range in thickness up to approximately 8 feet, and when classified consists of medium to high plasticity clays (CL and CH), clayey sands (SC), clayey sandy gravels (GC), sandy silty clays (ML-CL) and silty sands (SM). contained within the fill material. Some organic materials are In three of the borings, natural overburden soils were encountered at ground surface. From ground surface to depths of 2 to 3 feet below existing ground surface, the natural overburden soils are medium to high plasticity clays (CL and CH). Underlying the top 2 to 3 feet of overburden soils and the fill materials is a medium to high plasticity clay (CL and CH). Thickness of the fill materials and the overburden soils range from 5.1 to 13.0 feet. 6. The primary geologic formation encountered beneath the overburden soils consist of a clay shale tentatively identified as a portion of the Midway group of the Tertiary system. The clay shale is soft (rock classification) and ranges from highly weathered (altered to a clay consistency) immediately beneath the overburden-primary contact to weathered at depths 3 to 4 feet below the overburden-primary contact. The clay shale extended to the total depth investigated, 30 feet below existing ground surface. 7. All borings were allowed to stand open overnight to allow ground water levels to stabilize. Water levels at the time of drilling ranged from 2.8 to 19.5 feet below grade. feet. Average depth to ground water was about 9.5 Based on previous experience in the general area, it is believed that the water table is a perched water table associated with the lower overburden soils. F16 8. Laboratory Testing. Identification, moisture content, density, unconfined compression, one-point triaxial compression and controlled expansion-consolidation tests were performed on samples of subsurface materials. The compressive strength of the subsurface materials from results of unconfined compression tests and one-point triaxial compression tests ranged from 2.6 to 10.4 ksf. Expansion-consolidation test results from method C of ASTM D 4546 indicate expansive pressures from 0.50 to 2.0 ksf in excess of the overburden pressure, with deeper materials having the larger expansive pressures. Discussion 9. The proposed site is in an existing level plant area with little topographic relief (except for drainage ditches) across the site. A review of subsurface conditions and laboratory test data revealed three distinct potential founding strata: surface fill material, overburden clay, and primary clay shale. The fill material consists of a conglomerate of discontinuous layers And pockets of loosely compacted clays (CH and CL), sands (SC and SM), and clayey gravels (GC). This stratum does not express the strength to satisfactorily support the proposed structures. The clay overburden likewise does not possess the strength and consolidation characteristics to satisfactorily support the structures. The primary clay shale at a depth of approximately 24 feet below ground surface is capable of supporting the proposed structures. Footings bottomed at the above depth could be sized for an allowable bearing pressure of 10 ksf considering down load only. The disadvantage of using the clay shale as the founding medium is the potential heave of the clay overburden and shale on the pier shaft and heave of the clay shale beneath the footing base. It was computed that deep footings would move upward approximately 3 inches due to swelling of the subsurface materials. This amount of movement, either uniform or differential, is considered to be excessive for the type structure proposed. Assuming the foundation would experience 3 inches of differential movement, the angular distortion would be on the order of I to 100, a limit where structural damage would occur. 10. Based on the above engineering studies, it was concluded that the existing soils (overburden and primary) are not satisfactory founding media. The alternatives are to improve the engineering characteristics of the Fl7 existing soils or to remove the unsuitable existing soils to a reasonable depth and replace with compacted nonexpansive material. Considering the characteristics of the fill material, in place improvement is considered to be excessively expensive. Removal of this material and replacement with compacted fill is the best solution to the problem. Removal and replacement with compacted fill would provide an excellent stratum on which to support a shallow foundation and on which to support floor slabs. The foundation for the proposed structures can then consist of a ribbed mat slab supported on the compacted nonexpansive fill material. 11. The removal and replacement of the existing fill material does not entirely eliminate the potential for heave at the subject site. nonexpansive fill, by definition, will not heave. The The underlying CH overburden and upper primary soils, however, will experience some volume change. It was determined that the mat slab could experience 1.5 inches vertical movement resulting from heaving of the overburden and upper primary soils. Based on an analysis of existing moisture conditions, it is believed that this amount of expansion could occur within an 8-foot radius. Consequently, the foundation floor system should be stiffened to the extent that the angular distortion of the structures does not exceed 0.0015L (L distance between adjacent columns). Recommendations 12. Based on field investigations, laboratory testing and engineering studies, it is recommended that the proposed Light Track Vehicle Shop (Building 333), Material staging and Control Facility (Building 312) and Heat Treating Facility (Building 328) be founded on a reinforced concrete ribbed mat slab. The mat slabs should consist of a monolithic floor slab and beams. The beams should bottom not less than 24 inches below outside finished grade and should be sized in such a manner that an allowable bearing capacity value of 2.0 ksf is not exceeded. Beams and beam intersections should be widened and reinforced at column locations to form footings which will distribute column loads along the beams and over an area such that the above allowable bearing capacity is not exceeded. The load used to size the beams should consist of full dead load plus that portion of the live load that reacts continuously, usually 50 percent. F18 13. To prepare the subgrade for the three proposed structures, all of existing fill material (approximately 5 feet) should be removed. The excavated materials should then be replaced with nonexpansive fill materials. Nonexpansive fill materials should have a plasticity index equal to or less than 12 and should be compacted to not less than 92 percent maximum density as determined bvy ASTM D 1557. Any additional fill material required to bring the floor slabs up to required grade should also be nonexpansive and compacted to the same density. A polyethylene vapor barrier and a 6-inch capillary water barrier should be placed beneath all floor slabs on grade. The ribbed mat slabs should be designed in accordance with the AEIM, Chapter VI, Structural. Using the PTI method of designing the mat slab, the following design parameters should be used: inches, and ps - qa - 0.5. F19 2.0 ksf, em - 8.0 feet, ym - 1.5 APPENDIX G FIELD TESTS TABLE OF CONTENTS Page Heading I. II. III. IV. V. VI. VII. PRESSUREMETER TESTS .... CONE PENETRATION TESTS .... ............... . G2 ............. . G28 . G39 PLATE BEARING TESTS ..... ............... PIEZOMETRIC DATA ...... ................ I.G43 ................. . G44 EARTH PRESSURE DATA ..... ............... . G47 STRAIN GAGE DATA ...... ................ ELEVATION DATA ...... Gi G47 I. PRESSUREMETER TESTS Briaud Engineers 1805 Laura Lane College Station, Texas 77840 Purpose and Scope 1. The geotechnical investigation reported herein was undertaken as part of a program to evaluate the settlement of a raft foundation to be constructed at the Red River Army Depot near Texarkana, Texas. In this report, the results of pressuremeter tests performed at the site, Figure Gl, to a depth of 33.5 ft below the surface of the fill are presented. 8 tests were performed on November 26, 1983. A total of Also included is a method of estimating an equivalent modulus of deformation of the soil to be used in settlement analysis. Authorization 2. This work was authorized by Purchase Order No. DACA39-84-M-0073, signed by William M. Landes and Mary S. Parrette on November 7, 1983. Soil Conditions 3. The soil profile was obtained from the cuttings taken off the hand auger bucket and is shown in Figure G2. The location of the water table was not recorded during the test, but from previus studies it is expected to be 10 ft below ground surface. Tests 4. The pressuremeter used at the site was a pressuremeter model TEXAM developed at Texas A&M University and sold commercially by Roctest, Inc.; this is a monocell pressuremeter inflated with water which allows to perform preboring or selfboring tests. The probe is 58 mm (2.28 in.) in diameter and 3 has an initial deflated volume of 1050 cc (64.1 in.). A total of 8 tests were performed in addition to the two calibrations (volume losses and membrane resistance). A hand auger was used at the site and proved to provide a high quality borehole. The first hole drilled (BH 1) was terminated at 5 ft due to the presence of an unexpected concrete pipe. G2 The second hole (BH 2) was Access Road 10 t l-1 1 ft. 6 ft. (a) Plan of Site NOTE: Tests were performed from excavation level but are reported as of top of fill level. Top of Fill 3 ft.. Fill Fill Excavation Level 2 ft. Original Ground (b) Elevation Figure G1. G3 Site Net Limit Pressure, pL' kPa 0 1000 0 2000 1 ! 3000 1 4000 Top of Fill Sandy Fill 5 Clay no apparent fissures 10 Depth ft. 15 Clay 20 brittle, fissures 25 Clay 30 less fissured 35 Figure 02. Soil classification and net limit pressure profile G4 drilled approximately 10 ft from BH.l and was terminated at the desired depth. Figure Gl shows the location of the boreholes relative to Station 6+00, situated 5 ft away from the expected edge of the foundation. 5. The raw data obtained in the field was corrected for membrane resistance and volume losses in order to obtain the final corrected pressuremeter curves, shown in Figures G3 through G1O as curves. For each test, a first loading modulus a net limit pressure p* P versus AR/R0 E r and Ei, a reload modulus The first loading modulus was were calculated. obtained from the straight part of the pressuremeter (PMT) curve on the first loading; the reload modulus was obtained from the slope of the unload-reload cycle; the moduli were calculated from E G moduli assuming a The limit pressure was obtained by Poisson's ratio of 0.33 in all cases. manual extension of the curve. shear The results are tabulated, Table GI, and illustrated on Figures G2, GIl and G12. Coefficient of Earth Pressure at Rest 6. To obtain the total horizontal pressure at rest, POH' the initial part of the curves, Figures G3 through GIO, were plotted as (AR/R ) to accentuate the curvature. versus log A graphical procedure (similar to the calculation of the preconsolidation pressure obtain POH" P Pc (Casagrande 1936) is used to This new method is based on the definite analogy between the consolidation test on one hand and POH each test is presented in Figures G13 through G17. other tests. POH is impossible and and and the preboring pressuremeter This calculation for test on the other hand (Briaud, Tucker, Felio 1983) determination of P For some tests, the POH had to be estimated from the To calculate the coefficient of horizontal pressure at rest, K an evaluation of the vertical stress and pore water pressure is required. The kN/m 3 total vertical stress was computed by assuming a total unit weight of 18 and the pore pressure at the test level was taken as the hydrostatic pressure. The values of the coefficient of earth pressure at rest Table GI. K Figure G18 illustrates the POH K0 are given on profile and Figure G19 shows the profile at the site. *Refer to references at the end of this section, I. G5 PRESSUREMETER TESTS 5 0 0 [ - r-7 " T- r '1 '-- T 1- 1 f II 1 TI - I - -7 Test 1 Red River Army Depot Depth = 3.0 ft. BH"2 - 400 - N- Or 300 - P-V kPa 2 200- . - 190 kPa " ll6.kPa OHG 0 5 10 15 20 25 30 35 R o P1 = P 420 k.Pa kPa E = E = 22469 kPa Figure G3. t.R 128 4943 k.Pa Pressuremeter curve for Test 1, depth - 3.0 ft, for hole BH 2 G6 500 - - -,----r- - -r-- - - -r ---1,- Test 8 L Red River Army Depot Depth = 3.0 ft. BH.1 7 400 7 3k a-P P 7 0 7 G 200- kSGa _ 7 5Ok. ~up S- 100 0 130 kPa S ur F_-_I 0 5 * 10 I . . .. 15 , 20 .. 104 kPa a .. .... 25 30 0 P, . 410 kPa P = 28 kPa E. = 7684 kPa E = 38866 kPa 1 Figure G4. Pressuremeter curve for Test 8, depth for hole BH-I G7 = 3.0 ft, K"TTf-T - -r-r 1000 - r- 'r t- 1 r- T . -- ¢[T T I - Test 2 Red River Army Depot Dept. - 8.0 ft. 00- BH.2 700-/ Boo P kPa 600-/ I 500 - 400 --- fj r - / 285 kPa Su 200 Sur SuG 219 kPa.. ~ 10 5 0 10 15 29 25 38 35 R 0 P - 850 kPa L POH 40 kPa E, - 16747 kPa E - 106875 kPa r Figure G5. Pressuremeter curve for Test 2, depth for hole BH 2 G8 - 8.0 ft, - 140 - Test 3 Red River Army Depot Depth = 13.0 ft. BH'2 1200- /1 500 ep /1 - I"I kia - I Su uup1\520 kPa 400 i.4 - 200 kPa S / / 200 ur 110 kPa -SuG U 0 5 0 -. L r ' 10 I . 15 25 20 R P POH 0 - 1225 kPa 60 kPa Ei . 28092 kPa E r - 112350 kPa Figure G6. Pressuremeter curve for Test 3, depth for hole BH 2 G9 - 13.0 ft, - 300 - r--t- r-T- 0 - VI-T--- - ,--r -- J-- r-- -T-T Test 4 Red River Army Depot " Depth BH.2 = 18.0 ft. 2500 200 p 1500 kPa 1000- S up / 980 kPa S- 875 kPa Sur 0 2 4 j8 10 600 kPa 12 14 &R 0 PL - POH 2810 kPa 110 kPa E i . 88381 kPa rE = 518700 kPa Figure G7. Pressuremeter curve for Test 4, depth for hole BH 2 GIO - 18.0 ft, r-,TT-1 3000 LTest - , F-- TT 7'I r- 7--T-r -"r--"-r-- 5 Red River Army Depot Depth -23.0 ft. 25M8-~ . H" 7 2000 1 r 9k4a S0 ur ur * 2 4 6 8 10 12 14 550 kPa 16 18 20 6R 0 PL - 2850 kPa POH 90 kPa E. - 82225 kPa E Figure G8. r = 327180 kPa Pressuremeter curve for Test 5, for hole BH 2 Gil depth - 23.0 ft, 3000 r -F -- T- -,---- --T-- 1 -1--"] T - -- Test 7 - Red River Army Depot Depth - 26.5 ft. K 2500 - 0 'I 2000 - - P - ~0 p kPa 15 00 S = 1020 kPa up - 1000S 740 kPa ur 500- * 1 2 3 4 5 6 7 8 9 10 &_R R 0 2 PL l 3200 kPa = POH Ei - 135 kPa 136690 kPa E - 178270 kPa r Figure G9. Pressuremeter curve for Test 7, depth - 26.5 ft, for hole BH.2 G12 3007 r F ~ '-~ r r~ ' Test 6 Red River Army Depot Depth - 30.5 ft. BH.2/ I 2500 L . 2000 sup kPa 1700 kPa . .-- S r 1000 kPa ur (stimated) " I. *1 50 - 01 0 1 2 3 4 5 6 7 8 9 10 AR % R 0 PL - 3600 kPa (estimated) POH - 200 kPa (estimated) Ei = 56525 kPa E Figure GI0. r - 796230 kPa Pressuremeter curve for Test 6, depth - 30.5, for hole BH 2 G13 First Load Modulus, Ei. kPa x10 20 0 60 40 80 0 5 10 15 20 25 30 35L Figure G11. First load modulus profile G14 100 Reload Modulus, Ero kPa x 1 0 100 200 300 400 15 20 30 35L Figure Gl2. Reload modulus profile 015 500 250 200 Test 1 Depth P150 =3.0 B- kPa 100 50 P OR lkPa 18 00 Figure G13. POHdetermination for Test 1, depth OH for hole BH 2 G16 -3.0 ft, ft. 250 Test 8 200 Depth ft. =3.0 BHI1 150 P kP a 100 50 -~ ~ M 28 kPa 100 110 log R 0 Figure G14. POHdetermination for Test 8, depth for hole BH-l OH G17 =3.0 ft, 1000 800 Test 2 Depth 8 ft. BH.2 600- P kPa 400 200 1001, POH 0 40kPa - -100 1 10 100 log mR R0 Figure 015. POH determination for Test 2, depth - 8 ft, for hole BH.2 G18 1000 Test 5 800 6-Depth ft. =23.0 BIT.2 600 P 400 kPa 200 100 POH =90kPa 0 -100 p j I Ip111S l IIh 1On 3.10 0 Figure G16. POH determination for Test 5, depth for hole BH.2 OH G19 -23.0 ft, 1000 Test 7 800 Depth = 26.5 ft. BH.2 600 P 400 kPa 200 OH= 135 kPa 0 0 -100 1 10 i00 log L 0 Figure G17. %H determination for Test 7, depth for hole BH 2 G20 - 26.5 ft, Total Horizontal at Rest Pressure, POW, kPa 0 50 100 150 200 0 250 *Estimated 5 10 ft. 1 20 25 30 35L Figure G18. Total horizontal at rest pressure profile 021 Coefficient of Earth Pressure At-Rest, K 0 0 0.4 0.8 1.2 1.6 2.0 0 10 Depth ft. 25 20 25 30 35 Figure G19. Coefficient of earth pressure at rest profile C22 In In ~44JNr4 Oco r-I 0 , e4n ONI qwcoio a%' cya~(o N 49r-i cc~N H *N r, H(o c coco co h-lu-bO H- .- . NM r '.O '0 4 00 00.r- r- - 0 OD M cc m N C~%In %0 .N0 0 qw ODO ON N-r-CD LO 0 I co cmr N, N M0 HN 0 O Ln cir-N(noN u-I In D0000 0 0n. 0 0 (N 0 rn 0 0 . In O00O~~G~0( W '.0r %D H 0 C4 (N( c, n co HIr 00 to ) (N 0 n NH Ln N Kr ID ,4 H H Nl '0 0444 fI 0 0 In H In 0 0 co cc (N %.0 r M Ho v D (N n (n r r c "1 H(N (N G23 m 0 r rnHc N~ 0 0oo in 4J Shear Strength Parameters 7. To compute the undrained shear strength, the shear stress versus strain curve is constructed from the PMT curve and the peak and residual strengths are obtained (Baguelin et al, 1978). In addition, the method devised by Gibson and Anderson (1961) was used to calculate the shear strength. For some tests, however, this last method is inaccurate because the strain level in the soil was not sufficient. The shear strength parameters derived from the PMT tests are tabulated in Table Gl and illustrated on Figure G20. Equivalent Modulus Computations 8. To compute the settlement of the proposed raft foundation 300-ft square, three methods have been used. 9. Briaud Method. This general method was proposed by Briaud (1979). The method consists in assuming a strain influence factor distribution with depth and to weigh the layer moduli according to the corresponding areas under that distribution. According to this method the equivalent reload pressuremeter modulus is 489,000 kPa or 70,894 psi. 10. (1967). Gibson Soil Method. This approach is based on the work by Gibson It assumes a constant Poisson's ratio of 0.5 and a flexible footing uniformly loaded with a pressure increase linearly with depth G(z) - q. The shear modulus - is assumed to z: mz (G1) G m G(z) - z E - (G2) 2(l+p)z The solution for the vertical displacement at the ground level under the center of the raft exerting a pressure q on such a Gibson soil is (Poulos and David 1974): q p (G3) - For this problem the assumed bearing pressure is 100 kPa (2 ksf); the design Er modulus profile gives settlement is m - 2778 kPa/ft (Figure G12). p - 0.22 inches. G24 The calculated Undrained Shear Strength, Sus kPa 200 0 0 400 600 800 I I l 1000 0 5 10 /1 - Depth ft. I 1 20 I 25 Gibson and An d e r s o n 2 5 - -\ 30 Residual .%-. * Estimated 35 Figure G20. Undrained shear strength profile G25 11. depth. The previous analysis assumes a linearly increasing modulus with In the case of a homogeneous, semi-infinite half-space, the solution for a circular, flexible, uniformly loaded area of diameter B is -2 qB(l P- E* s Let E* s p - 0.5 and equate equation G3 to G4. The equivalent homogeneous modulus can be obtained for a linearly increasing modulus profile 3qB q 4E* -m (G5a) s or E* s = m - 2778 kPa/ft B - 300 ft (G5b) 2 In this case: So that according to this second method the equivalent reload modulus is E* s - 1,250,000 kPa or 178,955 psi. 12. (1983). Menard Method. This method is described in detail by Briaud et al. The settlement equation requires the computation of an equivalent initial modulus Ei within a zone of influence 8B deep. The expression for this equivalent modulus is 2; + 4 where Ep/q _ +3/4/5 2"5E 6 /7 /8 1 + T 5E (G6) 29/16 is the harmonic mean of the moduli of layers p to q. For example, 3 1 E3/4/5 1 3 + E4 1 + E5 Using this method and a linear increase of the initial modulus with depth given by El(z) - 500z where equivalent initial modulus El(z) is in kPa and z is in ft, the Ed - 124,000 kPa (17,752 psi). G26 The settlement for a bearing pressure oi 0.54 in. is E* 100 kPa (2 ksf) according to Menard method is p - Using this settlement value and Equation G4, the equivalent modulus - 500,000 kPa (71,582 psi). s References Baguelin, F., Jezequel, J. F., and Shields, D. H. 1978. The Pressuremeter and Foundation Engineering, Trans Tech Publications, Clausthal, Germany Briaud, J.-L. 1979. "The Pressuremeter: Application to Pavement Design," PhD Dissertation, Civil Engineering Department, University of Ottawa, Canada Briaud, J.-L., Tucker, L. M., and Felio, G. Y. 1983. "Pressuremeter, Cone Penetrometer and Foundation Design," Short Course Notes, Texas A&M University, College Station, TX Casagrande, A. 1936. "The Determination of the Preconsolidation Load and Its Practical Significance," Proceedings, First International Conference on Soil Mechanics and Foundation Engineering, Vol 3, Cambridge, MA pp A0-64 Gibson, R. E. 1967. "Some Results Concerning Displacements and Stresses in a Non-homogeneous Elastic Half-space," Geotechnique, Vol 17, pp 58-67; Also 1968, Vol 18, pp 275-276; 1969, Vol 19, pp 160-161. Poulos, H. G. and Davis, E. H. 1974. Elastic Solutions for Soil and Rock Mechanics, John Wiley & Sons, pp 193-194. G27 II. CONE PENETRATION TEST by 1 Klopp Recep Yilmaz and Rick A. FUCRO INTER, INC. 10165 Harwin, Suite 170 Houston, TX 77036 2 Authorization 13. Authorization to conduct this work was given by Contract/Purchase Order No. DACW39-84-M-3972 dated 8 August 1984. Location 14. The location was approximately 15 ft to the east of an existing concrete slab and was identified in the field by a representative of the Waterways Experiment Station. Equipment 15. The CPT sounding was conducted using our Mobile Electronic Cone Penetrometer System unit as described in the enclosed brochure. The system is particularly designed for foundation design and earthwork control applications where reliable, accurate on-site measurements of subsurface properties are required. 16. One of the greater advantages of the cone penetrometer is the speed of operations which permits stratigraphy and engineering properties to be determined quickly and economically. Another important advantage is the continuous penetration record which permits location of thin strata that could easily be missed by conventinal drilling and sampling. 17. contains The entire system is mounted on a rugged, all-terrain truck which 11 system components including strip-chart recorders and data processing equipment. The sounding was conducted using an electronic friction sleeve penetrometer tip. The tip was hydraulically pushed into the ground at a constant rate of 2 cm/sec and a continuous record of tip bearing resistance 1 Senior Staff Engineer 2 Supervisor, Onshore Operations 028 and side friction resistance on a sleeve located just above the tip was Strip-chart records of tip and sleeve friction resistance were obtained. continuously plotted and available for immediate evaluation of soil conditions. The data was also stored on magnetic tape for computer processing. An accurate determination of stratigraphy was possible from the evaluation of tip resistance (q), sleeve friction resistance (fs), and friction ratio (fr). The latter being the ratio of fs to qc, expressed as a percentage, and determined by means of our office-based computer. It is used as the basis for soil classification. Tests Fugro conducted a single Cone Penetration Test (CPT) sounding to a 18. depth of approximately 12.5 meters. Based upon the friction ratio, the general soil conditions were determined and are presented along with the CPT log on Figure G21. A key to soil classification and symbols used on the CPT Due to the friction buildup along the cone log is presented on Figure G22. rods, the 20-ton thrust capacity of the truck was exceeded at approximately 12.5 meters and the sounding was terminated. The general soil profile consisted of a silty clay to clayey silt strata from about 3 to 12.5 meters and was overlain by a silty fill deposit. Analysis. 19. The methods of interpretation of CPT data depends on whether the soil responds to the cone penetration in a drained or undrained manner. As generally accepted, most soils which classify as silty clay respond to cone penetration in an undrained manner. The measured undrained shear strength of clayey soils in the laboratory depends significantly on the type of test used, the rate of strain, and the orientation of the failure planes. When evaluating the undrained shear strength Cu from cone penetration testing, the following equation is used C u U (8) c Nk where q = 2 rip resistance, kg/cm v = total unit weight, kg/cm 3 G29 iRICTION SLEEVE, KSF O 4 8 12 0 TIP RESISTANCE, KSF 8 16 24 32 0 RATIO, PERCENT 0 246 810 0 31 6 2 9 4 15 5 18 z21 ai- 71 o24 -a 278 30 -9 33 - 36 39 12 42 -- O 200 400 600 0 IkPO) Figure G21. 4 8 12 (Mp0)) 16 0 2 4 6810 PERCENT Results of cone penetration test G30 KEY TO SOIL CLASSIFICATION AND SYMBOLS SAMPLE TYPE (Shown In Soa/ee Co SOIL TYPE ( Shown in Symbol Column) Sand Sill Undisturbed Clayey silty Sandy FILL 8m) Clay Split Spobn Rock Core No Recovery PredominaiV type snhownheavy TERMS DESCRIBING GRAINED SOILS COARSE CONSISTENCY OR CONDITION (MajorPortion Retained on No. 200 Sieve) Includes (1) clean gravels a &and described as tine ,mndium or coarse,depereding on distribution of groin sizes 8,M) silty or clayey gravels Eksands (3) tine grained low plasticity soils (Pt - 10) such as sandy silts. Condition is rated according to relative density, as determined by tab tests or estimated from resistance to sampler penetration. Descriptive Term Loose Medium Dense Dense Very Dense *B81 FINE GRAINED SOILS Relative o0to 40 to T0 to 90 to Penetration Resistance * 0-t 10-30 30-50 Over 50 /FP 140 hamrl 30 -drop Density 400/ 70-7 90% tOO0%/ (major Portion Passing No. 200 Sieve) Includes (I) inorganic 8 organic silts a ctays,(2) sandy, gravelly or silty clays, EM3)clayey silts. Consistency is rated according to shearing streirgth,as indicated bypenetrometer reading or byimcoifined comnpression tests for Soils with P1 - 10 Descr iptive Term Very Soft Soft Firm Stiff Very Stiff Hard ArorC- Cohesive Shear Tons/Sq. Less Than 0.125 to 0.25 to 0.50 to 1.00 to 2.00 and SLICKOWSIVIEDAND I"ISSURCO CLAY MAY AIEv LWE(R OWCONFINEV coMPRESSIVE SrRpewltiS 7,rAN SHOeW ABIOVE,BECAUSE OF PLANES OY WEAKNESS on9SNRINKAGE CRACKS; Coms~sremcr RArivais cof sucm soILS ARE OASEO ON KANO FeN~rRAME-rR READINGS TERMS CHARACTERIZING paper thin in size Porting Seam SOIL STRUCTURE Fioccu~ated pertaining to cohesive soils thai exhibit loose knit or tlakey structure Slickensided honing inclined planes at weaknes that ore slick and glossy in appearance 1/8-3"ticka Layer greater tthan 3 Fissured coailning shrinkage crackSs,frvguentl~ tilled with finre Sand Of silt ,isualln more or less "ertical pertaining to cohesive soils that ore subject to appreciable loss of strength when renmolded Ieredd composedl of alternate layers ot different sotelhtyded ypesplanes soil Sensitive Laminated Strength Ft. 0.125 0.25 0.50 1 .00 2.00 Higher composed ot thin layers ot varying color and texture conainng Colcrnou aprecbleguadties~$.des calciu al uaiso tu Calar cotiigaple co~buncleinto Well Graded having wde ratuge i groin sizes and substiintiri omn'"Is of oll niermndtf pamir lS izes y Graoded pimedoinotel ot one gfoin tiZe. or hoving airange Pbor )f sites with some nIermr ,,redii 5it rnfi-qn DEGREE OF SLICKENSIDED DEVELOPMENT Slightly Slichensided slickensides present at intervals at 1'.2', soil does not eaisily break along these planes Moderately Sheeneled sickensides spaced at Internals of I -2 , soil breaks easily along these Extremely Slickensided coitinfliO and interconnected slic"en- soc.:ed at internals of 4 -12 Soi reaks a Wqnthe sliCiensides o-eces 3--6-- size Intensely Slscitensded sicernsies spaced at intervals of less than 4 .. continuous in ol directions ;Sort breaks down aiong planes ~info jlas 1/4"-2"in FUGRO INTEFR,INC Figure G22. Key to soil classification and symbols G31 size The z - depth, cm Nk - cone factor for tip value equals a Terzaghi-type bearing capacity factor for the cohesive Nk contribution to bearing, but is applied here to the small-diameter, deep foundation case represented by qc data. Evaluation of Nk 20. Nk does not possess a constant value, but varies with the stress- strain properties of the soil. lower Nk value is obtained. In general, the more sensitive the clay, the Fugro's experience in clayey soils and data presented by Lunne and Kleven (1981) marine clays, Nk shows that for normally consolidated falls between 11 and 19 with an average of 15. The estimation of the undrained shear strength in silty soils becomes more difficult and the above equations may not accurately define the strength where cone penetration may cause a partially drained soil response. As an example of the difficulties in a silty soil, consider Figure G23 which shows a plot of Nk qc/Cu against undrained shear strength for a Fugro test site. The undrained shear strengths were measured with triaxial undrained unconsolidated (uu) and selfboring pressuremeter (SBP) tests and were representative of normally consolidated marine silty clays. 21. In an effort to obtain an appropriate Nk factor, we have conducted an analysis of CPT data, laboratory results of borings for various geotechnical projects in the Texarkana area, information supplied by the Waterways Experiment Station, and our past experience with similar soils. 22. A determination of the overconsolidation ratio (OCR) by use of the CPT data showed the deposit to be moderately overconsolidated. Values of Nk between 15 and 30 for overconsolidated deposits are suggested by Toolan and Fox (1977). For the soils encountered we have used a lower bound of 25 and an upper bound of 35 for Nk and have plotted this data on Figure G24 along with the recommended mean. 23. From conversations between Lawrence Johnson of the Waterways Experiment Station and Rick Klopp of Fugro, the results from laboratory *Refer to references in this section, II. G32 CONE PENETRATION TEST 400 360 320 C4 240 zo N+ 00 20 8 0.1T0 66 2 46PTST a SBP TEST. A07 4- UU TEST, A07 40 00 12 14 COWM 16 18 20 FACTOR, N k VARIATION OF CONE FACTOR WITH SHEAR STRENGTH INTERPPETATIONJ OF CPT DATA IN SILTY S)OILS FUGRO INTER, INC. ConSuoing E.nginferSand Geologisfti Figure G23. Variation of cone factor with shear strength interpretation of CP'. data in silty soils G23 2 S IKENG'rH LJ 0 2 2 - (KG./CMA2) 4 6 .. .. _i- ..... FILL MATERIAL 1-- - -r IK NK = K 30 35 -- 10 Figure G24. Recommended value for Nk at test site G34 testing of samples for determination of undrained shear strength conducted by the Waterways Experiment Station show values somewhat lower than our recommended mean. We believe that this may be due to sample disturbance. Elastic Soil Modulus 24. Based on the above discussion concerning undrained shear strength, and provided that the cone resistance relates to an undrained soil response, the methods for determining Young's Modulus in clays should be relevant. estimation of undrained Young's Modulus EU can be made using empirical correlations with the undrained shear strength Eu where a - An Cu in the form QC u G9) is a constant that depends on stress or strain level, OCR, sensitivity, and other factors. The choice of the relevant stress or strain level is very important due to the non-linear behavior of soil. presents data that shows the variation of the ratio Eu/Cu Figure G25 with stress level for seven different normally consolidated cohesive soils whose plasticity index PI ranged from 15 to 75. Figure G26 shows the variation of Eu/Cu with OCR at two stress levels for the same soils presented on Figure G25. Based on Waterways Experiment Station supplied laboratory data, soil types numbers 3, 4, and 5 show the best correlation. Using the charts presented on Figure G26 and the OCR of the soil, we estimate that Eu/Cu approximates 200 to 400 and have presented this data with depth on Figure G27. the shear stress level is a factor which has great influence on example, low values of Eu/C u As discussed, Eu . For would be expected for highly plastic clays with a high shear stress level, and higher values for lightly loaded clays of low plasticity. The actual use of the level that should be utilized. Eu data also has an effect on the stress For example, axial loading on piles yields a lower level of strain than lateral loading and the corresponding value of Eu would change. 25. Silty soils present some difficulties for accurate and reliable inerpretations for classification and for fundamental soil conventional electric friction cone data. properties based on An important factor relates to whether cone penetration evokes a drained or undrained soil response. It is considered that silty soils will respond in an undrained or partially drained G35 C 2000 2000 I CL Cloy P1:15 St-O LL: 35 - "2 .20 LLz41 P1:22 3 Bangkok CH Clay LL:65 Pi:41 '27 4 Maine CH OH 29 Cloy LL:65 PI :38 AGS CH Cloy .26 PI:40 Atcha LL:71falaya 3 LL:95 6CH Clay P1=-75 4 Tailor River 5 Peal 60", . ' 200- E 200 "\ 100 - w 50 0 .24 % - CK U simple shear " " 80- .20 Boston CL Cloy - " 600 400 400-* " Portsmouth - 1000 800 U No. DESCRIPTION - tests 6040 40- 6 - All soils normally consolidated 7 20 -- 0.2 0.4 0.6 0.8 APPLIED SHEAR STRESS RATIO T n U Figure G25. Chart for determination of stiffness ratio interpretation of CPT data in silty soils (after Ladd et al 1977) T C u T C nu 1/3 2/3 U 1000 1 IMv- - I 800 .400 __ E600 400 500 -- C v, C '4 6 2 6 200 1 2 4 6 64 8 10 1 OCR . 2 4 6 6 8 10 OCR Figure G26. Chart for determination of stiffness ratio with respect to OCR interpretation of CPT data in silty soils (after Ladd et al 1977) G36 YOUNG'S MODOLL'S (KG/CMA2) 500' 1000') 1500 (3 I jI IFILLt [IMATERIf 2 -j X (f) _ 8 LJ E~ /C ± I '001 2 1-, . - - L i-i 10 12 Figure G27. Young's soil modulus with depth G37 manner. Overconsolidation effects in silty soils also complicates determination of geotechnical properties. Therefore a need for local correlation with laboratory results becomes necessary. Cone penetration testing is useful for determination of the undisturbed values of Cu and Eu although empirical correlations are required. References Ladd, C. C., Foott, R., Ishihara, K., Schlosser, F., and Poulos, H. G. 1977. "Stress - Deformation and Strength Characteristics," Proceedings of the Ninth International Conference on Soil Mechanics and Foundation Engineering, Tokyo, Japan, Vol II, pp 421-494 Lunne, T. and Kleven, A. 1981. "Role of CPT in North Sea Foundation Engineering," Symposium on Cone Penetration Testing and Experience, Geotechnical Engineering Division, American Society of Civil Engineers, pp 4975 Toolan, F. E. and Fox, D. A. 1977. "Geotechnical Planning of Piled Foundations for Offshore Platforms", Proceedings of the Institute of Civil Engineers, Vol 62, Part 1, pp 221-244 G38 III. PLATE LOAD TESTS by Department of the Army Fort Worth District, Corps of Engineers P. 0. Box 17300, Fort Worth, TX 76102 Table G2. Test Data Summary Test Location Material PB-l 35 ft E 15 ft N of A-26 Natural. Grade, el 365.33 ft 323 280 PB-2 25 ft W 65 ft N of A-26 Compacted Fill, el 365.33 ft 333 290 PB-3 15 ft N of A-26 21 in. below Fill 364 310 PB-4 38 ft E of A-14 Upper Midway Clay Shale, el 358.68 ft 150 150 PB-5 40 ft S 40 ft W of A-19 Compacted Fill, el 365.33 ft 470 385 PB-6 At L-29 Compacted Fill, el 365.33 ft 455 360 Coefficient of Subgrade Reaction Uncorrected, pci Corrected, pci C39 .020 .010 -. 120 .030 .0'10 .050 .060 .070 .080 KFill~j .{~%h1V 090 Ril qirii 0L 1 i Vt! LI 20 ~~ 401 .010 .02 .0L 0 .E~ 04 : Figure G28. .050 .060 Plate bearing test PB-2 .070 090 090 C . .010 .020 .030 .040 . U2 0 .050 .060 .070 **r ii .060 090 t 41V~ L I ______W,_ 0 7 1 40 .0 10. 02 0I . 0. 4005.060 .110 DEFORMATION IN INCHES Figure G30. 10 Plate bearing test PB-4 .070 .090 o 10 . .010 .020 .030 .040 .010 .020 .050 .040 .050 .060 .070 .060 .070 .080 090 b0L 40______ 0 .050 DEFORMATION Figure G32. 0 0 .010 Plate bearing test .050 .040 .030 IN INCHES PB-5 .060 .070 .080 .090 L!i 20U' 0 .020 .05003 .010 .020 .050 .040 .030 DEFORMATION Figure 033. .060 IN INCHES Plate bearing test PB-6 G4 2 .070 .080 .090 IV. a. PIEZOMETRIC DATA Permeability From Falling Head Tests Piezometer Tip Depth, Ft 1 80 1o8 2 50 10 - 8 3 40 Io8 4 26 i0 5 8 I05 6 5 i0 b. Permeability, cm/sec Water Head in Piezometers Piezometer No. and Head, Ft Date 1 6/14/85 8/23/85 11/15/85 2/13/86 6/02/86 8/25/86 2/09/87 5/12/87 5/25/88 29.31 8.59 7.34 6.32 0.77 0.10 dry dry dry 2 29.88 19.32 20.54 21.90 22.01 24.80 27.02 28.20 31.73 3 32.94 33.88 33.71 32.61 33.05 34.04 33.05 33.28 33.28 G43 4 19.29 20.17 199.37 18.21 19.27 20.25 18.85 18.42 19.42 5 6.18 5.47 2.80 1.54 4.27 5.13 1.25 3.83 0.30 6 2.76 2.02 dry dry dry 0.53 dry 0.30 0.40 V. Location A-i A-2 B-1 B-2 D-1 D-2 A-4 B-4 A-6 A-8 B-8 A-10 B-10 A-13 B-13 A-15 B-15 A-17 B-17 B-6 A-19 B-19 A-21 B-21 A-23 B-23 A-25 B-25 A-27 B-27 A-29 B-29 A-30 B-30 A-26 A.5-26 B-26 B.5-26 C-26 C.5-26 D-26 D.5-26 E-26 E.5-26 Original el, Ft 9/06/84 366.061 366.061 366.014 366.013 366.062 366.055 366.047 366.038 366.039 366.041 366.001 366.041 366.039 366.064 366.058 366.041 366.046 366.037 366.073 366.079 366.056 366.035 366.066 366.049 366.066 366.085 366.070 366.037 366.055 366.058 366.076 366.065 366.078 366.067 366.036 366.012 366.018 366.026 366.048 366.026 366.032 366.043 366.038 366.065 ELEVATION DATA Date and Change in Elevation, inches 10/31/84 01/28/85 08/28/85 06/05/86 05/12/87 -0.108 -0.048 -0.108 -0.036 -0.120 -0.036 -0.156 -0.108 -0.204 -0.252 -0.120 -0.336 -0.204 -0.252 -0.120 -0.156 -0.120 -0.192 -0.096 -0.036 -0.132 -0.084 -0.252 -0.156 -0.120 -0.084 -0.096 -0.108 -0.084 -0.012 -0.072 -0.036 -0.012 0.000 -0.012 0.000 0.036 0.024 0.048 0.012 0.000 -0.012 0.036 -0.024 -0.108 -0.096 -0.096 -0.060 -0.168 -0.084 -0.276 -0.216 -0.228 -0.312 -0.036 -0.360 -0.180 -0.252 -0.072 -0.132 -0.132 -0.084 -0.012 -0.084 -0.024 -0.024 -0.156 -0.096 -0.204 -0.168 -0.144 -0.180 -0.144 -0.072 -0.060 -0.060 0.048 0.048 -0.024 -0.036 -0.084 -0.024 0.012 0.348 0.240 0.312 0.288 0.192 -0.300 -0.216 -0.252 -0.060 -0.216 -0.084 -0.288 -0.096 -0.324 -0.456 -0.132 -0.588 -0.324 -0.456 -0.168 -0.348 -0.252 -0.360 -0.168 -0.036 -0.216 -0.228 -0.444 -0.360 -0.276 -0.120 -0.192 -0.108 -0.192 -0.036 -0.156 -0.072 -0.156 -0.168 -0.084 -0.072 -0.012 0.012 0.060 0.024 -0.036 -0.012 0.036 -0.036 -0.384 -0.372 -0.348 -0.228 -0.252 -0.192 -0.276 -0.336 -0.336 -0.372 -0.324 -0.504 -0.324 -0.408 -0.096 -0.132 -0.120 -0.288 -0.204 -0.108 -0.192 -0.132 -0.240 -0.348 -0.132 0.012 -0.192 -0.180 -0.204 -0.108 -0.096 -0.012 0.060 0.000 -0.096 -0.228 -0.120 -0.216 -0.180 -0.312 -0.384 -0.504 -0.288 -0.324 -0.204 -0.084 -0.132 0.108 -0.108 0.036 -0.264 -0.060 -0.312 -0.480 -0.132 -0.540 -0.276 -0.420 -0.096 -0.276 -0.192 -0.360 -0.132 0.012 -0.252 -0.144 -0.528 -0.456 -0.276 -0.120 -0.168 -0.084 -0.216 -0.048 -0.180 -0.084 -0.132 -0.108 -0.036 -0.036 0.024 0.060 0.132 0.012 -0.036 -0.144 0.060 0.024 G44 Original el, Ft 9/06/84 10/31/84 01/28/85 08/28/85 06/05/86 05/12/87 F-26 F.5-26 G-26 G.5-26 H-26 H.5-26 J-26 J.5-26 K-26 K.5-26 L-26 L.5-26 M-26 M.5-26 N-26 D-10 D-13 D-19 D-21 D-29 D-30 F-I F-2 G-3 G-5 G-8 H-i H-2 F-10 H-10 G-13 G-15 G-17 F-21 H-21 366.056 366.048 366.059 366.068 366.074 366.067 366.037 366.065 366.045 366.089 366.092 366.038 366.026 366.015 366.036 366.044 366.045 366.054 366.065 366.063 366.066 366.063 366.050 366.030 366.038 366.031 366.052 366.098 366.043 366.035 366.075 366.069 366.053 366.054 366.054 0.000 0.048 0.012 0.060 0.072 0.096 0.060 -0.012 -0.024 0.048 0.012 0.048 0.024 -0.012 0.012 -0.156 -0.120 -0.144 -0.780 -0.036 -0.036 -0.048 -0.276 -0.108 -0.120 -0.108 -0.132 -0.204 -0.024 -0.012 -0.132 -0.156 -0.132 -0.948 -0.720 0.132 0.240 0.096 0.180 0.156 0.228 0.084 0.036 -0.012 0.108 0.072 0.120 -0.024 0.012 -0.072 -0.228 covered -0.168 -0.804 -0.048 0.084 covered covered -0.084 -0.048 0.036 -0.012 -0.096 0.168 0.192 -0.060 -0.060 -0.120 -0.948 stack on -0.048 -0.060 -0.096 0.000 0.060 -0.288 0.264 -0.348 -0.174 0.000 0.048 0.024 -0.024 -0.108 -0.204 -0.288 -0.204 -0.192 -1.020 -0.324 -0.288 -0.120 -0.276 -0.120 -0.072 0.048 tiles on -0.120 0.000 0.012 -0.120 -0.108 -0.156 -1.044 -0.924 -0.288 -0.240 -0.228 -0.144 -0.084 -0.132 -0.252 -0.468 -0.516 -0.408 -0.384 -0.336 -0.408 -0.456 -0.540 -0.492 -0.444 -0.456 -1.200 -0.264 -0.204 -0.120 -0.276 -0.168 -0.336 -0.300 -0.012 -0.096 -0.060 -0.132 -0.384 -0.312 -0.204 -1.044 -1.128 0.000 0.012 0.144 0.024 0.108 0.108 0.012 -0.144 -0.252 -0.108 -0.072 -0.084 -0.132 -0.288 -0.420 -0.276 -0.204 -0.276 -1.152 -0.252 -0.132 0.072 -0.012 0.084 0.012 0.072 0.048 0.084 0.072 0.036 -0.060 -0.108 -0.144 -1.200 -0.984 G-23 F-24 G-25 F-27 366.074 366.077 366.074 366.055 -0.168 -0.012 -0.012 -0.024 -0.060 0.060 -0.060 0.084 -0.096 -0.024 -0.132 -0.144 -0.192 -0.420 -0.384 -0.156 -0.180 -0.060 -0.168 -0.156 G-27 F-29 H-29 F-30 H-30 K-I M-1 366.063 366.058 366.053 366.055 366.074 366.062 366.065 -0.012 0.036 0.012 0.084 0.012 -0.168 -0.120 -0.024 0.060 -0.012 0.096 -0.012 0.000 -0.036 -0.216 -0.264 -0.396 -0.360 -0.456 -0.144 -0.132 -0.324 -0.180 -0.252 -0.096 -0.264 -0.216 -0.180 -0.252 -0.168 -0.228 -0.120 -0.240 0.084 0.048 Location Date and Change in Elevation, inches G45 Location N-I K-2 M-2 N-2 M-4 N-4 M-6 N-6 M-8 N-8 K-10 M-10 N-10 K-13 M-13 N-13 M-15 N-15 M-17 K-19 M-19 N-19 K-21 M-21 N-21 M-23 N-23 M-25 N-25 M-27 N-27 K-29 M-29 N-29 K-30 M-30 N-30 Original el, Ft 9/06/84 366.052 366.070 366.070 366.082 366.061 366.035 366.053 366.053 366.051 366.070 366.052 366.035 366.058 366.065 366.088 366.070 366.012 366.050 366.042 366.051 366.022 366.008 366.026 366.002 366.043 366.041 366.047 366.061 366.059 366.061 366.051 366.042 366.051 366.066 366.062 366.062 366.071 Date and Change in Elevation, inches 10/31/84 -0.144 -0.180 -0.156 -0.144 -0.168 -0.168 -0.132 -0.144 -0.168 -0.144 -0.156 -0.096 -0.120 -0.132 -0.168 -0.156 -0.192 -0.168 -0.132 -0.120 0.000 -0.048 -0.660 -0.672 -0.624 -0.024 -0.108 -0.012 -0.132 -0.012 -0.048 -0.024 -0.036 -0.012 -0.036 -0.024 0.000 01/28/85 08/28/85 0.060 -0.084 -0.024 0.072 0.084 0.060 0.072 0.024 -0.036 0.036 0.000 0.180 0.108 -0.084 -0.168 -0.120 -0.120 -0.168 covered -0.192 0.000 -0.120 -0.408 -0,768 -0.720 -0.084 -0.132 -0.036 -0.192 0.012 -0.048 0.024 -0.024 0.072 0.060 0.108 0.144 -0.048 -0.120 -0.048 -0.024 0.024 -0.012 0.036 -0.060 0.024 -0.108 -0.156 -0.072 -0.168 -0.192 covered -0.300 -0.156 -0.288 -0.180 -0.204 -0.036 -0.204 -0.912 -0.948 -0.924 -0.180 -0.336 -0.168 -0.420 -0.084 -0.192 -0.300 -0.288 -0.288 -0.336 -0.300 -0.240 G46 06/05/86 05/12/87 -0.036 -0.300 -0.156 -0.048 -0.216 -0.084 -0.252 -0.324 -0.300 -0.408 -0.444 -0.204 -0.276 -0.528 0.168 0.204 0.252 0.264 0.240 0.180 0.228 0.108 -0.132 0.000 -0.144 -0.120 -0.132 -0.252 -0.456 -0.540 -0.648 -0.360 -0.504 -0.348 -0.504 -1.200 -1.308 -1.296 covered -0.648 -0.564 -0.816 -0.348 -0.432 -0.300 -0.276 -0.288 -0.360 -0.180 -0.144 -0.324 -0.156 -0.288 -0.192 -0.240 -0.084 -0.312 -1.080 -1.152 -1.260 -0.120 -0.528 -0.180 -0.480 -0.204 -0.372 -0.216 -0.288 -0.300 -0.180 -0.240 -0.240 VI. Celt EARTH PRESSURE DATA m-3 M-5A M-4 m-5 M-6 M-1 M-7 m-2 M-8 M-9 M-10 M-11 2 9 17 31 49 62 74 88 99 112 124 138 M-12 Distance From A-26, Ft Date 152 Earth Pressure, psi 07/26/84 07/27/84 08/03/84 08/17/84 09/07/84 11/08/84 02/12/85 06/05/85 08/23/85 11/15/85 2.86 2.41 3.29 3.16 0.00 4.21 1.00 0.45 1.29 0.15 2.14 0.90 2.00 1.95 3.86 2.86 3.43 8.12 3.57 15.94 1.93 0.00 0.00 0.00 0.00 0.00 1.04 7.26 15.85 21.63 3.22 4.15 6.76 0.31 0.00 0.92 0.00 0.15 0.31 0.00 3.02 1.43 1.75 0.00 0.00 0.00 1.11 0.48 0.00 0.00 3.33 4.44 4.03 0.00 0.00 0.83 4.03 2.22 1.81 2.08 1.49 3.88 1.79 0.00 0.30 1.04 2.09 1.79 2.24 2.09 3.82 0.00 0.76 0.00 0.00 0.15 1.98 1.53 1.22 1.07 3.17 0.00 3.02 0.00 0.00 0.43 1.01 0.86 2.16 1.73 2.83 3.54 3.54 0.00 0.00 0.00 0.28 0.14 0.00 0.00 4.98 1.18 5.11 3.41 2.23 2.23 1.44 1.84 1.31 0.92 3.82 6.47 3.97 0.88 0.44 2.50 2.79 4.85 3.38 3.68 3.11 4.81 2.02 3.88 2.95 4.04 3.42 5.43 5.28 5.43 02/13/86 06/02/86 08/25/86 02/23/87 05/12/87 05/25/88 3.43 3.71 4.00 4.71 4.86 5.43 26.52 29.04 28.55 27.26 27.56 25.19 1.54 0.77 0.92 2.00 2.15 2.92 0.00 0.00 0.00 0.00 0.79 1.27 3.89 2.08 1.95 3.47 2.22 2.36 3.13 2.54 2.69 3.43 3.28 4.18 2.14 1.83 1.53 2.60 2.60 2.14 1.58 2.45 2.73 2.88 3.60 4.60 0.00 0.00 0.00 0.00 0.00 0.42 0.26 1.44 0.92 1.05 1.97 1.84 1.76 5.88 7.52 7.65 9.71 7.94 3.88 7.30 9.02 9.00 10.09 7.92 19.55 26.92 36.10 42.26 42.71 40.90 VI. Gage SG-1 STRAIN GAGE DATA SG-2 SG-3 SG-4 SG-5 SG-6 SG-7 SG-8 SG-9 SG-1O 112 80 38 16 142 112 75 38 16 - 82 - 98 - 84 - 85 - 95 - 93 - 84 - 86 -102 -112 -110 -113 -120 -120 - 93 - 60 -89 -61 -25 -22 - 30 - 12 9 -20 - 35 - 15 - 12 - 23 - 53 - 20 - 26 14 -68 -78 8 -60 - 63 - 21 -26 -38 - 52 33 - 26 - 34 - 49 - 24 - 53 -187 Distance From A-26, Ft 141 Date 07/26/84 07/27/84 08/03/84 08/17/84 09/07/84 11/08/84 02/12/85 06/05/85 08/23/85 11/15/85 02/13/86 06/02/86 08/25/86 02/23/87 05/12/87 05/25/88 Strain, Microinches/inch 52 116 158 378 321 655 796 376 303 469 660 -266 -3149 57 - 59 -461 - - 77 - 85 - 47 60 175 219 2 39 110 1 1 2 - 23 - 53 -153 - 97 - 83 - 47 - 51 -159 -277 -333 -308 -349 -360 -367 -386 -394 - 56 -127 -105 -103 - 98 -180 -226 -231 -235 -261 -267 -288 -300 -326 - 91 -112 -109 -110 - 98 -122 -121 -135 -146 -163 -294 -193 -188 16 - 79 - 61 - 91 - 96 - 93 -126 -155 -148 -155 -199 -221 -260 -277 -329 - 91 57 83 68 70 4 39 5 5 55 123 128 33 315 335 5 - Note: Negative strains refer to tension; positive strains refer to compression G47