FINITE ELEMENT METHOD ANALYSIS OF SLABS ON ELASTIC HALF .

FINITE ELEMENT METHOD ANALYSIS OFSLABS ON ELASTIC HALF SPACEEXPANSIVE SOIL FOUNDATIONSA DissertationbyRIFAT BULUTSubmitted to the Office of Graduate Studies ofTexas A&M Universityin partial fulfillment of the requirements for the degree ofDOCTOR OF PHILOSOPHYDecember 2001Major Subject: Civil Engineering

FINITE ELEMENT METHOD ANALYSIS OFSLABS ON ELASTIC HALF SPACEEXPANSIVE SOIL FOUNDATIONSA DissertationbyRIFAT BULUTSubmitted to Texas A&M Universityin partial fulfillment of the requirementsfor the degree ofDOCTOR OF PHILOSOPHYApproved as to style and content by:Robert L. Lytton(Chair of Committee)Kirk W. Brown(Member)Dallas N. Little(Member)Calvin E. Woods(Member)John M. Niedzwecki(Head of Department)December 2001Major Subject: Civil Engineering

iiiFinite Element Method Analysis of Slabs onElastic Half Space Expansive Soil Foundations(December 2001)Rifat BulutB.S., Middle East Technical University;M.S., Texas Tech UniversityChair of Advisory Committee: Dr. Robert L. LyttonABSTRACTA finite element computer program has been developed to analyze slabs on elastic half space expansive as well ascompressible soils. Mindlin orthotropic plate theory is adopted for structural analysis of ribbed or constant thickness slabs. Thefoundation soil is assumed to be an isotropic, homogeneous, and elastic half space. The behavior of an elastic half space iscalculated by dividing the surface of the elastic half space into rectangular regions. These regions are represented by stiffnessmatrices and they are assembled onto the rectangular plate finite elements.The shape of the soil surface underneath the slab is described by the differential soil movement (y m) and edge moisturevariation distance (e m). The mounded soil surface requires an iterative procedure in the computer program for this soil-structureinteraction system. The program calculates displacements, moments in x- and y-directions, twisting moments, and shear forces.The comparisons of the results with the Post Tensioning Institute’s (PTI) Design and Construction of Post-Tensioned Slabs-onGround manual examples show that the PTI analysis is conservative for the center lift case, but is not conservative for the edge liftcase.ACKNOWLEDGMENTSI am deeply grateful to my advisor Dr. Robert L. Lytton for his constant support, valuable guidance and inspiration during thecourse of my stay at Texas A&M University. I am fortunate to have had the opportunity of learning from him. I greatly appreciatehis advice, encouragement, guidance, and financial support, which made the completion of this dissertation possible.I would like to thank Dr. Kirk W. Brown, Dr. Dallas N. Little, and Dr. Calvin E. Woods for serving as the advisorycommittee and Dr. Gerald R. Bratton for serving as the graduate council representative. I would also like to extend my thanks toDr. J. N. Reddy for his help with the finite element method and its programming techniques.Finally, I am deeply indebted to all the members of my family for their constant support and encouragement.

ivTABLE OF CONTENTSPageABSTRACT .ACKNOWLEDGMENTS .TABLE OF CONTENTS .LIST OF FIGURES .LIST OF TABLES .CHAPTERIINTRODUCTION.1.1 The Problem.1.2 Background.1.3 Objective of Study.1.4 Outline of Dissertation.IIBACKGROUND OF RIBBED SLABS ON EXPANSIVE SOILS .2.1 Introduction.2.1.1 Volume Change Behavior of Expansive Soils .2.1.2 Structural Analysis of Slabs.2.2 Existing Design Methods.2.2.1 The Building Research Advisory Board (BRAB) Method .2.2.2 Lytton’s Method .2.2.3 Walsh’s Method .2.2.4 Fraser and Wardle Method.2.2.5 The Post Tensioning Institute (PTI) Method .2.3 Design Parameters y m and e m .2.3.1 The VOLFLO Program .2.3.1.1 Theory of Volume Change and Horizontal Moisture Flow as in VOLFLO .2.3.1.2 Naiser’s Study of Predicting Vertical Soil Movement .2.3.1.3 Mitchell’s Method of Predicting Suction Distribution in a Soil Profile .2.3.2 Edge Moisture Variation Distance .2.4 This Study.IIISOIL SUCTION AND EXPANSIVE SOILS .3.1 Soil Suction Concept .3.2 Soil Suction Measurement .3.2.1 The Filter Paper Method .3.2.1.1 Background of the Filter Paper Method .3.2.1.2 Calibration of the Filter Papers .3.2.1.3 Soil Total and Matric Suction Measurements with the Filter Papers .3.2.2 Thermocouple Psychrometers .3.2.3 Transistor Psychrometers .3.2.4 Pressure Plate and Pressure Membrane .3.3 Expansive Soils .3.3.1 Clay Minerals .3.3.1.1 Kaolinite Minerals .3.3.1.2 Illite Minerals .3.3.1.3 Montmorillonite Minerals .3.3.2 Summary .IVFOUNDATION MODEL .4.1 Introduction .4.2 Foundation Models .4.2.1 Pasternak Foundation .4.2.2 Hetenyi Foundation .4.2.3 Filonenko-Borodich Foundation .4.2.4 Vlasov Foundation .4.3 Elastic Half Space (or Elastic Continuum) Foundation .4.3.1 Soil Parameters Es and νs .4.3.1.1 Poisson’s Ratio νs .4.3.1.2 Modulus of Elasticity 617171718181819191919192020202121212121242424

vTABLE OF CONTENTS (Cont’d)PageVPLATE THEORY AND FINITE ELEMENT METHOD .5.1 Introduction .5.2 Plate Material Properties .5.3 Finite Element Model of Kirchhoff Plate Theory .5.3.1 Principle of Virtual Work .5.3.2 Displacement Function for the Finite Element Model .5.4 Finite Element Model of Mindlin Plate Theory .5.4.1 Displacement Function .5.4.2 Application of Virtual Work .5.4.3 Interpolation Functions for the Finite Element Model .VIDESCRIPTION OF COMPUTER PROGRAM .6.1 Introduction .6.2 General Description .6.2.1 Slab Geometry .6.2.2 Beams .6.2.3 Loading .6.2.4 Evaluation of Contact .6.2.5 The Output .6.3 General Outline of the Program .6.3.1 The Program Subroutines .VII APPLICATIONS OF THE COMPUTER PROGRAM.7.1 Introduction .7.2 Verification of the Computer Program .7.2.1 Example One .7.2.1.1 Example One Center Lift Analysis .7.2.1.2 Example One Edge Lift Analysis .7.2.2 Example Two .7.2.3 Example Three .VIII SUMMARY, DESIGN TOOLS FOR SLABS ON EXPANSIVE SOILS .8.1 Introduction .8.2 Soil Movement .8.2.1 VOLFLO-2 .8.2.2 Soil Movement Tables .8.3 Estimating Volume Change Coefficient .8.4 Edge Moisture Variation Distance (e m) .8.5 Structural Analysis of Slab on Expansive Soil.IXCONCLUSIONS AND RECOMMENDATIONS.9.1 Conclusions .9.2 Recommendations for Future Enhancement of the Program .REFERENCES .APPENDIX A .APPENDIX B .APPENDIX C .APPENDIX D .APPENDIX E .APPENDIX F .APPENDIX G .APPENDIX H .APPENDIX I 909192

viLIST OF 37.47.57.67.77.87.97.108.18.28.38.4PageTypical Environmental Effects on a House Foundation .

FINITE ELEMENT METHOD ANALYSIS OF SLABS ON ELASTIC HALF SPACE EXPANSIVE SOIL FOUNDATIONS A Dissertation by RIFAT BULUT Submitted to the Office of Graduate Studies of Texas A&M University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY December 2001 Major Subject: Civil Engineering