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An Effective Stress Equation for Unsaturated Granular Media in Pendular Regime University of Calgary PRISM: University of Calgary's Digital Repository Graduate Studies The Vault: Electronic Theses and Dissertations 2014-04-28 An Effective Stress Equation for Unsaturated Granular Media in Pendular Regime Khosravani, Sarah Khosravani, S. (2014). An Effective Stress Equation for Unsaturated Granular Media in Pendular Regime (Unpublished master's thesis). University of Calgary, Calgary, AB. doi:10.11575/PRISM/24849 http://hdl.handle.net/11023/1443 master thesis University of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission. Downloaded from PRISM: https://prism.ucalgary.ca UNIVERSITY OF CALGARY An Effective Stress Equation for Unsaturated Granular Media in Pendular Regime by Sarah Khosravani A THESIS SUBMITTED TO THE FACULTY OF GRADUATE STUDIES IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE DEPARTMENT OF CIVIL ENGINEERING CALGARY, ALBERTA April, 2014 c Sarah Khosravani 2014 Abstract The mechanical behaviour of a wet granular material is investigated through a microme- chanical analysis of force transport between interacting particles with a given packing and distribution of capillary liquid bridges. A single effective stress tensor, characterizing the ten- sorial contribution of the matric suction and encapsulating evolving liquid bridges, packing, interfaces, and water saturation, is derived micromechanically. The physical significance of the effective stress parameter (χ) as originally introduced in Bishop’s equation is examined and it turns out that Bishop’s equation is incomplete. More interestingly, an additional parameter that accounts for surface tension forces arising from the so-called contractile skin emerges in the newly proposed effective stress equation. Therefore, a so-called capillary stress is introduced which is shown to have two contributions: one emanating from suction between particles due to air-water pressure difference, and the second arising from surface tension forces along the contours between particles and water menisci. It turns out that the capillary stress is anisotropic in nature as dictated by the spatial distribution of water menisci, particle packing and degree of saturation, and thus engenders a meniscus based shear strength that increases with the anisotropy of the particle packing and the degree of saturation. The newly proposed effective stress equation is analyzed with respect to packing, liquid bridge distribution and strength issues. Finally, discrete element modelling is used to verify the micromechanical aspects of the proposed effective stress equation. ii Acknowledgments First of all, I am deeply indebted to my supervisor, Dr. Richard Wan, for his support, encouragement and constant guidance during my Master’s degree program. It was an honour for me to be a member of his research group, and I will be for ever grateful to Dr. Wan for giving me the opportunity to undertake graduate studies under his supervision and introducing me to deductive reasoning rather than inductive reasoning. I also would like to express my deepest gratitude to Dr. Bart Harthong and Mr. Mehdi Pouragha for their constructive comments and great help during my master’s thesis work. I am thankful to the Department of Civil Engineering and the Faculty of Graduate Studies at the University of Calgary for their financial assistance through teaching assis- tantships. This work was supported by the Natural Science and Engineering Research Council of Canada throughout my Master’s Program. Last but not least, I would like to address my sincere gratitude to Dr. Ron Wong, Dr. Jocelyn Grozic, Dr. Jeffrey Priest and Dr. Marcelo Epstein for accepting the favour of being in my examination committee. iii Dedication I dedicate this thesis to my parents, for their unconditional love and support! iv Table of Contents 1 Abstract ........................................ ii Acknowledgments .................................. iii Dedication ....................................... iv Table of Contents . v ListofTables ...................................... vii List of Figures . viii ListofSymbols..................................... xi 1 INTRODUCTION . 1 1.1 Introduction.................................... 1 1.1.1 Objectives . 2 1.1.2 Organization of Thesis . 3 2 LITERATURE REVIEW . 6 2.1 Introduction.................................... 6 2.2 Capillary Effect and Matric Suction . 6 2.2.1 Soil water characteristic curve . 13 2.3 Experimental Observations on Unsaturated Soil Behaviours . 18 2.3.1 Shear and tensile strengths of unsaturated soils . 18 2.3.2 Collapse behaviour . 24 2.4 Studies on Effective Stress of Unsaturated Soils - Existing Frameworks . 25 2.4.1 Phenomenological studies (Macroscale studies) . 26 2.4.1.1 Single effective stress approach . 26 2.4.1.2 Independent stress state variables approach . 30 2.4.2 Micromechanical studies . 34 2.5 Summary ..................................... 42 3 MICROMECHANICS OF EFFECTIVE STRESS IN MULTIPHASIC GRAN- ULAR MEDIA . 43 3.1 Introduction . 43 3.2 Force Transport in Dry Granular Media . 44 3.3 Force Transport in Saturated Granular Media . 47 3.3.1 Negligible contact area - rigid particles . 48 3.3.2 Finite contact area - compressible particles . 49 3.3.3 Effective stress in a fully saturated idealized compressible particle packing .................................. 51 3.4 Force Transport in Unsaturated Granular Media . 56 3.4.1 Effective stress parameters for idealized packing . 62 3.5 Summary ..................................... 67 4 COMPUTATION OF CAPILLARY STRESSES IN IDEALIZED GRANU- LAR PACKINGS . 69 4.1 Introduction . 69 4.2 Idealized Packing . 69 4.2.1 Simple cubic packing (SCP) . 70 v 4.2.2 Body-centeredcubicpacking(BCC). ... 71 4.2.3 Cubic Close Packing or Face Centered Packing (CCP or FCP).... 73 4.3 Theoretical SWCC for Regular Packing in Pendular Regime ......... 75 4.4 Effective Stress Parameters and Capillary Stress in RegularPacking . 80 4.4.1 Isotropicpackings ............................ 80 4.4.1.1 Effective stress parameters and capillary stresses in SCP and FCP............................... 80 4.4.1.2 Isotropic tensile strength in comparison with experimental results.............................. 85 4.4.2 Anisotropicpackings ........................... 90 4.4.2.1 Evolution of capillary stress in BCC packing-anisotropy aspects 90 4.4.2.2 Evolution of degree of anisotropy - link to strength issues. 93 4.5 Summary ..................................... 95 5 VALIDATION OF THE PROPOSED EQUATION USING DEM SIMULA- TION ....................................... 97 5.1 Introduction.................................... 97 5.2 Triaxial Tests Simulation at Various Controlled Matric Suctions . 98 5.2.1 Brief review on DEM modelling in unsaturated media . ...... 98 5.2.2 DEMsampledescription . 102 5.2.3 DEMtriaxialtestprocedureandresults . .... 103 5.2.4 Validation of the proposed effective stress equation with DEM simula- tionresults ................................ 108 5.3 Validation of the proposed effective stress equation using data from literature 111 5.4 Summary ..................................... 113 6 CONCLUSIONS AND RECOMMENDATIONS . 116 6.1 Conclusions .................................... 116 6.2 RecommendationsforFutureWork . 118 Bibliography ...................................... 120 A ToroidalApproximation ............................. 130 vi List of Tables 2.1 Review of the conventional modelling approaches in unsaturated soil mechan- ics(Buscarnera,2010) .............................. 33 4.1 Properties of BCC packings with various l′ ................... 72 4.2 SWCCcalculation ................................ 76 4.3 χij calculation................................... 81 4.4 Bij calculation................................... 82 4.5 Direct tensile test results of clean F-75 sand (Kim, 2001)........... 89 5.1 Simplified steps of DEM modeling of unsaturated granular media . 101 5.2 DEMsampleinputparameters. 103 5.3 Shear strengths of samples with various matric suctions,DEMresults . 105 5.4 DEM sample properties (Shamy & Groger, 2008) . ..... 112 vii List of Figures and Illustrations 2.1 Illustrationofsurfacetension . ...... 7 2.2 Waterincapillarytube. .. 8 2.3 Free body diagram of forces acting on air-water interfaceinacapillarytube 9 2.4 Curvedliquidandgasinterfaces . ..... 10 2.5 Conceptual demonstration of unsaturated sample in different regimes(Lu and Likos,2004) .................................... 11 2.6 Conventional soil water characteristic curve for sand and silt(Lu and Likos, 2004)........................................ 14 2.7 Demonstration of the ink-bottle effect during:(a)drying process and (b)wetting process(Marshalletal.,1996) . .. 15 2.8 Theoretical presentation of soil-water characteristic curve of an unsaturated sampleindifferentregimes(Luetal.,2007) . .... 16 2.9 General representation of shear strength in unsaturated samples (Ho and Fred- lund,1982) .................................... 18 2.10 Yield locus of glass beads R=46 micron (Pierrat et al., 1998)......... 20 2.11 Yield locus of glass beads R=90 micron (Pierrat et al., 1998)......... 20 2.12 Direct shear test results on cohesionless sands (DonaldI.,1956) ....... 21 2.13 Tensile strength versus water content (F-75-C),(Kim, 2001).......... 23 2.14 Tensile strength versus water content,(Kim,
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