学位論文 Discrete Element Simulations on Granular Materials under Generalized Three-Dimensional Stress System

Phusing Daraporn

内容記述
指導教員 : 鈴木輝一
Acknowledgements .............................................................................................................. iAbstract ............................................................................................................................... iiTable of Contents ............................................................................................................... ivList of Tables ................................................................................................................... viiiList of Figures .................................................................................................................... ixChapter 1 : Introduction .......................................................................................................... 11.1 Background ................................................................................................................... 11.2 Objectives ..................................................................................................................... 31.3 Organization of the dissertation .................................................................................... 3Chapter 2 Literature Review .................................................................................................. 52.1 Introduction ................................................................................................................... 52.2 The Influential Factors on Macro Behaviors and Microscopic of Granular Materials . 52.2.1 The intermediated stress ratio b value .................................................................... 52.2.2 Sample Density ...................................................................................................... 92.2.3 Interparticle Friction ............................................................................................. 102. 3 Fundamental Microscopic Description ...................................................................... 112.3.1 Micromechanical Data ......................................................................................... 112.3.2 Fundamental of Macro-Micro Relationship ......................................................... 122.3.3 Stress-Force-Fabric Relationship and Anisotropic Parameters ............................ 13Chapter 3 Discrete Element Method and Program OVAL ................................................... 173.1 Introduction ................................................................................................................. 173.2 Discrete Element Method (DEM) ............................................................................... 173.2.1 DEM Calculation Cycle ....................................................................................... 183.2.2 Law of Motion Implementation ........................................................................... 183.2.3 Force Displacement Law ...................................................................................... 213. 3 Computer program OVAL ......................................................................................... 223.3.1 Linear contact models .......................................................................................... 223.3.2 Periodic Space Boundary ..................................................................................... 233.3.3 Simulation Stability .............................................................................................. 243.3.4 Damping scheme .................................................................................................. 263. 4 Method to input stress rates for changing stress direction ......................................... 26Chapter 4 Macro-Micro Behavior under Continuously Varying b Value ............................ 284.1 Introduction ................................................................................................................. 284.2 Sample preparation and simulation program .............................................................. 304.3 Results ......................................................................................................................... 354.3.1 Stress-strain relationship ...................................................................................... 354.3.2 Dilatancy behavior ............................................................................................... 374.3.3 Principal Strain and Principal Deviatoric Strain .................................................. 414.3.4 Failure Surface, Stress Increment Vector and Strain Increment Vector .............. 414.3.5 Microscopic Evolution ......................................................................................... 494.3.6 Macro and Micro Relationship ............................................................................. 51Chapter 5 Stress-Force-Fabric Evolutions of Granular Materials under Continuously Varying b Value ..................................................................................................................... 535.1 Introduction ................................................................................................................. 535.2 Sample preparation and simulation program .............................................................. 555.3 Results ......................................................................................................................... 585.3.1 Stress-strain-dilation ............................................................................................ 585.3.2 Micromechanical behaviors ................................................................................. 605.3.3 Stress-Force-Fabric Relationship ......................................................................... 615.3.4 Stress-Force-Fabric Evolutions ............................................................................ 625.3.4 Increment Vectors of Strain and Anisotropy Coefficients ................................... 675.3.5 Deviatoric Anisotropy Coefficient Evolutions ..................................................... 67Chapter 6 Cyclic Behaviors of Granular Materials under Generalized Stress Condition .... 726.1 Introduction ................................................................................................................. 726.2 Sample preparation and isotropic compression .......................................................... 736.3 Simulation Program .................................................................................................... 756.4 Results ......................................................................................................................... 806.4.1 Stress-Strain-Dilation ........................................................................................... 806.5.2 Direction of Principal Strain Increment Vectors .................................................. 846.5.4 Micromechanical Response ................................................................................. 856.5.4 Macro-Micro Relationship ................................................................................... 88Chapter 7 Conclusions and Recommendations .................................................................... 937.1 Introduction ................................................................................................................. 937.2 Conclusions ................................................................................................................. 937.3 Recommendations ....................................................................................................... 96References ......................................................................................................................... 97
Most behaviors of granular materials have been studied under the limit conditions of stress paths, such as triaxial compression or extension tests where the intermediate principal stress σ2 has not been involved. In reality, granular materials are under generalized stress system where the major, intermediate and minor principal stresses σ1, σ2 and σ3 change continuously. The behavior of granular materials under generalized stress system is not well understood, particularly the relationships between the macro behavior and micro-scale response. Discrete Element Method (DEM), a numerical simulation, can simulate the macro behavior and explore the micromechanical behavior of granular materials. This study focused on the influence of intermediate stress ratio, specified by the b value [= (σ2-σ3)/(σ1-σ3)], on the mechanical behavior of granular materials under generalized stress system. There are three objectives of this research. The first is to simulate the macro behaviors and explore the micro characteristics of three-dimensional granular materials under continuously varying b value stress paths. The second one is to explain the relationship among the macro behaviors and microstructure parameters and load transmission in granular materials under continuously varying b value stress paths. And the third one is to describe the experimental phenomena of monotonic and cyclic loading tests on sand by using the micro variables. To this end, monotonic and cyclic loading under truly triaxial conditions, following the stress controlled method on 8,000 spheres, were simulated with continuously varying b value. For this research, it is found that DEM shows qualitative results of the macro behaviors of experiments of sand under monotonic as well as cyclic loading under continuously varying b value stress paths. The macro behavior and micro response data were described by the relationship between the stress ratio and fabric structures representing contacts of all particles as well as the strong contact regardless of the varying b value. Moreover, this study found that changing the b values continuously shows different distributions of the fabric and contact forces evolutions. The increments of anisotropy coefficients of average fabric, normal contact forces, and tangential contact forces differ depending on the b value. Furthermore, the continuously varying b value stress paths lead to change the increment directions of the stresses which cause some changes in the increment directions of those anisotropy coefficients. However, the differences in the directions of stress paths do not affect those anisotropy coefficients at the peak stress. Finally, the stress-force-fabric relationships under continuously varying b value stress paths were presented in terms of the anisotropy coefficients of fabric, normal contact forces, and tangential contact forces anisotropic. Regarding cyclic simulations, a qualitative comparison of the stress-strain-dilation between the DEM and experimental results under triaxial cyclic loading shows similarity tendency. Furthermore, micromechanical responses, indicated by coordination number and sliding contact fraction, can be used to explain the macro behavior in cyclic loading. Additionally, the macro-micro relationship is explained by using the relationship between stress ratio and fabric structures of all contacts, and only the strong ones. The study found that the unique macro-micro relationship does not depend on the more generalized cyclic stress path and the number of cycles.
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