Microscopic study of granular material behaviours under general stress paths

The granular material behaviour is determined by the local contact behaviour between particles and the spatial arrangement of particles. Investigation of particle-scale mechanism provides fundamental insights into global granular material behaviour. A multi-scale investigation has been carried out to study granular material behaviour under general stress paths using discrete element method (DEM). The commercial software Particle Flow Code in Three Dimensions (PFC3D) is employed for numerical simulations and the linear contact model is used to describe local contact behaviour. General loading paths were achieved by implementing a boundary control programme with independent control of both the magnitudes of three principal stresses and their principal directions. The intermediate principal stress ratio , where are the major, intermediate and minor principal stresses, and material anisotropy both had significant effect on granular material strength. The true triaxial simulation results indicated that the peak stress ratio was mainly contributed by the micro-scale contact force anisotropy. A smaller stress ratio was observed at greater a b value due to smaller degree of contact force anisotropy. Fabric anisotropy was another contributor to the material stress state. A lower peak stress ratio was obtained at a larger tilting major principal stress direction from the vertical deposition direction since smaller fabric anisotropy degree developed at larger . However, the material initial anisotropy had negligible effect on the critical stress ratio owing to the same contact force anisotropy and fabric anisotropy achieved. In true triaxial simulations, the intermediate strain increment rate ratio was generally larger than the stress ratio b since the particle-scale tangential force ratio was observed to be smaller than b value. The non-coaxial deformation observed in monotonic loading with various loading direction can be explained due to the non-coincidence between the principal fabric direction and the principal stress direction. And the degree of non-coaxiality decreased against shearing as the principal fabric direction approached loading direction gradually. The granular material response to rotational shear showed significant volumetric contraction and deformation non-coaxiality. The material internal structure rotated continuously along the principal stress rotation. The principal fabric direction did not exactly follow the rotation of principal stress direction. The fabric reorganisation mechanism accompanied by irrecoverable plastic deformation, leading to non-coaxial deformation behaviour. During rotational shear, the ultimate void ratio was determined by the stress ratio and b value but independent of initial void ratios. Under otherwise identical conditions, the greater internal structure anisotropy was observed at the higher stress ratio and at a greater b value, resulting in smaller ultimate void ratio (larger volumetric contraction). The general degree of deformation non-coaxiality decreased with increasing stress ratio and b value for rotational shear. The difference between the major principal stress direction and the major principal fabric direction was smaller at higher stress ratio and greater b value. It was interesting to note that the sample could fail during rotational shear, resulting in significant deviatoric strain developed in the first few cycles. The sample failed at a stress ratio , which was lower than the peak stress ratio obtained in monotonic loading but higher than the critical stress ratio . This indicated importance of considering stress rotation in geotechnical design and the material strength should be chosen based on the critical stress ratio rather than the peak value. The multi-scale investigation of granular material explains the strength characteristics from the micromechanical point of view. Observations on the fabric evolution have been made under various loading conditions. This may be useful information for the development of an advanced constitutive model

Microscopic study of granular material behaviours under general stress paths

The granular material behaviour is determined by the local contact behaviour between particles and the spatial arrangement of particles. Investigation of particle-scale mechanism provides fundamental insights into global granular material behaviour. A multi-scale investigation has been carried out to study granular material behaviour under general stress paths using discrete element method (DEM). The commercial software Particle Flow Code in Three Dimensions (PFC3D) is employed for numerical simulations and the linear contact model is used to describe local contact behaviour. General loading paths were achieved by implementing a boundary control programme with independent control of both the magnitudes of three principal stresses and their principal directions. The intermediate principal stress ratio , where are the major, intermediate and minor principal stresses, and material anisotropy both had significant effect on granular material strength. The true triaxial simulation results indicated that the peak stress ratio was mainly contributed by the micro-scale contact force anisotropy. A smaller stress ratio was observed at greater a b value due to smaller degree of contact force anisotropy. Fabric anisotropy was another contributor to the material stress state. A lower peak stress ratio was obtained at a larger tilting major principal stress direction from the vertical deposition direction since smaller fabric anisotropy degree developed at larger . However, the material initial anisotropy had negligible effect on the critical stress ratio owing to the same contact force anisotropy and fabric anisotropy achieved. In true triaxial simulations, the intermediate strain increment rate ratio was generally larger than the stress ratio b since the particle-scale tangential force ratio was observed to be smaller than b value. The non-coaxial deformation observed in monotonic loading with various loading direction can be explained due to the non-coincidence between the principal fabric direction and the principal stress direction. And the degree of non-coaxiality decreased against shearing as the principal fabric direction approached loading direction gradually. The granular material response to rotational shear showed significant volumetric contraction and deformation non-coaxiality. The material internal structure rotated continuously along the principal stress rotation. The principal fabric direction did not exactly follow the rotation of principal stress direction. The fabric reorganisation mechanism accompanied by irrecoverable plastic deformation, leading to non-coaxial deformation behaviour. During rotational shear, the ultimate void ratio was determined by the stress ratio and b value but independent of initial void ratios. Under otherwise identical conditions, the greater internal structure anisotropy was observed at the higher stress ratio and at a greater b value, resulting in smaller ultimate void ratio (larger volumetric contraction). The general degree of deformation non-coaxiality decreased with increasing stress ratio and b value for rotational shear. The difference between the major principal stress direction and the major principal fabric direction was smaller at higher stress ratio and greater b value. It was interesting to note that the sample could fail during rotational shear, resulting in significant deviatoric strain developed in the first few cycles. The sample failed at a stress ratio , which was lower than the peak stress ratio obtained in monotonic loading but higher than the critical stress ratio . This indicated importance of considering stress rotation in geotechnical design and the material strength should be chosen based on the critical stress ratio rather than the peak value. The multi-scale investigation of granular material explains the strength characteristics from the micromechanical point of view. Observations on the fabric evolution have been made under various loading conditions. This may be useful information for the development of an advanced constitutive model

Macro deformation and micro structure of 3D granular assemblies subjected to rotation of principal stress axes

This paper presents a numerical investigation on the behavior of three dimensional granular materials during continuous rotation of principal stress axes using the discrete element method. A dense specimen has been prepared as a representative element using the deposition method and subjected to stress rotation at different deviatoric stress levels. Significant plastic deformation has been observed despite that the principal stresses are kept constant. This contradicts the classical plasticity theory, but is in agreement with previous laboratory observations on sand and glass beads. Typical deformation characteristics, including volume contraction, deformation non-coaxiality, have been successfully reproduced. After a larger number of rotational cycles, the sample approaches the ultimate state with constant void ratio and follows a periodic strain path. The internal structure anisotropy has been quantified in terms of the contact-based fabric tensor. Rotation of principal stress axes densifies the packing, and leads to the increase in coordination numbers. A cyclic rotation in material anisotropy has been observed. The larger the stress ratio, the structure becomes more anisotropic. A larger fabric trajectory suggests more significant structure re-organization when rotating and explains the occurrence of more significant strain rate. The trajectory of the contact-normal based fabric is not centered in the origin, due to the anisotropy in particle orientation generated during sample generation which is persistent throughout the shearing process. The sample sheared at a lower intermediate principal stress ratio (b=0.0) (b=0.0) has been observed to approach a smaller strain trajectory as compared to the case b=0.5 b=0.5 , consistent with a smaller fabric trajectory and less significant structural re-organisation. It also experiences less volume contraction with the out-of plane strain component being dilative