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

Abstract

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 contactnormal 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) has been observed to approach a smaller strain trajectory as compared to the case 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.

3D DEM simulation of principal stress rotation in different planes of cross‐anisotropic granular materials

“…There are three main methods for imposing boundary conditions in DEM simulations: (1) rigid wall, (2) periodic boundary, and (3) flexible boundary. Rigid walls are the most widely used type of boundary . Li and Yu performed two‐dimensional DEM simulations of PSR with polygon samples enclosed by rigid walls.…”

“…Smaller initial density, larger stress ratio q / p , larger mean stress p , and larger intermediate principal stress ratio b all result in larger volume contraction in drained PSR tests. Noncoaxiality between the major principal directions of the stress tensor and the (plastic) deviatoric strain increment tensor is observed, while the classical theory of elasto‐plasticity gives coaxiality of stress and plastic strain increments. The macroscopic noncoaxiality is considered to originate from the evolution of fabric anisotropy and internal structures .…”

“…Many physical tests and Discrete Element Method (DEM) (as proposed by Cundall and Strack) simulations have been conducted to investigate the basic mechanical response of granular soils under PSR. With increasing number of PSR cycles, cumulative volume contraction (corresponding to increasing pore water pressure under undrained conditions) is noted .…”

“…Many physical tests and Discrete Element Method (DEM) (as proposed by Cundall and Strack) simulations have been conducted to investigate the basic mechanical response of granular soils under PSR. With increasing number of PSR cycles, cumulative volume contraction (corresponding to increasing pore water pressure under undrained conditions) is noted . Smaller initial density, larger stress ratio q / p , larger mean stress p , and larger intermediate principal stress ratio b all result in larger volume contraction in drained PSR tests.…”

Micro origins for macro behavior in granular media

“…Rotational cyclic loading has been a typical non-proportional test, widely encountered in soils during earthquake and offshore/coastal wave loads, and has been proven difficult to model within a continuum mechanical framework. Li et al [28] carried out 3D DEM simulations to examine the relation between deformation and fabric structure for a dense assembly subjected to a continuous rotation of the (applied) principal stress direction. Using the contact-based fabric tensor, they found that the rotation of the principle stress axes led to densification of their samples with greater coordination numbers and cyclically varying fabric anisotropy, as also reported by Kumar et al [17].…”