Dependency of Dilatancy Ratio on Fabric Anisotropy in Granular Materials

Abstract

The relationship between dilatancy and anisotropy is a fundamental aspect of anisotropic behavior of granular materials. Existing test data directly investigating this relationship are scarce and conflicting. Discrete element biaxial and triaxial numerical tests on idealized granular materials in both two-dimensional (2D) and three-dimensional (3D) are conducted in this study to acquire high quality stress, strain, dilatancy, and fabric data for various anisotropic samples, which are utilized to analyze the dependency of dilatancy ratio on fabric anisotropy. The test results indicate that the dilatancy ratio is not only dependent on the initial fabric anisotropy, but is also influenced by the evolution of fabric, especially the contact normal fabric. At low deviatoric stress ratio under biaxial and triaxial loading, difference in initial fabric anisotropy of granular materials can lead to distinctly different dilatancy ratios. As loading continues, the deviatoric stress ratio, void ratio, and fabric of granular materials evolve toward the unique critical state, causing the dilatancy ratio to converge irrespective of its initial value. The anisotropic critical state theory (ACST) is shown to be capable of providing a framework for quantitative mathematical depiction of the dependency of dilatancy ratio on fabric anisotropy.

Three‐dimensional anisotropic plasticity model for sand subjected to principal stress value change and axes rotation

“…For the five fabric anisotropy‐related parameters || F nin ||, Δ 1 , Δ 2 , c 2, and c 3 , calibration should ideally be conducted based on measurements of fabric anisotropy under conventional triaxial loading on specimens with different initial fabric anisotropy. This is easily achieved when the fabric tensor can be directly measured, such as in DEM numerical tests, which has been exhibited in two recent works 27,29 . However, although technology for direct measurement of fabric is being developed for laboratory tests, 76,77 such measurements are still not easily achievable.…”

“…DEM numerical tests on virtual granular materials offer a convenient alternative. Though DEM test results may differ quantitatively from their physical world counterparts, studies have shown that the qualitative behavior patterns of sand can be reproduced for monotonic loading, 27,29,30 cyclic loading, 85,86 and PSAR 7,8,40,66 . Xue et al 8 proposed a 3D force‐line method to apply arbitrary stress boundary conditions on DEM specimens that allows for the application of any 3D stress paths, which enables simulations with principal stress axes rotating in any arbitrary plane as is in engineering reality.…”

“…Overcoming these limitations requires understanding of the dilatancy, 12,13,17,20,23 hardening, 12,17,20 noncoaxiality between strain rate and stress, 12,20,24 and fabric evolution and its effects 21,25–31 under PSAR , which can be enhanced not only by laboratory tests, 32–37 but also by discrete element method (DEM) 38 numerical tests, which allow for more control over stress path and easier microscopic observations 7,8,39,40 …”

Evolution of fabric anisotropy of granular soils: x-ray tomography measurements and theoretical modelling

“…The microstructure includes the arrangement of particles, voids and interparticle contacts. This microstructure has a significant influence on the behaviour of granular soils, in particular on the shear strength and dilatancy, as has been shown by experiments [2][3][4], micromechanical studies [5][6][7][8][9][10][11][12][13][14][15] and Discrete Element Method (as proposed in [16]; DEM for short) simulations [17][18][19][20][21][22][23][24].…”

On the evolution law of a contact normal-based fabric tensor for granular materials

“…induced anisotropy). Fabric anisotropy and its evolution may exert significant effects on the strength and deformation properties of discrete granular materials [1,4,17,[22][23][24], for example, the shear strength [20,[25][26][27], elastic moduli [28], non-coaxial plastic flow [29][30][31][32] and dilatancy [10,[33][34][35]. These behaviours of granular materials are closely associated with the stability and buckling of force chains at a mesoscopic scale and sliding and rolling at contacts, thus governed by the grain-scale structural characteristics and processes.…”