Evolution of granular media under constant-volume multidirectional cyclic shearing

Abstract

By means of the three-dimensional discrete element method, we study the long-time evolution toward liquefaction state in granular materials composed of spherical particles under multidirectional cyclic shearing at constant volume. Extensive simulations were carried out along 1-D linear, 2-D linear, circular/oval, and 8-like shear paths, and the evolution of the system was analyzed in terms of pore pressure, shear strain, and granular texture. The macroscopic stress path and stressstrain response agree well with laboratory experiments. We find that the liquefaction resistance, i.e., the number of cycles necessary to reach the liquefaction state, is generally lower under multidirectional loading as compared to unidirectional loading. As the transient vanishing of mean stress does not occur for all stress paths, we introduce a shear strain-based liquefaction criterion that can be consistently applied to all strain paths. The granular texture is monitored through the coordination number, particle connectivity, force and fabric anisotropies, and friction mobilization. In particular, a particlevoid descriptor, named centroid distance, is found to be closely related to the shear strain accumulation. We show that the force anisotropy tensors become almost proportional to the deviatoric stress tensor more quickly than the fabric anisotropy tensor, which takes most of the pre-liquefaction period to follow the external loading. The relationship between deviatoric stress ratio and the force and fabric anisotropies, known to hold in monotonic triaxial loading, also holds with high accuracy in the studied multidirectional cyclic shearing paths; the contributing weights of the anisotropies level off in the post-liquefaction period and do not depend on the shear path.

Effect of particle shape on cyclic liquefaction resistance of granular materials

“…This approach ensures that I consistently remains below 10 À3 prior to the occurrence of sample liquefaction. It is, however, important to note that I may exceed this threshold during the sample liquefaction due to unstable deformation and a significant decrease in p, as observed in previous DEM studies [33,62,63]. Such behavior is an intrinsic feature of cyclic liquefaction only and is not influenced by variations in the shear rate.…”

“…The value of l is retained as 0.5 during the subsequent cyclic shearing stage. This two-step isotropic compression procedure, adapted from [47], is a numerical technique employed to obtain samples with different densities, and has also been utilized in other recent studies [7,[60][61][62][63]. By setting l prep to 0 and 0.5 in the first step of isotropic compression, samples with extreme void ratios are obtained, typically representing the loosest and densest achievable states, respectively.…”

Multiscale modeling of granular dynamics on flowslide triggering and runout

“…However, it is known that small approximations in the contributions of peripheral particles can lead to significant and inaccurate calculation of the homogenized stress tensor. 45,46 Figure 4 illustrates the results of a constant-volume simple shear test on a loosely isotropically consolidated DEM sample, subjected to two different loading rates characterized by the dimensionless inertial number 𝐼. The cases with 𝐼 = 1e-4 and 2e-2 represent the quasi-static and dynamic loading conditions, respectively.…”

“…The DEM sample is prepared following a four‐stage sample preparation process 37,38 : (1) using a small tangential friction coefficient $$\mu =\mu _{\text{I}}$$ and compressing the sparse cell by moving the six rigid walls at a constant small velocity until the void ratio $$e$$ reaches 1.2; (2) setting the velocities of all six walls to zero and using a servo‐control algorithm to densify the sample isotropically to the target mean stress $$p=0.1\sigma _0$$ with the same $$\mu _{\text{I}}$$; (3) replacing the four lateral sides with periodic boundaries, increasing the target mean stress to $$0.2\sigma _0$$, and continuing isotropic compression with the same $$\mu _{\text{I}}$$; (4) modifying $$\mu =0.5$$ for further compressing the sample anisotropically to the final target stress state where three normal stresses reach $$\sigma _0$$ and shear stress $$\sigma _{zx}$$ equals $$\tau _0$$. It should be noted that the choice of $$\mu _{\text{I}}$$ determines the sample density.…”

“…The Love‐Weber formula is applicable in cases where no exterior contacts exist, such as a cubic DEM sample with all six sides as periodic boundaries. However, it is known that small approximations in the contributions of peripheral particles can lead to significant and inaccurate calculation of the homogenized stress tensor 45,46 …”