Rate effects in dense granular materials: Linear stability analysis and the fall of granular columns

Abstract

SUMMARYIn this paper, the suitability of rate-dependent constitutive relationships to model the rheology of granular materials is investigated. In particular, the formation of shear bands as predicted by this approach is studied. First, a rate-dependent model is investigated in terms of a linear stability analysis. It turns out that at low to moderate strain rates, the orientation of shear bands tends to vary from the so-called Roscoe and Coulomb solutions towards a unique admissible orientation with an increase of the so-called inertial number I . This effect is confirmed by numerical simulations of a compression test performed with a particle in cell finite element program. To further assess the validity of continuum approaches for the simulation of dense granular flows, a quasi-static fall of a granular column is studied numerically and the results are confronted to available experimental data. It is shown that a satisfying agreement is obtained at different aspect ratios and for the two materials investigated in this paper, i.e. sand and glass beads. The results reported in the present paper demonstrate the relevance of continuum approaches in the modelling of dense granular flows.

Stress-strain behavior of sand at high strain rates

“…They reported that while the Mohr-Coulomb theory approximates measured shear band inclinations closely at low strain rates of loading, under HSR loading the two measurements deviate by up to 10 . Recent numerical analyses also suggest a change in the orientation of the shear band in sand as strain rates increase [136,137]. These studies also suggest a change in thickness of the shear band with increasing strain rate.…”

“…22 suggests that increasing the confining pressure apparently magnifies the increase in dilation rate at failure. The increase in rate of dilation may be attributed to the decrease in grain fracture in two ways: (1) as grain fracture is prohibited under HSR loading shear may be accommodated only through further rolling and rearrangement of grains [43,136], and (2) Reduction in grain fracture decreases the associated local contraction, thereby magnifying the role of dilation in the global response.Indications of the latter mechanism have been observed in quasi-static loading as well [42]. Considering the importance of the aforementioned discussion, further research is required in order to understand the effects particle crushing, particle size, shape and mineralogy on HSR response of sand at various confining pressures.…”

Styles of rifting and fault spacing in numerical models of crustal extension

“…Normal fault dips have a diffuse volume distribution between 40 and 60 ∘ , where normal faults are thought to first form with steep dips and then rotate as extension progresses [ Jackson , ]. Upon examination of the difference between the angle distributions of models using the Drucker‐Prager rheology in comparison to models using Anisotropic Frictional Rheology, both in two and three dimensions, the slip plane angle distributions resulting from the models using Anisotropic Frictional Rheology had modal values closer to the predicted angles from Mohr‐Coloumb theory [ Lemiale et al , ], whereas models using the Drucker‐Prager rheology had modal values matching Arthur or Roscoe orientations [ Kaus , ].…”

Solid–fluid transition modelling in geomaterials and application to a mudflow interacting with an obstacle

“…Many models belong to this family: from very simple ones (for instance, Bingham's model, Figure a) to much elaborated ones (for example, the model developed by Jop et al . for dense granular flows and successfully applied with a Lagrangian integration point finite element method (FEM) in ). However, their main drawback is that, even if the flowing domain is bounded by what can be considered as a solid–fluid transition criterion, the solid behaviour inside this surface (in the stress space) is not defined.…”