Microscopic and macroscopic numerical simulation of the progressive failure of granular materials

Abstract

<p indent="0mm">The onset and propagation mechanisms of strain localization in granular materials have been analyzed from both discontinuous microscale discrete element modeling (DEM) and continuum mechanics-based finite element modeling standpoints. Through DEM, the mechanical response before and after the inception of strain localization is obtained. The evolution characteristics of the shear band are obtained by analyzing the relative displacement angle of particles. By analyzing the size effect of strain localization in granular materials, the relationship between the sample size-to-average particle size ratio and the thickness of the shear band is obtained. A generalized thermodynamics framework based on the micromorphic approach is adopted, where a nonlocal microvariable as an additional kinematics variable is introduced. An implicit gradient softening plasticity model considering pressure dependence is then proposed. The additional so-called Helmholtz partial differential equation is derived using the principle of virtual power and the second law of thermodynamics. A regularized finite element method coupling displacement and microvariable are proposed. Numerical simulations of plane strain compression tests show that the proposed numerical method can produce solutions, which are independent of the spatial discretization, verifying the applicability of the proposed model on regularizing ill-posed boundary value problems of strain-softening granular materials. Through analyses of the bearing capacity of the foundation and the stability of the tunneling surface, the effects of strain-softening behavior on the inelastic strain localization characteristics and macroscale mechanical responses are investigated. The results show that strain-softening behavior results in smaller active instability regions and more concentrated localized deformation.