Evaluation of Three Weight Functions for Nonlocal Regularization of Sand Models

Abstract

Nonlocal regularization is frequently used to resolve the mesh dependency issue that is caused by strain softening in finite-element (FE) simulations. Some or all variables that affect strain softening are assumed to depend on the local, neighboring, or both in this method. The weight function is the main component of a regularization method. There are three widely used weight functions, which include the Gaussian distribution (GD), Galavi and Schweiger (GS), and over-nonlocal (ON) functions. All of them could alleviate or eliminate the mesh dependency in simple boundary value problems (BVPs), such as plane strain compression; the evaluation of their performance in real-world BVPs is rare. A detailed comparison of these functions has been carried out based on an anisotropic sand model that accounts for the evolution of anisotropy. The increment of void ratio is assumed nonlocal. All functions give mesh-independent force–displacement relationships in drained and undrained plane strain compression tests. The shear band thickness shows a small variation when the mesh size is smaller than the internal length. None could eliminate the mesh dependency of shear band orientation. The GS method is the most efficient in eliminating the mesh dependency in the strip footing problem. The ON method could give excessive overpredictions of the volume expansion around strip footings, which leads to unrealistic low reaction forces on strip footings at large deformations. All three weight functions give mesh-independent results for the earth pressure that acts on a retaining wall.