A new strategy for discrete element numerical models: 1. Theory

Abstract

A new derivative of the particle‐based discrete element method (DEM) for computationally modeling the mechanics of granular materials is suggested. In contrast to the conventional DEM, the new stress‐based discrete element method (SDEM) presented here is formulated using a macroscopic parameterization, lending itself well for structural geomodeling for which the Mohr‐Coulomb constitutive relation is the underlying model assumption. In SDEM, consistency exists between the macroscopic properties of a particle assembly and the microscopic parameters specified for each particle, unlike for the standard DEM for which microscopic and macroscopic properties can at best be calibrated through troublesome testing experiments. Importantly, this consistency allows for modeling realistically unforced formation and growth of faults and shear zones, with orientations as predicted by Mohr‐Coulomb theory and in agreement with general observations. By measuring the virtual deformation of spherical elastic particles rather than just virtual particle overlaps, this new formulation introduces strain rate and stress tensors at the particle level. Strain rates are obtained by adopting interpolation techniques from the methodology of meshless continuum methods like smoothed particle hydrodynamics, while the appealing discrete kinematic of DEM, including inherent dilatation effects and stick‐slip instabilities, is preserved as particles interact by finite contact forces. The SDEM theory, the computational strategy, and test examples are presented here. In the companion paper, SDEM computational “sandbox‐type” models illustrate the method's potential for contributing insight into the dynamics and kinematics of more advanced geomechanical processes.