The Mohr-Coulomb model is still the most widely used constitutive model in soil and rock engineering for its generality, simplicity, and ease of calibration of material constants from routine experiments. The failure envelope evolves shear and tension failure. One non-physical behavior of the conventional Mohr-Coulomb constitutive model regarding the tensile failure is that the tensile plastic strain is assumed to be irreversible. Any reversal of the plastic strain that caused failure in tension results in immediate generation of the compressive stresses and, consequently, accumulation of irreversible volumetric strain. Typically, tensile fractures need to close completely before compressive stresses are generated in the direction perpendicular to the fracture. One consequence of this approximation in the Mohr-Coulomb model is that when material fails in tension during cyclic loading, it continuously dilates or increases in volume. This can be a problem, for example, in cases of dynamic response (e.g., earthquake or blasting) or deformation of the overburden above the undercut that involves opening of the cracks as the immediate roof collapses followed by closure of the cracks as the entire overburden subsides. The constitutive model presented in this paper (MohrT) is an extension of the Mohr-Coulomb constitutive model that considers tensile plastic strains to be reversible and prevents generation of compressive normal stresses (perpendicular to cracks) before cracks close. The general principles and its implementation in FLAC3D are presented. Several examples showing the benefits of this model compared to the conventional Mohr-Coulomb formulation are illustrated. One highlight of this model is that it requires no additional material constants compared to the conventional Mohr-Coulomb model.

1. Introduction

The Mohr-Coulomb model is one of the most widely accepted constitutive models and is available in almost all commercial software frameworks for soil and rock strength and deformation analyses. The shear yielding criteria of the Mohr-Coulomb model, which defines the shear strength of geomaterials at different effective stresses, is based on the classical Coulomb (1776) failure theory and the Mohr (1990) assumption that failure depends only on the maximum and minimum principal stresses. To define the tensile strength of materials, the Mohr-Coulomb model usually requires a tension yield criterion (tension cut-off) as well as the shear yield criteria. The Mohr-Coulomb model requires only six material parameters: two parameters (i.e., bulk and shear moduli) define elastic behavior of a material; another two parameters (i.e., friction angle and cohesion) characterize the shear strength; one (dilation angle) characterizes the flow rule; and the last parameter represents tensile strength. All the material parameters can be readily obtained from routine experiments.

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