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A computational methodology is described for simulating inelastic deformation and fracture of rock (in which a densely packed assembly of arbitrarily sized circular particles bonded together at their contact points represents the rock) using the distinct-element code PFC2D (Itasca, 1995a). Use of the distinct-element method allows dynamic stress waves to propagate through the assembly and allows the conglomerate to slip or separate, with unlimited displacement, under the action of applied forces. The PFC2D model of rock exhibits complex macroscopic behaviors such as strain softening, dilation, and fracture that arise from extensive microcracking throughout the bonded assembly. Such behavior is demonstrated by comparing synthetic properties with physical properties of Lac du Bonnet granite subjected to confined and unconfined compression tests. The PFC2D model produces a quantitative match of strength and deformation characteristics of Lac du Bonnet granite in terms of Youngs modulus and unconfined compressive strength as well as a qualitative match of micro-mechanical data in terms of micro-crack orientations and localizations.
Few materials of practical interest are perfect; rather, most materials contain some form of disorder (i.e., a spatial variation in local material properties). The length scale at which the disorder occurs has a large impact on the macroscopic material behavior, and the process of fracture, in particular, is extremely sensitive to disorder. For materials in which the disorder occurs at the atomic scale (e.g., metals which contain dislocations and inclusions), calculation of inelastic deformation and fracture can be based on a homogeneous model. Such materials typically develop a small number of well-defined fractures in response to quasi-static load application and can be modeled adequately by linear elastic and elasto-plastic fracture mechanics. For materials in which the disorder occurs at the mesoscopic scale (i.e., a scale much larger than the atomic one but still much smaller than the sample size e.g., rock and concrete, which consist of grains embedded within a matrix of cementing material), calculation of inelastic deformation and fracture should be based on a heterogeneous model. Such materials typically develop a large number of microcracks in response to quasi-static load application and have been modeled by a number of approaches, none of which is adequate for describing all aspects of the behavior. The approaches for modeling inelastic deformation and fracture of brittle heterogeneous materials such as rock can be classified into two categories, depending on whether damage is represented indirectly via its effect on constitutive relations or directly by the formation and tracking of a large number of discrete cracks. Most computational models used to describe the mechanical behavior of rock for engineering purposes are based upon the indirect approach, while those used to understand the behavior in terms of the progress of damage development and rupture are based upon the direct approach. In the indirect approach, the densely cracked material is treated as a continuum, and the constitutive relation can then exhibit strain-softening, a phenomenon where the matrix of tangential elastic moduli ceases to be positive definite (Bazant, 1986).
