A MULTIPLE-CRACK MODEL OF BRITTLE-FRACTURE .1. NON TIME-DEPENDENT SIMULATIONS

A numerical multiple-crack interaction model is developed to simulate the failure process in brittle solids containing significant populations of flaws. The model, which is two dimensional, allows for the growth of microcracks on a regular array of potential crack sites. Individual cracks may be oriented vertically, horizontally, or at 45-degrees to the sample axes. Quasi-static equilibrium equations are expressed in terms of finite difference approximations and are solved by applying a Renormalization Group theory approach. More than 5800 potential crack sites are included in the current version of the model. We have successfully duplicated a variety of brittle fracture phenomena observed in laboratory rock mechanics studies by employing a limited number of parameters and relations in the model. Included in the model are (1) Lame constants-lambda and mu for intact material, (2) a coefficient of friction for friction on cracks, (3) a normal stress-dependent crack closure algorithm and (4) an initial crack population. A fracture mechanics approach is used to determine crack growth. Approximate stress intensity factors are computed for all cracks, and when critical values are exceeded, cracks are allowed to grow in either mode I (tension) or mode II (in-plane shear). Simulations are performed by specifying a combination of stress and strain boundary conditions. The model is capable of duplicating experimentally observed features such as elastic moduli, dilatancy, acoustic velocities, peak strength, Mohr-Coulomb failure envelope and, to a limited degree, crack coalescence. A mode II critical stress intensity factor was required to produce a concave failure envelope, as is observed in laboratory experiments. This curvature in the failure envelope reflects a transition from mode I crack growth at low confining pressure to mode II growth at high confining pressure.