Mathematical Modeling Of Progressive Cracking And Fracture Of Rock

Due to their heterogeneity, most rocks fracture with a zone of distributed cracking ahead of the fracture front. This makes linear elastic fracture mechanics inapplicable. The present study describes a mathematical model in which the progressive microcracking is taken into account by strain-softening stress-strain relation. In a simpler version of the model, the triaxial strain-softening stress- strain relation is obtained by direct adjustment of the elements of the compliance matrix. This formulation is rigorous only if the principal stress directions do not rotate during fracture formation within the fracture process zone. As a more sophisticated and generally applicable model, the so-called microplane model which is an analogue of the slip theory of plasticity is outlined. Comparison with fracture data for various rocks are given.