Numerical modelling of fracture initiation and propagation in biaxial tests on rock samples

Abstract

A two-dimensional boundary element code, based on the displacement discontinuity method is used to simulate a confined compression test. The method takes account of the granular nature of the rock and of the presence of pre-existing defects. Fracture propagation is thought to depend, amongst other factors, on the crack orientation, the residual friction angle, the dilation angle, and the confining pressure. To obtain a more precise understanding of the influence of these properties on the crack growth process, their influence on the normal stress and the excess shear stress on potential fracture planes ahead of the crack tip are investigated for a single crack configuration. The orientation of the potential fracture planes proves to be the most important parameter determining fracture growth. A series of numerical experiments is carried out to determine the influence of the tessellation pattern used to represent the granular nature of the rock. Both the influence of the type of tessellation and the tessellation density are evaluated, and reasons for the differences in behaviour are presented. The results of the simulations with the Delaunay and a Voronoi tessellation with internal fracture paths compare well with the fracture pattern obtained in laboratory tests. The pre-peak non-linearity in the stress-strain response obtained with the Voronoi tessellation and the post-peak strain softening obtained with the Delaunay tessellation are combined in one model. For that purpose, a Voronoi tessellation with internal fracture paths is used, whereby the properties of the elements of the polygons and of the internal fracture paths are assigned different values. The role that is played by shear failure and the influence of dilation on the localization process is determined by means of some further numerical experiments. It is shown that at the scale, at which the material is modelled, shear failure is required for a shear band to develop.