Analysis of crack coalescence in rock-like materials containing three flaws - Part II: Numerical approach

By using a Rock Failure Process Analysis code, RFPA2D, numerical simulations on samples of rock-like material containing three flaws under uniaxial compressive loading are conducted to investigate the failure mechanism and crack coalescence modes. The preexisting flaws are arranged in different systematic geometrics. Friction in closed flaws is modelled by inserting ideal elasto-plastic materials into the flaws. As the uniaxial compression load is increased, new cracks propagate from the flaws and eventually coalesce. The simulations replicate most of the phenomena observed in actual experiments, such as initiation and growth of wing and secondary cracks, crack coalescence, and the macro-failure of the sample. For the samples containing three pre-existing flaws, four types of crack coalescence mode are obtained: the tensile mode (T); the compression mode (C); the shear mode (S); and the mixed tension/shear mode (TS). The C mode is mainly formed by coalescence of small tensile fractures in the form of a shear band, and is believed to correspond to the formation and growth of en-echelon cracks. The applied load required to initiate coalescence depends on which mode (tensile or shear) dominates the coalescence process. A higher load is required to cause coalescence in the shear mode (S) than that for coalescence in the tensile mode (T) and mixed mode (TS). A total of four types of samples containing three parallel inclined frictional flaws and nine samples containing two parallel inclined frictional flaws are numerically simulated. It is concluded that crack coalescence will occur following the weakest coalescence path among all possible paths between any two flaws. The results obtained in the simulations are qualitatively in good agreement with experiments presented in Part 1 of the accompanying paper and other reported experimental observations.