Comprehensive simulations of rock fracturing with pre-existing cracks by the numerical manifold method

Rock is generally regarded as a heterogeneous and anisotropic material containing massive initial defects, such as cracks, joints, and porosities. In the present work, based on the maximum tensile stress and Mohr–Coulomb criteria, the fracturing modeling algorithm implemented into the numerical manifold method (NMM) is perfected and applied to a comprehensive simulation study of the fracturing of rock specimens. Disc and semi-disc specimens containing a single pre-existing crack, along with rectangular specimens containing two parallel pre-existing cracks, are simulated, respectively, to verify the fracturing modeling algorithm in terms of crack initiation, propagation, interaction, and coalescence. On this basis, four rectangular specimens containing multiple randomly distributing cracks are also simulated and the effective mechanical response of the specimen is investigated. The simulation of disc and semi-disc indicates that the crack initiation, propagation, and final crack path are all in great agreement with the experimental results. The simulation of rectangular specimens with two parallel pre-existing cracks shows the crack interaction and coalescence of the crack pairs. The results are also in good agreement with the experimental and theoretical results. For the simulation of complicated model with multiple cracks, results indicate that the increase in the crack density leads to a dramatic decrease in the effective elastic modulus and compressive strength as the evolution of pre-existing cracks. The NMM enriched with the fracturing modeling algorithm can be applied to solve more rock fracturing problems with diverse type and large number of initial defects.