An improved SPH method for simulating crack propagation and coalescence in rocks with pre-existing cracks

Abstract

An improved smoothed particle hydrodynamics (SPH) method is proposed to simulate the failure process of rock samples with pre-existing cracks under compression loads. By improving the kernel function of SPH, the brittle fracture characteristics of rock materials are captured. In the improved SPH, a prefabricated node segment (PNS) method is used to generate arbitrarily complex open or closed cracks, avoiding the kernel truncation caused by digging out particles. In order to improve numerical stability, the tension instability control (TIC) technique is embedded in the momentum equation. Moreover, the improved SPH adopts the coupled dynamic buffer solid boundary treatment algorithm, which reduces the configuration of boundary virtual particles, makes the application of boundary conditions more efficient. The accuracy of the improved SPH method and the feasibility of TIC technique are verified by a benchmark example. Then, the effect of the center dislocation spacing of the pre-existing cross crack on the failure mode and compressive strength of rock samples is studied. In addition, the effects of confining pressure on the coalescence type and penetration failure mode of cracks in a rock sample with two pre-existing cracks are also investigated. The numerical results agree well with the experimental results, which verifies the accuracy and validity of the improved SPH method.