An Improved Smoothed Particle Hydrodynamics Method and Its Application in Rock Hydraulic Fracture Modelling

In this study, the smoothed particle hydrodynamics method was modified to the two-phase-improved kernel of smoothed particle hydrodynamics (2P-IKSPH). By mapping the water pressure of the water base particles to the solid base particles, the hydraulic fracturing processes of rock masses were realised in a set of unified equations, which could reduce the amount of calculation and improve calculation efficiency. The kernel function in the traditional SPH method was improved to realise the brittle fracture characteristics of solids. A solid-water coupling algorithm was also proposed to automatically transform the damaged solid base particles to water base particles; therefore, eliminating the need to search and regenerate the water base particles. The particle domain searching method was used to realise arbitrary generations of the initial fissure base particles, initial tunnel base particles, and initial water base particles. Three numerical examples are presented to illustrate the effectiveness of 2P-IKSPH, and the correctness of the proposed method was verified by comparison with previous experiments and numerical results. Finally, an engineering example of the progressive failure of a horseshoe-shaped tunnel during stress balance, tunnel excavation, and water filling was numerically simulated, indicating that 2P-IKSPH can be effectively applied to rock engineering.