Numerical Simulation of Rock Thermal Fracture Considering Friction Effect in the Framework of Smooth Particle Hydrodynamics Based on Total Lagrangian Formula

In the framework of smoothed particle hydrodynamics based on total Lagrangian formula (TLF_SPH), a new coupled thermo-mechanical bond-based TLF_SPH (TM-BB-TLF_SPH) method considering the friction effect is proposed to simulate the thermal fracture process of rocks. In the TLF_SPH program, the interaction between particles is represented by virtual bonds. According to the Hoek–Brown strength criterion, the fracture of virtual bonds between particles is determined, and then, the fracture mode of rock can be captured during the thermal cracking process. The unbroken virtual bond can not only bear compressive stress and friction between particles, but also bear tensile stress and shear stress between particles, while the broken virtual bond can only bear compressive stress and friction between particles. Moreover, the hybrid friction contact (HFC) algorithm based on particle–segment contact and particle–particle contact is embedded in the bond-based TLF_SPH thermo-mechanical coupling model to simulate the frictional behavior between solid particles, and the contact force between solid particles is expressed based on the partial penetration criterion. Compared with the friction algorithm based on particle–particle contact in GPD framework and particle–segment contact in SPH framework, the HFC algorithm in TLF_SPH framework is more efficient, stable, and accurate. Finally, two numerical examples are used to verify the accuracy and feasibility of the proposed HFC algorithm and the coupled thermo-mechanical bond-based TLF_SPH method considering the friction effect. The numerical results are in good agreement with the theoretical and experimental results. Highlights A thermo-mechanical coupling model considering the friction effect is proposed. The hybrid friction contact algorithm has higher accuracy and robustness. The thermal cracking mode of rock disk depends on the thermal expansion coefficient.