Continuum-discrete coupled model for dynamic impact of heterogeneous rock with X-shaped joints under biaxial preloading

The response mechanism of surrounding rock at excavation-induced free surfaces presents complexity under strong external disturbances in deep underground engineering. This study develops a two-dimensional mesoscale continuous-discrete coupled numerical model for granite using the Grain-Based Model (GBM) within a biaxial Hopkinson system, effectively capturing its inherent mineral heterogeneity and joint structures to reproduce dynamic mechanical response and failure modes at the laboratory scale. The simulation results accurately reconstruct the deformation and failure processes of the specimens. The displacement field along the impact direction exhibits significant gradient differentiation and spatial variation for specimens with X -shaped joints. Rock fracture initiation at the mesoscale can be attributed to the failure and reorganization of contact force chain networks. Stress concentration at the tips of intersecting joints induces local instability in the force chain networks and initiates microcracks. Local redistribution of contact forces intensifies the reorganization of the contact force chain networks and the propagation and coalescence of microcracks. Due to the coordinated control of joint geometry and principal stress direction, arcuate fracture zones on both sides of the X -shaped joints appear and gradually extend toward the specimen ends. Spatial localization and magnitude distribution of acoustic emission (AE) events were achieved in the particle discrete element model. Based on R -value analysis, the failure mode was determined to be predominantly tensile, which progressively triggered implosion and shear failure. The shift of b -values from high to low at various loading stages indicates that a cross-scale evolution of the failure mechanism from disordered nucleation to ordered coalescence occurs. The distribution patterns of microcracks under different strain rates present similarities with the progressive evolution law of microcracks under high strain rates. The multi-stage progressive evolution of the crack system (wing cracks, anti-wing cracks, coplanar cracks, and extension cracks) reflects defect-dominated damage and failure.