Numerical Investigation of Mixed Mode I-III Fracture Behavior in Sandstone Under Static and Dynamic Loading

Mixed mode I–III fracture commonly occurs in rock masses under complex three-dimensional stress states, yet the combined effects of loading conditions and fracture mode remain unclear. In this study, a heterogeneous sandstone disc model is developed in ABAQUS by coupling the Drucker–Prager elastoplastic model, an equivalent-strain damage model, and cohesive elements. The model is validated against static Brazilian splitting tests and dynamic SHPB tests. ENDB specimens are then employed to investigate mode I, mode III, and mixed mode I–III fracture under static and dynamic loading with offset angles ranging from 0° to 62.5°. As the offset angle increases, crack propagation evolves from straight tensile extension to deflected, twisted, and fragmented patterns dominated by anti-plane shear. Dynamic loading intensifies crack segmentation, localized damage, and transient instability while increasing the peak load, fracture toughness, and fracture energy. In contrast, the effective fracture toughness and fracture energy decrease monotonically with increasing offset angle under both loading conditions. A linear trend consistent with R2 > 0.99 is observed between the mode I–III mixing coefficient and the effective fracture toughness based on single-realization simulations, the effective fracture toughness under dynamic loading is approximately 2.22 times that under static loading based on direct comparison of calculated values. These findings improve the understanding of loading-dependent mixed mode I–III fracture in sandstone and provide guidance for rock mass stability assessment.