Clarifying the mechanical properties and failure patterns of layered coal–rock combinations in coal-measure strata is critical to guiding hydraulic fracturing design in petroleum and mining engineering. This paper investigates the mechanical properties, failure patterns, and stress distributions of sandstone–coal–sandstone (SCS) and mudstone–coal–mudstone (MCM) combinations under different confining pressures and thickness ratios based on the 3D combined finite–discrete element method (3D FDEM). The results show that the mechanical strength of the SCS combination is higher than that of the MCM combination under the same conditions. As the thickness ratio increases, the overall peak stress and elastic modulus of the combination decrease gradually and eventually approach those of the pure coal. As confining pressure increases, the peak stress of layered coal–rock combinations rises gradually, plastic behaviors become increasingly prominent, and the failure mode of the mudstone layer transitions from tensile-dominated to shear-dominated. Under different thickness ratios and confining pressures, the coal layer in the combinations primarily develops shear-dominated cracks, whereas the sandstone layer mainly generates tensile-dominated cracks. An increase in confining pressure elevates the critical thickness ratio for sandstone layer failure in the SCS combination. Essentially, the changes in stress state caused by rock types, thickness ratios, and confining pressures are important reasons for the variations in the failure patterns of each layer in layered coal–rock combinations. The key findings of this paper are expected to provide theoretical guidance for the field design of petroleum and coal mine engineering.

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.