A Comprehensive Investigation on Compression-Shear Failure of Rocks: Considering Loading Conditions, Constitutive Models and Material Homogeneity

The compression-shear failure of intact rocks exhibits complex patterns due to multifactorial influences, causing a marked deviation between the actual failure plane (α) and the nominal shear angle (β). This complicates fracture surface prediction in practice. This study investigates the effects of compression-to-shear ratio, brittle-ductile-hardening constitutive behavior, and material homogeneity on rock fracture patterns through numerical simulations of variable-angle shear tests. The results indicate that: (1) The compression-shear failure pattern is governed by an energy dissipation mechanism involving synergistic competition between the primary shear zone and conjugate shear zone. The propagation of the primary shear zone is dominated by shear stress ( $${{\tau }_{N}}$$ ) on the compression-shear plane, leading to a run-through fractures, whereas the development of the conjugate shear zone is controlled by normal compressive stress ( $${{\sigma }_{N}}$$ ), resulting in dispersed-distributed shear bands. (2) Under high compression-shear ratios (i.e., small shear angles β), the conjugate shear zone preferentially develops toward the $${{\sigma }_{N}}$$ direction, causing the primary shear zone to be offset centrally and resulting in an inverted “Z”-shaped fracture pattern. As the compression-shear ratio decreases and the shear angle β increases, the conjugate shear zone shifts toward the $${{\tau }_{N}}$$ direction, ultimately causing both shear zones to merge into a straight-line (“—”-shaped) configuration. (3) As the material constitutive behavior transitions from brittle to ductile and hardening, the development of conjugate shear zones progressively intensifies. This is accompanied by an expansion in shear band width and an increase in damage density, ultimately leading to the convergence and localization of the overall fracture zone. (4) When the material’s Weibull homogeneity coefficient m < 1, macroscopic failure surfaces cannot form regardless of increasing compression-shear ratio or altering material brittleness-ductility. Conversely, when m > 1, the conjugate shear band width narrows while the primary shear band widens progressively with increasing m. (5)The compression-shear failure surface and the actual compression-shear failure surface and the internal friction angle relationship varies by material: $$\alpha > {{\beta }_{r}}$$ and $$\phi $$ shows no obvious regularity for brittle materials, $$\alpha = {{\beta }_{r}}$$ and $$\phi \approx 25^\circ $$ for brittle-ductile materials, $$\alpha = {{\beta }_{r}}$$ and $$\phi \approx 36^\circ $$ for ductile materials, and $$\alpha = - 45^\circ $$ or $$\alpha \approx {{\beta }_{r}}$$ , $$\phi \approx 26^\circ $$ for hardening materials. These findings provide critical insights for addressing a series of rock mechanics problems induced by compression-shear damage, including slope stability, tunnel engineering, rock burst and seismic hazards, coal and gas outbursts, as well as hydraulic fracturing applications.