Equivalent shear-slip roughness as a displacement-field descriptor of shear behavior transition in bimrocks

Predicting shear-behavior transitions in block-in-matrix rocks (bimrocks) requires a descriptor that links mesoscale localization to macroscopic strength mobilization. Volumetric block proportion (VBP) specifies composition, whereas conventional interpretations based on peak friction-angle increments do not directly quantify the geometry of the active shear path. Here, equivalent shear-slip roughness is defined from the statistical centerline of a displacement-gradient-derived slip field and used to characterize the VBP-dependent transition. A three-dimensional Voronoi-expansion method and a heterogeneous discrete-element model are used to resolve stress-displacement responses, crack evolution, contact-force networks, and slip fields for VBP = 10-70%. Increasing VBP changes the response from localized matrix-through fracture with post-peak softening to distributed interface-guided shearing and stable frictional/block-rearrangement bearing. Concurrently, the residual equivalent slip path becomes progressively more tortuous, while load transfer evolves from matrix cohesion to frictional contact and block interlocking. The proposed roughness therefore complements VBP by quantifying how the imposed block proportion is expressed in the evolved localization geometry. Although evaluated from the post-deformation field, the residual numerical roughness converges toward the first-order theoretical estimate, indicating that the fully mobilized slip state is consistent with the model assumptions across the investigated VBP range. These results provide a measurable structure-mechanics link and support future roughness-informed strength formulations. Block morphology, orientation, gradation, anisotropy, and scale can be incorporated as refinements in broader validation.