Confinement-dependent brittle-to-ductile transition in rocks: an elastoplastic SPH-phase-field framework

Rocks subjected to increasing confinement commonly transition from localized brittle failure with abrupt post-peak strength loss to distributed inelastic deformation with sustained load-bearing capacity. Accurately capturing this transition is important for stability assessment and failure-mechanism analysis in deep rock engineering. To reproduce the associated evolution of strength, post-peak response, and failure localization with confinement, this study develops an elastoplastic SPH-phase-field model of the confinement-dependent brittle-to-ductile transition in rocks. The formulation couples Drucker–Prager plasticity and phase-field damage through a cohesive–hardening resistance jointly governed by accumulated plastic hardening and the phase-field variable. A confinement- and phase-field-dependent law is further proposed to partition each plastic-work increment into crack-driving and non-crack-driving contributions, allowing the fracture-driving role of plastic deformation to evolve with prescribed confinement and the local phase-field state. For robust SPH computation during damage localization, a state-dependent stabilization treatment combines a damage-based weighting function with a deviatoric-stress residual. The model is assessed through compression simulations of homogeneous and heterogeneous specimens under different confining pressures, including variations in height-to-width ratio and pre-existing-flaw configuration. The proposed model reproduces the confinement-induced increase in peak strength, attenuation of post-peak softening, sustained residual load-bearing capacity, and progressive transition from localized failure to broadly distributed plastic deformation and phase-field damage, providing a meshfree framework for modeling the brittle-to-ductile transition of rocks.