Brittle-Ductile Transition in Porous Rocks by Cap Model

A pressure-dependent cap model that is capable of describing the brittle-ductile transition in porous rocks is proposed. The model consists of a hardening Drucker-Prager yield cone with a nonassociative flow rule, an ellipsoidal cap with an associative flow rule, and a failure or limiting surface. This surface designates the stress states at the inception of failure below brittle-ductile transition, or the onset of ideally plastic response above brittle-ductile transition. The appropriately combined structures of the associative and nonassociative flow rules eliminate the difficulties associated with a singular corner region at the intersection of the cap and failure surface. A cross hardening between the cap and cone is discussed. The model is capable of a good qualitative agreement with experimental data, as demonstrated by the results of the triaxial compression tests under various amounts of the confining pressure. A stress-strain response with inelastic volume dilatancy at lower confinements, and an increased ductility and hardening rates at higher confinements, are well predicted.