Multi-scale constitutive modeling of the brittle–ductile transition behavior of rocks with microcracks and two populations of pores

The present paper is devoted to multi-scale constitutive modeling of the brittle–ductile transition in rocks. The rocks are considered as heterogeneous media composed of solid phase weakened by microcracks at the microscale and two different populations of pores at the micro and mesoscales. A Drucker–Prager type criterion is first formulated considering microcracking-induced damage in the solid phase. By means of a two-step modified secant variational method, this criterion is then adopted to derive a micro–macro model for double porous medium taking into account the effects of pores. Considering that the operative deformation mechanism in brittle rocks is microcracking, the Drucker–Prager type microcrack damage model is applied to describe the transition of three typical brittle rocks from brittle faulting to dilatant ductile flow by establishing a linear relation between the critical damage caused by microcrack propagation and confining pressure. By introducing an appropriate plastic hardening law and taking into account the influence of confining pressure on plastic hardening parameter and dilatancy coefficient, the micro–macro model for porous rocks is applied to describe the transition from brittle faulting to compactive ductile flow in two typical porous rocks. Comparisons between numerical simulations and experimental data show that the main features of brittle–ductile transition of two types of rocks are well captured by the proposed model.