Constitutive modeling of rock failure behavior under pressure conditions spanning the brittle–ductile transition

Abstract

The brittle–ductile transition is a fundamental mechanical characteristic of rocks in a range of engineering applications. While various constitutive models have been proposed to predict rock failure, only a few are capable of quantitatively capturing the brittle–ductile transition. Moreover, to date, few existing models are able to uniformly describe the distinct mechanical behaviors of rocks in the brittle and ductile regimes. This paper presents a unified elastoplastic damage model capturing the mechanical behavior of rocks spanning the brittle–ductile transition. A subtly single cap-type plastic yield criterion is formulated in the effective stress space and a monotonic hardening function is introduced into the yield criterion to describe pre-peak hardening behavior accurately. The post-peak softening behavior is solely due to material damage, for which we propose a damage criterion. Unlike prevailing models, our hypothesis suggests that the damage process begins with localized cracking after reaching the peak stress, eliminating any accumulation of damage prior to the peak stress. In this context, the yield surface at peak stress state constitutes the real strength envelope. Furthermore, to accurately replicate post-peak softening behavior and brittle–ductile transition in rocks, we establish a theoretical correlation between residual damage and confining pressure. Numerical simulations are performed for three types of rock subjected to conventional triaxial compression. Comparisons between numerical predictions and test data demonstrate that the model effectively captures key features of mechanical behavior observed in these rocks. Particularly noteworthy is its ability to simulate the brittle–ductile transition.