An enhanced constitutive model for quasi-brittle rocks with localized damage

Localized deformation is the failure precursor of quasi-brittle rocks. The objective herein is to propose an enhanced constitutive model incorporating the evolution of localized damage in quasi-brittle rocks. The plastic and damage behaviors are assumed inside the localization zone, and elastic deformation is considered outside the zone. As a consequence, the macroscopic responses are obtained by using a volume average procedure incorporating the evolution of the volume fraction of the localization zone. The plastic and damage behaviors inside the localization zone are, respectively, described by a nonlinear yield criterion and an exponential damage criterion. The onset of localized failure is defined by introducing a critical value of localized damage parameter. For application, a semi-implicit return mapping algorithm is developed to deal with the numerical implementation at the material level. Finally, the validity of the model and the robustness of the algorithm are assessed by the consistent comparison between simulation results and the triaxial compression test of three typical quasi-brittle rocks. The post-peak snapback and brittle-ductile transition behaviors are captured by adjusting the evolution rates of localization zone and localized damage, respectively. This model has two main innovative features: (1) the simulated peak strength of the model only depends on the strength parameters and is not affected by the damage and localization parameters, and (2) the proposed approach can effectively overcome the overestimation of plastic deformation by the traditional associated plastic flow rule and accurately describe the post-peak mechanical behaviors of quasi-brittle rocks.

Automated summary

This study proposes an enhanced constitutive model for quasi-brittle rocks by incorporating the evolution of localized damage. The model accurately predicts the strength and post-peak mechanical behaviors of rocks.