A Novel Elastoplastic Damage Model for Hard Rocks under True Triaxial Compression: Analytical Solutions and Numerical Implementation

In this work, a novel elastoplastic damage model is proposed to capture the mechanical and deformation behaviors of hard rocks subjected to true triaxial compression (TTC). A yield function based on the Mogi–Coulomb strength criterion is constructed in the stress space. Generalized plastic shear strain as a function of a continuous and smooth hardening or softening variable is adopted in the yield function; this guarantees that the yield function at the peak stress level has the same form as the strength criterion. Moreover, a proper damage criterion is derived, considering the development of microcrack-induced damage. The novelty of the proposed model consists in the ability to derive its analytical solutions under a novel TTC loading with a constant load angle; this is helpful for calibrating the model parameters. For application, an efficient and convergent semi-implicit return mapping (SIRM) algorithm involving a plasticity-damage decoupling correction procedure is then developed for the numerical implementation of the proposed model under general loading cases. The robustness of the SIRM algorithm is examined through comparisons between numerical results and the derived analytical solutions. An interesting observation is that, for the SIRM algorithm, plasticity and damage evolution are insensitive to the size of the load step. The verification of the model is finally shown through applications to Westerly and Linghai granite under a typical TTC loading path.