Elastoplastic model of statistical mechanics of rock masses (SMRM): Theory and verification

The prediction of the deformation of jointed rock masses is one of the critical problems in the discipline of rock mechanics. Reasonably describing the effect of joint sets on the deformation of jointed rock masses within the framework of continuum mechanics has always been a goal pursued by scientists and engineers. An equivalent elastic constitutive model, named the statistical mechanics of rock masses (SMRM), had been developed to achieve the goal. However, since this model of SMRM initially did not consider the plastic deformation of rock masses, its application in rock engineering had always been constrained. In this study, an elastoplastic theory of the SMRM model is established by combining the classical elastic theory of SMRM and the classical Mohr-Coulomb strength criterion. Then, the reliability of the proposed elastoplastic SMRM model is extensively verified through a series of analytical solutions and experimental tests for jointed rock masses. It is indicated that the proposed elastoplastic SMRM model can effectively consider the spatial, mechanical and geometric characteristics of joint planes, and it can also effectively describe the influence of the density and orientation of joints on the strength and deformation of jointed rock masses. The elastoplastic SMRM model proposed in this study could potentially provide a new solution for some rock engineering problems.