Elastoplastic behavior of jointed rock masses as homogenized media and finite element analysis

A comprehensive 3D formulation for the strength properties and elastoplastic constitutive equations of jointed rock masses are derived in this paper. The approach is based on the implementation of the homogenization method of randomly heterogeneous media within the frameworks of limit analysis and elastoplasticity. A rigorous closed-form expression of the macroscopic strength criterion is first given as a function of the failure conditions of the rock matrix and of the joints. As an example of implementation of such a homogenized criterion, the stability analysis of an underground gallery in a jointed rock masses is presented and the scale effects, which prevail if the number of joints is relatively low, are investigated through comparisons with the results derived from direct calculations. Assuming elastoplastic constitutive laws for the rock matrix and the joints, a micromechanical reasoning is used for the formulation of the overall behavior. The macroscopic elastic stiffness as well as the plastic criterion and the plastic flow rule are derived from the knowledge of the mechanical properties of the individual constituents. This anisotropic model is then implemented in a F.E computer code. Due to the multi-potential character of the macroscopic plastic flow rule, the numerical analysis is particularly focused on the iterative algorithm of plastic integration. Examples of numerical simulations dealing with jointed rock structures are finally given.