Multi-scale limit load analysis for discontinuous rock mass based on the homogenization method

A new method to evaluate the strength of rock mass structures is proposed and examined. The method is based on the collapse load analysis of elasto-perfectly plastic material along with the homogenization method, which enables the multi-scale analyses for heterogeneous media. The homogenization process replaces a rock mass with cracks by an equivalent continuum medium with macroscopic stiffness while the failure criterion for the rock mass is estimated in the localization process. It is shown that both the averaged stiffness and the macroscopic failure criterion of the discontinuous rock mass are numerically obtained via the finite element analyses. Thus, the failure strength of a rock mass structure is evaluated by the collapse load analysis in the form of Linear Programming with the macroscopic failure criterion. This is the first attempt to apply the homogenization method to the strength analysis of rock mass.