Strength evaluation of discontinuous rock mass by multi-scale limit load analysis

A method of multi-scale limit load analysis to predict strength of discontinuous rock mass is proposed. The rock mass is regarded as a body that involves microstructures comprised of rock material and cracks and its mechanical behavior is treated rigorously in two sets of governing equations in macro- and microscopic scales. The macroscopic problem describes the averaged mechanical behavior of the whole body, while solutions of the microscopic problem gives a nonlinear relation between the averaged macroscopic stress and strain, which is strongly affected by the complicated microstructure. In other words, the microscopic problem plays a role of nonlinear constitutive law. In this study, a frictional contact model of a single crack is used in the microstructure. Then a method utilizing the localization process for evaluating the strength characteristics of the macro-body is presented. Several numerical examples are shown to validate the proposed method and to demonstrate its potential usefulness in the field of rock mechanics and rock engineering.