8 - Continuum Models for Layered and Blocky Rock

Abstract

This chapter presents the framework of Cosserat continuum theory (CT) to model the behavior of granular, layered, and blocky rock. The materials of geomechanics are distinguished from other engineering materials such as steel and concrete, primarily by their visible inhomogeneity. The mechanical modeling of such materials is complex but is needed for the numerical and analytical prediction or back-analysis of forces and displacements within rock bodies around engineering structures. Nonhomogeneous materials can be modeled by conventional continuum theories only if the characteristic fabric length of the material is vanishingly small, as compared to some characteristic structural length. The chapter discusses the most important kinematic and static relationships for plane, infinitesimal deformations of Cosserat's continuum. The absence of any characteristic length for the localized strain in conventional continuum models is the reason for the critical dependence of finite element calculations in related boundary value problems on the employed finite element grid. Analytical solutions of boundary value problems of Cosserat theory require approximately the same mathematical effort as corresponding boundary value problems of conventional continuum mechanics.