ABSTRACT:
This paper focuses on the performance of the finite element (FE) equivalent continuum approach in simulating the behaviour of layered rock. The effect of length scale, which is a function of the layer thickness or joint spacing and shear stiffness of the joints, is investigated through the elastic behaviour of the laminar continuum. The performance of the classical equivalent continuum approach based on a conventional transversely isotropic formulation is been compared with that of a Cosserat equivalent continuum approach, and the FE explicit joint model.
1 INTRODUCTION
Rock mass discontinuities include structural features such as fractures, faults and bedding planes that may be treated as thin layers of material distinct from the adjacent intact material. The joint planes separating the layers result in a directional dependence in behaviour of the continuum. Two main approaches have been used to simulate these highly anisotropic materials: i) techniques which explicitly model the jointed nature of the material, e.g., Discontinuous Displacement Analysis (DDA), Shi (1998), Discrete Element Method (DEM), Cundall et al. (1978), and the Finite Element Method (FEM) utilizing an explicit joint model, Goodman (1968), and ii) the FEM equivalent continuum approach, Zienkiewicz & Pande (1977). Due to its many advantages, the equivalent continuum or smeared joint model using FEM has been widely used to simulate the behaviour of layered rock masses. In this approach, the layered material is replaced by a conventional anisotropic material. Consequently, despite its widespread use, it remains problematic where the characteristic length of the problem or bending stiffness cannot be neglected. This shortcoming is a consequence of the fundamental assumption of classical continuum theory which neglects the effects of micro moments on equilibrium of the system. In Section 2, the basics of the equivalent continuum approach, its mathematical basis and finite element (FE) formulation are discussed.
