Application Of Elasto-Plastic Analysis In Rock Mechanics By Finite Element Method

The finite element method of analysis was introduced by Clough.1 Within a short period, it has developed into a powerful solution technique in structural and continuum mechanics. It has been used to solve boundary value problems in two and three-dimensional elasticity.2-5 Anisotropy and heterogeneity of materials were allowed for at the earliest stages. 1,4 Its application has been extended to allow for cracks,5 creep and viscoelasticity, 6,7 incremental construction,6-8 nonlinear elasticity3,9 effect of joints in rock,10 and to materials with different behavior in tension and compression.7 Because of its versatility, the finite element method has found increasing application in the field of rock mechanics. In fact, several of the more significant developments have been motivated by problems in this field. Elasto-plastic material behavior based on the incremental or rate-type theory of plasticity rather than the deformation theory was considered by Reyes and Deere11 A material law based on a generalization 12 of the Mohr-Coulomb criterion was used. In this chapter, the formulation of material laws developed by Reyes and Deere 11 is used. An efficient analysis procedure, incorporating recent developments in finite element analysis, is developed for plane-strain conditions. To demonstrate its effectiveness, the procedure is applied to three cases, one for which an exact solution is available, another for which field observations had been made, and a third one for which a parallel study was made, using an accepted limit-equilibrium method.