Lower bound solutions for bearing capacity of jointed rock

This paper applies numerical limit analysis to evaluate the bearing capacity of strip footings on an anisotropic, homogenous material. While solutions exist for footings on jointed rock [Proceedings of the Third International Conference on Computational Plasticity 2 (1992) 935; Proceedings of the International Conference on Structural Foundations on Rock 3 (1980) 83] little work has been done on the effect of variation of joint strength and relative joint orientation (for cases with two or more joint sets). From a macroscopic point of view, many jointed materials such as rock may be assumed to have anisotropic homogenous properties. The overall behaviour of a jointed rock mass is controlled by the mechanical properties of the intact rock as well as the strength and orientation of the discontinuities. The formulation presented here assumes plane strain conditions, and makes use of the Mohr-Coulomb failure criterion. In order to utilise the lower bound theorem of classical plasticity two basic assumptions must be made. Firstly the material is assumed to exhibit perfect plasticity and obey an associated flow rule without strain hardening or softening. Secondly, it is assumed that the body undergoes only small deformations at the limit load so that the effect of geometry changes is small. By using a Mohr-Coulomb approximation of the yield surfaces, the proposed numerical procedure computes a statically admissible stress field via linear programming and finite elements. The stress field is modelled using linear three-noded triangular elements and allows statically admissible stress discontinuities at the edges of each triangle. By imposing equilibrium, yield and stress boundary conditions on the unknown stresses, an expression of the collapse load is formed which can be maximized subject to a number of linear constraints on the nodal stresses. As all the requirements are met for a statically admissible stress field, the solution obtained is a rigorous lower bound on the actual collapse load. An extensive parametric analysis is presented to investigate the effects of joint orientation and strength properties on the overall bearing capacity of jointed rock. The analysis overcomes the limitations of previous solutions in that non-orthogonal joint sets are considered. Consequently this work represents an invaluable tool for designers. (C) 2003 Elsevier Ltd. All rights reserved.