Limit analysis of the bearing capacity of fissured materials

Formulations for the upper and lower bound theorems of plasticity are presented for ®ssured soil and jointed rock. The methods ignore elastic deformations and are based on the assumption that the ®ssured soil or rock mass can be treated as an anisotropic, rigid-plastic continuum. In the upper bound formulation, velocity discontinuity multipliers are introduced to deal with the discontinuities in the velocity ®eld. For both the upper and lower bound formulations, linearized failure surfaces for the ®ssured materials are developed. The illustrative examples indicate that the new procedures are very ecient even when a quite coarse mesh is used to represent the mass of failing material, and that the `exactʹ failure loads are always bracketed by the upper bound and lower bound calculations. Moreover, by increasing the number of planes in the failure surface or/and re®ning the meshes, the accuracy of the bounds is raise