Stability Analysis in Geomechanics by Linear Programming. I: Formulation

Abstract

The limit analysis of stability problems in geomechanics is formulated as a pair of primal‐dual linear programs that encode, respectively, the kinematic and static limit theorems in a discrete version. The failure surface can take any arbitrary shape. The soil domain is divided, into rigid elements connected by interfacing Mohr‐Coulomb layers. For an assumed finite element mesh, the solution of either linear program identifies the critical collapse mechanism among all the possible failure mechanisms contained within the mesh, and gives the associated values of both the static and kinematic variables as well as the critical load parameter. This solution is both kinematically and statically admissible for the discretized system; for the continuum, it is an upper‐bound solution. The proposed method is able to deal with external forces acting on a soil mass with varying pore‐water pressure, and inhomogeneous materials having both cohesion and internal friction. An illustrative example is presented; this kinematic formulation accurately gives the upper‐bound solution.