Stability Analysis in Geomechanics by Linear Programming. II: Application

The limit analysis for stability problems in geomechanics can be formulated as a pair of primal‐dual linear programs. This formulation provides a solution that is both kinematically and statically admissible for a discretized soil mass; for the continuum, it gives an upper‐bound solution. This paper investigates the accuracy and the scope of applicability of this kinematic formulation. Several numerical examples of bearing capacity and slope stability problems are presented, including problems of a cohesive and frictional soil mass with inhomogeneous properties and varying pore‐water pressure. In bearing‐capacity analysis, the bearing pressure is considered to be “activating,” while the surcharge and self‐weight are considered to be “fixed.” In evaluating the safety factor for slope stability analysis, two different approaches are used: for frictional materials, the actual loading is considered to be “fixed,” and a fictitious horizontal loading is introduced as “activating”; for purely cohesive materials, the vertical loading is treated as “activating.” The computed results agree very well with analytical values and other numerical results. A comparison of this kinematic method with standard limit equilibrium methods is also presented.