Three-dimensional block elements plastic lower bound limit analysis method for slope stability

By using the discrete means of the block element method, the 3D slope is partitioned into a proper number of block elements conjoined with the structural planes. It assumes block elements are rigid, stresses only existed in structural planes. Base on the lower bound limit theorem, and regarding the stresses of structural plane as unknown variables, the statically admissible stress fields that satisfy the equilibrium, boundary conditions and yield criterions are constructed. A linearization yield criterion is used for avoiding nonlinear mathematical programming. Finally, the lower bound limit analysis model of linear and nonlinear mathematical programming for 3D slope stability is established; four examples are used and the results agreed well with those from the rigid limit equilibrium and upper bound method.