Load-displacement and upper-bound solutions of a loaded laterally pile in clay based on a total-displacement-loading EMSD method

A total-displacement-loading approach based on the extended mobilisable strength design (EMSD) method is developed for predicting nonlinear foundation responses and upper-bound capacities with continuous velocity fields. Different from EMSD, the new approach turns optimizing a minimum energy solution into solving an elastic problem with strain-dependent equivalent elastic modulus. The strain-dependent modulus is determined by a nonlinear iterative method. This transform guarantees that the reaction force is consistent with the elastic solution in early stages of loading and gradually approaches an upper-bound solution at a large value of displacement. The approach is demonstrated on a problem of the laterally loaded pile.