Application of element integration method in bearing capacity analysis of foundation

Bearing capacity analysis based on the upper bound theorem of plasticity could be numerically performed by element integration method.Small triangle elements were used to discretize the foundation soil.A kinematically admissiable velocity field was supposed independent of the element meshing.Work done by the body forces,surface loads,as well as internal energy dissipations within an element were conveniently obtained under such a failure mechanism.The total energy could be calculated from the energy integration among all the elements.The limit external load could therefore be solved from the upper bound limit theorem,and its minimum value could be obtained from the optimization method.For single block mechanism,such as log-spiral slip surface,the validity of the proposed method was verified with two typical examples.