Load–displacement solutions for piles and shallow foundations based on deformation fields and energy conservation

The paper presents an energy approach for the prediction of non-linear foundation behaviour. The formulation entails three main stages: (a) assumption of admissible pattern functions from which displacement fields can be assembled; (b) equating external work to internal work; and (c) minimisation of internal work by variation of the displacement field using the different pattern functions. The approach is demonstrated on two problems: (a) a vertically loaded shallow foundation; and (b) laterally loaded piles. The approach is evaluated by comparison with finite difference analyses using three different constitutive models. It is shown that the approach provides a fair estimation of the overall foundation response. Under large displacements the method degenerates into conventional upper-bound calculations.