Bearing capacity and settlement of circular shallow foundations using a non-linear constitutive relationship

The design of shallow foundations is dominated by issues of settlement, rather than by bearing capacity per-se. The ability to predict the settlement of foundations at a given factor of safety is hence of key importance in design. In this paper, the energy method for a linear-elastic perfectly plastic method utilizing the von Mises’ yield criterion with associated flow developed by McMahon et al. (2013a) is extended to consider the non-linear behaviour of soil. The energy method is used to investigate the load-settlement behaviour of shallow foundations by utilizing an ellipsoidal cavity-expansion mechanism and deformation fields within the boundaries of the classical Hill and Prandtl mechanisms. An elastic mechanism obtained from an analysis in ABAQUS was also investigated using this energy method. The upper-bound approach demonstrates that the cavity-expansion mechanism produces a better solution at small values of settlement, whereas at greater settlements the Prandtl mechanism is shown to produce a more optimal upper-bound solution.