An extended Prandtl solution for analytical modelling of the bearing capacity of a shallow foundation on a spatially variable undrained clay

Classical bearing capacity theory was developed mainly based on spatially uniform soil properties, which cannot account for the influence of inherent soil variability. If the soil strength is heterogeneous, then using the average strength may overestimate the bearing capacity of foundations, because the failure mechanism may preferentially mobilise the weaker soils. In this study the aim is to establish a theoretical model using upper-bound solutions applied to the bearing capacity analysis of shallow foundations on undrained clay considering spatial variability. The model is derived on the principle of least energy dissipation using a four-parameter variation on Prandtl's mechanism. The theoretical model developed is verified by the random finite-element (FE) method in spatially varying soil conditions. The results show that the model can accurately capture the effect of spatially varying strength on the shallow foundation failure mechanism. The difference of bearing capacity factor between the proposed model and the FE model is within 5%, which demonstrates that the four-parameter model has an accuracy that is comparable to FE analysis with many hundreds of degrees of freedom. Another advantage of the theoretical model is that the possible non-convergence in FE analysis can be avoided, and hence, the calculation efficiency is significantly enhanced. The model is therefore suitable for rapid quantification of bearing capacity in spatially varying soils.