Bearing capacity of spatially random soil: the undrained clay Prandtl problem revisited

By merging elasto-plastic finite element analysis with random field theory, an investigation has been performed into the bearing capacity of undrained clays with spatially varying shear strength. The object of the investigation is to determine the extent to which variance and spatial correlation of the soil's undrained shear strength impact on the statistics of the bearing capacity. Throughout this study, bearing capacity results are expressed in terms of the bearing capacity factor, N_c, in relation to the mean undrained strength. For low coefficients of variation of shear strength, the expected value of the bearing capacity factor tends to the Prandtl solution of N_c = 5·14. For higher values of the coefficient of variation, however, the expected value of the bearing capacity factor falls quite steeply. The spatial correlation length is also shown to be an important parameter that cannot be ignored. The results of Monte Carlo simulations on this non-linear problem are presented in the form of histograms, which enable the interpretation to be expressed in a probabilistic context. Results obtained in this study help to explain the well-known requirement that bearing capacity calculations require relatively high factors of safety compared with other branches of geotechnical design.