Analytical undrained bearing capacity models for spatially variable soils: mechanisms, uncertainty, and diagnostic maps

Soil strength exhibits natural spatial variability, which obscures the stochastic link between failure mechanisms and bearing capacity. This study establishes an analytical framework that couples multiple kinematically admissible mechanisms with random field theory to quantify the undrained bearing capacity of footings on soil with spatially variable strength. The analytical solutions show good agreement with numerical simulations in evaluating the undrained bearing capacity. Subsequently, the influence of spatial variability in undrained shear strength on the statistics of bearing capacity was investigated, providing insight into the distribution of critical failure mechanisms. Furthermore, this study introduces a failure-frequency map representing the spatial distribution of failure possibility, which can serve as a diagnostic tool to guide ground improvement from a random field perspective. Overall, the analytical model offers direct insights into critical failure mechanisms and their associated influence on bearing capacity under random field conditions, while still retaining the fidelity of probabilistic analyses involving extensive Monte Carlo simulations.