Worst-case phenomenon analysis of strip footing on spatially variable slope by finite element limit analysis

This study performs a series of stochastic analyses to assess the reliability (defined as the probability that the maximum load a footing can sustain falls below its design bearing capacity) of a strip footing located at the crest of a slope, employing a self-developed finite element limit analysis method integrated with random field theory. The primary focus is to explore how the failure probability of the footing is influenced by various factors, including the coefficient of variation, the factor of safety, and the slope angle. Additionally, the study aims to provide deeper insights into the worst-case behavior of this system. The results demonstrate that as the coefficient of variation increases, the worst-case phenomenon becomes more pronounced. Furthermore, a higher coefficient of variation corresponds to a larger worst-case correlation length. To aid in preliminary conservative design in the absence of precise and comprehensive in-situ data, a design table summarizing the failure probabilities for various scenarios is provided.