Probabilistic analysis of shallow foundation on earth slope using an active learning surrogate-centered procedure

In geotechnical engineering, the use of increasingly complex numerical models for design and assessment presents a significant challenge for the application of probabilistic analysis where computational time is crucial. Recently, adaptive (or active learning) surrogate modeling methods have emerged as effective solutions to address this issue. The present study proposes a novel probabilistic analysis procedure centered on Adaptive Polynomial Chaos-Kriging (A-PCK), aimed at reducing computational time and providing informative results for decision-making in geotechnical problems. The procedure comprises two probabilistic analysis steps: the first employs a random variable approach to encompass as much uncertainty as possible in the modeling and deliver a quick and comprehensive reliability estimate, while the second evaluates the reliability of geo-structures considering soil spatial variability modeled by random fields to provide a precise failure probability estimate. The proposed procedure is applied to a shallow foundation resting on an earth slope, considering three failure modes (sliding, bearing capacity, and settlement) and nine input parameters modeled as random variables in the first step. Based on sensitivity analysis results from the first step, only the significant input parameters are modeled by random fields in the second step, updating the failure probability estimate. Excessive settlement is identified as the most critical failure mode for the studied case. Incorporating soil spatial variability in reliability analysis reduces the failure probability estimate of the studied system by two orders of magnitude for sliding and bearing capacity failure mode, and one order of magnitude for settlement failure mode. Additionally, a discussion on the effects of foundation geometry on the three failure modes is conducted by varying the foundation distance to the slope and dimensions, aiding engineers in making decisions regarding optimal structure dimensions and positioning based on probabilistic approaches.