Kriging Numerical Models for Geotechnical Reliability Analysis

When the performance function is an implicit numerical model, geotechnical reliability analysis can be challenging due to the coupling between the deterministic numerical evaluation and reliability analysis. Previously, the kriging method was used in geotechnical engineering for modeling the spatial variability of soil properties. In this paper, we illustrate a first-order reliability analysis method based on a kriging approximation of the deterministic numerical model. The key idea in this method is to first calibrate a kriging model to approximate the deterministic numerical model, and then to evaluate the failure probability based on the kriging model. As any stand-alone software for deterministic geotechnical numerical analysis can be potentially used to generate samples for calibrating a kriging model, it can then be ultimately used for a reliability analysis. As such, this method provides a practical way for practitioners to perform reliability analysis based on existing deterministic geotechnical software. The effectiveness of the suggested method is illustrated through a pile foundation example, a shallow foundation example, and a slope example in which the performance functions do not have explicit forms. The kriging method is used here as a tool for interpolating and approximating deterministic numerical models. The present paper does not address any type of spatial variation of soil properties.