Practical second-order reliability analysis applied to foundation engineering

Abstract

A practical and efficient approach of implementing second-order reliability method (SORM) is presented and illustrated for cases related to foundation engineering involving explicit and implicit limit state functions. The proposed SORM procedure is based on an approximating paraboloid fitted to the limit state surface in the neighborhood of the design point and can be easily carried out in a spreadsheet. Complex mathematical operations are relegated to relatively simple user-created functions. The failure probability is calculated automatically based on the reliability index and principal curvatures of the limit state surface using established closed-form SORM formulas. Four common foundation engineering examples are analyzed using the proposed method and discussed: immediate settlement of a flexible rectangular foundation, bearing capacity of a shallow footing, axial capacity of a vertical single pile, and deflection of a pile under lateral load. Comparisons with Monte Carlo simulations are made. In the case of the laterally loaded pile, the friction angle of the soil is represented as a one-dimensional random field, and pile deflections are computed based on finite element analysis on a stand-alone computer package. The implicit limit state function is approximated via the response surface method using two quadratic models.