Reliability-based optimization of geotechnical design using a constrained optimization technique

Uncertainty and risk are inherent in geotechnical engineering. Reliability-based optimization (RBO) is a methodology that determines the best design solution according to certain design criteria while explicitly considering the effects of uncertainty. RBO ensures a design that is economical as well as reliable in the presence of uncertainties. This paper suggests a direct method for RBO of geotechnical systems by coupling reliability assessment and cost minimization. RBO is proposed as a double-loop (or nested-loop) constrained optimization problem, with cost optimization of geotechnical system through the outer loop repeatedly calling the inner reliability evaluation loop. First-order reliability method is used to compute the reliability index. An algorithm based on constrained optimization is proposed. MATLAB's constrained optimization function, fmincon, is used in two loops: the outer loop to minimize the cost of geotechnical system, and the inner loop to minimize the reliability index to a target value while satisfying geotechnical design requirements. The proposed method is employed to obtain the optimal design of a gravity retaining wall, and compared with other methods, and found to be robust, accurate and feasible.