Robust geotechnical design of earth slopes using fuzzy sets

This paper presents a fuzzy set-based robust geotechnical design (RGD) approach for the design of earth slopes in which uncertain soil parameters are represented as fuzzy sets. For a slope with fuzzy sets as inputs, the stability (factor of safety) of the slope is also a fuzzy set. The failure probability of the slope can readily be determined based on the obtained fuzzy factor of safety; further, the design robustness in terms of the signal-to-noise ratio (SNR) can also be evaluated. The purpose of the RGD is to derive a design that is robust against the uncertainty in the input parameters, with an explicit consideration on safety and cost. Therefore, a multiobjective optimization is performed and a three-dimensional or two-dimensional Pareto front showing a trade-off between objectives can be obtained, which allows for an informed design decision. The effectiveness of the proposed fuzzy set-based RGD approach is demonstrated through an illustrative example.