Reliability-based design of slope angles for spatially varying slopes based on inverse first-order reliability method

Stability analysis and design of soil slopes are a classic problem in geotechnical engineering. The current commonly-used deterministic analysis (e.g., single factor of safety) approach does not quantify the influences of various uncertainties in slope engineering, while the probabilistic analysis approach is time-consuming because it often requires performing multiple rounds of reliability analyses. A slope model reconstruction method that can well adapt to different slope angles is proposed. The reliability-based design of slope angles for spatially varying slopes based on a small amount of test data is carried out using the inverse first order reliability method. To validate the effectiveness of the proposed method, a representative sandy slope is taken as an example, to conduct the reliability-based design of slope angles. The results indicate that the proposed method can obtain a design scheme of slope angle based on a small amount of test data, which is well consistent with engineering practice. It thereby provides an effective tool for the reliability-based design of slope angles for spatially varying slopes. For the sandy slope in this study, an optimized slope angle that achieves various target probabilities of failure can be obtained after 4 or 5 iterative calculations. In contrast, the deterministic analysis method will obtain a biased design scheme since it cannot quantitatively account for the influences of multiple sources of uncertainties in the slope engineering. To yield a target probability of failure of 1×10^-4 which is often acceptable for stability evaluation of slopes, the slope angle of the sandy slope designed using the proposed method should be smaller than 14.13°. By contrast, the slope angle designed using the deterministic analysis approach differs significantly from that designed using the proposed method.