Nonprobabilistic Reliability Solution Method of Slope Convex Set Model

In the analysis of slope engineering stability, due to the limitation of the original sample information of the obtained parameters and the limitation of the conventional reliability calculation method based on probabilistic reliability, the non-probabilistic comprehensive indicator of the slope convex set model is introduced, and a solution method by non-probabilistic reliability of slope under the condition of fuzzy characterstics of sample information is formed. First, based on the limited sample information, a rough interval is delineated for the parameters, and the slope hyper-ellipsoid convex set model is constructed in this interval. Then, Latin hypercube sampling is used for sampling within the interval. Since the limit state equation of slope engineering is generally highly nonlinear and implicit, the Kriging proxy model is used to fit its function. Finally, according to the compatibility of non-probabilistic reliability and probabilistic reliability, non-probabilistic index η is introduced to comprehensively evaluate the stability of the slope. When η>1, the evaluation criterion is the shortest distance from the origin of the coordinates to the limit state surface in the standard vector space; When 0 < η < 1, probability reliability is used as the evaluation index. At this time, the slope reliability indicator can be obtained by using the Monte Carlo method relying on the MATLAB programming language. The calculation examples show that the method is feasible, efficient in calculation and accurate in results. It has made beneficial extensions and supplements for the probabilistic reliability method, and also provided new possibilities for solving slope reliability. Finally, using this method when the sample information of an actual slope project is incomplete, the results show that the failure risk of the slope is very low, which is consistent with the analysis conclusion of the simplified Bishop method, and conforms to the target reliability index standard of highway subgrade in "Unified Standard for Reliability Design of Highway Engineering Structures" (JTG 2120—2020).