Searching for sliding surfaces in multi-level loess slopes based on the brachistochrone

As a key problem in slope-stability analysis, searching for potential sliding surfaces has attracted the attention of experts and scholars for a long time. However, the commonly used sliding surface curves are only considered in terms of shape approximation and lack physical significance. The search process involved in stability analysis of multi-level slopes is complex and a large amount of calculation is required. In order to solve this problem, this paper proposes a new sliding surface form based on physical interpretation of the brachistochrone, and establishes a search model for the brachistochrone sliding surface of a multi-level loess slope. At the same time, in order to further expand the search range and find a more ideal potential sliding surface curve shape and position with a lower safety factor, we recommend continuing the sliding-surface search after the brachistochrone is improved. We compared the calculation results for the position of the potential sliding surface and the stability safety factor with the corresponding results for an arc sliding surface (in combination with a calculation example) to verify its rationality. The approach offered here not only provides a new choice of sliding surface curve form for slope-stability analysis, but also significantly improves search efficiency for potential sliding surfaces of multi-level loess slopes.