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.
Combined with the deformation characteristics of flexible retaining structure, the horizontal displacement calculation method of loess fill slope supported by frame prestressed anchors is proposed. Based on the minimum potential energy method, the analytical solution of horizontal displacement of slope under self-weight and additional load is derived, and the influence of soil parameters and supporting structure parameters on displacement is analyzed. The proposed calculation method is applied to a practical engineering and compared with the numerical simulation, which shows that the method is reasonable and reliable. The minimum potential energy method is clear in concept and simple in solving the horizontal displacement of loess fill slope supported by frame prestressed anchors. The calculation method proposed in this paper can be applied to the structural optimization design of loess fill slope supported by frame prestressed anchors, and further enrich the displacement calculation theory of slope supported by flexible retaining structure.
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