Modeling slope stability according to various sliding curves

Landslide phenomena with loss of stability of soil slopes occur both in natural landscapes and during excavation operations with a violation of the stability of folded rocks, including during the construction and operation of soil dams and fencing dams, automobile and railway embankments, etc. The stability of slopes depends on a variety of factors, the most important of which are the physical and mechanical characteristics of the soil, which can be either homogeneous throughout the massif, or heterogeneous in the form of various layers, etc. Aim. Expanding the possibilities of a comprehensive assessment of slope stability by considering additional (to the circular) families of hyperbolic sliding curves for the case of a base with different strength characteristics. Methods. Methods are used to determine the outlines of the sliding curves of a landslide slope with the least margin of stability, based on a comparison of the calculated results of families of circular, lower-hyperbolic, and upper-hyperbolic curves. The calculations are performed using the Terzaghi method by dividing the proposed area of soil mass slide into vertical sections and determining the local holding and shearing forces for each section. The final result is the ratio of the total values of these forces. Results. A comprehensive method for determining the outlines of the most dangerous sliding curves of soil massifs based on the Terzaghi method is proposed, considering families of circular and hyperbolic (with low and high curvature) sliding lines. The results obtained, tested for the ground slope at the specified two points on the sliding line, showed: adequacy of the proposed analytical solution for circular curves (~ 2 %) in comparison with the results of numerical calculation according to the OTKOS-22 program; the line of least stability for the case under consideration is the lower hyperbolic sliding curve with a stability coefficient 11% less than the slope stability along the circular sliding curve; the stability coefficients of slopes with relatively small differences in sliding lines can vary significantly; in the considered case, the stability coefficients for slopes with sufficiently close hyperbolic outlines of the lower and upper curvature differ by more than 19 %. Conclusions. A comprehensive method for determining the outlines of the most dangerous sliding curves of soil massifs based on the Terzaghi method is proposed, considering families of circular and hyperbolic (with low and high curvature) sliding lines, which significantly expands the search area for lines of least slope stability.