Calculation of the stability of two-layer ledges of excavations with elastic-plastic stress distribution

In this paper, the results of research work on the stability of two-layer ledges of the slopes of excavations with elastic-plastic stress distribution are presented. The problem of determining the stability of the two-layer ledge is extremely useful in practical engineering activities. In particular, the situations when soil poured onto the surface of the slope has compacted since it has been laying on the slope for a long time may appear. The accuracy of solving the problem of the stability of the slope ledges in view of the impossibility of absolutely accurately determining the physical and mechanical characteristics of the soils making up the slope seems to be rather relative. On the other hand, the exact solutions of this problem in the elastic-plastic formulation are extremely cumbersome from the point of view of applying mathematical apparatus. Therefore, the authors have considered it necessary to compare the results of elastic and elastic-plastic solutions of the problem of the stability of slope ledges. For this purpose, the numerical values of stresses at various points of the selected design model have been determined, using the finite element method, as well as using the methods of the theory of functions of a complex variable. As a result, it has been calculated that even if there is a two-layer ledge of a slope of plastic regions in the soil massif, the stability coefficient determined when solving elastic and elastic-plastic problems is practically the same.