Equivalence of effects for a limiting stress state

Abstract

The article considers the possibility of an equivalent substitution of the volume forces for a limiting stress state by a surface loading. For any reason causing the stresses in a slope, in the final analysis these effects are considered in the system of equations for an under-limiting stress state with the help of forced strains, surface and volume forces and in the system of equations for a limiting stress state - with the help of surface and volume forces.The determination of forced strain values, values of surface and volume forces require a thorough analysis of engineering geological situation at the slope and the performance of some simple calculations. Depending on the problem, there can be no influence from the part of forced strains and surface forces. As to the volume forces, they always act as the own weight forces even if the slope is not subject to any process.Methods. The methodology of physical modeling of stresses in a non-uniform slope is stated.Result. The problem of determination of limiting stresses caused by volume forces in the slope is reduced to the problem of determination of stresses caused by fictitious surface forces. Considered a non-uniform slope containing n layers, the volume masses (weights) of which equal γn. The boundaries between the layers are not plane. The volume forces are piecewise-constant. The solution of the problem is represented as the sum of solutions of n problems.Conclusion. The solution obtained through the developed methodology identically coincides with the known solution This fact testifies to the truth of the developed methodology.