Study of the soil stability theory problems by the simplex method

Abstract

The questions of linear programming methods application to the main problems of stability theory - problems on slope stability, problems on ultimate pressure of soil on enclosures (case of landslide pressure), and problems on bearing capacity of horizontal base of a die are considered. The problems of stability theory are formulated as linear programming tasks. It is shown that the given systems of equations are linear with respect to the unknowns and may be solved by the Simplex method. The results of soil stability problems calculation by Simplex method are compared with the results of calculations according to the most known classical schemes. It is shown that a great scatter of final results is observed in calculating the stability of slopes by classical methods, and in this case, the results obtained by the Simplex method are the most trustworthy ones. The situation with landslide pressure definition is especially complicated in this sense where classical methods give a scatter of landslide pressure values by several times. It is established that with increasing discretization of the computational domain, the results tend to exact solutions of the limit equilibrium theory, obtained, for example, by the method of characteristics. The latter point is illustrated using the example of the problem of a die pushing into a ground massif with a Hill scheme bulge.