UDC 622.271.33/624.121.(532+537)+625.033.38+627.43

Theory of calculation of stability of slopes and bases. General theory of calculation of stability of homogeneous slopes

A. V. Zhabko 

This article is the second part of the published work on the creation of a unified theory of calculating the stability of slopes. There is no theory for arbitrary geological conditions and even in homogeneous rock masses. Those individual calculation methods that already exist have a number of significant drawbacks. Therefore, the aim of this study is to develop a rigorous method for evaluating the stability of similar slopes and its further modification under more difficult conditions. The paper presents and proposes the use of a fundamentally new theory for calculating the stability of slopes and grounds, designed by the author and based on the fundamental theorems and principles of mechanics, such as the principle of possible displacements of Lagrange, Gauss principle of least constraint, Ostrogradskiy theorem of least lost work, and so on. The basis of the mathematical apparatus of the proposed theory is vibrational, differential and integral calculus. Drawing on the theory, author developed the method of calculation of stability of homogeneous slopes.

Using the principle of virtual displacements, the author deduces the condition of stability of the prism offset in general. On the basis of the theorem of least lost work author obtains an equation that allows to overcome the static uncertainty of the problem for assessment of equilibrium of the elementary compartment (unit). Author studied law of distribution of interblock reactions along the sliding surface with the corresponding proof of the results. The article also shows the derived formulas for the construction of the weakest sliding surfaces in homogeneous isotropic slopes. Author constructed sliding surfaces for the most commonly used values of slope angles and internal friction. One can see an assessment of the stability and extreme geometrical parameters of flat homogeneous slopes. Author received a nomogram of stability of flat homogeneous slopes. There also is a timetable for determining the width of the prism of possible collapse.

Keywords: slope; limit equilibrium method; method of limiting stressed state; the equilibrium condition; sustainability; extremum of the functional; differential equation; sliding surface; anisotropy; inhomogeneity; angle bending; used slope; stability of waste dumps; weak base; water cut.

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