 ISSN 2307-2091 (Print)  ISSN 2500-2414 (Online) Theory of calculation of the stability of slopes and bases. Calculation of anisotropic, heterogeneous and undermined slopes pdf

A. V. Zhabko

This article is the third 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. Existing individual calculation methods have significant drawbacks. Basically, methodology for calculating the stability of inhomogeneous and undermined slopes does not exist. As for the anisotropic slopes, nowadays there is only one method of calculation. This methodology is based on the fact that the break point of sliding surface satisfies the conditions of the ordinary and special marginal Coulomb balance. However, this technique has some significant drawbacks. The main drawback of said method is that when one determines the bend angle of sliding surface he has to neglect the influence of the stress state (principal stresses), and as a result, a certain bend angle does not depend on the angle of incidence of surface weakening. Methods of study of this work are variational, differential and integral calculus and the theory of stability of homogeneous slopes, which was published earlier. In the first part of the research author examines the general theory of determining of the bend angles of sliding surfaces in the transition from one lithological layer to another and a bend on the weakening surface. The research presents a calculation for anisotropic slope in the case where weakening surface entirely coincides with the sliding surface. In the second part of the research author solves specific examples on the stability of an inhomogeneous, anisotropic and undermined slopes and escribes in detail the procedure for solving of the problems. One can find a comprehensive mathematical apparatus for the implementation of these solutions. All solutions are given in strict mechanical and mathematical formulation.

Keywords: slope; anisotropic slope; inhomogeneous slope; undermined slope; slope angle; angle of internal friction; cohesion; height of the slope; limit equilibrium method; the condition of equilibrium; stability; sliding surface; weakening the surface; bend angle; the angle of rupture.

REFERENCES

Mochalov A. M. 1971, Raschet ustoychivosti sloistykh otkosov [Calculation of the stability of layered slope], Trudy VNIMI [Proceedings of VNIMI], Leningrad, vol. 83.
1998, Pravila obespecheniya ustoychivosti otkosov na ugol’nykh razrezakh: utv. Gosgortekhnadzorom RF 16.03.98. [Rules to ensure the stability of slopes in the coal mines: approved by the State Technical Supervision of the Russian Federation 16.03.98], Saint Petersburg, 208 p.
Lavrent’ev M. A., Lyusternik L. A. 1950, Kurs variatsionnogo ischisleniya [Variational calculus course], Moscow, 296 p.