«InzhEnergoProekt» JSC, Moscow, Russia:

Mukaev I. R., Head of Department, e-mail: imukaev@injenergoproekt.ru

Institute for Problems in Mechanics of Russian Academy of Sciences, Moscow, Russia:

Salganik R. L., Leading Researcher, Professor, Doctor of Physical and Mathematical Sciences

Moscow State Mining University, Moscow, Russia:

Skvortsov A. A., Post-graduate Student

Moscow University of Aviation Technology, Moscow, Russia:

Fedotov A. А., Senior Lecturer, Candidate of Engineering Sciences

This article considers the problem of a stress state of horizontal layered rock massif (or soil bodies) with a relief nominal horizontal earth surface. The massif has an extensive mine working with a circular cross-section or a shallow tunnel, which had been constructed practically at the same instant, in comparison with the typical deformation relaxation of massif.

The layers are assumed to be elastic, isotropic, homogeneous and both non-slide.

The problem is solved in the assumption of a plane strain state in a sections, which are normal to the axles of working. The mine working is assumed to be placed under the top layer of massif, and the earth surface relief is gently sloping and non-changed along the working axel.

Its height differences are much smaller than the thickness of the top layer of massif.

The problem is solved by method of successive approximations. In zero approximation, the day surface is considered to be ideally flat. In first approximation (being the last one taken into account), a correction in the stress-strain state found in zero approximation is taken into account as the relief effect. To the numerically solving of zero approximation problem, the Finite
Elements Method (FEM) was used with realistic parameter values of the problem. To find the correction of the first approximation, there was used the well known analytical solution of corresponding problem. There were presented the results for the longitudinal normal stress distribution, calculated in zero- and first approximations just beneath the day surface. These results are important for calculation of the surface relief effect on mechanical behavior of the soil massif near its day surface.

This research paper was done with the partial financial support of Russian Foundation for Basic Research (project 11-01-00801).

1. Khusu A. P., Vittenberg Yu. R., Palmov V. A. Sherokhovatost poverkhnostey (teoretiko-veroyatnostnyy podkhod) (Surface roughness. Theoretical and probabilistic approach). Moscow : Nauka, 1975, 344 p.

2. Sheynin V. I., Ruppenpeyt K. V. Nekotorye statisticheskie zadachi rascheta podzemnykh sooruzheniy (Some statistical problems of calculation of underground facilities). Moscow : Nedra, 1969, 152 p.

3. Goodman R. E. Mekhanika skalnykh porod (Introduction to rock mechanics). Moscow : Stroyizdat, 1987, 232 p.