Approach to construction of mathematical models of geo-massif stress-deformed state under the influence of natural and technogenic forces

Abstract

The paper presents the developed approach to the construction of mathematical models of the stress-strain state of a geo-massif under the influence of natural and technogenic forces. According to the proposed concept, the geological environment is considered as a nonlinear hierarchically organized multiscale system. The natural state of the geo-massif is formed as a result of the influence of gravitational, geotectonic forces and internal pressure of fluids, and the man-made impacts lead to a change in the natural stress field as a result of formation of disturbances in the integrity of rocks in the unloaded zones and stress concentrators around the areas. Description of the stressed-deformed state of the geo-massif is carried out through a hierarchical family of mathematical models, which are constructed in the form of boundary value problems of the theory of deformable solid. First, at the lower hierarchical level, the determining relationships are developed, in which the influence of natural forces is taken into account, and then the generalization of the obtained models for determining technogenic impacts is carried out at the upper level. The proposed approach allows the links in the resulting hierarchical structure of models to be built, which makes it possible to carry out studies of both the disturbed and the natural state of the geo-massif.