Abstract
The authors propose to solve the problems connected with high pressure gradients using a model of a linearly elastic body with a structural parameter. The closed finite difference system of equations is formulated for plain strain deformation conditions. The problem on deformation of rock mass in the vicinity of an underground opening affected by mixed-type gravity-and-tectonic stress field is solved. It is demonstrated that addition of the structure in the solution changes the value of the stress concentration coefficient.
Highlights
Rocks possess very complicated elastoplastic and rheological properties
There are no universal mathematical models of rock masses, and the research seems unpractical in this respect
The simplest mathematical model of a geomedium is a linear elastic model. It is widely used for solving different problems in geomechanics and is a basic model [3,4,5]
Summary
Rocks possess very complicated elastoplastic and rheological properties. In some situations, elastic effects prevail, in other circumstances, internal friction, dilatancy, creep, etc. dominate. For this reason, there are no universal mathematical models of rock masses, and the research seems unpractical in this respect. The second direction is development of the basic model of an elastic body. The basic elastic model rests upon two hypotheses: 1) the Hooke law holds true; 2) the field of displacements is smooth, i.e. has partial derivatives of coordinates. Rocks contain abundances of pores and fractures of different scales For this reason, the condition of the displacement field smoothness should be slackened. Let us discuss one of possible implementations of the model [10]
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