Geodesic
The stability of monolithic lining of the vertical mine workings
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 20 (2016) no. 3, pp. 457-474.

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A mathematical model has been made that describes the basic stress-strain state of the monolithic lining vertical excavation for materials with a porous structure, the skeleton of which has compressed the hardening elastoplastic properties. The deformation of the porous medium under the action of given radial compressive loads is divided into two interconnected parts: the elastic deformation of the porous medium and the inelastic deformation of the compressed matrix. The problem of determining the fields of stresses and displacements lining vertical production at each stage of deformation is solved within the framework of the plane strain. It does not take into account the effects due to the fact that the excavation has a finite depth. The equations define the field of stresses and displacements in the first and second stages of the deformation. The conditions of compatibility are the continuity conditions of the selected components of stresses and displacements in the elastic-plastic boundary and plastic strains are equal to zero on it. Within the framework of the exact three-dimensional equations of stability, the stability of the ground state of the monolithic lining vertical excavation in rock mass with tight pores has been studied. The estimation of influence on the value of the boundary between the elastic and plastic deformation of the initial porosity of the media and the yield strength of the material has been explained. The main component of the stress state of the coordinate values for different values of the initial solution pores and other physical and mechanical and geometric parameters of the material and the design have been studied and verified.
Keywords: dimensional stability theory, porous structure, complex rheology of the compressed matrix, geometrically linear deformation theory. 
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D. V. Gotsev; A. E. Buntov. The stability of monolithic lining of the vertical mine workings. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 20 (2016) no. 3, pp. 457-474. http://geodesic.mathdoc.fr/item/VSGTU_2016_20_3_a3/

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