Abstract
The paper defines the regularities of stress state of unsupported working occurring in a layered massif. The relevance of the performed research is substantiated by the importance of determining the stresses of the contour of unsupported working when the elastic modulus of the matrix and the layer is varied. Since the application of analytic methods for this case is complex, we used a numerical finite element method, implemented in the SCAD. We developed a finite-element model of the above working, where the elastic moduli of the matrix and the layer varied greatly, while its position was unchanged (the layer laying in the middle of the working). The results of the numerical analysis allowed us to build the regularities of three stress components. In order to normalize cases of elastic modulus variation, a dimensionless χ -parameter is introduced which characterizes the relation between the elastic modulus of the matrix and the layer. The obtained regularities of the stress state of the χ-parameter have a functional character and allow to determine the stresses on the contour of the unsupportedworking, depending on the relation between the elastic moduli of the matrix and the layer for all possible spectrum of these parameters.
Highlights
In geomechanics, mechanics of underground structures and wider in mechanics of rigid deformable body, the task of determining the stress state of an unsupported working or opening is well-elaborated
The obtained results for characteristic points allowed to construct the graphs of dependency of stresses of the unsupported working occurring in a layered massif on the parameter (Fig. 4-6)
With the help of the found regularities it is possible to determine the stress state in the five characteristic points of the contour of unsupported working occurring in a layered massif
Summary
Mechanics of underground structures and wider in mechanics of rigid deformable body, the task of determining the stress state of an unsupported working or opening is well-elaborated. This is evidenced by a number of fundamental works that consider workings of various forms in a massif of different properties – isotropic, transversally isotropic, anisotropic, varying degrees of fracturing, elastic, elastic-plastic, viscoelastic, viscoplastic etc. To solve the problem of determining the unsupported working stress state, the mostly used methods, before widespread introduction of PC, were mathematical methods, for example, that of complex potentials developed by H.V. Kolosov – N.I. Muskhelishvili [1]. After the powerful development of numerical methods and their implementation on a PC in a number of calculation complexes, the solution of this problem was determined during mathematical modeling by, for example, the finite element method [4,5,6]
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