Determination of stress state in coal seam based on inverse problem solution using acoustic sounding data
| 1 | 071400 VKO Semey, Kazakhstan, st. Mangilik El 11, Kazakh Humanitarian Juridical Innovative University |
| 2 | 010008 Nur-Sultan, Kazakhstan, korpus 2, st. Pushkina 11, L.N. Gumilyov Eurasian National University |
CORRESPONDING AUTHOR
Mels Kudaibergenovich Kudaibergenov
071400 VKO Semey, Kazakhstan, st. Mangilik El 11, Kazakh Humanitarian Juridical Innovative University
071400 VKO Semey, Kazakhstan, st. Mangilik El 11, Kazakh Humanitarian Juridical Innovative University
Mining Science 2019;26:173–187
KEYWORDS
TOPICS
Application of fundamental science to miningMining geomechanics and geotechnicsGeodesy, geoinformatics and mine surveying
ABSTRACT
The paper presents an algorithm for calculating the horizontal, vertical and tangential stresses in a horizontal coal seam lying between galleries. These stresses are expressed in terms of the Airy function, which satisfies a homogeneous biharmonic equation. For its numerical solution it is necessary to set boundary conditions. Practical limitations do not allow us to determine the tangential stresses on horizontal boundaries of the coal seam. Calculations of stresses are proposed to be carried out in two steps. The first step is to solve the inverse problem for the biharmonic equation to find unknown tangential stresses on horizontal boundaries of the coal seam. The inverse problem is solved by minimizing the residual functional. Its strong convexity is proved, which implies the existence and uniqueness of the solution of the inverse problem. The second step is to solve the boundary value problem for the biharmonic equation to calculate stresses in the coal seam. The result of a numerical experiment is presented.
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