Ill-Posed Problems in Rock Mechanics
V. E. MIRENKOV
Chinakal Institute of Mining, Siberian Branch, Russian Academy of Sciences, Krasnyi pr. 54, Novosibirsk, 630091 Russia
Keywords: rock block, boundary, stress, displacement, singular equation, inverse problem, solution
Abstract
Boundary value problems of rock mechanics include many variables that exercise complex influence on the problem solutions. The influence of some variables may be considerable while the other variables have minor effect. The nature of the variable-solution relationship becomes evident after conversion of a boundary value problem. The conversion and the analysis of the solution versus variable is as a rule carried out numerically, which raises questions on the solution accuracy and description of the influence of simultaneously changed variables on the solution. Currently there are known solutions to single-variable inverse subproblems. This article offers a new method for solving multi-variable inverse problems based on obtained exact solutions connecting boundary values of stresses and displacements and eliminating regularization.
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