Novosibirsk, Russia, May, 30 – June, 4, 2011

"Modern Problems of Applied Mathematics and Mechanics: Theory, Experiment and Applications", devoted to the 90th anniversary of professor Nikolai N. Yanenko

## Серяков В.М.## Efficient algorithms to solve rock mechanics problemsThe author considers the topical rock mechanics problems dealing with evaluation of the stress-strain state of a rock mass in mining areas where worked out areas are backfilled with consolidating mixtures. The analysis of the formation and deformation of a fill mass makes it evident that the earlier the fill mass section is formed, the greater load it carries at the current moment. Hence, when modeling the stress-strain state of a rock mass it is imperative to consider sequence of the fill-mass formation and to develop methods and algorithms to calculate the mechanical rock-mass state with consideration for the sequence order of the formation and the stowing of worked-out areas. The calculation process, based on the use of the single stiffness matrix, created at the first calculation stage to representing the initial rock mass, is proposed to solve the problems in question. The new-developed algorithm implies that the mine working development is indicated by vanishing of all the stress-tensor components in finite elements located in a mined-out area. The iteration of the initial stress method is employed to fulfill this condition. The initial stress method is also used to model the stress state in a fill mass, exhibiting mechanical characteristics differing from those of the initial rock mass. Thus, the new-proposed simple and efficient algorithm for calculation of the geomechanical rock mass state uses the initial stress method to take account of the mining sequence at all stages of the modeling. The cases when the new method and the software package are employed to evaluate the stress-strain state of the fill and host rock masses in different stoping processes designed to mine complex deposits are reported. Prospects of the process, calculation data obtained are discussed and a number of practical recommendations are worked out.
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