Mathematical modeling of the disturbed state of a fragmented rock media | Mekhanika | kompozitsionnykh | materialov i konstruktsii
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Mathematical modeling of the disturbed state of a fragmented rock media

Abstract:

We find the three-dimensional representation of the stress state of a fragmented rock body, generalizing the representation in the Mohr plane to the stress tensor asymmetry case. We construct the mathematical model of the limit state (flow) of a geomaterial with account for grain rotation, which leds to reduction of the internal friction and adhesion of the rock. It is shown that the microrotations of the blocks form an ordered structure with the acheivement of the limit equilibrium state on the macroscale, which makes it possible to explain the nonuniformity of the rotation field and the stress field in the block medium that is observed in nature and in experiments. The microrotations of the blocks lead to localization of the deformation, and determine its structure and scale with satisfaction of the limit conditions. The propagation of the dynamic disturbances is solitonic in nature and is described by the sine-Gordon equation. This make it possible to develop the model of the generation of solitary deformation and seismic waves. It is found that in the case of plastic macroflow of a block medium the regime of generation of chaotic microrotations of the blocks is possible.

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