The paper is devoted to theoretical investigation of peculiarities of mechanical response of fragments of block-structured geological media that experience non-equiaxial compression under shear deformation. The investigation was based on computer- aided simulation using the movable cellular automaton method. The results of investigations show that increasing the level of inner stresses in bloc-structured medium leads to the changing of the dominated deformation mechanism. This leads to changing of some characteristics of response of the medium, such as values of ultimate shear strain, shear strength, etc.
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