The research purpose is to develop a methodology that increases the reliability of reproduction and research on models made of equivalent materials of complex nonlinear processes of deformation and destruction of structured rock masses under the influence of underground mining operations to provide a more accurate prediction of the occurrence of dangerous phenomena and assessment of their consequences. New approaches to similarity criterion based on the fundamental laws of thermodynamics; new

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... pes of equivalent materials that meet these criteria; systems for the formation of various initial and boundary conditions regulated by specially developed computer programs; new technical means for more reliable determination of stresses in models; new methods for solving inverse geomechanical problems in the absence of the necessary initial field data have been developed. Using the developed methodology, a number of complex nonlinear problems have been solved related to estimates of the oscillatory nature of changes in the bearing pressure during dynamic roof collapse processes; ranges of changes in the frequency of processes during deformation and destruction of rock mass elements, ranges of changes in their accelerations; parameters of shifts with a violation of the continuity of the rock mass under the influence of mining: secant cracks, delaminations, gaping voids, accounting for which is necessary to assess the danger of the formation of continuous water supply canals in the water-protection layer.