Rock Mass as a Nonlinear Dynamic System. Mathematical Modeling of Stress-Strain State Evolution in the Rock Mass around a Mine Opening

The paper briefly reviews the fundamental (general) evolution properties of nonlinear dynamic systems. The stress-strain state evolution in a rock mass with mine openings has been numerically modeled, including the catastrophic stage of roof failure. The results of modeling the catastrophic failure of rock mass elements are analyzed in the framework of the theory of nonlinear dynamic systems. Solutions of solid mechanics equations are shown to exhibit all characteristic features of nonlinear dynamic system evolution, such as dynamic chaos, self-organized criticality, and catastrophic superfast stress-strain state evolution at the final stage of failure. The calculated seismic events comply with the Gutenberg-Richter law. The cut-off effect has been obtained in numerical computation (downward bending of the recurrence curve in the region of large-scale failure events). Prior to catastrophic failure, change of the probability density functions of stress fluctuations, related to the average trend, occurs, the slope of the recurrence curve of calculated seismic events becomes more gentle, seismic quiescence regions form in the central zones of the roof, and more active deformation begins at the periphery of the opening. These factors point to the increasing probability of a catastrophic event and can be considered as catastrophic failure precursors.