It is shown in the paper that the system of equations of solid mechanics, which has a mixed type, demonstrate the most common features of evolution of nonlinear dynamic systems. Previous investigations of seismic process were carried out on the base of simplified (sand-pile, land-slide) models which gave a graph of recurrence of seismic events and information about the state of self-organized criticality (SOC). However, these simplified models do not contain the information about the stress-strain state of the loaded geomedia and its proximity to the critical state. In the proposed paper the model of rock mass with excavation is constructed and general step of roof caving is modelled. On the base of these modeling the formation of critical state in loaded geomedia is studied. The fluctuations of stress-strain state at different points of geomedia are studied as the reflection of fracture process occurring in the main elements of rock mass: roof and floor, when the coal face is advanced. It is shown that the probability distribution function (PDF) dependencies, amplitude-frequency characteristics reflect the state of the rock mass and might be considered as the fractal characteristics of fracture process within. The evolution of these dependencies shows the dramatic change when the critical state is formed in the rock mass surrounding the underground opening.
Mathematical modeling, fractal characteristics, coal mining, roof caving, stress fluctuations, critical states, damage accumulation
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