A model for the phenomenon of rock bursts has been assumed. Inside a deflected rock beam A located between the seam C and the overlying rock layer B a region of tensile strains is formed above the neutral axis of the beam and a region of compressive strains below that axis. When the resistance limit of the medium is exceeded at the moment t 0, a fissure π is formed. The formation of this fissure initiates longitudinal waves propagating in the regions above and below the neutral axis of the beam. The problem is regarded as unidimensional, assuming the equation of state of the medium in the form σ = σ(ɛ, ∂ɛ/∂t) (σ is stress, ɛ is strain). The strain within the beam above its neutral axis is ɛ > 0 at the instant t = t 0. After the fissure π has been formed during the time t > t 0, it is followed by compression. Within the beam, below its neutral axis, there is ɛ < 0 at the instant t = t 0. During the time t > t 0 expansion takes place. In a particular case of a non-linear dependence σ = σ(ɛ) when d 2σ/dɛ 2 ≠ 0, these phenomena are described by a quasi-linear system of hyperbolic equations. The conditions are given for the generation of a shock wave depending on the form of the equation of state of the medium and the boundary conditions on the surfaces S 1 and S 2 of the fissure π. A programmed execution of these conditions would direct the process of the formation of a shock wave and in this way enable control of the rock burst phenomenon to be achieved. When σ = σ(∂ɛ/∂t), the conditions for the generation of a shock wave do not exist.
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