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Keywords: rock mechanics,broken rock,non-Darcy gas flow,nonlinear dynamics,saddle-node bifurcation,fold catastrophe

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In fields of coal mining,geotechnical engineering,the flow in broken rock is nonlinear,instable and time-varying for seepage parameters.Under the external disturbance,the gradual variation of the seepage parameter is apt to result in the catastrophe of the dynamic responses of the flow system and induces disasters such as water inrush and gas outburst.The study of the flow stability on the broken rock mass induced by mining is a basic subject of a series of important research topics such as controlling the stability of the surrounding rock,preventing the outburst disaster,exploiting and using the underground resources.The theories of bifurcation and catastrophe in nonlinear science are used to study the dynamic mechanism of instability of gas flow in broken rock.The nonlinear dynamical equations of one-dimensional non-Darcy and unsteady gas flow in broken rock are established.The solution diagram of dimensionless velocity under steady-state is given and the distribution laws along the direction of flow are obtained for the pore pressure and the steady-state flow velocity;namely,along the flow direction,the product of the pore pressure and the flow velocity of the dimensionless steady-states is a constant and the square of the pore pressure descends linearly.With low relaxation iteration,the dynamical responses corresponding to the different flow parameters of seepage system are also given.The results indicate that there is a saddle-node bifurcation in dynamic system of flow in broken rock;and at the bifurcation point,the breaking of edges and corners of rock grains is remarkable;thus an arbitrary weak perturbing at this point may result in a fold catastrophe of flow system and induce some dynamic disasters such as gas outburst,etc..


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