采动围岩中参变渗流系统的稳定性分析

用谱截断法讨论了采动围岩渗流系统在时变渗透特性和时变边界条件下的动力学响应.在对采动围岩的渗透特性和边界条件时变特性提出几点假设的基础上,考虑水的压缩性,建立了Forcheimor型非Darcy渗流系统的动力学方程.用Chebyshev配点法将系统的控制方程降阶为含有限个状态变量的非线性常微分方程组和由状态变量表示的边界条件和初始条件,用自选步长的四阶Runge-Kutta法分别得到采动围岩渗流在时变渗透特性和时变边界条件下的动力学响应;根据数值计算结果提出系统的失稳条件,通过研究渗流系统失稳,分析了煤矿突水的机理.研究结果表明:当渗透特性和边界压力在某段时间内满足一定条件时,采动围岩渗流系统可能失去稳定性,即发生突水;在周期性压力边界条件下,系统可能在新平衡位置附近产生周期运动,也可能失稳.

Analysis on stability of parametric system of seepage flow in wall rock affected by mining

Dynamic response of the system of seepage flow in wall rock affected by mining is studied by truncated spectral method, in the system the seepage properties and boundary pressure are variable. Based on a few assumptions about the change of seepage properties and boundary pressure, the dynamic equations of the system of Forcheimor's non-Darcy flow in wall rock are established taking into account the compressibility of water. By using Chebyshev allocation method, the dynamic equations are reduced into ordinary differential equations involving finite state variables, and the dynamic response of the system is gained by Runge-Kutta method. By force of numeric analysis, the instability condition of the system is presented, and the mechanism of water inrush is uncovered with a view to instability of seepage flow in post-failure rock. It is indicated that the system will be unstable if the seepage properties and boundary satisfy a certain relation during a time interval, and water inrush may take place. Under the action of periodic boundary pressure, the system may either be unstable or develop into a periodic movement around a new steady state.