峰后岩石非Darcy渗流的分岔行为研究

THE BIFURCATION OF NON-DARCY FLOW IN POST-FAILURE ROCK

煤矿采动围岩大多处于峰后应力状态或破碎状态,其渗流一般不符合Darcy定律,为非Darcy渗流系统.峰后岩石非Darcy渗流系统的失稳和分岔是煤矿突水和煤与瓦斯突出动力灾害发生的根源.文中用谱截断方法建立了Ahmed-Sunada型非Darcy渗流系统的降阶动力学方程,再由变量代换得到以无量纲变量表示的平衡态附近的演化方程,分析了系统的分岔条件,给出了系统的各种吸引子图案,并结合采矿工程实际,用非线性数学的观点揭示了煤矿突水和煤与瓦斯突出的机理.研究表明:当非Darcy渗流系统渗流特性和边界压力的初始值满足一定条件时,系统由平衡转向不稳定,即存在跨临界Hopf分岔和切分岔,并且,系统的动力学响应不随渗透特性连续变化,即该系统存在突变性.

Seepage flow in post-failure rock, in which the stress is beyond the compressive strength, is not controlled by Darcy's Law further, and it can be described as a nonlinear dynamic system. Compared with that of anti-failure rock, the corresponding permeability of this rock increases sharply by several orders of amount. Rock strata around coal face are generally under post-failure state, or even under broken state, and therefore, the instability and bifurcation of non-Darcy flow in rock may lead to water irruption, coal and gas outburst, etc. in coal mines. So, it is of practical importance to study the complicated behavior of non-Darcy flow system. On the base of compression relations of porous and fluid, and conservations of mass and momentum, the developing equations of Ahmed-Sunada's non-Darcy flow in the vicinity of steady state are obtained through reasonable simplification. In this paper, the partial differential equations are reduced to ordinary differential equations by truncated spectra method, which involve 6 state variables. The stability and bifurcation of the system are analyzed by Lyapunov' s first method. The numerical results of the dynamic response, such as steady state attracter, periodical attracter, chaotic attracter, instability and disordered movements, are worked out. Combined with mining engineering, the mechanism of water irruption and gas burst is explained in nonlinear dynamics. It is considered that water irruption or coal and gas outburst is the result of the instability of seepage flow of water or gas in post-failure rock. The results show that the system may be unstable when both the seepage properties and initial pressure on boundary coincide with certain conditions, that is, trans-critical Hopf's bifurcation and tangential bifurcation exist in the system. Moreover, the dynamic response of the system does not change continuously with the seepage properties, i.e. there is cataclysm in the system. Because the permeability of post-failure rock is in the range of 10^(-17)-10^(-12)m2, and non-Darcy flow βfactor is in the range of 10~6-10^(10)m-1, numerical stability of solving of the differential equations should be paid more attentions, and it is well overcome with the help of constructing a set of dimensionless variables. This study provides engineers a new idea to prevent and cure the disasters in mines, including water inrush, coal and gas outburst, and will get wide use in mining engineering.