破碎岩体非等温渗流的非线性动力学研究

分别从固体及流体导热的能量方程出发,导出破碎岩体非等温渗流的能量本构方程, 结合渗流的连续性方程、运动方程、状态方程等建立了破碎岩体非等温渗流的一维非线性动力学方程组；结合Mathcad软件计算得到了系统的无量纲化平衡态, 利用逐次亚松弛迭代法分析了对应于不同参数时平衡态的稳定性；指出非等温渗流系统存在鞍结分岔及折叠突变, 与等温渗流相比, 考虑温度场的破碎岩体渗流动力系统更容易发生渗流突变. 

STUDY ON NONLINEAR DYNAMICS OF NON-ISOTHERMAL FLOW IN BROKEN ROCK

The special physical environment with the high ground stress, high ground temperature, high karst hydraulic pressure, and intense mining disturbance`` in deep broken rocks, determines that their mechanic system is a complicated nonlinear dynamical one. Given a relative stable stress field, the flow in broken rock can be considered as a non-isothermal one, and the dynamical mechanism on the instability of non-isothermal flow in broken rock is analyzed by the theory of bifurcation and catastrophe of nonlinear science. (1) According to the energy equations of the fluid and the solid, the energy constitutive equation on non-isothermal flow in the broken rock is developed, and combining with the continuity equation, kinetic equation and the state equation of the flow, the one-dimensional nonlinear dynamical equations of non-isothermal flow in broken rock are established. (2) Using these equations and boundary conditions, the dimensionless steady states of the flow system are obtained by using Mathcad software. It is indicated that the obtaining of the steady states for the non-isothermal flow system is much more difficult than that for the isothermal flow system and there are analytical solutions of steady states in isothermal flow system, while for the non-isothermal flow system, its analytical solutions of steady states can not be obtained. (3) The branch figure of the steady states of flow velocity for the non-isothermal flow system is drawn by the numerical analysis and compared with the isothermal flow, both the limited equilibrium point corresponding to the non-isothermal seepage field and the parameter value when the hysteresis appears all have an offset. (4) The stability of the steady states is analyzed by the iteration method of successive lower relaxation, and the non-isothermal flow system has a saddle-node bifurcation and a fold catastrophe. But its catastrophe position exist a rightward deviation, and the absolute value of the limited parameter $b$ decreases a magnitude, so the catastrophe is apt to take place in the non-isothermal flow dynamical system , namely, even if the breaking phenomenon is not very serious, the fold catastrophe may take place possibly in the non-isothermal flow system.