矿山岩体破坏突水非达西流模型及数值求解

Non-Darcy flow model and numerical simulation for water-inrush in fractured rock mass

为模拟突水流体瞬态流动全过程并揭示突水流体流动机制,针对矿山岩体破坏突水过程中流体的高速非达西流特征和流场动力学统一性特征,基于流体质量守恒和压力平衡原理建立耦合Darcy方程、Forchheimer方程和Navier-Stokes方程的矿山岩体破坏突水非达西流模型,将含水层水源、破碎岩体突水通道和采场巷道出口整个水流路径有机联系在统一流动场中;并基于有限元弱形式和有限体积法耦合积分方程,提出有限元和有限体积法相结合的数值计算方法,应用FEPG有限元软件编译FORTRAN源程序,模拟突水瞬态流动全过程。通过算例对比达西和非达西流结果表明,对于矿山岩体破坏突水问题采用非达西流模型计算十分必要,破碎岩体作为导水通道沟通含水层和巷道的水力联系,导水通道内高速水流的惯性作用是含水层充足的补给水量沿破碎带进入巷道形成突水的主要原因。

In order to simulate the complete process of water-inrush and to reveal the mechanism of water-inrush in mines,two principal properties of water-inrush such as the high-speed non-Darcy flow and the unity of dynamic flow field were considered. A non-Darcy flow model for water-inrush in mines was established based on the conservation of mass and the pressure equilibrium. The corresponding model with the coupled relation of Darcy,Forchheimer and Navier-Stokes equations established the connection of water source in aquifer,water-inrush channel and the exit of tunnel in a uniform flow field. A numerical model was developed based on the coupled integral equations between the week form of the finite element method and the finite volume method. Using the software of Finite element program generator（FEPG）,the FORTRAN source programs were compiled and applied to simulate the complete flowing process of water-inrush. By comparison of the results for Darcy and non-Darcy flow models,the necessity of adopting non-Darcy model for water-inrush in mines was explained. It was also found that the fractured rock mass was the channel connecting the confined aquifer and tunnel. The inertia effect of the high-speed flow in the channel was the main cause leading to the water-inrush through the fractured rock mass.