适于岩溶地区渗流场计算的改进折算渗透系数法和变渗透系数法

IMPROVED CONVERTING PERMEABILITY COEFFICIENT METHOD AND VARIABLE PERMEABILITY COFFICIENT METHOD FOR SEEPAGE CALCULATION IN KARST REGION

在总结各种岩溶地下水渗流计算方法的基础上,针对岩溶地区渗流场的特点,提出可同时考虑达西和非达西渗流流态的2种岩溶渗流计算方法:(1)改进折算渗透系数法。该方法从Colebrook公式出发,推求适用于求解紊流3个区沿程水头损失系数λ的公式,从而使岩溶管道水流与孔隙、裂隙水流统一起来;(2)变渗透系数法。该方法是将岩溶管道的渗透系数表示成待求水头和流态指数的函数,使岩溶管道中的非达西流与其他介质中的达西流统一起来。针对现有折算渗透系数法中的缺陷,推导了整体坐标系下岩溶管道渗透张量的计算公式。根据非稳定岩溶渗流基本微分方程式,基于Galerkin有限元法推导出了适用于岩溶渗流计算的有限元方程。经算例验证,提出的2种方法是合理可行的。

Based on summarizing all kinds of methods used to calculate karst groundwater seepage,aiming at the seepage characteristics in karst region,two methods considering Darcy and non-Darcy fluid simultaneously are put forward:(1) improved converting permeability coefficient method. In this method,a formula suitable for solving the stream wise head loss coefficient λ of three turbulence zones is deduced from Colebrook C. F. formula,which can integrate flows in karst conduits with voids as well as cracks;and (2) variable permeability coefficient method. It expresses the permeability coefficient of karst conduits as the function of water head to be solved and the exponent of flow regime,which can integrate the non-Darcy flow in karst conduits with the Darcy flow in other media. To overcome the disadvantage of converting permeability coefficients method,the formulas to calculate tensor of karst conduit in global coordinate system are deduced. According to the basic differential equation for karst seepage,the finite element method(FEM) equations applied for calculating karst seepage are developed on the basis of Galerkin FEM. Verified by examples,the two methods are reasonable and feasible.