Reynolds控制方程下粗糙节理渗流空腔模型研究

Study of void model for fluid flow through rough joints—taking Reynolds equation as governing equation

在研究节理的渗流时,渗流控制方程对节理渗流分析结果具有显著影响。首先介绍了节理渗流分析中的控制方程:Navier-Stokes方程、Stokes方程、Reynolds方程和立定定理,并分析了各控制方程在节理渗流分析中的适用性。以Reynolds方程作为渗流分析控制方程,建立了粗糙节理渗流空腔模型。然后以节理试件为研究对象,在实测节理三维表面形貌并计算隙宽分布后,分别进行相同渗流边界条件下的室内渗流试验和空腔模型计算,得到节理在不同接触状态下的渗流量实测值和计算值,并分别将计算结果与立方定理下的空腔模型、将整个节理简化为光滑平行板模型的立方定理以及速宝玉经验公式的计算结果进行比较,结果表明,Reynolds方程下的节理渗流空腔模型计算结果与实测值最为吻合,可以较为准确地反映节理的渗流情况。同时,根据Reynolds方程下空腔模型得到的渗流流量分布可以呈现节理渗流的曲折现象,为从本质上研究节理渗流特性奠定了理论基础。

Governing equation has significant effects on the results of fluid flow through rough joint. In order to investigate flow through a rough joint, Navier-Stokes equation, Stokes equation, Reynolds equation and cubic law, which are commonly used in analyses of flow through a rough joint, are firstly introduced and their applicability are evaluated. And Reynolds equation is chosen as the governing equation, a void model is established to analyze fluid flow through a rough joint. Then taking artificial rock joints as objects, laboratory flow tests are first performed and the flow rates through joint derived from void model under the same boundary conditions are also predicted after obtaining the joint aperture distributions. Three other models including void model taking cubic law as governing equation, Cubic law referred to the whole joint surface and Su B.Y. empirical modified cubic law are also applied to predict the volumetric flow rates through joint samples. The predictions of four models are compared with experimental observations. It is found from the comparisons that flow rates derived from void model based on Reynolds equation agree well with experimental observations; while the predictions of other three models have large discrepancy from experimental observations. According to the comparison, Reynolds equation is able to predict flow rates through rough joint exactly. In addition, tortuosity phenomenon of flow through joints can also be derived from the distributions of volumetric flow rates vectors, which provides a theoretical basis for investigating the influences of tortuosity on flow rates in a rough joint.