黄土节理二维稳态流流量方程

Two-dimensional steady flow rate equation for loess joints

黄土节理渗流属于沿节理方向入渗和垂直于节理方向往黄土体入渗的二维渗流问题,对此问题目前尚少有研究。考虑节理内流体向土体的入渗及土体自身流速的影响,建立了黄土节理二维渗流模型,采用欧拉变数法推导了流体元运动微分方程,得到了以流速为函数的渗流微分方程。进而基于黄土节理渗流特征及边界条件,推导得到黄土节理二维稳态流的流量方程,表明岩体节理立方定律可归结为此方程在特定条件下的简化形式。进一步结合达西定律推导得到黄土节理渗透系数的表达式。通过现场试验和数值分析所反应出的趋势说明该公式有一定的应用价值。

The problem of jointed loess flows is a two-dimensional one including the flows both along the joint and perpendicular to the joint direction. This matter lacks research. Considering the vertical flows into the loess and the flow speed in the loess itself, a two-dimensional model for loess joints is established. By using this model, a seepage differential equation of flow velocity is derived by means of the Eulerian variational method. A two-dimensional steady flow equation for loess joints is further derived based on the flow characteristics and the boundary conditions of loess joints. This equation can be treated as an extension of the cubic law in the research field of rock joints. What＇s more, based on the Darcy＇s law, a permeability coefficient for loess joints is also derived.