均勻降雨時坡地之水理分析

Abstract

本研究針對在均勻降雨時水流流經一傾斜坡面，以半解析解方式，分析漫地流流經坡面之流況，藉此瞭解土壤特性對水流流動之影響。將流場分為水層及土層兩部分，土層為具滲透性之多孔介質，而土層中水流則以孔隙介質流視之，以此對流場進行解析研究，其結果亦可反映地表水流速度不為零的真實情況。 探討流況之過程利用宋長虹(1993)所建立之多孔介質層流模式搭配那維爾-史托克斯方程式作為控制方程式，求解得到水、土兩層流速之分佈，並且對流速積分得到各層流量，接著探討影響流況之參數因子。最後使用阮奇-庫特法建立水深與流速之關係，得到對應的流況資訊。 文中將土層厚度分為有限厚度和無限厚度兩種情況來分別探討，在求解出漫地流流況後，藉由改變各項坡面參數因子，觀察流況和水深之變化。發現當坡度因子增大、降雨強度因子減小、土壤滲透性因子增大或厚度增加時，皆會使水層之水深降低，其中又以坡度因子對整體流況影響最大。亦發現在僅改變降雨強度因子時，將對整體水深產生上下平移的現象，而其水面線依然維持同一形狀。在土壤質地方面，粗砂滲透性因子較大，透水性佳，因此水面線較其他土壤低，砏土及黏土由於滲透性因子極低，其流況與不透水表面幾乎相同。

This study analyzes water flow on an inclined plane under a uniform rainfall by a semi-analytical approach. The flow field is divided into two regions: water layer and soil layer. The soil layer is a porous medium. The flow inside the soil layer is a porous media flow. We observe how the soil affects the overland flow, and consider the flow velocity is nonzero on the ground surface. The velocity distribution in each layer can be solved by applying Song's(1993) laminar model and Navier-Stokes equation. Then the flow discharge is obtained by integrating the flow velocity. After solving the velocity of overland flow, the influence of each parameter will be discussed. By using Runge-Kutta method, the flow depth can be found. Then the relationship between flow velocity and water depth is built. There are two kinds of thickness, finite and infinite, that could be discussed. After the solutions of overland flow are obtained, water depth could be observed by changing the parameter of incline plane. We found that the water depth decreases with rainfall intensity and increases with the slope, permeability and thickness of soil layer. The slope factor affects the water depth most of all. When the rainfall intensity is changed, the water surface line will translate up and down, but its pattern doesn't change by the rainfall intensity. Different kinds of soil are also compared. It is obvious that the water depth of ocarse sand is the lowest. Since the permeabilities in silt and clay are low, the water depths in such soils are almost the same as that in impermeable ground.