Abstract A modified Green-and-Ampt model is formulated to quantify infiltration on sloping terrain underlain by homogeneous soil wetted by surficial water application. This paper’s theory for quantifying infiltration relies on the mathematical statement of the coupled partial differential equations (pdes) governing infiltration and runoff. These pdes are solved by employing an explicit finite-difference numerical method that yields the infiltration, the infiltration rate, the depth to the wetting front, the rate of runoff, and the depth of runoff everywhere on the slope during external wetting. Data inputs consist of a water application rate or the rainfall hyetograph of a storm of arbitrary duration, soil hydraulic characteristics and antecedent moisture, and the slope’s hydraulic and geometric characteristics. The presented theory predicts the effect an advancing wetting front has on slope stability with respect to translational sliding. This paper’s theory also develops the 1D pde governing suspended sediment transport and slope degradation caused by runoff influenced by infiltration. Three examples illustrate the application of the developed theory to calculate infiltration and runoff on a slope and their role on the stability of cohesive and cohesionless soils forming sloping terrain.

中文翻译：

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坡地入渗及其对产流和边坡稳定性的影响

摘要 改进的 Green-and-Ampt 模型被公式化，以量化由地表水湿润的均质土壤下伏的倾斜地形的入渗。本文用于量化下渗的理论依赖于控制下渗和径流的耦合偏微分方程 (pdes) 的数学表述。这些 pdes 是通过使用显式有限差分数值方法求解的，该方法产生渗入、渗入速率、润湿前沿的深度、径流速率以及外部润湿期间斜坡上各处的径流深度。数据输入包括施水率或任意持续时间的风暴的降雨量流图、土壤水力特征和前期水分，以及斜坡的水力和几何特征。所提出的理论预测了前进的湿锋对平移滑动方面的斜坡稳定性的影响。本文的理论还发展了控制悬浮泥沙输运和由入渗影响的径流引起的斜坡退化的一维 pde。三个例子说明了所开发的理论在计算斜坡上的入渗和径流方面的应用，以及它们对形成斜坡地形的粘性和无粘性土壤稳定性的作用。