基于最小作用原理的积水土坡水分入渗路径及规律研究

基于最小作用原理,以时间为最小作用量,建立了二维Richards方程水分入渗路径的泛函,提出了积水条件下土坡水分入渗的变分解,并在此基础上利用Brooks-Corey模型计算了锋面以上土体的水力坡降并讨论了入渗曲线的形态,同时利用Hydrus 2D软件分析了第一类边界条件下土坡内含水量分布。结果表明:二维斜面入渗的变分解与一维水平入渗、垂直入渗变分解具有相同形式；入渗曲线表现为外凸形态；数值计算得到的入渗量与湿润锋深度呈线性关系,与变分解的分析结果一致；变分解求得的湿润锋深度、含水量分布用于分析边坡稳定等宏观工程问题是可行的。

Research on water infiltration path and law of ponding soil slopes based on minimum action principle

Based on the principle of minimum action and taking time as the minimum action quantity, the functional of two-dimensional Richards equation was established. The variational solution of soil slope water infiltration under ponding was proposed. Brooks-Corey model was used to calculate the hydraulic slope of soil mass and the shape of the infiltration curve was discussed. Hydrus 2D software was used to analyze the water content distribution in the slope under the first type of boundary conditions. The results show that the variational solution of the 2-D infiltration has the same form as that of the 1-D horizontal infiltration and vertical infiltration. The infiltration path is convex shape. The infiltration capacity is linearly related to the depth of the wetting front, which is consistent with the results obtained by variational solution. Therefore, the depth of wet front and the distribution of water content obtained by the variational solution are feasible to analyze the macro-engineering problems such as slope stability.