A simple analytical solution of the equation for the one-dimensional horizontal permeability of soil water is important for estimating the hydraulic properties of soil. Our main objective was to develop analytical solutions to the nonlinear Richards equation, with constant-saturation upper boundary and an arbitrary initial soil water content (SWC) for horizontal absorption. We estimated the infiltration rate based on the hypothesis proposed by Parlange and carried out a series of transformations based on the Brooks–Corey model to obtain a theoretical function of the one-dimensional movement of water in unsaturated soil under an arbitrary initial SWC. The algebraic analytical solutions were simple, and the selection of the initial SWC was arbitrary. We assumed three scenarios of linear distributions of initial SWC, and Hydrus-1D software was used to simulate horizontal infiltration. Based on the comparison of algebraic and numerical results, the corrected algebraic model was proposed and verified by the arbitrary initial water content conditions when the maximum SWC was less than the half of saturated water content. The proposed method provides a description of horizontal infiltration for the heterogeneous initial SWCs.

一个简单的土壤水一维水平渗透率方程的解析解对于估算土壤的水力特性很重要。我们的主要目的是为非线性Richards方程开发解析解决方案，该方程具有恒定饱和的上限和用于水平吸收的任意初始土壤含水量（SWC）。我们根据Parlange提出的假设估算了入渗率，并基于Brooks-Corey模型进行了一系列转换，从而获得了任意初始SWC下非饱和土壤中水的一维运动的理论函数。代数解析解很简单，并且初始SWC的选择是任意的。我们假设了初始SWC的线性分布的三种情况，用Hydrus-1D软件模拟水平入渗。在比较代数和数值结果的基础上，提出了修正的代数模型，并在最大SWC小于饱和水含量的一半的情况下，通过任意初始含水量条件进行了验证。所提出的方法描述了异构初始SWC的水平渗透。