A generalized analytical solution for one-dimensional nonlinear horizontal infiltration in unsaturated soil is presented. The solution is an improved functional extremum method based on the principle of stationary action. Any prior assumption about the form of moisture diffusion functions is not implemented in the method. By considering a function of time, the water content type governing equation in the horizontal infiltration process is transformed into a function extremum problem. After solving the Euler–Lagrange equation, combined with boundary conditions, a linear relationship between the moisture diffusion function and the ratio of spatial location to the wetting-front distance is proposed. Furthermore, by using the square relationship between the wetting front and time, the spatial and temporal distribution characteristics of the water content profile are finally expressed. In contrast to most other work, the physical meanings of the parameters in this study are clear and can be derived explicitly. By utilizing the simultaneous Brooks–Corey moisture diffusion function, the development and distribution law of the water content profile was explicitly presented. The results of the solution matched well with the existing theoretical results of the four different soil samples. Owing to the high nonlinearity of the van Genuchten moisture diffusion function, the distribution of the water content profile was implicitly found based on the study method. The results obtained using this method were also consistent with the MATLAB routine, pdepe, numerical solutions for different types of soil properties.

给出了非饱和土中一维非线性水平入渗的广义解析解。解决方案是基于静止作用原理的改进的泛函极值法。在该方法中没有实现任何关于水分扩散函数形式的先验假设。通过考虑时间函数，将水平入渗过程中的含水量型控制方程转化为函数极值问题。求解欧拉-拉格朗日方程后，结合边界条件，提出水分扩散函数与空间位置与润湿前沿距离之比的线性关系。此外，利用润湿锋面与时间的平方关系，最终表达了含水量剖面的时空分布特征。与大多数其他工作相比，本研究中参数的物理意义是明确的，可以明确地推导出来。利用同步 Brooks-Corey 水分扩散函数，明确地呈现了含水量剖面的发展和分布规律。该解决方案的结果与四种不同土壤样品的现有理论结果吻合良好。由于 van Genuchten 水分扩散函数的高度非线性，基于研究方法隐式地找到了含水量剖面的分布。使用这种方法获得的结果也与 MATLAB 程序、pdepe、不同类型土壤特性的数值解一致。