The exact contribution of the pressure head gradient term during the vertical infiltration process, occurring in homogeneous porous media under zero ponding head, is determined analytically to advance the knowledge related to the infiltration phenomenon. This contribution is smaller than that of the horizontal infiltration by a factor at which is a measurable function of the infiltration time t, characteristic of each porous body. By adding to this contribution that of gravity, a new two-term analytical equation is formulated which exactly reproduces an available vertical cumulative curve and satisfies the physics governing infiltration process. The properties of at allow the derivation of an equation accurate for small and moderate t and of another one accurate for all t, including large values. By applying new methodologies, the values of the sorptivity and hydraulic conductivity are determined analytically from an available cumulative infiltration curve. Philip’s two-term equation, which does not satisfy the physical requirements at the upper extreme of t, and three other equations that do satisfy it, are examined in the light of the findings of the present work. The proposed equations are able to describe the vertical infiltration process and may be used to provide the hydraulic properties.

中文翻译：

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研究垂直渗透的新方法

垂直渗透过程中压力水头梯度项的确切贡献，发生在零积水水头下的均质多孔介质中，通过分析确定以推进与渗透现象相关的知识。这种贡献比水平渗透的贡献小一个因子，在该因子是渗透时间 t 的可测量函数，每个多孔体的特征。通过添加重力的这一贡献，制定了一个新的两项分析方程，该方程精确地再现了可用的垂直累积曲线并满足控制渗透过程的物理学。at 的属性允许推导出一个对小和中等 t 准确的方程，以及另一个对所有 t 准确的方程，包括大值。通过应用新方法，吸着性和水力传导率的值由可用的累积渗透曲线分析确定。菲利普的两项方程不满足 t 上限的物理要求，以及其他三个满足它的方程，根据当前工作的发现进行了检查。所提出的方程能够描述垂直渗透过程，并可用于提供水力特性。