Quantitative descriptions of the temporal and spatial variations of volumetric water content and total water potential in unsaturated soils have for more than nine decades focused on diffusive mechanisms as represented by the Richards equation (Richards, 1931). However, recent laboratory studies (Lo et al., 2017) have revealed short-time transient behavior of water in non-deforming unsaturated soils that is distinctly oscillatory, not diffusive. In this paper, we establish a theoretical framework to generalize the Richards equation in a systematic way to account for non-diffusive mechanisms giving rise to oscillatory behavior in the water content and total water potential. A partial differential equation is developed, with the total water potential as the dependent variable, based on the coupling of mass and linear momentum balance within the continuum theory of mixtures. This new differential equation becomes equivalent to the Richards equation when non-diffusive mechanisms can be neglected, but when this condition is not met, the governing equation describes damped propagating wave behavior of the total water potential. This dynamic wave differs from a poroelastic wave in respect to solid framework motions and wave speed, as well as time and length scales. For a rigid, homogeneous unsaturated soil, the governing equation reduces to the Telegraph Equation, which can be solved analytically. An inherent feature of our approach is the appearance of natural time and length scales characteristic of total water potential waves. Consideration of these natural scales for three representative soils of differing texture helps to prescribe more precisely the domain of applicability of the Richards equation.

九个多世纪以来，对非饱和土壤中体积含水量和总水势的时空变化的定量描述一直集中在由 Richards 方程（Richards，1931）所代表的扩散机制上。然而，最近的实验室研究（Lo et al., 2017) 揭示了水在非变形非饱和土壤中的短时瞬态行为，这种行为明显是振荡的，而不是扩散的。在本文中，我们建立了一个理论框架，以系统的方式概括理查兹方程，以解释导致含水量和总水势中的振荡行为的非扩散机制。基于混合物连续介质理论中质量和线性动量平衡的耦合，开发了一个以总水势为因变量的偏微分方程。当可以忽略非扩散机制时，这个新的微分方程等效于理查兹方程，但是当不满足这个条件时，控制方程描述了总水势的阻尼传播波行为。这种动态波在固体框架运动和波速以及时间和长度尺度方面不同于多孔弹性波。对于刚性、均质的非饱和土壤，控制方程简化为电报方程，可以解析求解。我们方法的一个固有特征是总水势波的自然时间和长度尺度特征的出现。考虑三种不同质地的代表性土壤的这些自然尺度有助于更准确地规定理查兹方程的适用范围。我们方法的一个固有特征是总水势波的自然时间和长度尺度特征的出现。考虑三种不同质地的代表性土壤的这些自然尺度有助于更准确地规定理查兹方程的适用范围。我们方法的一个固有特征是总水势波的自然时间和长度尺度特征的出现。考虑三种不同质地的代表性土壤的这些自然尺度有助于更准确地规定理查兹方程的适用范围。