This study presents the analytical expressions of drainable and fillable porosity for layered soils under shallow groundwater environments. The expressions of drainable porosity λ_d and fillable porosity λ_f for two-layered soils are first derived with water table depth change ∆d→0 under dynamic soil moisture conditions. The expressions of λ_d and λ_f consider the dynamic soil moisture conditions through the assumption of vertical fluxes in the unsaturated zone, varying as functions of water table elevation h. The analytical expressions of λ_d and λ_f have the same formula form but different values under evapotranspiration and recharge conditions, which is also verified using the numerical calculation. The case comparisons indicate that the vertical distribution of soil layers and the fluxes have significant effects on the performance of λ_d and λ_f. Our proposed expressions could effectively characterize the effects of soil layering and vertical fluxes on λ_d and λ_f. They could improve the accuracy of the previous expressions for single-layer soils, and complement the lack of description for layered soils under dynamic soil moisture conditions in previous expressions. Furthermore, under the hydrostatic assumption (static equilibrium of soil water pressure distribution) in the unsaturated zone, the expressions of drainable porosity λ_d* and fillable porosity λ_f* for two-layered soils with large water table fluctuations are derived based on λ_d and λ_f (asterisks in λ_d* and λ_f* is to distinguish them from λ_d and λ_f derived based on ∆d→0). Verification with drainage experimental data indicates that the proposed expressions can be extended to well capture the λ_d* and λ_f* changes for two-layered soils. Application scenarios suggest that our analytical expressions of drainable and fillable porosity are useful to improve the application performance of related subsurface modeling and groundwater estimation for layered soils under shallow water table environments.

中文翻译：

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浅层地下水环境下层状土可排水和可充孔隙度的解析表达式

本研究提出了浅层地下水环境下层状土壤可排水和可充填孔隙度的解析表达式。在动态土壤水分条件下，根据地下水位深度变化Δd→0，首先导出了两层土壤的可排水孔隙率λ _d和可填充孔隙率λ _f的表达式。λ _d和λ _f的表达式通过假设非饱和区的垂直通量考虑动态土壤水分条件，随着地下水位高度h的函数变化。λ _d和λ _f的解析表达式在蒸散和补给条件下具有相同的公式形式但不同的值，这也通过数值计算得到验证。案例比较表明，土层的垂直分布和通量对λ _d和λ _f的性能有显着影响。我们提出的表达式可以有效地表征土壤分层和垂直通量对λ _d和λ _f的影响. 它们可以提高先前表达式对单层土壤的准确性，并补充先前表达式中动态土壤水分条件下层状土壤的描述不足。此外，在非饱和区的静水力假设（土壤水压分布的静态平衡）下，基于λ _d推导了地下水位波动较大的两层土的可排水孔隙率λ _d * 和可充填孔隙率λ _f * 的表达式。和λ _f（λ _d * 和λ _f * 中的星号是为了将它们与λ _d和λ区分开来_f基于 ∆ d →0)。排水实验数据验证表明，所提出的表达式可以扩展到很好地捕捉两层土壤的λ _d * 和λ _{f * 变化。}应用场景表明，我们的可排水和可填充孔隙度的解析表达式有助于提高浅水位环境下层状土壤的相关地下建模和地下水估算的应用性能。