Analytical Expressions of Drainable and Fillable Porosity for Layered Soils Under Shallow Groundwater Environments

      This study presents the analytical expressions of drainable and fillable porosity for layered soils under shallow groundwater environments. The expressions of drainable porosity λd and fillable porosity λf for two-layered soils are first derived with water table depth change ∆d→0 under dynamic soil moisture conditions. The expressions of λd and λf 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 λd and λf 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 λd and λf. Our proposed expressions could effectively characterize the effects of soil layering and vertical fluxes on λd and λf. 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 λd* and fillable porosity λf* for two-layered soils with large water table fluctuations are derived based on λd and λf (asterisks in λd* and λf* is to distinguish them from λd and λf derived based on ∆d→0). Verification with drainage experimental data indicates that the proposed expressions can be extended to well capture the λd* and λf* 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.

       本研究推导了地下水浅埋深条件下层状土壤的可排水孔隙率（给水度）与可填充孔隙率的解析式。首先，在基于稳态通量假设和不考虑滞后效应的条件下，提出了地下水埋深变化趋近于零的可排水孔隙率λd与可填充孔隙率λf解析式。该解析式有效提高了现有表征方程的精度，并将其适用性拓展至非均质土壤条件。进一步的，基于埋深变化趋近于零的λd与λf解析式，提出了较大水位变化幅度时的可排水孔隙率λd*与可填充孔隙率λf*的解析式，弥补了现有解析式在近饱和段刻画不足的问题，并将其适用性拓展至非均质土壤条件。所提出的方程揭示了重要水文地质参数可排水孔隙率与可填充孔隙率在空间尺度高度非线性的变化规律，完善了该参数现有的量化表征方法。对于提高地下水相关的模型精度及水量评估的准确性具有重要作用，在地下水资源高效利用和管理方面具有重要意义。