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 lambda(d) and fillable porosity lambda(f) for two-layered soils are first derived with water table depth change increment d -> 0 under dynamic soil moisture conditions. The expressions of lambda(d) and lambda(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 lambda(d) and lambda(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 lambda(d) and lambda(f). Our proposed expressions could effectively characterize the effects of soil layering and vertical fluxes on lambda(d) and lambda(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 lambda(d)* and fillable porosity lambda(f)* for two-layered soils with large water table fluctuations are derived based on lambda(d) and lambda(f) (asterisks in lambda(d)* and lambda(f)* is to distinguish them from lambda(d) and lambda(f) derived based on increment d -> 0). Verification with drainage experimental data indicates that the proposed expressions can be extended to well capture the lambda(d)* and lambda(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.