New approximate solutions of horizontal confined–unconfined flow

SummaryNew approximate solutions of horizontal confined–unconfined flow are developed to extend the solution of Li et al. [Li, L., Lockington, D.A., Barry, D.A., Parlange, J.-Y., Perrochet, P., 2003. Confined–unconfined flow in a horizontal confined aquifer. Journal of Hydrology 271, pp. 150–155] to more general hydraulic conditions. Both initial water table and storativity of the confined zone are considered. The Boltzmann transformation is applied to simplify the mathematical model with dimensionless variables and lumped parameters. A closed-form analytical solution is obtained for flow in the confined zone. A high-precision numerical solution with the Runge–Kutta method and an iterative process is proposed for nonlinear flow in the unconfined zone. For an initially dry aquifer, an approximate analytical solution is derived. In comparison with the initially dry condition, the initial water table condition will lead to a faster moving speed of the confined–unconfined conversion interface. The initial water table condition is beyond the scope of Li et al.’s (2003) method. The groundwater level could be overestimated by neglecting storativity of the confined zone. By introducing an equivalent storage coefficient, the developed new solutions can also be applied to analyze the unconfined flow in a double-layer aquifer system. In the case study on a confined–unconfined groundwater flow induced by rise of the water table in a reservoir of a hydropower station in China, the calculated distribution of groundwater level with the new solutions generally agrees with the observations at the field site.