Steady-state water table height estimations with an improved pseudo-two-dimensional Dupuit-Forchheimer type model

SummaryThe study of unconfined steady aquifer flow is usually based on either the numerical integration of the Laplace equation or on its analytical solution using the complex variable theory. A further approach that uses Adomian's method of decomposition yields simple analytical solutions in higher dimensions, does not require linearisation of the free-surface boundary condition and yields the elevation of the seepage face. A common approach is the introduction of simplified one-dimensional models that are often accurate enough for practical applications. However, the water table estimates derived by the so-called Dupuit-Forchheimer theory do not always fulfil the required accuracy. This work improves the Dupuit-Forcheimer hypotheses to obtain more precise results. For this purpose, the stream function of the groundwater flow net is formulated in natural, curvilinear coordinates. Next, an approximate one-dimensional model for the water table height is derived considering Darcy's law, retaining the curved features of the flow net. The proposed model is a higher order Dupuit-Forchheimer type approach, which was favourably compared with 2D results for Polubarinova-Kochina's rectangular dam problem and the drainage to symmetrically located ditches under steady-state conditions.

► We present a new approximate 1D model which, in the simplest way, retains the 2D features. ► The model is applied to the rectangular dam problem and the drainage of flows with recharge. ► The existence of the seepage surface is investigated and theoretical limitations discussed in depth. ► The present model is a higher order 1D Dupuit-Forchheimer model. ► The model is further compared to the full 2D solution, resulting in good agreement.