摘要
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Summary
The 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鈥檚 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鈥檚 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鈥檚 rectangular dam problem and the drainage to symmetrically located ditches under steady-state conditions.
