Boussinesq equation-based model for flow in drainage layer of highway

Abstract

In order to study the water flow in the drainage layer of highway under steady-state condition, one-dimensional (1D) Boussinesq equation-based model with Dupuit-Forchheimer assumption was established and the semi-analytical solutions to predict the water-table height were presented. In order to validate the model, a two-dimensional (2D) saturated flow model based on the Laplace equation was applied for the purpose of the model comparison. The water-table elevations predicted by 1D Boussinesq equation-based model and 2D Laplace equation-based model match each other well, which indicates that the horizontal flow in drainage layer is dominated. Also, it validates the 1D Boussinesq equation-based model which can be applied to predict the water-table elevation in drainage layer. Further, the analysis was conducted to examine the effect of infiltration rate, hydraulic conductivity and slope of drainage layer on the water-table elevation. The results show that water-table falls down as the ratio of Is to K decreases and the slope increases. If the aquifer becomes confined by the top of drainage layer due to the larger ratio of Is to K or smaller slope, the solution presented in this work can also be applied to approximate the water-table elevation in unconfined sub-section as well as hydraulic head in the confined sub-section.