Boussinesq Equation-Based Model for Flow in the Drainage Layer of Highway with Capillarity Correction

Abstract

The current engineering design of the highway drainage layer is typically based on the groundwater table elevation predicted by saturated flow models. Capillary effects may become significant, with unsaturated flow playing an important role in conducting water out of the drainage layer. With the capillarity neglected, saturated flow models such as the Boussinesq equation-based model (BM) and the Laplace equation-based model (LM) over predict the groundwater table elevation. This paper aims to modify the traditional BM to account for the capillary effects on the drainage. A correction term was added to the BM to incorporate predominantly horizontal flow in the unsaturated zone above the water-table, with vertical flow neglected. Analytical solutions to the governing equation were developed for both flat and sloping drainage layers. The modified model and analytical solutions were validated against predictions of a Richards equation-based model (RM) that simulated the variably saturated flow directly. The results showed that the assumption of negligible vertical flow made in the modified Boussinesq equation model (MBM) was sound. With capillary effects incorporated, this model predicted well the behavior of the water-table as simulated by the RM with relative errors typically less than 2% for the base case considered. The improvement made through the capillarity correction will enable the MBM to be used for analyzing and predicting the groundwater table in the design of the highway drainage layer.