Improved Boussinesq Equation–Based Model for Transient Flow in a Drainage Layer of Highway: Capillary Correction

Abstract

Currently, time to drain and depth of flow are the two basic concepts for designing the drainage layer of highway, both of which are based on the saturated flow and cannot reasonably evaluate the drainage efficiency of drainage layer. A recent study demonstrated that capillary effects could become significant with unsaturated flow playing an important role in conducting water out of the drainage layer in some cases. In view of the disadvantages of the two methods, it is reasonable to combine them to guide the design of a drainage layer. Here, a model was established based on the one-dimensional (1D) transient Boussinesq equation with a capillary correction. The general solution to the governing equation was obtained using the method of separation variables. Furthermore, the presented model was validated against numerical simulations predicted by a finite-difference method (the MATLAB program) and the finite-element method (SUTRA program). A comparison was conducted to demonstrate the difference between the saturated drainage and unsaturated drainage processes. The results showed that the time to drain the same water volume based on the saturated model is much less than that based on the unsaturated model. The present model with capillary correction performs better than the saturated model in predicting time to drain in the drainage layer.