Forchheimer flow in gently sloping layers: Application to drainage of porous asphalt

Abstract

This paper presents analytical solutions for the problem of steady one‐dimensional Forchheimer flow in an unconfined layer. The study's motivation is the drainage behavior of a highway pavement called permeable friction course. Permeable friction course is a layer of porous asphalt placed on top of impermeable pavement. Porous overlays are growing in popularity because they reduce noise, mitigate the hazards of wet weather driving, and produce cleaner runoff. Several of these benefits occur because water drains within the pavement rather than on the road surface. Drainage from the friction course is essentially that of an unconfined aquifer and has been successfully modeled using Darcy's law and the Dupuit‐Forchheimer assumptions. Under certain cases, drainage may occur outside of the range where Darcy's law applies. The purpose of this paper is to identify cases where the assumption of Darcy flow is violated, develop analytical solutions based on Forchheimer's equation, and compare the solutions with those obtained for the Darcy case. The principle assumptions used in this analysis are that the relationship between hydraulic gradient and specific discharge is quadratic in nature (Forchheimer's equation) and that the Dupuit‐Forchheimer assumptions apply. Comparing the Darcy and Forchheimer solutions leads to a new criterion for assessing the applicability of Darcy's law termed the discharge ratio.