A hydrodynamic diffusion wave model for stormwater runoff on highway surfaces at superelevation transitions
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Superelevation transition is often used to help balance the centrifugal forces on vehicles through curved roadway sections. Such transitions have regions with near-zero cross-slope as the pavement cross-section rotates from a negative to positive grade. For drainage of roadway surfaces, regions with near-zero slope constitute 'irregular topography'. This condition promotes extended stormwater runoff drainage path lengths and may result in excessive splash from vehicles and hydroplaning. A critical concern is the effect of longitudinal slope on stormwater drainage through superelevation transition. The overall goal of this study is to provide design guidance on longitudinal slope at superelevation transitions through application of a numerical simulation model of highway drainage. Sheet flow on urban pavement surfaces is very shallow, typically measuring a depth less than one centimeter. For modeling of such flow conditions, any small discontinuity or over-simplification of the surface geometry may result in failure in the flow computation. The kinematic wave approximation to the full Saint-Venant equations is often used in many surface and subsurface water models due to its simplicity in application. However, this model fails when backwater effects, ponding, or flow on reverse slope occurs in the local scale. Furthermore, due to the complexity in the surface geometry and the existence of drainage systems, the kinematic wave model is not sufficient for modeling urban stormwater runoff. On the other hand, the full dynamic wave (DW) model usually requires more computational effort. The long computation time of DW model often compromises the accuracy of the model, making the model practically inefficient. In this study, an algorithm was developed to properly represent the irregularly shaped roadway surfaces near superelevation transition areas with unevenly spaced curvilinear grids based on the geometry profile provided by a roadway design software package such as MicroStation CAD. With this accurately defined geometric representation, a nonlinear hydrodynamic diffusion wave model for hydraulic analysis developed in this research estimates the flow depth and runoff volume on the pavement surfaces. The model computes the flow responses for rising hydrographs using a preconditioned general Conjugate Gradient method. Kinematic boundary conditions developed for the open boundaries at the upstream and downstream boundaries compute the boundary values explicitly at each time step. The result of a numerical experiment shows that the spread and concentration of sheet flow is closely related to the transition in cross slope, longitudinal slope, rainfall intensity, and the width of the road. The characteristics of the sheet flow on superelevation transition areas are analyzed to find the optimal longitudinal slope. It is found that the longitudinal slope in the range of 0.3%-0.4% is the optimal slope at superelevation transition areas which minimizes the depth of stormwater runoff. An example application of the model on a rural highway in Texas is also presented. It is found that a significant amount of stormwater may exist on traffic lanes at the superelevation transitions tested. The predicted ponding depth exceeds the minimum value for potential hydroplaning, and the pattern of the flow concentration may cause differential drag forces on traffic vehicles.