Resistance coefficient for large-scale roughness with seepage through porous bed

Abstract

Resistance coefficient is an important parameter in estimating the energy loss for bed roughness in open channels. The Manning–Strickler (MS) formula has been used widely over the past decades. However, it is not suitable for calculating the resistance coefficient of large-scale roughness. The problem becomes more complex when penetration through roughness is considered. This paper proposed a new resistance coefficient formula for quantifying the flow resistance for large-scale bed roughness considering the seepage effect. A two-layer dynamic model was established for the turbulent flow over large-scale roughness. In this model, the flow was divided into two part: the free-flow layer and permeable layer. The resistance formula was derived based on the two-layer model that considered the roughness area and seepage effect through roughness elements. Two sets of large-scale roughness data, namely, gravel-bed data and experimental data of the tetrahedral permeable frames, were used to validate and calibrate the derived formula. For gravel, qualitative analysis was undertaken to estimate the reliability of formula. For tetrahedral permeable frames, the coefficient of determination and Nash-Sutcliffe model efficiency were used to evaluate the model performance, which showed the formula reliably simulated measured data. Results indicate that the formula can be applied to different kinds of large-scale bed roughness with seepage flow by adjusting the shape factor. This research could provide a theoretical basis for the application of large-scale roughness in river engineering and management.