Abstract
In this paper, for the first time, the effect of the longitudinal profile shape of the rill (uniform, concave, and convex) on flow resistance law was studied. The first part of the paper is based on a theoretical equation to estimate the Darcy–Weisbach friction factor f, deduced from the power velocity distribution and rill measurements performed on a plot. At first, the equation to estimate the Γ parameter of the velocity profile was calibrated using all available measurements. Then an analysis of the hydraulic characteristics at reach scale, for comparable values of discharge, was carried out, comparing the different profile shapes. To assess the influence of the rill profile shape on flow resistance law, this calibration was also carried out using the data categorized by profile. In the second part of the paper, an analysis of the scour depth and eroded rill volume was developed for four rills of each configuration. The results showed that an accurate estimate of f can be obtained by calibrating the flow resistance equation for each profile shape. The component of the Darcy–Weisbach friction factor that is due to the profile shape varied from 0.68 to 14.6% of the overall friction factor for the concave profile, and from 3.4 to 26.9% for the convex profile. The analysis also showed that, for the convex profile, the scour was concentrated downstream of the slope change, while for the uniform and concave profiles, it was uniformly distributed. Furthermore, the scour depth measured in correspondence of the rill thalweg had a generally increasing trend, with discharge for all the investigated profile shapes. Total eroded rill volume of the concave profile was lower than those detected for the uniform and convex profiles and was characterized by a reduction of 57.9%, as compared to the uniform profile.
Highlights
IntroductionRieke-Zapp and Nearing [2] carried out laboratory experiments to determine the relationship between slope shapes and soil erosion using five slope shape treatments (convex-linear, concave-linear, nose slope, head slope and uniform)
Many researchers have studied the effects of length and slope gradient on runoff and soil loss using uniform plots, i.e., having a constant slope, while a small number of studies have focused on the effect of profile shape [1,2].Young and Mutchler [3,4] investigated experimentally the effect of slope shape on runoff and soil loss at plot scale and showed that concave hillslopes tends to have reduced total sediment loss compared to a uniform profile slope.Rieke-Zapp and Nearing [2] carried out laboratory experiments to determine the relationship between slope shapes and soil erosion using five slope shape treatments
The experimental runs were carried out for Reynolds numbers corresponding to turbulent flow (2764 ≤ Re ≤ 11015 for the uniform profile, 2282 ≤ Re ≤ 14346 for the concave one, and 2486 ≤ Re ≤ 9487 for the convex one) and for Froude number values corresponding to subcritical and supercritical flow conditions
Summary
Rieke-Zapp and Nearing [2] carried out laboratory experiments to determine the relationship between slope shapes and soil erosion using five slope shape treatments (convex-linear, concave-linear, nose slope, head slope and uniform). These experiments demonstrated that rill patterns, sediment yield and runoff, all changed with slope shape. Sensoy and Kara [5] carried out an experimental investigation using nine experimental field plots with different profile shapes, established on a 30% hillslope, subjected to natural rainfall This field experiment indicated that slope shape (uniform, concave, convex) affected both runoff and soil loss. The uniform slope was characterized by the highest values of runoff and soil loss, while the concave slope produced the lowest values
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