Abstract:A one-dimensional uncoupled model governed by this research is a physics-based modelling of the rainfall-runoff induced erosion process. The presented model is composed of three parts of a three-dimensional (3D) hillslope geometry, a nonlinear storage (kinematic wave) model for hillslope hydrological response, and an unsteady physically based surface erosion model. The 3D hillslope geometry model allows describing of the hillslope morphology by defining their plan shape and profile curvature. By changing these two topographic parameters, nine basic hillslope types are derived. The modelling of hillslope hydrological response is based on a flow continuity equation as the relation of discharge and flow depth is passed on kinematic wave approximation. The erosion model is based on a mass conservation equation for unsteady flow. The model assumes that suspended sediment does not affect flow dynamics. The model also accounts for the effect of flow depth plus loose soil depth on soil detachment. The presented model was run for two different precipitations, slope content, and length, and results were plotted for sediment detachment/deposition rate. Based on the obtained results, in hillslopes with convex and straight profile curvatures, sediment detachment only occurred in the whole length of the hillslope. However, in concave ones, sediment detachment and deposition only occurred together in hillslope. The hillslopes with straight profiles and convergent plans have the highest rate of detachment. Also, results show that most detachment rates occur in convex profile curvatures, which are about 15 times more than in straight profiles.
The geometry of hillslopes (plan and profile) affects soil erosion under rainfall-runoff processes. This issue comprises of several factors, which must be identified and assessed if efficient control measures are to be designed. The main aim of the current research was to investigate the impact of surface Roughness Coefficients (RCs) and Complex Hillslopes (CHs) on runoff variables viz. time of generation, time of concentration, and peak discharge value. A total of 81 experiments were conducted with a rainfall intensity of 7 L min−1 on three types of soils with different RCs (i.e., low = 0.015, medium = 0.016, and high = 0.018) and CHs (i.e., profile curvature and plan shape). An inclination of 20% was used for three replications. The results indicate a significant difference (p-value ≤ 0.001) in the above-mentioned runoff variables under different RCs and CHs. Our investigation of the combined effects of RCs and CHs on the runoff variables shows that the plan and profile impacts are consistent with a variation in RC. This can implicate that at low RC, the effect of the plan shape (i.e., convergent) on runoff variables increases but at high RC, the impact of the profile curvature overcomes the plan shapes and the profile curvature’s changes become the criteria for changing the behavior of the runoff variables. The lowest mean values of runoff generation and time of concentration were obtained in the convex-convergent and the convex-divergent at 1.15 min and 2.68 min, respectively, for the soil with an RC of 0.015. The highest mean of peak discharge was obtained in the concave-divergent CH in the soil with an RC of 0.018. We conclude that these results can be useful in order to design planned soil erosion control measures where the soil roughness and slope morphology play a key role in activating runoff generation.
Scouring in the downstream of all weirs, including Piano Key Weirs (PKWs), can have major safety implications. Since the research on downstream scouring of PKWs is very limited, and the weir geometry is also known to have an impact on downstream scouring, this study investigated scouring in the downstream of PKWs with rectangular and trapezoidal geometries and two different heights. The scour hole measurements showed that in both rectangular and trapezoidal models, scour hole parameters increased both with the increase in discharge rate and the increase in weir height. Under similar discharge conditions, the scour depth downstream from the rectangular model was greater than the one downstream from the trapezoidal model. The dimensionless maximum scour depth, the distance of maximum scour depth from the weir toe, and the scour hole length for the trapezoidal PKW were, on average, 6, 13, and 11% lower than the corresponding ones for the rectangular PKW, respectively. However, these differences decreased with the increase in falling height. For both weir geometries, the maximum scour depth was aligned with the outlet keys. In addition, the maximum scour depth under the outlet keys was 13% greater than the one under the inlet keys.
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