Rill erosion and morphological evolution: A simulation model

Abstract

A mathematical model is advanced to simulate dynamically and spatially varied shallow water flow and soil detachment, transport, and deposition in rills. The model mimics the dynamic process of rill evolution, including variable rates of sediment redistribution along the bed and changes in local bed morphology. The sediment source term in the model uses a point scale, probabilistic relationship based on turbulent flow mechanics and a recently developed sediment transport relationship for rills based on stream power. The interdependent feedback loops between channel bed morphology, local flow hydraulics, and local scour and deposition, within the framework of the full hydrodynamic equations with inertial terms, constitute a mathematical model with the capacity to represent spatial variability and temporal evolution of the rill. Finite elements were applied to numerically solve the hydrodynamic and sediment continuity equations. A series of laboratory flume experiments were performed to evaluate the model. Initial bed slopes were 3, 5, and 7% with step increases of water inflow rates of 7.6, 11.4, and 15.2 L min−1. The soil material used in the flume was a kaolinitic, sandy‐clay loam. The rill model equations were solved for increasingly complex cases of spatial and temporal variabilities. The model followed measured patterns of morphological changes as the rill evolved, which suggests that the feedback loops in the model between erosion, bed morphological changes, and hydraulics were adequate to capture the essence of rill evolution.

The characteristics of rill development and their effects on runoff and sediment yield under different slope gradients

“…Then it experienced an increase with the rate proportional to slope gradient. At last, it kept at stable levels (Figure 2), which are in a good agreement with Lei et al (1998) and Yan et al (2008), who stated that sediment concentration tends to approach a stable maximum value in the processes of rill erosion that is limited by the transport capacity of the water flow and is a function of slope energy that depends on the slope gradient (Nord and Esteves 2010). In general, the sediment concentration is positively related to the slope gradient in this study, and the rate of sediment concentration, increasing at any given …”

Quantifying the effect of a freeze–thaw cycle on soil erosion: laboratory experiments

“…When other experimental conditions are the same, greater slope produces greater sediment concentrations from both bins. Like Lei et al (1998) the eroded FT and C concentrations have no clear relationship to flow. The FT/C ratios of these concentrations are all significantly greater than 1, indicating a primary effect of the FT cycle on rill sediment erosion.…”

“…Though parameter values are slightly different, the overall patterns are very similar. Flume experiments of Lei et al (1998) indicated that sediment concentrations increased with bed slope, but did not generally increase with flow rate. In our experiments there is a strong and consistent dependence in both FT and C concentrations on the bed slope.…”

Hidráulica do escoamento e transporte de sedimentos em sulcos em solo franco-argilo-arenoso

“…O fundo e as paredes do sulco variam de geometria quando o solo é erodido, alterando as características hidráulicas do escoamento, as quais são responsáveis pela dinâmica de formação dos sulcos (Lei et al, 1998). A necessidade do conhecimento das relações hidráulicas e da morfologia dos sulcos, para determinar a capacidade de desagregação e transporte neste escoamento, levou à utilização da prática de conduzir os sulcos por meio da pré-formação, os quais, dessa forma, são expostos à ação cisalhante do escoamento, como preconizam Laflen & Thomas (1987) e Elliot et al (1989).…”