An Experimental Study of the Morphological Evolution of Rills on Slopes under Rainfall Action

Abstract

Accurately monitoring the morphology and spatiotemporal evolution characteristics of the entire process of slope erosion rill development is essential to circumvent the limitations inherent in traditional methods that rely on average flow velocity for hydrodynamic parameter calculations. This study employs an environmental chamber and a self-developed slope erosion test device to perform erosion tests on slopes with varying gradients and rainfall intensities. By integrating the structure-from-motion (SfM) method, fixed grid coordinate method, and continuous camera combined with the dye tracer technique, the morphological indexes and hydrodynamic parameters of the entire rill development process are precisely computed. The main conclusions are as follows: The entire process of slope rill development can be divided into three distinct stages. The initial stage is characterized by the appearance of tiny rills with mild erosion. The middle stage involves severe transverse spreading erosion and longitudinal undercutting, resulting in diverse rill morphologies. The final stage is marked by the stabilization of morphological characteristics. The peak slope soil loss is observed during the middle stage of rill development. The most effective parameters for characterizing slope soil loss from the beginning to the end are the Reynolds number and flow shear stress, the Froude number and flow shear stress, and the Froude number during different periods. Throughout the development of rills, the flow velocity initially decreases and then gradually increases until it stabilizes. The morphological indexes, including rill density, dissected degree, inclination, and complexity, generally show an increasing trend. However, in the middle stage, the rate of increase slows down, followed by a sharp rise at certain points. The optimal hydraulic parameters for evaluating rill density across different slope gradients, which were found to be the Darcy–Weisbach drag coefficient and real-time flow velocity, for assessing rill dissected degree, complexity, and inclination, were the Reynolds number and flow power. Under varying rainfall intensities, the most effective hydraulic and kinetic parameters for evaluating rill density, dissected degree, and inclination were flow shear stress and Reynolds number; for assessing rill complexity, the Reynolds number and flow power were used. The findings of this research enhance the accuracy of hydrodynamic parameter calculations in rill erosion tests, enable precise prediction of rill development trends on slopes, and offer innovative approaches for real-time dynamic monitoring of rill morphology and characteristics. These advancements are of significant importance for soil and water conservation and sustainability.

1. Introduction

Methods for monitoring slope erosion rills primarily consist of contact and non-contact measurements [1,2,3,4,5]. Contact methods encompass the stylus method, cross-section measurement, filling method, total station method, and GPS method. Non-contact methods include laser scanning, stereo photogrammetry, and remote sensing interpretation. The stylus method faces challenges in controlling deployment density. The cross-section method reflects only the overall change in the erosion rill without indicating its spatial development direction, and its measurement accuracy is lower. The filling method is time-consuming and inefficient. The total station method is more complex, the GPS method is susceptible to signal interference, the laser scanning method is costly, and the remote sensing method is suitable only for long-term monitoring of areas exceeding 50 km². The structure-from-motion (SfM) technique is a type of stereo photogrammetry that was first applied to erosion rill measurement in 2014 [1,2,6,7]. This method offers lower cost, shorter processing time, and higher portability and efficiency compared to other methods. Consequently, it is predominantly utilized for the accurate and rapid measurement of small watersheds or indoor erosion rill studies.

Scholars have extensively studied slope erosion under various rainfall conditions. Field experiments involving water discharge scouring tests have been conducted to determine the factors influencing flow production and to establish the functional relationships between these factors [8,9,10]. Field-simulated rainfall experiments on slope scouring have been conducted to identify the main factors influencing slope erosion and the patterns of runoff variation [11,12,13,14,15,16,17]. Indoor simulation tests of the slope erosion process have been performed in artificial rainfall halls. These tests reveal that gravity erosion is the primary factor causing fluctuations in slope sand production. The studies also determine the hydrodynamic parameters and their functional relationships with influencing factors, showing that rainfall impacts slope soil erosion more significantly than runoff effects [18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37]. Indoor modeling tests using simulated rainfall devices have been conducted to determine the hydrodynamic parameters and the variation laws of influencing factors. These studies divide the soil erosion process into stages and propose that soil erosion is the result of the combined effects of hydraulic and gravity erosion [38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53]. Research on the characteristics of rill morphology has yielded significant findings. However, further in-depth studies are needed to understand the spatiotemporal changes in rill morphology on slopes and the relationship between rill erosion and rill morphology on slopes.

Rill water flow is characterized by high flow velocity, shallow flow depth, high sediment concentration, and constant changes in rill channels, which constrain the use of conventional methods for slope flow parameter measurement. Additionally, the commonly used manual direct measurement method in the slope runoff field is subject to disturbances and prone to secondary computational errors. Considering the limitations of existing slope rill erosion monitoring and testing methods, this study employs an environmental chamber and a self-developed slope erosion test device for rainfall erosion tests. In the experiment, the structure-from-motion method, the fixed grid coordinate method, the continuous camera, and the dye tracer method were used to monitor the morphological evolution of rills on slopes under rainfall action. The experimental system can accurately monitor and analyze the morphology and the variation patterns of the flow velocity field at various stages of rill development during slope erosion, accurately calculate the hydrodynamic parameters during erosion, and identify the optimal characterization parameters at various stages of rill development. The findings of this research offer novel methods and support for real-time dynamic monitoring of rill morphology and characteristics on slopes, which is of significant importance for soil and water conservation and sustainability.

2. Materials and Methods

2.1. Materials

The natural volumetric water content of arsenic sandstone in Ordos, China, is 0.13, and the maximum dry density is 2.05 g/cm³. The particle analysis results of arsenic sandstone are shown in

Table 1. Particle analysis results for arsenic sandstone.

Particle Size Range (mm)	<0.075	0.075~0.10	0.10~0.25	0.25~0.50	0.50~1.00	>1.00
Content (%)	5.1	38.4	30.5	19.8	5.6	0.6

. The content of particle size <0.075 mm is 5.1%. According to the classification standard of soil body in the “Specification for Geotechnical Engineering Investigation GB50021-2001” (Ministry of Construction, PRC, 2002) [54], it can be known that the arsenic sandstone in Ordos, China, is fine sand.

2.2. Methods

2.2.1. Rainfall Erosion Test on Slope

The slope erosion test apparatus, depicted in Figure 1, comprises a soil trough, a lifting system, a support frame, a mobile device, loss collection components, grid line coordinate points, and an image and video acquisition system. The soil trough is constructed from iron plates and lacks a roof. It is 150 cm in length, 100 cm in width, and 45 cm in height. The side plates are 0.5 cm thick, and the bottom plate is 3 cm thick. Flanges 5 cm in width are positioned on the left, right, and top rear side plates to facilitate grid line coordinate drawing. The bottom plate features uniformly distributed 0.5 cm diameter holes spaced 20 cm apart to allow downstream water infiltration and discharge during testing. The lifting system comprises a side-turning cylinder multi-section ball hydraulic jack, a manual valve hydraulic pump station, and an oil pipeline. The hydraulic jack, divided into five sections with a total stroke of 800 mm, is situated between the support frame and the soil trough. The manual valve hydraulic pump station is a 4 kw, 6-way station capable of controlling the lifting and lowering of the six hydraulic jack sections simultaneously. The 2 m oil pipeline includes matching stainless steel wire joints. This lifting system can achieve slope gradients ranging from 0 to 30° by changing the lifting height at the rear of the soil trough and keeping the front of the soil trough unchanged. The support frame, constructed from square steel with a thickness of 0.3 cm, measures 150 cm in length and 100 cm in width. The mobile device features four universal wheels, each with a capacity of 0 to 4 t and equipped with a braking mechanism. These wheels are installed at the vertices of the rectangular support frame, enabling free movement of the slope erosion test device within the environmental chamber. The loss collection components, made of 0.5 cm thick iron plates and shaped like a funnel, are located at the front end of the soil trough. The connection between the loss collection components and the soil trough forms a 100 × 10 cm rectangle, while the other end serves as the water outlet with dimensions of 4 × 4 × 4 cm. The ends of the square tube are open. These components, in conjunction with buckets, facilitate the collection of soil particle loss during testing. The grid line coordinate points, drawn with white spray paint, are located on the top flanges of the left, right, and rear side plates, and at the top connection between the loss collection component and the soil trough. These lines, spaced 5.3 cm apart, are primarily used to analyze the morphological evolution of rills during testing using the fixed grid coordinate method. The image and video acquisition system utilizes a Canon EOS 70D SLR camera (Canon Inc., Tokyo, Japan) with a Canon EF-S 18–135 mm zoom lens to manually capture the morphological evolution of rills from various angles. The camera is positioned at an average distance of 50 cm from the target, with a focal length of 18 mm and 15 shooting control points spaced 30 cm apart. Each pair of adjacent images overlaps by more than 60%, ensuring successful image matching in subsequent processing.

The base of the soil trough in the slope erosion test apparatus was lined with a 5 cm layer of gravel, overlaid with a thin layer of highly permeable gauze to create a seepage channel for water flow. Subsequently, soil was filled and compacted in layers, adhering to a natural volumetric water content of 0.13 and a compaction degree of 63%, resulting in a total soil thickness of 30 cm within the trough. A rainfall intensity of 30 mm/h was applied one day prior to the main test to pre-wet the slope until water flow was observed on the surface. This pre-conditioning was done to ensure uniform initial soil water content across test variables, consolidate dispersed soil particles, and minimize the spatial variability of the soil surface. Following the pre-rainfall period, the soil trough was covered with a plastic sheet and allowed to stand for 24 h before commencing the rainfall test.

The environmental chamber, equipped with an advanced rainfall system, drainage system, and lighting system, as shown in Figure 2, can simulate various rainfall intensities. The slope erosion test device was positioned in the chamber to conduct rill morphology evolution tests at slope gradients of 10°, 15°, and 20°, and rainfall intensities of 50% (40 mm/h), 65% (55 mm/h), and 80% (70 mm/h) are set through the control interface of the environmental chamber. The rainfall intensity rate was calibrated before commencing the test. The test proceeded when rainfall uniformity exceeded 90% and the discrepancy between the measured and target rainfall intensities was within 5%. Rainfall intensity was monitored in real time. During the test, a 200-mesh bag (pore size 0.075 mm) collected soil particles every 5 min, which were dried and weighed. The filtered water was collected in a bucket, and its volume measured. Samples from the bucket were measured for volume, then filtered through filter paper, dried, and weighed to calculate the amount of soil particles smaller than 0.075 mm lost every 5 min.

Agisoft Metashape 2.1.0 (Agisoft LLC., St. Petersburg, Russia) was employed to generate three-dimensional models from the images of the evolved rill morphology captured during the test. No more than 15 poorly focused images with quality values <0.5 evaluated by the software Agisoft Metashape 2.1.0 (Agisoft LLC., St. Petersburg, Russia) were excluded, resulting in a total of about 400 images. These images were subjected to a standard structure-from-motion (SfM) workflow to generate a sparse point cloud. As a result, the root mean square reprojection error of tie points was 0.72 pix, on average, and the root mean square error of control points was about 1.73 mm in the horizontal directions (x and y axes) and 1.95 mm in the vertical direction (z axis). Using multi-view stereo algorithms, a dense point cloud was then derived and later extrapolated to a three-dimensional model. Figure 3 displays high-definition photographs alongside three-dimensional reconstructed models. A comparative analysis of the number, density, inclination, and the convergence and bifurcation of rills reveals that the parameters in both high-definition photographs and three-dimensional models are identical. This indicates that the three-dimensional models generated by Metashape software accurately reflect the development process of slope rill morphology, facilitating subsequent data extraction and analysis of rill evolution.

The fixed grid coordinate method involves drawing grid lines based on the coordinate points on a three-dimensional reconstructed image. This ensures that the grid line deformation aligns with the lens aberration by capturing the rill morphology. Consequently, this method allows precise location and analysis of rill morphology evolution under rainfall and enables accurate real-time calculation of rill flow velocity.

The morphological evolution of the rill on the slope was continuously recorded using high-definition equipment, positioned atop the environmental chamber to minimize the impact of rainfall on recording quality, with the recording angle maintained parallel to the slope surface. During the test, a dye (potassium pertechnetate) was applied to the top of the slope at 5 min intervals. Using the continuous recording data from the high-definition equipment and the fixed grid coordinate method to determine the water flow paths, the real-time flow velocity of a rill can be precisely calculated. This improves the accuracy of hydrodynamic parameterization and mitigates errors associated with traditional methods, such as calculating flow velocity by dividing the total flow rate by the average cross-section of the rill and flow duration.

2.2.2. Numerical Simulation

The two-phase Euler–Euler flow model is employed to calculate and analyze the morphological evolution of slope erosion rills. The two-phase Euler–Euler flow model considers water flow and sediment as a continuous medium occupying the entire computational domain. Based on the two-phase micro-local conservation equations for mass and momentum, the two-phase continuity and momentum equations are derived using time- or spatial-averaged methods [55,56].

(1)

Water flow control equation

The local instantaneous continuity and momentum equations for water flow are similar in form to the single-phase fluid control equations and can be expressed as:

$${\displaystyle \frac{\mathsf{\partial }{\rho }_f}{\mathsf{\partial }t}}+\nabla \cdot \left({\rho }_f{\mathit{u}}_f\right)=0$$

(1)

$${\displaystyle \frac{\mathsf{\partial }}{\mathsf{\partial }t}}\left({\rho }_f{\mathit{u}}_f\right)+{\rho }_f{\mathit{u}}_f\nabla \cdot {\mathit{u}}_f=-\nabla p+\nabla \cdot {\mathit{T}}_f+{\rho }_f\mathit{g}$$

(2)

where:

• ${\mathit{u}}_f$—velocity vector of the water flow. ${\mathit{u}}_f=\left(u_{fi},u_{fj},u_{fk}\right)=\left(u_f,v_f,w_f\right)$, m/s;
• $\mathit{g}$—gravitational acceleration vector, $\mathit{g}=\left(g_x,g_y,g_z\right)$, m/s²;
• ${\rho }_f$—water density, kg/m³;
• $p$—pressure, KN;
• t—time, s;
• ${\mathit{T}}_f$—hydraulic stress tensor, ${\mathit{T}}_f=\left[\begin{array}{ccc}{\sigma }_{fxx}& {\tau }_{fxy}& {\tau }_{fxz}\\ {\tau }_{fyx}& {\sigma }_{fyy}& {\tau }_{fyz}\\ {\tau }_{fzx}& {\tau }_{fzy}& {\sigma }_{fzz}\end{array}\right]$

Following the derivation process of the equations as outlined by researchers in the literature [55,56], the relationship between the body-averaged values and their derivatives for each variable of the water flow is established using the Newton–Leibniz formula and Gauss’s law. By neglecting the phase change effects between the water and sediment, the water flow control equation is expressed as follows:

$${\displaystyle \frac{\mathsf{\partial }}{\mathsf{\partial }t}}\left({\epsilon }_f{\rho }_f\right)+\nabla \cdot \left({\epsilon }_f{\rho }_f{\mathit{u}}_f\right)=0$$

(3)

$${\displaystyle \frac{\mathsf{\partial }}{\mathsf{\partial }t}}\left({\epsilon }_f{\rho }_f{\mathit{u}}_f\right)+{\rho }_f{\mathit{u}}_f\nabla \cdot \left({\epsilon }_f{\mathit{u}}_f\right)=-{\epsilon }_f\nabla p+\nabla \cdot \left({\epsilon }_f\cdot {\mathit{T}}_f\right)+{\epsilon }_f{\rho }_f\mathit{g}+{\mathit{F}}_{fs}$$

(4)

where:

• ${\epsilon }_f$—water flow volume fraction;
• ${\mathit{u}}_f$—velocity vector of the water flow, ${\mathit{u}}_f=\left(u_{fi},u_{fj},u_{fk}\right)=\left(u_f,v_f,w_f\right)$, m/s;
• $\mathit{g}$—gravitational acceleration vector, $\mathit{g}=\left(g_x,g_y,g_z\right)$, m/s²;
• ${\rho }_f$—water density, kg/m³;
• $p$—pressure, KN;
• t—time, s;
• ${\mathit{T}}_f$—hydraulic stress tensor, ${\mathit{T}}_f=\left[\begin{array}{ccc}{\sigma }_{fxx}& {\tau }_{fxy}& {\tau }_{fxz}\\ {\tau }_{fyx}& {\sigma }_{fyy}& {\tau }_{fyz}\\ {\tau }_{fzx}& {\tau }_{fzy}& {\sigma }_{fzz}\end{array}\right]$;
• ${\mathit{F}}_{fs}$—sediment force on water flow at a phase interface, KN.

(2)

Sediment control equation

In conjunction with references [55,56] and analogous to the derivation process of the water flow control equation, the sediment control equation can be formulated as follows:

$${\displaystyle \frac{\mathsf{\partial }}{\mathsf{\partial }t}}\left({\epsilon }_{ks}{\rho }_{ks}\right)+\nabla \cdot \left({\epsilon }_{ks}{\rho }_{ks}{\mathit{u}}_{ks}\right)=0$$

(5)

$${\displaystyle \frac{\mathsf{\partial }}{\mathsf{\partial }t}}\left({\epsilon }_{ks}{\rho }_{ks}{\mathit{u}}_{ks}\right)+{\rho }_{ks}{\mathit{u}}_{ks}\nabla \cdot \left({\epsilon }_{ks}{\mathit{u}}_{ks}\right)=-{\epsilon }_{ks}\nabla p+\nabla \cdot \left({\epsilon }_{ks}\cdot {\mathit{T}}_{ks}\right)+{\epsilon }_{ks}{\rho }_{ks}\mathit{g}+{\mathit{F}}_{ksf}+{\mathit{F}}_{ks,ms}$$

(6)

where:

• ${\rho }_{ks}$—phase k particle flow density, kg/m³;
• ${\epsilon }_{ks}$—volume fraction of solid particles in the phase k, with ${\epsilon }_f+{\displaystyle \sum _k{\epsilon }_{ks}}$=1;
• ${\mathit{u}}_{ks}$—velocity vector of the kth phase particle flow, ${\mathit{u}}_{ks}=\left(u_{ks},v_{ks},w_{ks}\right)$, m/s;
• ${\mathit{T}}_{ks}$—phase k particle flow stress tensor, ${\mathit{T}}_{ks}=\left[\begin{array}{ccc}{\sigma }_{sxx}& {\tau }_{sxy}& {\tau }_{sxz}\\ {\tau }_{syx}& {\sigma }_{syy}& {\tau }_{syz}\\ {\tau }_{szx}& {\tau }_{szy}& {\sigma }_{szz}\end{array}\right]$;
• $\mathit{g}$—gravitational acceleration vector; $\mathit{g}=\left(g_x,g_y,g_z\right)$, m/s²;
• ${\mathit{F}}_{ksf}$—force of water flow at the phase interface on the phase k sediment particle flow, KN;
• ${\mathit{F}}_{ks,ms}$—force of the phase m sediment particle flow on the phase k sediment particle flow at the phase interface, KN, $k\ne m$.

Utilizing the aforementioned theoretical model, the software COMSOL Multiphysics 6.2 (Comsol AB, Stockholm, Sweden) is employed to numerically simulate the slope rainfall erosion test. Corresponding boundary conditions: the sidewalls have no-slip boundary conditions, the exit is connected to the atmosphere and only allows gas to pass through, so the boundary conditions include atmospheric pressure, 101,325 Pa, and the solid-phase exit has no-slip boundary conditions. Initial conditions: the initial void ratio is set according to the physical index of soil in the rainfall erosion test, and the velocity of both gas and solid phases in the soil trough is zero.

3. Results

3.1. The Developmental Stage Delineation of Slope Rill Erosion

Rainfall erosion on the slope surface gradually transitions from pitting to rill erosion. This transition is characterized by changes in slope erosion rill inclination (the average angle between the rill direction and the slope), rill density (the total length of all rills per unit area), rill dissected degree (the sum of the planar area of all rills per unit area, indicating slope fragmentation and rill erosion intensity), and rill complexity (the ratio of the total length of a rill and its bifurcations to the corresponding vertical effective length, indicating the richness of the slope rill network) [57,58]. The development of rills on the slope under rainfall action can be divided into three stages. Initially (T₁), rainfall erosion transforms the slope surface from pitting to rill erosion. Subsequently (T₂), rainfall converges, leading to the merger and bifurcation of small rills, accompanied by transverse sidewall expansion and longitudinal undercutting erosion. Finally (T₃), the development of rills enters a stable state, marking the end of rill evolution. These stages are depicted in Figure 4.

3.2. Erosion and Morphological Evolution of Slope Rill with Different Slope Gradients and Rainfall Intensities

The test slope gradients were set at 10°, 15°, and 20°, with corresponding rainfall intensities in the environmental chamber at 50% (40 mm/h), 65% (55 mm/h), and 80% (70 mm/h). The slope erosion rill inclination, density, dissected degree, and complexity were employed to reflect the ductility of the erosion rill in both horizontal and vertical directions, the degree of slope fragmentation, the intensity of erosion, and the richness of the rill network on the slope surface, respectively.

Figure 5 illustrates the soil loss per 5 min for particles larger and smaller than 0.075 mm under varying slope gradients and rainfall intensities.

Based on Figure 5, as the rill erosion develops on the slope surface, soil loss initially increases, then decreases, and eventually stabilizes. During the early stage of rill development (T₁), water convergence is minimal, and the capacity to transport soil particles is weak, resulting in relatively low soil loss. As the water flow converges, the rills widen and deepen, leading to significant erosion of the rill sidewalls and bottom. Severe erosion at the bottom of the rill and sidewall collapse signify the transition to the middle stage of development (T₂). Soil loss peaks during this stage as the rill sidewall and bottom erosion intensifies. As this erosion gradually weakens, soil loss decreases and stabilizes, marking the final stage of rill development (T₃). Within the same time period, slope gradient, and rainfall intensity, soil particles smaller than 0.075 mm are lost in significantly greater quantities than larger particles, indicating that smaller particles are more readily transported by water flow under rainfall conditions.

At a constant rainfall intensity, soil loss on the slope surface escalates with steeper gradients, attributable to the heightened potential energy of water flow. This increase augments the water flow’s capacity for lateral expansion, vertical undercutting erosion, and soil particle transport. Conversely, under consistent slope gradients, soil loss amplifies with escalating rainfall intensity, correlating with the intensified scouring and transport capabilities of increased water flow.

The evolution of slope rill erosion at various stages manifests distinct patterns in water flow velocity over time, as depicted in Figure 6.

Based on Figure 6, during the initial phase of rill development, water flow on the slope accumulates gradually, with rill water flow initially restrained by soil particles, leading to a decline in velocity. As rill development progresses, water accumulation intensifies, leading to heightened water flow velocity amid the significant constraints imposed by the rill, fostering pronounced expansion and undercutting erosion phenomena. Towards the latter stages of fine rill development, the erosive impact on the rill sidewalls and base gradually diminishes, aligning the geometry of the slope rill erosion more closely with optimal water flow conditions, resulting in a gradual stabilization of water flow velocity within the rill.

The temporal evolution of slope erosion rill inclination is depicted in Figure 7.

Based on Figure 7, the temporal evolution of slope erosion rill inclination makes it apparent that during the initial phase of slope rill development, the rills exhibit frequent convergence and bifurcation, accompanied by dynamic shifts in water flow direction, leading to a gradual increase in rill inclination. As rill development progresses to the middle stage, a well-defined erosion pattern emerges on the slope, characterized by the convergence of numerous rills, leading to a continuous acceleration in flow velocity and resulting in pronounced sidewall expansion and erosion, consequently augmenting the inclination of the erosion rill. During this phase, rill sidewall collapse occurs, intensifying the erosive impact of water flow on the rill sidewall, leading to a rapid increase in rill inclination over certain time intervals. Towards the culmination of rill development, the erosive force of water flow on the rill diminishes, resulting in a stable geometric configuration, with inclination remaining relatively constant.

The influence of various slope gradients and rainfall intensities is evident in the density and dissected degree of erosion rills on the slope surface, as depicted in Figure 8 and Figure 9, respectively.

Based on Figure 8 and Figure 9, throughout the rill development process, both exhibit a progressive increase over time. During the initial phase of rill development, the emergence of rills on the slope surface was accompanied by a rapid increase in their quantity, resulting in a pronounced acceleration in both the density and the dissected degree of eroded rills, as depicted by steeper change curves. In the concluding phase of rill development, the spatial configuration stabilizes, with minimal changes observed in the quantity and area of the rills, leading to stable change curves for both the density and dissected degree of the eroded rills.

Analysis of the erosion rill density and dissected degree change curves reveals a consistent trend: as slope gradient and rainfall intensity rise, the erosion rill density and dissected degree on the slope concurrently increase, indicating a direct correlation between slope fragmentation and rill erosion intensity with escalating slope gradient and rainfall intensity.

Figure 10 illustrates the variations in rill complexity on the slope surface under different slope gradients and rainfall intensities throughout the entire process of rill development.

Based on Figure 10, as the slope gradient and rainfall intensity increase, the complexity of eroded rills on the slope surface escalates, indicating that higher slope gradients and rainfall intensities enhance the richness of the rill network on the slope surface. During the initial stage of rill development, rills appear on the slope surface, continuously increasing and merging, leading to a rise in erosion rill complexity. In the intermediate stage of rill development, significant expansion and undercutting erosion occur, accompanied by bifurcation and sidewall collapse, promoting the horizontal ductility of rills. The complexity curve of erosion rills continues to increase, with steep rises observed during certain periods. In the final stage of rill development, the number and morphology of rills stabilize, and the complexity of eroded rills tends to reach equilibrium.

3.3. Numerical Simulation to Verify the Accuracy of Slope Rainfall Erosion Tests

The two-phase Euler–Euler flow model, in conjunction with COMSOL Multiphysics 6.2 (Comsol AB, Stockholm, Sweden) software, was employed to numerically simulate slope erosion under varying slopes and rainfall intensities. The numerical simulation results for water flow velocity of the rills causing slope erosion, considering different slopes and rainfall intensities, are presented alongside experimental results in

Table 2. Numerical simulation results and experimental results for water flow velocity of rills.

Gradient (°)/Rainfall Intensity (%)	Rill Developmental Stages/Test Time (min)	Numerical Simulation Results (cm/s)	Experimental Results (cm/s)	Difference in Value
10/50	T1/5	3.51	3.50	0.01
	T2/30	3.91	3.89	0.02
	T3/55	5.62	5.61	0.01
15/50	T1/5	3.80	3.80	0
	T2/30	4.32	4.34	0.02
	T3/55	6.03	6.00	0.03
20/50	T1/5	4.59	4.60	0.01
	T2/30	4.99	5.00	0.01
	T3/55	7.40	7.40	0
10/65	T1/5	4.02	4.00	0.02
	T2/30	4.53	4.55	0.02
	T3/55	7.03	7.00	0.03
15/65	T1/5	3.96	3.95	0.01
	T2/30	4.99	5.00	0.01
	T3/55	7.83	7.83	0
20/65	T1/5	4.55	4.55	0
	T2/30	5.56	5.56	0
	T3/55	8.25	8.23	0.02
10/80	T1/5	4.26	4.25	0.01
	T2/30	4.81	4.80	0.01
	T3/55	7.15	7.12	0.03
15/80	T1/5	4.51	4.50	0.01
	T2/30	5.30	5.30	0
	T3/55	8.13	8.13	0
20/80	T1/5	4.99	5.00	0.01
	T2/30	6.00	6.00	0
	T3/55	8.58	8.60	0.02

.

Analysis of the data in Table 2 reveals that the maximum discrepancy between the numerical simulation results for water flow velocity in the rills causing slope erosion under varying slopes and rainfall intensities and the experimental results is 0.02, while the minimum discrepancy is 0. This suggests that conducting slope erosion tests with different slopes and rainfall intensities using the slope erosion test device developed in this study and environmental chamber equipment is feasible. Moreover, the accuracy of the data obtained through the proposed monitoring technology and experimental method is high for slope erosion tests under these conditions.

3.4. Relationship between Rill Erosion and Hydrodynamic Parameters on Slopes

The correlation coefficients between soil loss (D) from rills on the slope during the early stage of erosion (T₁ stage) and various hydrodynamic parameters, including real-time flow velocity (v), Reynolds number (Re), Froude number (Fr), Darcy–Weisbach drag coefficient (f), flow shear stress (τ), flow power (ω), and unit water flow power (φ), were calculated under different slope gradients and rainfall intensities, as shown in Figure 11. A test value of p ≤ 0.05 indicates a significant relationship, marked by (*).

Based on Figure 11, soil loss (D) is significantly negatively correlated with the Froude number (Fr), not significantly correlated with real-time flow velocity (v), and significantly positively correlated with the other hydrodynamic parameters. The correlation coefficients rank in the order of τ > ω > Re > Fr > f > φ > v.

During the initial stage of slope rill development, the increasing flow velocity of water is the primary factor causing mild erosion to the rill sidewalls. Analysis of the significance level and magnitude of the correlation coefficients between slope rill loss and hydrodynamic parameters indicates that the Reynolds number (Re) and flow shear stress (τ) during the T₁ stage of slope rill development are the most effective hydraulic and kinetic parameters for characterizing slope rill loss.

The correlation coefficients between soil loss (D) and hydrodynamic parameters during the middle stage of rill development (T₂ stage) under varying slope gradients and rainfall intensities are presented in Figure 12.

Based on Figure 12, soil loss (D) shows a significant negative correlation with the Froude number (Fr) and a significant positive correlation with the Reynolds number (Re), Darcy–Weisbach drag coefficient (f), and flow shear stress (τ). No significant correlations are observed with the other hydrodynamic parameters. The correlation coefficients are ranked in the order of Fr > f > Re > τ > ω > φ > v.

During the T₂ stage of slope erosion rill development, horizontal expansion erosion and vertical downcutting erosion become significant. Analysis of the correlation between slope rill soil loss and hydrodynamic parameters, along with the correlation coefficient magnitudes, indicates that in the middle stage of slope erosion rill development, the Froude number (Fr) and flow shear stress (τ) are the most effective hydraulic and kinetic parameters for characterizing slope rill loss.

In the final stage of slope erosion rill development (T₃ stage), the correlation coefficients between soil loss (D) and hydrodynamic parameters under varying slope gradients and rainfall intensities are presented in Figure 13.

Based on Figure 13, the correlation coefficients indicate that soil loss (D) has a significant negative correlation with the Froude number (Fr) and a significant positive correlation with the Reynolds number (Re). Other hydrodynamic parameters do not show significant correlations. The correlation coefficients are ranked as follows: Fr > Re > v > ω > τ > φ > f.

In the final stage of slope erosion rill development, the morphology of the rill becomes stable, and sidewall erosion gradually diminishes. Analysis of the significance level and correlation coefficients between soil loss on the slope and hydrodynamic parameters indicates that the Froude number (Fr) is the most effective parameter for characterizing soil loss on the slope during the T₃ stage of erosion development.

3.5. Optimal Characterization Parameters for Morphological Characterization of Slope Rill

(1)

Correlation between morphologic characteristics of rills and hydrodynamic parameters at different slopes

The correlation coefficients between morphological characteristics and hydrodynamic parameters throughout the development of eroded rills on slopes with varying gradients are presented in Figure 14.

Based on Figure 14, rill density (ρ) is significantly negatively correlated with the Darcy–Weisbach drag coefficient (f) and positively correlated with real-time flow velocity (v), Froude number (Fr), and Reynolds number (Re), with correlation coefficients in the following order: f/v > Re > Fr > τ > ω > φ. The rill dissected degree (μ) is significantly positively correlated with the Reynolds number (Re), real-time flow velocity (v), and water flow power (ω) in the following order: Re > v > ω > τ > φ > f > Fr. Rill complexity (c) is significantly positively correlated with Reynolds number (Re), real-time flow velocity (v), water flow power (ω), and unit water flow power (φ), and significantly negatively correlated with the Darcy–Weisbach drag coefficient (f), with correlation coefficients in the following order: Re/v > ω > f > φ > Fr > τ. Rill inclination (δ) has a significant positive correlation with flow power (ω), flow shear stress (τ), unit flow power (φ), Reynolds number (Re), and real-time flow velocity (v), with correlation coefficients ranked as follows: ω > τ > φ > Re > v >f > Fr. Analysis of the significance levels and correlation coefficients between rill morphology and hydrodynamic parameters indicates that the best parameters for evaluating rill density (ρ) are the Darcy–Weisbach drag coefficient (f) and real-time flow velocity (v), consistent with the findings of Xiao Peiqing and Zheng Fenli [59,60]. To evaluate the dissected degree (μ), rill complexity (c), and rill inclination (δ), the best parameters are Reynolds number (Re) and flow power (ω), aligning with the results of Xiao Peiqing and Zheng Fenli [59,60].

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Correlation between morphologic characteristics of rills and hydrodynamic parameters at different rainfall intensities.

The correlation coefficients between morphological characteristics and hydrodynamic parameters throughout the development of eroded rills on slopes under varying rainfall intensities are presented in Figure 15.

Based on Figure 15, rill density (ρ) shows significant positive correlations with flow shear stress (τ), flow power (ω), Reynolds number (Re), unit flow power (φ), real-time flow velocity (v), and the Darcy–Weisbach drag coefficient (f), while exhibiting a significant negative correlation with the Froude number (Fr). The correlation coefficients are ranked as follows: τ > ω/Re > Fr > φ > v > f. The dissected degree (μ) exhibits significant positive correlations with water flow shear stress (τ), water flow power (ω), Reynolds number (Re), Darcy–Weisbach drag coefficient (f), unit water flow power (φ), and real-time flow velocity (v), and a significant negative correlation with the Froude number (Fr). The correlation coefficients are ordered as follows: τ > ω/Re > Fr > f > φ/v. Rill complexity (c) shows significant positive correlations with flow power (ω), Reynolds number (Re), flow shear stress (τ), unit flow power (φ), and real-time flow velocity (v), with correlation coefficients ranked as follows: ω/Re > τ > φ/v > Fr > f. Rill inclination (δ) exhibits significant positive correlations with flow shear stress (τ), flow power (ω), Reynolds number (Re), unit flow power (φ), and real-time flow velocity (v). The correlation coefficients are ordered as follows: τ > ω/Re > φ/v > Fr > f. Analysis of the significance levels and correlation coefficients between slope rill morphology and hydrodynamic parameters indicates that the best parameters for evaluating rill density (ρ), dissected degree (μ), and rill inclination (δ) are flow shear stress (τ) and Reynolds number (Re), consistent with the findings of Xiao Peiqing and Zheng Fenli [59,60]. The optimal parameters for evaluating rill complexity (c) are Reynolds number (Re) and flow power (ω), also aligning with the results of Xiao Peiqing and Zheng Fenli [59,60].

4. Discussion

4.1. The Development Process of Slope Rill Erosion under the Action of Rainfall

The hydrodynamic properties of slope runoff predominantly influence the erosion patterns of rills on slopes, and these characteristics can elucidate the energy dynamics of runoff, thereby affecting the detachment, transport, and deposition of soil on slopes. The hydraulic properties of slope rill erosion during rainfall can be precisely characterized by parameters such as flow velocity, Reynolds number, Froude number, and Darcy–Weisbach drag coefficient. These findings align with those of Xiao Peiqing and Zheng Fenli [59,60], An [61], Reichert [62]. In investigating the dynamic mechanisms of rill erosion on slopes during rainfall, flow shear stress, flow power, and unit flow power were selected to precisely reveal the erosion mechanisms. These results corroborate the studies by Guanghui Zhang [63], Xuan Wang [64], Xiao Peiqing [59], and Reichert [62]. In the study of optimal characterization parameters for the morphology of rills on different slopes, the Darcy–Weisbach drag coefficient and flow velocity are identified as the best hydraulic parameters for evaluating the density of rills, and the Reynolds number and flow power are determined as the most suitable hydraulic and kinetic parameters for assessing dissected degree, complexity, and inclination. Additionally, under varying rainfall intensities, the Reynolds number and flow shear force are recognized as the best hydraulic and kinetic parameters for evaluating the density, dissected degree, and inclination of rills, and the Reynolds number and flow power are recognized as the best hydraulic and kinetic parameters for evaluating the complexity of rills. These findings are consistent with the studies by Xiao Peiqing and Zheng Fenli [59,60].

4.2. Limitations of This Study

This paper investigates the morphological evolution characteristics of slope rill erosion throughout the entire process of rainfall. It proposes optimal hydrodynamic parameters for evaluating these morphological characteristics, providing novel methods for real-time dynamic monitoring of slope rill morphology. This has significant implications for soil and water conservation and sustainable development. However, this study has several limitations. It does not account for the influence of the upper catchment effect on a slope, different rainfall patterns, or the scale and boundary effects of modeling experiments. In future studies, we will analyze the influence of the upper catchment and different rainfall patterns on the morphological evolution of slope erosion rills. We will conduct modeling experiments at various scales, establish the relationship between modeling scale factors and morphological indexes of slope erosion rills and hydrodynamic parameters, and further refine the modeling of slope erosion rills under rainfall conditions.

5. Conclusions

A self-developed slope erosion test apparatus was utilized to perform slope rill erosion experiments under simulated rainfall conditions within an environmental chamber. The morphological characteristics throughout the entire process of slope erosion rill development were meticulously monitored utilizing structure from motion techniques, fixed grid coordinate methods, continuous video recording, and dye tracing. This comprehensive methodology enhances the precision of computing characterization parameters for different phases of slope erosion rill development, holding significant implications for soil and water conservation and sustainability. The primary conclusions derived from this study are as follows:

• Based on the spatiotemporal evolution characteristics of rill morphology on slopes, the evolution process can be delineated into three distinct stages. The initial stage of rill development involves the formation of incipient rills accompanied by mild erosion. In the intermediate stage, rills begin to merge and bifurcate and produce transverse rill sidewalls, spreading erosion, with the longitudinal rill base undercutting the erosion of the already formed smaller rills, resulting in variable rill morphology. In the terminal stage, the development of rills is almost complete and their morphological characteristics are in a stable state.
• During the intermediate stage of rill development, erosion intensifies, and the peak of slope soil loss is observed. In the initial stage of rill development, flow velocity decreases due to obstruction by slope soil, but gradually increases and stabilizes after rill formation. Rill density, dissected degree, inclination, and complexity all exhibit an increasing trend as the rill progresses. However, the rate of increase in these morphological characteristics decelerates due to intense erosion in the intermediate stage, accompanied by sidewall collapse and sporadic steep increases.
• Throughout the development of rills due to slope erosion, the optimal parameters characterizing rill soil loss across the three stages are as follows: Reynolds number (Re) and water flow shear stress (τ) in the initial stage, Froude number (Fr) and water flow shear stress (τ) in the intermediate stage, and Froude number (Fr) in the terminal stage. By observing the change pattern of the optimal parameters characterizing each stage of rill development, the specific stage of rill development can be determined and the evolution trend of rill morphology can be predicted.
• Under diverse slope conditions, the Darcy–Weisbach drag coefficient (f) and instantaneous flow velocity (v) are identified as the most efficacious hydraulic parameters for evaluating rill density (ρ). Moreover, the Reynolds number (Re) and flow power (ω) emerge as the optimal hydraulic and kinetic parameters for quantifying the dissected degree (μ), rill complexity (c), and rill inclination (δ). Under varying rainfall intensities, the Reynolds number (Re) and water flow shear stress (τ) are recognized as the most suitable hydraulic and kinetic parameters for assessing rill density (ρ), dissected degree (μ), and inclination (δ).