Effects of different tillage practices on the hydraulic resistance of concentrated flow on the Loess Plateau in China

Catena 185 (2020) 104293

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Effects of different tillage practices on the hydraulic resistance of concentrated flow on the Loess Plateau in China Jiaqian Suna, Gerard Goversb, Mingxin Shia, Yanbin Zhaic, Faqi Wuc,

T

⁎

a

Institute of Soil and Water Conservation, Northwest A&F University, Yangling 712100, China Laboratory for Experimental Geomorphology, Catholic University of Leuven, Leuven 3000, Belgium c College of Natural Resources and Environment, Northwest A&F University, Yangling 712100, China b

A R T I C LE I N FO

A B S T R A C T

Keywords: Tillage practice Concentrated flow Flume experiment Friction factor Froude number

Numerous fixed or movable flume experiments have been conducted to characterize the hydraulic resistance of concentrated flow on natural and tilled surfaces. However, few studies have elucidated how the friction factor of flow resistance evolves over time on tilled surfaces. Since hydraulic resistance and concentrated flow interact with each other, it is critical to explore the underlying principles controlling their equilibrium under tillage practices. The objective of this paper is to study how during erosion, roughness and the relationship between the hydraulic characteristics and friction factor changed under different soil surface condition and tillage practices. We performed a series of flume experiments on rough soil surfaces under three treatments (manual dibbling, manual hoeing, and contour drilling). We then analyzed the changes in the Darcy-Weisbach friction factor based on surface roughness, hydraulic characteristics (slope gradient and unit discharge), Reynolds number, and Froude number. The results show that the temporal changes in surface roughness are associated with the tillage practices applied, and initial roughness cannot predict the surface responses adequately. Time plays a key role in the relationship between friction factor and hydraulic characteristics; therefore, different tilled surfaces exhibit inconsistent initial roughness values in addition to their varying evolution trends over time. There is a power function relationship between Reynolds number and friction factor, so that the effects of roughness and time should not be disregarded. The friction faction–Froude number relationship can also be expressed as a power function. However, the friction factor varies from one tillage practice to another and time remains a key factor in an erosion event. In addition, the Froude number is close to 1 in all cases, which may be an underlying principle controlling the dynamic equilibrium between flow hydraulics and surface roughness under tillage practices.

1. Introduction As one of the most severely eroded regions globally, the Loess Plateau in China is facing a major environmental challenge. Soil erosion on sloping cropland, which is also a global land degradation challenge, has been a major threat to the development and sustainability of agriculture in the plateau region (Zhang and Liu, 2005; Cerdà et al., 2009; Mandal and Sharda, 2013; Zhao et al., 2013; Moreno-Ramón et al., 2014; Borrelli et al., 2015). Tillage practices can alter soil surface roughness on sloping cropland across large scales. Soil surface roughness is an index describing the surface microtopography induced by natural events and human activities, which result in surface undulations. The roughness index is considered one of the crucial factors in erosion research on slopes (Bradford and Huang, 1994; Moreno-García et al., 2008; Chu et al. 2012). Soil surface roughness is thought to affect

the resistance encountered by water flowing over soil; flow resistance, in combination with water discharge and surface slope, affect flow velocity, which would in turn influence rill flow erosivity and transporting capacity (Gimenez and Govers, 2001). Understanding the relationship between morphological surface roughness and hydraulic resistance, therefore, facilitates the assessment of the potential effects of tillage practices on runoff velocity and erosion rate. Several hydraulic parameters such as the Reynolds number (Re) and the Froude number (Fr) are used to describe concentrated flow. The Reynolds number is a dimensionless number defined as the ratio of the inertial force to the viscous force within a fluid. The Reynolds number is calculated as follows (Emmett, 1970): (1)

Re = VR/ ν

−1

where Re is the Reynolds number, V is the mean flow velocity (m s

),

⁎ Corresponding author at: College of Natural Resources and Environment, Northwest A&F University, 3 Taicheng Road, Yangling 712100, Shaanxi Province, China. E-mail address: [email protected] (F. Wu).

https://doi.org/10.1016/j.catena.2019.104293 Received 8 June 2018; Received in revised form 21 September 2019; Accepted 25 September 2019 0341-8162/ © 2019 Elsevier B.V. All rights reserved.

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R is the hydraulic radius (m), and ν is the kinematic viscosity (m2 s−1). The Froude number is a dimensionless number defined as the ratio of the flow inertia to the external field. The Froude number is calculated as follows (Peng et al., 2015):

Fr = V / gh

regarding flow friction on natural and tilled hillslope surfaces, in addition to the effect of surface topography (e.g., Abrahams et al., 1994; Zheng et al., 2004; Knapen et al., 2007). In most cases, movable surfaces have been employed infrequently and soil detachment rates have been so low that the surfaces underwent with only minor changes in the course of the experiments. Recently, it has been reported that there is a feedback between flow hydraulics and surface roughness on erodible surfaces. Over time, the roughness characteristics are not constant but are modified by flow, leading to a dynamic equilibrium. Such a feedback mechanism explains why, in numerous cases, steady-state flow velocities on hillslopes seem to be independent of slope gradient (Govers, 1992; Nearing et al., 2017). Specifically, Govers (1992) postulated that the equilibrium flow velocities in rills on eroded hillslopes are controlled by the alternation between critical and subcritical flows, leading to an average Froude number of 1. Although Nearing et al. (2017) concluded that the above-mentioned phenomenon could not be explored in their experiments, they confirmed the existence of a strong feedback between flow erosion (which shapes the flow bed) and flow hydraulics. This finding implies that there is no fixed friction factor that could be used to predict concentrated flow characteristics from measured surface roughness, since concentrated flow resistance would change as a function of discharge rate, slope gradient, and time. Previous experimental studies have revealed key insights into the feedback between erosion and flow characteristics, which establishes a dynamic equilibrium. However, little is known about the time scale over which a tilled surface evolves towards such equilibrium, and whether there is a general pathway through which surface roughness evolves over time. Understanding the temporal evolution of soil surface roughness is important since the most serious erosion events are often associated with intensive rainfalls over short durations. Soil surface roughness potentially evolves in the course of such events but equilibrium states are not attained. In addition, concentrated flow discharge would vary across time at any point on the slope. Therefore, ideally, dynamic descriptions of the soil erosion–surface roughness–hydraulic resistance feedback should be integrated into erosion models. To achieve that, the time scales over which tilled surfaces evolve when subjected to erosive concentrated flow would need to be better constrained. This would not only facilitate the prediction of how soil erosion and surface runoff evolve over time, but would also be an important criterion for the selection of appropriate tillage practice (which would create a surface topography to reduce concentrated flow velocities considerably over extended periods). Because soil surface roughness affects soil infiltration, surface runoff generation, flow concentration, soil detachment, and flow transport capacity (Darboux and Huang, 2005), the roughness index has been and continues to be a major topic of study in hillslope hydrology and soil erosion. Tillage is a common soil surface treatment for sloping cropland and it changes the soil surface roughness considerably on the Loess Plateau. Currently, studies on the interactions between soil surface roughness and concentrated flow resistance on tilled surfaces are limited. In addition, relatively few studies have focused on how flow resistance evolves on tilled surfaces over time since the erosion process causes changes in surface roughness. Investigating how soil surface roughness affects flow resistance and the relationship between flow resistance and hydraulic parameters could facilitate the development of an empirical model for the effective prediction of hydraulic resistance on sloping cropland under tillage practices. The aim of the present study was to investigate the unique hydraulic resistance of concentrated flow on sloping cropland in the Loess Plateau region under tillage practices. The key objectives of this study were to investigate how tillage practices affect the friction factor of flow resistance, the relationship between friction factor and hydraulic parameters (slope gradient, unit discharge, Reynolds number and Froude number), and the role of time in an erosion event on sloping cropland. In addition, the effect of time may vary from one tillage practice to another; thus, time could affect the resistance law and erosion process

(2)

where Fr is the Froude number, g is the acceleration of gravity (m s−2), and h is the flow depth (m). Many studies have reported a power function relationship between the Darcy-Weisbach friction factor (f) and the Reynolds number (Rouse, 1961; Henderson, 1966; Roels, 1984). According to Yong and Harry (1971) and Shen and Li (1973), the friction factor increases with increasing Reynolds number when Re is < 2000, while it remains constant when Re is > 2000. Moreover, Peng et al. (2015) experimentally established that slope gradient affects the f–Re relationship substantially: on gentle slopes (< 10°), the friction factor decreases gradually with increasing Reynolds number; on steeper slopes (12–15°), the friction factor increases with increasing Reynolds number. Based on these contrasting trends, Peng et al. (2015) suggested that slope gradient is a key parameter controlling the equilibrium between the two different processes. Thus, on a gentle slope, the decrease in surface roughness with increasing Reynolds number due to an increase in flow depth is greater than the increase in surface roughness due to changes in sediment load and rill morphology. Conversely, on a steeper slope, when the Reynolds number increases, flow velocity increases more than flow depth and morphological friction affects flow resistance. The role of slope gradient is still a subject of debate because of its contentious effects on flow velocity and bed roughness in rills (Abrahams et al., 1996; Foster et al., 1984; Govers, 1992; Nearing et al., 1997; Torri et al., 2012). Abrahams et al. (1996) and Foster et al. (1984) demonstrated that the flow velocity in rills increases with increasing slope gradient in a fixed-bed condition. However, Govers (1992) and Nearing et al. (1997) indicated that flow velocity tends to be independent of slope gradient for a rill flow over a mobile bed. According to Govers (1992), a feedback mechanism exists in the process, so that the effect of an increase in slope gradient on erosion rate would counteract its effect on flow velocity. Therefore, based on the friction factor equation, the Darcy-Weisbach friction factor should increase with increasing slope gradient. Recently, Di Stefano et al. (2018) developed an equation based on a mobile-bed experiment, illustrating that the Darcy-Weisbach friction factor increases as a power function of slope gradient characterized by the regression coefficient of the slope that is approximately equal to 1. Rainfall is always considered to be a key factor influencing flow resistance when multiple roughness elements (e.g., sand grains, stones, vegetation cover, and rainfall) are present in the flow; these elements form a composite resistance that consists of different separate resistance elements (Weltz et al., 1992; Ferro, 2018; Palmeri et al., 2018). Raindrops directly affect flow resistance through their impact on water surface fluctuation and such up-and-down motion certainly creates an additional form of resistance. Additionally, rainfall generates flow disturbance, which also increases turbulence and flow resistance. Extensive studies have investigated bed-load effects on flow resistance experimentally to determine the relationship between particle motion and flow resistance (Vanoni et al., 1960; Baiamonte et al., 1997; Song et al., 1998; Gao et al., 2004; Hu et al., 2004; Recking et al., 2008). Vanoni et al. (1960) did not observe a clear difference in flow resistance between a mobile bed and a fixed bed. Song et al. (1998) concluded that particle motion could increase flow resistance based on the effect of bed-load movement on friction factor. In addition, some experiments have been performed to investigate the hydraulic 65 factors that affect friction factor, revealing that surface roughness and slope gradient are the major factors (Shi, 2015). Experimental studies on concentrated flow resistance began in the 1970s (Foster et al., 1984). Currently, there is a large body of literature 2

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Table 1 Chemical composition and particle size distribution of the soil used in the experiments. Chemical composition

Content (g kg−1)

Particle size (μm)

Percentage (%)

Organic matter Total nitrogen Alkaline nitrogen Total phosphorus Total potassium

5.0–15.0 0.5–1.3 0.5–1.3 0.002–0.023 17.1–40.8

10,000–2500 2500–500 500–100 100–50 50–10 < 10

0.4 8.6 44.2 13.5 21.7 11.6

Notes: D50 = 1.17 × 102 μm; D84 = 3.68 × 102 μm; D90 = 4.67 × 102 μm.

approximately 12% by storing the soil in a cool and dry place under a waterproof cover. Three different tillage practices were tested in the experiments, manual dibbling (MD), manual hoeing (MH), and contour drilling (CD), all of which are agricultural practices used extensively on cropland across the Loess Plateau. Details on the tillage practices are as follows (Fig. 3): (1) MD creates a dense system of pits (0.15 m by 0.15 m, ~0.05-m deep) using a drill barrow; (2) MH creates ellipsoidal shallow pits (~0.035-m deep) using a hoe; and (3) CD creates ridges (~0.035-m high) at 0.15-m intervals in the transverse direction using a plow. The experiments were performed using five different discharge rates (0.10, 0.15, 0.20, 0.25, and 0.30 L s−1 m−1) at six different slope gradients (2°, 4°, 6°, 8°, 10°, and 12°). Before each experiment, the flume was set at the selected slope gradient. At the beginning of an experiment, the water supply system was turned on to apply a preset discharge rate at the upper flume end. Incoming discharge was controlled using a flowmeter. The flowmeter was calibrated before each experiment to ensure the actual discharge rate was equivalent to the design discharge rate. Each experiment lasted 20 min during which hydraulic measurements were performed. At the bottom end of the flume, samples were collected for measuring the outgoing discharge rates and the sediment loads.

Fig. 1. A photo of the experimental flume used in this study.

on sloping cropland. Here time was considered a key factor in the prediction model to improve the effectiveness and accuracy of the model. The results of the present study could improve the understanding of the interactions between soil surface roughness and concentrated flow, and facilitate further research into concentrated flow erosion on tilled cropland in the Loess Plateau region. 2. Materials and methods 2.1. Flume experiments The experiments were carried out in a rectangular flume (6.0-m long, 1.0-m wide, and 0.3-m deep). The flume was divided into two parts by a glass wall located at the centerline of the flume so that two replicate experiments could be run at once (Fig. 1). The flume walls and bed were made of toughened glass and fixed with metal rods. A hydraulic jack located under the flume allowed the adjustment of the slope gradient (0–15°). The lower 0.05 m of the flume was filled with natural fine gravel (2–4 mm) and a 0.1-m thick layer of test soil was placed on top of the fine gravel (Fig. 2). The soil was collected from the plough layer (0–0.3 m) in cropland in Yangling, Shaanxi Province, China. The soil is classified as Lou soil, a common type of soil in Guanzhong Plain on the south edge of the Loess Plateau, North China. The Lou soil is an excellent agricultural soil formed by long-term cultivation of cinnamon soil. The soil has a greybrown color (10YR5/2) and a granular structure. It is classified as sandy loam in texture according to USDA texture classification. Some key properties of the soils are listed in Table 1. The flume was filled with fresh soil (sieved at 0.01 m) before each experiment. While the flume was being filled, the soil was tapped gently to achieve a near-uniform bulk density of approximately 1.35 g cm−3. The initial gravimetric soil moisture content was maintained at

2.2. Quantification of hydrodynamic parameters Soil surface roughness was measured using the chain method proposed by Saleh (1993). A 7.5-m long chain was placed on the slope along the direction of the steepest slope and pressed against the soil surface in the longitudinal direction. Then, the projected length of the chain on the slope and the real length of the chain were measured using tape. Soil surface roughness was calculated as follows:

Cr = (1 −

L2 ) × 100 L1

(3)

where Cr is the surface roughness, L1 is the real length of the chain, and L2 is the projected length of the chain. The surface roughness was measured five times at different positions on the slope before each

Fig. 2. A sketch of the mobile-bed experiment set-up. 3

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Fig. 3. Topography and layouts of the three different tillage practices.

Fig. 4. Size of the four sections on the slope (overhead view). 4

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the friction factor ranges were much greater on the rougher surfaces. Table 3 presents the mean flow velocity and depth data at the begging of the experiment under different tillage practices. At the end of the experiment, the average Darcy-Weisbach friction factors were significantly lower (P < 0.05) than the initial values in all cases. Among the three tillage practices, CD yielded the greatest decline in surface roughness, resulting in a mean value that was even lower than the value under MH (Table 4).

experiment and the means of the measurements were used in subsequent analyses. To quantify the evolution of flow velocity and depth along the flume accurately, the slopes were divided into four 1-m by 0.5-m sections (Fig. 4). Flow velocity was measured using potassium permanganate as a dye. A small amount of potassium permanganate solution was injected into the flow. The travel time of the dye cloud over a distance of 1 m in each section was recorded and the mean flow velocity in the section was calculated as the mean of three measurements. Considering the flow velocity measured using the dye-tracing technique is not the average velocity, a correction factor of 0.8 was used according to previous study (Di Stefano et al., 2018). Flow depth was measured using a needle gauge, which was located at the center of the main flow line in the section. As overland flow became concentrated with tillage, flow width, which was measured at the millimeter scale, decreased. Flow velocities, depths, and widths in all four sections were measured every 4 min, so that five sets of data were collected over the duration of the experiment (20 min). Water temperature was measured before and after each experiment and the mean of the two measurements was obtained. Kinematic viscosity was then calculated as follows (Wang, 2004):

ν = 1.775 × 10−6/(1 + 0.0337t + 0.00022t 2)

3.2. Resistance coefficient–time (f–t) relationship The scouring of the soil surface by runoff and the ensuing soil erosion greatly affected the resistance characteristics of the soil surface considerably by altering the tillage-induced surface roughness at a rapid rate. For example, the Darcy-Weisbach friction factor changed over time under the three tillage practices on a 4° slope with a discharge rate of 0.2 L s−1 m−1 (Fig. 6). Trends were similar for the other discharge rates and slope gradients. In general, the Darcy-Weisbach friction factor showed a decreasing trend with an increase in time. The decrease was the greatest on the roughest surface (CD) and the least on the smoothest surface (MD). To assess how discharge rate (q), slope gradient (S), and time (t) affect the Darcy-Weisbach friction factor under each tillage practice, we carried out a multiple regression analysis. The following equations were obtained for the MD, MH, and CD surfaces, respectively:

(4)

2 −1

where ν is the kinematic viscosity (m s ) and t is the water temperature (°C). The Darcy-Weisbach friction factor was calculated as follows (Abrahams et al., 1996):

8gRJ / V 2

(5)

R = hd/(d + 2h)

(6)

f=

f = 2.695S 0.415q−0.665t −0.339

R2 = 0.804

(7)

f = 9.434S 0.113q−0.504t −0.563

R2 = 0.774

(8)

f = 21.314S 0.581q−1.002t −0.959

where f is the Darcy-Weisbach friction factor, g is the acceleration of gravity (m s−2), R is the hydraulic radius (m), J is the hydraulic gradient, which can be calculated as the sine of the slope angle, V is the mean flow velocity (m s−1), h is the flow depth (m), and d is the flow width (m). Table 2 summarizes the hydrodynamic data under different tillage practices.

R2 = 0.753

(9)

The regression coefficients for time were r = −0.339 (MD), −0.563 (MH), and −0.959 (CD), indicating that time had a greater effect on the friction factoron a rougher surfaces. The effects of slope gradient and discharge rate were also strikingly different. Slope gradient had a significant positive effect (P < 0.05) on friction factor on the MD and CD surfaces, but not on the MH surface. The effect of discharge rate was similar under all the tillage practices, where the friction factor decreased with increasing unit discharge, and a much greater effect was observed on the CD surface.

2.3. Statistical analysis Data were analyzed using IBM SPSS Statistics 19 (IBM Corp., Armonk, USA). One-way analysis of variance and Fisher's least significant difference tests were used to compare the Darcy-Weisbach friction factors among the different tillage practices. All results were reported at the α = 0.05 level of significance. Regression analysis was used to evaluate the relationships between Darcy-Weisbach friction factors and hydraulic parameters. The coefficient of determination (R2) was used to evaluate the performance of the regression equations.

3.3. Resistance coefficient–Reynolds number (f–Re) relationship The f–Re relationship varied with different tillage practices and time periods (Fig. 7). Specifically, the Darcy-Weisbach friction factor decreased on the MH and CD surfaces but remained stable on the MD surface, despite the Reynolds number increasing overall over time on the MD surface. Notably, irrespective of the tillage practice, the final friction factors varied minimally (1.0–2.0) when the Reynolds number exceeded 2000. The f–Re relationship for different time periods of the experiment was analyzed under each tillage practice using regression analysis: For the MD surface:

3. Results 3.1. Resistance coefficient–surface roughness (f–Cr) relationship The average initial roughness of the MD, MH, and CD surfaces were 2.32, 3.96, and 7.69, respectively. To evaluate how initial differences in topographic roughness affects flow hydraulics, we first analyzed the hydraulic measurements obtained at the beginning of the experiment (0–4 min). The data were then compared with those obtained at the end of the experiment (16–20 min) to evaluate the temporal evolution of hydraulic roughness. The Darcy-Weisbach friction factor ranges under the different tillage practices are illustrated in Fig. 5. The friction factor changed significantly over time in all cases. In the first 4 min, the average friction factors of the MD, MH, and CD surfaces were 2.21, 7.50, and 9.16, respectively, which indicates that the initial Darcy-Weisbach friction factors were higher on the rougher topographic surfaces. In addition,

0 − 4min: f = 14.694Re−0.319 16 − 20min: f =

0.556Re 0.116

R2 = 0.325

(10)

R2

= 0.225

(11)

R2 = 0.368

(12)

For the MH surface:

0 − 4min: f = 29.314Re−0.228 16 − 20min: f =

645.181Re−0.779

R2

= 0.647

(13)

For the CD surface:

0 − 4min: f = 8.530Re 0.149 16 − 20min: f = 5

R2 = 0.297

88.554Re−0.553

R2

= 0.440

(14) (15)

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Table 2 Summary of hydrodynamic parameters under three different tillage practices. Tillage practice

S (°)

q (L s-1 m−1)

t (min)

h (m)

d (m)

V (m s−1)

Dr (g m−2 s−1)

MD

2

0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2 0.25 0.25 0.25 0.25 0.25 0.3 0.3 0.3 0.3 0.3

4 8 12 16 20 4 8 12 16 20 4 8 12 16 20 4 8 12 16 20 4 8 12 16 20

0.002 0.004 0.006 0.006 0.005 0.002 0.003 0.005 0.005 0.006 0.003 0.005 0.005 0.006 0.008 0.003 0.005 0.007 0.008 0.008 0.007 0.007 0.007 0.008 0.008

0.102 0.085 0.073 0.058 0.083 0.103 0.129 0.079 0.065 0.064 0.121 0.096 0.088 0.081 0.057 0.108 0.077 0.060 0.065 0.069 0.071 0.083 0.088 0.087 0.088

0.049 0.078 0.139 0.131 0.131 0.069 0.079 0.148 0.179 0.194 0.131 0.141 0.176 0.198 0.223 0.132 0.166 0.238 0.274 0.257 0.222 0.262 0.259 0.273 0.268

– – – – 0.068 – – – 0.022 0.085 – – 0.108 0.543 0.668 – 0.019 0.318 0.889 0.764 – 0.078 1.159 2.913 3.566

4

0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2 0.25 0.25 0.25 0.25 0.25 0.3 0.3 0.3 0.3 0.3

4 8 12 16 20 4 8 12 16 20 4 8 12 16 20 4 8 12 16 20 4 8 12 16 20

0.002 0.003 0.004 0.007 0.005 0.003 0.004 0.004 0.004 0.004 0.002 0.003 0.003 0.006 0.007 0.006 0.005 0.010 0.009 0.007 0.006 0.006 0.008 0.010 0.011

0.196 0.143 0.087 0.051 0.068 0.080 0.075 0.073 0.067 0.052 0.112 0.096 0.085 0.081 0.067 0.079 0.096 0.078 0.069 0.075 0.108 0.081 0.081 0.071 0.064

0.094 0.102 0.134 0.186 0.183 0.133 0.136 0.150 0.161 0.220 0.140 0.132 0.147 0.254 0.267 0.168 0.202 0.219 0.268 0.309 0.213 0.301 0.334 0.328 0.334

– – – – 0.049 – – – 0.013 0.260 – 0.247 0.148 1.249 2.321 – 0.619 2.968 2.908 2.726 – 1.012 4.136 4.192 3.793

6

0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2 0.25 0.25 0.25 0.25 0.25 0.3 0.3 0.3

4 8 12 16 20 4 8 12 16 20 4 8 12 16 20 4 8 12 16 20 4 8 12

0.003 0.004 0.006 0.006 0.008 0.005 0.007 0.007 0.008 0.009 0.004 0.005 0.008 0.010 0.011 0.008 0.009 0.009 0.010 0.009 0.006 0.009 0.010

0.056 0.043 0.039 0.040 0.041 0.087 0.067 0.066 0.061 0.065 0.083 0.071 0.053 0.045 0.044 0.094 0.077 0.063 0.059 0.064 0.109 0.070 0.079

0.112 0.150 0.173 0.171 0.213 0.147 0.180 0.174 0.211 0.230 0.153 0.234 0.323 0.312 0.299 0.215 0.321 0.306 0.301 0.310 0.200 0.298 0.297

– – 0.056 0.225 2.564 – – 0.089 0.369 2.884 – 0.246 1.736 4.332 2.558 3.610 7.256 6.168 3.231 1.632 5.135 3.849 7.775

(continued on next page) 6

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Table 2 (continued) Tillage practice

q (L s-1 m−1)

t (min)

h (m)

d (m)

V (m s−1)

Dr (g m−2 s−1)

0.3 0.3

16 20

0.008 0.010

0.098 0.076

0.314 0.308

5.385 4.641

8

0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2 0.25 0.25 0.25 0.25 0.25 0.3 0.3 0.3 0.3 0.3

4 8 12 16 20 4 8 12 16 20 4 8 12 16 20 4 8 12 16 20 4 8 12 16 20

0.003 0.004 0.005 0.009 0.008 0.003 0.007 0.006 0.008 0.011 0.004 0.006 0.009 0.010 0.011 0.003 0.006 0.010 0.011 0.012 0.004 0.010 0.011 0.013 0.015

0.054 0.047 0.041 0.034 0.044 0.081 0.049 0.053 0.053 0.051 0.076 0.062 0.054 0.063 0.060 0.116 0.073 0.072 0.061 0.058 0.077 0.060 0.077 0.063 0.054

0.136 0.145 0.154 0.231 0.278 0.171 0.218 0.259 0.277 0.272 0.193 0.228 0.266 0.304 0.277 0.192 0.312 0.338 0.320 0.318 0.193 0.345 0.337 0.318 0.306

– – 0.086 0.377 4.579 – 2.287 7.781 3.808 1.638 – 1.017 8.441 3.447 2.146 1.607 15.897 10.522 2.162 1.399 2.727 15.791 16.431 5.851 2.385

10

0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2 0.25 0.25 0.25 0.25 0.25 0.3 0.3 0.3 0.3 0.3

4 8 12 16 20 4 8 12 16 20 4 8 12 16 20 4 8 12 16 20 4 8 12 16 20

0.003 0.003 0.003 0.004 0.004 0.003 0.004 0.008 0.010 0.010 0.003 0.006 0.011 0.010 0.011 0.004 0.007 0.009 0.012 0.013 0.005 0.007 0.012 0.013 0.014

0.073 0.061 0.067 0.065 0.069 0.093 0.079 0.060 0.051 0.048 0.098 0.074 0.061 0.060 0.054 0.087 0.065 0.054 0.055 0.057 0.091 0.080 0.063 0.061 0.055

0.155 0.148 0.155 0.178 0.177 0.136 0.212 0.294 0.281 0.259 0.174 0.271 0.349 0.304 0.315 0.191 0.321 0.326 0.302 0.274 0.236 0.322 0.363 0.361 0.357

– – 0.126 0.543 6.741 – 2.976 8.005 11.886 2.189 – 2.893 9.803 12.533 2.589 1.501 15.952 18.209 5.265 2.265 1.566 2.099 20.025 19.296 13.553

12

0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2 0.25 0.25 0.25 0.25 0.25 0.3 0.3

4 8 12 16 20 4 8 12 16 20 4 8 12 16 20 4 8 12 16 20 4 8

0.003 0.004 0.004 0.006 0.006 0.004 0.006 0.010 0.011 0.012 0.004 0.009 0.011 0.011 0.012 0.004 0.010 0.012 0.013 0.015 0.004 0.012

0.095 0.083 0.066 0.049 0.042 0.072 0.054 0.041 0.037 0.036 0.091 0.071 0.052 0.044 0.045 0.093 0.049 0.047 0.046 0.047 0.093 0.049

0.111 0.156 0.214 0.244 0.298 0.158 0.237 0.268 0.292 0.285 0.184 0.249 0.329 0.321 0.319 0.203 0.339 0.331 0.360 0.370 0.314 0.354

– 0.317 0.298 2.839 4.366 – 3.156 9.214 12.551 3.096 0.425 4.690 11.523 10.903 8.806 2.035 11.041 13.445 9.272 7.313 4.750 18.342

S (°)

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Table 2 (continued) Tillage practice

MH

q (L s-1 m−1)

t (min)

h (m)

d (m)

V (m s−1)

Dr (g m−2 s−1)

0.3 0.3 0.3

12 16 20

0.016 0.019 0.015

0.046 0.055 0.051

0.421 0.445 0.468

14.087 14.790 10.639

2

0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2 0.25 0.25 0.25 0.25 0.25 0.3 0.3 0.3 0.3 0.3

4 8 12 16 20 4 8 12 16 20 4 8 12 16 20 4 8 12 16 20 4 8 12 16 20

0.004 0.005 0.005 0.006 0.008 0.003 0.004 0.006 0.008 0.012 0.007 0.006 0.006 0.013 0.013 0.005 0.006 0.009 0.011 0.010 0.007 0.008 0.009 0.013 0.017

0.086 0.076 0.068 0.063 0.059 0.102 0.091 0.101 0.072 0.064 0.085 0.075 0.064 0.044 0.047 0.071 0.08 0.065 0.063 0.049 0.097 0.085 0.080 0.064 0.052

0.046 0.056 0.059 0.062 0.072 0.048 0.059 0.088 0.111 0.129 0.061 0.062 0.087 0.126 0.163 0.065 0.084 0.112 0.150 0.165 0.083 0.090 0.100 0.139 0.187

– – – – 0.006 – – – 0.058 0.222 – – 0.036 0.156 0.654 – – 0.049 0.286 1.227 – 0.053 0.057 0.290 2.235

4

0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2 0.25 0.25 0.25 0.25 0.25 0.3 0.3 0.3 0.3 0.3

4 8 12 16 20 4 8 12 16 20 4 8 12 16 20 4 8 12 16 20 4 8 12 16 20

0.004 0.006 0.007 0.011 0.010 0.006 0.007 0.007 0.011 0.011 0.007 0.006 0.007 0.008 0.012 0.007 0.006 0.012 0.011 0.015 0.010 0.008 0.017 0.016 0.012

0.085 0.063 0.072 0.054 0.057 0.078 0.073 0.066 0.050 0.053 0.096 0.079 0.082 0.081 0.063 0.098 0.094 0.080 0.071 0.049 0.055 0.074 0.069 0.056 0.059

0.067 0.066 0.088 0.123 0.115 0.077 0.083 0.097 0.116 0.133 0.072 0.079 0.101 0.121 0.144 0.075 0.084 0.128 0.143 0.190 0.089 0.138 0.138 0.175 0.265

– – – – 0.076 – – – 0.137 0.128 – – 0.072 0.325 1.394 – – 0.240 0.818 4.058 – 0.499 0.703 1.996 7.028

6

0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2 0.25 0.25 0.25 0.25 0.25 0.3

4 8 12 16 20 4 8 12 16 20 4 8 12 16 20 4 8 12 16 20 4

0.005 0.006 0.006 0.007 0.008 0.005 0.005 0.005 0.009 0.009 0.006 0.006 0.009 0.010 0.010 0.007 0.008 0.012 0.014 0.013 0.007

0.079 0.056 0.067 0.052 0.047 0.055 0.070 0.069 0.055 0.056 0.071 0.055 0.065 0.058 0.050 0.056 0.070 0.051 0.039 0.046 0.072

0.087 0.084 0.094 0.101 0.142 0.078 0.077 0.094 0.118 0.125 0.079 0.087 0.109 0.183 0.211 0.087 0.133 0.172 0.225 0.240 0.113

– – – 0.153 0.767 – – 0.066 0.625 1.159 – 0.017 0.075 0.706 1.450 – 1.018 3.413 2.523 4.182 –

S (°)

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Table 2 (continued) Tillage practice

q (L s-1 m−1)

t (min)

h (m)

d (m)

V (m s−1)

Dr (g m−2 s−1)

0.3 0.3 0.3 0.3

8 12 16 20

0.008 0.010 0.012 0.011

0.073 0.072 0.052 0.053

0.114 0.142 0.207 0.253

1.050 2.408 7.873 12.049

8

0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2 0.25 0.25 0.25 0.25 0.25 0.3 0.3 0.3 0.3 0.3

4 8 12 16 20 4 8 12 16 20 4 8 12 16 20 4 8 12 16 20 4 8 12 16 20

0.005 0.005 0.006 0.006 0.008 0.005 0.007 0.009 0.009 0.010 0.006 0.008 0.011 0.013 0.012 0.007 0.012 0.014 0.012 0.013 0.007 0.013 0.014 0.013 0.014

0.069 0.053 0.049 0.046 0.041 0.064 0.068 0.055 0.045 0.044 0.075 0.064 0.056 0.047 0.046 0.077 0.049 0.048 0.053 0.046 0.083 0.057 0.048 0.052 0.053

0.074 0.094 0.124 0.121 0.162 0.085 0.112 0.172 0.197 0.220 0.102 0.142 0.185 0.241 0.250 0.114 0.185 0.195 0.232 0.256 0.131 0.182 0.237 0.283 0.292

– – – – 0.816 – 0.161 1.410 3.852 10.099 – 0.274 1.524 4.947 11.504 – 3.651 6.125 10.578 18.365 0.274 5.361 8.922 15.395 26.398

10

0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2 0.25 0.25 0.25 0.25 0.25 0.3 0.3 0.3 0.3 0.3

4 8 12 16 20 4 8 12 16 20 4 8 12 16 20 4 8 12 16 20 4 8 12 16 20

0.005 0.005 0.006 0.006 0.008 0.005 0.006 0.007 0.007 0.009 0.006 0.006 0.006 0.008 0.011 0.006 0.009 0.016 0.010 0.009 0.005 0.007 0.011 0.011 0.011

0.045 0.039 0.036 0.033 0.036 0.064 0.053 0.047 0.052 0.046 0.058 0.063 0.059 0.054 0.047 0.064 0.068 0.057 0.054 0.057 0.090 0.077 0.064 0.062 0.067

0.122 0.112 0.117 0.123 0.141 0.096 0.105 0.124 0.16 0.218 0.145 0.148 0.168 0.236 0.339 0.155 0.208 0.310 0.346 0.389 0.148 0.216 0.274 0.316 0.342

– 0.031 0.176 0.040 0.111 – 0.245 1.667 4.052 11.669 0.216 1.269 5.337 9.133 17.210 0.248 2.669 10.698 16.025 25.602 0.392 4.162 15.459 24.313 36.308

12

0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2 0.25 0.25 0.25 0.25 0.25

4 8 12 16 20 4 8 12 16 20 4 8 12 16 20 4 8 12 16 20

0.004 0.005 0.005 0.006 0.009 0.005 0.005 0.008 0.011 0.012 0.005 0.010 0.012 0.011 0.009 0.006 0.009 0.012 0.013 0.010

0.040 0.039 0.037 0.039 0.044 0.061 0.066 0.050 0.045 0.042 0.067 0.059 0.051 0.049 0.055 0.064 0.059 0.055 0.059 0.065

0.102 0.101 0.111 0.125 0.163 0.114 0.119 0.178 0.234 0.271 0.124 0.199 0.279 0.317 0.308 0.147 0.202 0.282 0.314 0.404

– 0.087 0.115 0.305 4.270 – 0.091 0.384 11.363 19.468 0.316 1.589 9.633 25.321 18.828 0.360 1.702 20.459 44.613 32.907

S (°)

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Table 2 (continued) Tillage practice

CD

q (L s-1 m−1)

t (min)

h (m)

d (m)

V (m s−1)

Dr (g m−2 s−1)

0.3 0.3 0.3 0.3 0.3

4 8 12 16 20

0.006 0.011 0.015 0.014 0.012

0.074 0.065 0.069 0.059 0.059

0.153 0.260 0.341 0.405 0.427

1.891 19.211 53.098 43.222 15.292

2

0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2 0.25 0.25 0.25 0.25 0.25 0.3 0.3 0.3 0.3 0.3

4 8 12 16 20 4 8 12 16 20 4 8 12 16 20 4 8 12 16 20 4 8 12 16 20

0.007 0.008 0.007 0.008 0.009 0.007 0.007 0.009 0.009 0.010 0.007 0.010 0.009 0.010 0.009 0.008 0.008 0.010 0.010 0.008 0.009 0.009 0.010 0.009 0.010

0.156 0.125 0.133 0.101 0.068 0.106 0.064 0.043 0.047 0.039 0.092 0.083 0.118 0.056 0.049 0.121 0.119 0.056 0.049 0.059 0.065 0.087 0.079 0.079 0.070

0.059 0.068 0.073 0.086 0.106 0.085 0.129 0.154 0.179 0.208 0.086 0.155 0.161 0.217 0.255 0.113 0.133 0.236 0.260 0.283 0.128 0.186 0.248 0.262 0.295

– – – – 0.100 – – – – 0.296 – – – 0.220 0.314 – – 1.253 1.260 1.402 – – 1.398 2.016 2.647

4

0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2 0.25 0.25 0.25 0.25 0.25 0.3 0.3 0.3 0.3 0.3

4 8 12 16 20 4 8 12 16 20 4 8 12 16 20 4 8 12 16 20 4 8 12 16 20

0.005 0.006 0.008 0.008 0.009 0.006 0.009 0.010 0.010 0.010 0.007 0.016 0.010 0.008 0.007 0.013 0.013 0.012 0.012 0.008 0.016 0.014 0.013 0.010 0.012

0.085 0.074 0.049 0.050 0.040 0.086 0.065 0.056 0.052 0.052 0.081 0.074 0.063 0.058 0.051 0.071 0.053 0.057 0.050 0.075 0.039 0.060 0.056 0.062 0.054

0.052 0.074 0.096 0.101 0.133 0.084 0.121 0.134 0.171 0.219 0.116 0.132 0.171 0.224 0.217 0.143 0.141 0.194 0.291 0.341 0.186 0.173 0.296 0.316 0.317

– – – – 0.263 – – – – 0.457 – – – 2.438 3.143 – – 0.298 2.849 3.390 – 0.443 3.691 7.331 8.730

6

0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2 0.25 0.25 0.25 0.25

4 8 12 16 20 4 8 12 16 20 4 8 12 16 20 4 8 12 16

0.007 0.008 0.012 0.011 0.009 0.008 0.010 0.011 0.011 0.010 0.011 0.012 0.012 0.012 0.012 0.015 0.013 0.015 0.012

0.065 0.056 0.043 0.077 0.074 0.112 0.109 0.085 0.093 0.080 0.072 0.098 0.082 0.073 0.068 0.053 0.072 0.075 0.094

0.075 0.087 0.098 0.177 0.207 0.086 0.102 0.192 0.234 0.249 0.124 0.207 0.261 0.267 0.326 0.222 0.249 0.248 0.307

– – – – 0.387 – – – 0.483 1.866 – – 1.024 4.783 10.036 – – 11.861 17.351

S (°)

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Table 2 (continued) Tillage practice

q (L s-1 m−1)

t (min)

h (m)

d (m)

V (m s−1)

Dr (g m−2 s−1)

0.25 0.3 0.3 0.3 0.3 0.3

20 4 8 12 16 20

0.012 0.013 0.016 0.015 0.014 0.012

0.084 0.125 0.067 0.084 0.100 0.097

0.374 0.225 0.343 0.370 0.351 0.359

18.334 – 0.743 17.515 21.236 27.493

8

0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2 0.25 0.25 0.25 0.25 0.25 0.3 0.3 0.3 0.3 0.3

4 8 12 16 20 4 8 12 16 20 4 8 12 16 20 4 8 12 16 20 4 8 12 16 20

0.008 0.008 0.010 0.011 0.012 0.016 0.015 0.015 0.012 0.012 0.010 0.014 0.013 0.012 0.011 0.014 0.014 0.013 0.012 0.014 0.019 0.017 0.015 0.011 0.011

0.136 0.102 0.094 0.100 0.090 0.088 0.089 0.112 0.082 0.072 0.122 0.113 0.093 0.089 0.078 0.081 0.093 0.087 0.085 0.075 0.128 0.113 0.076 0.078 0.070

0.098 0.124 0.152 0.217 0.213 0.095 0.130 0.214 0.226 0.247 0.122 0.160 0.303 0.336 0.349 0.132 0.198 0.311 0.388 0.361 0.260 0.337 0.368 0.404 0.381

– – – – 0.386 – – – 1.029 9.520 – – – 12.148 23.614 – – 10.247 28.086 29.815 – 3.096 50.414 22.387 10.713

10

0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2 0.25 0.25 0.25 0.25 0.25 0.3 0.3 0.3 0.3 0.3

4 8 12 16 20 4 8 12 16 20 4 8 12 16 20 4 8 12 16 20 4 8 12 16 20

0.009 0.011 0.013 0.014 0.012 0.017 0.016 0.014 0.013 0.013 0.010 0.013 0.016 0.015 0.012 0.016 0.017 0.015 0.017 0.010 0.012 0.019 0.017 0.017 0.013

0.068 0.059 0.043 0.056 0.064 0.065 0.072 0.067 0.081 0.067 0.072 0.067 0.048 0.042 0.033 0.120 0.123 0.083 0.082 0.076 0.216 0.133 0.087 0.094 0.079

0.103 0.111 0.143 0.195 0.192 0.147 0.144 0.161 0.228 0.256 0.249 0.225 0.295 0.364 0.383 0.240 0.210 0.318 0.348 0.355 0.160 0.254 0.324 0.399 0.439

– – – – 1.414 – – – 6.911 16.388 – – 17.738 13.813 5.793 – – 52.277 47.709 18.838 – 3.607 46.330 70.601 13.118

12

0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2 0.25 0.25 0.25

4 8 12 16 20 4 8 12 16 20 4 8 12 16 20 4 8 12

0.020 0.015 0.014 0.014 0.010 0.016 0.018 0.013 0.014 0.010 0.022 0.015 0.014 0.014 0.011 0.022 0.019 0.017

0.069 0.055 0.040 0.049 0.047 0.075 0.070 0.053 0.044 0.045 0.111 0.084 0.054 0.036 0.046 0.106 0.059 0.052

0.126 0.188 0.179 0.192 0.331 0.139 0.216 0.272 0.343 0.401 0.151 0.235 0.323 0.339 0.379 0.156 0.267 0.413

– – – 0.199 11.629 – – 2.426 16.013 17.925 – 4.452 41.052 34.642 11.727 – 14.516 52.182

S (°)

(continued on next page) 11

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Table 2 (continued) Tillage practice

S (°)

q (L s-1 m−1)

t (min)

h (m)

d (m)

V (m s−1)

Dr (g m−2 s−1)

0.25 0.25 0.3 0.3 0.3 0.3 0.3

16 20 4 8 12 16 20

0.014 0.011 0.019 0.019 0.019 0.013 0.012

0.039 0.040 0.087 0.05 0.042 0.046 0.050

0.476 0.426 0.242 0.368 0.496 0.509 0.529

33.841 42.629 – 44.981 73.971 26.691 9.042

Note: Tillage practices: MD = manual dibbling, MH = manual hoeing, and CD = contour drilling. “–” means there is no outflow at the end of the flume. Hydrodynamic parameters: S = slope gradient, q = discharge rate, t = time, h = flow depth, d = flow width, V = mean flow velocity, and Dr = soil detachment rate.

indicating that topographic roughness indeed affected the friction factor considerably. 3.4. Resistance coefficient-Froude number (f − Fr) relationship The evolution of the estimated Froude number over time under different tillage practices is illustrated in Fig. 8. Generally, the Froude number increased with an increase in time at the beginning of the experiments. However, in some cases, a stabilization of the Froude number was observed, with the eventual values being < 1. Based on the experimental data, the Froude number remained within a relatively small range (0.01–1.22) in the whole course of the experiments, and most of the values were < 1, which implies that concentrated flow was essentially subcritical flow under tillage practices. Overall, there was a strong f − Fr relationship (Fig. 9), while multiple regression analysis revealed an additional slope effect:

f = 4.821Fr −1.769S 0.820Q−0.052 Fig. 5. Ranges of the Darcy-Weisbach friction factor under different tillage practices: (a) 0–4 min; (b) 16–20 min. Under each tillage practice, significant differences between 0 and 4 min and 16–20 min (P < 0.05) are denoted by different letters. MD = manual dibbling, MH = manual hoeing, and CD = contour drilling.

Table 3 Mean values of flow velocity and depth at the begging of the experiments (0–4 min) under three different tillage practices. MD

MH

CD

Roughness Mean flow velocity (m s−1) Mean flow depth (mm)

2.32 ± 0.26 0.14 4.38

3.96 ± 0.35 0.08 5.82

7.69 ± 0.51 0.09 14.16

MH

CD

Roughness before experiment Roughness after experiment Difference in roughness

2.32 ± 0.26 1.81 ± 0.21 −0.51

3.96 ± 0.35 2.73 ± 0.29 −1.23

7.69 ± 0.51 3.11 ± 0.44 −4.58

Note: MD = manual dibbling, MH = manual hoeing, and CD = contour drilling. Roughness = .the mean ± standard deviations.

Surface roughness and time affected the f–Re relationship. Combining these two factors to account for the differences in relation to tillage practice and time yielded the following regression equation:

f = 23.527Re−0.255 Cr 0.778t −0.595

R2 = 0.518

(18)

Soil surface roughness is generally considered a key factor affecting concentrated flow resistance, with a potentially positive correlation between these two factors (Shi, 2015). However, according to the results of the present study, the relationship between surface roughness and Darcy-Weisbach friction factor (Cr–f) was not always stable and changed in the course of concentrated flow erosion under tillage practices. Using a series of flume experiments, we investigated how soil surface roughness evolved over time under different tillage practices. According to the results, changes in surface roughness varied among the three tillage practices (Table 4). At the beginning of the experiment, initial roughness and friction factor were in the order MD < MH < CD. A larger initial roughness under a tillage practice resulted in a more considerable reduction in surface roughness, with the final roughness trend remaining unaltered, MD < MH < CD. Although the greatest final roughness value was observed under CD, this tillage practice yielded the lowest friction factor (Fig. 4). This result implies that initial roughness is not the only factor affecting the Darcy-Weisbach friction factor directly under different tillage practices. The Darcy-Weisbach friction factor decreased with an increase in time under all the tillage practices (Fig. 6). According to Eq. (3), the friction factor was positively correlated with flow depth and negatively correlated with flow velocity. In addition, both flow depth and velocity increased with an increase in time (Table 2). This result indicates that increasing flow velocity is the reason why the Darcy-Weisbach friction factor decreases with time and such an increasing velocity trend is

Table 4 Topographical roughness of soil surfaces before and after experiments under three different tillage practices. MD

R2 = 0.928

4. Discussion

Note: MD = manual dibbling, MH = manual hoeing, and CD = contour drilling. Roughness = the mean ± standard deviation.

Tillage practice

(17)

Based on the regression coefficients, the Darcy–Weisbach friction factor could be expressed based on the Froude number (r = −1.769) and slope gradient (r = 0.820) without unit discharge (r = −0.052). Therefore, the new regression equation would be expressed as follows:

f = 5.301Fr −1.775S 0.827

Tillage practice

R2 = 0.930

(16)

The regression coefficient for surface roughness was r = 0.778, 12

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Fig. 6. The Darcy-Weisbach friction factor versus time relationship based on different slope gradients and discharge rates under the three tillage practices (MD = manual dibbling, MH = manual hoeing, and CD = contour drilling).

roughness can be explained based on the varying roughness trends under different tillage practices. According to Table 4, rougher surfaces had greater decreases in roughness over time; therefore, they could be affected more over time, which was consistent with the regression coefficients for time in Eqs. (7)–(9) (MD = −0.339, MH = −0.563, and CD = −0.959). Therefore, the three surfaces exhibited distinct roughness characteristics in terms of not only initial roughness but also their evolution trends over time, which were affected largely by the topographic features. For example, the MD surface had a low initial resistance, which did not offer considerable protection against highflow velocities. The CD surface had a high initial resistance, which was transformed rapidly due to the penetration of ridges and thus offered protection for a limited period. The MH surface had an intermediate

largely due to a decrease in surface roughness under all tillage practices (Table 4). Furthermore, rapid adjustments were observed and a simple characterization of initial roughness may not be adequate for the assessment of surface responses during an erosion event. In the present study, there were discernible differences among the tilled surfaces. In the case of the MD surface, the friction factor was low initially, and on average, did not evolve considerably. For the MH surface, there was an intermediate friction factor initially, which decreased with an increase in time, and the evolution was relatively slow. On the CD surface, the friction factor was very high initially and it evolved rapidly to a very low value. The decrease in the friction factor was the greatest on the roughest surface (CD) and the least on the smoothest surface (MD). The relationship between the decreasing rate of friction factor and 13

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Fig. 7. The Darcy-Weisbach friction factor versus Reynolds number relationship for different time periods under the three tillage practices.

number. The Reynolds number has been demonstrated to have a clear power function relationship with friction factor in numerous reports, since the f–Re relationship is often described as follows (Roels, 1984; Abrahams et al., 1994):

initial resistance, which was well maintained, and, therefore, was less susceptible to erosion compared to CD. The CD surface may offer protection against minor erosion events but not against major erosion events. According to Eqs. (7)–(9), flow resistance increased with an increase in slope gradient under the tillage practices, which is similar to the finding of Govers (1992). According to Govers, flow velocity is independent of slope gradient and it has been hypothesized that there is a feedback mechanism between flow erosivity and bed morphology (Gimenez and Govers, 2001). Increase in soil erosion rate with increasing slope gradient alters bed morphology and increases surface roughness, which could decrease flow velocity and counteract the expected increasing trend with increasing slope gradient. However, flow velocity increased with an increase in slope gradient in the present study (Fig. 10). This difference is attributed to an opposite roughness trend, where soil surface roughness decreased due to erosion because tilled surfaces had a high initial roughness while soil erosion disintegrated the tilled surface gradually, leading to a decrease in surface roughness and an increase in flow velocity. Notably, such diverse trends did not alter the positive correlation between Darcy-Weisbach friction factor and slope gradient (f–S; Eqs. (7)–(9)). This result indicates that the positive effect of increasing slope gradient and flow depth on flow resistance is greater than the negative effect of increasing flow velocity, which also explains the different regression coefficients under various tillage practices (MD = 0.415, MH = 0.113, and CD = 0.581). Among the three tillage practices tested in this study, flow velocity on the MH surface displayed a greater increase than on the other two surfaces, which counterbalanced the increase in the Darcy-Weisbach friction factor. In addition, the f–S relationship seemed to not affect initial roughness on the tilled surfaces, which indicates that it is the surface topography induced by the tillage practice that had a major influence. According to Di Stefano et al. (2018), the applicability of Eq. (3) is linked to the ability of the investigated rills to adjust their geometry (e.g., wetted perimeter and surface roughness), which certainly affects the hydraulic roughness and in turn the friction factor. In our study, soil surface roughness changed substantially in the course of the experiment (Fig. 11). Surface roughness is not the only parameter that affects flow pattern; the different topographic features induced by the tillage practices (Fig. 3) also play a critical role in the process. There is also a relationship between hydraulic resistance and flow regime, which can be expressed using the Reynolds number and the Froude

f = aRe x

(19)

In the present study, we performed a regression analysis of the f–Re relationship under each tillage practice for different time periods. Comparison of Eqs. (10)–(15) revealed differences among the regression coefficients for the Reynolds number, which indicates that it may be inappropriate to ignore roughness and time when developing a model for friction factor. Therefore, we established a new regression relationship (Eq. (16)), where the regression coefficients for roughness (r = 0.778) and time (r = −0.595) were consistent with our hypothesis. In addition, the Reynolds number ranges for the tilled surfaces reached high levels (99.301–4480.368; Fig. 5), indicating the existence of three flow regimes (laminar flow, transition flow, and turbulent flow) under all conditions. The result also showed that the f–Re relationship became flat when the Reynolds number reached a high value of > 3000 (Fig. 7). Abrahams et al. (1994) have investigated the relationship between drag coefficient and flow regime, which can be expressed as follows:

Di = Cd Ai ρV 2

(20)

where Di is the drag, Cd is the drag coefficient, Ai is the wetted crosssectional area of the element, and ρ is the fluid density. According to the study (Abrahams et al., 1994), the drag coefficient decreases with the Froude number when Fr is > 0.5. Here we also found the Froude number was positively correlated with Reynolds number under the tillage practices (Fig. 12). Since the expressions of Reynolds number and Froude number (Eqs. (1), (2)) reveal that they both increase with flow velocity the Fr–Re relationship is consistent with the experimental result. Therefore, the drag coefficient declines as the Froude number increases along with Reynolds number. The decline in drag coefficient offsets the increase in flow velocity (Eq. (20)); thus, the friction factor changes slightly with varying Reynolds number. The Froude number is another key factor affecting friction factor. According to Eq. (18), the Darcy-Weisbach friction factor was well described as a power function of Froude number and slope gradient. Data from the experiments performed by Di Stefano et al. (2018) also revealed a similar power function of the f–Fr relationship (Fig. 13), 14

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Fig. 8. The Froude number versus time relationship based on different slope gradients and discharge rates under the three tillage practices.

revealed an inherent link between the f–t relationship and the Fr–t relationship, since they exhibited similar variation patterns. The Fr–t relationship was not surprising. A comparison of the measured friction factors and the corresponding values calculated using Eq. (18) revealed essentially a 1:1 relationship, which implies that the concentrated flow in our experiments had a very wide rectangular cross-section (Fig. 15). Therefore, we could assume that flow depth is approximately equal to hydraulic radius; therefore, the following new equation is obtained by combining Eqs. (2) and (3):

where the friction factor decreased with increasing Froude number and increased with increasing slope gradient. When Eq. (18) was used to predict the friction factor based on the Froude number and slope gradient, a good correlation was observed, although the friction factors reported by Di Stefano et al. (2018) were generally 30% lower than our predicted values (Fig. 14). The Froude number basically increased with an increase in time under all the tillage practices; however, the curves still displayed inconsistent trends among different tillage practices (Fig. 7): For the MD surface, the Froude number was high in the beginning and increased slightly in the first 4 min and then did not evolve considerably afterwards. For the MH surface, the Froude number was intermediate in the beginning and evolved relatively slowly, while for the CD surface, the Froude number was low in the beginning but evolved rapidly to a high value in the course of the experiment. A comparison of the results

f = 8S / Fr 2

(21)

The new equation (Eq. (21)) can explain the similarity between the f–t relationship and the Fr–t relationship, and it is similar to the deduced regression equation (Eq. (18)). According to Govers (1992), in rills, the average Froude numbers at 15

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Fig. 9. The Darcy-Weisbach friction factor versus Froude number relationship for different time periods under the three tillage practices.

equilibrium hydraulic conditions; in the course of an erosion event, the Darcy-Weisbach friction factor is likely to decrease, while the Froude number would increase, potentially up to a maximum value of 1. This poses a significant challenge for event-based modeling of friction factor since such temporal evolution needs to be accounted for. According to Gimenez and Govers (2002), unit length shear force and shear stress are two optimal predictors of soil detachment in rills, both of which evolve over time. This further illustrates how critical it is to consider the implications of such temporal changes during concentrated flow erosion.

steady state are always 1, so that velocities are independent of slope gradient. Later studies revealed that average Froude numbers on stony surfaces are well below 1; however, flow velocities are still independent of slope gradient (Nearing et al., 2017). The slope independence of flow velocities on mobile beds is due to a feedback between rill bed morphology and flow conditions, and the final rill flow velocity is characterized by a constant average Froude number (Gimenez and Govers, 2001). The final Froude numbers in our experiments were also generally below 1 (Fig. 7). However, it remains unclear whether erosionflow feedback always leads to critical flow. In some experiments, Froude numbers > 1 were measured near the end, which could be associated with soil depletion, i.e., the flow hitting the gravel bed below the soil (soil thickness was limited). Final Froude number was well below 1 in most experiments; however, some of them were not yet steady states. The results imply that when a freshly tilled surface is considered, most of the erosion would take place under non-

5. Conclusions The results of the present study show that soil surface roughness evolves over time on tilled slope surfaces in the course of concentrated flow erosion. The temporal changes depend on the different tillage practices, with rougher tilled surfaces displaying greater decreases in

Fig. 10. The flow velocity versus slope gradient relationship based on a unit discharge of 0.2 L s−1 m−1. 16

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Fig. 11. The final topography of soil surface under each tillage practice after experiments.

hoeing because the considerable increase in flow velocity under manual hoeing counteracted the increase in flow depth and slope gradient. The friction factor basically decreased with an increase in unit discharge under all the tillage practices. The Reynolds number and the friction factor (Re–f) had a clear power function relationship, which is consistent with the findings of most previous studies. However, the Reynolds number alone cannot describe the friction factor accurately for the tilled surfaces, as surface roughness and time also play a major role in the relationship. The Re–f relationship becomes flat when Re is > 2000, because the decrease in drag coefficient offsets the effect of an increase in flow velocity;

surface roughness. However, initial roughness is not adequate for assessing the evolution of a tilled surface in addition to changes in concentrated flow resistance in the course of an erosion event. Time has a much greater effect on the Darcy-Weisbach friction factor for a rougher surface. Under different tillage practices, the three surfaces exhibited distinct characteristics in terms of not only initial roughness but also their evolution trends over time, which were indicated largely by their specific topographic features. In addition, slope gradient and discharge rate are key factors; however, they exhibit strikingly different effects. Slope gradient had a significant positive effect on the friction factor under manual dibbling and contour drilling, but not under manual

Fig. 12. The Darcy-Weisbach friction factor versus Froude number relationship for different time periods under the three tillage practices. 17

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Fig. 13. The Darcy-Weisbach friction factor versus Froude number relationship in Di Stefano’s experiment (Di Stefano et al., 2018).

Fig. 14. Comparison of predicted and measured Darcy-Weisbach friction factor values based on the experimental data from Di Stefano et al. (2018),

Fig. 15. Comparison of predicted and measured Darcy-Weisbach friction factor values based on the experimental data from this study.

therefore, the friction factor changes relatively slightly with varying Reynolds number. The friction factor decreased with an increase in the Froude number, which has been demonstrated to be the underlying mechanism of the evolution of the friction factor over time based on a similarity between the friction factor–time (f–t) and Froude number–time (Fr–t) relationships. In addition, the Froude number was close to 1 in all cases, which may the underlying principle controlling the dynamic equilibrium between surface roughness and flow hydraulics on tilled surfaces.

influence the work reported in this paper. Acknowledgements This study was supported by the National Natural Science Foundation of China (Grant No. 41271288). References Abrahams, A.D., Parsons, A.J., Wainwright, J., 1994. Resistance to flow on semiarid grassland and shrubland hillslopes, Walnut Gulch, Southern Arizona. J. Hydrol. 156 (1–4), 343–363. Abrahams, A.D., Li, G., Parsons, A.J., 1996. Rill hydraulics on a semiarid hillslope, southern Arizona. Earth Surf. Process. Landf. 21 (1), 35–47. Baiamonte, G., Ferro, V., 1997. The influence of roughness geometry and Shields parameter on flow resistance in gravel-bed channels. Earth Surf. Process. Landf. 22 (8), 759–772.

Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to 18

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