Effects of Simulated Gravel on Hydraulic Characteristics of Overland Flow Under Varying Flow Discharges, Slope Gradients and Gravel Coverage Degrees

To quantify the hydraulic characteristics of overland flow on gravel-covered slopes, eight flow discharges (Q) (8.44–122 L/min), five slope gradients (J) (2°–10°) and four gravel coverage degrees (Cr) (0–30%) were examined via a laboratory flume. The results showed that (1) gravel changed flow regime. Gravel increased the Reynolds number (Re) by 2.94–33.03%. Re were less affected by J and positively correlated with Cr and Q. Gravel decreased the Froude number (Fr) by 6.83–77.31%. Fr was positively correlated with Q and J and negatively correlated with Cr. (2) Gravel delayed the flow velocity (u) and increased the flow depth (h) and flow resistance (f). Gravel reduced u by 1.20–58.95%. u was positively correlated with Q and J and negatively correlated with Cr. Gravel increased h by 0.12–2.41 times. h was positively correlated with Q and Cr and negatively correlated with J. Gravel increased f by 0.15–18.42 times. f were less affected by J, positively correlated with Cr and negatively correlated with Q. (3) The relationships between hydraulic parameters and Q, J and Cr identified good power functions. Hydraulic parameters were mainly affected by Cr. These results can guide the ecological construction of soil and water conservation.


Materials and Methods
Site description. The experiment was conducted in a rainfall simulation hall at the Key Laboratory of Soil and Water Conservation and Desertification Combating, which is located in Jiufeng National Forestry Mountains, Beijing, China. The laboratory belongs to the Beijing Forestry University, is located on a 10-25% slope and has a temperate continental climate with an average annual temperature of 9 °C. The altitude is 140 m, and the average annual precipitation is 600 mm, of which more than 80% falls between June and September. The active growing season extends from April to October. The soil is a shallow (from 0.3 to 1 m with an average of 0.5 m) gravelly loam with a mean 13.9% coarse fraction (>2 mm diameter), and the highest gravel fraction is 30% 30 . Experimental conditions and treatments. All experiments were processed using runoff scouring equipment inside the laboratory in the rainfall simulation hall. Runoff scouring equipment consisted of four main components: a water supply system, a flow discharge control system, flat water facilities, and a hydraulic flume. The flow discharge control system was composed of an electromagnetic flow meter and valve, and it was used to display and control the size of the flow discharge. Flat water facilities included a steady flow box and hump, which allowed the water to flow smoothly into the hydraulic flume. The hydraulic flume was 6 m long, 0.5 m wide, and 0.3 m deep, and it had 12-mm-thick tempered glass on the bottom and could be adjusted to slope gradients from 0 to 15°. The schematic diagram is shown in Fig. 1.
Four underlying surfaces were used in the hydraulic flume: a bare slope as the control and three gravel-covered slopes (Fig. 2). Sixty mesh sand cloths with a particle size of 0.25 mm were placed on the bottom of the hydraulic flume to simulate the underlying soil surface. Well-defined elements, such as plastic hemispheres, were used in this study to accurately describe the geometric characteristics of natural gravel 31 . Plastic hemispheres with a diameter of 2 cm and a certain roughness were evenly affixed to the sand cloth in a plum blossom arrangement to simulate gravel-covered slopes. Considering the natural gravel content, the maximum gravel coverage degree www.nature.com/scientificreports www.nature.com/scientificreports/ was designed to be 30% in this experiment. Generally, four levels of gravel coverage (0%, 10%, 20%, and 30%) were implemented.
Considering the range of rainfall intensities and the slope gradient in rocky mountainous areas of North China 30 , five slope gradients (2°, 4°, 6°, 8° and 10°) and eight flow discharges (8.44, 11.26, 22.52, 45.03, 70.36, 84.43, 100 and 122 L/min) were utilized in this experiment. A total of 160 group tests were conducted with a complete combination test.
Experimental measurements. Prior to each test, the slope gradient and flow discharge were adjusted to the designed value. The flow discharge was controlled by an electromagnetic flow meter, and the valve and volume method was utilized to calibrate the flow discharge at the outlet end of the hydraulic flume. Measurements of flow depth and water temperature were performed after the flow discharge stabilized.
For each test, five measurement sections were set along the slope direction (Fig. 3). The initial measurement section was 0.7 m at the inlet of the hydraulic flume. The distance between each measurement section was 1 m. The five measurement sections were 1.7, 2.7, 3.7, 4.7 and 5.7 m, respectively. Four measurement points in each  The five green lines refer to five measurement sections; twenty purple-red points are twenty measurement points; two blue triangles refer to the arrangement of gravels in the form of plum blossoms; two bright-red arrows indicate the direction of water flow; "+" symbols refer to sand cloth; and grey-filled circles refer to gravel. measurement section were set at 0.1 m intervals. Accordingly, there were 20 measurement points on the slopes. Because of the flow phenomenon around gravel, measurement sections and measuring points on gravel-covered slopes were located between the two plastic hemispheres. In addition, the backwater area and the wake area were avoided to eliminate the influence of water surface inhomogeneity on the test results as much as possible. Flow depth was measured using a digital level probe (SX40-A, Chongqing Hydrological Equipment Factory) with a precision of 0.01 mm. The flow depth of each point was measured with three replicates. The average of 60 flow depths was considered the flow depth for that combination. Water temperature was measured using a mercury thermometer with an accuracy of 0.1 °C at the beginning and end of the test to calculate the kinematic viscosity coefficient of the water flow. Data analysis. The average flow velocity (u) can be calculated by the mean flow depth. u is calculated by Eq. (1) 32 : where u is the mean flow velocity (m/s), Q is the flow discharge (m 3 /s), and h is the mean flow depth (m). The effect of gravel on the unit flow discharge was considered. The effective runoff width was not equal to the hydraulic flume width because of the protuberant obstacles, and it can be calculated using Eq. (2) 33 : where b e is the effective runoff width (m), b is the hydraulic flume width (m), and Cr is gravel coverage degree (%). q is then computed by dividing the flow discharge Q by b e . The Reynolds number (Re) represented the flow regime condition by the ratio of the runoff inertial force to the viscous force. Re is calculated by Eq. (3) 34 : where h is the mean flow depth (m) and v m is the viscosity coefficient of water flow (cm 2 /s), which can be calculated using Eq. (4) 34 : where t is the water flow temperature (°C). The Froude number (Fr) was defined as the ratio of inertia forces to gravitational forces, which reflects the interaction between the flow depth and flow velocity. Fr is calculated by Eq. (5) 35 : = Fr u gh (5) where g is gravitational acceleration (m/s 2 ).
The resistance coefficient (f) reflected the resistance of the underlying surface to overland flow and is calculated by Eq. (6) 35 : where J is the hydraulic gradient. The Nash Sutcliffe efficiency coefficient (NES) was used to test the simulation effect of the hydraulic model and is calculated by Eq. (7) 36 : Chicago, Illinois, United States). A correlation matrix of the Pearson correlation coefficient was used to analyze the correlations between the hydraulic parameters and gravel coverage degrees, slope gradients and flow discharges. A regression analysis was implemented to quantify the relationship between independent and dependent variables.

Results and Discussion
Flow velocity. The mean flow velocity (u) ranged from 0.12 to 0.68 m/s on slopes without gravel and from 0.06 to 0.63 m/s on slopes with gravel. Gravel reduced u by 1.20-58.95% in comparison to the slopes without gravel. Under various experimental conditions, gravel had the largest impact on u when the gravel coverage degree was 30%, the slope gradient was 2° and the flow discharge was 22.52 L/min, and the rate of reduction was 58.95%. Gravel had the lowest impact on u when the gravel coverage degree was 10%, the slope gradient was 10° and the flow discharge was 22.52 L/min, and the rate of reduction was 1.20%. www.nature.com/scientificreports www.nature.com/scientificreports/ u increased significantly with flow discharge, and the slope gradient increased and the gravel coverage degree decreased (Fig. 4). On slopes with a gravel coverage degree of 0%, when the flow discharge increased from 8. u was significantly positively correlated with Q (r = 0.716, P < 0.01**) and J (r = 0.674, P < 0.01**) and significantly negatively correlated with Cr (r = −0.846, P < 0.01**) ( Table 1). The relationship between u and Q and J and Cr presented a power function ( Table 2). The NSE of Equation (10) was 0.962, demonstrating that the equation was superior. According to Equation (10), the exponent of Cr (1.539) was higher than that of Q (0.574) and J (0.340), which indicated that u was mainly affected by Cr followed by Q and J. www.nature.com/scientificreports www.nature.com/scientificreports/ u is not only an index to describe hydrological processes under different erosion conditions but also the basis for calculating other hydraulic variables, such as the flow shear force, flow power and unit flow power, which are used to simulate soil separation and sediment transport 37,38 . A larger flow velocity indirectly increased the runoff power, resulting in a larger capacity for sediment transportation 39,40 . In our study, gravel had the effect of retarding u compared with the slopes without gravel cover. The reasons were as follows. On the one hand, gravel prolonged the flow path and increased losses along the way. On the other hand, the eddies that formed around the gravel increased the local losses 41,42 . Both of them greatly decreased the kinetic energy of water flow. Consequently, u decreased.
With the increase in gravel coverage degree, the reduction effect of gravel enhanced u. This finding was consistent with studies from Foster et al. 43 . As the flow discharge and the slope gradient increased, u increased. The relationship between u and flow discharge and slope gradient was a power function and showed a positive correlation. Nearing et al. 44 and Foster et al. 45 reported similar results. However, Zhang et al. 46 thought that u of overland flow was mainly controlled by the flow discharge, and the slope gradient had little effect on the u on bare slopes through indoor drainage and scouring experiment. King and Norton 47 and Ali et al. 37 considered that the slope gradient had no significant effect on u for mobile beds covered with soil. The reason for this difference may be related to the different underlying surface conditions. Flow depth. The mean flow depth (h) ranged from 2.24 to 8.45 mm on slopes without gravel and from 3.03 to 18.69 mm on slopes with gravel. Gravel increased h by 0.12-2.41 times in comparison to the slopes without gravel. Under various experimental conditions, gravel had the largest impact on h when the gravel coverage degree was 30%, the slope gradient was 2°, and the flow discharge was 22.52 L/min; and the increased time was 2.41. Gravel had the lowest impact on h when the gravel coverage degree was 10%, the slope gradient was 10° and the flow discharge was 22.52 L/min; and the increased time was 0.12.
h increased significantly with flow discharge, the gravel coverage degree increased and the slope gradient decreased (Fig. 5). On slopes with a gravel coverage degree of 0%, when the flow discharge increased from 8 h was significantly positively correlated with Q (r = 0.729, P < 0.01**) and Cr (r = 0.774, P < 0.01**) and significantly negatively correlated with J (r = −0.678, P < 0.01**) ( Table 1). The relationship between h and Q and J and Cr presented a power function ( Table 3). The NSE of Equation (13) was 0.922, demonstrating that the equation was superior. According to the Equation (13), the exponent of Cr (2.472) was higher than that of Q (0.402) and J (0.333), which indicated that h was mainly affected by Cr followed by Q and J.
h affects the transport process of sediment particles and the extent of soil erosion 48 . Nevertheless, the water depth of overland flow is very shallow, which is strongly affected by the external disturbance such as surface coverage. Meanwhile, limited by the measurement methods, it is not easy to directly measure the water depth of overland flow in the field. Therefore, the study on the relationships between the water depth and flow discharge, slope gradient and coverage degree have not yet in-depth research at present 49 . In this experiment, the roughness is stable at the bottom of the flume, there is no problem of sediment deposition in flowing water, so the water depth can be measured accurately. Gravel had the function of backup h in this research. This was mainly attributed to the reduction in b e and u on gravel-covered slopes. h increased depending on Eq. (1). A larger flow depth improved the runoff shear stress, leading to greater disturbance to the soil surface 50 .
With the increase in gravel coverage degree, the backup effect of gravel on h was more obvious. Bunte 41 presented similar results. On the contrary, Fu et al. 51 obtained that h tended to decrease with the increase of gravel coverage degree through artificial rainfall simulation experiment. This discrepancy may be related to soil infiltration. In addition, under an identical gravel coverage degree, h increased with increasing flow discharge and slope gradient. Similar research results were obtained by Zhang et al. 46 .
Reynolds number. The Reynolds number (Re) is the ratio of inertial forces to the viscous force, and it represents the overland flow regime conditions. As the Reynolds number increases, the probability of a turbulent overland flow also increases. Hydraulic theory states that overland flow is turbulent when the Re is greater than 6500 and laminar when the Re is less than 580. Overland flow is transitional when the Re is between 580 and  www.nature.com/scientificreports www.nature.com/scientificreports/ 6500 52 . Overland flow is laminar when the flow discharge is less than 22.52 L/min. Conversely, overland flow is transitional.
Gravel increased the Re by 2.94-33.03% in comparison with the slopes without gravel. A higher Re may be due to the presence of gravel reducing the b e . Among all the treatments, gravel had the largest impact on the Re when the gravel coverage degree was 30%, the slope gradient was 2° and the flow discharge was 122 L/min, and the rate of increase was 33.03%. Gravel had the least impact on the Re when the gravel coverage degree was 10%, the slope gradient was 10° and the flow discharge was 8.44 L/min, and the rate of increase was 2.94%.
The Re did not change significantly with increasing slope gradient 53 (Fig. 6). However, the present result was inconsistent with the findings of Zhai et al. 54 . This difference may be caused by the water flow temperature. The Re was positively correlated with the unit width discharge and negatively correlated with the viscosity coefficient (see Eq. (3)). Under an identical flow discharge and identical gravel coverage degree, the unit width discharge had little difference under different slope gradients. Thus, the Re was mainly affected by the viscosity coefficient under gravel covered slopes with different slope gradients, and this coefficient was primarily affected by the water flow temperature. The experiment took place in autumn, and the water flow temperature changed little with the weather. Therefore, the viscosity coefficient of water flow fluctuated slightly under gravel covered slopes with different slope gradients, which led to the similar Re values under the five slope gradients.
The Re increased significantly with increasing flow discharge and gravel coverage degree (Fig. 6). On slopes with a gravel coverage degree of 0%, when the flow discharge increased from 8.44 to 122 L/min, the Re increased from 281 to 4077, which represented an increase of 13.49 times. On slopes with a gravel coverage degree of 10%   www.nature.com/scientificreports www.nature.com/scientificreports/ under identical conditions, the Re increased from 296 to 4368, which represented an increase of 13.78 times. On slopes with a gravel coverage degree of 20% under identical conditions, the Re increased from 320 to 4770, which represented an increase of 13.90 times. On slopes with a gravel coverage degree of 30% under identical conditions, the Re increased from 356 to 5357, which represented an increase of 14.06 times.
The Re was significantly positively correlated with Q (r = 0.989, P < 0.01**) and Cr (r = 0.712, P < 0.01**) and not correlated with J (r = −0.008, P > 0.01) ( Table 1). The relationship among Re, Q and Cr presented a power function ( Table 4). The NSE of Equation (16) was 0.999, demonstrating that the equation was superior. According to Equation (16), the exponent of Q (0.995) was higher than that of Cr (0.760), which showed that the Re was mainly affected by Q followed by Cr.
The Re is an important parameter for measuring the soil disturbance caused by overland flow. The Re increased with increasing the flow discharge and the gravel coverage degree 41 . Our results differed from those presented by Li et al. 55 , who found that the Re decreased with increases in the gravel coverage degree when the gravel coverage degree and flow discharge were relatively small. As the gravel coverage degree and the flow discharge increased, the trend gradually diminished and then reversed. Furthermore, Salman et al. 56 and Rieke-Zapp et al. 12 suggested that the Re did not change significantly with increases in the gravel coverage degree based on their experimental data. The discrepancy could be related to a greater amount of surface roughness and a higher infiltration rate on natural gravel-covered slopes.

Cr
Equation .  www.nature.com/scientificreports www.nature.com/scientificreports/ Froude number. The Fr reflects the ratio of inertial force to gravity and characterizes the overland flow pattern conditions. Inertial force plays a leading role in water flow, and supercritical flow occurs when Fr < 1. Gravity is equal to inertial force in water flow, and critical flow occurs when Fr = 1.

Re
The Fr varied from 0.75 to 2.89 on slopes without gravel and from 0.21 to 2.42 on slopes with gravel. Gravel reduced the Fr by 6.83-77.31% in comparison to the slopes without gravel. Under various experimental conditions, gravel had the largest impact on the Fr when the gravel coverage degree was 30%, the slope gradient was 2° and the flow discharge was 22.52 L/min, and the rate of reduction was 77.31%. Gravel had the least impact on the Fr when the gravel coverage degree was 10%, the slope gradient was 10° and the flow discharge was 22.52 L/min, and the rate of reduction was 6.83%.
Under identical gravel coverage degree conditions, the Fr increased significantly with increasing flow discharge and slope gradient. The flow pattern developed from a subcritical flow to a supercritical flow. However, with the increase in gravel coverage degree, the Fr tended to decrease. The flow pattern developed from supercritical flow to subcritical flow (Fig. 7). On slopes with a slope gradient of 2°, when the flow discharge increased from 8.44 to 122 L/min, the Fr increased from 0.74 to 1.67, 0.36 to 0.86, 0.25 to 0.75, and 0.21 to 0.72 when the gravel coverage degree was 0%, 10%, 20% and 30%, respectively. On slopes with a slope gradient of 4°, when the flow discharge increased from 8.44 to 122 L/min, the Fr increased from 0.80 to 1.90, 0.45 to 1.10, 0.34 to 0.94, and 0.30 to 0.87 when the gravel coverage degree was 0%, 10%, 20% and 30%, respectively. On slopes with a slope gradient

Fr
The Fr was significantly positively correlated with Q (r = 0.623, P < 0.01**) and J (r = 0.699, P < 0.01**) and significantly negatively correlated with Cr (r = −0.851, P < 0.01**) ( Table 1). The relation between Fr and Q and J and Cr presented a power function ( Table 5). The NSE of Equation (19) was 0.931, demonstrating that the equation was superior. According to Equation (19), the exponent of Cr (2.936) was higher than that of Q (0.378) and J (0.498), which indicated that the Fr was mainly affected by Cr followed by J and Q.
The flow depth and the flow velocity determine the sediment carrying capacity and runoff shear force. Fr reflects the relationship between the flow depth and the flow velocity. Gravel retarded the Fr , which indicated that the presence of gravel reduced the turbulence of water flow. This effect was primarily attributed to the reduction in flow velocity and increase in flow depth due to gravel cover. Accordingly, the Fr decreased depending on expression (5). Salman et al. 56 and Guo et al. 42 showed that the Fr was mainly controlled by the underlying surface and tended   www.nature.com/scientificreports www.nature.com/scientificreports/ to decrease as the gravel coverage degree increased and the flow pattern transformed from supercritical flow to subcritical flow, which was consistent with the results of this study. In addition, as the flow discharge and the slope gradient increased, the Fr increased. This finding was consistent with studies from Jing et al. 57 and Ye et al. 58 . The larger Fr meant smaller runoff shear force and a larger sediment carrying capacity 38 . Resistance coefficient. The Darcy-Weisbach resistance coefficient (f) varied from 0.10 to 1.94 on slopes without gravel and from 0.24 to 8.88 on slopes with gravel. Gravel increased f by 0. 15-18.42 times in comparison to the slopes without gravel. Under various experimental conditions, gravel had the largest impact on f when the gravel coverage degree was 30%, the slope gradient was 2°, and the flow discharge was 22.52 L/min, thus presenting an increase of 18.42 times. Gravel had the least impact on f when the gravel coverage degree was 10%, the slope gradient was 10° and the flow discharge was 22.52 L/min, thus presenting an increase of 0.15 times.
f did not demonstrate significant regularity with increasing slope gradient 38 (Fig. 8). However, there were some inconsistent opinions on the relationship between f and slope gradient. Yao 59 considered that f was positively correlated with slope gradient. Pan and Shangguan 60 thought that f was negatively correlated with slope gradient. The reason for the difference may be explained by the different experimental conditions and different experimental methods.
f decreased significantly with increasing flow discharge and decreasing gravel coverage (Fig. 8). On slopes with a gravel coverage degree of 0%, when the flow discharge increased from 8.44 to 122 L/min, f decreased from 1.93 to 0.10, which represented a reduction of 1.83. On slopes with a gravel coverage degree of 10% under identical conditions, f decreased from 4.73 to 0.23, which represented a reduction of 4.50. On slopes with a gravel coverage degree of 20% under identical conditions, f decreased from 6.39 to 0.49, which represented a reduction of 5.90. On slopes with a gravel coverage degree of 30% under identical conditions, f was decreased from 8.88 to 0.52, which represented a reduction of 8.36.
f was significantly positively correlated with Cr (r = 0.962, P < 0.01**) and significantly negatively correlated with Q (r = −0.868, P < 0.01**) but not correlated with J (r = −0.038, P > 0.01) ( Table 1). The relation between f and Q and Cr presented a power function ( Table 6). The NSE of Equation (22) was 0.841, demonstrating that the equation was superior. According to Equation (22), the exponent of cr (3.652) was higher than that of Q (0.701), which indicated that f was mainly affected by Cr followed by Q.
f is an important variable in the soil erosion model and reflects the resistance of the underlying surface to overland flow. With the increase in the gravel coverage degree, the contact area between gravel and water flow increased, and flow resistance played a dominant role, leading to an increase in overland flow resistance. A higher f on gravel-covered slopes indicated that overland flow was not only affected by particle resistance but also by the flow resistance around gravel. Engman 61 studied the resistance coefficient of farmland based on data collected from runoff plots. Savat 62 described the resistance coefficients for various surfaces. Gilley et al. 63 constructed a resistance coefficient equation under pebble cover based on a flume experiment. In these studies, f decreased with increasing flow discharge and decreasing gravel coverage degree, and these findings are consistent with the results of this study.

Conclusions
Gravel can change water flow patterns, reduce flow velocity, and increase water depth and resistance. The h, Re, and f values on gravel-covered slopes were 0.12-2.41 times, 2.94-33.03%, and 0.15-18.42 times higher, respectively, than those of the slopes without gravel. However, the u and Fr values on gravel-covered slopes were 1.20-58.95% and 6.83-77.31% lower, respectively, than those of the slopes without gravel.
Q, J and Cr affected the hydraulic characteristics of overland flow. u and Fr were positively correlated with both Q and J and negatively correlated with Cr. h was positively correlated with both Q and Cr and negatively correlated with J. The Re and f were less affected by J and positively correlated with Cr. However, the Re increased and f decreased with an increase in Q.
The relationships among hydraulic parameters and Q, J and Cr were described by good power functions (R 2 > 0.7, NSE > 0.7). The Re was most affected by Q, and the other hydraulic parameters were most affected by Cr. The results provide insights into the mechanism underlying gravel's control of soil erosion and can guide the ecological construction of soil and water conservation. Further research is needed on the effects of different particle sizes and arrangement patterns on the hydraulic characteristics of gravel-covered slopes.