# Characteristics of the Sediment Transport Process in Vegetation Hillslopes under Different Flow Rates

^{1}

^{2}

^{*}

## Abstract

**:**

^{−1}m

^{−1}, and two different sediment concentrations of 40 and 120 g L

^{−1}. The whole process of overland flow was monitored, and sediment and particle size samples from the inflow and outflow were collected and measured. The results showed that the changes in sediment concentration did not significantly affect the corresponding coefficients in the power function relationship between overland flow rate and velocity. Using the Reynolds number alone cannot effectively indicate the flow pattern of overland flow on vegetation hillslopes. The peak particle size and linear function were effective in describing the relationship between sediment particle composition and delivery rate during the sediment-trapping process by VFSs. During the sediment-trapping process, the sediment-trapping capacity of VFSs continued to decrease. The increase in sediment discharge was accompanied by a higher proportion of coarse particles. Under the same flow rate conditions, when the sediment concentration was higher, the coarse particles and their proportion also increased faster. Therefore, using only a certain particle size threshold to distinguish suspended and transported sediment may lead to inaccurate estimation of the sediment-trapping performance of VFSs. This study deepened the understanding of the mechanism of water–sediment processes on vegetation hillslopes and promoted the widespread and efficient application of VFSs management technology.

## 1. Introduction

^{−1}m

^{−1}) do not lead to significant differences in sediment deposition amount and a higher sediment concentration corresponds to a greater sediment deposition amount and lower sediment-trapping efficiency [19]. There was a power function relationship between the flow rate and sediment transport capacity [20]. The study results of Pan et al. indicated that the flow rate is positively proportional to the total amount of trapped sediment [21].

^{−1}slope to study the particle selectivity of sediment transport in shallow flow [22]. The results showed that the maximum flow rate (0.816 L s

^{−1}m

^{−1}) has enough energy to transport all sediment particles but the particles in the range of 355–595 μm are preferentially transported. The lower flow rates (0.399, 0.292, and 0.139 L s

^{−1}m

^{−1}) can also transport particles of all sizes but always give priority to transportation of the sediment particles in the size range of 45–125 μm. Jin and Römkens used simulated grass strips in a flume to conduct sediment-trapping tests and found that the deposited sediment particle sizes were mostly greater than 150 μm [17]. With the increase in slope gradient, the sediment deposition area moved to the downhill section of grass strips and the particle sizes of deposited sediment were also coarser.

^{−1}m

^{−1}), and sediment concentrations in the range of 100–300 g L

^{−1}. The results indicate that the proportion of coarse particles > 25 μm was greater, while the deposition efficiency of particles < 1 μm and 10–25 μm was greater than that of particles of 1–10 μm [19]. This study explained some particle selectivity characteristics of silt-laden overland flow passing through VFSs but did not further explore the differences in the process caused by different flow rates.

_{50}was employed to express the sediment-trapping efficiency [19]. In some formulae for calculating the sediment-trapping capacity of overland flow proposed by Zhang et al., d

_{50}was used to quantify the overall particle size of sediment [25]. To accurately quantify the process of sediment transported by the overland flow on vegetation hillslopes, it is necessary to pay attention to the movement of different-sized particles, as well as the effects of flow rate and sediment concentration slope on the movement law of sediment particles with different sizes.

## 2. Materials and Methods

#### 2.1. Experimental Apparatus and Treatments

^{−2}, its height was in the range of 30–90 cm, and its coverage rate was >90%. Spring and winter have less rainfall and usually do not produce overland flow, making them inactive seasons for soil erosion. Therefore, this study has good representativeness of the Loess Plateau region in China. To eliminate differences in soil moisture among experiments, the grassland was sprinkled evenly before each experiment until overland flow occurred. To avoid interference from sediment deposited in previous experiments, the sediment deposited on the bed surface of the grassland in each experiment was flushed away using slow-flowing clean water.

^{−1}m

^{−1}) with two different sediment concentrations (i.e., 40 and 120 g L

^{−1}) were applied [27]. The experimental conditions were nonsubmerged overland flow. In the “Grain for Green Project” of China, 15° is adopted as one of the main limiting criteria for determining the suitability of a hillslope area for inclusion in the program [4]. Therefore, a 15° slope was chosen for the experiments in this study. For further details of the experimental design, see Table 2.

#### 2.2. Data Measurement and Analysis

_{4}, Henan Huakai Biotechnology Co., Ltd., Henan, China) method [29]. When using the dye tracer (KMnO

_{4}) method to measure the flow velocity on vegetation hillslopes, the leaves are pushed aside at the measurement location to prevent obstruction of the view. The experimental vegetation in this study was rigid and the leaves did not directly contact the overland flow, which did not affect the flow velocity. Five sections were selected along the grassland. Each section and its interval were both 1 m long. The mean overland flow velocity (V) was calculated by

_{s}represent the correction coefficient and the measured surface velocity of overland flow, respectively. The grass strip used in this study had a rough bed surface, so μ = 0.75 for transitional or turbulent flow [30]. The Froude number (Fr) and Reynolds number (Re) are often used to describe surface roughness characteristics and express the resistances to overland flow offered by bed surfaces and vegetation, and they were calculated using the following equations [31]:

^{−2}) is gravity acceleration, and h (m) and ν

_{m}(m

^{2}s

^{−1}) represent the mean depth and kinematic viscosity coefficient of overland flow, respectively. The overland flow is considered laminar when Re < 500 and turbulent flow when Re > 500. h was calculated as

^{3}s

^{−1}) is the flow rate and B (m) is the width of the water-crossing section.

## 3. Results and Discussion

#### 3.1. Overland Flow Pattern under Different Inflow Rates

^{−1}m

^{−1}. The median values of overland flow velocity were 0.060, 0.078, 0.082, and 0.093 m s

^{−1}for the 40 g L

^{−1}experimental group and 0.067, 0.082, 0.092, and 0.096 m s

^{−1}for the 120 g L

^{−1}group. The relationship between the discharge and velocity of overland flow is commonly written as

_{s}is the surface velocity of overland flow (m s

^{−1}), S is the slope gradient of the hillslope (−), q is the inflow rate (L min

^{−1}m

^{−1}), and γ, m, and n are the corresponding coefficient values [29]. In this study, a 15° hillslope was used in all experiments, and the slope gradient was constant, so the relationship between q and V

_{s}could be simplified as follows:

^{2}is 0.89, which shows a good fitting effect. As shown in Figure 3, the two sets of points were evenly distributed on both sides of the curve, which indicated that the difference in sediment concentration of inflow does not significantly affect their relationship, as shown in Equation (7). The unit of flow rate (q) can affect the coefficient φ value but does not affect the value of n. The value of n was only decided by the power function relationship between q and V

_{s}. Pan et al. conducted experiments on grass strips with 8.7–50% slope, 0.1–0.9 cm

^{2}s

^{−1}inflow rate, and 70% vegetation cover rate [29]. The results showed that n = 0.687, which was ˃0.197, the n value in this study. This may be because the vegetation cover rate (70%) was smaller than that in this study (˃90%). Vegetation had a smaller effect on overland flow, and the direct effect of flow rate on velocity was greater than that in this study. In addition, the hydrodynamic change caused by the flow rate will further affect sediment transport and deposition on vegetated hillslopes.

^{−1}, slope gradients of 8.8–25.9%, and stem covers of 0–30%. The results showed that the Fr ranged from 0.07 to 3.98 and the overland flows were supercritical (torrent flow) when the stem cover was between 0 and 2.5% and subcritical (tranquil flow) when the stem cover was greater than 2.5% [32]. Luo et al. conducted experiments under the conditions of a 5° slope, 30 L min

^{−1}m

^{−1}unit flow rate, and 120 g L

^{−1}sediment concentration to study the effects of different aboveground structural parts of grass strips on the sediment-trapping process [33]. The Fr range was 0.09–0.49 under the completed grass strip treatment tests, which was also tranquil flow. Fr ˃ 1 only occurred with both green grass and litter removed in the treatment tests. These results were consistent with those of this study. Zhao et al. used coarse PVC tubes to simulate vegetation stems and conducted tests with four levels of vegetation cover (0%, 4%, 11%, and 17%), two flow rates (15 and 30 L min

^{−1}), and one slope gradient of 9% [18]. The Fr values were ˂1 when the flow rate was 15 L min

^{−1}, while Fr values were ˃1 when 30 L min

^{−1}. The torrent flow might be caused by the diameter of the simulated stems used in the tests of 2.0, 3.2, and 4.0 cm, which were much thicker than that of natural hillslope grass. The diameter of natural grass stems is generally at the millimeter level. Moreover, the bottom layer was a smooth iron sheet. Therefore, the resistances to overland flow were small. These results indicated that the overland flow on vegetation hillslopes is generally tranquil flow, which is very important for the study of erosion and deposition processes.

^{−1}m

^{−1}. Figure 2e,f show that Re ˂ 500 (laminar flow) when the flow rates were 7.5 and 15 L min

^{−1}m

^{−1}, except for some outliers. Fu et al. investigated the soil erosion properties of bare hillslopes and economic forests [34]. The shallow flow was pseudo laminar flow under 0.5, 1.2, and 1.8 mm min

^{−1}rainfall, and the runoff upslope was tranquil flow and then changed to torrential flow downslope with increasing hillslope length.

_{4}) method, the dye droplets significantly diffused while migrating downhill. The overland flow should be pseudo laminar flow. Therefore, only using Re to judge the flow pattern of shallow overland flow on vegetation hillslopes has great limitations.

#### 3.2. Relationship between Representative Particle Sizes and Sediment Delivery Rate

_{50}is often used to quantify the overall particle size level of sediment. In addition, the peak particle diameter d

_{p}, which accounts for the highest proportion of sediment, can also be used to describe the major characteristics of sediment particle size composition. The d

_{50}and d

_{p}of outlet sediment samples during the experimental process are plotted as solid lines and dotted lines in Figure 5, respectively. In the two sets of tests, sediment concentrations were 40 and 120 g L

^{−1}, which showed that the d

_{50}and d

_{p}of outflow sediment both gradually increased at the beginning and then stayed at a stable level. This result indicated that an increasing number of coarse particles can be exported from the hillslope vegetation area during this process. Initially, the greater the inflow rate was, the larger the d

_{50}and d

_{p}of the outflow sediment. However, there was almost no difference among tests with different flow rates in the stable stage. That is, the change in the inflow rate had no significant effect on the sediment particle size of the outflow at the stable stage. There were the same significant differences between d

_{50}and d

_{p}. The d

_{p}values were commonly greater than the corresponding d

_{50}in the same test, but they were not strictly proportional. Therefore, there are generally some differences in describing the sediment transport process on vegetation hillslopes using d

_{50}and d

_{p}.

_{50}and d

_{p}) and sediment delivery rate (T) at the outlet. The results are listed in Table 4. It was feasible to use d

_{50}or d

_{p}, and a power or linear function, to express the relationship, as the goodness of fit values R

^{2}were generally good. However, there were still some differences in the overall effectiveness among these formulas in Table 4.

_{50}and power function were used for the eight tests; among these R

^{2}values, one was ˃0.8, three ranged from 0.7 to 0.8, and two ranged from 0.6 to 0.7. The two remaining R

^{2}values were 0.34 for S15Q15SC120 and 0.38 for S15Q45SC120. When d

_{50}and the linear function were chosen, the maximum R

^{2}value was 0.91, one was in the range of 0.8–0.9, and two were in the range of 0.7–0.8. The R

^{2}value of S15Q15SC40 decreased slightly from 0.61 to 0.59, that of S15Q45SC120 was not changed, still 0.38, and those of the other six tests were improved to different degrees. Therefore, it was better to describe the relationship between d

_{50}and the sediment delivery rate at the outlet with a linear function.

_{p}and the sediment delivery rates of outflow. For the power function, except for S15Q30SC40, which decreased slightly from 0.72 to 0.71, the other R

^{2}values of d

_{p}were greater than those of d

_{50}. For example, the R

^{2}values of S15Q15SC40 and S15Q45SC40 were improved from 0.61 and 0.73 to 0.73 and 0.86, respectively. In particular, that of S15Q45SC120 significantly increased from 0.38 to 0.58. When d

_{p}was used, the fitting effects of linear and power functions were compared. The results showed that except for the R

^{2}value of S15Q15SC40, which decreased slightly from 0.73 to 0.71, the R

^{2}values of the other tests were increased. In particular, S15Q15SC120 and S15Q45SC120 increased significantly from 0.39 and 0.58 to 0.44 and 0.63, respectively.

_{50}and the peak particle size d

_{p}in units of μm. Even if there is very little sediment at the outlet, when detected, d

_{50}and d

_{p}are still values greater than 0. Therefore, the intercept of the vertical axis should theoretically be negative. Most of the results are consistent with this situation, with only S15Q15SC40 showing a positive ordinate intercept, 1.94 for d

_{50}and 1.66 for d

_{p}. This may be due to the high initial sampling particle size and measurement results.

^{2}is the goodness of fit rather than the correlation coefficient. The low values of R

^{2}in some tests (S15Q15SC120 and S15Q45SC120) may be due to the large size of the experimental plot, which is 10 m in length. It is difficult to ensure that the optimal state can be achieved during each experimental process, which may result in some experimental data being biased. However, under the same data conditions, linear models exhibit better stability.

#### 3.3. Particle Sorting of Sediment Transport by Overland Flow in VFSs

_{50}and/or peak particle diameter d

_{p}, generally cannot clearly describe the particle size distributions of outlet sediment during the sediment-trapping process by VFSs. The sediment delivery rates of each particle size at the outlet are plotted in Figure 6. They were obtained by multiplying particle size distribution percentages and instantaneous sediment delivery rates. The ordinate of each point in these curves represents the instantaneous sediment delivery rate of the corresponding particle size on the horizontal axis, and the unit is g S

^{−1}. The results showed that the first sample was mostly collected within 1 or 2 min of each test, and the sediment amount at the outlet was very small at the beginning. The main particle size ranged from 5.6 to 56.4 μm. In the two tests under 120 g L

^{−1}sediment concentration with 7.5 (Figure 6e) and 30 L m

^{−1}min

^{−1}(Figure 6g) flow rates, the sediment amounts of the first sample were too small, so their particle size distributions were not obvious. The d

_{p}of the initial sediment sample at the outlet was 10.0–22.4 μm.

## 4. Conclusions

- (1)
- During the process of sediment trapping by VFSs, the differences in sediment concentration of overland flow do not affect the parameters in the power relationship between the discharge and flow velocity.
- (2)
- The calculation results showed that some measurement points were still laminar flow when Re was used to indicate the flow pattern of the shallow overland flow on the vegetation hillslope. Under the influence of dense vegetation on the slope, it is difficult to form laminar flow when the slope flow is disturbed. Therefore, using Re alone may not be effective in determining the flow pattern on vegetation-covered hillslopes.
- (3)
- When describing the relationship between sediment particle size and sediment delivery rate on vegetation hillslopes, the peak particle size was better than the median particle size and the linear function was more stable than the power function. Therefore, they can be considered for the construction of relevant erosion models.
- (4)
- During the sediment-trapping process by VFSs, the sediment-trapping capacity of VFSs gradually decreases and the increase in sediment discharge is accompanied by a greater proportion of coarse sediment particles. Under the same flow rate conditions, when the sediment concentration was greater, the amount and proportion of coarse sediment particles at the outlet increased faster. Using only a certain particle size threshold to distinguish suspended and bed load sediment may lead to inaccurate estimation of sediment-trapping performance by VFSs. The assumption that the coverage of sediment deposition changes the original underlying surface, resulting in a decrease in sediment-trapping efficiency, should be considered simultaneously.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Overland flow pattern under different experimental treatments. Subfigures (

**a**,

**c**,

**e**) are the V, Fr, and Re of tests under the conditions of the sediment concentration of 40 g L

^{−1}with flow rates of 7.5, 15, 30, and 45 L min

^{−1}m

^{−1}; (

**b**,

**d**,

**f**) are V, Fr, and Re of tests under the conditions of the sediment concentration of 120 g L

^{−1}with flow rates of 7.5, 15, 30, and 45 L min

^{−1}m

^{−1}, respectively. Note(s): These figures are box plots. The middle red line represents the median. The lower and upper blue lines represent the first and third quartiles, respectively. The two black lines above and below the blue box are the maximum and the minimum values (except the outliers), respectively. The red plus signs are the outlier points. The outliers of the box plots in this study were identified via the following process. The lower and upper quartiles (D

_{1}and D

_{3}) are the 25% and 75% positions of the ascending sequence, respectively. The interquartile range (IQR) $={D}_{3}-{D}_{1}$. In a box plot, the data of $>{D}_{3}+\frac{3}{2}IQR$ or $>{D}_{1}-\frac{3}{2}IQR$ were identified as outliers in this study.

**Figure 5.**Variation process of the median particle size (d

_{50}) and the peak particle diameter (d

_{p}) of sediment in outlet runoff. Subfigures (

**a**,

**b**) are the d

_{50}and d

_{p}of two sets of experiments under conditions of sediment concentrations of 40 and 120 g L

^{−1}, respectively.

**Figure 6.**Composition of sediment particle size at the outlet. Subfigures (

**a**–

**d**) are the results of tests under the conditions of sediment concentration of 40 g L

^{−1}with flow rates of 7.5, 15, 30, and 45 L min

^{−1}m

^{−1}; (

**e**–

**h**) are the results of tests under the conditions of a sediment concentration of 120 g L

^{−1}with flow rates of 7.5, 15, 30, and 45 L min

^{−1}m

^{−1}, respectively.

Soil Type | Soil Texture | The Median Diameter (d_{50}/μm) | ||||||
---|---|---|---|---|---|---|---|---|

Loessial soil | Sandy loam soil | 39.9 ± 2.7 | ||||||

Particle size distribution (%)/μm | ||||||||

>1000 | 1000−500 | 500−250 | 250−100 | 100−50 | 50−20 | 20−2 | 2−1 | <1 |

0 | 0.55 ± 0.34 | 1.14 ± 0.07 | 5.27 ± 1.48 | 29.15 ± 2.73 | 46.04 ± 1.43 | 15.32 ± 2.15 | 0.87 ± 0.11 | 1.66 ± 0.14 |

Test Code * | Slope and Sediment Concentration | Designed Flow Rate Q (L min^{−1} m^{−1}) | Duration t (min) |
---|---|---|---|

S15Q7.5SC40 | S = 15° SC = 40 g L ^{−1} | 7.5 | 250 |

S15Q15SC40 | 15 | 162 | |

S15Q30SC40 | 30 | 88 | |

S15Q45SC40 | 45 | 62 | |

S15Q7.5SC120 | S = 15° SC = 120 g L ^{−1} | 7.5 | 156 |

S15Q15SC120 | 15 | 90 | |

S15Q30SC120 | 30 | 58 | |

S15Q45SC120 | 45 | 60 |

^{−1}m

^{−1}, and the sediment concentration is 40 g L

^{−1}.

**Table 3.**The ranges of the mean velocity (V), Froude number (Fr), and Reynolds number (Re) of overland flow in the different treatment experiments.

Experimental Code | V (m/s) | Fr | Re |
---|---|---|---|

S15Q7.5SC40 | 0.051~0.079 | 0.22~0.49 | 110~585 |

S15Q15SC40 | 0.070~0.097 | 0.31~0.50 | 268~842 |

S15Q30SC40 | 0.065~0.098 | 0.20~0.36 | 606~1115 |

S15Q45SC40 | 0.076~0.110 | 0.22~0.35 | 828~1083 |

S15Q7.5SC120 | 0.058~0.081 | 0.25~0.47 | 243~436 |

S15Q15SC120 | 0.071~0.104 | 0.35~0.60 | 247~612 |

S15Q30SC120 | 0.072~0.110 | 0.22~0.49 | 606~1141 |

S15Q45SC120 | 0.086~0.109 | 0.25~0.36 | 771~1257 |

**Table 4.**The fitting results of the relationship between the representative particle sizes (d

_{50}and d

_{p}) and sediment delivery rate (T) at the outlet.

Test Code | $\mathit{T}=\mathit{\alpha}{\mathit{d}}_{50}^{\mathit{\beta}}$ | $\mathit{T}=\mathit{k}{\mathit{d}}_{50}+\mathit{b}$ | $\mathit{T}=\mathit{\alpha}{\mathit{d}}_{\mathit{p}}^{\mathit{\beta}}$ | $\mathit{T}=\mathit{k}{\mathit{d}}_{\mathit{p}}+\mathit{b}$ | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

α | β | R^{2} | k | b | R^{2} | α | β | R^{2} | k | b | R^{2} | |

S15Q7.5SC40 | 0.028 | 1.471 | 0.65 | 0.196 | −1.55 | 0.69 | 0.016 | 1.520 | 0.72 | 0.141 | −1.38 | 0.74 |

S15Q15SC40 | 0.881 | 0.623 | 0.61 | 0.246 | 1.94 | 0.58 | 0.694 | 0.717 | 0.73 | 0.205 | 1.66 | 0.71 |

S15Q30SC40 | 0.026 | 1.927 | 0.72 | 0.944 | −10.23 | 0.76 | 0.026 | 1.758 | 0.71 | 0.640 | −8.39 | 0.74 |

S15Q45SC40 | 0.010 | 2.291 | 0.73 | 1.730 | −26.83 | 0.78 | 0.002 | 2.632 | 0.86 | 1.458 | −30.89 | 0.91 |

S15Q7.5SC120 | 0.009 | 2.072 | 0.78 | 0.647 | −8.56 | 0.84 | 0.009 | 1.945 | 0.79 | 0.488 | −6.96 | 0.83 |

S15Q15SC120 | 0.116 | 1.632 | 0.34 | 1.734 | −21.28 | 0.39 | 0.024 | 1.913 | 0.39 | 1.277 | −23.01 | 0.44 |

S15Q30SC120 | 0.028 | 2.269 | 0.86 | 3.722 | −48.24 | 0.91 | 0.012 | 2.313 | 0.90 | 2.538 | −41.64 | 0.92 |

S15Q45SC120 | 3.071 | 0.917 | 0.38 | 2.429 | −4.04 | 0.38 | 0.308 | 1.511 | 0.58 | 3.145 | −43.95 | 0.63 |

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## Share and Cite

**MDPI and ACS Style**

Luo, M.; Pan, C.; Peng, J.; Wang, L.
Characteristics of the Sediment Transport Process in Vegetation Hillslopes under Different Flow Rates. *Water* **2023**, *15*, 2922.
https://doi.org/10.3390/w15162922

**AMA Style**

Luo M, Pan C, Peng J, Wang L.
Characteristics of the Sediment Transport Process in Vegetation Hillslopes under Different Flow Rates. *Water*. 2023; 15(16):2922.
https://doi.org/10.3390/w15162922

**Chicago/Turabian Style**

Luo, Mingjie, Chengzhong Pan, Jun Peng, and Li Wang.
2023. "Characteristics of the Sediment Transport Process in Vegetation Hillslopes under Different Flow Rates" *Water* 15, no. 16: 2922.
https://doi.org/10.3390/w15162922