Experimental study on the variation characteristics of runoff sediment concentration with slope length in the loess region of western Shanxi Province of northern China
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摘要:
目的 坡长是影响坡面径流形成及土壤侵蚀过程的重要因子。本研究以晋西黄土区坡面不同坡长处的含沙量为研究对象，旨在探明坡面径流含沙量随坡长的变化规律，阐明坡长因素对坡面侵蚀过程的影响。 方法 分别在5°和20°的坡面采用7.5 和10.0 L/(min·m)的单宽流量开展放水冲刷试验，测定0 ~ 5 m坡长内不同位置的径流含沙量和土壤剥蚀速率。 结果 （1）径流含沙量随坡长增加逐渐增大，且在较大坡度与流量条件下增加更快。此外，坡度和流量条件的增大会提高坡面径流含沙量。（2）土壤剥蚀速率随坡长增加先增加后减小，出现峰值的位置随着流量和坡度条件的增大向坡顶方向移动。土壤剥蚀速率随着坡度和流量条件的增加而增大。（3）S型曲线能很好地拟合各条件下径流含沙量与坡长的关系，决定系数R2 ≥ 0.96。曲线模型中的3个参数能很好地反映坡面侵蚀特征，分别为最大含沙量随坡度与流量条件的增大而增大，侵蚀最快的位置随坡度与流量条件的增大而减小，含沙量变化速率随流量与坡度的增大而增大。（4）基于S型曲线过程理论与试验计算值，若以60 mm/h强度的降雨为防范对象，建议5°条件下的植被工程护坡措施与坡顶间距不应超过426 cm，20°条件下的植被工程护坡措施与坡顶间距不应超过313 cm；若以90 mm/h强度的降雨为防范对象，建议5°条件下的植被工程护坡措施与坡顶间距不应超过366 cm，20°条件下的植被工程护坡措施与坡顶间距不应超过283 cm。 结论 本研究基于坡面侵蚀理论过程与冲刷试验结果提出并模拟了泥沙含量随坡长呈现出缓慢增加—快速增加—缓慢增加至饱和的S型曲线增长过程，根据曲线的特征提出了晋西黄土区护坡措施的布设方式。这有助于深入理解坡面侵蚀机理，为晋西黄土区坡面侵蚀模型参数估算与水土保持措施布设提供依据。 Abstract:Objective Slope length is an important factor affecting the formation of slope runoff and soil erosion processes. This study focused on the sediment concentration at different slope lengths in the loess area of western Shanxi Province of northern China, aiming to explore the variation of sediment concentration in slope runoff with slope length and elucidate the influence of slope length factors on slope erosion process. Method In order to reveal the variation law of runoff sediment concentration with slope length and to clarify the slope erosion process, the runoff sediment concentration and soil detachment rate at different locations within 0−5 m slope length were measured using 7.5 and 10.0 L/(min·m) unit width discharge on the 5° and 20° slopes, respectively. Result (1) The runoff sediment concentration increased gradually with the increase of slope length, and increased faster under the larger slope gradient and flow discharge. In addition, the increase of slope gradient and flow discharge will increase the runoff sediment concentration. (2) The soil detachment rate first increased and then decreased with the increase of slope length, and the peak position moved toward the slope top with the increase of flow discharge and slope gradient. The soil detachment rate increased with the increase of slope gradient and flow discharge. (3) The S-shaped curve can well fit the variation of runoff sediment concentration with slope length under various conditions, and the coefficient of determination R2 ≥ 0.97. The three parameters in the curve model can well reflect the characteristics of slope erosion, namely, the maximum sediment carrying force (a) increased with the increase of slope gradient and flow discharge, the position with the fastest erosion rate (xc) decreased with the increase of slope gradient and flow discharge, and the changing rate of sediment concentration (k) increased with the increase of slope gradient and flow discharge. (4) Based on the S-curve process theory and experimental calculation value, if the rainfall intensity of 60 mm/h was taken as the prevention object, it was recommended that the distance between vegetation engineering slope protection measures and slope top under 5° conditions should not exceed 426 cm, and the distance between vegetation engineering slope protection measures and slope top under 20° conditions should not exceed 313 cm. If the rainfall intensity of 90 mm/h was taken as the object of prevention, it was recommended that the distance between the vegetation engineering slope protection measures and the slope top under 5° conditions should not exceed 366 cm, and the distance between the vegetation engineering slope protection measures and the slope top under 20° conditions should not exceed 283 cm. Conclusion Based on the theoretical process of slope erosion and the results of erosion tests, this study proposes and simulates an S-shaped curve growth process of slow increase, rapid increase, and slow increase to saturation of sediment content with slope length. Based on the characteristics of the curve, the layout method of slope protection measures in the loess area of western Shanxi Province is proposed. This helps to deeply understand the mechanism of slope erosion and provide a basis for estimating the parameters of slope erosion models and laying out soil and water conservation measures in the loess area of western Shanxi Province. -
图 2 各组合条件下土壤剥蚀速率随坡长的变化
Figure 2. Variation of soil detachment rate with slope length under various combination conditions
图 3 各组合条件下径流含沙量随坡长的变化
Figure 3. Variation of runoff sediment concentration with slope length under various combination conditions
图 4 各组合条件下径流含沙量的预测值与实际值
Figure 4. Predicted and actual sediment concentration under various combination conditions
图 5 坡面侵蚀过程示意图
x1为坡面径流即将侵蚀土壤颗粒的位置，x2为坡面径流中含沙量增加速率最快的位置，x3为坡面径流携带泥沙达到饱和的位置。x1 is the location of soil particles that are about to be eroded by slope runoff, x2 is the location where sediment content in slope runoff increases at the fastest rate, and x3 is the location where slope runoff carries sediment to saturation.
Figure 5. Schematic diagram of slope erosion process
表 1 不同试验条件下实测径流含沙量
Table 1. Measured runoff sediment carrying force under different experimental conditions
坡长
Slope
length/cm含沙量
Sediment concentration/（kg·m−3）坡度5°
Slope of 5°坡度20°
Slope of 20°单宽流量 7.5 L/（min·m）
Discharge per unit width
7.5 L/(min·m)单宽流量 10.0 L/（min·m）
Discharge per unit width
10.0 L/(min·m)单宽流量 7.5 L/（min·m）
Discharge per unit width
7.5 L/(min·m)单宽流量 10.0 L/（min·m）
Discharge per unit width
10.0 L/(min·m)20 0.80 ± 0.02 2.00 ± 0.08 3.80 ± 0.11 5.70 ± 0.30 40 1.20 ± 0.07 3.20 ± 0.25 7.40 ± 0.19 11.70 ± 0.24 60 2.40 ± 0.10 4.40 ± 0.47 11.19 ± 0.48 17.90 ± 0.61 80 3.30 ± 0.49 6.79 ± 1.06 15.99 ± 0.81 25.80 ± 0.84 100 4.80 ± 0.32 8.39 ± 1.35 19.79 ± 0.65 31.80 ± 0.74 120 5.20 ± 0.45 9.60 ± 0.44 25.59 ± 0.37 38.90 ± 1.92 140 6.60 ± 0.19 10.80 ± 0.25 29.00 ± 0.03 46.80 ± 0.18 160 7.39 ± 0.78 12.78 ± 2.04 35.60 ± 0.01 57.30 ± 1.59 180 8.19 ± 0.76 15.18 ± 1.59 42.76 ± 2.20 68.30 ± 2.97 200 9.59 ± 1.17 18.58 ± 2.10 52.56 ± 2.39 83.30 ± 5.12 250 12.58 ± 1.83 25.76 ± 3.62 71.94 ± 3.73 152.40 ± 9.53 300 17.17 ± 2.75 38.14 ± 6.08 113.06 ± 7.89 209.90 ± 18.78 400 30.57 ± 2.93 69.92 ± 8.57 175.04 ± 9.14 298.60 ± 15.06 500 44.76 ± 3.93 92.90 ± 10.58 214.24 ± 9.13 356.70 ± 19.11 
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表 2 模型参数
Table 2. Model parameters
模型条件
Model condition$y=\dfrac{a}{1 + {{\rm{e}}}^{-k（x-{x}_{\mathrm{c} }）} }$ R2 P a/（kg·m−3） xc/cm k/（l·m−1） 5°，7.5 L/(min·m) 68.908 426.715 0.008 0.966 3.15 × 10−15 5°，10.0 L/(min·m) 117.316 366.993 0.010 0.979 1.35 × 10−17 20°，7.5 L/(min·m) 238.981 313.052 0.012 0.988 1.56 × 10−17 20°，10.0 L/(min·m) 370.937 283.499 0.014 0.988 1.04 × 10−16 注：y为某一坡长处的含沙量，kg/m3；a为所能达到的最大含沙量，kg/m3；k为含沙量随坡长变化的速率，1/m；xc为含沙量增长最快（斜率最大）的点对应的坡长，m。Notes: y is the sediment content of a slope, kg/m3; a is the maximum attainable sediment content, kg/m3; k is the changing rate of sediment content with slope length, 1/m; xc is the slope length corresponding to the point with the fastest growth in sediment content (maximum slope), m.
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