坡面漫流土壤剥蚀

土壤表面的坡面漫流是相互交织或编织的水道，没有明显的沟渠，而不是深度均匀的薄层水。水流被石头和卵石以及植被覆盖物打断，经常绕着草丛和小灌木旋转。

流动的剪切应力

在雷诺数和弗劳德数的基本水力关系中，重要的因素是流速，通常用曼宁公式表示

$v={\frac {r^{\frac {2}{3}}s^{\frac {1}{2}}}{n}}$ (1.7)

其中 $r$ 是水力半径， $s$ 是坡度， $n$ 是曼宁糙率系数。该公式假设完全湍流流过粗糙表面。

由于土壤的固有阻力，速度必须达到临界值才能开始侵蚀。基本上，当水流施加的力超过保持土壤颗粒静止的力时，单个土壤颗粒就会从土壤团块中分离出来。当河流中相对平缓的斜坡上的颗粒运动开始时，所涉及的过程和起作用的力受无量纲剪切应力 $\Theta$ 和颗粒粗糙雷诺数 $Re$ 的临界条件控制，分别定义为

$\Theta ={\frac {\rho _{w}u_{*}^{2}}{g(\rho _{s}-\rho _{w})D}}$ (1.8)

$Re^{*}={\frac {u_{*}D}{v}}$ (1.9)

其中 $\Theta$ 是希尔兹（1936）数^[1]， $\rho _{w}$ 和 $\rho _{s}$ 分别是水和土壤的密度， $g$ 是重力加速度， $D$ 是相应土壤颗粒的直径， $u_{*}$ 是流动的剪切速度，表示为

$u_{*}=(grs)^{\frac {1}{2}}$ (1.10)

当 $Re^{*}$ 的值大于 40（湍流）时， $\Theta$ 的临界值在颗粒运动中保持恒定的 0.05。不幸的是，当颗粒没有完全浸没或流动处于层流范围内时，该值不成立，就像地面径流的情况一样。对浅层流中岩石碎片的研究表明， $\Theta$ 的值约为 0.01（Poesen，1987^[2]；Torri 和 Poesen，1988^[3]）。

Figure 1.2: Critical shear velocity for soil particle detachment in turbulent water flow as function of particle size (Savat, 1982) — 图 1.2：湍流水流中土壤颗粒脱离的临界剪切速度与颗粒尺寸的关系^[4]

其他研究（Govers，1987^[5]；Guy 和 Dickinson，1990^[6]；Torri 和 Borselli，1991^[7]）表明，谢弗数始终高估了颗粒运动的水力要求。这意味着颗粒运动的开始不仅仅是流体剪切应力的现象，而是由其他因素增强。

雨滴冲击对流动的影响，

颗粒相对于地面坡度的休止角，

随着坡度陡度的增加，重力的强烈影响，

土壤的凝聚力，

随着流中泥沙浓度增加，流体密度的变化，

流动中的颗粒与下方土壤之间的磨损。

由于上述方法没有证明令人满意，因此 Savat（1982）^[8] 采用了经验方法，基于流动剪切速度的临界值来启动颗粒运动（图 1.2）。一旦超过颗粒运动的临界条件，土壤颗粒可能以取决于流的剪切速度和单位流量的速率从土壤体中分离出来（Govers 和 Rauws，1986）^[9]。

然而，这只有在剪切速度完全作用于土壤颗粒时才有效，这意味着对流动的阻力完全是由于颗粒阻力。这种情况只有在完全光滑的裸露土壤表面上才成立。实际上，由于土壤表面的微地形形态和植被覆盖而产生的阻力通常更为重要，颗粒阻力可能仅占流动所承受的总阻力的 5%（Abrahams 等人，1992）^[10]。

土壤剥蚀

由于很难确定颗粒阻力的水平，因此只能开发非常普遍的关系来描述剥蚀率 $D_{f}$ ，这取决于剥蚀与流速之间简化的关系。通过整合连续性和曼宁的流速方程，Meyer（1965）^[11] 表明

$v=s^{\frac {1}{2}}Q^{\frac {1}{3}}$ (1.11)

对于恒定的粗糙度条件，其中 $Q$ 是流量或流速。假设剥蚀率 $D_{f}$ 随速度的平方而变化，Meyer 和 Wishmeier（1969）^[12] 表明

$D_{f}\propto Q^{f}s^{j}$ (1.12)

其中 $f={\tfrac {2}{3}}$ ，以及 $j={\tfrac {2}{3}}$ 。Quansah（1985）^[13] 通过实验获得了更精确的指数值，f = 1.5，j = 1.44，适用于从粘土到沙子的各种土壤类型。这两个版本仅与水流在土壤表面上的作用有关。当流动伴随着降雨时，他发现指数值降低到 f = 1.12 和 j = 0.64，表明雨滴的冲击抑制了流动剥蚀土壤颗粒的能力。

然而，剥离取决于流中已悬浮的沉积物量（Meyer 和 Monke，1965）^[14]， $D_{f}$ 在公式 1.12 中适用于仅在水流清澈时发生的剥离能力。在其他条件下， $D_{f}$ 取决于流中实际沉积物浓度 $C$ 与流所能容纳的最大浓度 $C_{max}$ 之间的差异（Foster 和 Meyer，1972）^[15]

$D_{f}\propto (C_{max}-C)$ (1.13)

这意味着理论上，随着流中沉积物浓度的增加，剥离速率下降，当达到最大沉积物浓度时，剥离速率变为零。

Flanagan 和 Nearing (1995)^[16] 将沟间剥离速率 $D_{f,i}$ 描述为基线沟间侵蚀性的明确函数 $K_{i}$ 、有效降雨强度 $I_{e}$ 、沟间径流率 $Q_{i}$ 、冠层、地面覆盖物和沟间坡度调整因子 $C_{c}$ 、 $C_{g}$ 和 $C_{s}$ 、沟的间距和宽度 $R_{s}$ 和 $w$ ，以及沉积物输送率 ${SDR}$

$D_{f,i}=K_{i}I_{e}Q_{i}C_{c}C_{g}C_{s}{\frac {R_{s}}{w}}{SDR}$ (1.14)

其中

$C_{c}=1-F_{c}e^{-0.34h_{c}}$ (1.15)

$C_{g}=e^{-2.5f_{g}}$ (1.16)

$C_{s}=1.05-0.85e^{4\sin \alpha }$ (1.17)

其中 $f_{c}$ 是土壤被冠层覆盖的比例， $h_{c}$ 是有效冠层高度， $f_{g}$ 是沟间表面被植物残体覆盖的比例，而 $\alpha$ 是沟间坡度角。根据 Foster (1982)^[17] ${SDR}$ 可以被估计为土壤表面随机粗糙度、沟间坡度和沟间沉积物粒度分布的函数。

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参考文献

↑ Shields, A. (1936). Anwendung der Aehnlichkeitsmechanik und der Turbulenzfoschung auf die Geschiebebewegung, volume 26 of Mitteilungen der Preussischen Anstalt Wasserbau und Schiffbau.
↑ Poesen, J. (1987). Transport of rock fragments by rill flow: a field study. Catena Supplement, 8:35–54.
↑ Torri, D. and Poesen, J. (1988). Incipient motion conditions for single rock fragments in simulated rill flow. Earth Surface Processes and Landforms, 13:225–237.
↑ Savat, J. (1982). Common and uncommon selectivity in the process of fluid transportation: field observations and laboratory experiments on bare surfaces. Catena Supplement, 1:139–160.
↑ Govers, G. (1987). Initiation of motion in overland flow. Sedimentology, 34:1157–1164.
↑ Guy, B. and Dickinson, W. (1990). Inception of sediemnt transport in shallow overland flow. Catena Supplement, 17:91–109.
↑ Torri, D. and Borselli, L. (1991). Overland flow and soil erosion: some processes and their interactions. Catena Supplement, 19:129–137.
↑ Savat, J. (1979). Laboratory experiments on erosion and deposition of loess by laminar sheet flow and turbulent rill flow. In Vogt, H. and Vogt, T., editors, Colloque sur l’erosion agricole des sols en milieu tempere non Mediterraneen, pages 139–143. L’Universite Lois Pasteur, Strasbourg.
↑ Govers, G. and Rauws, G. (1986). Transporting capacity of overladn flow on a plane and on irregular beds. Earth Surface Processes and Landforms, 11:515–524.
↑ Abrahams, A., Parsons, A., and Hirsch, P. (1992). Field and laboratory studies of resistance to interrill overland flow on semi-arid hillslopes, southern arizona. In Parsons, A. and Abrahams, A., editors, Overland flow: hydraulics and erosion mechanics, pages 1–23. UCL Press, London.
↑ Meyer, L. (1965). Mathematical relationships governing soil erosion by water. Journal of Soil and Water Conservation, 20:149–150.
↑ Meyer, L. and Wishmeier, W. (1969). Mathematical simulation of the process of soil erosion by water. Transactions of the American Society of Agricultural Engineers, 12:754–758,762.
↑ Quansah, C. (1985). Rate of soil detached by overland flow, with and without rain, and its relationship with discharge, slope steepness and soil type. In El-Swaify, S., Moldenhauer, W., and Lo, A., editors, Soil erosion and conservation, pages 406–423. Soil Conservation Society of America, Ankeny, IA.
↑ Meyer, L. and Monke, E. (1965). Mechanics of soil erosion by rainfall and overland flow. Transactions of the American Society of Agricultural Engineers, 8:572–577.
↑ Foster, R. and Meyer, L. (1972). A closed-form soil erosion equation for upland areas. In Shen, H., editor, Sedimentation. Department of Civil Engineering, Colorado State University, Cort Collins.
↑ Flanagan, D. and Nearing, M. (1995). USDA-Water Erosion Prediction Project (WEPP: Technical Documentation, volume 10 of NSERL Report. National Soil Erosion Research Laboratory, West Lafayette, IN.
↑ Foster, G. (1982). Modelling the soil erosion process. In Haan, C., Johnson, H., and Brakensiek, D., editors, Hydrologic modelling of small watersheds, volume 5, pages 940–947. American Society of Agricultural Engineers Monograph.

[1] Shields, A. (1936). Anwendung der Aehnlichkeitsmechanik und der Turbulenzfoschung auf die Geschiebebewegung, volume 26 of Mitteilungen der Preussischen Anstalt Wasserbau und Schiffbau.

[2] Poesen, J. (1987). Transport of rock fragments by rill flow: a field study. Catena Supplement, 8:35–54.

[3] Torri, D. and Poesen, J. (1988). Incipient motion conditions for single rock fragments in simulated rill flow. Earth Surface Processes and Landforms, 13:225–237.

[4] Savat, J. (1982). Common and uncommon selectivity in the process of fluid transportation: field observations and laboratory experiments on bare surfaces. Catena Supplement, 1:139–160.

[5] Govers, G. (1987). Initiation of motion in overland flow. Sedimentology, 34:1157–1164.

[6] Guy, B. and Dickinson, W. (1990). Inception of sediemnt transport in shallow overland flow. Catena Supplement, 17:91–109.

[7] Torri, D. and Borselli, L. (1991). Overland flow and soil erosion: some processes and their interactions. Catena Supplement, 19:129–137.

[8] Savat, J. (1979). Laboratory experiments on erosion and deposition of loess by laminar sheet flow and turbulent rill flow. In Vogt, H. and Vogt, T., editors, Colloque sur l’erosion agricole des sols en milieu tempere non Mediterraneen, pages 139–143. L’Universite Lois Pasteur, Strasbourg.

[9] Govers, G. and Rauws, G. (1986). Transporting capacity of overladn flow on a plane and on irregular beds. Earth Surface Processes and Landforms, 11:515–524.

[10] Abrahams, A., Parsons, A., and Hirsch, P. (1992). Field and laboratory studies of resistance to interrill overland flow on semi-arid hillslopes, southern arizona. In Parsons, A. and Abrahams, A., editors, Overland flow: hydraulics and erosion mechanics, pages 1–23. UCL Press, London.

[11] Meyer, L. (1965). Mathematical relationships governing soil erosion by water. Journal of Soil and Water Conservation, 20:149–150.

[12] Meyer, L. and Wishmeier, W. (1969). Mathematical simulation of the process of soil erosion by water. Transactions of the American Society of Agricultural Engineers, 12:754–758,762.

[13] Quansah, C. (1985). Rate of soil detached by overland flow, with and without rain, and its relationship with discharge, slope steepness and soil type. In El-Swaify, S., Moldenhauer, W., and Lo, A., editors, Soil erosion and conservation, pages 406–423. Soil Conservation Society of America, Ankeny, IA.

[14] Meyer, L. and Monke, E. (1965). Mechanics of soil erosion by rainfall and overland flow. Transactions of the American Society of Agricultural Engineers, 8:572–577.

[15] Foster, R. and Meyer, L. (1972). A closed-form soil erosion equation for upland areas. In Shen, H., editor, Sedimentation. Department of Civil Engineering, Colorado State University, Cort Collins.

[16] Flanagan, D. and Nearing, M. (1995). USDA-Water Erosion Prediction Project (WEPP: Technical Documentation, volume 10 of NSERL Report. National Soil Erosion Research Laboratory, West Lafayette, IN.

[17] Foster, G. (1982). Modelling the soil erosion process. In Haan, C., Johnson, H., and Brakensiek, D., editors, Hydrologic modelling of small watersheds, volume 5, pages 940–947. American Society of Agricultural Engineers Monograph.

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