Acta Geographica Sinica ›› 1999, Vol. 54 ›› Issue (4): 347-356.

### Theoretical Analysis and Experimental Study on the Critical Slope of Erosion

HU Shi xiong1, JIN Chang xing 2

1. 1. International Research and Training Center on Erosion and sedimentation, Beijing 100044;
2. The Institute of Geography, Chinese Academy of Science, Beijing 100101
• Received:1998-01-01 Revised:1998-11-01 Online:1999-07-15 Published:1999-07-15
• Supported by:
National Natural Science Foundation of China,No.49501002;No.59890200

Abstract: The overland flow is defined as the flow of water over the land surface toward a stream channel and is the initial phase of surface runoff. The sediment yielding from overland flow erosion increases with the increasing slope if the slope is smaller than a critical value, and reduces following further increase of the slope if the slope is larger than the critical slope. With Energy Theory, Sediment Transportation Mechanism and data from laboratory and field experiments, the critical slope of overland flow erosion was studied in detail. Firstly, from the viewpoint of energy analysis, the detachment capacity of overland flow is directly proportional to the flow shear stress, and the shear stress is directly proportional to the kinetic energy of overland flow. A theoretical formula is derived which indicated that the energy of overland flow is closely related to the flow rate per unit width, composition of soil particle size, runoff depth and slope gradient. The maximum flow shear stress occurs if the slope is between 22° and 26°. Therefore, the conclusion from the energy analysis is obtained that the critical slope of overland flow erosion is about 22°～26°. Secondly, the analysis from dimensionless shear ratio and sediment transportation mechanism shows that the capacity of overland flow carrying sediment reach its maximum at the slope gradient approximate to the frictions angle of sediment under water. The sediment carried by overland flow is mainly composed by the silt and fine sand, whose friction angle under water is measured at 22°～27°. This means that critical slope of over land erosion is between 22°～27°, which is coincident with the critical slope derived from energy analysis. Thirdly, simulation experiment in laboratory shows that the maximum sediment yield is obtained at the slope of 23°～27°, which verified the result induced from the theoretical analysis. Finally, it is concluded that the critical slope gradient of sheet erosion and rill erosion is about 22°～27°, and that of rainsplash transportation is below 22°, and critical slope gradient of gully and gravitational erosion will be bigger than that of sheet erosion and rill erosion. Another conclusion of this paper is that the critical slope gradient is not a fixed value, but a range of values, and discussion of the critical slope of erosion should refer to concrete erosion way and boundary conditions.

CLC Number:

• S157