used the point at which sediment particles were first observed to move as 

 their criterion. Sato and Tanaka identified two different criteria to 

 describe critical conditions - the first characterized by surface layer (1-3 

 grain diameters in depth) movement only and the second by completely active 

 movement in both the surface and supporting layers . 



Bed- Load Transport in Unidirectional Flows 



9. Although numerous bed-load equations have been suggested, most are 

 concerned with the total shear (bed and fluid) that resists sediment 

 transport. In addition, most agree that bed- load transport q b can generally 

 be expressed as a function of 



q b = f [x ol T: c ,g,d,p e ,p,]i] 



(13) 



where 



r = bed or boundary shear stress, lb f /ft 2 



r c = critical boundary shear stress to initiate movement, lb f /ft 2 



H = fluid dynamic viscosity, lb f sec/ft 2 



10. Generally, there have been three basic approaches to studying the 

 bed- load transport problem in unidirectional flows - the duBoys method, the 

 Schoklitsch method, and the Einstein method. These approaches are similar in 

 that each was developed largely from laboratory flume studies, and all 

 empirical coefficients are based on these laboratory studies. These methods 

 are well -documented in other sources, but are briefly summarized here. 



11. duBoys analysis The duBoys analysis (duBoys 1879) assumes that 

 layers of the bed move over one another in such a way that the velocity of the 

 elements of each layer decreases linearly with depth. The velocity decreases 

 until it is zero at the top of the layer that does not move, since its 

 frictional resistance is just in balance with the shear force due to motion of 

 the water. The formula developed by duBoys is given below for unit width of 

 bed- load volume q b with units determined by the coefficient ip: 



<&= + M T o-* c ) ( 14 > 



In this equation, ^ is a constant which must be determined for a given bed. 

 Although this model has received much criticism, it has frequently been used 

 as a conceptual model. Based on two-dimensional laboratory tests, Straub 

 (1942) used the duBoys analysis method to develop the following expression for 



15 



