minor component of the total load, so a total load formula comprised of bed-load 

 developed theories should be appropriate. 



Nielsen (1992) presents a modified form of the Meyer-Peter and Muller 

 (1948) relationship for dimensionless transport that accounts for some 

 consideration of "high stress" flows (i.e., flows that would tend to increase 

 suspended sediment). Verification of the reasonable approximation of this 

 modified formula should be directed to Nielsen (1992). Nielsen's (1992) 

 relationship is: 



(D = 12(^'-6'JV^ (1) 



where 



$ = dimensionless sediment-transport rate 

 d ' = effective Shield's parameter 

 6'c = critical Shield's parameter 



Dimensionless bed-load transport, Ob is defined as: 



^.= u ^\ 3 (2) 



where 



<I)b = dimensionless bed-load transport 



Qb = depth integrated bed-load transport, L"/T 



5 = specific gravity of sediment, Ps/Pw 



g - acceleration because of gravity 



d - D50 grain size 



Combining Equations 1 and 2 to solve for Qb (bed load per unit width) gives: 



a = 12(^'-^, )y[&^{s-l)gd' (3) 



The Shield's parameter is a descriptor of the initiation of sediment motion. In 

 Shield's original work, laboratory experiments were used to measure velocities 

 and calculate bottom shear stress for flows that caused movement in various sedi- 

 ments. The famous Shield's curve was created defining the critical bottom shear 

 stress causing sediment movement. Shield's original work however is awkward 

 for practical application because it involves a cumbersome iteration to determine 

 the Shield's parameter for a given flow condition and sediment type. Madsen and 

 Grant (1976) modified the Shield's parameter so that the curve more clearly 

 represents a relationship between fluid flows and sediment characteristics, thus 

 avoiding the iterative process. 



Chapter 5 Sediment Transport 23 



