transport are given below: 



<3t> 

 Ps 9 \ P s -P 



(*r 



(19) 



where $ is a dimensionless measure of bed- load transport and d^ represents 

 uniform grain size. Also, 



* 



Ps-P I d u 



P ) R h S 



(20) 



and 



* = f-(ijr) 



(21) 



with R h , the hydraulic radius, defined as the cross-sectional area divided by 

 the wetted perimeter. Since the equations above were developed for uniform 

 grain size, most field uses require adjustment of $ and ij) . Adjusted values 

 for individual size classes are given as $ and \j> in Figure 4, using d g in 

 Equation 20 to obtain V • 



** 

















^v 



\ 











V 



\ 



.001 .01 



Figure 4. Einstein's relationship between $ and V (Herbich et al. 1984) 



Bed- Load Transport Under Wave Action 



14. Einstein's analysis for unidirectional bed-load transport has been 

 used as a building block for analysis of wave -induced bed- load sediment 

 transport. Kalkanis (1963) used the Einstein approach and laboratory tests 

 with an initially plane sand bed to develop approximations for bed- load 

 transport in oscillatory flow regimes. These relationships were further 



17 



