Determination of Sediment Transport Parameter, k2

The value of k2 varies from 0.637 to 0.857 depending on the critical shear stress of bed material to the boundary shear stress in the normal channel section. For clear-water flow it is 0.857 and for live-bed flows it is less depending on the ratio of shear stress to the critical shear stress of the bed material. Laursen (2) established the variation of k2 value as a function of tc/t1 as shown in Figure 2.24 in ASCE Manual on Sedimentation (2). This curve may be approximated by the following equation for the English System:

k2= 0.11(tc/t1 + 0.4)2.2 + 0.623
Where:
tc is the critical shear stress and t1 is the boundary shear stress in the upstream or normal channel section. If tc is equal to or greater than t1, then clear water scour can be expected to take place at the bridge, and the value of k2 should be selected as 0.857.

Critical shear stress, tc, may be calculated by several methods. For non-cohesive materials and for fully developed clear-water scour, Laursen (1) used the following simple equation for the English System:

tc = 4D50 
Where:
D50 is the median particle size in the section (channel bed or overbank area) under consideration. On overbank areas, estimating the critical shear stress may also involve consideration of the flood plain vegetation.

The boundary shear stress, t1, in the approach channel or overbank subarea may be calculated as:

t 1 = g y1S
Where: g  is the water unit weight, y1 is the average flow depth or hydraulic depth and S is the energy slope of the flow.