Estimating critical conditions for initiation of motion in wave or current environment ( Cont.)

per unit area applied to the sediment bed surface by water movement.

This critical value is usually called the critical shear stress for initiation of

motion. Estimating the shear stress for given conditions is not a simple

calculation and may depend on a multitude of variables. However, under

many conditions, given a few basic parameters, an estimate can be made

for the shear stress that can tell the engineer if sediment deposits are in the

range where sediment movement may occur (i.e., above the critical value).

This can be done for a wave environment or a current environment. This

section contains graphs that, if a few basic parameters are known (such as

median grain size, wave height, wave period, water depth, and current), a

reasonable estimate of stress can be developed. The calculations for com-

bined current/wave environments cannot be plotted easily. Under these

conditions, the relationships become much more complex, and a detailed

study is required to determine the bottom stresses and ultimate dispersive/

nondispersive classification of the site.

The dashed lines in Figure 25 plot the critical value of the vertically

averaged current velocity (ucr) versus the median grain size (d50) for vari-

ous water depths. The expression for ucr, as described by van Rijn

(1993), is defined as a function of the water depth h and grain size distri-

bution. This simplified equation, based on Shields curve for initiation of

motion and assuming effective bed roughness can be estimated as 3d90

(where d90 is the 90th percentile grain size, i.e., 90 percent of the material

is finer) and d90 = 2d50 can be expressed as:

 12h 

ucr = 0.19(d50 )

0.1

for 0.0001 ≤ d50 ≤ 0.0005 m



log

 3d90 

 12h 

ucr = 8.50(d50 )

0.6

for 0.0005 ≤ d50 ≤ 0.002 m

log



 3d90 

As stated previously, the above equations calculate the approximate

critical vertically averaged velocity value for the initiation of sediment

movement. At these values, the particles will start to roll or move across

the bottom in fairly regular jumps (saltation). There are also higher stress

levels at which the particles will leave the turbulent bottom boundary

layer and be brought into suspension. These values are called the critical

velocities for initiation of suspension and are indicated by the solid lines

in Figure 25. These values can be approximated, using the same assump-

tions as for ucr, by:

 12h 

[

]

(Θcr ,s )

ucr ,s = 5.75 (s - 1)gd50

0.5

log 



 3d90 

where s is the sediment specific gravity; g is acceleration of gravity; and

Θcr,s, the critical Shields parameter for suspension, is defined by:

Θcr ,s =

for 1 < D * ≤ 10

D *2 (s - 1) gd50

Chapter 8 Long-Term Cap Stability