Estimating critical conditions for initiation of motion Evaluation of Erosion Potential (Cont.)

Under wave-dominated conditions, the orbital velocities produced by

waves will be the primary force agitating the sediment bed surface and

producing erosion. Because of the unsteady nature of the orbital veloci-

ties (compared with the relatively steady currents), a peak orbital velocity

of similar magnitude to a current velocity will not result in similar shear

stresses at the sediment-water interface. The current boundary layer is

fully developed and much thicker than that for continually changing or-

bital velocities. Therefore, bottom shear stresses created by a similar mag-

nitude orbital velocity will be much greater than that for current velocity

and Figure 25 will not apply. Due to the complexity of wave/bottom

stress complexities, there is no general agreement amongst researchers on

a proper method for estimating bottom effects. However, it is possible,

without a detailed analysis, to develop a first order magnitude estimate

that will assist the engineer in determining site stability for a plane bed.

The method described here was developed by van Rijn (1989), and a brief

overview is presented in van Rijn (1993). Figure 26 plots wave period, T,

versus the critical peak orbital velocity at the bed, uδ,cr. The solid lines

are the experimentally determined values of the critical value for the in-

itiation of motion. The average inaccuracy of the curves is 25 percent.

The value of Uδ for conditions at a specific site can be evaluated by:

πH

Uδ =

T sinh (kh)

where

H = significant wave height

T = wave period

k = wave number

The wave number k can be determined from the wave length L by the

equation k = 2p/L. The wave length in turn is determined by iteration of

the equation:

gT 2

tanh (2πh L)

2π

The user can then compare the value of Uδ to the critical value, Uδ,cr, for

a known median grain size and wave period using Figure 26. If the values

of Uδ is greater than Uδ,cr, then the potential for erosion is significant.

Even if the value is only slightly less than critical, given the margin of er-

ror in the estimates presented in Figure 26, the engineer should seek fur-

ther detailed analysis to determine site stability. However, if the value is

significantly less than critical, the site can be assumed stable.

Chapter 8 Long-Term Cap Stability