ERDC/CHL CHETN-III-64
June 2002 (revised)
wc
armor
layer
Ae
ta
hc
h
υ
Figure 2. Rubble-mound structure cross section
This damage formulation was popularized by van der Meer (1988). Melby and Kobayashi
(1998a) utilized S as a general damage description and further defined the eroded profile using
several engineering parameters: the maximum eroded depth E = de/Dn50, the minimum remaining
cover depth C = dc/Dn50, and the maximum cross-shore length of the eroded region L = le/Dn50.
These damaged section descriptors are shown in Figure 1. A typical structure cross section is
shown in Figure 2. The maximum eroded depth and minimum remaining cover depth may not
occur at the same location along a structure because of the variability of the armor layer
thickness.
PREDICTIVE RELATIONS: Melby and Kobayashi (1998a) conducted a series of experiments
measuring the erosion of a stone armor layer for varying wave and water-level conditions. The
structure profile was measured repeatedly throughout the test at up to 32 sections alongshore.
The 32 profiles were used to obtain mean damage and mean damaged profile as well as the
alongshore variability of damage and the profile.
The empirical equation proposed by Melby and Kobayashi (1998a) for predicting the temporal
progression of mean eroded area as a function of time domain wave statistics is
( Ns )5
(t 0.25 - tn.25 ) for tn ≤ t ≤ tn+1
0
n
S (t ) = S (tn ) + 0.025
(2)
(Tm )0.25
n
where S (t) and S (tn) are predicted and known mean eroded areas at times t and tn, respectively,
with t > tn. Ns = Hs / (∆Dn50) is the stability number based on the average of the highest one-third
wave heights from a zero-upcrossing analysis, ∆ = Sr -1 where Sr is the armor stone specific
gravity, and Tm is the mean period. The wave parameters are defined 5Hs seaward of the
structure toe, which is the travel distance of large breaking waves. Equation 2 provides a means
to compute damage over a sequence of N events, each of relatively constant wave conditions,
where each event is defined over a time period from tn to tn+1, 1 ≤ n ≤ N.
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