N s(∞ )
D fs = D∞
(A6)
N fs (Rd∞ )
where Rs(∞) is the nonovertopped limit of the stability number. To calculate the
size of the armor units of the crest, Dc, first the front-slope size of the units is
calculated as Equation A6 and applied to rescale the nondimensional freeboard
(Rd = R/Dfs). The size of the armor units is:
N fs (Rd )
Dcs = D fs
(A7)
N sc (Rd )
Figure A8 is based on this methodology (Vidal, Medina, and Martin 2000).
The analysis extends the available knowledge on stone size for conventional,
emergent, breakwaters to submerged breakwaters. In this case, the Hudson
formula and values of the coefficients Kd found in the Shore Protection Manual
(1984, Tables 7-8) are inserted to calculate the stable stone size needed for a
submerged breakwater, (Kd =2 and freeboard = 3 m).
Stability formulae for conventional surface-piercing (emergent) rubble-
mound structures are based on an extensive set of experimental and prototype
data. However, the formulae and data applied in the previous section for
submerged structures are based on a much more limited data set (e.g., Vidal et al.
1992; Vidal, Losada, and Mansard 1995; van der Meer 1988; Givler and
Srensen 1986). As a result only limited design formulae are available (e.g., van
der Meer and Pilarczyk 1990; Vidal, Medina, and Martin 2000) with which to
evaluate stability of a submerged spur in the north jetty environment. Further, the
limited experimental data are more applicable to structures that have steeper
slopes and are closer to the surface than the design concepts being evaluated for
the north jetty. Also, much of the physical testing to date has been based on
intermediate water depths and few, if any, are based on shallow water and
breaking waves (Melby and Kobayashi 1998). Caution is appropriate in
evaluating the results presented thus far. A physical model test is indicated given
the scope of this project.
A11
Appendix A
Stability Analysis of a Submerged Spur, North Jetty, Grays Harbor, WA
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