where a = -0.028 + 0.045C′ + 0.034 hc′/h - 610-9 Bn2 and At is the area of
structure cross-section, C'=exp(aNs*), Bn = At/Dn502, and h is the water depth.
Van der Meer and Pilarczyk (1990) show that the previous equations are
valid over a wider range of conditions than the Ahrens (1987, 1989) original
equations for hc. It is possible to draw design curves from these equations, which
*
give the crest height as a function of either N s or Hs.
The previous equations are for dynamically stable reef-type structures where
R > 0. Van der Meer and Pilarczyk (1990) give a stability formula for statically
stable submerged structures that includes the previous class:
(
)
′
hc
= (2.1 + 0.1S )exp - 0.14 N s
*
(A5)
h
Thus, a functional relationship is provided between the relative crest height
of a submerged breakwater, the damage level, S, and the spectral stability
number, Ns*. Stability of submerged breakwaters is a function of the relative crest
height, the damage level, S, and the spectral stability number.
For fixed crest height, water level, damage level, and wave height and
period, the required ∆Dn50 can be calculated, giving finally the required stone
weight (diameter). Also, wave height versus damage curves can be derived. The
analysis conducted by van der Meer and Pilarczyk (1990) did not consider
damage to different breakwater segments or the effects of structure side slopes on
stability.
The previous analysis by van der Meer and Pilarczyk (1990) is based on the
limited experimental data of van der Meer (1988) and Givler and Srensen
(1986) and is valid only for side slopes of 1.5 to 2.5. Van der Meer and Pilarczyk
(1990) suggest that because wave attack is concentrated on the crest and less on
the seaward slope of a submerged structure, it may be possible to exclude the
effect of slope in the analysis. The stability formula (Equation A5) is based upon
0.5< hc/h < 1 and Ns*< 12. Van der Meer and Pilarczyk (1990) noted a large
increase in the stability number as hc/h decreases below 0.45.
Figure A7 shows stable crest stone size as a function of deepwater wave
height calculated using the method of van der Meer and Pilarczyk (1990) for a
structure with 0.4 < hc/h < 0.6. The calculations shown are made for the onset of
damage (S = 2) for selected wave periods from 10 to 22 sec and for water levels
between mllw and mhhw plus storm surge and including mean water level (mwl).
Stone size increases with increasing wave height until depth-limited breaking
criterion is reached for the north jetty environment. Depth-limited breaking wave
heights were estimated assuming a constant nearshore slope of 0.0265 (1:38) and
a breaking criterion of Hb/h = 0.78 and follows the methodology in the Coastal
Engineering Manual (2003), Part II, Chapter 4.
A9
Appendix A
Stability Analysis of a Submerged Spur, North Jetty, Grays Harbor, WA
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