Storm Hazard Mitigation Structures 30.2 Coastal Armoring Structures 667
Part C | 30.2
pact load, then estimate the horizontal force, F h D
15w gd
2
.H s =d/
3:134 [30.41]. This can be used as
a reference value.
Step 7: Estimate the percentage of breaking waves
(P i% ) that produce impacts. Use results to decide
and confirm the loading case type from the following levels of Pi%:
– Pi% < 2%: Little breaking. Wave loads are primarily nonbreaking.
– 2% < Pi% < 10%: Breaking waves give impacts.
– Pi% > 10%: Heavy breaking may give impacts
or broken wave forces.
Unfortunately, space does not permit the procedure
and formulas needed to compute Pi% and the reader
must see Oumeraci et al. [30.5, pp. 78–82].
Step 8: Estimate impact force. This is a key result
within the PROVERBS project that gives a new
procedure based on the statistical distribution of
forces [30.42]. The relative wave force F
h is found
from
F
h D
˛
f1 Πln P.F
h /
g C ˇ :
(30.20)
The wave force on the structure F h divided by gH
2
b
gives the relative wave force F
h . And H b is the individual or maximum wave height at breaking [30.5,
p. 99] calculated taking into account local refraction, shoaling, and reflections from the structure
that modify a version of the Miche breaking formula [30.43] adapted for irregular, significant wave
heights by Vrijling and Bruinsma [30.44]. The calculation of H b is first used in Step 7 to find Pi%.
Again space does not permit us to explain all the
details.
This expression for F
h is a generalized extreme
value (GEV) distribution [30.8] and dependent on
three statistical parameters ˛, ˇ, and with the key
variable P.F
h /, the probability of non exceedance
for the impact force. The values for ˛, ˇ and
depend on the bed slope and number of tests conducted to measure the wave force F h . The summary
PROVERBS report [30.5] recommends using ˛ D
3:97, ˇ D 7:86, and D D0:32 as determined from
large-scale model tests closest to prototype conditions.
Step 9: Impact rise time and duration. The spike
in the impact load (force) over the wave period
(Fig. 30.10, bottom) can be estimated by formulas representing a triangular force distribution in
time with .F h / maximum taken at the 90% non exceedance level.
Step 10: Estimate uplift forces under impacts. Uplift force, uplift pressure distribution, and uplift
moment arm location formulas are presented to calculate the structure stability.
Step 11: Scale corrections. When conditions in steps
6 and 7 warrant impact loads, the PROVERBS
includes some scaling corrections in the force calculation.
Step 12: Pressure distributions. Formulas are presented to estimate the pressure distribution over the
vertical face of the wall and used to find the location for the moment arm of the horizontal force.
Again, when the Steps 6 and 7 reveal that the impact loads are important, these formulas should be
employed.
Finally, space does not permit us to provide the details needed to follow steps 9–12 herein and the reader
must refer to Oumeraci et al. [30.5] to implement the
parameter map (Fig. 30.10) and apply the results for
vertical, monolithic structure design. A section is included for the case of broken waves hitting the vertical
wall.
When the vertical breakwater is made up of relatively short, individual sections, the sudden, direct
impact of a plunging, breaking wave may be along
the length of one, short, caisson section. Then clearly,
the impact load formulas from the PROVERBS project
should be used to check the design.
The development of spreadsheets greatly facilitates
the design process. The key design variable is the caisson width B which dictates cost. The crest elevation can
also be varied (for the same width) so that the minimum,
caisson cross-sectional area can be determined.
Oumeraci et al. [30.5] also included a section on
what are labeled alternative, low-reflection structures,
namely perforated vertical walls.
In summary, for many designs, use of Fig. 30.10
to determine the loading case will reveal that the
Goda [30.34] method is adequate. And when it is not,
following Steps 6–12 for the impact loading case will
provide a safe design.
Seawalls and Bulkheads
As illustrated in Fig. 30.4, (a) seawalls and (b) bulkheads are backed by soils which provide substantial
resistance to water level forces and wave forces. The
geotechnical loadings of the soils on the wall or bulkhead often governs the design. and are beyond the scope
of discussion in this chapter. Proper seawall design requires the combined efforts of coastal engineers (wave
and water level forces on the vertical wall, toe scour
at the base of the wall to locate the lowest beach elevation, potential down drift impacts, etc.); geotechnical
engineers (soil properties behind the wall, active and
passive soil pressures on the wall, active and passive
Part C | 30.2
pact load, then estimate the horizontal force, F h D
15w gd
2
.H s =d/
3:134 [30.41]. This can be used as
a reference value.
Step 7: Estimate the percentage of breaking waves
(P i% ) that produce impacts. Use results to decide
and confirm the loading case type from the following levels of Pi%:
– Pi% < 2%: Little breaking. Wave loads are primarily nonbreaking.
– 2% < Pi% < 10%: Breaking waves give impacts.
– Pi% > 10%: Heavy breaking may give impacts
or broken wave forces.
Unfortunately, space does not permit the procedure
and formulas needed to compute Pi% and the reader
must see Oumeraci et al. [30.5, pp. 78–82].
Step 8: Estimate impact force. This is a key result
within the PROVERBS project that gives a new
procedure based on the statistical distribution of
forces [30.42]. The relative wave force F
h is found
from
F
h D
˛
f1 Πln P.F
h /
g C ˇ :
(30.20)
The wave force on the structure F h divided by gH
2
b
gives the relative wave force F
h . And H b is the individual or maximum wave height at breaking [30.5,
p. 99] calculated taking into account local refraction, shoaling, and reflections from the structure
that modify a version of the Miche breaking formula [30.43] adapted for irregular, significant wave
heights by Vrijling and Bruinsma [30.44]. The calculation of H b is first used in Step 7 to find Pi%.
Again space does not permit us to explain all the
details.
This expression for F
h is a generalized extreme
value (GEV) distribution [30.8] and dependent on
three statistical parameters ˛, ˇ, and with the key
variable P.F
h /, the probability of non exceedance
for the impact force. The values for ˛, ˇ and
depend on the bed slope and number of tests conducted to measure the wave force F h . The summary
PROVERBS report [30.5] recommends using ˛ D
3:97, ˇ D 7:86, and D D0:32 as determined from
large-scale model tests closest to prototype conditions.
Step 9: Impact rise time and duration. The spike
in the impact load (force) over the wave period
(Fig. 30.10, bottom) can be estimated by formulas representing a triangular force distribution in
time with .F h / maximum taken at the 90% non exceedance level.
Step 10: Estimate uplift forces under impacts. Uplift force, uplift pressure distribution, and uplift
moment arm location formulas are presented to calculate the structure stability.
Step 11: Scale corrections. When conditions in steps
6 and 7 warrant impact loads, the PROVERBS
includes some scaling corrections in the force calculation.
Step 12: Pressure distributions. Formulas are presented to estimate the pressure distribution over the
vertical face of the wall and used to find the location for the moment arm of the horizontal force.
Again, when the Steps 6 and 7 reveal that the impact loads are important, these formulas should be
employed.
Finally, space does not permit us to provide the details needed to follow steps 9–12 herein and the reader
must refer to Oumeraci et al. [30.5] to implement the
parameter map (Fig. 30.10) and apply the results for
vertical, monolithic structure design. A section is included for the case of broken waves hitting the vertical
wall.
When the vertical breakwater is made up of relatively short, individual sections, the sudden, direct
impact of a plunging, breaking wave may be along
the length of one, short, caisson section. Then clearly,
the impact load formulas from the PROVERBS project
should be used to check the design.
The development of spreadsheets greatly facilitates
the design process. The key design variable is the caisson width B which dictates cost. The crest elevation can
also be varied (for the same width) so that the minimum,
caisson cross-sectional area can be determined.
Oumeraci et al. [30.5] also included a section on
what are labeled alternative, low-reflection structures,
namely perforated vertical walls.
In summary, for many designs, use of Fig. 30.10
to determine the loading case will reveal that the
Goda [30.34] method is adequate. And when it is not,
following Steps 6–12 for the impact loading case will
provide a safe design.
Seawalls and Bulkheads
As illustrated in Fig. 30.4, (a) seawalls and (b) bulkheads are backed by soils which provide substantial
resistance to water level forces and wave forces. The
geotechnical loadings of the soils on the wall or bulkhead often governs the design. and are beyond the scope
of discussion in this chapter. Proper seawall design requires the combined efforts of coastal engineers (wave
and water level forces on the vertical wall, toe scour
at the base of the wall to locate the lowest beach elevation, potential down drift impacts, etc.); geotechnical
engineers (soil properties behind the wall, active and
passive soil pressures on the wall, active and passive