3-14-00, Composite/Vertical Wall Breakwater Design
Ref:Shore Protection Manual, USACE, 1984
Basic Coastal Engineering, R.M. Sorensen, 1997
Coastal Engineering Handbook, J.B. Herbich, 1991
EM 1110-2-2904, Design of Breakwaters and Jetties, USACE, 1986
Breakwaters, Jetties, Bulkheads and Seawalls, Pile Buck, 1992
Coastal, Estuarial and Harbour Engineers' Reference Book, M.B. Abbot and W.A. Price, 1994, (Chapter 29)
Coastal Engineering, K. Horikawa, 1978
Topics
Composite/Vertical Wall Breakwater Design
Wave Force Calculations
Caisson Width
Sliding and Overturning Stability
Soil Bearing Capacity Calculations
Summary of Design Procedure
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Composite/Vertical Wall Breakwater Design
Wave Force Calculations
A characteristic of vertical wall breakwaters is that the kinetic energy of the wave is stopped suddenly at the wall face. The energy is then reflected or translated by vertical motion of the water along the wall face. The upward component of this can cause the wave crests to rise to double their deep water height (non-breaking case). The downward component causes very high velocities at the base of the wall and horizontally away from the wall for ½ of a wavelength, thus causing erosion and scour.
Many analytical and laboratory studies and field observations have been undertaken to understand the wave pressure and develop wave pressure formulas. However, most of the formulas are based on monochromatic regular wave of constant height and period.
Non-Breaking Waves - assumes forces are essentially hydrostatic
Linear Wave Theory
- standing wave (known as the "clapotis")
- total reflection crest to trough excursion of the water surface = 2H
amplitude of the dynamic pressure,
at the bottom (z = -h)
Sainflou's Formula (1928)
- Based on standing waves
- Non-breaking waves (assumes force is essentially hydrostatic)
- Uses trochoidal wave theory
Pressure distribution when wave crest arrives:
at free surface (zo = 0), p = 0
at bottom (zo = -h),
Pressure distribution when wave trough arrives:
at free surface (zo = 0), p = 0
at bottom (zo = -h),
Experience shows that Sainflou under estimates wave pressure in the mean water level zone under storm conditions if H1/3 is used as design wave height
Miche-Rundgren Formula (1944, 1958) - modified Sainflou (recommended by SPM)
- Based on standing waves
- Non-breaking waves
- Uses 2nd order wave theory
- Assumes linear depth-dependent pressure distribution below the water line
Radiation stress considerations show the reflected wave causes a set-up (ho) at the vertical wall
Simplified formula assumes a linear pressure distribution below the water level (conservative assumption, see diagram)
Increase in pressure due to the standing wave:
where = wave reflection coefficient (1.0 for vertical wall with total reflection)
This pressure on the seaside is opposing the hydrostatic pressure on the lee-side. The corresponding resultant forces (R) and moments (M) are:
(1) wave crest (subscript e)
(2) wave trough (subscript i)
Breaking Waves
Waves breaking directly against the structure face sometimes exert high, short-duration, dynamic pressure that acts near the region where the crests hits the structure.
At present, Minikin's equation is widely used in the United States; in Japan, Hiroi's equation is generally accepted. Minikin's equation yields considerably higher peak pressure than Hiroi's, although the resulting total forces given by these two equations are similar for shallow-water cases. Both equations overestimate the total force and overturning moment when the water depth gets deeper.
Hiroi' Formula (1919) - used in Japan up to 1979 when Goda's formulas were adopted
- Assumes uniform pressure distribution
- Based on field observations
- pressure acts from bottom to 1.25H above SWL
- If crown height (R) < 1.25H, press. acts from bottom to crown height
Total horizontal force
Minikin's Formula (1950) - used in U.S.
Based on wave pressure records and shock press. work by Bagnold
pressure distribution with peak pressure at or near the still-water level
- vertical breakwater resting on rubble mound
- impact pressure decreases parabolically to zero at z = -0.5H
- generally overestimates pressures
Dynamic Pressure
Static Pressure
USACE EM-1110-2-2904 (1986) recommended equations
Peak impact pressure:
Total Force (Ft)
If H/Lo < 0.045, tons/ft
If H/Lo > 0.045, tons/ft
Moment (M)
If H/Lo < 0.045, ft-tons/ft, (d as in Minikin)
If H/Lo > 0.045, ft-tons/ft
Goda (1974) - current Japanese standard
- based on model tests
- breaking and non-breaking waves
- design against single largest wave force in design sea state
- uses highest wave in wave group
- Hmax is estimated at 5H1/3 seaward of breakwater
- THmax= TH1/3
- modified to incorporate random wave breaking model
- assumes trapezoidal shape for pressure distribution along front
- Caisson is imbedding into the rubble mound
- Uplift pressure distribution is assumed triangular
Hmax should be based on Goda's random wave breaking model
Sorensen recommends Hmax = 1.8Hs
Elevation to which wave pressure is exerted:
= direction of waves with respect to breakwater normal
(for waves approaching normal to breakwater, = 0)
Pressure on Front of Vertical Wall
Effect of wave period on pressure distribution
minimum = 0.6 (deep water), maximum = 1.1 (shallow)
Increase in wave pressure due to shallow mound
Linear pressure distribution
hb = water depth at 5Hs seaward of breakwater
Buoyancy and Uplift Pressure
(Japanese found that pu = p3 was too conservative)
Decrease in Pressure from Hydrostatic under Wave Trough
Example
(1) shallow mound
from dispersion relation L = 20.9 m, k = 0.301 m-1 at h = 4 m
Assume non-breaking waves:
Miche-Rundgren
Goda
from dispersion relation k = 0.272 m-1 at hs = 6 m
hc= 2.5 m < *
assume hb = h = 6 m
hw = 6.5 + (4.5 - 4) = 7 m
2 = 0.0225
Horizontal forces:
Miche-Rundgren7.9 t/m
Goda5.7 t/m
(2) no mound
Miche-Rundgren
No change Re = 7.9 t/m
Goda
k = 0.301 m-1 at hs = 4 m, hc= 2.5 m < * , assume hb = h = 4 m, hw = 7 m
2 = 0
Horizontal forces:
Miche-Rundgren7.9 t/m
Goda5.9 t/m
Miche-Rundgren is now 1.3 times Goda's
Caisson Width and Mound Dimensions Guidance
Caisson width:
General guidance: B = 1.7 - 2.6 H1/3 for reflective to breaking waves
Wave transmission is of primary concern.
Caisson Crest Elevation:
General guide: hc = 0.5 - 0.75 H1/3 , however design requirement become more important:
- allowed overtopping specifications
- lee-side wave transmission requirements
Overtopping is less critical for structurally integrity compared to rubble mound breakwaters (i.e. there is no armor layer vulnerable to wave attack). However, a shorter caisson will have a shorter moment arm (see overturning stability discussion below).
Mound Crest Elevation:
General guidance: d/h < 0.6 for breaking waves.
Scour at the base of the caisson is still a concern, especially in a breaking wave environment. Therefore, the height of the rubble mound should be limited. However, as seen below in the soil bearing capacity discussion, higher mounds distribute the load more and enhance the ability of the soil to support the more concentrated weight of the caisson. Large key stones may be placed at the base of the caisson to reduce scour problems.
Sliding and Overturning Stability
To assess the sliding and overturning stability of the upright section, the weight (W), buoyancy (B), the horizontal wave induced force (Fh) and uplift force (U) must be considered. Buoyancy is the weight of the water displaced by the submerged volume of the upright section. The dynamic uplift pressure is assumed to vary linearly from the seaside to the lee-side.
Safety Factors (S.F.) are calculated as follows:
(1) For sliding, the friction due to the net downward forces opposes the horizontal wave induced force
,
where is the coefficient of friction between the upright section and the rubble mound (or the bottom). For a new installation 0.5. After the initial shakedown, 0.6.
(2) For overturning, moments are calculated about the lee-side toe
for a symmetric section with no eccentricity:
In designing breakwaters for harbor protection, safety factors are taken as 1.2 or higher.
"The overturning of a caisson implies very high pressures on the point of rotation. The bearing capacity of the stone underlayer will be exceeded and the crushing of stones at the caisson heel will take place. In reality the bearing capacity of the underlayer and the sea-bed sets the limiting conditions. The soil mechanics methods of analyzing the bearing capacity of a foundation when exposed to eccentric inclined loads should be applied, i.e. slip failure or the use of bearing capacity diagrams." (Abbott and Price, p. 422)
Soil Bearing Capacity Calculations
Generally, a rubble mound will distribute the weight of the caisson according to its friction angle. Higher base mounds will distribute the load over a wider area and reduce the load on the soil. Weak soil may also be replaced with a sand key which will further distribute the load.
Guideline (D = depth of top sand layer or sand key):
- D 2B only consider soil strength in sand (neglect clay below)
- 2B > D > 1.5B use combined strength by spreading the load
- D 1.5B use clay load, sand may still be added to (1) increase drainage, (2) help distribute load, (3) give better, more even surface
Eccentricity will shift the load as well.
As previously the allowable load developed from a bearing capacity analysis must equal or exceed the actual load. The eccentricity (e) can be calculated from the angle of the resultant force. Since the soil cannot support a tension stress, the load must be corrected as follows:
For :
For :; where
Summary of Design Procedure
- Specify design conditions: design wave, water levels, etc.
- Set rubble mound dimensions
- Compute external wave loading
- Perform stability analysis
- Sliding stability
- Overturning stability
- Slip stability: local, translational and global
- Perform a bearing capacity analysis
- At mound level (i.e. at the toe of the caisson)
- At the foundation level
- Determine caisson stability under towing conditions and during the installation phase
- Stress configurations
- During towing and installation
- Side
- Bottom
- Internal panel
- Post installation
- Side
- Bottom
- Internal panel
- Structural Detailing