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11 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 Coastal Engineering Manual (VI-5), USACE, 2003
Topics
Composite/Vertical Wall Breakwater Design Wave Force Calculations Caisson Width Sliding and Overturning Stability Soil Bearing Capacity Calculations Summary of Design Procedure
--------------------------------------------------------------------------------------------------------------------- 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.
Wave-generated pressures on structures are complicated functions of the wave conditions and geometry of the structure. For this reason laboratory model tests should be performed as part of the final design of important structures. For preliminary designs the formulae presented in this section can be used within the stated parameter limitations and with consideration of the uncertainties.
Two-dimensional wave forces on vertical walls.
Non-breaking waves incident on smooth, impermeable vertical walls are completely reflected by the wall giving a reflection coefficient of 1.0. Where wales, tiebacks, or other structural elements increase the wall surface roughness and retard the vertical water motion at the wall, the reflection coefficient will be slightly reduced. Vertical walls built on rubble bases will also have a reduced reflection coefficient.
The total hydrodynamic pressure distribution on a vertical wall consists of two time-varying components: the hydrostatic pressure component due to the instantaneous water depth at the wall, and the dynamic pressure component due to the accelerations of the water particles. Over a wave cycle, the force found from integrating the pressure distribution on the wall varies between a minimum value when a wave trough is at the wall to a maximum values when a wave crest is at the wall as illustrated below for the case of non-overtopped walls or caissons.
Pressure distributions for a non-breaking wave
The resulting total hydrodynamic load when the wave trough is at the vertical wall is less than the hydrostatic loading if waves were not present and the water was at rest. For bulkheads and seawalls this may be a critical design loading because saturated backfill soils could cause the wall to fail in the seaward direction. Therefore, water level is a crucial design parameter for calculating forces and moments on vertical walls.
Pressure distribution on an overtopped wall
Wave overtopping of vertical walls provides a reduction in the total force and moment because the pressure distribution is truncated as shown schematically above. Engineers should consider the effect overtopping might have on land-based vertical structures by creating seaward pressure on the wall caused by saturated backfill or ponding water.
Three Types of Wave Forces on Vertical Walls
1) Non-breaking Waves
2) Breaking (plunging) waves with almost vertical fronts
3) Breaking (plunging) waves with large air pockets
1) Non-breaking waves: Waves do not trap an air pocket against the wall. The pressure at the wall has a gentle variation in time and is almost in phase with the wave elevation. Wave loads of this type are called pulsating or quasi-static loads because the period is much larger than the natural period of oscillation of the structures. (For conventional caisson breakwaters the period is approximately one order of magnitude larger.) Consequently, the wave load can be treated like a static load in stability calculations. Special considerations are required if the caisson is placed on fine soils where pore pressure may build up, resulting in significant weakening of the soil.
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, ( )kh cosh
zhkcoshHdp +γ= , z = 0 at surface;
at the bottom (z = -h) khcosh
Hpdγ
±=
2) Breaking (plunging) waves with almost vertical fronts: Waves that break in a plunging mode
develop an almost vertical front before they curl over (see Figure VI-5-57b). If this almost vertical front occurs just prior to the contact with the wall, then very high pressures are generated having extremely short durations. Only a negligible amount of air is entrapped, resulting in a very large single peaked force followed by very small force oscillations. The duration of the pressure peak is on the order of hundredths of a second.
3) Breaking (plunging) waves with large air pockets: If a large amount of air is entrapped in a pocket, a double peaked force is produced followed by pronounced force oscillations as shown in Figure VI-5-57c. The first and largest peak is induced by the wave crest hitting the structure at point A, and it is similar to a hammer shock. The second peak is induced by the subsequent maximum compression of the air pocket at point B, and is it is referred to as compression shock, (Lundgren 1969). In the literature this wave loading is often called the “Bagnold type.” The force oscillations are due to the pulsation of the air pocket. The double peaks have typical spacing in the range of milliseconds to hundredths of a second. The period of the force oscillations is in the range 0.2-1.0 sec.
Formula Wave Type Structure Type CEM Table Sainflou formula (modified by Miche-Rundgen, 1958)
Standing Impermeable vertical wall VI-5-52
Goda formula 2-D oblique Impermeable vertical wall VI-5-53 Goda formula (modified by Takahashi, Tanimoto, and Shimosako 1994)
Provoked breaking
Impermeable vertical wall VI-5-54
Goda formula forces and moments
Provoked breaking
Impermeable vertical wall VI-5-55
Goda formula (modifed by Tanimoto and Kimura 1985)
2-D head-on Impermeable inclined wall VI-5-56
Goda formula (modified by Takahashi and Hosoyamada 1994)
2-D head-on Impermeable sloping top VI-5-57
Goda formula (modified by Takahashi, Tanimoto, and Shimosako 1990)
2-D head-on Horizontal composite structure VI-5-58
Goda formula (modifed by Takahashi, Tanimoto, and Shimosako 1994)
3-D head-on Vertical slit wall VI-5-59
•
o
CEM Table VI-5-52 through VI-5-59 provide formulae for estimating pressure distributions and corresponding forces and overturning moments on vertical walls due to non-breaking and breaking waves.
Wave pressure distributions for breaking waves are estimated using Table VI-5-54, o
• o o
o
o
o
•
•
corresponding forces and moments are calculated from Table VI-5-55.
Minikin's Method: Older breaking wave forces method of Minikin (Shore Protection Manual, 1984) can result in very high estimates of wave force, “as much as 15 to 18 times those calculated for non-breaking waves.” These estimates are too conservative in most cases and could result in costly structures. There may be rare circumstances where waves could break in just the right manner to create very high impulsive loads of short duration, and these cases may not be covered by the range of experiment parameters used to develop the guidance given in Table VI-5-54. In addition, scaled laboratory models do not correctly reproduce the force loading where pockets of air are trapped between the wave and wall (CEM Figure VI-5-57). For these reasons, it may be advisable to design vertical-front structures serving critical functions according to Minikin's method.
Most of the methodology is based on the method presented by Goda (1974) and extended by others to cover a variety of conditions. These formulae provide a unified design approach to estimating design loads on vertical walls and caissons.
NOTE: All of the methods calculate the pressure distribution and resulting forces and moments for only the wave portion of the hydrodynamic loading. The hydrostatic pressure distribution from the SWL to the bottom is excluded.
o
o
For a caisson structure (with water on both sides), the SWL hydrostatic forces would exactly cancel (i.e. hydrostatic pressure on the seaside would be opposed by the pressure on the lee-side); however, it will be necessary to include the effect of the SWL hydrodynamic pressure for vertical walls tied into the shoreline or an embankment.
Non-Breaking Waves: Sainflou's Formula (1928) modified by Miche-Rundgren (1944, 1958)
(CEM Table VI-5-52, p. VI-5-138) • Derived theoretically for regular, non-breaking waves and a vertical wall, but may be
applied to irregular waves • Uses 2nd order wave theory • Assumes linear depth-dependent pressure distribution below the water line (assumes
force is essentially hydrostatic) • cannot be used for breaking waves or overtopping
( )os
osw21 Hh
Hhppδ++
δ+γ+=
s
w2 khcosh
Hp γ=
( )ow3 Hp δ−γ=
Radiation stress considerations show the reflected wave causes a set-up (δo) at the vertical wall
•
s
2
o khcothLHπ
=δ , L2k π
=
Simplified formula assumes a linear pressure distribution below the water level (conservative assumption, see reflected wave diagram)
•
• Increase in pressure due to the standing wave:
γχ+=
s
w1 khcosh
H2
1p
where χ = wave reflection coefficient (1.0 for vertical wall with total reflection)
• Pressure for calculating uplift force is p2
Breaking Waves: Goda (1974) (CEM Table VI-5-53, p. VI-5-139)
• based on model tests • design against single largest wave force in design sea state, uses highest wave in
wave group • Hdesign is estimated at a distance of 5×Hs seaward of breakwater (Hdesign = 1.8Hs) • hb = water depth at 5×Hs seaward of breakwater • L (or k) is calculated at hb using Ts = 1.1Tm (Tm is the average period) • modified to incorporate random wave breaking model • assumes trapezoidal shape for pressure distribution along front • Caisson is imbedded into the rubble mound • Uplift pressure distribution is assumed triangular
p
Note: hs includes wave setu
Elevation to which wave pressure is exerted:
( ) designHcos175.0 β+=∗η β = direction of waves with respect to
breakwater normal (for waves approaching normal to breakwater, β = 0)
Pressure on Front of Vertical Wall:
( )( ) design2
11 Hcoscos15.0p γβα+αβ+= ∗
≤∗η
>∗η
∗η
−=
c
c1c
2
hfor 0
hfor ph1p
133 pp α= Buoyancy and Uplift Pressure ( ) design31u Hcos15.0p γααβ+=
(α1) Effect of wave period on pressure distribution
2
1 2sinh25.06.0
+=α
s
s
khkh
minimum = 0.6 (deep water), maximum = 1.1 (shallow)
(α*) Increase in wave pressure due to shallow mound
design
2sinde
b
b2 H
d2or d
Hh3
dh of minimum
−
=α=α∗
(α3) Linear pressure distribution
−
−−=α
ss
cw3 khcosh
11h
hh1
Decrease in Pressure from Hydrostatic under Wave Trough
−<γ−<≤−γ
=designdesign
design
H5.0z:H5.00zH5.0:z
p
Tanimoto etal. (1976) added structure type modification factors (λ1, λ 2, λ 3) which are one for a
vertical wall (λ1 = λ = λ = 1) 2 3
( ) design1Hcos175.0 λβ+=∗η
( )( ) design2
2111 Hcoscos15.0p γβαλ+αλβ+= ∗
≤∗η
>∗η
∗η
−=
c
c1c
2
hfor 0
hfor ph1p
( ) design313u Hcos15.0p γααλβ+=
Takahashi, Tanimoto and Shimosako (1994) Table VI-5-54 modified the shallow mound coefficient (α*) for head-on breaking waves
Takahashi, Tanimoto and Shimosaka (1994) Table VI-5-54 modified the shallow mound coefficient (α*) for head-on breaking waves
Tanimoto and Kimura (1985) Table VI-5-56 updated the λ3 modification factor to account for inclined walls
Takahashi and Hosoyamada (1994) Table VI-5-57 developed corrections to p1, p2, p3 to account for a structure with a sloped portion beginning just below the waterline
Takahashi, Tanimoto and Shimosako (1990) Table VI-5-58 updated the structure type modification factors (λ1, λ 2, λ 3) to account for a vertical wall structure protected by a rubble mound
Tanimoto, Takahashi and Kitatani (1981) and Takahashi, Shimosako and Sakaki (1991) Table
VI-5-59 updated the structure type modification factors (λ1, λ 2, λ 3) to account for caissons with vertical slit fronts faces and open wave chambers
Force and Moment Calculations Basic Calculation (refer to Sainflou), forces and moments are per unit length of structure
B
FG = FB - W p1
WFH hw hs
dh FB
p2
pu
FU bu
For Wave Crest ( )[ ]BHhhF oswcG δ++γ−γ=
( ) ( )( )( ) 2
sw21
ossw221
os221
osw21
H
hHhhp
HhpHhF
γ−δ++γ+=
δ+++δ+γ=
BpF u21
U = where pu = p2 for Sainflou (conservative) and γc is the specific weight of the caisson Overturning moments is then:
( ) ( )( )( ) 3
sw612
ossw261
3sw6
12os26
12ossw6
1
hHH
hHhhp
hHhpHhh
dFM
γ−δ++γ+=
γ−δ+++δ++γ=
=
and
( ) 2
u31
32
uU BpBFM ==
Similar calculations can be made for the pressure distribution under the wave trough Table VI-5-55, p VI-5-141 has the formulae for the Goda equations which include biasing and uncertainty corrections
EM 1110-2-1100 (Part VI)Proposed Publishing Date: 30 Apr 03
Fundamentals of Design VI-5-141
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Table VI-5-55Resulting Wave Induced Forces and Moments, and Related Uncertainties and Bias When Calculated From Wave LoadEquations by Goda and Takahashi
Minikin's Method (1950) • 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 = - ½ H • generally overestimates pressures (15-18×)
Dynamic Pressure: ( ) hbmax LHhd1d101p +γ=
2
bmaxm H
z21pp
−= , 2Hz ≤
Hydrostatic Pressure: ( )b2
1d Hdp +γ=
pmax = max dynamic pressure at SWL pm = dynamic pressure z = vertical distance from SWL h = the depth of water a distance L from the
wall, h = d + Ldm Ld = the wavelength at depth d Lh = the wavelength at depth h Hb = breaker height
combined
m 1
Force under the dynamic distribution (acting at the SWL): bmax3
1m HpF =
Overturning Moment from the dynamic force: dHpM bmax31
m =
adding the hydrostatic force and moments to these gives: total force: ( )2b2
121
bmax31
total HdHpF +γ+=
total overturningmoment: ( )3b21
61
bmax31
total HddHpM +γ+=
Minikin's Method for a wall on a low rubble mound Dynamic Pressure
h
bmax L
Hhd1d101p
+γ=
2
bmaxm H
z21pp
−= , b2
1 Hz ≤
Static Pressure
<γ
<≤
−γ
=0z zH
Hz0 H
z21Hp
b21
b21
b21
s
ps pmax
0.5Hz
0.5H
d h
Minikin's Method for a wall with top below the design breaker crest using reduction factors (rm and a) from plots below
Dynamic force component: ( )bmax3
1mm Hpr'F =
Dynamic component of overturning moment
( )( )[ ]( )[ ]aadrHp
r1addHp'M
mbmax31
mbmax31
m
−+=
−+−=
Hb b'
½
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
b'/Hb
rm
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
b'/Hb
2a/Hb
Caisson Width and Mound Dimensions Guidance
Caisson width: General guidance: B = 1.7 to 2.6 × H1/3 for reflective to breaking waves Wave transmission is of primary concern.
hc
h
d
~ 5m
key stone(scour protection)
Caisson Crest Elevation: General guide: hc = 0.5 to 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.
Fh
U
W
B
β
dh
bu
Slip circles
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
( ) hFUBWFS −−µ=.. ,
where µ is the coefficient of friction between the upright section and the rubble mound (or the bottom). For a new installation µ ≈ 0.5. After the initial shakedown, µ ≈ 0.6.
(2) For overturning, moments are calculated about the lee-side toe
( ) puW MMMFS −=..
for a symmetric section with no eccentricity:
( )BWMW −β= 5.0
UUbM uU β== 3/2
hhp FdM =
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
φ
B
Soft Soil - higher mound willdistribute the load more
sand
clay
sand
Sand Key
φ
B
Soft Soil - replace clay withsand key
clay
D
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.
φ
α
φ−αφ+α
W-B-U
Fh
B
e te
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 Be 61≤ :
BW
Bep
BW
Bep
−=
+=
61, 61 21
For Be 61> : 0,
32
21 == ptWp
e
; where eBte −=2
p1p2
Load on soil
qa = allowable load( )212
1 ppqa +≥
B'Soil cannot support tension
Correction since soil cannot support tension
p1
Summary of Design Procedure
1. Specify design conditions: design wave, water levels, etc.
2. Set rubble mound dimensions
3. Compute external wave loading
4. Perform stability analysis
a. Sliding stability b. Overturning stability c. Slip stability: local, translational and global
5. Perform a bearing capacity analysis
a. At mound level (i.e. at the toe of the caisson) b. At the foundation level
6. Determine caisson stability under towing conditions and during the installation phase
7. Stress configurations
a. During towing and installation i. Side ii. Bottom iii. Internal panel
b. Post installation i. Side ii. Bottom iii. Internal panel
8. Structural Detailing
Recommended