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