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
--------------------------------------------------------------------------------------------------------------------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, p d 
at the bottom (z = -h)  pd  
H
cosh kh
H cosh k h  z 
cosh kh
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:
p
 cosh k h  z o  sinh k h  z o 
  zo  H 

w
sinh kh 
 cosh kh
at free surface (zo = 0), p = 0
at bottom (zo = -h), p   w h  H / cosh kh
Pressure distribution when wave trough arrives:
p
 cosh k h  zo  sinh k h  zo 
  zo  H 

w
sinh kh 
 cosh kh
at free surface (zo = 0), p = 0
at bottom (zo = -h), p   w h  H / cosh kh
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
crest
trough
z
z
h
Pressure distribution under standing waves based on Sainflou's theory
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
H 2
ho 
coth kh
L
Simplified formula assumes a linear pressure distribution below the water level
(conservative assumption, see diagram)
Increase in pressure due to the standing wave:
1    H 
p1 
2  cosh kh 
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)
h  H  ho h  p1   h 2
Re 
2
2
2
h  H  ho  h  p1   h 3
Me 
6
6
(2) wave trough (subscript i)
h 2 h  ho  H h  p1 
Ri 

2
2
2
3
h h  ho  H  h  p1 
Me 

6
6
Breaking Waves
Waves breaking directly against the structure face sometimes exert high, shortduration, 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
pb  1.5H
d 

Total horizontal force  F  1.88  1.5 s  H 2
H

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
2
p m  p max 1  2 z H 
p max  101d 1  d h  H L
z H 2
Static Pressure
0.5H 1  2 z H  0  z  H 2
ps  
0.5H
z0

pmax
ps
0.5H
z
0.5H
h
d
Minikin's Formula
USACE EM-1110-2-2904 (1986) recommended equations
Peak impact pressure: Pm  2.5H
Total Force (Ft)
If H/Lo < 0.045
Ft  3H  P1 (Sainflou) , tons/ft
If H/Lo > 0.045
Ft  4H , tons/ft
Moment (M)
If H/Lo < 0.045
M  8 H 2 d , ft-tons/ft, (d as in Minikin)
If H/Lo > 0.045
M  12.5 H 3 , 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:
  0.751  cos H max
 = direction of waves with respect to breakwater normal
(for waves approaching normal to breakwater,  = 0)
Pressure on Front of Vertical Wall
p1  0.51  cos 1   2 cos 2 H max

h 
1  c  p
p 2      1

0

for   hc
for   hc
p3   3 p1
Effect of wave period on pressure distribution
2
 2khs 

1  0.6  0.5
sinh
2
kh
s 

minimum = 0.6 (deep water), maximum = 1.1 (shallow)
Increase in wave pressure due to shallow mound
h  d  H max 
2d
 2  minimum of b

 or
3hb  d 
H max
Linear pressure distribution
2

hw  hc 
1
1 

hs  cosh khs 
hb = water depth at 5Hs seaward of breakwater
3  1 
Buoyancy and Uplift Pressure
pu  0.51  cos 1 3 H max
(Japanese found that pu = p3 was too conservative)
Decrease in Pressure from Hydrostatic under Wave Trough
z
: 0.5H max  z  0

p
: z  0.5H max
 0.5H max
Example
(1) shallow mound
6.5m
H1/3 = 1.0m
Hmax = 1.8m
T1/3 = 4 sec
Lo = 25 m
=1
4m
4.5m
6m
from dispersion relation  L = 20.9 m, k = 0.301 m-1 at h = 4 m
Assume non-breaking waves:
Miche-Rundgren
1.8 2
ho 
coth 0.301  4  0.58 m
20.9

11 
1 1.8
p1 
 0.99 t/m 2


2  cosh 0.301  4
Re 
Goda
4  1.8  0.581 4  0.99  1 4 2
2
2
 7.9 t/m
  0.751  cos 01.8  2.7 m
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  0.272  6 
1  0.6  0.5
  0.63
 sinh 2  0.272  6 
2
6  4  1.8 
24
 4.4
   0.0225 or
3 6  4 
1.8
2
 2  minimum of
2 = 0.0225

7  2.5 
1
1 
  0.53
3  1 
6  cosh 0.272  6 
p1  0.51  10.63  0.0225 111.8  1.2 t/m 2
h 

 2.5 
2
p2  1  c  p1  1 
1.2  0.09 t/m
 2.7 
  
p3  0.53 1.2  0.6 t/m 2
R  12 hc  p1  p2   12  p1  p3 hw  hc 
 12 2.5  1.2  0.1  12 1.2  0.67  2.5  5.7 t/m
Horizontal forces:
Miche-Rundgren
Goda
7.9 t/m
5.7 t/m
(2) no mound
H1/3 = 1.0m
Hmax = 1.8m
T1/3 = 4 sec
Lo = 25 m
=1
6.5m
4m
4.5m
Miche-Rundgren
No change  Re = 7.9 t/m
Goda
  2.7 m
k = 0.301 m-1 at hs = 4 m, hc = 2.5 m < * , assume hb = h = 4 m,
hw = 7 m
 2  0.301 4 
1  0.6  0.5
  0. 7
 sinh 2  0.301 4 
2
4  4  1.8 
24
 2  minimum of
 4.4
   0 or
3 4  4 
1.8
2
2 = 0
3  1 

7  2.5 
1
1 
  0.49
4  cosh 0.301 4 
p1  0.51  10.7  0 11.8  1.3 t/m 2
h 

 2.5 
2
p2  1  c  p1  1 
1.3  0.09 t/m


2
.
7




2
p3  0.49 1.3  0.6 t/m
R  12 2.5  1.3  0.09  12 1.3  0.67  2.5  5.9 t/m
Horizontal forces:
Miche-Rundgren
Goda
7.9 t/m
5.9 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.
hc
d
h
~ 5m
key stone
(scour protection)
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.

W
Fh
Slip circles
dh
B
U
bu
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 
S.F .  W  B  U  Fh ,
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
S .F .  M W  M u  M p
for a symmetric section with no eccentricity:
M W  0.5W  B 
M U  buU  2 / 3U
M p  d h Fh
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
B
B
Soft Soil - higher mound will
distribute the load more
Soft Soil - replace clay with
sand key


sand
Sand Key
D
clay
sand
clay
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.
e
te
Fh

W-B-U



B
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 e  16 B :
 6e  W
p1  1   ,
BB

For e  16 B :
p1 
2W
,
3 te
p 2  0 ; where t e 
B
e
2
Soil cannot
support tension
Load on soil
p2
 6e  W
p 2  1  
BB

B'
p1
qa = allowable load
qa 
1
2
 p1  p2 
Correction since soil
cannot support tension
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)
p1
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