2-10-00, Environmental Factors in the Coastal Region, Waves

08 Rubble Mound Structure 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)
Topics
Rubble Mound Breakwater Design
Layout Options for Rubble Mound Breakwaters and Jetties
General Description
Design Wave
Water Levels and Datums
Design Parameters
Design Concept/ Procedure
Structure Elevation, Run-up and Overtopping
Crest/Crown Width
Armor Unit Size and Stability
Underlayer Design
Bedding and Filter Design
Toe Structures
Low Crested Breakwaters
--------------------------------------------------------------------------------------------------------------------Rubble Mound Breakwater Design
Layout Options for Rubble Mound Breakwaters and Jetties
1. Attached or Detached.
a. Jetties Æ usually attached to stabilize an inlet or eliminate channel shoaling.
b. Breakwaters Æ attached or detached.
i. If the harbor is on the open coastline, predominant wave crests approach
parallel to the coastline, a detached offshore breakwater might be the best
option.
ii. An attached breakwater extended from a natural headland could be used to
protect a harbor located in a cove.
iii. A system of attached and detached breakwaters may be used.
iv. An advantage of attached breakwaters is ease of access for construction,
operation, and maintenance; however, one disadvantage may be a negative
impact on water quality due to effects on natural circulation.
2. Overtopped or Non-overtopped.
a. Overtopped:
crown elevation allows larger waves to wash across the crest Æ
wave heights on the protected side are larger than for a non-overtopped structure.
b. Non-overtopped: elevation precludes any significant amount of wave energy from
coming across the crest.
c. Non-overtopped breakwaters or jetties
i. Greater degree of wave protection
ii. More costly to build because of the increased volume of materials required.
d. Crest elevation determines the amount of wave overtopping expected
i. Hydraulic model investigation to find the magnitude of transmitted wave
heights
ii. Optimum crest elevation Æ minimum height that provides the needed
protection.
e. Overtopped breakwater
i. Crest elevation may be set by the design wave height that can be expected
during the period the harbor will be used (especially true in colder climates).
ii. Overtopped structures are more difficult to design because their stability
response is strongly affected by small changes in the still water level.
3. Submerged Breakwater
a. Example: A detached breakwater constructed parallel to the coastline and designed to
dissipate sufficient wave energy to eliminate or reduce shoreline erosion.
b. Advantages:
i. Less expensive to build.
ii. May be aesthetically more pleasing (do not encroach on any scenic view)
c. Disadvantages:
i. Significantly less wave protection is provided
ii. Monitoring the structure's condition is more difficult.
iii. Navigation hazards may be created.
4. Single or Double.
a. Jetties: Double parallel jetties will normally be required to direct tidal currents to
keep the channel scoured to a suitable depth. However, there may be instances where
coastline geometry is such that a single updrift jetty will provide a significant amount
of stabilization. One disadvantage of single jetties is the tendency of the channel to
migrate toward the structure.
b. Breakwaters: Choice of single or double breakwaters will depend on such factors as
coastline geometry and predominant wave direction. Typically, a harbor positioned in
a cove will be protected by double breakwaters extended seaward and arced toward
each other with a navigation opening between the breakwater heads. For a harbor
constructed on the open coastline a single offshore breakwater with appropriate
navigation openings might be the more advantageous.
5. Weir Section. Some jetties are constructed with low shoreward ends that act as weirs.
Water and sediment can be transported over this portion of the structure for part or all of
a normal tidal cycle. The weir section, generally less than 500 feet long, acts as a
breakwater and provides a semi-protected area for dredging of the deposition basin when
it has filled. The basin is dredged to store some estimated quantity of sand moving into
the basin during a given time period. A hydraulic dredge working in the semi-protected
waters can bypass sand to the downdrift beach.
6. Deflector Vanes. In many instances where jetties are used to help maintain a navigation
channel, currents will tend to propagate along the ocean-side of the jetty and deposit their
sediment load in the mouth of the channel. Deflector vanes can be incorporated into the
jetty design to aid in turning the currents and thus help to keep the sediments away from
the mouth of the channel. Position, length, and orientation of the vanes can be optimized
in a model investigation.
7. Arrowhead Breakwaters. When a breakwater is constructed parallel to the coastline
navigation conditions at the navigation opening may be enhanced by the addition of
arrowhead breakwaters. Prototype experience with such structures however has shown
them to be of questionable benefit in some cases.
General Description
Multi-layer design. Typical design has at least three major layers:
1. Outer layer called the armor layer (largest units, stone or specially shaped concrete
armor units)
2. One or more stone underlayers
3. Core or base layer of quarry-run stone, sand, or slag (bedding or filter layer below)
•
•
Designed for non-breaking or breaking waves, depending on the positioning of the
breakwater and severity of anticipated wave action during life.
Armor layer may need to be specially shaped concrete armor units in order to provide
economic construction of a stable breakwater.
Design Wave
1. Usually H1/3, but may be H1/10 to reduce repair costs (Pacific NW) (USACE
recommends H1/10)
2. The depth limited breaking wave should be calculated and compared with the
unbroken storm wave height, and the lesser of the two chosen as the design wave.
(Breaking occurs in water in front of structure)
3. Use Hb/hb ~ 0.6 to 1.1
4. For variable water depth, design in segments
Jetties with Weir section and Deflector Vanes
Arrowhead Breakwaters
Breaking Wave Considerations (SPM, Chapter 7)
The design breaker height (Hb) depends on the depth of water some distance seaward
from the structure toe where the wave first begins to break. This depth varies with tidal
stage.
Therefore, the design breaker height depends on the critical design depth at the structure
toe, the slope on which the structure is built, incident wave steepness, and the distance
traveled by the wave during breaking.
Assume that the design wave plunges on the structure Æ
Hb =
ds
γ − mτ p
ds = depth at structure toe, γ = hb/Hb, m = nearshore slope,
τp = dimensionless plunge distance,
= breaker travel distance (xp) / breaker height (Hb)
If the maximum design depth at the structure toe and the incident wave period are known,
the design breaker height can be determined from the chart below (Figure 7-4 of the
SPM, 1984). Calculate ds/(gT2), locate the nearshore slope and determine Hb/ds.
Water Levels and Datums. Both maximum and minimum water levels are needed for the
designing of breakwaters and jetties. Water levels can be affected by storm surges,
seiches, river discharges, natural lake fluctuations, reservoir storage limits, and ocean
tides.
• High-water levels are used to estimate maximum depth-limited breaking wave heights
and to determine crown elevations.
• Low-water levels are generally needed for toe design.
a. Tide Predictions, The National Ocean Service (NOS) publishes tide height predictions
and tide ranges. Figure 2-l shows spring tide ranges for the continental United States.
Published tide predictions are sufficient for most project designs; however, prototype
observations may be required in some instances.
b. Datum Planes. Structural features should be referred to appropriate low-water datum
planes. The relationship of low-water datum to the National Geodetic Vertical Datum
(NGVD) will be needed for vertical control of construction. The low-water datum for the
Atlantic and Gulf Coasts is being converted to mean lower low water (MLLW). Until the
conversion is complete, the use of mean low water (MLW) for the Atlantic and Gulf
Coast low water datum (GCLWD) is acceptable. Other low-water datums are as follows:
• Pacific Coast: Mean lower low water (MLLW)
• Great Lakes: International Great Lakes Datum (IGLD)
• Rivers: River, low-water datum planes (local)
• Reservoirs: Recreation pool levels
Design Parameters
h
hc
R
ht
B
Bt
α
αb
t
W
•
•
•
water depth of structure relative to design high water (DHW)
breakwater crest relative to DHW
freeboard, peak crown elevation above DHW
depth of structure toe relative to still water level (SWL)
crest width
toe apron width
front slope (seaside)
back slope (lee)
thickness of layers
armor unit weight
DHW varies Æ may be MHHW, storm surge, etc.
SWL may be MSL, MLLW, etc.
Wave setup is generally neglected in determining DHW
B
crown/cap
crest
armor layer, W
R
DHW
hc
SWL
α
ht
h
first underlayer
αb
second underlayer
t
toe
core/base
Bt
bedding and/or filter layer
Design Concept/ Procedure
1. Specify Design Condition Æ design wave (H1/3, Hmax, To, Lo, depth, water elevation,
overtopping, breaking, purpose of structure, etc.)
2. Set breakwater dimensions Æ h, hc, R, ht, B, α, αb
3. Determine armor unit size/ type and underlayer requirements
4. Develop toe structure and filter or bedding layer
5. Analyze foundation settlement, bearing capacity and stability
6. Adjust parameters and repeat as necessary
Structure Elevation, Run-up and Overtopping
Wave breaking on a slope causes up-rush and down-rush. The maximum and minimum
vertical elevation of the water surface from SWL is called run-up (Ru) and run-down (Rd).
Non-dimensionalize with respect to wave height Æ Ru/H and Rd/H.
•
•
•
•
•
Overtopping occurs if the freeboard (R) is less than the set-up + Ru.
Generally neglect wave setup for sloped structures
Freeboard may be zero if overtopping is allowed. Freeboard may also be set to
achieve a given allowed overtopping.
Run-up and run-down are functions of ξ, permeability, porosity and surface
roughness of the slope.
Effects of Permeability - Flow fields induced in permeable structures by wave action
result in reduced run-up and run-down, but increased destabilizing forces (see
diagram).
SWL
Run-up = Ru
Run-down = Rd
Internal water level
Run-up
Run-down
SWL
SWL
Run-up may be determined by surf similarity parameter (ξm) and core permeability
(Abbot and Price, 1994)
ξ m = tan α
H s Lm
, where Lm is the wave length for the modal period, Tm (deep
water assumed) Æ Lm =
gTm2
2π
van der Meer (1988)
Ru H S = aξ m for ξm < 1.5
Ru H S = bξ cm for ξm > 1.5
for permeable structures (P > 0.4) run-up is limited to Ru H S = d
Ru exceedence
probability (%)
0.1
2
5
10
50
a
1.12
0.96
0.86
0.77
0.47
b
1.34
1.17
1.05
0.94
0.60
c
0.55
0.46
0.44
0.42
0.34
d
2.58
1.97
1.68
1.45
0.82
Reduction factors are applied to the Run-up formula to account for roughness, oblique
waters and overtopping
R uR H S = (R u H S )product(γ i )
Reduction factor (γ)
Smooth impermeable (including smooth
concrete and asphalt)
1 layer of stone rubble on impermeable base
Gravel
Rock rip-rap with thickness > 2D50
1.0
0.8
0.7
0.5-0.6
Run-down is typically 1/3 to ½ of the run-up and may be used to determine the minimum
downward extension of the main armor and a possible upper level for introducing a berm
with reduced armor size.
Designing to an Allowable Overtopping - Overtopping depends on relative freeboard,
R/Hs, wave period, wave steepness, permeability, porosity, and surface roughness.
Usually overtopping of a rubble structure such as a breakwater or jetty can be tolerated
only if it does not cause damaging waves behind the structure.
R may be determined based on acceptable Q for the design
Owen (1980, 1982)
Rm* =
R
Hs
H
sm
, where s m = s
2π
Lm
mean overtopping discharge ( Q in m3/s/m or ft3/s/ft):
(
Q ( gH sTm ) = a exp − b Rm* γ
)
use run-up reduction factors, γ, above
for straight smooth slopes (no berms), non-depth limited waves
Slope
a
b
1:1
0.008
20
1:1.5
0.010
20
1:2
0.013
22
1:3
0.016
32
1:4
0.019
47
Typical values of acceptable overtopping:
Harbor protection
Q ≤ 0.5 m 3 /s/m
Vehicles on breakwater
Q ≤ 0.01 m 3 /s/m
Pedestrians on breakwater
Q ≤ 0.05 m 3 /s/m
Concrete Caps - considered for strengthening the crest, increasing crest height, providing
access along crest for construction or maintenance. Evaluate by calculating cost
of cap vs. cost of increasing breakwater dimensions to increase overtopping
stability
Crest/ Crown Width
Depends on degree of allowed overtopping. Not critical if no overtopping is
allowed. Minimum of 3 armor units or 3 meters for low degree of overtopping.
1/ 3
W 
B = 3k ∆   , where W = median weight of armor unit, γa = unit weight
 γa 
of armor, k∆ = layer thickness coefficient (see Table 2)
Wave Transmission
Wave transmission behind rubble mound breakwaters is caused by wave
regeneration due to overtopping and wave penetration through voids in the
breakwater. Affected by:
•
•
•
•
•
•
Crest elevation
Crest width
seaside and lee-side face slopes
Rubble size
Breakwater porosity
Wave height, wave length and water depth
Transmission coefficient (KT)
KT = H T H i
HT = transmitted wave height
Hi = incident wave height
Given an acceptable lee-side wave height, the crest elevation (hc) and width (B)
can be determined by using the diagram below (note: the diagram is based on
experiments by N. Tanaka, 1976, on a symmetric breakwater with 1:2 seaside and
lee-side slopes.)
Armor Unit Size and Stability
Considerations:
• Slope: flatter slope Æ smaller armor unit weight but more material req'd
Seaside Armor Slope - 1:1.15 to 1:2
Harbor-side (leeside) Slope
Minor overtopping/ moderate wave action - 1:1.25 to 1:1.5
Moderate overtopping/ large waves - 1:1.33 to 1:1.5
* harbor-side slopes are steeper, subject to landslide type failure
• Trunk vs. head (end of breakwater) Æ head is exposed to more concentrated wave
attack Æ want flatter slopes at head (or larger armor units)
• Overtopping Æ less return flow/ action on seaward side but more on leeward
• Layer dimensions Æ thicker layers give more reserve stability if damaged
• Special placement Æ reduces size req'ts, gen. limited to concrete armor units
• Concrete armor units (may be required for more extreme wave conditions)
Advantage - increase stability, allow steeper slopes (less mat'l req'd), lighter wt.
Disadvantage - breakage results in lost stability and more rapid deterioration.
Hydraulic studies have indicated that up to 15 percent random breakage of doles
armor units may be experienced before stability is threatened, and up to five
broken units in a cluster can be tolerated.
Considerations
1. Availability of casting forms
2. Concrete quality
3. Use of reinforcing (req'd if > 10-20 t)
4. Placement
5. Construction equipment availability
**When using special armor units, underlayers are sized based on stone armor unit weight
Hudson's Formula for Determining Armor Unit Weight
Hudson, R. Y. (1959) “Laboratory Investigations of Rubble-Mound Breakwaters,” Proceedings of
the American Society of Civil Engineers, American Society of Civil Engineers, Waterways and
Harbors Division, Vol. 85, NO. WW3, Paper No. 2171.
Formula is based on a balance of forces to ensure each armor unit maintains
stability under the forces exerted by a given wave attack.
W = median weight of armor unit
D = diameter of armor unit
γa = unit weight of armor
H = design wave height (note affect of cubic power on armor wt.)
KD = stability coefficient (Table 1 below, from SPM)
(gen. SG = 2.65 for quarry stone, 2.4 for concrete)
SG = γa/γw = ρa/ρw
α = slope angle from the horizontal
Neglecting inertia forces, balance weight of each armor unit (FG) with
drag and lift forces induced by the waves (FD, FL)
FG
g (ρ a − ρ w )D
1
g (SG − 1)D (SG − 1)D
∝
→
=
=
2
2
FD + FL
H
Ns
ρ wv
gH
(
H  γa 
Ns =
 
(SG − 1)  W 
1/ 3
)
γaH 3
Æ W=
(SG − 1)3 N s3
Experiments related the stability number to the face slope and armor unit
shape
1/ 3
N s = (K D cot α )
Combining gives Hudson's equation for minimum required armor unit
weight
W=
γaH 3
K D (SG − 1) cot α
3
Restrictions on Hudson equation:
1. KD not to exceed Table 1 (from SPM) values
2. Crest height prevents minor wave overtopping
3. Uniform armor units Æ 0.75W to 1.25W
4. Uniform slope Æ 1:1.5 to 1:3
5. 120 pcf ≤ γa ≤ 180 pcf (1.9 t/m3 ≤ γa ≤ 2.9 t/m3)
Not considered in Hudson equation
• incident wave period
• type of breaking (spilling, plunging, surging)
• allowable damage level (assumes no damage)
• duration of storm (i.e. number of waves)
• structure permeability
Bottom elevation of Armor Layer (How deep should armor extend?)
Armor units in the cover layer should be extended downslope to an elevation
below minimum still water level equal to 1.5H when the structure is in a depth
greater than 1.5H. If the structure is in a depth of less than 1.5H, armor units
should be extended to the bottom. Toe conditions at the interface of the
breakwater slope and sea bottom are a critical stability area and should be
thoroughly evaluated in the design.
The weight of armor units in the secondary cover layer, between -1.5H and -2H,
should be approximately equal to one-half the weight of armor units in the
primary cover layer (W/2). Below -2H. the weight requirements can be reduced to
approximately W/l5 . When the structure is located in shallow water, where the
waves break, armor units in the primary cover layer should be extended down the
entire slope.
The above-mentioned ratios between the weights of armor units in the primary
and secondary cover layers are applicable only when stone units are used in the
entire cover layer for the same slope. When pre-cast concrete units are used in the
primary cover layer, the weight of stone in the other layers should be based on the
equivalent weight of stone armor.
For example:
tetrapods armor design
conditions: 20 foot non-breaking wave attack on a structure trunk
γa = 150 lbf/ft3 for tetrapods Æ SG = 150/64 = 2.34
slope = lV:2H
KD = 8.0 for tetrapod armor
KD = 4.0 for rough angular stone
(
150)20 3
for tetrapod: W =
=
= 15.6 tons
3
K D (SG − 1) cot α 8(2.34 − 1)2
(165)20 3 = 21 tons
for stone armor: W =
4(2.58 − 1)2
γaH 3
The secondary cover layer from -1.5H to the bottom should be as thick as
or thicker than the primary cover layer and sized for W = 21 tons.
Armor layer thickness (t) use to calculate size of layer
W
t = nk ∆ 
 γa



1/ 3
, where n = number of layers
Number of units per surface area A,
2/3
P  γ a 

Na
= nk ∆ 1 −
 
A
 100  W 
Table 1, Stability Coefficient, KD (breaking occurs before the wave reaches the structure)
Structure Trunk
(b)
KD
Non-breaking
wave
Structure Head
KD
Breaking Non-breaking
Wave
wave
Slope
Armor units
n(a)
Placement
Breaking
Wave
Quarry stone
Smooth rounded
Smooth rounded
Rough angular
2
>3
1
Random
Random
Random (d)
1.2
1.6
(d)
2.4
3.2
2.9
1.2
1.4
(d)
1.9
2.3
2.3
1.5 to 3.0
(c)
(c)
Rough angular
2
Random
2.0
4.0
1.9
1.6
1.3
3.2
2.8
2.3
1.5
2.0
3.0
Rough angular
Rough angular
Parallelepiped (f)
>3
2
2
Special (e)
Special (e)
Random
2.2
5.8
7.0 - 20.0
4.5
7.0
8.5 - 24.0
2.1
5.3
--
4.2
6.4
--
(c)
(c)
(c)
Tetrapod and
Quadripod
2
Random
7.0
8.0
5.0
4.5
3.5
6.0
5.5
4.0
1.5
2.0
3.0
Tribar
2
Random
9.0
10.0
8.3
7.8
6.0
9.0
8.5
6.5
1.5
2.0
3.0
Dolos
2
Random
15.0 (g)
31.0 (g)
8.0
7.0
16.0
14.0
2.0 (h)
3.0
Modified Cube
2
Random
6.5
7.5
--
5.0
(c)
Hexapod
2
Random
8.0
9.5
5.0
7.0
(c)
Toskanes
2
Random
11.0
22.0
--
--
(c)
Tribar
1
Uniform
12.0
15.0
7.5
9.5
(c)
Quarrystone (KRR)
Graded angular
--
Random
2.2
2.5
--
--
--
cot α
(a)
n is the number of wits comprising the thickness of the armor layer.
Applicable to slopes ranging from 1 on 1.5 to 1 on 5.
(c)
Until more information is available on the variation of KD value with slope, the use of KD should be limited to
slopes ranging from 1 on 1.5 to 1 on 3. Some armor units tested on a structure head indicate a KD slope
dependence.
(d)
The use of a single layer of quarry stone armor units subject to breaking waves is not recommended, and only
under special conditions for non-breaking waves. When it is used, the stone should be carefully placed.
(e)
Special placement with long axis of stone placed perpendicular to structure face.
(f)
Long slab-like stone with the long dimension about three times its shortest dimension.
(g)
Refers to no-damage criteria (~5 percent displacement, rocking, etc.); if no rocking (<2 percent) is desired, reduce
KD 50 percent.
(h)
Stability of dolos on slopes steeper than 1 on 2 should be substantiated by site-specific model tests.
(b)
NOTE : Breaking wave stability coefficients for stone and dolos were developed using a 1V:10H foreslope.
Table 2, Layer Thickness Coefficient and Porosity
Type of
Placing
Armor Unit
n (1)
Technique
Smooth stone
2
Random
Rough stone
2
Random
Tetrapod
2
Random
Quadripod
2
Random
Hexapod
2
Random
Modified Cube
2
Random
Tribar
2
Random
Tribar
1
Uniform
Toskane
2
Random
Dolos
2
Random
(1)
Number of layers of armor units
Layer Thickness
Coefficient, k∆
1.00
1.00
1.04
0.95
1.15
1.10
1.02
1.13
1.03
0.94
Porosity
Percent
38
37
50
49
47
47
54
47
52
56
Table 3, H/HD=0 as a function of cover layer damage
Damage (D), Percent
Unit
0-5
5 - 10
10 - 15
15 - 20
20 - 30
30 - 40
40 - 50
Quarry stone (smooth)
1.00
1.08
1.14
1.20
1.29
1.41
1.54
Quarry stone (rough)
1.00
1.08
1.19
1.27
1.37
1.47
1.56 (b)
Tetrapods
and
1.00
1.09
1.17 (c)
1.24 (c)
1.32 (c)
1.41 (c)
1.50 (c)
Quadripods
Tribar
1.00
1.11
1.25 (c)
1.36 (c)
1.50 (c)
1.59 (c)
1.64 (c)
(c)
(c)
(c)
(c)
Dolos
1.00
1.10
1.14
1.17
1.20
1.24
1.27 (c)
(a)
Breakwater trunk, n = 2, random-placed armor units, non-breaking waves, and minor overtopping
conditions.
(b)
Values in italics are interpolated or extrapolated.
(c)
CAUTION: Tests did not include possible effects of unit breakage. Waves exceeding the design wave
height conditions by more than 10 percent may result in considerably more damage than the values
tabulated.
Modified Allowable Wave Height Based on Damage
The concept of designing a rubble-mound breakwater for zero damage is
unrealistic, because a definite risk always exists for the stability criteria to be
exceeded in the life of the structure. Table 3 shows results of damage tests where
H/HD=0 is a function of the percent damage, D, for various armor units. H is the
wave height corresponding to damage D. HD=0 is the design wave height
corresponding to 0 to 5 percent damage, generally referred to as the no-damage
condition.
Information presented in table 3 may be used to estimate anticipated annual repair
costs, given appropriate long-term wave statistics for the site.
If a certain level of damage is acceptable, the design wave height may be reduced.
Example:
Rough quarry stone breakwater with a design wave height for D =
0% of H = 3 m and acceptable D = 10-15% Æ H/HD=0 = 1.14
If the 10-15% damage at H = 3 m is acceptable, the design wave
height may be reduced to (3 m)/1.14 = 2.6 m.
Underlayers Design
Armor Layer provides structural stability against external forces (waves)
Underlayers prevent core or base material from escaping.
Requirements:
1. Prevent fine material from leaching out.
2. Allow for sufficient porosity to avoid excessive pore pressure build-up
inside the breakwater that could lead to instability or liquefaction in
extreme cases
Note: requirements are in conflict, Eng. must provide an optimum solution
•
Armor layer units are large Æ satisfy (2) above readily
•
Based on spherical shape geometry , core material cannot escape the cover
layer if the diameter ratio of the cover material (D) to the core material (d) is
less than six. (i.e. D/d < 6)
•
For sorted material (e.g. quarry stones) under static (calm) load :
•
Under dynamic load (i.e. wave forces), more restrictive rules apply:
D15
<5
d 85
D50
W
≤ 2.5 to 3 , which gives
≤ 15 to 25 (assumes W ∝ D3)
d 50
wbase
Recommended Sizes (see diagram)
Layer
Primary Armor Layer
First Underlayer
Second Under Layer
Base/ Core Material
Weight Ratio
W/1
W/10
W/200
W/4000
Equivalent Diameter Ratio
1
2.15
2.7
2.7
(Guidance from SPM)
First Underlayer (directly under the armor units)
minimum two stone thick (n = 2)
(1) under layer unit weight = W/10
• if cover layer and first underlayer are both stone
• if the first underlayer is stone and the cover layer is concrete
armor units with KD ≤ 10
(2) under layer unit weight = W/15 when the cover layer is of armor units
with KD > 10
Second Underlayer - n = 2 thick, W/200
Bedding or Filter Layer Design
• Layer between structure and foundation or between cover layer and bank material for
revetments.
• Purpose is to prevent base material from leaching out, prevent pore pressure build-up
in base material and protect from excessive settlement.
•
Should be used except when:
1. Depths > 3Hmax, or
2. Anticipated currents are weak (i.e. cannot move average foundation material),
or
3. Hard, durable foundation material (i.e. bedrock)
•
Cohesive Material: May not need filter layer if foundation is cohesive material. A
layer of quarry stone may be placed as a bedding layer or apron to reduce settlement
or scour.
Coarse Gravel: Foundations of coarse gravel may not require a filter blanket.
Sand: a filter blanket should be provided to prevent waves and currents from
removing sand through the voids of the rubble and thus causing settlement.
When large quarry-stone are placed directly on a sand foundation at depths where
waves and currents act on the bottom (as in the surf zone), the rubble will settle into
the sand until it reaches the depth below which the sand will not be disturbed by the
currents. Large amounts of rubble may be required to allow for the loss of rubble
because of settlement. This, in turn, can provide a stable foundation.
•
•
•
Criteria for granular filter design:
•
•
•
D15
< 4 to 5
d 85
d85 = dia. exceeded by the coarsest 15% of the base mat'l
D15 = dia. exceeded by the coarsest 85% of the filter mat'l
(important in breakwater design)
D
To prevent pore pressure build-up: 15 > 4 to 5 (important for embankment
d15
design)
D
To maintain filter layer internal stability: 60 < 10 (i.e. well sorted material is
D10
D
preferred). Poorly sorted material is not suitable for filters Æ 60 ≥ 20
D10
(internally unstable Æ too much washes out)
To prevent material from leaching out:
General guidelines for stability against wave attack.
Bedding Layer thickness should be:
• 2-3 times the diameter for large stone
• 10 cm for coarse sand
• 20 cm for gravel
•
For foundation stability Bedding Layer thickness should be at least 2 feet
•
Bedding Layer should extend 5 feet horizontally beyond the toe cover stone.
Geotextile filter fabric may be used as a substitute for a bedding layer or filter blanket,
especially for bank protection structures.
When a fabric is used, a protective layer of spalls or crushed rock (7-inch
maximum to 4-inch minimum size) having a recommended minimum thickness of
2 feet should be placed between the fabric and adjacent stone to prevent puncture
of the fabric. Filter criteria should be met between the protective layer of spalls
and adjacent stone.
Advantages: uniform properties and quality.
Disadvantage: susceptible to weathering, tearing, clogging and flopping.
Toe Structures
No rigorous criteria. Design is complicated by interactions between main structure,
hydrodynamic forces and foundation soil. Design is often ad hoc or based on laboratory
testing. Toe failure often leads to major structural failure.
Functions of toe structure:
1. support the armor layer and prevent it from sliding (armor layer is subject to
waves and will tend to assume the equilibrium beach profile shape)
2. protect against scouring at the toe of the structure
3. prevent underlying material from leaching out
4. provide structural stability against circular or slip failure
Toe Structure Functions
EBP
Armor layer support
Protect against scour
Protecting against leaching
weak soil
Prevent circular failure
Toe Structure Stability
For larger ht Æ smaller stone sizes are required (wave action is reduced as depth
increases). From experiments (CIAD report, 1985):


ht
H1/ 3
= f ( N s ) = 0.22 
 for 50% confidence level
h
 (SG − 1)D50 


ht
H1/ 3
= 0.253
 for 90% confidence level
h
 (SG − 1)D50 
 6W
assumes D50 = 
 γπ
•
•
•



1/ 3
, i.e. spherical
Above equations are guidelines.
CEM/SPM recommends berm width at toe be at least 3 armor stones and the height at
least 2.
Actual width and height should be checked by circular stability analysis. (see
discussion below on width design for scour considerations)
Scour Consideration
If no Toe Structure is used, armor layer should extend below maximum scouring
depth and the breakwater slope may require adjustment to reduce scour.
Return flow
and vortex formation
ds
Toe is protected by toe structure
scour hole
Generally:
ds
= f (ξ ) = 0.5 to 1.0 , with 1.0 at ξ ~ 2.7
H
The following design equations are based on preventing or minimizing scour in front of
vertical structures (Tanimoto, K., Yagyu, T., and Goda, Y., 1982)
Toe Apron Width (Bt) - width should be the maximum of Bt = 2H or Bt = 0.4h
(at least 3 stones)
Toe Stone Weight (minimum stone weight)
γ H3
Wmin = 3 a
3
N s (SG − 1)
where Ns = stability number is the maximum of

(1 − K )2 ht 
1− K  h
N s = 1.3 1 / 3  t + 1.8 exp − 1.5

K 1/ 3 H 
 K H

or
Ns = 1.8
where K = a parameter associated with the maximum horizontal velocity
at the edge of the toe apron
K=
2kht
sin 2 kBt
sinh 2kht
Additional Toe Structure Design References:
Headquarters, Department of the Army. (1985) “Design of Coastal Revetments,
Seawalls, and Bulkheads,” Engineer Manual 1110-2-1614, Washington, DC
Hudson, R. Y. (1959) “Laboratory Investigations of Rubble-Mound
Breakwaters,” Proceedings of the American Society of Civil Engineers,
American Society of Civil Engineers, Waterways and Harbors Division, Vol.
85, NO. WW3, Paper No. 2171.
Shore Protection Manual. (1984) 4th cd., 2 Vols., US Army Engineer Waterways
Experiment Station, Coastal Engineering Research Center, US Government
Printing Office, Washington, DC, Chapter 7, pp. 242-249.
Tanimoto, K., Yagyu, T., and Goda, Y. (1982) “Irregular Wave Tests for
Composite Breakwater Foundations,” Proceedings of the 18th Coastal
Engineering Conference, American Society of Civil Engineers, Cape Town,
Republic of South Africa, Vol. III, pp. 2144-2161.
Low Crested Breakwaters (from Sorensen)
Highest part of breakwater is at or below MSL
1. Stabilize beach/ retain sand after nourishment
2. Protect larger structures
3. Cause large storm waves to break and dissipate energy before reaching the beach
Traditional high-crested breakwaters with a multi-layered cross section may not be
appropriate for a structure used to protect a beach or shoreline. Adequate wave protection
may be more economically provided by a low-crested or submerged structure composed
of a homogeneous pile of stone.
** Failure occurs by loss of stones from the crest.
As = area of structure
profile from which stone
has been removed/lost
h
hc
Use a modified stability number
N =
*
s
H 2 / 3 L1 / 3
(SG − 1)W γ 
a

1/ 3
ÆW=
γaH 2L
(SG − 1)3 (N s* )3
L is the wave length at the structure depth and is calculated using peak period (Tp)
for random waves.
AS
, where As = area of damage (see diagram) and
D502
D50 = median stone size of the breakwater
Damage Level (S) is defined as: S =
∴Given S, hc, h Æ determine Ns* from
(
hc
= (2.1 + 0.1S )exp − 0.14 N s*
h
hc = height of the wave crest above the sea floor
h = water depth at the structure
)
Table VI-5-50 (CEM)
Weight and Size Selection Dimensions of Quarrystone1
Weight
Dimension
Weight
Dimension
Weight
Dimension
kg
(lb)
cm
(in.)
kg
(lb)
m
(ft)
mt
(tons)
m
ft
0.01
(0.025)
1.88
(0.74)
45.36
(100)
0.30
(0.97)
0.907
(1)
0.81
(2.64)
0.02
(0.050)
2.36
(0.93)
90.72
(200)
9.38
(1.23)
1.814
(2)
1.02
(3.33)
0.03
(0.75)
2.70
(1.06)
136.08
(300)
0.43
(1.40)
2.722
(3)
1.16
(3.81)
0.04
(0.100)
2.97
(1.17)
181.44
(400)
9.50
(1.54)
3.629
(4)
1.28
(4.19)
0.06
(0.125)
3.20
(1.26)
226.80
(500)
0.51
(1.66)
4.536
(5)
1.38
(4.52)
0.07
(0.150)
3.40
(1.34)
272.16
(600)
0.54
(1.77)
5.443
(6)
1.46
(4.80)
0.08
(0.175)
3.58
(1.41)
317.52
(700)
0.57
(1.86)
6.350
(7)
1.54
(5.05)
0.09
(0.200)
3.73
(1.47)
362.88
(800)
0.60
(1.95)
7.258
(8)
1.61
(5.28)
0.10
(0.225)
3.89
(1.53)
408.24
(900)
0.62
(2.02)
8.165
(9)
1.67
(5.49)
0.11
(0.250)
4.04
(1.59)
453.60
(1000)
0.64
(2.10)
9.072
(10)
1.73
(5.69)
0.23
(0.5)
5.08
(2.00)
498.96
(1100)
0.66
(2.16)
9.979
(11)
1.79
(5.88)
0.45
(1.0)
6.40
(2.52)
544.32
(1200)
0.68
(2.23)
10.866
(12)
1.84
(6.05)
0.68
(1.5)
7.32
(2.88)
589.68
(1300)
0.70
(2.27)
11.793
(13)
1.89
(6.21)
0.91
(2.0)
8.05
(3.17)
635.04
(1400)
0.72
(2.35)
12.700
(14)
1.94
(6.37)
1.13
(2.5)
8.66
(3.41)
680.40
(1500)
0.73
(2.40)
13.608
(15)
1.98
(6.51)
1.36
(3.0)
9.22
(3.63)
725.76
(1600)
0.75
(2.45)
14.515
(16)
2.03
(6.66)
1.59
(3.5)
9.70
(3.82)
771.12
(1700)
0.76
(2.50)
15.422
(17)
2.07
(6.79)
1.81
(4.0)
10.13
(3.99)
816.48
(1800)
0.78
(2.55)
16.330
(18)
2.11
(6.92)
2.04
(4.5)
10.54
(4.15)
861.84
(1900)
0.80
(2.60)
17.237
(19)
2.15
(7.05)
2.27
(5)
10.92
(4.30)
907.20
(2000)
0.81
(2.64)
18.144
(20)
2.19
(7.17)
4.54
(10)
13.77
(5.42)
6.81
(15)
15.77
(6.21)
9.07
(20)
17.35
(6.83)
11.34
(25)
18.70
(7.36)
13.61
(30)
19.86
(7.82)
15.88
(35)
20.90
(8.23)
18.14
(40)
21.84
(8.60)
20.41
(45)
22.73
(8.95)
22.68
(50)
23.55
(9.27)
24.95
(55)
24.31
(9.57)
27.22
(60)
25.02
(9.85)
29.48
(65)
25.70 (10.12)
31.75
(70)
26.34 (10.37)
34.02
(75)
26.95 (10.61)
36.29
(80)
27.53 (10.84)
38.56
(85)
28.09 (11.06)
40.82
(90)
28.65 (11.28)
43.09
(95)
29.16 (11.48)
45.36
(100)
29.54 (11.63)
1
Dimensions correspond to size measured by sieve, grizzly, or visual inspection for stone of 25.9 kilo-newtons per cubic meter unit
weight. Do not use for determining structure crest width or layer thickness