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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
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Rubble Mound Breakwater Design
Layout Options for Rubble Mound Breakwaters and Jetties
1. Attached or Detached. a. Jetties usually attached to
stabilize an inlet or eliminate channel shoaling. b. Breakwaters
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
wave heights on the protected side are larger than for a
non-overtopped structure.
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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 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.
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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
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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
p
sb m
dH =
ds = depth at structure toe, = hb/Hb, m = nearshore slope, p =
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.
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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
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Design Parameters h water depth of structure relative to design
high water (DHW) hc breakwater crest relative to DHW R freeboard,
peak crown elevation above DHW ht depth of structure toe relative
to still water level (SWL) B crest width Bt toe apron width front
slope (seaside) b back slope (lee) t thickness of layers W armor
unit weight
DHW varies may be MHHW, storm surge, etc. SWL may be MSL, MLLW,
etc. Wave setup is generally neglected in determining DHW
h
B
ht
hc
t
armor layer, W
b
Bt
DHW
SWL
R
crown/cap
crest
first underlayer
second underlayer
toecore/base
bedding and/or filter layer
Design Concept/ Procedure 1. Specify Design Condition design
wave (H1/3, Hmax, To, Lo, depth, water elevation,
overtopping, breaking, purpose of structure, etc.) 2. Set
breakwater dimensions h, hc, R, ht, B, , b 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
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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 Ru/H and Rd/H.
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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 , 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 = RuRun-down = Rd
SWL
Run-downSWL
Run-up
Internal water level
Run-up may be determined by surf similarity parameter (m) and
core permeability (Abbot and Price, 1994)
ms
m LH= tan , where Lm is the wave length for the modal period, Tm
(deep
water assumed) = 22
mm
gTL
van der Meer (1988)
mSu aHR = for m < 1.5 cmSu bHR = for m > 1.5
for permeable structures (P > 0.4) run-up is limited to dHR
Su = Ru exceedence
probability (%) a b c d 0.1 1.12 1.34 0.55 2.58 2 0.96 1.17 0.46
1.97 5 0.86 1.05 0.44 1.68
10 0.77 0.94 0.42 1.45 50 0.47 0.60 0.34 0.82
Reduction factors are applied to the Run-up formula to account
for roughness, oblique waters and overtopping
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( ) ( )iSuSuR productHRHR = Reduction factor () Smooth
impermeable (including smooth concrete and asphalt) 1.0 1 layer of
stone rubble on impermeable base 0.8 Gravel 0.7 Rock rip-rap with
thickness > 2D50 0.5-0.6
Run-down is typically 1/3 to 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)
= 2* m
sm
sHRR , where
m
sm L
Hs =
mean overtopping discharge (Q in m3/s/m or ft3/s/ft):
( ) ( )= *exp mms RbaTgHQ use run-up reduction factors, ,
above
for straight smooth slopes (no berms), non-depth limited waves
Slope 1:1 1:1.5 1:2 1:3 1:4 a 0.008 0.010 0.013 0.016 0.019 b 20 20
22 32 47
Typical values of acceptable overtopping:
Harbor protection /s/mm 5.0 3Q Vehicles on breakwater /s/mm 01.0
3Q Pedestrians on breakwater /s/mm 05.0 3Q
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.
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3/1
3
= aWkB , where W = median weight of armor unit, a = unit
weight
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)
iTT HHK = 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 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) head is exposed to more
concentrated wave
attack want flatter slopes at head (or larger armor units)
Overtopping less return flow/ action on seaward side but more on
leeward Layer dimensions thicker layers give more reserve stability
if damaged Special placement 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.
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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 a =
unit weight of armor H = design wave height (note affect of cubic
power on armor wt.) KD = stability coefficient (Table 1 below, from
SPM) SG = a/w = a/w (gen. SG = 2.65 for quarry stone, 2.4 for
concrete) = slope angle from the horizontal
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Neglecting inertia forces, balance weight of each armor unit
(FG) with drag and lift forces induced by the waves (FD, FL)
( ) ( )( ) ( ) sw waLD G NH DSGgH DSGgv DgFF F 11122 == +
( )3/1
1
= WSG
HN as ( ) 333
1 sa
NSGH
=W
Experiments related the stability number to the face slope and
armor unit shape
( ) 3/1cot = Ds KN Combining gives Hudson's equation for minimum
required armor unit weight
( ) =
cot1 33
SGKHW
D
a
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 0.75W to
1.25W 4. Uniform slope 1:1.5 to 1:3 5. 120 pcf a 180 pcf (1.9 t/m3
a 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
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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 a = 150 lbf/ft3 for tetrapods SG = 150/64 = 2.34 slope =
lV:2H KD = 8.0 for tetrapod armor KD = 4.0 for rough angular
stone
for tetrapod: ( )( )( ) tons6.152134.28
20150cot1
3
3
3
===
SGKH
D
aW
for stone armor: ( )( ) tons212158.2420165 3 ==W
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
3/1
= aWnkt , where n = number of layers
Number of units per surface area A, 3/2
1001
= W
PnkAN aa
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Table 1, Stability Coefficient, KD (breaking occurs before the
wave reaches the structure) Structure Trunk Structure Head KD(b) KD
Slope
Armor units n(a) Placement Breaking
Wave Non-breaking
wave Breaking
Wave Non-breaking
wave cot Quarry stone Smooth rounded 2 Random 1.2 2.4 1.2 1.9
1.5 to 3.0 Smooth rounded >3 Random 1.6 3.2 1.4 2.3 (c) Rough
angular 1 Random (d) (d) 2.9 (d) 2.3 (c)
1.9 3.2 1.5 1.6 2.8 2.0 Rough angular 2 Random 2.0 4.0 1.3 2.3
3.0
Rough angular >3 Special (e) 2.2 4.5 2.1 4.2 (c) Rough
angular 2 Special (e) 5.8 7.0 5.3 6.4 (c) Parallelepiped (f) 2
Random 7.0 - 20.0 8.5 - 24.0 -- -- (c)
5.0 6.0 1.5 4.5 5.5 2.0 Tetrapod and Quadripod 2 Random 7.0 8.0
3.5 4.0 3.0
8.3 9.0 1.5 7.8 8.5 2.0 Tribar 2 Random 9.0 10.0 6.0 6.5 3.0
8.0 16.0 2.0 (h) Dolos 2 Random 15.0 (g) 31.0 (g) 7.0 14.0
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 -- -- --
(a) n is the number of wits comprising the thickness of the
armor layer. (b) 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 (
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Table 2, Layer Thickness Coefficient and Porosity Type of
Armor Unit n (1) Placing
Technique Layer Thickness Coefficient, k
Porosity Percent
Smooth stone 2 Random 1.00 38 Rough stone 2 Random 1.00 37
Tetrapod 2 Random 1.04 50 Quadripod 2 Random 0.95 49 Hexapod 2
Random 1.15 47 Modified Cube 2 Random 1.10 47 Tribar 2 Random 1.02
54 Tribar 1 Uniform 1.13 47 Toskane 2 Random 1.03 52 Dolos 2 Random
0.94 56
(1) Number of layers of armor units 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 Quadripods
1.00 1.09 1.17 (c) 1.24 (c) 1.32 (c) 1.41 (c) 1.50 (c)
Tribar 1.00 1.11 1.25 (c) 1.36 (c) 1.50 (c) 1.59 (c) 1.64 (c)
Dolos 1.00 1.10 1.14 (c) 1.17 (c) 1.20 (c) 1.24 (c) 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% 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.
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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 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 : 585
15 10 Second Underlayer - n = 2 thick, W/200
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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:
To prevent material from leaching out: 5 to485
15 dD (important for embankment
design)
To maintain filter layer internal stability: 1010
60