@_rubble Mound Structure Design

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