08 Rubble Mound Structure Design

Transcription

1 08 Rubble Mound Structure Deign Ref: Shore Protection Manual, USACE, 1984 Baic Coatal Engineering, R.M. Sorenen, 1997 Coatal Engineering andbook, J.B. erbich, 1991 EM , Deign of Breakwater and Jettie, USACE, 1986 Breakwater, Jettie, Bulkhead and Seawall, Pile Buck, 1992 Coatal, Etuarial and arbour Engineer' Reference Book, M.B. Abbot and W.A. Price, 1994, (Chapter 29) Topic Rubble Mound Breakwater Deign Layout Option for Rubble Mound Breakwater and Jettie General Decription Deign Wave Water Level and Datum Deign Parameter Deign Concept/ Procedure Structure Elevation, Run-up and Overtopping Cret/Crown Width Armor Unit Size and Stability Underlayer Deign Bedding and Filter Deign Toe Structure Low Creted Breakwater Rubble Mound Breakwater Deign Layout Option for Rubble Mound Breakwater and Jettie 1. Attached or Detached. a. Jettie uually attached to tabilize an inlet or eliminate channel hoaling. b. Breakwater attached or detached. i. If the harbor i on the open coatline, predominant wave cret approach parallel to the coatline, a detached offhore breakwater might be the bet option. ii. An attached breakwater extended from a natural headland could be ued to protect a harbor located in a cove. iii. A ytem of attached and detached breakwater may be ued. iv. An advantage of attached breakwater i eae of acce for contruction, operation, and maintenance; however, one diadvantage may be a negative impact on water quality due to effect on natural circulation. 2. Overtopped or Non-overtopped. a. Overtopped: crown elevation allow larger wave to wah acro the cret wave height on the protected ide are larger than for a non-overtopped tructure.

2 b. Non-overtopped: elevation preclude any ignificant amount of wave energy from coming acro the cret. c. Non-overtopped breakwater or jettie i. Greater degree of wave protection ii. More cotly to build becaue of the increaed volume of material required. d. Cret elevation determine the amount of wave overtopping expected i. ydraulic model invetigation to find the magnitude of tranmitted wave height ii. Optimum cret elevation minimum height that provide the needed protection. e. Overtopped breakwater i. Cret elevation may be et by the deign wave height that can be expected during the period the harbor will be ued (epecially true in colder climate). ii. Overtopped tructure are more difficult to deign becaue their tability repone i trongly affected by mall change in the till water level. 3. Submerged Breakwater a. Example: A detached breakwater contructed parallel to the coatline and deigned to diipate ufficient wave energy to eliminate or reduce horeline eroion. b. Advantage: i. Le expenive to build. ii. May be aethetically more pleaing (do not encroach on any cenic view) c. Diadvantage: i. Significantly le wave protection i provided ii. Monitoring the tructure' condition i more difficult. iii. Navigation hazard may be created. 4. Single or Double. a. Jettie: Double parallel jettie will normally be required to direct tidal current to keep the channel coured to a uitable depth. owever, there may be intance where coatline geometry i uch that a ingle updrift jetty will provide a ignificant amount of tabilization. One diadvantage of ingle jettie i the tendency of the channel to migrate toward the tructure. b. Breakwater: Choice of ingle or double breakwater will depend on uch factor a coatline geometry and predominant wave direction. Typically, a harbor poitioned in a cove will be protected by double breakwater extended eaward and arced toward each other with a navigation opening between the breakwater head. For a harbor contructed on the open coatline a ingle offhore breakwater with appropriate navigation opening might be the more advantageou. 5. Weir Section. Some jettie are contructed with low horeward end that act a weir. Water and ediment can be tranported over thi portion of the tructure for part or all of a normal tidal cycle. The weir ection, generally le than 500 feet long, act a a breakwater and provide a emi-protected area for dredging of the depoition bain when it ha filled. The bain i dredged to tore ome etimated quantity of and moving into the bain during a given time period. A hydraulic dredge working in the emi-protected water can bypa and to the downdrift beach.

3 6. Deflector Vane. In many intance where jettie are ued to help maintain a navigation channel, current will tend to propagate along the ocean-ide of the jetty and depoit their ediment load in the mouth of the channel. Deflector vane can be incorporated into the jetty deign to aid in turning the current and thu help to keep the ediment away from the mouth of the channel. Poition, length, and orientation of the vane can be optimized in a model invetigation. 7. Arrowhead Breakwater. When a breakwater i contructed parallel to the coatline navigation condition at the navigation opening may be enhanced by the addition of arrowhead breakwater. Prototype experience with uch tructure however ha hown them to be of quetionable benefit in ome cae. General Decription Deign Wave Multi-layer deign. Typical deign ha at leat three major layer: 1. Outer layer called the armor layer (larget unit, tone or pecially haped concrete armor unit) 2. One or more tone underlayer 3. Core or bae layer of quarry-run tone, and, or lag (bedding or filter layer below) Deigned for non-breaking or breaking wave, depending on the poitioning of the breakwater and everity of anticipated wave action during life. Armor layer may need to be pecially haped concrete armor unit in order to provide economic contruction of a table breakwater. 1. Uually 1/3, but may be 1/10 to reduce repair cot (Pacific NW) (USACE recommend 1/10 ) 2. The depth limited breaking wave hould be calculated and compared with the unbroken torm wave height, and the leer of the two choen a the deign wave. (Breaking occur in water in front of tructure) 3. Ue b /h b ~ 0.6 to For variable water depth, deign in egment Jettie with Weir ection and Deflector Vane

4 Arrowhead Breakwater Breaking Wave Conideration (SPM, Chapter 7) The deign breaker height ( b ) depend on the depth of water ome ditance eaward from the tructure toe where the wave firt begin to break. Thi depth varie with tidal tage. Therefore, the deign breaker height depend on the critical deign depth at the tructure toe, the lope on which the tructure i built, incident wave teepne, and the ditance traveled by the wave during breaking. Aume that the deign wave plunge on the tructure b d = γ mτ p d = depth at tructure toe, γ = h b / b, m = nearhore lope, τ p = dimenionle plunge ditance, = breaker travel ditance (x p ) / breaker height ( b ) If the maximum deign depth at the tructure toe and the incident wave period are known, the deign breaker height can be determined from the chart below (Figure 7-4 of the SPM, 1984). Calculate d /(gt 2 ), locate the nearhore lope and determine b /d.

5

6 Water Level and Datum. Both maximum and minimum water level are needed for the deigning of breakwater and jettie. Water level can be affected by torm urge, eiche, river dicharge, natural lake fluctuation, reervoir torage limit, and ocean tide. igh-water level are ued to etimate maximum depth-limited breaking wave height and to determine crown elevation. Low-water level are generally needed for toe deign. a. Tide Prediction, The National Ocean Service (NOS) publihe tide height prediction and tide range. Figure 2-l how pring tide range for the continental United State. Publihed tide prediction are ufficient for mot project deign; however, prototype obervation may be required in ome intance. b. Datum Plane. Structural feature hould be referred to appropriate low-water datum plane. The relationhip of low-water datum to the National Geodetic Vertical Datum (NGVD) will be needed for vertical control of contruction. The low-water datum for the Atlantic and Gulf Coat i being converted to mean lower low water (MLLW). Until the converion i complete, the ue of mean low water (MLW) for the Atlantic and Gulf Coat low water datum (GCLWD) i acceptable. Other low-water datum are a follow: Pacific Coat: Mean lower low water (MLLW) Great Lake: International Great Lake Datum (IGLD) River: River, low-water datum plane (local) Reervoir: Recreation pool level

7 Deign Parameter h h c R h t B B t α α b t W water depth of tructure relative to deign high water (DW) breakwater cret relative to DW freeboard, peak crown elevation above DW depth of tructure toe relative to till water level (SWL) cret width toe apron width front lope (eaide) back lope (lee) thickne of layer armor unit weight DW varie may be MW, torm urge, etc. SWL may be MSL, MLLW, etc. Wave etup i generally neglected in determining DW B crown/cap cret armor layer, W DW R h c firt underlayer h SWL toe h t α t core/bae α b econd underlayer B t bedding and/or filter layer Deign Concept/ Procedure 1. Specify Deign Condition deign wave ( 1/3, max, T o, L o, depth, water elevation, overtopping, breaking, purpoe of tructure, etc.) 2. Set breakwater dimenion h, h c, R, h t, B, α, α b 3. Determine armor unit ize/ type and underlayer requirement 4. Develop toe tructure and filter or bedding layer 5. Analyze foundation ettlement, bearing capacity and tability 6. Adjut parameter and repeat a neceary

8

9 Structure Elevation, Run-up and Overtopping Wave breaking on a lope caue up-ruh and down-ruh. The maximum and minimum vertical elevation of the water urface from SWL i called run-up (R u ) and run-down (R d ). Non-dimenionalize with repect to wave height R u / and R d /.

10 Overtopping occur if the freeboard (R) i le than the et-up + R u. Generally neglect wave etup for loped tructure Freeboard may be zero if overtopping i allowed. Freeboard may alo be et to achieve a given allowed overtopping. Run-up and run-down are function of ξ, permeability, poroity and urface roughne of the lope. Effect of Permeability - Flow field induced in permeable tructure by wave action reult in reduced run-up and run-down, but increaed detabilizing force (ee diagram). SWL Run-up = R u Run-down = R d Internal water level SWL Run-up SWL Run-down Run-up may be determined by urf imilarity parameter (ξ m ) and core permeability (Abbot and Price, 1994) ξ m = tan α L water aumed) m van der Meer (1988) R R u u S S, where L m i the wave length for the modal period, T m (deep L m m gt = 2 m 2π = aξ for ξ m < 1.5 = bξ for ξ m > 1.5 c m for permeable tructure (P > 0.4) run-up i limited to Ru S = d R u exceedence probability (%) a b c d Reduction factor are applied to the Run-up formula to account for roughne, oblique water and overtopping

11 R ur S = ( R ) product( γ ) u S i Reduction factor (γ) Smooth impermeable (including mooth concrete and aphalt) layer of tone rubble on impermeable bae 0.8 Gravel 0.7 Rock rip-rap with thickne > 2D Run-down i typically 1/3 to ½ of the run-up and may be ued to determine the minimum downward extenion of the main armor and a poible upper level for introducing a berm with reduced armor ize. Deigning to an Allowable Overtopping - Overtopping depend on relative freeboard, R/, wave period, wave teepne, permeability, poroity, and urface roughne. Uually overtopping of a rubble tructure uch a a breakwater or jetty can be tolerated only if it doe not caue damaging wave behind the tructure. R may be determined baed on acceptable Q for the deign Owen (1980, 1982) R R = * m m, where 2π = m L m mean overtopping dicharge (Q in m 3 //m or ft 3 //ft): Q * ( g T ) = aexp( b R γ) m ue run-up reduction factor, γ, above for traight mooth lope (no berm), non-depth limited wave Slope 1:1 1:1.5 1:2 1:3 1:4 a b Typical value of acceptable overtopping: 3 arbor protection Q 0.5 m //m Vehicle on breakwater Pedetrian on breakwater m Q 0.01m Q 0.05 m Concrete Cap - conidered for trengthening the cret, increaing cret height, providing acce along cret for contruction or maintenance. Evaluate by calculating cot of cap v. cot of increaing breakwater dimenion to increae overtopping tability Cret/ Crown Width 3 3 //m //m Depend on degree of allowed overtopping. Not critical if no overtopping i allowed. Minimum of 3 armor unit or 3 meter for low degree of overtopping.

12 Wave Tranmiion 1/ 3 W 3 B = k, where W = median weight of armor unit, γ a = unit weight γ a of armor, k = layer thickne coefficient (ee Table 2) Wave tranmiion behind rubble mound breakwater i caued by wave regeneration due to overtopping and wave penetration through void in the breakwater. Affected by: Cret elevation Cret width eaide and lee-ide face lope Rubble ize Breakwater poroity Wave height, wave length and water depth Tranmiion coefficient (K T ) K = T T i T = tranmitted wave height i = incident wave height Given an acceptable lee-ide wave height, the cret elevation (h c ) and width (B) can be determined by uing the diagram below (note: the diagram i baed on experiment by N. Tanaka, 1976, on a ymmetric breakwater with 1:2 eaide and lee-ide lope.) Armor Unit Size and Stability Conideration: Slope: flatter lope maller armor unit weight but more material req'd Seaide Armor Slope - 1:1.15 to 1:2 arbor-ide (leeide) Slope Minor overtopping/ moderate wave action - 1:1.25 to 1:1.5 Moderate overtopping/ large wave - 1:1.33 to 1:1.5 * harbor-ide lope are teeper, ubject to landlide type failure Trunk v. head (end of breakwater) head i expoed to more concentrated wave attack want flatter lope at head (or larger armor unit) Overtopping le return flow/ action on eaward ide but more on leeward Layer dimenion thicker layer give more reerve tability if damaged Special placement reduce ize req't, gen. limited to concrete armor unit Concrete armor unit (may be required for more extreme wave condition) Advantage - increae tability, allow teeper lope (le mat'l req'd), lighter wt.

13 Diadvantage - breakage reult in lot tability and more rapid deterioration. ydraulic tudie have indicated that up to 15 percent random breakage of dole armor unit may be experienced before tability i threatened, and up to five broken unit in a cluter can be tolerated. Conideration 1. Availability of cating form 2. Concrete quality 3. Ue of reinforcing (req'd if > t) 4. Placement 5. Contruction equipment availability **When uing pecial armor unit, underlayer are ized baed on tone armor unit weight udon' Formula for Determining Armor Unit Weight udon, R. Y. (1959) Laboratory Invetigation of Rubble-Mound Breakwater, Proceeding of the American Society of Civil Engineer, American Society of Civil Engineer, Waterway and arbor Diviion, Vol. 85, NO. WW3, Paper No Formula i baed on a balance of force to enure each armor unit maintain tability under the force exerted by a given wave attack. W = median weight of armor unit D = diameter of armor unit γ a = unit weight of armor = deign wave height (note affect of cubic power on armor wt.) K D = tability coefficient (Table 1 below, from SPM) SG = γ a /γ w = ρ a /ρ w (gen. SG = 2.65 for quarry tone, 2.4 for concrete) α = lope angle from the horizontal

14 Neglecting inertia force, balance weight of each armor unit (F G ) with drag and lift force induced by the wave (F D, F L ) D L ( ρ ρ ) D g( SG 1) w ( g ) ( SG 1) FG g a w D D 1 = = 2 2 F + F ρ v N N 1/ 3 = ( SG 1) γ a W W = γ 3 a ( SG ) N Experiment related the tability number to the face lope and armor unit hape N K cot α 1/ ( ) 3 = D Combining give udon' equation for minimum required armor unit weight W = K D γ a ( SG 1) 3 cot α 3 Retriction on udon equation: 1. K D not to exceed Table 1 (from SPM) value 2. Cret height prevent minor wave overtopping 3. Uniform armor unit 0.75W to 1.25W 4. Uniform lope 1:1.5 to 1: pcf γ a 180 pcf (1.9 t/m 3 γ a 2.9 t/m 3 ) Not conidered in udon equation incident wave period type of breaking (pilling, plunging, urging) allowable damage level (aume no damage) duration of torm (i.e. number of wave) tructure permeability Bottom elevation of Armor Layer (ow deep hould armor extend?) Armor unit in the cover layer hould be extended downlope to an elevation below minimum till water level equal to 1.5 when the tructure i in a depth greater than 1.5. If the tructure i in a depth of le than 1.5, armor unit hould be extended to the bottom. Toe condition at the interface of the breakwater lope and ea bottom are a critical tability area and hould be thoroughly evaluated in the deign. The weight of armor unit in the econdary cover layer, between -1.5 and -2, hould be approximately equal to one-half the weight of armor unit in the primary cover layer (W/2). Below -2. the weight requirement can be reduced to approximately W/l5. When the tructure i located in hallow water, where the

15 wave break, armor unit in the primary cover layer hould be extended down the entire lope. The above-mentioned ratio between the weight of armor unit in the primary and econdary cover layer are applicable only when tone unit are ued in the entire cover layer for the ame lope. When pre-cat concrete unit are ued in the primary cover layer, the weight of tone in the other layer hould be baed on the equivalent weight of tone armor. For example: tetrapod armor deign condition: 20 foot non-breaking wave attack on a tructure trunk γ a = 150 lbf/ft 3 for tetrapod SG = 150/64 = 2.34 lope = lv:2 K D = 8.0 for tetrapod armor K D = 4.0 for rough angular tone for tetrapod: W = K D γ a 3 3 ( SG 1) 3 ( 165) 20 4( 2.58 ) = cot α 8 3 ( 150) 20 ( 2.34 ) = 15.6 ton 1 2 for tone armor: W = = 21 ton 1 2 The econdary cover layer from -1.5 to the bottom hould be a thick a or thicker than the primary cover layer and ized for W = 21 ton. Armor layer thickne (t) ue to calculate ize of layer t = nk W γ a 1/ 3 Number of unit per urface area A, N a P γ = 1 a nk A 100 W, where n = number of layer 2 / 3

16 Table 1, Stability Coefficient, K D (breaking occur before the wave reache the tructure) Armor unit n (a) Placement Structure Trunk Breaking Wave K D (b) Non-breaking wave Breaking Wave Structure ead K D Non-breaking wave Slope Quarry tone Smooth rounded 2 Random to 3.0 Smooth rounded >3 Random (c) Rough angular 1 Random (d) (d) 2.9 (d) 2.3 (c) cot α Rough angular 2 Random Rough angular >3 Special (e) (c) Rough angular 2 Special (e) (c) Parallelepiped (f) 2 Random (c) Tetrapod and Quadripod 2 Random Tribar 2 Random (h) Dolo 2 Random 15.0 (g) 31.0 (g) Modified Cube 2 Random (c) exapod 2 Random (c) Tokane 2 Random (c) Tribar 1 Uniform (c) Quarrytone (KRR) Graded angular -- Random (a) n i the number of wit compriing the thickne of the armor layer. (b) Applicable to lope ranging from 1 on 1.5 to 1 on 5. (c) Until more information i available on the variation of K D value with lope, the ue of K D hould be limited to lope ranging from 1 on 1.5 to 1 on 3. Some armor unit teted on a tructure head indicate a K D lope dependence. (d) The ue of a ingle layer of quarry tone armor unit ubject to breaking wave i not recommended, and only under pecial condition for non-breaking wave. When it i ued, the tone hould be carefully placed. (e) Special placement with long axi of tone placed perpendicular to tructure face. (f) Long lab-like tone with the long dimenion about three time it hortet dimenion. (g) Refer to no-damage criteria (~5 percent diplacement, rocking, etc.); if no rocking (<2 percent) i deired, reduce K D 50 percent. (h) Stability of dolo on lope teeper than 1 on 2 hould be ubtantiated by ite-pecific model tet. NOTE : Breaking wave tability coefficient for tone and dolo were developed uing a 1V:10 forelope.

17 Table 2, Layer Thickne Coefficient and Poroity Type of Armor Unit n (1) Placing Technique Layer Thickne Coefficient, k Poroity Percent Smooth tone 2 Random Rough tone 2 Random Tetrapod 2 Random Quadripod 2 Random exapod 2 Random Modified Cube 2 Random Tribar 2 Random Tribar 1 Uniform Tokane 2 Random Dolo 2 Random (1) Number of layer of armor unit Table 3, / D=0 a a function of cover layer damage Damage (D), Percent Unit Quarry tone (mooth) Quarry tone (rough) (b) Tetrapod and (c) 1.24 (c) 1.32 (c) 1.41 (c) 1.50 (c) Quadripod Tribar (c) 1.36 (c) 1.50 (c) 1.59 (c) 1.64 (c) Dolo (c) 1.17 (c) 1.20 (c) 1.24 (c) 1.27 (c) (a) Breakwater trunk, n = 2, random-placed armor unit, non-breaking wave, and minor overtopping condition. (b) Value in italic are interpolated or extrapolated. (c) CAUTION: Tet did not include poible effect of unit breakage. Wave exceeding the deign wave height condition by more than 10 percent may reult in coniderably more damage than the value tabulated. Modified Allowable Wave eight Baed on Damage The concept of deigning a rubble-mound breakwater for zero damage i unrealitic, becaue a definite rik alway exit for the tability criteria to be exceeded in the life of the tructure. Table 3 how reult of damage tet where / D=0 i a function of the percent damage, D, for variou armor unit. i the wave height correponding to damage D. D=0 i the deign wave height correponding to 0 to 5 percent damage, generally referred to a the no-damage condition. Information preented in table 3 may be ued to etimate anticipated annual repair cot, given appropriate long-term wave tatitic for the ite. If a certain level of damage i acceptable, the deign wave height may be reduced. Example: Rough quarry tone breakwater with a deign wave height for D = 0% of = 3 m and acceptable D = 10-15% / D=0 = 1.14 If the 10-15% damage at = 3 m i acceptable, the deign wave height may be reduced to (3 m)/1.14 = 2.6 m.

18 Underlayer Deign Armor Layer provide tructural tability againt external force (wave) Underlayer prevent core or bae material from ecaping. Requirement: 1. Prevent fine material from leaching out. 2. Allow for ufficient poroity to avoid exceive pore preure build-up inide the breakwater that could lead to intability or liquefaction in extreme cae Note: requirement are in conflict, Eng. mut provide an optimum olution Armor layer unit are large atify (2) above readily Baed on pherical hape geometry, core material cannot ecape the cover layer if the diameter ratio of the cover material (D) to the core material (d) i le than ix. (i.e. D/d < 6) D For orted material (e.g. quarry tone) under tatic (calm) load : 15 < 5 d Under dynamic load (i.e. wave force), more retrictive rule apply: D d W 2.5 to 3, which give 15 to 25 (aume W D 3 ) w bae 85 Recommended Size (ee diagram) Layer Weight Ratio Equivalent Diameter Ratio Primary Armor Layer W/1 1 Firt Underlayer W/ Second Under Layer W/ Bae/ Core Material W/ (Guidance from SPM) Firt Underlayer (directly under the armor unit) minimum two tone thick (n = 2) (1) under layer unit weight = W/10 if cover layer and firt underlayer are both tone if the firt underlayer i tone and the cover layer i concrete armor unit with K D 10 (2) under layer unit weight = W/15 when the cover layer i of armor unit with K D > 10 Second Underlayer - n = 2 thick, W/200

19 Bedding or Filter Layer Deign Layer between tructure and foundation or between cover layer and bank material for revetment. Purpoe i to prevent bae material from leaching out, prevent pore preure build-up in bae material and protect from exceive ettlement. Should be ued except when: 1. Depth > 3 max, or 2. Anticipated current are weak (i.e. cannot move average foundation material), or 3. ard, durable foundation material (i.e. bedrock) Coheive Material: May not need filter layer if foundation i coheive material. A layer of quarry tone may be placed a a bedding layer or apron to reduce ettlement or cour. Coare Gravel: Foundation of coare gravel may not require a filter blanket. Sand: a filter blanket hould be provided to prevent wave and current from removing and through the void of the rubble and thu cauing ettlement. When large quarry-tone are placed directly on a and foundation at depth where wave and current act on the bottom (a in the urf zone), the rubble will ettle into the and until it reache the depth below which the and will not be diturbed by the current. Large amount of rubble may be required to allow for the lo of rubble becaue of ettlement. Thi, in turn, can provide a table foundation. Criteria for granular filter deign: D15 To prevent material from leaching out: < 4 to 5 d85 d 85 = dia. exceeded by the coaret 15% of the bae mat'l D 15 = dia. exceeded by the coaret 85% of the filter mat'l (important in breakwater deign) D15 To prevent pore preure build-up: > 4 to 5 (important for embankment d15 deign) D60 To maintain filter layer internal tability: < 10 (i.e. well orted material i D10 D60 preferred). Poorly orted material i not uitable for filter 20 D10 (internally untable too much wahe out) General guideline for tability againt wave attack. Bedding Layer thickne hould be: 2-3 time the diameter for large tone 10 cm for coare and 20 cm for gravel

20 For foundation tability Bedding Layer thickne hould be at leat 2 feet Bedding Layer hould extend 5 feet horizontally beyond the toe cover tone. Geotextile filter fabric may be ued a a ubtitute for a bedding layer or filter blanket, epecially for bank protection tructure. When a fabric i ued, a protective layer of pall or cruhed rock (7-inch maximum to 4-inch minimum ize) having a recommended minimum thickne of 2 feet hould be placed between the fabric and adjacent tone to prevent puncture of the fabric. Filter criteria hould be met between the protective layer of pall and adjacent tone. Advantage: uniform propertie and quality. Diadvantage: uceptible to weathering, tearing, clogging and flopping. Toe Structure No rigorou criteria. Deign i complicated by interaction between main tructure, hydrodynamic force and foundation oil. Deign i often ad hoc or baed on laboratory teting. Toe failure often lead to major tructural failure. Function of toe tructure: 1. upport the armor layer and prevent it from liding (armor layer i ubject to wave and will tend to aume the equilibrium beach profile hape) 2. protect againt couring at the toe of the tructure 3. prevent underlying material from leaching out 4. provide tructural tability againt circular or lip failure Toe Structure Function EBP Armor layer upport Protecting againt leaching Protect againt cour weak oil Prevent circular failure

21 Toe Structure Stability For larger h t maller tone ize are required (wave action i reduced a depth increae). From experiment (CIAD report, 1985): h t 1/ 3 = f ( N ) = 0.22 for 50% confidence level h ( SG 1) D50 h t 1/ 3 = for 90% confidence level h ( SG 1) D50 aume D 50 6W = γπ 1/ 3, i.e. pherical Above equation are guideline. CEM/SPM recommend berm width at toe be at leat 3 armor tone and the height at leat 2. Actual width and height hould be checked by circular tability analyi. (ee dicuion below on width deign for cour conideration) Scour Conideration If no Toe Structure i ued, armor layer hould extend below maximum couring depth and the breakwater lope may require adjutment to reduce cour. Return flow and vortex formation d cour hole Toe i protected by toe tructure d, with 1.0 at ξ ~ 2.7 Generally: = f ( ξ) = 0.5 to1. 0 The following deign equation are baed on preventing or minimizing cour in front of vertical tructure (Tanimoto, K., Yagyu, T., and Goda, Y., 1982) Toe Apron Width (B t ) - width hould be the maximum of B t = 2 or B t = 0.4h (at leat 3 tone) Toe Stone Weight (minimum tone weight) 3 γ a Wmin = N 3 ( SG 1) 3 where N = tability number i the maximum of

22 N 2 ( 1 K ) 1 K h t ht = exp 1.5 or N 1/ 3 1/ = 1.8 K K 3 where K = a parameter aociated with the maximum horizontal velocity at the edge of the toe apron 2kht K = inh 2kh t 2 in kb t Additional Toe Structure Deign Reference: eadquarter, Department of the Army. (1985) Deign of Coatal Revetment, Seawall, and Bulkhead, Engineer Manual , Wahington, DC udon, R. Y. (1959) Laboratory Invetigation of Rubble-Mound Breakwater, Proceeding of the American Society of Civil Engineer, American Society of Civil Engineer, Waterway and arbor Diviion, Vol. 85, NO. WW3, Paper No Shore Protection Manual. (1984) 4 th cd., 2 Vol., US Army Engineer Waterway Experiment Station, Coatal Engineering Reearch Center, US Government Printing Office, Wahington, DC, Chapter 7, pp Tanimoto, K., Yagyu, T., and Goda, Y. (1982) Irregular Wave Tet for Compoite Breakwater Foundation, Proceeding of the 18 th Coatal Engineering Conference, American Society of Civil Engineer, Cape Town, Republic of South Africa, Vol. III, pp

23 Low Creted Breakwater (from Sorenen) ighet part of breakwater i at or below MSL 1. Stabilize beach/ retain and after nourihment 2. Protect larger tructure 3. Caue large torm wave to break and diipate energy before reaching the beach Traditional high-creted breakwater with a multi-layered cro ection may not be appropriate for a tructure ued to protect a beach or horeline. Adequate wave protection may be more economically provided by a low-creted or ubmerged tructure compoed of a homogeneou pile of tone. ** Failure occur by lo of tone from the cret. A = area of tructure profile from which tone ha been removed/lot h h c Ue a modified tability number 2 / 3 1/ 3 * L N = W = 1/ 3 ( SG 1) W γ a γ a 3 * ( SG ) ( N ) 3 2 L 1 L i the wave length at the tructure depth and i calculated uing peak period (T p ) for random wave. AS Damage Level (S) i defined a: S =, where A 2 = area of damage (ee diagram) and D 50 D 50 = median tone ize of the breakwater Given S, h c, h determine N * hc * from = ( S ) exp( 0.14N ) h c = height of the wave cret above the ea floor h = water depth at the tructure h 2

24 Table VI-5-50 (CEM) Weight and Size Selection Dimenion of Quarrytone 1 Weight Dimenion Weight Dimenion Weight Dimenion kg (lb) cm (in.) kg (lb) m (ft) mt (ton) m ft 0.01 (0.025) 1.88 (0.74) (100) 0.30 (0.97) (1) 0.81 (2.64) 0.02 (0.050) 2.36 (0.93) (200) 9.38 (1.23) (2) 1.02 (3.33) 0.03 (0.75) 2.70 (1.06) (300) 0.43 (1.40) (3) 1.16 (3.81) 0.04 (0.100) 2.97 (1.17) (400) 9.50 (1.54) (4) 1.28 (4.19) 0.06 (0.125) 3.20 (1.26) (500) 0.51 (1.66) (5) 1.38 (4.52) 0.07 (0.150) 3.40 (1.34) (600) 0.54 (1.77) (6) 1.46 (4.80) 0.08 (0.175) 3.58 (1.41) (700) 0.57 (1.86) (7) 1.54 (5.05) 0.09 (0.200) 3.73 (1.47) (800) 0.60 (1.95) (8) 1.61 (5.28) 0.10 (0.225) 3.89 (1.53) (900) 0.62 (2.02) (9) 1.67 (5.49) 0.11 (0.250) 4.04 (1.59) (1000) 0.64 (2.10) (10) 1.73 (5.69) 0.23 (0.5) 5.08 (2.00) (1100) 0.66 (2.16) (11) 1.79 (5.88) 0.45 (1.0) 6.40 (2.52) (1200) 0.68 (2.23) (12) 1.84 (6.05) 0.68 (1.5) 7.32 (2.88) (1300) 0.70 (2.27) (13) 1.89 (6.21) 0.91 (2.0) 8.05 (3.17) (1400) 0.72 (2.35) (14) 1.94 (6.37) 1.13 (2.5) 8.66 (3.41) (1500) 0.73 (2.40) (15) 1.98 (6.51) 1.36 (3.0) 9.22 (3.63) (1600) 0.75 (2.45) (16) 2.03 (6.66) 1.59 (3.5) 9.70 (3.82) (1700) 0.76 (2.50) (17) 2.07 (6.79) 1.81 (4.0) (3.99) (1800) 0.78 (2.55) (18) 2.11 (6.92) 2.04 (4.5) (4.15) (1900) 0.80 (2.60) (19) 2.15 (7.05) 2.27 (5) (4.30) (2000) 0.81 (2.64) (20) 2.19 (7.17) 4.54 (10) (5.42) 6.81 (15) (6.21) 9.07 (20) (6.83) (25) (7.36) (30) (7.82) (35) (8.23) (40) (8.60) (45) (8.95) (50) (9.27) (55) (9.57) (60) (9.85) (65) (10.12) (70) (10.37) (75) (10.61) (80) (10.84) (85) (11.06) (90) (11.28) (95) (11.48) (100) (11.63) 1 Dimenion correpond to ize meaured by ieve, grizzly, or viual inpection for tone of 25.9 kilo-newton per cubic meter unit weight. Do not ue for determining tructure cret width or layer thickne