wave loads on breakwaters, seawalls, and other marine structures

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H. Oumeraci, E-mail: h.Oumeraci@tu-bs.deLeichtweiß-Institute for Hydromechanics and Coastal Engineering, Technical University Braunschweig, BraunschweigCoastal Research Centre, University Hannover and Technical University Braunschweig, Hannover

Wave Loads on Breakwaters, Sea-Walls and other Marine StructuresWave Loads on Breakwaters, Sea-Walls and other Marine Structures

Introduction

Main Experimental Facilities and Expertise

Leichtweiss-Institute for Hydraulic EngineeringLeichtweiss-Institute for Hydraulic Engineering

Hydromechanics & Coastal Engineering

Homepage: http://www.LWI.tu-bs.de

Technical University Braunschweig

Length ≈ 90m

Depth = 1,25m

WaveWave

(a) Plan view of twin-flume

b) Twin-Wave Paddle (Synchron or independent)

up to 30cm high solitary waves

Coastal Research Centre (FZK) in HannoverCoastal Research Centre (FZK) in Hannover

Coastal Research Centre

FZKJoint Central Institution of

the University of Hannover and theTechnical University of Braunschweig

Large Wave Flume (GWK)

Homepage:http://www.hydrolab.de/

Dimensions

330m x 5m x 7m

up to 1m high solitary waves

Seadikes and Revetments Rubble Mound Breakwaters Caisson-Breakwaters

Wave Absorber as a Sea Wall Wave Absorber as Artificial Reef Innovative Sea Walls

Beach Profile Development underStorm Surge Conditions

Dune Stability and Reinforcementwith Geotextile Constructions

Wave Impact Loading& Scour (in progress)

Investigated Coastal Marine Structure (Selected)Investigated Coastal Marine Structure (Selected)

Waves & Water Levels(at Structure)

Wave Refelction

IncidentWaves

(Farfield)

Waves & Water Levels(Nearfields)

StructureLoad

Wave Transmission

StructureLoad

Structure- and Soil Parameters

Structureresponse

Wave Overtopping

Structure Response Wave Transmission

Structure Parameters

Indirect Loadingof Foundation Soil

Direct Loadingof Foundation SoilTF

Sea Wave-Structure-Foundation InteractionSea Wave-Structure-Foundation Interaction

CoV ≥ 10%CoV ≥ 20%

CoV = Coefficient of VariationTF = Transfer function (Model)

CoV > 50%

CoV ≥ 20%

CoV > 30%

CoV > 20%CoV > 30%

CoV ≥ 15%

Research StrategyResearch Strategy

Validated predictive formulae and graphs (empirical/semi-empirical)

Identify most essential and crucial features of processes to be predicted

Conceptual model (original idea/hypothesis)

Numerical modelling to supplement/support small scale

model study

Physical Modelling (small scale model tests for systematic

parameter study)

Qualitative (and partly quantitative) understanding of physical processes to be

investigated

and/or

Improved quantitative understanding of processes to be predicted

Ultimate Scientific Result:

Prototype observations and measurements (model and scale effects)

Processes observed in nature

Validated sophisticated numerical model used as a research predictive tool

Large-scale model tests (scale effects)

Detailed conceptual model (generalized and validated)

Processes observed in nature

1. Introduction

2. Wave Loads on Pile Structures

3. Wave Forces on Submerged Bodies

4. Wave Loads on Monolithic Breakwater and Sea Walls

OutlineOutline

2. Wave Loads on Pile Structures (3D)

2.1 Wave Load Classification

Non Slender and Slender StructuresNon Slender and Slender Structures

Ht≠Hi

D > 0.05LNon Slender Structures(Diffraction + Reflection)

π⋅D/L= Diffraction parameter

Incident Wave

D < 0.05LSlender Structures

(Hydraulically transparent)

Incident Wave

Relative Importance of Drag and Inertia Forces FD and FMRelative Importance of Drag and Inertia Forces FD and FM

D> (1/16.h/L)HD ≥ 0,2H

(1/100.h/L)H<D<

(1/16.h/L)H

(H/32)<D<(H/5)

D< (1/100.h/L)HD≤ (H/32)

Transition & Shallowwater

(h/L < 0,5)

Deep water(h/L ≥ 0,5)

D= H(1

6. h/L

Drag forces dominate for smaller D and larger wave

heights H

Inertia forces dominate for larger D and smaller wave

heights H

Transtion Deep waterShallow water

D= H(100.h/L)

100,01 1,00,1

MORISON-Formula:

FTot = FM

FTot = FM + FD

FTot = FD

Total Force FTot

hπ⋅ ∂

= ⋅ρ ⋅ ⋅ ⋅ + ⋅ρ ⋅ ⋅∂

ges D w m w

Drag component Inertiacomponent

1 D uf C D u u c

(Deep water)D= H/32

D= H/5 (Deep water)

Both Drag and Inertia are important

Wave Load at Different LocationsWave Load at Different Locations

FH (t)FH

generally quasi-static generally dynamic generally dynamic

Seawards of surf zoneNon breaking waves

Shorewards of surf zoneBroken waves (bores)

Surf zoneBreaking waves

Wave Load Classification

FH (t)

Seaward of shoreline

Landward of shoreline

enough knowledge available insufficient knowledge

2.2 Breaking Wave Impact Load on Single Pile in Deeper Water

References:

• Wienke, J. (2001): Impact loading of slender pile structures induced by breaking waves in deeper water, PhD-Thesis, Leichtweiss-Institute, TU Braunschweig (in German)

Extreme Loads Due to Breaking WavesExtreme Loads Due to Breaking Waves

PROTOTYPE GWK MODEL

Breaking Wave Forces on Slender CylindersBreaking Wave Forces on Slender Cylinders

λ = „Curling Factor“

Breaking wave

Total force =

FTot = FM + FD + FI

C Fη‘

λ.η'

inertia/drag force (quasi-static force

impact force+

Slamming Coefficient and Pile-up EffectsSlamming Coefficient and Pile-up Effects

no pile-uppile-up effect

CS(t=0)=πvon

Karman(1929)

CS(t=0)=2πWagner(1932)

Theoretical Formulae for Slamming ForcesTheoretical Formulae for Slamming Forces

ηb V.t

pile-up effect

flat plate

• analytical solution by flat plate approximation

• experimentally verified by pressure measurement

t / R/V0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

f/ ρ R

ignoring pile-up effect

new approach

Theoretical Formulae for Slamming ForcesTheoretical Formulae for Slamming Forces

Line force ρ= ⋅ ⋅ ⋅ 2maxf SC R V

= ⋅1332D

Impact load duration:

with CS = Slamming Factor

Loading Cases for Vertical Cylinder in GWKLoading Cases for Vertical Cylinder in GWK

Wave breaking behind pile

Wave breaking at pile

Wave breaking just in front of pile

Wave breaking in front of pile

Broken wave at pile

SWL SWL SWL SWL SWL

TimeFo

quasi-static

1. 2. 3. 4. 5.

Broken wave at pile

SWL SWL SWL SWL SWL

TimeFo

quasi-static

1. 2. 3. 4. 5.

Broken wave at pile

SWL SWL SWL SWL SWL

TimeFo

quasi-static

1. 2. 3. 4. 5.

Broken wave at pile

SWL SWL SWL SWL SWL

TimeFo

quasi-static

1. 2. 3. 4. 5.

Broken wave at pile

SWL SWL SWL SWL SWL

TimeFo

quasi-static

1. 2. 3. 4. 5.

Loading Cases Investigated in GWK for Vertical & Inclined Cylinders (1)Loading Cases Investigated in GWK for Vertical & Inclined Cylinders (1)

-45° -25° 0° +24,5° +45°

quasi-static

Loading Cases Investigated in GWK for Vertical & Inclined Cylinders (2)Loading Cases Investigated in GWK for Vertical & Inclined Cylinders (2)

quasi-static

Loading Case 3 for Different Pile Inclination AnglesLoading Case 3 for Different Pile Inclination Angles

-45° Inclined against wave direction

-25° Inclined against wave direction

0° vertical pile

+24.5° Inclined in wave

direction

+45° Inclined in wave

direction

Loading Case 3

SWL SWL SWL SWL SWL

Slamming Forces: Definition SketchSlamming Forces: Definition Sketch

time [s]

0,0 0,4 0,8 1,2 1.6

actualtotal force

Impact Force for Loading Case 3 Different Pile InclinationsImpact Force for Loading Case 3 Different Pile Inclinations

( )π λ η ρ= ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 21 2 'F R V

α [°]-45.0 -25.0 0.0 24.5 45.0

F1 [kN]

mittel

Loading Case 3

Breaking Wave Impact on Slender Structures (Video)Breaking Wave Impact on Slender Structures (Video)

Breaker Heights up to 3.25m generated!

HB ≈ 2.8m just in Front of Cylinder

Wave With Vertical Front at Cylinder and Splash GenerationWave With Vertical Front at Cylinder and Splash Generation

SplashSplash

wave crests

Wave withvertical front at

cylinder

Breaking Wave Impact as a Radiation ProcessBreaking Wave Impact as a Radiation Process

Breakingwave at cylinder

Splash

wave crests

(a) Side View (b) Front View

Splash

SWL SWL

Theoretical 3D-Model for Impact ForceTheoretical 3D-Model for Impact Force

F = FD + FM + FI

MorisonForce

Impact Force

For time: t = 0 : ÷1 R8 V cos γ

γ γ−

⎡ ⎤⎛ ⎞ ⎛ ⎞= ρ η γ π −⎢ ⎥⎜ ⎟ ⎜ ⎟

⎢ ⎥⎝ ⎠ ⎝λ

⎠⎣ ⎦l b

V cos 1 V cost 1 t

R 4 RF Rv² cos² 2 2 arctanh

For time t´ = , with t´ = t - :3 R32 V cos γ

÷ 12 R32 V cos γ

1 R32 V cos γ

−⎡ ⎤γ γ γ γ⎛ ⎞⎢ ⎥= ρ η γ π −λ −⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

1 V cos 8 V cos V cos V cosF Rv² cos² t́ t́ arctanh 1 t́ 6 t́

6 R 3 R R R

Duration TD of Impact Force FI

32 V cos, mit C(TD) = R

Wienke, J; Oumeraci, H (2005): Breaking wave impact on a vertical and inclined slender pile –theoretical and large-scale model investigation. Coastal Engineering. Elsevier vol. 52 pp 435-462.

• Adopted in ISO/CD 21650 “Actions from wave and currents” (in print)

• Adopted in New German Lloyd Guidelines (2005)

λ = 0.46 für α = 0

„Curling Factor“ for Vertical and Inclined Cylinder„Curling Factor“ for Vertical and Inclined Cylinder

λ . ηb

Impact area

VVγg.t α

( )CV cos

cos⊥ = ⋅ α − ββ

β für α = -45° bis +45°und β ≈ -45°

( )coscos

α − βλ =

Time Dependent Slamming Coefficient (Wienke and Oumeraci, 2005)Time Dependent Slamming Coefficient (Wienke and Oumeraci, 2005)

Wagner (1932)

Von Karman (1929)

Wienke (2001)

Campbell & Weynberg(1979)

Campbell et al. (1977)Cointe (1989)

Goda et al. (1966)

Fabula(1957)

2.3 Breaking Wave Impact Load on Single Pile in Shallow Water

References:

• Irschik, K. (2007): Impact loading of slender pile structures induced by depth limited breaking waves, PhD-Thesis, TU Braunschweig (in German)

Breaking Wave Loads (Slamming Coefficient Approach)Breaking Wave Loads (Slamming Coefficient Approach)

= ρ Δ'T o t wD

2C z ) u u

− ≈D,non breakingwith C 0,7= ≈ ≈b b

For shallow water :

u c gh gH

2bu u u gH= =

Hb Δ = =Dz Impact height of f f(Breaktype) :

bz HΔ ≈

≈ ρ ⋅ ⋅ ⋅ 2Tot w bF 0,88 g D H

≈D, breakingC 1,75

−≈'D,breaking D non breakingC 2,5(C )

(FM≈0 ⇒ FTot≈ FD)

Problem: Response characteristics of structure not considered.

Quasi-Static Force and Impact ForcesQuasi-Static Force and Impact Forces

( )= + +D M IF F F F

Non-breaking wave:

• quasi-static force

MD FFF +=MORISON equation

Breaking wave:

• quasi-static + impact force

λ . ηb

Cs: slamming coefficient

λ: curling factor

= ⋅ ⋅ ⋅ ⋅ ⋅⋅2 2cosI s bF R V C λ ηρ α

Curling Factor for Depth Limited Wave BreakingCurling Factor for Depth Limited Wave Breaking

( )α⋅η⋅λ⋅⋅⋅⋅ρ=

cosCVRF

Non-breaking wave:

• quasi-static force

MD FFF +=MORISON equation

Breaking wave:

• quasi-static + impact force

λ . ηb

Cs: slamming coefficient

λ: curling factor

Estimation of curling factor λ for depth limited breaking waves

PhD-Thesis of Mr. IRSCHIK to be completed in Summer 2007

Model Set-up in GWK (1)Model Set-up in GWK (1)

5 inclinations of test cylindera = -45°/-22,5°/0°/22.5°/45°

Model Set-up in GWK (2)Model Set-up in GWK (2)

Flume wall:

• current meters (8)propeller probes (4)Acoustic Doppler Velocimeters (ADV) (4)

• wave gauges (20)

Test cylinder:

• five inclinationsα = -45°/-22,5°/0°/22.5°/45°

• force transducers -strain gauges- (8)top and bottom bearinginline and transverse

• pressure transducers (16)front-line

• wave gauges (4)

Wave Conditions Tested in GWKWave Conditions Tested in GWK

GWK-Datax= 201m GWK-Data

x= 201m

Breaker TypeBreaker Type

Example 1: T = 4s (Plunging Breaker)

Example 2: T = 8s (Collapsing Breaker)

collapsing breaker

breaker tongue at SWL

very small air gap

breaker tilt angle >45°

plunging breaker plunging breaker

breaker tongue at top

air gap

breaker tilt angle 30-45°

collapsing breaker

Breaker Tilt AngleBreaker Tilt Angle

Breaker Tilt AnglesBreaker Tilt Angles

collapsing breaker

breaker tongue at SWL

very small air gap

breaker tilt angle >45°

plunging breaker

breaker tongue at top

air gap

breaker tilt angle 30-45°

Breaking Wave Loads in Shallow WaterBreaking Wave Loads in Shallow Water

Normalized Max Total ForceNormalized Max Total Force

F tot/ρ

-8 -6 -4 -2 0 2 4distance xb-xcyl [m]

quasi-static load (constant)

Time Dependentimpact force

(highly variable)

3D model of Wienke(2001)

Morison equation

x = xb = Breaking Point Location:

Curling FactorsCurling Factors

Curling factor

CR)t(C

η⋅⋅⋅⋅ρ=λ 2

-6 -4 -2 0 2 4distance xb-xcyl [m]

Wiegel (1982)

The time history of the impact can be estimated using the same curling factors for both plunging and collapsing breakers

areaimpactofheightη

Impact Force: Curling Factor lImpact Force: Curling Factor l

Estimation of curling factor λ for maximum loading caseCu

Impact Force: Curling Factor lImpact Force: Curling Factor l

Comparison with Goda et al. (1966), Wiegel (1982) and Wienke (2001)Wienke (2001): transient wave packets on horizontal bottom – “freak waves”

Mean of 10% highest values.

ng –

Wienke (2001)loading case 3(most critical)

Wienke, J (2001): Impact loading of slender pile structures induced by breaking waves in deeper water, PhD-Thesis, Leichtweiss-Institute, TU Braunschweig (in German)

Irschik, K. (2007): Impact loading of slender pile structures induced by depth limited breaking waves, PhD-Thesis, TU Braunschweig (in German)

2.4 Effect of Neighbouring Piles on Wave Loading of Slender Pile

References:

• Sparboom, U; Hidelbrandt, A; Oumeraci, H. (2006): Group interaction effects of slender cylinders under wave attack. Proc. ICCE´06

Measuring Cylinder in GWKMeasuring Cylinder in GWK

Model set-up in theLarge Wave ChannelCROSS - SECTION

SWL+4.26m

0.00 m

+2.40m

Support structure

Wave gauges

Straingauges

MeasuringcylinderD = 0.324m

Currentmeters

Measuring Cylinders and Locations of Neighbouring CylindersMeasuring Cylinders and Locations of Neighbouring Cylinders

Model set-up in theLarge Wave ChannelPLAN VIEW

Wave gauges

107.29 m

106.64 m

105.99 m

104.69 m

104.04 m

103.39 m

102.74 m

102.09 m

105.34 m

Location in front of the wavemaker

Currentmeters

Video control

Measuring cylinder

Cylinder Group Configurations TestedCylinder Group Configurations Tested

Measuring cylinder

Neighbouring cylinder

D = Cylinder diameter

c = Incident wave direction

15 Investigated cylinder group configurations

see paper Sparboom, U.; Hildebrandt, A.; Oumeraci, H in Proc. ICCE ´06

Loading Cases for the Selected Cylinder Group Configurations (1)Loading Cases for the Selected Cylinder Group Configurations (1)

Loading case 1

waves waves

wavesCylinder configur-ations D

Loading case 2

Loading case 3

Loading Cases for the Selected Cylinder Group Configurations (2)Loading Cases for the Selected Cylinder Group Configurations (2)

Loading case 5

waves waves

wavesCylinder configur-ations D

Loading case 4

Tested Wave ConditionsTested Wave Conditions

Water Depthd = 4.26 m

(a) Regular Non-Breaking Waves

(b) Irregular Non-Breaking Waves(JONSWAP)

(c) Breaking Waves(Gaussian Wave packets)

Water Depthd = 4.26 m

Instrumented Cylinder with Two Lateral Cylinders (Video)Instrumented Cylinder with Two Lateral Cylinders (Video)

Instrumented Cylinder

3D 3DD

Surface elevation and wave height development in thenear field of a single isolated cylinder for loading cases 1-5Surface elevation and wave height development in thenear field of a single isolated cylinder for loading cases 1-5

00,511,52t [s]

η [m]

loading case 1 loading case 2

loading case 3loading case 4

loading case 5

5 6 7 8 9 10 11 12 13

0 1.3 m1.3 m 2.6 m2.6 m

wave gauge location

(a) Locations of wave gauges and cylinder

(b) Surface elevation above SWL

(c) Wave development in front and behind the cylinder

Bending moments and surface elevation for isolated single cylinderBending moments and surface elevation for isolated single cylinder

My (t)

η (t) : surface elevation at cylinder location

Mx (t)

Mr (t)

Mx= Moment in longitudinal directionMy= Moment in transverse directionMr= Resulting MomentΔt= Phase lag related to ηmax

Regular Waves: H = 1.4m; T = 4s

Measured wave kinematics with calculated accelerationsMeasured wave kinematics with calculated accelerations

u= horizontal Particle velocityv= vertical Particle velocity

η(t) u(t)

du/dtdv/dt

Bending moments and surface elevation for side-by-side arrangementBending moments and surface elevation for side-by-side arrangement

My (t)

η (t)

Mx (t) Mr (t)

Mx= Moment in longitudinalMy= Moment in transverse directionMr= Resulting MomentΔt= Phase lag related to ηmax

: surface elevation at cylinder location

Wave kinematics for side-by-side arrangementWave kinematics for side-by-side arrangement

u= horizontal Particle velocityv= vertical Particle velocity

du/dtdv/dt

η(t) u(t)

Reduction Amplification Factor for Loading Cases 1-5 Reduction Amplification Factor for Loading Cases 1-5

Configuration no.2 Configuration no.7 Configuration no.12

LC 1 0,50 1,19 1,11LC 2 0,62 1,27 1,04LC 3 0,59 1,24 1,05LC 4 0,64 1,31 1,11LC 5 0,78 1,17 0,92

Coefficient C =

Mgroup

Msingle

[ ] D D

Reduction Amplification

Factor

= group

sin gle

waves waves wavesD D

3. Wave Forces on Submerged Bodies

References:

• Recio, J.; Oumeraci, H. (2006): Geotextile Sand Containers for Coastal Structures – Hydraulic Stability Formulae and Experimental Determination of Drag, Inertia and Lift Coefficients. Progress Report LWI (1st Draft), December 2006

Sliding and Overturning StabilitySliding and Overturning Stability

+⎡ ⎤⎣ ⎦≥∂

Δ −∂

D L2c(overt.)

0.05C 1.25Cl u

u0.5 g 0.1Ct

Overturning Formula

+ μ⎡ ⎤⎣ ⎦≥∂

μΔ −∂

D L2c(sliding)

0.5C 2.5Cl u

Sliding Formula( )= μ −Resisting GSC liftF F F

Resisting Force:Weight of GSC-Lift Force-Buoyancy

Horizontal Sliding

Mobilising force:Drag + Inertia force

Resisting Force

∂+ = ρ + ρ

D M w D s M w

uF F 0.5 u C A C V

Resisting Moment

Mobilising force:Drag + Inertia force

Mobilising Moment >=Resisting Moment

≥ + +c c c cGSC D M L

l l l lF F F F

2 10 10 2Mobilising Moment:(Drag force + Inertia force) x

lc/10:

+c cD M

l lF F

10 10 cl10

Rotation Point 0

a) Overturning Stability

a) Sliding Stability b) Analysed condition

b) Analysed condition

Empirical Coefficients (CD, CM and CL) needed

Tested Configurations (1)Tested Configurations (1)

Reynolds Numbers and KC Numbers for Tested ConditionsReynolds Numbers and KC Numbers for Tested Conditions

Comparison Aceleration Data-Linear TheoryComparison Aceleration Data-Linear Theory

Comparison with COBRAS-ComputationsComparison with COBRAS-Computations

Horizontal Forces

Time [s]

z= 0.13m

Calc. CobrasMeasured

Difference within12%

0 10 20 30

Drag DominanceDrag Dominance

Horizontal Velocity

Horizontal Force

Maximum Solitary Wave Generated in LWI-Twin Wave FlumeMaximum Solitary Wave Generated in LWI-Twin Wave Flume

Comparison of Solitary Wave Shape Measured with CobrasComparison of Solitary Wave Shape Measured with Cobras

(a) Free Surface experiment (b) Free Surface Cobras

110 115

4. Wave Loads on Monolithic Breakwaters and Sea Walls

4.1 Wave Loads Classification

Parameter Map for Classification of Loading CasesParameter Map for Classification of Loading Cases

Oumeraci et al (2001):Prohabilistic Design of Vertical Breakwaters. Balkema, Amsterdam 316 p.

α= = = = = +

hh B FH eq* * * * *b s bhwith h ; H ; B ; F and B Bs eqb h b2h h L 2tanρ g Hs s h bs

*sH35.0 <

Large wave

6.0*sH2.0 <<

Large wave

6.0*sH2.0 <<

Large wave

2.0*sH1.0 <<

Small wave

35.0*sH <

Small wave

6.0*sH >

Very large wave

2.0*sH1.0 <<

Small wave

0.1 0.20.0

4.0 Fhmax F hq

0.1 0.20.0

4.0 F hmax Fhq

2. Slightly breaking wave 4. Broken waves

0.2 0.40.0

4.0Fhmax F hq

1. Quasi-standing wave

(quasi-static analysis) (quasi-static analysis) (dynamic analysis) (quasi-static dynamic/analysis)

max,hF≈ 5.2

max,hF0.1 <<

0.1 0.20.0

max,hF>

t/T t/T

3. Impact loads

B08.0 <<

Narrow berm

B12.0 <<

Moderate berm

Wide berm

Composite breakwater

SWL SWL

Moderate mound

0.6 < hb < 0.9*

Low mound

0.3 < hb < 0.6*

Vertical breakwater

hb < 0.3*

Crown wall of rubble-mound breakwater

hb > 1.0*

High mound

0.9 < hb < 1.0*

Characteristics of Pulsating and Impact Wave LoadsCharacteristics of Pulsating and Impact Wave Loads

a) quasi-static load (pulsating)

2h hF F / gH= ρ

uFTN= natural period of

structure oscillation

h,maxF

d dt t / T=

h,maxP

u,maxP h,max

0,5g H

≈ρ ⋅ ⋅

b) Impact load

2h h bF F / gH= ρ

h,maxP

u,maxP

F 2,5 bis 15

t 0,01 bis 0,001

T= Wave period

P2 bis 50

≈ρ ⋅ ⋅

d dt t / T=

h,maxF

(*) Figures represent only order of magnitude

4.2 Breaking Wave Loads

Breaking Wave Loading of Caisson Breakwaters in GWKBreaking Wave Loading of Caisson Breakwaters in GWK

VerticalBreakwater

Breaking Wave Loads and Splash in GWK (Video)Breaking Wave Loads and Splash in GWK (Video)

Breaking Wave LoadsBreaking Wave Loads

Slightly breaking waves(pulsating load!)

Strongly breaking waves(impact load)

h,maxFh,maxF

2h bF / gHρ 2

h bF / gHρ

t / Th,max

F1,0 2,5

F= ÷ h,max

GODA-Formulae(static stability analysis)

T = Wave period

PROVERBS-Approach(dynamic stability analysis)

Simplified Force Time HistorySimplified Force Time History

t rFh t

F h,max

rFhI rFhIdFhI

F (t)h h

Actual load Idealised load

Fh,max

p3 = 0.45 p1

Fh (t)

Fh,max

SWL = Static Water Level

= 0.8HbR = freeboardc

Simplified Impact Pressure Distribution (Parameterization)Simplified Impact Pressure Distribution (Parameterization)

Calculation of Static Equivalent Wave Loads (1)Calculation of Static Equivalent Wave Loads (1)

( )h D h,maxstatF F= ν ⋅

Calculation of dynamic load factor νD by assuming a triangular load-time function:

with νD = dynamic load factor

For more details see Oumeraci, H. (2004): „Caisson breakwaters“ in Planning and Design of Ports and Marine Terminals, pp. 155-262 2nd Edition by H. Agerschou, Thomas Telford, London.

•Rise time of Impact force tr:

2A w s

t g H4F

π ⋅= ρ ⋅ ⋅ ⋅

• Total load duration td:

⎡ ⎤⎛ ⎞= ⋅ + ⋅ −⎢ ⎥⎜ ⎟⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

tt t 2.0 8 exp 18

or approximated by: ≈d At 2.5 t

h = Water depthdirectly at thewall

Tp = PeakPeriode

• Maximum Impact force Fh,max[kN/m]:

2h,max w bF 10 g H≈ ρ ⋅ ⋅ Hb = Breaker height(2)

⎡ ⎤ ⎡ ⎤⎛ ⎞ ⎛ ⎞⎢ ⎥ν = + π⎢ ⎥⎜ ⎟ ⎜ ⎟⎢ ⎥ ⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦⎣ ⎦

⎛ ⎞= ⎜ ⎟

⎝ ⎠

Dynamic load factor

t t1.4 tanh 0.25 2 c

twith c 0.55

h,maxF

Timetrtd

Calculation of static Equivalent Wave Loads (2)Calculation of static Equivalent Wave Loads (2)

stat,equ D dyn,maxF F= ν ⋅

d Nt / T −⎡ ⎤⎣ ⎦

orν D

relative Load Duration

K≈ π

Natural Period:

M=Mass, Ks= Stiffness

tA tEtd

⎡ ⎤ ⎡ ⎤⎛ ⎞ ⎛ ⎞ ⎛ ⎞⎢ ⎥ν = + π =⎢ ⎥⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎢ ⎥ ⎢ ⎥⎝ ⎠ ⎝ ⎠ ⎝ ⎠⎣ ⎦⎣ ⎦

0,55 0,63

d d dD

Dynamic load factor

t t t1.4 tanh 0.25 2 c with c 0.55

T T t(6)

Effect of Successive Breaking Wave LoadsEffect of Successive Breaking Wave Loads

(a) Horizontal breaking waveforce

(b) Accumulation of residual displacement

(c) Caisson displacements

horiz. Force Fh [kN/m]

Time [s]

Total horiz. Displacement of Structure [cm]

Time [s]

SAKATA-Habour (Japan)SAKATA-Habour (Japan)

hc=11.63m-3.43m

B=17.0m

-9.00m

±0.00

Storm surge (1973/74):Hmax: ≈10.0m (tD=0.6s)TP : 13.0s

Static Standard Approach: Dynamic calculation (tD=0.6s):

Caisson dimensions:Width: B=17.0mHeight : hc=11.63mLength: L=20.95m

ηS= Safety coefficient against sliding

ηS=1.2 ηS=0.50

Breaking Wave Impact on SAKATA BreakwaterBreaking Wave Impact on SAKATA Breakwater

Storm surge im Winter 73/74 ⇒ Hmax=10m, Tp=13s Credit: Dr. Takahashi, PARI

Sliding of Caisson in SAKATA-Harbour in the Storm Surge1973/74Sliding of Caisson in SAKATA-Harbour in the Storm Surge1973/74

B=17m; h=11-12m; L≈21m ⇒ Hs≈7m; T=13s

Although safety coefficient against sliding ηs=1.2 and against tilting ηov>5 according to static (Standard) approach.

Credit: Dr. Takahashi, PARI

Dynamic Stability Calculation of SAKATA BreakwaterDynamic Stability Calculation of SAKATA Breakwater

Impact load forHmax=10m, Tp=13s and d=3.43m

Adhesion and frictionforce

Horizontal displacementof Caisson: ca. 20mm/Impact event

Caisson-Length: L≈21m

HS= 6.9mTp= 13.0sd = 3.43m

hc=11.63m-3.43m d

B=17.0m

-9.00m

±0,00

Seaward Impact Loading Induced by Wave OvertoppingSeaward Impact Loading Induced by Wave Overtopping

Seaside

Uplift

Harbour side

Seaward impactpressure

Fh, sea

Overtopping plume

Entrapped air

Schüttrumpf, A. (2006): Uplift force on monolithic structures induced by breaking waves and under overtopping conditions – PhD-Thesis, TU Braunschweig (1st Draft)

Research Performed in PROVERBS for Wave Impact of VerticalStructuresResearch Performed in PROVERBS for Wave Impact of VerticalStructures

Parameter Mapfor classification of loading case

Berm heightand width

Water depth &wave conditions

at structure

IMPACT LOADING

Slamming on topslab Fv,2

outside Proverbs

Effect of waveovertopping

Seaward impactloads Fs,2

see Section 2.5.2

Vertical Loads(uplift)

New prediction methodswith following steps:

* pressure distribution

* correction of Ffor aeration

* force historyF = f (duration)

* statistical distributionof max. force (F )

Constructional Measures to Reduce Impact Forces

* Rubble as Damping Layer (Section 2.8.2)* Perforated Structures (Section 2.8.1)

* Unconventional Alternatives Related to Front Geometry (MCS-Project) and foundation (Section 3)

Horizontal Loads(shoreward)

New prediction methodswith following steps:

* pressure distribution

* correction of Ffor aeration

* force historyF = f (duration)

* statistical distributionof max. force (F )

(Oumeraci et al, 2001)

4.3 Scale Effects Associated with Breaking Wave Impacts

Physical Processes Involved in the Wave Load History and Associated scaling ProblemsPhysical Processes Involved in the Wave Load History and Associated scaling Problems

Time t

Compression of AirPocket

Impact of BreakerTongue

Oscillations of AirPocket

Escape of AirMaximal Run-up

FROUDE

FROUDE MACH-CAUCHY

AND FROUDE

MACH-CAUCHY

MACH-CAUCHYAND FROUDE

F = N Fh, nature h, modelLt = N tnature modelL

C FROUDE: α = 3 and α = 0.5C MACH-CAUCHY: α = 2 and α = 1.0

C ALTERNATIVE Scaling depending on air entrainment: α = 2 to 3 α = 0.5 to 1.0 t

(Oumeraci & Hewson, 1997)

Suggested Procedure for Scaling the Various Components of the Wave Load HistorySuggested Procedure for Scaling the Various Components of the Wave Load History

quasi-static compon

F (Froude)q

Time t

F (t) impact component governed by compressibility

governed by gravity

F (MACH- Cauchy)dyn

oscillatory component

F (Mach-Cauchy)osc

governed by compressibility

Cauchy: t rt di

t dt q

Froude:Cauchy - Froude:

Froude:

scaling of total force history:

F (t) =tot (F ) + (F ) + (F )dyn oscMACH-Cauchy

Froude[ ]

(Oumeraci et al, 2001)

Scale Effects in Modelling Breaking Wave Loading and Response of Sea DikesScale Effects in Modelling Breaking Wave Loading and Response of Sea Dikes

SurfaceCAUCHY

( REYNOLDS )

Breaker and Impact

WEBERREYNOLDSCAUCHY

Run-up and down

REYNOLDS( WEBER )

Bottom friction

REYNOLDSCore material

CAUCHY

WaveFROUDE

(after Führböter, 1986)

1:1 1:10 1:100

Gravity

Friction

Elasticity

SurfaceTension

FROUDE

REYNOLDS

CAUCHY

1 1:100

1:31.6

1:1000

1:10000

Force ScaleModelLaw

4.4 Broken Wave Loads on Sea Walls

(a) Seawall front landwardof shoreline

Broken Wave Loads: Load Cases According to SPM (1984)Broken Wave Loads: Load Cases According to SPM (1984)

(b) Seawall seawardof shoreline

SeawallFront of seawall

Beach slope

Shoreline

Virtual max. run-up

Front of seawallSeawall

Shoreline

Broken wave

Assumption According to CEM (2003)Assumption According to CEM (2003)

BH bH ´

(Breaking depth)

Beach slope 1:m

Bore height

Bore velocity

b bH ´ 0,78 H= ⋅

b b bv c g h= = ⋅

hH 0,2 0,58 H

h⎛ ⎞

= + ⋅ ⋅⎜ ⎟⎝ ⎠

w1 b bv c g h= = ⋅

RWS bH 0,2 H= ⋅

RWS b bv c g h= = ⋅

xH 0,2 H 1

x⎛ ⎞

= ⋅ −⎜ ⎟⎝ ⎠

2w2 b b

xv c g h 1

x⎛ ⎞

= = ⋅ ⋅ −⎜ ⎟⎝ ⎠

w1HSWLH

Linear decrease of bore heightmax. run-up

Av 0=A

( )A maxz

(shoreline)U

( )A A maxx z / tan= α

linear decrease of bore velocity from

at max. run-up

= ⋅ =SWL b Av g h to v 0

linear decrease of bore height

Seawall front seawards of shoreline

Seawall front landwards of shoreline

Breaker height

bc bc bc

(1) (2) (3) (4)

(5) (6) (7) (8)

Seawall Front Seawards of Shoreline: Wave Load FormulaeSeawall Front Seawards of Shoreline: Wave Load Formulae

Wave pressure

shorelineU

hH 0,2 0,58 H

h⎛ ⎞

= + ⋅ ⋅⎜ ⎟⎝ ⎠

2wo w1

1F g H ;

2= ⋅ ρ ⋅ ⋅

wu w1 wF g H h ;= ρ ⋅ ⋅ ⋅

= ρ ⋅

w w1p g H= ρ ⋅ ⋅

bv g h= ⋅

= ⋅SWL bH 0,2 H

hydrostatic pressure

stat w1p g h= ρ ⋅ ⋅ w w1p g H= ρ ⋅ ⋅

hb = Breaking depth

Hb = Breaker height for water depth hb

Force Components:

stau b w11

F g h H2

= ⋅ ρ ⋅ ⋅ ⋅

2stat w1

1F g H

2= ⋅ ρ ⋅ ⋅

Seawall front landwards of shoreline: Wave Loads FormulaeSeawall front landwards of shoreline: Wave Loads Formulae

(maximum run-up)A

2= ρ ⋅

w w2p g H= ρ ⋅ ⋅

xv g h 1

x⎛ ⎞

= ⋅ ⋅ −⎜ ⎟⎝ ⎠

= ⋅SWL bH 0,2 H

U (shoreline)2xα

xH 0,2 H 1

x⎛ ⎞

= ⋅ ⋅ −⎜ ⎟⎝ ⎠

HSWL = Bore height at shoreline Hw2 = Bore height at wall

2wo w2

1F g H

2= ⋅ ρ ⋅ ⋅

2stau b w2

x1F g h H 1

2 x⎛ ⎞

= ⋅ ρ ⋅ ⋅ ⋅ ⋅ −⎜ ⎟⎝ ⎠

A Ax z / tan= α

zA= max. wave run-upSee also PhD-Thesis RAMSDEN (Caltech).

4.5 Wave Force Reduction by Armouring (Tests Performed in Large Wave

Flume)

Wave Force Reduction by ArmouringWave Force Reduction by Armouring

Caisson

B bottom

Sandd sand

DWL Rc

B crownTetrapodlayer

1 Definition of parameters:• DWL = design water level• Bcrown = crest width (larger than two armour blocks)• m = cot α = 1.35 to 1.50• Rc = freeboard• Lhs = wave length for depth hs at toe• b0 = width of dissipating mound at height of DWL

+bottom crown

0 crown ss c

B Bb B h

Damping of Pulsating Wave Loads by ArmouringDamping of Pulsating Wave Loads by Armouring

0 0.5 1 1.5 2 2.5 3 3.5 4

Time t [s]

without dissipating mound

(μD,h)max

(Fh)max = 1.2

(Fh)max = 0.6

0 0.5 1 1.5 2 2.5 3 3.5 4

Time t [s]

with dissipating mound

(Fu)max = 0.9

(Fu)max = 0.5

(μD,u)max

μD,h=Fh -Fh,D

μD,u=Fu -Fu,D

(Oumeraci, 2004)

≈ 50%

≈ 40%

Damping of Pulsating Wave Loads by ArmouringDamping of Pulsating Wave Loads by Armouring

30 0.5 1 1.5 2 2.5 4

Time t [s]

3.53.53.5

Fh max( )

μ D,h =Fh -F h,D

Fh max( )

(μD,h)max

0 0.5 1 1.5 2 2.5 3 3.5 4

Time t [s]

(μD,u)max

(Fu)max = 2.6

(Fu)max = 0.7

μD,u=Fu -Fu,D

(Oumeraci, 2004)

≈ 80%≈ 60%

with dissipating mound with dissipating mound

4.6 Stability of Structure Foundation Under Extreme Wave Loads

Main Modes of Vertical Breakwater FailureMain Modes of Vertical Breakwater Failure

OVERALL FAILURE MODES

a) Sliding b) Overturning

c) Settlement followed by slipfailure and seaward tilt

d) Settlement followed by slipfailure and shoreward tilt

SWL SWL

SWLSWL

F vμ (W' - F )v

LOCAL FAILURE MODES

f) Punching failure at seaward andshoreward edges

e) Erosion beneath seaward andshoreward edges

g) Seabed scour and toe erosion

SWLSWL

Erosion ofrubble mound toeScour hole

Wave Induced Dynamic Process in Foundation of Coastal StructuresWave Induced Dynamic Process in Foundation of Coastal Structures

Measuring Devices:

0.00 m Flume Bottom

2.45 m

3.45 m

7.00 m Wave Flume (Top Level)

4.05 m SWL

3.30 m

2.50 m

7.20 m

Sand D50 = 0.21 mm

Impermeable Sheets

CaissonwithSandfill

Sand D50 = 0.35 mm

Separation Wall (Sandbags)

HS, TP

4.05 m SWL

Sand BermD50 = 0.35 mm

Bedding layer 0.2 mSand layer 2.45 m

Pressure1

Wave GaugesInductive Displacement

Meters

Pore Water Pressure2

2 2 2 2 2 2 2

2 2 2 2

Pore Water Pressure + Total Stress (isotropic)3

3 3Electrical ConductivityMeasurement

Caisson Breakwater Construction in GWKCaisson Breakwater Construction in GWK

Loading cycles [-]

d v,b [

Processes Leading to Partial Soil LiquefactionProcesses Leading to Partial Soil Liquefaction

Regular waves: H=0.9m, T=6.5s, hs=1.6m

(d)Residual pore pressure (P36)

(e)Residual deformation (vertical)

0S ≈ 373 cycles

692Number of wave load cycles [-]

Mean Value Mt,max ≈ 210 kNm/m

(c)Transient pore pressure (P36)

(b)Transient motions of theshoreward caisson edge

(a)Total moment around caisson heel

Wave-Induced Pore Pressure and Soil Deformation BenesthStructures (Soil Liquefaction)Wave-Induced Pore Pressure and Soil Deformation BenesthStructures (Soil Liquefaction)

Regular waves with H=0.7m, T=6.5s, hs=1.6m

Δdv,b=0.3 mm

(a) Vertical caisson motion dv,b (t)

Residual

Transient

100 200 300 400 500 600 700 800 900 1000Time [ s ]

(b) Pore pressure response u(t) under the shoreward edge of the caisson (P36)

Δur=0.2 kPaZoom

Residual

Transient

Residual pore pressure

Transient pore pressure

S≈54 cycles

-2.0 -1.5 -1.0 -0.5 0.0Downward motion

amplitude dv,b [mm]

Dr≈0.31Dr≈0.31Dr≈0.35Dr≈0.35Dr≈0.40Dr≈0.40

Residual Pore Pressure vs. Caisson MotionsResidual Pore Pressure vs. Caisson Motions

(dv,b)crit= -0.3mm

PulsatingLoad

ImpactLoad

Dr ≈ 0.31

Dr ≈ 0.35

Dr ≈ 0.40

dv,bhs

Thank you for your attention!

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