Wave Impact Loads

COPEDEC VI, 2003, Colombo, Sri Lanka

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NEW GUIDANCE FOR WAVE FORCES ON JETTIES IN EXPOSEDLOCATIONS

byby K.J. McConnell1, N.W.H. Allsop2, G. Cuomo3 and I.C. Cruickshank4

1 INTRODUCTION1.1 BackgroundTrade activities of coastal nations rely on jetties for berthing of vessels for the loading and dischargeof cargo. Traditionally, these facilities were constructed in sheltered locations or sheltered bybreakwaters hence hydraulic loadings were relatively small.

In recent years there has been increased demand for development of large single use industrialterminals (especially those for Liquid Natural Gas (LNG), and Liquid Petroleum Gas (LPG)) whichrequire deep water and sheltered berths for larger vessels, but do not necessarily need shelter to theapproach trestles carrying the delivery lines. These terminals are often required in remote locationswhere there is no wave shelter, no existing infrastructure and the construction of new protectivebreakwaters for the whole facility may not be cost effective. Therefore, in many instances the jettiesand/or their approach trestles are being constructed in exposed locations without breakwaterprotection. Views of a typical jetty approach trestle are shown in Figures 1 and 2.

Figure 1: Typical exposed jetty

1 Senior Engineer, HR Wallingford, Howbery Park, Wallingford, Oxon, UK, OX10 8BA, Tel:+44 (0)1491 822304, Fax: +44 (0)1491 832233, Email: [email protected]

2 Technical Director, Coastal Structures, HR Wallingford, UK & Visiting Professor, University ofSouthampton

3 Marie Curie Visiting Research Fellow, University of Rome 3, c/o HR Wallingford, UK4 Principal Engineer & Project Manager, HR Wallingford, UK


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Figure 2: Typical approach trestle

Other examples of exposed jetties include small jetties on open coasts in tropical regions servingsmall fishing communities, ferry services and emergency access to remote locations. For most of theirdesign life, the environmental conditions may be benign but occasionally cyclone and hurricaneconditions hit, putting the exposed jetty under significant hydraulic loading.

1.2 Wave loadingsOf particular concern in these locations is the risk of occurrence of wave forces on the jettysuperstructure and the likely magnitude of such forces should they occur. As well as being importantfor the design of structure elements, these loads need to be considered when assessing the potentialfor damage to equipment located on approach trestles and jetty heads. There are also potentialenvironmental risks arising from damage to exposed jetty facilities, particularly those carrying oil orother hazardous materials.

Existing guidance on such loadings mainly derives from the offshore industry. In this field anapproach termed the 'air gap' approach is generally adopted for platform design. Following thisapproach, the maximum wave crest elevation is predicted for the design condition and the deck (orsoffit) level is located at an allowance or 'air gap' above this elevation to ensure a low probability ofoccurrence of wave forces on the superstructure.

The 'air gap' approach is often adopted in the design of shore connected trestles and jetties, howeverthe design of structures in this environment may be dictated by other constraints which prevent theadoption of this method. Constraints may include vessel freeboard at berth, the need for loading /offloading and tidal range, all of which dictate practical deck levels to ensure efficient operations. Inaddition there may be considerations such as material costs, member sizes and constructionmethodology.

In such cases there may be a risk of wave loads on the structure. Methods available to the designerfor prediction of the forces are limited, complex to apply and practical guidance for their use is notreadily available.


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1.3 The "exposed jetties" research projectIn response to the demand for design guidance for predicting wave forces on jetties, a researchproject entitled 'hydraulic design of exposed jetties' was undertaken at HR Wallingford funded by theUK government. The project was guided by a Project Steering Group from industry, includingdesigners, contractors and owners. These research studies reviewed existing knowledge andundertook a new series of model tests to evaluate loads on deck elements and provide new guidancethat could be readily applied by the design engineer.

For the purposes of the project, an exposed jetty was defined as:

"A solid vertical or open piled structure, possibly with cross-bracing, providing a berth or berthsconstructed in a location where wave forces have a significant influence on the design"

"These structures can be remote from the land in deep water (where the influence of shallow water issmall) or in exposed locations such as marginal quays (where the influence of shallow water impactsare more significant)"

2 MODEL TESTS2.1 Model set-up and test conditionsFollowing a review of available literature and methods for prediction of wave forces, a series of modeltests were designed. The tests are described in more detail in Tirindelli et al (2002).

The model test section comprised a typical jetty head on cylindrical piles constructed fromdownstanding cross-beams and a solid deck, contructed at a scale equivalent to 1:25. The modeldesign was developed in consultation with the Project Steering Group to ensure that it wasrepresentative of typical real structures, such as the jetty head shown in Figure 3.

Figure 3: Typical jetty head (courtesy Kier)


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Figure 4: Physical model in wave flume

The model was located in a 2-dimensional wave flume capable of generating random waves, Figure 4.Within the superstucture of the model, two beam and two deck elements were fitted with forcetransducers, see Figure 5, which recorded force measurements at a sampling frequency of 200Hz.

During testing it was clear that there could be strong 3-dimensional flow effects around the structure,particularly as the structure deck was inundated. As a result, an additional series of tests wascompleted with panels fixed to each side of the deck to prevent 3-dimensional inundation of thestructure. This provided data for the 2-d scenario which allowed 3-d effects to be quantified and alsoprovided a scenario that was more comparable with some of the prediction methods available whichconcentrated on 2-d scenarios. In addition, a third test series was undertaken with the decksuperstructure inverted such that the underside was a flat deck. This configuration did not includeside panels. Thus three configurations were tested as follows:

• Configuration 1 - deck with downstand beams• Configuration 2 - flat deck• Configuration 3 - deck with downstand beams (as for configuration 1) with side panels to limit 3-d

flow effects.

The test programme covered a range of wave conditions and relative water and deck levels,summarised in Table 1.

Parameter Model Prototype (at 1:25)Hs (m) 0.1 - 0.22 2.5 - 5.5Tm (s) 1 - 3 5 - 15Water depth, h (m) 0.75, 0.6*** 18.75, 15***

Clearance, cl (m)0.06 - 0.16*0.01 - 0.11**

1.5 - 4*0.25 - 2.75*

Wave height to clearance ratio, Hs/cl 1.1 ñ 18Wave height to water depth ratio, Hs/h 0.13 ñ 0.33Relative water depth, h/Lm 0.1 0.48Sampling frequency (Hz) 200 40Notes: * Configurations 1 & 3, ** Configuration 2, *** Configuration 3 only

Table 1: Range of test conditions


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B1 B2D1 D2

Waves

CB1

LB1

CB2 CB3 CB4 CB5

LB2

LB3

LB4

LEGEND

CB = CrossBeams

LB =LongitudinalBeams

B = BeamElements

D = Deck Slabs

A B C D = ForceTransducers

A B C D

Down-standing crossbeams(1.50 x 1.50 x 25.00)(60 x 60 x 1000)

6.50 / 260

Down-standinglongitudinal beams(2.50 x 2.50 x 27.50)(100 x 100 x 1100)

Deck slab

Slender element(1.50 x 1.50 x 5.00)(60 x 60 x 200)

7.50 / 300

27.50 / 1100

Deck element(0.5 x 5.00 x 5.00)(20 x 200 x 200)

25.001000

dia = 2.50 / 50

7.50 / 300

7.50 / 300

6.50 / 260 6.50 / 260 6.50 / 260

Figure 5: Underside of model deck showing measurement elements Note: dimensions given as prototype (model)

2.2 Preliminary analysisThe time series from the various force measurements were processed to extract a number of keyforce parameters. These were identified for each force 'event' which occurred as a wave hit thestructure. One such event is shown in Figure 6, which defines the various force parameters, definedas:

Fmax Impact force (short duration, high magnitude)

Fqs+, v or h Maximum positive (upward or landward) quasi-static (pulsating) force

Fqs-, v or h Maximum negative (downward or seaward) quasi-static (pulsating) force


6

-4

-2

0

2

4

6

8

76.5 77 77.5 78 78.5 79 79.5

Time (s)

Force (N)

Fqs-

Fqs+

Fmax

Figure 6: Definition of force parameters (model units)

The extracted force parameters were then processed to derive the force at 1/250 level for each test,that is the average of the highest 4 loads in 1000 waves. For most test conditions, many waves willhave generated loads, so F1/250 is relatively well supported. For a few tests however, there may berelatively fewer loads contributing to F1/250 defined in this way, and the measure may be less stable.All the results presented in this paper are based on F1/250.

Preliminary analysis of the results and comparison with predictive models is discussed in Tirindelli etal (2002). The results of the analysis demonstrated that methods available (eg. Kaplan (1992, 1995),Shih & Anastasiou (1992)) may underpredict wave forces on jetty components. An examplecomparison is shown in Figure 7 for seaward deck elements.

Figure 7: Comparison of measured and predicted uplift forces on jetty deck elements,after Tirindelli et al (2002) (model units)

3 RESULTS3.1 Discussion on presentation of resultsFollowing on from the analysis described in Tirindelli et al (2002), the data were processed andpresented in dimensionless format. A range of dimensionless parameters were considered for

0

10

20

30

40

50

60

70

80

0 0.05 0.1 0.15 0.2 0.25

Hs (m)

F 1/250 (N)

MeasuredKaplan


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presentation of the results, in order to provide some useful means of using the data for forceprediction.

Firstly a means of non-dimensionalising the forces was considered. From the perspective of thedesigner, it was considered that the force measurements might be most usefully be presented as afunction of a force value that can be easily calculated from design information. A notional or 'basicwave force' F* is therefore defined. F* is calculated based on the predicted maximum wave crestelevation, ηmax, whilst assuming no (water) pressure on the reverse side of the element. F* iscalculated separately for vertical and horizontal forces. F*v is defined by a simplified pressuredistribution using hydrostatic pressures, p1 and p2, at the top and bottom of the particular elementbeing considered. F*h is calculated assuming a uniform pressure p2 over the base of the element. F*vand F*h are defined in Figure 8, and can be calculated as follows:

22* pbbdApF lw

b bv

w l

⋅⋅≅⋅= ∫ ∫ (1)

( )22

max*

max pcbdApF lw

bc

hydhw

l

⋅−⋅=⋅= ∫ ∫ ηη

for hl bc +≤maxη (2)

( )2

21* ppbbdApF hw

b

bc

chydh

w

hl

l

+⋅⋅=⋅= ∫ ∫

+

for hl bc +>maxη (3)

where

p1 = [ηmax ñ (bh+cl)]·ρg (4)

p2 = (ηmax ñ cl)·ρg (5)

and

p1, p2 pressures at top and bottom of the elementbw element width (perpendicular to direction of wave attack)bh element depthbl element length (in direction of wave attack)cl clearance (distance between soffit level and still water level, SWL)ηmax maximum wave crest elevation (relative to SWL).

Figure 8: Definition of 'basic wave forces' F*v and F*h

In order to derive the maximum wave crest elevation, ηmax, the maximum wave height, Hmax, must becalculated. A method is given by Goda (1985) for a range of conditions and by Battjes & Groenendijk(2000) for shallow foreshores. The maximum wave crest elevation, ηmax, can then be calculated fromHmax using various non-linear wave theories. In deep water, a simple approximation for ηmax is given


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by Stansberg (1991). This gave good agreement with Stream Function Theory and Fenton's Fouriertheory for the range of conditions tested, however for shallower water depths the more sophisticatedapproaches should be used.

The dimensionless forces, Fqs/F*, are presented against the dimensionless parameter (ηmaxñcl)/Hs,which describes the incident wave conditions and geometry. When written as (ηmax/Hs)ñ(cl/Hs) thisparameter describes the relative elevation of the wave crest (ηmax/Hs), often between 1.0 and 1.3, thenthe relative excess of the wave over the clearance (cl/Hs). Over the test range, relatively little effect ofeither wave steepness or relative depth was detected in these data, although that conclusion may bespecific to the relative size of the test elements considered.

The following forces were analysed and are discussed in this paper:

• vertical upward acting force, Fvqs+ caused by slam on the underside of the deck or beam• vertical downward acting force, Fvqs- caused by inundation of the deck or beam, which can

persist after the wave has passed beneath the structure• horizontal landward force, Fhqs+ caused by the wave front hitting the beam• horizontal landward force, Fhqs- caused by the wave hitting the back of the beam, most

likely due to the wave being trapped by the decksubstructure

It should be noted that the discussion in this paper concentrates on slowly-varying or quasi-staticforces (Fqs). Shorter duration impact forces, Fmax, as defined in Figure 6, were also processed and arediscussed briefly in this paper. Further discussion of these results will be given in Cuomo et al (2003).

In some cases forces experienced by the outer, seaward measurement elements differed to thoseexperienced by the internal elements, which were influenced by the deck configuration. In some casesbeams and deck elements showed significantly different behaviour and for some elements there was aclear influence of 3-dimensional effects. The influence of each of these factors was assessed and thedata sorted such the the influence of these parameters could be identified.


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3.2 Vertical quasi-static forcesVertical loads on the seaward beam and deck elements were found to be relatively unaffected by theconfiguration of the test structure, and were similar in magnitude for both element types. These cantherefore be considered together, see Figures 9 and 10 for upward and downward acting forcesrespectively. It is worth noting that the smooth deck tended to give lower element loads that the deckwith downstanding beams.

0

0.5

1

1.5

2

2.5

3

3.5

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

( ηmax - cl ) / Hs

F vqs+ / F* v

Seaward elements - downstandbeam configurationSeaward elements - flat deckconfiguration

Figure 9: Vertical (upward) forces on seaward elements

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8( ηmax - cl ) / Hs

F vqs- / F* v

Seaward elements - downstandbeam configuration

Seaward elements - flat deckconfiguration

Figure 10: Vertical (downward) forces on seaward elements

Conditions for the internal elements are more complex, with the deck and beam elements showingdifferent trends. The results for upward and downward loads on the internal deck element are shownin Figures 11 and 12 respectively. Upward loads were not obviously influenced by 3-d effects,however local 3-dimensional effects did significantly influence downward loads, resulting in largerloads than the simplified 2-d scenario.


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It is worth noting that the flat deck configuration also experienced lower downward forces, most likelydue to the fact that this configuration was represented simply by turning the deck over and theresulting upstanding beams will have blocked 3-dimensional flow effects over the measurementelement to some degree.

0

1

2

3

4

5

6

7

8

9

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

( ηmax - cl ) / Hs

F vqs+ / F* v

Internal deck

Figure 11: Vertical (upward) forces on internal deck

-2

-1.8

-1.6

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

( ηmax - cl ) / Hs

F vqs- / F* v

Internal deck - 3-d effectsInternal deck - 2-d effects

Figure 12: Vertical (downward) forces on internal deck


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Vertical wave forces on the internal beam are also complex, but the loss of some test data resulted ina less clear trend than that identified for the deck element. Upward and downward forces are shownin Figures 13 and 14, respectively.

0

0.5

1

1.5

2

2.5

3

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

( ηmax - cl ) / Hs

F vqs+ / F* v

Internal beam

Figure 13: Vertical (upward) forces on internal beam

-2.5

-2

-1.5

-1

-0.5

0

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

( ηmax - cl ) / Hs

F vqs- / F* v

Internal beam

Figure 14: Vertical (downward) forces on internal beam

Some general observations can be made for vertical forces for all of the test elements:

• For (ηmaxñcl)/Hs > 0.8, F*v seems to give a safe estimation of Fvqs+• For (ηmaxñcl)/Hs < 0.8, downward forces are usually less than respective upward loads• For (ηmaxñcl)/Hs < 1, upward and downward forces increase relative to F*v as (ηmaxñcl)/Hs

decreases• For (ηmaxñcl)/Hs < 1, relative forces show significant scatter.


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3.3 Horizontal quasi-static forcesFor horizontal forces on beams, seaward and internal beam elements are considered separately asthe loads on internal beams are influenced by the deck structure, while loads on the seaward beamare unaffected by the structure configuration. Positive forces, acting in the direction of wave attack i.e.landward, Fhqs+ are presented in Figures 15 and 16 for seaward and internal beams respectively,plotted against (ηmaxñcl)/Hs. The scatter for these data is much less than for vertical loads for almostall of the data, with scatter increasing for smaller values of (ηmaxñcl)/Hs.

0

2

4

6

8

10

12

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

( ηmax - cl ) / Hs

F hqs+ / F* h

Seaward beam

Figure 15:Horizontal (shoreward) forces on seaward beams

0

1

2

3

4

5

6

7

8

9

10

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

( ηmax - cl ) / Hs

F hqs+ / F* h

Internal beam

Figure 16: Horizontal (shoreward) forces on internal beams


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Seaward-acting (or negative) horizontal forces, Fhqs-, are shown in Figures 17 and 18 for seaward andinternal beams respectively. The following can be noted:

• For seaward elements, landward forces are generally greater than negative (seaward) ones, thedifference increasing with decreasing (ηmaxñcl)/Hs.

• For internal elements, landward and seaward forces are of similar magnitude.

-3

-2

-1

0

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

( ηmax - cl ) / Hs

F hqs-/ F*h

Seaward beam

Figure 17:Horizontal (seaward) forces on seaward beams

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

( ηmax - cl ) / Hs

F hqs- / F* h

Internal beam

Figure 18: Horizontal (seaward) forces on internal beam

3.4 Wave impact forcesShort duration impact forces on beam and deck elements were also measured in the tests. In order toassess the importance of impact forces, information is necessary on their duration and also thedynamic response characteristics for the structure in question. Wave impact forces are not discussedin detail here, but a comparison is given of vertical impact forces and quais-static impact forces for


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each test, where Fmax is the largest impact force recorded in a test and Fvqs+ is the quasi-static force at1/250 level. The results are presented in Figure 19 where it can be seen that none of the impactforces measured exceed their quasi-static components by more than 4 times. The magnitude ofimpacts that can be measured will be limited by the sampling frequency of the instrumentation used, inthis case 200Hz (at model scale), as the sampling rate may miss the actual peak of the impact. Fastersampling frequencies may well result in higher magnitude, shorter duration events being registered. Itshould also be noted that impact loads are very localised in nature and local pressures may be higherthan the average force acting on the element in question. It should also be noted that there was somesignal corruption induced by dynamic response of measurement instruments. Dynamic loads andresponses will be discussed further in Cuomo et al (2003).

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

(ηmax-cl) / Hs

F max / F vqs+

Seaward DeckInternal DeckSeaward BeamInternal Beam

Figure 19:Ratio of vertical impact forces to quasi-static forces

4 FORCE PREDICTIONThe various data sets from the model tests are presented in Figures 9 to 18 for both vertical andhorizontal quasi-static forces. Best fit regression lines fitted to each data set are shown by a solid lineon the graphs. The general form of the regression line is :

b

s

l*qs

H)c(η

aF

F

−=

max

(6)

where

Fqs quasi-static force of interest (Fvqs+, Fvqs-, Fhqs+ or Fhqs-)F* 'basic wave force', either F*v or F*h, delined in Equations (1) to (3)cl clearance (distance between soffit level and still water level, SWL)ηmax maximum wave crest elevation (relative to SWL)a,b coefficients

Coefficients a and b for the various configurations are given below in Table 2 for vertical forces and inTable 3 for horizontal forces.


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Wave load and configuration a b

Upward vertical forces (seaward beam & deck) 0.82 0.61

Upward vertical forces (internal beam only) 0.84 0.66

Upward vertical forces (internal deck, 2 and 3-d effects) 0.71 0.71

Downward vertical forces (seaward beam & deck) -0.54 0.91

Downward vertical forces (internal beam only) -0.35 1.12

Downward vertical forces (internal deck, 2-d effects) -0.12 0.85

Downward vertical forces (internal deck, 3-d effects) -0.80 0.34

Table 2: Coefficients for calculation of vertical wave forces using Equation 6

Wave load and configuration a b

Shoreward horizontal forces, Fhqs+ (seaward beam) 0.45 1.56

Shoreward horizontal forces, Fhqs+ (internal beam) 0.72 2.30

Seaward horizontal forces, Fhqs- (seaward beam) -0.20 1.09

Seaward horizontal forces, Fhqs- (internal beam) -0.14 2.82

Table 3: Coefficients for calculation of horizontal wave forces using Equation 6

There is a significant degree of scatter in the data in Figures 9 to 18 and upper and lower envelopeshave also been fitted to the data. The upper bounds can be calculated by applying a coefficient,Cupper, to Equation 6. Similarly lower bounds can be calculated by applying a coefficient, Clower.

It is generally considered that the best estimate obtained from Equation 6 will be sufficient for design,although for critical elements the upper bound estimate may be used. Uncertainty in wave loading willnormally be accounted for by applying safety factors during design. The lower bound is not likely to beused in deterministic design, although it may be useful for probabilistic calculations.

Coefficients for the upper and lower bounds are given in Tables 4 and 5 for vertical and horizontalforces respectively.

Wave load and configuration C upper C lower

Upward vertical forces (seaward beam & deck) 1.5 0.5

Upward vertical forces (internal beam only) 1.4 0.5

Upward vertical forces (internal deck, 2 and 3-d effects) 2.2 0.1

Downward vertical forces (seaward beam & deck) 1.6 0.4

Downward vertical forces (internal beam only) 1.8 0.5

Downward vertical forces (internal deck, 2-d effects) 2.1 -

Downward vertical forces (internal deck, 3-d effects) 1.4 0.65

Table 4: Coefficients for upper and lower limits of vertical force data


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Wave load and configuration C upper C lowerShoreward horizontal forces, Fhqs+ (seaward beam) 2 0.25

Shoreward horizontal forces, Fhqs+ (internal beam) 1.8 -

Seaward horizontal forces, Fhqs- (seaward beam) 2 0.15

Seaward horizontal forces, Fhqs- (internal beam) 3 -

Table 5: Coefficients for upper and lower limits of horizontal force data

5 APPLICATION TO CASE STUDIESThe methods described above have been applied to a number of case studies. These have includedjetty structures in relatively open water where exposure is high, and also structures within harbourswhich are exposed to wave induced forces as structure elevations are close to the still water level, dueto operational requirements.

5.1 Case study 1: Damage to under-slung servicesDescriptionThe method given in Section 4 was used to back-calculate wave forces on a jetty that hadexperienced damage during a storm event.

The jetty is located within a harbour. Despite being protected by breakwaters, it was exposed to fairlysevere waves during a storm. From descriptions of the storm and the reported overtopping of the jetty,it is estimated that the incident wave conditions were approximately Hs=2.5m, estimated as having areturn period in excess of 1:10 years. This was assumed to have a wave steepness of sm = 0.04,typical for storm waves. During the storm, services slung beneath the jetty were damaged and thepower supply to the end of the jetty failed.

This example addresses the partial failure of pipe fittings beneath the jetty deck. The pipes weresuspended by pipe hangers fitted to Halfen Channels cast into the soffit of the deck. During the storm,the hangers were pushed sideways in the channels.

The jetty is constructed from a concrete slab with longitudinal beams on tubular steel piles. Keyparameters are as follows:

Hs = 2.5mHmax = 4.3m, using Goda (1985)Tm = 7sMWL = +1.6mOD (MHWS)Deck level = +4.0mODSoffit level = +3.6mODTop of pipe = +3.2mODBottom of pipe = +3.0mOD

Assuming that the pipe can be considered as a beam, the following parameters are defined (seeFigure 8):

bl = 0.2m (pipe diameter)bh = 0.2 m (pipe diameter)bw assume 1m length (perpendicular to direction of wave attack)clearance, cl = 1.4m (bottom of pipe ñ MWL)ηmax = 3.2m (=+4.8mOD), using Fenton (1988)

Force calculationsIn order to assess the wave forces that occurred during the storm when the damaged occurred,horizontal forces on the pipe are calculated, treating it as a downstand beam. The 'basic horizontalwave force', F*h, is calculated using Equations (1) and (2) with the input pressures, p1 and p2calculated using equations (4) and (5):


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p1 = 16.2 kN/m2

p2 = 18.2 kN/m2

F*h = 3.4 kN/m

The horizontal forces on the pipe can then be calculated using Equation 6 and coefficients from Table3, assuming the pipe can be considered as an internal beam (a = 0.72, b=1.56, based on the data inFigure 16).

The following parameter is required:

(ηmax ñ cl)/Hs = 0.72

The horizontal quasi-static force on the pipe, acting in the direction of wave travel is thereforecalculated as:

Fhqs+ = 5.3kN/m

The pipe supports had a capacity of 40 kN/fixing for horizontal sliding. Each cast in channel was2.25m long and carried three pipes. Each support had two bolts giving a sliding capacity of 80 kN (2 x40kN). The supports are at 4m centres along the pipes. The weight of the pipe is taken as 0.3kN/m.

Maximum horizontal force per support is therefore:

Fhqs+ = 4m x 5.3kN/m = 21.2kN

The data for impact forces shown in Figure 19 demonstrates that short duration impact forces can beseveral times greater than quasi-static forces. Figure 19 is for vertical forces however analysis of themodel test data indicated that horizontal impact measurements showed similar relative orders ofmagnitude. Thus impact forces may be up to 4 times the quasi-static force. It is likely that lightcomponents such as pipework and fixings will respond to these short duration loadings and hence itcan be assumed that the pipe supports could experience forces in excess of 80kN. Thesecalculations demonstrate that the capacity of the fixings could have been exceeded by wave loadsduring the storm, causing damage.

The assumption that the pipe acts like a beam on the structure is a simplification as the gap betweenpipe and soffit will mean that there is also some flow over the pipe, constrained by the deck, whichmay increase the wave loading on the pipe and which will also provide additional forces on the fixings.

5.2 Case study 2: wave-induced forces on a pierDescriptionA new ferry terminal comprises a 200m long central pier, with pairs of dolphins on either sidesupporting vehicle access bridges and passenger access walkways. The central pier is designed tofunction as a wave absorbing structure to reduce wave reflections and transmission. The pier isessentially constructed as a concrete box divided into a series of chambers with large voids in thesides, located around the water line to provide energy dissipation. The box is supported on piles witha soffit level at +1.5m CD and a deck level of +12m CD. The tidal range at the terminal is 7m and seabed levels at the berth are around ñ9mCD.

The geometry of the structure and its secondary function to absorb wave energy prevented adoptionof an air-gap approach, by raising the structure above the maximum water level. Wave forces on thestructure therefore had to be considered. Loads on the structure during construction were of particularconcern, as the individual precast elements forming the pier box construction were lowered into place.Excess loading prior to fixing of these elements could lead to displacement of the units.

Wave-induced forces were assessed for the following components:

• Precast concrete units forming the soffit of the central pier• Vehicle access bridges

Wave conditionsThe new ferry terminal is located within a harbour and is relatively sheltered from storm waves. Thesite is however exposed to long period swell waves that propagate into the harbour.


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Wave measurements from a physical model study were available for points along the structure for arange of return periods up to 1:50 years. These were extrapolated to estimate conditions for moreextreme return periods.

In order to derive maximum wave crest elevations for use in wave force calculations, Hmax had to bedetermined. The maximum wave height, Hmax, was calculated as 1.8Hs, using the method of Goda(1985). The maximum wave crest elevation was then calculated for a range of conditions, usingFenton (1988).

Quasi-static force calculationsVertical uplift forces on the underside of the elements (at +1.5mCD) were of particular interest in thedesign of the pier. The underside of the precast elements was flat with no downstand beams. Clearlywith such a large tidal range there will be scenarios where the units are partially submerged. Themost critical case for vertical wave forces on the soffit elements was considered to be when the waterlevel was close to the level of the base of the units. As a result wave forces were calculated for waterlevels close to the soffit level, giving small clearance, cl, values.

Equation (1) was used to calculate the ëbasic wave forceí F*v, per metre area of the soffit elements.This was then used to calculate the quasi-static vertical wave forces using Equation (6), using thecoefficients for seaward beam and deck elements, based on the data shown in Figure 9. The resultsare summarised in Table 6. The 1:1 year conditions are of interest for the construction scenario. The1:50 and 1:500 year conditions are of interest for the permanent scenario and show the variation inwave forces with increasing wave height.

It should be noted that the Table includes results at +1.5mCD, the scenario where the water level is incontact with the underside of the deck, i.e. zero clearance. This is outside the range of conditionstested and therefore represents extrapolation beyond the region of validity. From the resultspresented this suggests increased forces where the water level is at or very close to the underside ofthe structure, as might be expected.

Wavecondition

return period

SWL Hs Tm Hmax ηmax (ηmax-cl)/Hs F*v Fvqs+

years mCD m s m m - kN/m2 kN/m2

+1mCD 1 9 1.8 1.05 0.53 5.6 6.61:1

+1.5mCD 1 9 1.8 1.03 1.05 10.4 8.4

+1mCD 1.36 10 2.45 1.53 0.76 10.2 101:50

+1.5mCD 1.36 10 2.45 1.51 1.13 15.5 11.8

+1mCD 1.57 11 2.82 1.86 0.87 13.7 12.31:100

+1.5mCD 1.57 11 2.82 1.83 1.18 18.5 13.8

Table 6: Case study 2 - summary of results

Comparison of the conditions shown in Table 6 with the model test results presented in Figure 9allows some assessment of the potential variability in wave forces. The data for the flat deck is alsopresented in Figure 9, generally giving lower forces that the equivalent tests for the downstand beamconfiguration. As the soffit elements do not have downstand elements it is likely that they will behavemore like the flat deck configuration and so the forces in Table 6 might be considered to be an upperlimit for vertical quasi-static forces on the structure.

Impact forcesImpact forces had to be assessed to check the risk of overall uplift of the relatively lightweight bridgeunits and soffit units during the construction scenario, before they were fixed in place. Determination ofan appropriate ratio of Fmax to Fqs+ was based on judgement of the importance of a structural member


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and its ability to respond globally to short-duration forces. Ratios in the range of 3 to 4 are plausible byinspection of Figure 19, suggesting short duration vertical impact forces on the lightweight elementsmay be up to 4 times greater than quasi-static vertical forces.

5.3 Case study: wave forces on a quay in the vicinity of reflective wallsDescriptionA ferry quay is located within a harbour, sheltered by a main breakwater. The quay deck level is at+3.5mCD and the soffit level is +2.5mCD. The local bed level is around ñ10mCD. It is consideredthat there is some risk of the deck of the quay experiencing wave forces under certain conditions.

Wave conditions at the quay are complicated by waves reflected from parts of the quay itself, so atsome points it is possible that incident and reflected waves may combine. For these calculations,some simplifying assumptions on the possible addition of wave energy were made, using assumedreflection coefficients, in the absence of more detailed site specific data.

The following extreme incident wave conditions were available from model studies:

Hs = 2.5mTp = 12s (assume Tm = 0.87 Tp = 10.4s)Hmax = 4.0m

In the vicinity of the quay, there are a combination of solid vertical wall and perforated chambersections which will have different reflection characteristics. The reflection performance of theperforated chamber sections will be very dependent on the wave period of the incident waveconditions, as these structures are generally tuned to give the reflection coefficients quoted aboveover only a narrow range of wave periods. They are normally tuned for short period, frequentlyoccurring wave conditions as these will be the conditions that affect day to day operations within theharbour. Thus reflection performance for longer wave periods will be poorer, tending towards that of asimple vertical wall. Assuming therefore that wave reflections in the vicinity of the quay are close to100%, an estimate of maximum wave height at the quay due to incident and reflected wave energycan be made by summing the energies of the two wave components. This calculation is made forboth Hs and Hmax, as follows:

Hs(i+r) = (Hs(i)2 + Hs(r)2)0.5 = (2.52 + 2.52)0.5 = 3.5m

Hmax(i+r) = (Hmax(i)2 + Hmax(r)2)0.5 = (42 + 42)0.5 = 5.7m

where

i denotes incident waver denotes reflected wavei+r denotes incident and reflected wave.

The first stage in estimating the occurrence of wave forces is to determine maximum wave crestelevation for the design wave condition, ηmax. Calculations are done for two water levels,LLW = 0.0mCD and HHW = +2.0mCD, using Fenton (1988) as for Case study 2.

LLW = 0.0mCD ηmax = 4.48mHHW = +2.0mCD ηmax = 4.2m

Vertical uplift wave forces on the quay deck can then be calculated following the same methodology ofCase study 2, using coefficients for exterior beam and deck from Table 2. The results aresummarised in Table 7.

SWL Hs(i+r) Tm Hmax(i+r) ηmax (ηmax-cl)/Hs F*v Fvqs+mCD m s m m - kN/m2 kN/m2

+0mCD 3.5 10.4 5.7 4.5 0.56 20.2 23.3

+2mCD 3.5 10.4 5.7 4.2 1.05 37.4 29.8

Table 7: Case study 3 - summary of results


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It is worth noting that there is significant inundation of the deck of the quay under these conditions(deck level at +3.5mCD). Inspection of Figures 9 and 10 show that downward inudation forces on thedeck can be close to the upward acting forces which act on the underside of deck and beam elements.

6 CONCLUSIONSThe paper has summarised model tests undertaken as part of a UK government research project toquantify wave forces on jetties in exposed locations. A method for prediction of wave forces on deckand beam elements is presented. A series of case study examples demonstrate application of themethod to real scenarios.

7 ACKNOWLEDGEMENTSModel tests and analysis described in this paper were undertaken by Matteo Tirindelli and GiovanniCuomo. The authors wish to acknowledge the following contributors to the research project: theIndustrial Steering Committee of DTI PII Project 39/5/130 cc2035 who provided practical guidance andcase study information as well as photographs acknowledged in the paper; Matteo Tirindelli and Prof.Alberto Lamberti University of Bologna; Prof. Leopoldo Franco, University of Rome 3; visitingresearchers Amjad-Mohammed Saleem and Oliver de Rooij.

Giovanni Cuomo's studentship was supported by EU Marie Curie Fellowship, HR Wallingford andUniversity of Rome 3.

8 REFERENCESBattjes J.A. & Groenendijk H.W. (2000) "Wave height distributions on shallow foreshores" CoastalEngineering Vol 40 pp161-182, Elsevier Science.

Cuomo G., Allsop N.W.H., McConnell K.J. (2003) "Dynamic wave loads on coastal structures: analysisof impulsive and pulsating wave loads" Proc. Conf. Coastal Structures 2003, ASCE / CPRI, Portland

Fenton J.D. (1988) "The numerical solution of steady water wave problems" Computers andGeosciences 14(3) 357-368, 1988.

Goda Y. (1985) "Random seas and maritime structures" University of Tokyo Press, Tokyo.

HR Wallingford (2003) "Wave loads on exposed jetties" Report SR583, August 2003.

Kaplan P. (1992) "Wave Impact Forces on Offshore Structures: Re-examination and NewInterpretations" Paper OTC 6814, 24th OTC, Houston, Offshore Technology Conference

Kaplan P., Murray J.J. & Yu W.C. (1995) ìTheoretical Analysis of Wave Impact Forces on PlatformDeck Structuresî Volume 1-A Offshore Technology, OMAE Copenhagen, June 1995, OffshoreMechanics and Arctic Engineering Conference

McConnell K.J., Allsop N.W.H. and Cruickshank I.C (2003) "Guidelines for the design of exposedjetties" TO BE PUBLISHED.

Shih R.W.K. & Anastasiou K. (1992) "A Laboratory Study of the Wave-induced Vertical Loading onPlatform Decks" Proc. ICE, Water Maritime and Energy, Vol. 96, No 1, pp 19-33, publn ThomasTelford, London.

Tirindelli M., Cuomo G., Allsop N.W.H. & McConnell K.J. (2002) "Exposed jetties: inconsistencies andgaps in design methods for wave-induced forces" Coastal Conundrums, 28th International Coastal onCoastal Engineering, ICCE 2002, Cardiff UK, ASCE, USA.

Tirindelli M., Cuomo G., Allsop N.W.H. & McConnell K.J. (2003) ìPhysical model studies of wave-induced forces on exposed jetties: towards new prediction formulaeî Proc. Conf. Coastal Structures2003, ASCE / CPRI, Portland.

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