NEW GUIDANCE FOR WAVE FORCES ON JETTIES IN EXPOSED
LOCATIONS
by
by K.J. McConnell1, N.W.H. Allsop2, G. Cuomo3 and I.C. Cruickshank4
1 INTRODUCTION
1.1 Background
Trade activities of coastal nations rely on jetties for berthing of vessels for the loading and discharge of cargo. Traditionally, these facilities were constructed in sheltered locations or sheltered by breakwaters hence hydraulic loadings were relatively small.
In recent years there has been increased demand for development of large single use industrial terminals (especially those for Liquid Natural Gas (LNG), and Liquid Petroleum Gas (LPG)) which require deep water and sheltered berths for larger vessels, but do not necessarily need shelter to the approach trestles carrying the delivery lines. These terminals are often required in remote locations where there is no wave shelter, no existing infrastructure and the construction of new protective breakwaters for the whole facility may not be cost effective. Therefore, in many instances the jetties and/or their approach trestles are being constructed in exposed locations without breakwater protection. 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 of
Southampton
3 Marie Curie Visiting Research Fellow, University of Rome 3, c/o HR Wallingford, UK 4 Principal Engineer & Project Manager, HR Wallingford, UK
Figure 2: Typical approach trestle
Other examples of exposed jetties include small jetties on open coasts in tropical regions serving small fishing communities, ferry services and emergency access to remote locations. For most of their design life, the environmental conditions may be benign but occasionally cyclone and hurricane conditions hit, putting the exposed jetty under significant hydraulic loading.
1.2 Wave loadings
Of particular concern in these locations is the risk of occurrence of wave forces on the jetty superstructure and the likely magnitude of such forces should they occur. As well as being important for the design of structure elements, these loads need to be considered when assessing the potential for damage to equipment located on approach trestles and jetty heads. There are also potential environmental risks arising from damage to exposed jetty facilities, particularly those carrying oil or other hazardous materials.
Existing guidance on such loadings mainly derives from the offshore industry. In this field an approach termed the 'air gap' approach is generally adopted for platform design. Following this approach, the maximum wave crest elevation is predicted for the design condition and the deck (or soffit) level is located at an allowance or 'air gap' above this elevation to ensure a low probability of occurrence of wave forces on the superstructure.
The 'air gap' approach is often adopted in the design of shore connected trestles and jetties, however the design of structures in this environment may be dictated by other constraints which prevent the adoption 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. In addition there may be considerations such as material costs, member sizes and construction methodology.
In such cases there may be a risk of wave loads on the structure. Methods available to the designer for prediction of the forces are limited, complex to apply and practical guidance for their use is not readily available.
1.3 The "exposed jetties" research project
In response to the demand for design guidance for predicting wave forces on jetties, a research project entitled 'hydraulic design of exposed jetties' was undertaken at HR Wallingford funded by the UK government. The project was guided by a Project Steering Group from industry, including designers, contractors and owners. These research studies reviewed existing knowledge and undertook a new series of model tests to evaluate loads on deck elements and provide new guidance that 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 berths constructed 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 is small) or in exposed locations such as marginal quays (where the influence of shallow water impacts are more significant)" 2 MODEL TESTS 2.1 Model set-up and test conditions Following a review of available literature and methods for prediction of wave forces, a series of model tests 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 from downstanding cross-beams and a solid deck, contructed at a scale equivalent to 1:25. The model design was developed in consultation with the Project Steering Group to ensure that it was representative of typical real structures, such as the jetty head shown in Figure 3.
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 force transducers, 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 was completed with panels fixed to each side of the deck to prevent 3-dimensional inundation of the structure. This provided data for the 2-d scenario which allowed 3-d effects to be quantified and also provided a scenario that was more comparable with some of the prediction methods available which concentrated on 2-d scenarios. In addition, a third test series was undertaken with the deck superstructure inverted such that the underside was a flat deck. This configuration did not include side 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 - 5.5 Tm (s) 1 - 3 5 - 15 Water depth, h (m) 0.75, 0.6*** 18.75, 15*** Clearance, cl (m) 0.01 - 0.11**0.06 - 0.16* 0.25 - 2.75*1.5 - 4* Wave height to clearance ratio, Hs/cl 1.1 ñ 18 Wave height to water depth ratio, Hs/h 0.13 ñ 0.33 Relative water depth, h/Lm 0.1 0.48 Sampling frequency (Hz) 200 40 Notes: * Configurations 1 & 3, ** Configuration 2, *** Configuration 3 only Table 1: Range of test conditions
B1 D1 B2 D2 Waves CB1 LB1 CB2 CB3 CB4 CB5 LB2 LB3 LB4 LEGEND CB = Cross Beams LB = Longitudinal Beams B = Beam Elements D = Deck Slabs A B C D = Force Transducers A B C D Down-standing cross beams (1.50 x 1.50 x 25.00) (60 x 60 x 1000) 6.50 / 260 Down-standing longitudinal 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) 25.00 1000 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 analysis
The time series from the various force measurements were processed to extract a number of key force parameters. These were identified for each force 'event' which occurred as a wave hit the structure. One such event is shown in Figure 6, which defines the various force parameters, defined as:
Fmax Impact force (short duration, high magnitude)
Fqs+, v or h Maximum positive (upward or landward) quasi-static (pulsating) force
-4 -2 0 2 4 6 8 76.5 77 77.5 78 78.5 79 79.5 Time (s) F orce (N ) F qs-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 will have generated loads, so F1/250 is relatively well supported. For a few tests however, there may be
relatively 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 et al (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 example comparison 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 RESULTS
3.1 Discussion on presentation of results
Following on from the analysis described in Tirindelli et al (2002), the data were processed and presented 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
H
s(m)
F
1/ 250(N)
Measured
Kaplan
presentation of the results, in order to provide some useful means of using the data for force prediction.
Firstly a means of non-dimensionalising the forces was considered. From the perspective of the designer, it was considered that the force measurements might be most usefully be presented as a function of a force value that can be easily calculated from design information. A notional or 'basic wave force' F* is therefore defined. F* is calculated based on the predicted maximum wave crest elevation, ηmax, whilst assuming no (water) pressure on the reverse side of the element. F* is
calculated separately for vertical and horizontal forces. F*v is defined by a simplified pressure
distribution using hydrostatic pressures, p1 and p2, at the top and bottom of the particular element
being considered. F*h is calculated assuming a uniform pressure p2 over the base of the element. F*v
and F*h are defined in Figure 8, and can be calculated as follows: 2 2 * p dA b b p F w l b b v w l ⋅ ⋅ ≅ ⋅ =
∫ ∫
(1)(
)
22 max * max p c b dA p F w l b c hyd h w l ⋅ − ⋅ = ⋅ =∫ ∫
η η for ηmax ≤cl +bh (2)(
)
2 2 1 * p dA b b p p F w h b b c c hyd h w h l l + ⋅ ⋅ = ⋅ =∫ ∫
+ for ηmax >cl +bh (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 element bw element width (perpendicular to direction of wave attack) bh element depth bl 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*hIn order to derive the maximum wave crest elevation, ηmax, the maximum wave height, Hmax, must be
calculated. 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 from
by Stansberg (1991). This gave good agreement with Stream Function Theory and Fenton's Fourier theory for the range of conditions tested, however for shallower water depths the more sophisticated approaches 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) this
parameter describes the relative elevation of the wave crest (ηmax/Hs), often between 1.0 and 1.3, then
the relative excess of the wave over the clearance (cl/Hs). Over the test range, relatively little effect of
either wave steepness or relative depth was detected in these data, although that conclusion may be specific 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 deck substructure
It should be noted that the discussion in this paper concentrates on slowly-varying or quasi-static forces (Fqs). Shorter duration impact forces, Fmax, as defined in Figure 6, were also processed and are
discussed 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 those experienced by the internal elements, which were influenced by the deck configuration. In some cases beams and deck elements showed significantly different behaviour and for some elements there was a clear influence of 3-dimensional effects. The influence of each of these factors was assessed and the data sorted such the the influence of these parameters could be identified.
3.2 Vertical quasi-static forces
Vertical loads on the seaward beam and deck elements were found to be relatively unaffected by the configuration of the test structure, and were similar in magnitude for both element types. These can therefore be considered together, see Figures 9 and 10 for upward and downward acting forces respectively. It is worth noting that the smooth deck tended to give lower element loads that the deck with 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 Fvqs + / F * v Seaward elements - downstand beam configuration Seaward elements - flat deck configuration 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 Fvqs - / F * v Seaward elements - downstand beam configuration Seaward elements - flat deck configuration Figure 10: Vertical (downward) forces on seaward elements
Conditions for the internal elements are more complex, with the deck and beam elements showing different trends. The results for upward and downward loads on the internal deck element are shown in 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 larger loads than the simplified 2-d scenario.
It is worth noting that the flat deck configuration also experienced lower downward forces, most likely due to the fact that this configuration was represented simply by turning the deck over and the resulting upstanding beams will have blocked 3-dimensional flow effects over the measurement element 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 Fvqs + / 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 Fvqs - / F * v Internal deck - 3-d effects Internal deck - 2-d effects Figure 12: Vertical (downward) forces on internal deck
Vertical wave forces on the internal beam are also complex, but the loss of some test data resulted in a less clear trend than that identified for the deck element. Upward and downward forces are shown in 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 Fvqs + / 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 Fvqs - / 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
3.3 Horizontal quasi-static forces
For horizontal forces on beams, seaward and internal beam elements are considered separately as the loads on internal beams are influenced by the deck structure, while loads on the seaward beam are 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 almost
all 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 Fhqs + / 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 Fhqs + / F * h Internal beam Figure 16: Horizontal (shoreward) forces on internal beams
Seaward-acting (or negative) horizontal forces, Fhqs-, are shown in Figures 17 and 18 for seaward and internal beams respectively. The following can be noted: • For seaward elements, landward forces are generally greater than negative (seaward) ones, the difference 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 Fhqs -/ 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 Fhqs - / F * h Internal beam Figure 18: Horizontal (seaward) forces on internal beam 3.4 Wave impact forces Short duration impact forces on beam and deck elements were also measured in the tests. In order to assess the importance of impact forces, information is necessary on their duration and also the dynamic response characteristics for the structure in question. Wave impact forces are not discussed in detail here, but a comparison is given of vertical impact forces and quais-static impact forces for
each test, where Fmax is the largest impact force recorded in a test and Fvqs+ is the quasi-static force at
1/250 level. The results are presented in Figure 19 where it can be seen that none of the impact forces measured exceed their quasi-static components by more than 4 times. The magnitude of impacts that can be measured will be limited by the sampling frequency of the instrumentation used, in this case 200Hz (at model scale), as the sampling rate may miss the actual peak of the impact. Faster sampling frequencies may well result in higher magnitude, shorter duration events being registered. It should also be noted that impact loads are very localised in nature and local pressures may be higher than the average force acting on the element in question. It should also be noted that there was some signal corruption induced by dynamic response of measurement instruments. Dynamic loads and responses 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 Fma x / Fvqs+ Seaward Deck Internal Deck Seaward Beam Internal Beam Figure 19: Ratio of vertical impact forces to quasi-static forces 4 FORCE PREDICTION
The various data sets from the model tests are presented in Figures 9 to 18 for both vertical and horizontal quasi-static forces. Best fit regression lines fitted to each data set are shown by a solid line on the graphs. The general form of the regression line is : b s l * qs H ) c (η a F 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 in Table 3 for horizontal forces.
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 envelopes have 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 will normally be accounted for by applying safety factors during design. The lower bound is not likely to be used 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 horizontal forces 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
Wave load and configuration C upper C lower Shoreward 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 STUDIES The methods described above have been applied to a number of case studies. These have included jetty structures in relatively open water where exposure is high, and also structures within harbours which are exposed to wave induced forces as structure elevations are close to the still water level, due to operational requirements.
5.1 Case study 1: Damage to under-slung services Description
The method given in Section 4 was used to back-calculate wave forces on a jetty that had experienced damage during a storm event.
The jetty is located within a harbour. Despite being protected by breakwaters, it was exposed to fairly severe 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 a return 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 the power supply to the end of the jetty failed.
This example addresses the partial failure of pipe fittings beneath the jetty deck. The pipes were suspended 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. Key parameters are as follows: Hs = 2.5m Hmax = 4.3m, using Goda (1985) Tm = 7s MWL = +1.6mOD (MHWS) Deck level = +4.0mOD Soffit level = +3.6mOD Top of pipe = +3.2mOD Bottom of pipe = +3.0mOD
Assuming that the pipe can be considered as a beam, the following parameters are defined (see Figure 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 calculations
In 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 horizontal wave force', F*h, is calculated using Equations (1) and (2) with the input pressures, p1 and p2
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 Table 3, assuming the pipe can be considered as an internal beam (a = 0.72, b=1.56, based on the data in Figure 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 therefore calculated as:
Fhqs+ = 5.3kN/m
The pipe supports had a capacity of 40 kN/fixing for horizontal sliding. Each cast in channel was 2.25m long and carried three pipes. Each support had two bolts giving a sliding capacity of 80 kN (2 x 40kN). 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 be several times greater than quasi-static forces. Figure 19 is for vertical forces however analysis of the model test data indicated that horizontal impact measurements showed similar relative orders of magnitude. Thus impact forces may be up to 4 times the quasi-static force. It is likely that light components such as pipework and fixings will respond to these short duration loadings and hence it can be assumed that the pipe supports could experience forces in excess of 80kN. These calculations demonstrate that the capacity of the fixings could have been exceeded by wave loads during the storm, causing damage.
The assumption that the pipe acts like a beam on the structure is a simplification as the gap between pipe and soffit will mean that there is also some flow over the pipe, constrained by the deck, which may 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 pier
Description
A new ferry terminal comprises a 200m long central pier, with pairs of dolphins on either side supporting vehicle access bridges and passenger access walkways. The central pier is designed to function as a wave absorbing structure to reduce wave reflections and transmission. The pier is essentially constructed as a concrete box divided into a series of chambers with large voids in the sides, located around the water line to provide energy dissipation. The box is supported on piles with a soffit level at +1.5m CD and a deck level of +12m CD. The tidal range at the terminal is 7m and sea bed levels at the berth are around ñ9mCD. The geometry of the structure and its secondary function to absorb wave energy prevented adoption of an air-gap approach, by raising the structure above the maximum water level. Wave forces on the structure therefore had to be considered. Loads on the structure during construction were of particular concern, 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 conditions The new ferry terminal is located within a harbour and is relatively sheltered from storm waves. The site is however exposed to long period swell waves that propagate into the harbour.
Wave measurements from a physical model study were available for points along the structure for a range of return periods up to 1:50 years. These were extrapolated to estimate conditions for more extreme return periods.
In order to derive maximum wave crest elevations for use in wave force calculations, Hmax had to be
determined. 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, using Fenton (1988).
Quasi-static force calculations
Vertical uplift forces on the underside of the elements (at +1.5mCD) were of particular interest in the design of the pier. The underside of the precast elements was flat with no downstand beams. Clearly with such a large tidal range there will be scenarios where the units are partially submerged. The most critical case for vertical wave forces on the soffit elements was considered to be when the water level was close to the level of the base of the units. As a result wave forces were calculated for water levels 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 the coefficients for seaward beam and deck elements, based on the data shown in Figure 9. The results are summarised in Table 6. The 1:1 year conditions are of interest for the construction scenario. The 1:50 and 1:500 year conditions are of interest for the permanent scenario and show the variation in wave forces with increasing wave height.
It should be noted that the Table includes results at +1.5mCD, the scenario where the water level is in contact with the underside of the deck, i.e. zero clearance. This is outside the range of conditions tested and therefore represents extrapolation beyond the region of validity. From the results presented this suggests increased forces where the water level is at or very close to the underside of the structure, as might be expected.
Wave condition 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 6.6 1:1 +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 10 1:50 +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 12.3 1:100 +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 9 allows some assessment of the potential variability in wave forces. The data for the flat deck is also presented in Figure 9, generally giving lower forces that the equivalent tests for the downstand beam configuration. As the soffit elements do not have downstand elements it is likely that they will behave more like the flat deck configuration and so the forces in Table 6 might be considered to be an upper limit for vertical quasi-static forces on the structure. Impact forces Impact forces had to be assessed to check the risk of overall uplift of the relatively lightweight bridge units and soffit units during the construction scenario, before they were fixed in place. Determination of an appropriate ratio of Fmax to Fqs+ was based on judgement of the importance of a structural member
and its ability to respond globally to short-duration forces. Ratios in the range of 3 to 4 are plausible by inspection of Figure 19, suggesting short duration vertical impact forces on the lightweight elements may 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 walls Description A 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 considered that 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 at some 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 assumed reflection coefficients, in the absence of more detailed site specific data.
The following extreme incident wave conditions were available from model studies: Hs = 2.5m
Tp = 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 chamber sections which will have different reflection characteristics. The reflection performance of the perforated chamber sections will be very dependent on the wave period of the incident wave conditions, as these structures are generally tuned to give the reflection coefficients quoted above over only a narrow range of wave periods. They are normally tuned for short period, frequently occurring wave conditions as these will be the conditions that affect day to day operations within the harbour. Thus reflection performance for longer wave periods will be poorer, tending towards that of a simple vertical wall. Assuming therefore that wave reflections in the vicinity of the quay are close to 100%, an estimate of maximum wave height at the quay due to incident and reflected wave energy can be made by summing the energies of the two wave components. This calculation is made for both 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 wave r denotes reflected wave
i+r denotes incident and reflected wave.
The first stage in estimating the occurrence of wave forces is to determine maximum wave crest elevation 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 = 4.48m
HHW = +2.0mCD ηmax = 4.2m
Vertical uplift wave forces on the quay deck can then be calculated following the same methodology of Case study 2, using coefficients for exterior beam and deck from Table 2. The results are summarised 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
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 the deck can be close to the upward acting forces which act on the underside of deck and beam elements. 6 CONCLUSIONS The paper has summarised model tests undertaken as part of a UK government research project to quantify wave forces on jetties in exposed locations. A method for prediction of wave forces on deck and beam elements is presented. A series of case study examples demonstrate application of the method to real scenarios.
7 ACKNOWLEDGEMENTS
Model tests and analysis described in this paper were undertaken by Matteo Tirindelli and Giovanni Cuomo. The authors wish to acknowledge the following contributors to the research project: the Industrial Steering Committee of DTI PII Project 39/5/130 cc2035 who provided practical guidance and case 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; visiting researchers Amjad-Mohammed Saleem and Oliver de Rooij.
Giovanni Cuomo's studentship was supported by EU Marie Curie Fellowship, HR Wallingford and University of Rome 3.
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