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WAVE IMPACTS AT SEA WALLS
Conference Paper · April 2005
DOI: 10.1142/9789812701916_0327
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1
WAVE IMPACTS AT SEA WALLS
GIOVANNI CUOMODepartment of Civil Engineering, University of
Roma TRE, Via Vito Volterra, 62
Roma, 00146, Italy
WILLIAM ALLSOPTechnical Director, HR Wallingford, Howbery Park,
Wallingford OX10 8BA UK
(e-mail: [email protected])
This paper reports recent advances in knowledge on impulsive
wave loads on vertical /steep walls, based results of experiments
in the CIEM / LIM flume at Barcelona underthe VOWS project (Violent
Overtopping of Waves at Seawalls). Wave impact forcesfrom the new
data set have been compared with predictions by the more
realisticmethods available in literature. For most of the methods
analyzed, scatter has been foundto be large over the measurement
range. A simple and intuitive new prediction formula isintroduced
which seems to give better estimation of wave impact forces. To
supplementthese improvements, new data are presented on durations
of wave impacts, together withthe vertical distribution of
pressures up the wall.
1. Introduction
Over the last 10 years, improved awareness of wave impact
induced failures, hasfocused attention on the need to include
dynamic responses to wave impact loadsin analysis of loadings to
maritime structures. Recent experimental work hastherefore focused
more strongly on recording and analyzing violent waveimpacts. These
new data are however only useful if methodologies are availableto
evaluate dynamic responses of maritime structures to short-duration
loads.
For seawalls or crown walls, dynamic analysis has been rare, and
waveimpact loads are often ignored in design despite their
magnitude. A rare exampleof analysis of both impact load and
structure response on a small (1m high) wavewall was reported by
Allsop (2000), where short–duration impulsive loads ofFimp ≈
180kN/m gave an effective load of Feff ≈ 42kN/m when dynamic
responseof the wall was included. Improvements in these predictions
require thedevelopment of more complete wave load models (as
suggested by Oumeraci etal., 2000), based on new measurements and
experiments.
This paper reports measurements of impulsive wave loads on a
steeplybattered (10:1) wall from tests in the large wave flume at
Barcelona under theVOWS project (Violent Overtopping of Waves at
Seawalls). These data are
-
2
used to support a revised simple prediction formula for wave
impact forces onvertical walls.
The paper also discusses dynamic characteristics of linear
single degree offreedom systems to non-stationary excitation.
Responses are derived to pulseexcitation similar to those induced
by wave impacts for undamped systems.Response to short pulses is
dominated by the ratio of impact rise time tr to thenatural period
of the structure Tn., so new data on impact durations are
given.
2. Wave forces, pulsating and impact
Since first experiments were carried out by Bagnold (1939), time
histories ofwave loads caused by impulsive breaking against a wall
have been recognized asresulting from superposition of the short
duration spike on a much less violentquasi-static oscillation. A
comprehensive review of the physics behind waterwave impact on
walls is given by Peregrine (2003).
Although this general description fits sufficiently well to many
observationson idealied structures, pressure and force time history
loads on example maritimestructures are usually highly variable,
even for very similar wave conditions andstructural configurations.
Detailed descriptions of the behaviour of breakingwaves, and
impacts on walls, are given by Hattori et al. (1994).
2.1. Definitions and examples
For waves at more complex structures, load time histories may be
much morecomplex, and distinguishing between impact and
quasi-static components ismuch less straightforward. This is
confirmed by recent observations fromphysical model tests of the
Turner Contemporary Gallery at HR Wallingford.Wave pressures on the
Gallery were measured in a 1:40 3-dimensional modeltested under
random waves in a wave basin (see Fig. 1).
3.01m ODN
4.90 ODN8.98m ODN
13.46m ODN
13
87
465
10923.01m ODN
4.90 ODN8.98m ODN
13.46m ODN
13
87
465
1092
13
87
465
1092
764.4 764.6 764.8 765 765.2 765.4 765.6 765.8-50
0
50
100
150
200
250
Pres
sure
(kPa
)
Time (s)
764.4 764.6 764.8 765 765.2 765.4 765.6 765.8-50
0
50
100
150
200
250
Pres
sure
(kPa
)
Time (s)
Fig. 1. (A) Physical model at HR Wallingford for Turner Gallery
at Margate, UK.(B) Pressure time-histories from transducers on
front face (for 1:10’000 year return period):- top Transducer No. 2
(dotted line), 9 (dashed line) & 10 (solid line)- bottom
Transducer No. 7 (dotted line), 8 (dashed line) & 1 (solid
line)
A B
-
3
As the overall loading process depends on both the applied
loadings andthe dynamic characteristics, the use of very simple
definitions of short durationand quasi-static loads in analysis of
load time-histories (see e.g. Fig. 1) may beless useful. The
dynamic characteristics of the structure should be used indefining
the various types of loading.
For the generality, however, this paper will define as “impacts”
or “short-duration loads” all loads that act on the structure for
durations comparable withthe natural resonance period of the
structure (or element). We define “quasi-static” (also called
“pulsating” or “slowly-varying”) any loads that act for longerthan
that resonance period. In figures:
(1)
where: T0 = period of resonance of the structure for the mode of
vibratingcorresponding to the applied load.
2.2. Previous work
Although many researchers have focused on these issues since the
1930’s,understanding of wave impact loads on maritime structures is
still limited,partially due to difficulties in measuring wave
impact pressures at high-speed,and in the sheer volume of data to
be stored and analysed. Appropriate data-logging and storage
devices have only became available relatively recently.
Small scale physical model tests (see e.g. Allsop et al. 1996a,
Allsop et al.1996b, Cuomo et al. 2003) have recently demonstrated
that wave impacts onwalls and suspended deck structures can be much
higher then those predicted bystandard prediction methods,
suggesting further investigations were needed toachieve a deeper
understanding of the complexity of interactions of wave andcoastal
structures.
3. New experimental work – Big VOWS (tests at UPC Barcelona)
Bearing these uncertainties in mind, it was decided to extend a
set of large-scaleexperiments at the CIEM / LIM wave flume at
Universitat Politècnica deCatalunya, Spain. These tests were
primarily aimed at quantifying scale-effectson overtopping of
vertical / battered walls under the Big-VOWS project, seeresults by
Pearson et al. (2002), but they were extended by the addition of
waveload measurements.
The LIM wave flume is 100m long, 3m wide along its full length,
and hasan operating depth of up to 4m at the wave-absorbing sliding
wedge paddle. For
loads static-quasiimpacts
22
0
0
⋅>⋅≤TT
tr
-
4
these experiments, a 1:13 concrete approach beach was
constructed up to the teststructure shown in Fig. 2. Each test
consisted of approximately 1000 irregularwaves to a JONSWAP
spectrum with γ = 3.3. A test matrix of about 30
differentconditions is shown in Table 1 and Fig. 3. Three
structural configurations weretested, respectively:
1. 10:1 Battered wall2. Vertical wall3. Vertical wall with
recurve
Results in this paper refer only to the 10:1 battered wall.Three
different water depths h were used (0.53m, 0.83m and 1.28m).
Test
conditions for the full set of experiments are summarized in
Table 1.
Table 1. Summary of test conditions
Test Series Configuration Nominal waveperiod Tm [s]
Nominal wave heightHis [m]
1A & 1B Rc = 1.16m / 1.40mh = 0.83m
2.563.123.293.641.98
0.48, 0.45, 0.370.60, 0.56, 0.39
0.670.600.25
1C Rc = 1.46mh = 0.53m
1.982.563.123.293.64
0.25, 0.220.48, 0.45, 0.37, 0.230.63, 0.60, 0.56, 0.39
0.670.60
1D & 1E Rc = 0.71m / 0.95 mh = 1.28m
1.972.543.123.65
0.26, 0.230.44, 0.44, 0.35, 0.23
0.58, 0.50, 0.340.55
Fig. 2. Experimental set-up: overall view with pressure
transducers
-
5
Pressures up the wall were measured by mean of a vertical array
of 8pressure transducer, logging at a frequency of 2000Hz. More
detaileddescriptions of the experimental setup are given in Pearson
et al. (2002).
3.1. Recent observations (Pressure time-histories)
A snapshot of the pressure time-history during a wave-impact is
given in Fig. 4for the nominal (model) condition of:
Hs=0.48m,Tm=2.56s.
The characteristic impulsive load spike is only evident in the
time-historyrecorded by transducer No. 5, confirming that the high
pressure peak is localizedin both time and space. Variations in
time and space (up the wall) of thepulsating components are clearly
visible, but relatively smaller.
0 0.25 0.5 0.75 1-5
0
5
10
15
20
25
t / Tm
0 0.25 0.5 0.75 1-5
0
5
10
15
20
25
t / Tm
0 0.25 0.5 0.75 1-5
0
5
10
15
20
25
t / Tm
0 0.25 0.5 0.75 1-5
0
5
10
15
20
25
t / Tm
P /
ρ g
Hs
0 0.25 0.5 0.75 1-5
0
5
10
15
20
25
t / Tm
0 0.25 0.5 0.75 1-5
0
5
10
15
20
25
t / Tm
0 0.25 0.5 0.75 1-5
0
5
10
15
20
25
t / Tm
0 0.25 0.5 0.75 1-5
0
5
10
15
20
25
t / Tm
P /
ρ g
Hs
Fig. 4. Snapshot from pressure time-history up the wall.
Pressure transducers numbered frombottom (1) to top (8).
8 7 6 5
4 3 2 1
B1.5
2.0
2.5
3.0
3.5
4.0
0.2 0.3 0.4 0.5 0.6 0.7
H (m)
T (s
)
Fig. 3. Large scale tests at LIM-UPC. Wave matrix (A) and
snapshot of a wave impact duringphysical model tests (B).
A B
-
6
4. Comparison with existing methods
Wave loads measured in these tests (at exceedance level F1/250,
i.e. theaverage of the highest four waves out of a 1000-wave test)
have been comparedwith a range of methods, including those
suggested in the Coastal EngineeringManual (CEM), British Standards
BS-6349, and the guidelines fromPROVERBS. Wave impact loads are
compared here with predictions by Goda(2000), Blackmore &
Hewson (1984), Allsop & Vicinanza (1996) and Oumeraciet al.
(2001) in Fig. 5. The scatter is large for all the prediction
methods usedover the range of measured forces. Points falling above
the 1:1 line represent un-safe predictions.
Substantial scatter is seen in each graph although departures
from thepredictions are reduced by the Goda or Allsop &
Vicinanza methods. For thosemethods, ratios of measured / predicted
value are plotted against Hs/d in Fig 6.
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100
Predicted (kN) - Goda (CEM)
Mea
sure
d (k
N)
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100
Predicted (kN) - Blackmore & Howson (BS6349)
Mea
sure
d (k
N)
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100
Predicted (kN) - PROVERBS
Mea
sure
d (k
N)
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100
Predicted (kN) - Allsop & Vicinanza
Mea
sure
d (k
N)
Fig. 5. Comparison of new data set with existing prediction
methods
0
1
2
3
4
5
6
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
HS / d
Mea
sure
d / P
redi
cted
0
5
10
15
20
25
30
35
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1HS / d
Mea
sure
d / P
redi
cted
Fig. 6. Ratio between measured and predicted values for after
Goda and Allsop & Vicinanza.
-
7
Predictions by Allsop & Vicinanza are close to measurements
for 0.4< Hs/d
-
8
of measurements, confirmed by the much lower value of RMS error
shown inTable 2.
Table 2. Goodness of fit in terms of root mean square error
Prediction method RMSEGoda 23.5
Minikin 26.7Blackmore & Howson 28.4
PROVERBS 37.1Allsop & Vicinanza 23.7
Equation 2 14.9
6. Wave impacts
By definition, impulsive wave loads are applied dynamically to
maritimestructure. Any loading therefore depends on the dynamic
characteristics of thestructure, so describing the impulsive load
by its magnitude only cannot besufficient for design purposes.
Dynamic analysis of structural response to wave impacts
needsparameterisation of the recorded time-histories. Goda (1994)
assumed wavepressures to rise linearly from zero to Pmax at time t
= tb, and then drop to aconstant value Ps. Oumeraci &
Kortenhaus (1994) suggest an equivalenttriangular force defined by
peak value Fmax, rise time tr and duration time td.
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100
Predicted (kN)
Mea
sure
d (k
N)
Fig. 8. Comparison of wave impact loads from new data sets with
prediction by Eq. 2, α = 0.6
-
9
Using observations of time-history loads from the Big-VOWS model
tests,we suggest here a simple model to give first estimates of
impact loads.
6.1. Variability in time
The suggested simplified load-history is a single triangular
spike characterizedby the maximum signal during loading (Fmax) and
time taken to get to Fmax from 0(tr). An example idealised
load-history is superimposed on an original signal inFig. 9, where
the shaded area in Fig. 9A represents momentum transfer to
thestructure during the impact, the impulse. Even though peak
pressure (Pmax) andrise time (tr) both exhibit large variations
under very similar conditions, theimpulse, derived by integrating
the signal over the rise time, is far morerepeatable.
As the impulse represents a finite quantity, shorter rise time
will correspondto more violent impacts and vice versa. This is
demonstrated in Fig 9B, wherevalues of Fmax from 1000 wave model
tests are plotted against corresponding trexpressed by the
following relation between Pmax and tr of general form derivedby
(Hattori et al., 1994):
(3)
where A and B are empirical coefficients.The large variation in
coefficients A and B given in literature (Weggel et
al., 1970, Blackmore & Hewson, 1984, Kirkgoz, 1990, Hattori
et al., 1994) is, atleast partially, due to the difficulties of
recording consistent impact pressuresbetween tests.
Eq. 3 can be rewritten in dimensionless terms as:
(4)
0.22 0.2225 0.225 0.2275 0.23 0.2325 0.235-5
0
5
10
15
20
25
t / Tm
P /
ρ g
Hs
0.05 0.1 0.15 0.2 0.25
2
4
6
8
10
12
14
16
18
20
22
Fim
p / F
qs+(
1/25
0)
tr / Tm
Fig. 9. (A) Spike-shaped time-history model; (B) Dimensionless
impact force versus rise timeextracted out of a 1000-waves
test.
A B
BrtAP ⋅=max
B
m
r
qs TtAF
F
⋅=
+ 250
max
-
10
For wave impact on exposed piers / jetties, coefficients A and B
in Eq. 4are given in by Cuomo et al. (2003) for different
structural elements
6.1.1. Joint probability of Fmax and tr
Coefficients A & B are usually chosen so that the maximum
impact pressurerecorded within each experiment falls beneath the
curve of Eq. 4 which thereforerepresents the envelope of observed
values within these experiments.
If the population of paired values of (Fmax:& tr) is
statistically meaningful, itis possible to determine coefficients A
and B for Eq. 4 at any given level of jointprobability. This is far
more useful for design purposes, especially since
recentinternational design guidance are semi-probabilistically
oriented.
Dimensionless wave impact forces extracted from big-VOWS test
series1A, 1B and 1C are plotted in Fig. 10A versus relative rise
time. The solid line inFig. 10A has been obtained fitting
parameters in Eq. 4 to the joint probabilitycontour at 98.8% level,
giving: A = 1.45 and B = -0.49.
6.2. Variability in space
Analysing pressures meaasured at eight points up the wall allows
the descriptionof the vertical distribution of pressures. Maximum
wave impact pressures up thewall (P1/250) are plotted in Fig. 10B
for test series 1B & 1C in Table 1,confirming the general
observations by Hull & Muller (2002).
7. Structural response
For monolithic structures like seawalls, structural responses to
applied loads maybe similar to that of a single degree of freedom
(SDF) system of known mass(m), rigidity (k) and viscous damping
(c), subject to a force f(t) arbitrarilyvarying in time. For this
simple case the equation of motion gives:
0 5 10 15 20 250.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2Impact
Pmax
/ ρ g Hs
z/d
Fig. 10. (A) Dimensionless impact force versus rise time and
joint probability contour at 98.8%non-exceedance level. (B)
Pressure distribution up the wall. Test series 1B & 1C.
A B
-
11
)()()()( tftkutuctum =++ &&& (5)A dynamic
amplification factor Φ can be then defined as the ratio between
themaximum displacement of the system u(t)max and the displacement
u0 of the samesystem due to the static application of the maximum
force Fmax:
(6)
For linear systems, solution to Eq. 4 at time t can be expressed
as the sum of theresponses up to that time by the convolution
integral:
∫ −=t
dthftu0
)()()( τττ (7)
Where h(t-τ) is the unit input-response function. For a SDF
system, Eq.6specializes (Chopra, 2001) in:
[ ]∫ −= −−t
Dt
D
dtefm
tu0
)( )(sin)(1)( 0 ττωτω
τζω (8)
with 20 1 ζωω −=D , mk /0 =ω and 02/ ωζ mc= is the dampingratio.
Eq.8 is known as Duhamel’s integral, and, together with the
assigned initialconditions, provides a general result for
evaluating the response of a linear SDFsystem subject to an
arbitrarily time-varying force. Example displacement time-histories
obtained by solving Eq. 8 for a spike-shaped pulse are shown in
Fig10A for the cases of ζ = 0 and ζ = 0.06.
For an un-damped system subject to pulse excitation, the
deformation ofthe system only depends on the pulse shape and on the
ratio between the durationof the pulse (tr) and the period of
resonance of the system (Tn). For a given shapeof the exciting
pulse, the amplification factor of an un-damped system only
0 0.5 1 1.5 2 2.5-1.5
-1
-0.5
0
0.5
1
1.5
u(t)
/ u 0
t / T0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
0.5
1
1.5
u max
(t) /
u0
tr / T0
Fig. 10. Dynamic response of a SDF system to spike-shaped pulse
excitation.(A) Dimensionless displacement time-history for ζ = 0
(solid line) and ζ = 0.06 (dashed line)superimposed to input
spike-shaped pulse time-history load (dotted line).(B)
Amplification factor for ζ = 0 (black) and ζ = 0.06 (grey)
A B
ktFu
utu max
00
max )()( ==Φ
-
12
depends on the ratio tr / T0. Amplification factor for the cases
of spike-shapedand triangular pulses are plotted in Fig. 11B as a
function of tr / T0.
When the system is excited by a single pulse, energy dissipated
by dampingis much smaller and relative importance of damping on
maximum displacementdecreases. As a result, variation of
amplification factor with damping is lessimportant than for systems
subject to harmonic excitation. (Fig. 11B).
8. Initial conclusions & further work
New measurements of wave impact loads at large scale have been
compared withhistorical prediction methods. Scatter is large over
the range of condition tested.A simple and intuitive new prediction
formula has been suggested which uses themost informative
parameters and seems to give a better estimate of wave impactloads.
A joint-probability approach has been introduced for the estimation
ofwave impact durations, together with a simple methodology which
takes accountof dynamic response of structure when evaluating
design impact loads.
Further analysis of the whole data set will extend the
confidence of the newprediction methods, allowing at the same time
to take into account the relativeimportance of different structural
configurations on both impact and pulsatingwave loads at sea
walls.
Acknowledgments
This paper follows from work completed by Universities of
Edinburgh, Sheffieldand Southampton, and HR Wallingford under a
number of projects. Additionalsupport by Universities of Rome 3, HR
Wallingford and the Marie Curieprogramme of the EU
(HPMI-CT-1999-00063) are gratefully acknowledged.Previous research
data were supported in UK by DTI under contracts PECD7/6/263 &
312, CI 39/5/96, CI 39/5/125 (cc 1821), and PROVERBS (ECcontract
MAS3-CT95-0041). The Big-VOWS team of Tom Bruce, Jon Pearson,and
Nick Napp, supported by the UK EPSRC (GR/M42312) and
XavierGironella and Javier Pineda (LIM UPC Barcelona) supported by
EC programmeof Transnational Access to Major Research
Infrastructure, Contract nº: HPRI-CT-1999-00066, are thanked for
test data on wave forces at large scale. JohnAlderson & Jim
Clarke from HR Wallingford are also warmly acknowledged.
References
Allsop N.W.H. (2000) “Wave forces on vertical and composite
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KEYWORDS – ICCE 2004
WAVE IMPACTS ON SEA WALLSGiovanni Cuomo, William Allsop569
Wave impactsWave forcesSeawallsDynamic responseJoint
probability
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