WAVE FLUME INVESTIGATION ON DIFFERENT MOORING SYSTEMS FOR FLOATING BREAKWATERS
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WAVE FLUME INVESTIGATION ON DIFFERENT MOORING
SYSTEMS FOR FLOATING BREAKWATERS
Piero Ruol1, Luca Martinelli2
This paper investigates on different types of mooring systems for floating breakwaters
(FBs): chains with different initial tensions or piles. The principal aim is to describe the
wave transmission and the statistics of the loads on the moorings. The latter analysis is
particularly innovative because it defines in the details the condition of snapping, that can
be reached along the chains and is frequent in many practical cases. Physical model tests
have been carried out in the wave flume of the Maritime Laboratory of the University of
Padova. The tested structure resembles typical FBs located in Italian lakes in scale 1:10.
Regular and irregular waves were generated. Stiffness of the mooring systems was
modified by varying the initial stress and the results obtained by the tests are in depth
described. Simple numerical simulations, based on irrotational flow, which are commonly
used for design of moorings, were seen not to be suitable to describe the maximum loads.
The added value of a more detailed investigation, in particular by means of physical
testing, is established.
INTRODUCTION
In the last years an evolution of floating breakwater (FB) types was seen, both
regarding the largest structures protecting big harbours and the smaller ones
defending craft harbours or marinas.
Focussing on traditional types of FBs, their advantages and their
disadvantages have been widely analyzed and described for instance by
McCartney (1985) and Headland (1986). Obviously, the choice of the mooring
technology is rather important as it affects the overall performance of the
floating body. Loose chains, flexible lines or vertical piles are the typically used
mooring systems.
Chains hinder the average drift but as a rule do not quickly respond to the
direct wave load; this means that the chains are heavy enough to prevent the FB
to drift away, but they are generally so long to allow some FB intra-wave
motions without snapping (i.e. without reaching the “straight-line” condition).
Snapping is indeed associated to a major and undesired increase of the forces
acting on the chains and on the structure itself. In some conditions (intermediate
waters, high tides, “large” waves) it is rather expensive to ensure that snapping
is firmly avoided, specially during the highest design wave attacks, and
therefore it is of practical interest to quantify the mooring forces throughout
these events. Yet, there is little literature on the assessment of forces acting
1 IMAGE, University of Padova, Via Ognissanti 39, 35129 -Padova, Italy, Fax 0498277988, piero.ruol@unipd.it
2 DISTART, University of Bologna, Viale Risorgimento 2, 40136 - Bologna, Italy, Fax 051 6448346,
luca.martinelli@mail.ing.unibo.it
12
during cable snapping. Only the physics of the problem is relatively well
known, see for instance Triantafyllou (1994) and Gobat & Grosenbaugh (2001).
The use of vertical piles, as an alternative mooring system, largely limit the
FB movements: the piles are subject to the direct wave forces acting on the
floating body, surely higher than the drift forces, but most probably lower than
the maximum loads due to the cable snapping. When applicable, the use of piles
may therefore result economical and may give better performance in terms of
wave transmission.
Objective of the paper is to investigate on the wave transmission and on the
loads affecting the FB mooring systems in extreme conditions, i.e. when a
protection is most needed and the risk of failure is higher.
DESCRIPTION OF THE TESTS
Tests have been carried out in the wave flume of the maritime laboratory of the
IMAGE Department of Padova University.
The facility
The facility dimensions are 33 x 1.0 x 1.3 (m). The oleodynamic wavemaker is
equipped with a hardware wave absorption system.
Some tests have been repeated in the 4.0 m wide wave basin, in order to
evaluate the 3D behaviour of FBs, and are presented in (Martinelli et al., 2007).
To perform the wave flume tests, a fixed bottom was built up, with a
constant slope 1:100 (after an initial ramp). Water depth was 0.8 m at the wave
paddles, and 0.515 m at the structure.
The model
The chosen cross-section resembles that of typical FBs deployed in Italian
lakes, in scale 1:10. The structure is 98 cm large, which is only slightly less than
the channel width (1.0 m). The FB has therefore only 3 degrees of freedom
(DoF), related to movements in the cross sectional plane, and this is typical for
long structures.
As in many prototypes, buoyancy is assured by the presence of a
polystyrene core. The skeleton is in aluminium (whose specific weight is 2.7)
except at the two ends, where the moorings are placed, that are in Teflon
(PTFE) with specific weight of 2.2, both similar to concrete.
Further geometric and dynamic properties are given in Table 1 and
Figure 1.
Two structures have been used, with a substantial difference with respect to
the connection with the different moorings (chains or piles). In Figure 1 the
module suited to be moored with piles is also shown.
Tab. 1. Structure characteristics (heights are referred to still water level)
Mass Inertia to roll Freeboard Height of Height of Distance between
(around gravity center of center of metacenter and
center) gravity buoyancy center of buoyancy
2
16.0 kg 0.17 kg m 50 mm +4.6 mm -3.4 mm 80 mm3
Mooring characteristics
As anticipated, two mooring systems have been examined: chains and piles.
Chains were constrained at the bottom and at the FB as given in Figure 2.
Their weight is 89.2 g/m (submerged weight 77.8 g/m). By varying their length
of a small amount, three different pretensions have been applied. Target values
were 1.5, 3 and 4 N. In the first case the angle at the bottom was small, in the
latter case the chains were almost fully tightened. Details of the mooring system
for the different initial stress are given in Table 2.
Figure 1. Cross section of the tested structure (mm) and 3D view of the module
The pre-tensioning modifies, in theory, also the total vertical force. In
practice, the buoyancy force is approx. 160N, i.e. 50-100 times larger than the
vertical force applied by the moorings, which becomes negligible. The
additional draught due to the high pretension is indeed smaller than 1.0 mm.
Also the stiffness of the system in the vertical direction and rotation is
mainly given by buoyancy (index 2 refer to rotation, index 3 to the vertical
direction):
K'22_idr = M g hM = 12.6 N m/rad ; K'33_idr = ρ g Lc Bc = 2403 N/m,
where the ' apex is used to indicate that in this case the reference system is
centred on the centre of floating, rather than on the centre of gravity. The
proper trivial transformation is needed to change the reference system:
K=P-1 K P , where P=[1 hG 0; 0 1 0; 0 0 1].
Figure 2. Position of the chains at rest4
Tab. 2. Characteristics of the chain mooring systems for the 3 different pretensions
Low pretension Typical pre-tension High pretension
Long Short Long Short Long Short
chains chains chains chains chains chains
1-2 3-4 1-2 3-4 1-2 3-4
Tension in chain* [N] 1.72 1.70 2.94 2.93 3.92 3.91
Horizontal tension [N] 1.37 2.53 3.45
Length of chain [cm] 113.40 109.66 112.48 108.84 112.30 108.69
Horizontal length* [cm] 102.0 98.5 102.0 98.5 102.0 98.5
Vertical length* [cm] 46.5 45.5 46.5 45.5 46.5 45.5
Angle at bottom 8.4° 9.3° 16.0° 16.6° 18.3° 18.8°
Angle at top 38.3° 38.1° 32.3° 32.3° 30.3° 30.4°
* Measured quantities. Stress is related to single chains.
In the horizontal direction, stiffness is only given by the presence of the
mooring system. Stiffness at rest is given in Table 3. Index 1 is relative to
horizontal displacements. Table 3 was obtained numerically, accounting for the
different lengths of the two couples of chains. In order to have the stiffness per
unit length, values should be divided by the caisson length (0.98 m).
Piles, when present, constrain the sway motion, thus reducing one degree of
freedom of the FB, and limit the maximum roll. The system stiffness is only
given by buoyancy.
Figure 5 shows the pile geometry together with the set-up to measure of the
horizontal loads.
Tab. 3. Stiffness due to mooring system (two couples of chains).
Reference system is the centre of gravity
Low pretension Typical pretension High pretension
K11_moor [N/m] 280 1700 4300
K12_moor =K21_moor [N/rad] -0.19 -1.4 -4.8
K22_moor [N m/rad] 0.08 0.15 0.20
K33_moor [N/m] 71 430 1100
Monitoring system
Wave gauges: 8 resistance type wave gauges (WGs) were used to measure the
wave field. Their position is given in Figures 3. WGs 1÷4 are used to measure
incident and reflected waves, WGs 4÷8 to measure transmission, WGs 4÷7 to
check the homogeneity of the waves across the wave flume.
Load cells: the forces on the moorings were measured by means of 4 load cells.
In these type of transducers, suitable both for tension and compression
applications, the load is applied through the mounting stud.
Figure 3 and 4 show the location of the cells in presence of chains. The
load is transferred by means of Kevlar strings, after a 45° curve. The friction
with Teflon is small and differences between measurements and loads on the
chains are assumed negligible.5
Figure 3 Plan view of the model. Position of wave gauges and load cells
Figure 4. Pictures of the model anchored with chains (left) and piles (right)
Figure 5 shows the position of the cells used to measure the loads acting on
the piles. The two piles are hinged at the bottom and connected to a fixed frame
placed 93.5 cm above, through two cells.
Displacement-meters: displacements are measured by means of 2/3
potentiometers connected to wheels. Strings of nylon are attached to the FB, run
across wheels thus turning the potentiometers by friction, and are connected to a
small weight (a common bolt) that assure tension along the wires.
A sketch of the set up is given in Figure 6. The wheel connected to the
potentiometers are labelled "A", "E" and "F". When the FB is moored with
piles, it can not move horizontally and therefore the horizontal displacement-
meter "F" is not installed.
Wave conditions
One regular wave (H=5.0 cm and T=0.87) and 19 irregular wave conditions
were generated, with target Jonswap spectrum (enhancement factor 3.3). The
test sequence is given in Table 4, and comprises 5 wave heights and 5 wave
periods; these waves have steepness always lower than 7%.6
At first the sequence of waves was run in absence of the FB, in order to
calibrate the wavemaker and to measure the generated wave conditions in
absence of structure.
Figure 5. Cross-section of the model showing the position of load cells with piles
Figure 6. position of displacement-meters
Tab. 4. Generated waves. Target values
Test Hs Tp Test Hs Tp
(cm) (s) (cm) (s)
A0 2.5 0.58 B3 4.2 1.00
B0 4.2 0.58 C3 5.8 1.00
A1 2.5 0.72 D3 7.5 1.00
B1 4.2 0.72 E3 9.2 1.00
C1 5.8 0.72 A4 2.5 1.15
A2 2.5 0.87 B4 4.2 1.15
B2 4.2 0.87 C4 5.8 1.15
C2 5.8 0.87 D4 7.5 1.15
D2 7.5 0.87 E4 9.2 1.15
A3 2.5 1.007
Then, the sequence of waves was run with the following 5 configurations:
1. structure anchored by chains with low pretension, in absence of load cells on
the structure; 2. structure anchored by chains with low pretension, with 4 cells
measuring mooring forces: 3. structure anchored by chains with medium
pretension, with 4 cells measuring mooring forces; 4. structure anchored by
chains with high pretension, with 4 cells measuring mooring forces; 5. structure
anchored by piles, in presence of load cells on the structure.
ANALYSIS OF THE FB NATURAL PERIODS OF OSCILLATION
Numerical model
Simulations are carried out by means of a classical FE model, presented in
details in Martinelli & Ruol (2006). The model solves the scattered and
radiated problem with the hypothesis of irrotational flow and linear waves and
finds the FB dynamics accounting for 3 DoF using the analytic solution, which
approximates the non-diagonal terms of the damping matrix.
As a validity check, the same structure analyzed by Drimer et al (1992) was
investigated. The analysed case was a box-type FB with width equal to the
water depth and draught equal to 70% of this value. The results were in perfect
agreement, so that it was concluded that the numerical model was correctly set
up and could be extended to different geometries.
Natural modes of oscillations of the FB anchored with chains are a vertical
oscillation (heave) and two rotations, the first centred almost on the barycentre,
very similar to roll, and the second around a low centre, therefore well
represented by sway. Table 5 shows the natural periods of oscillation due to the
different mooring systems evaluated according to the model: damping appears
to be much smaller for heave and roll than for sway.
Tab. 5. Computed natural frequencies of oscillations
Low pretension Typical pretension High pretension
T1(sway) [s] 2.88 1.27 0.95
T2(roll) [s] 0.95 0.86 0.65
T3(heave) [s] 0.85 0.81 0.76
Direct evaluation of natural frequencies
In order to evaluate the natural frequencies of oscillation of the system, and to
check the numerical model predictions, specific tests were carried out in the
laboratory. The FB was hit by a sudden impulse (a hammer) and the excited
sway, heave and roll movements were measured (by means of displacement
meters).
Only one case of mooring system was examined (“low pretension"), and in
this case the measured values appeared quite different from the computed ones.
Figure 7a presents the measured sway, heave and roll provoked on the FB
by releasing it from an initial offset. It can be seen that the natural period of the8
sway and roll are slightly larger than the heave one. Figure 7b shows a detail of
the sway oscillations obtained by hitting the FB.
The displacements have been separately fitted to a sinusoidal curve of the
type: η=A sin(ω t) e-zt. It resulted that z=0.10 was a fairly good fitting of
damping for all oscillation modes (Figure 7b).
The measured three natural periods of oscillations are approximately 1.45,
1.35 and 0.75 s for sway, roll and heave. These values appear different from
those obtained with the numerical simulations. Differences may be due to a non-
linear behaviour of the system. Applied excitation are of finite amplitude, with
sway of order 2 cm, roll of 10° and heave of 0.5 cm. During such movements,
the added masses, the stiffness due to chains and buoyancy vary significantly
whereas they are assumed constant in the model.
Test134
0.04
0.03
0.02
0.01
0
-0.01
-0.02 Sway
Period = 1.45s z=0.12
-0.03
0 2 4 6 8 10
Figure 7 a,b. Direct measure of the oscillations artificially induced on the FB
SYNTHESIS OF THE RESULTS
Results of the tests are graphically summarised in the following figures (Figure
8, 9, 10, 11, 12), in terms of transmission, reflection, displacements and loads
on anchoring systems.
Analysing Figure 8 it does appear that for shorter wave periods, no
significant influence of the mooring system is revealed; for medium periods
high pretension and piles are more effective; for larger periods high pretension
is more efficient.
As far as wave reflection is concerned (Figure 9), it can be noticed that for
shorter periods large reflection can be expected in any case, but for medium and
large periods the reflection coefficient decreases with increasing wave period.
Piles and high pretension cases are the more reflective ones.
Referring to displacements (Figure 10), it does appear that measured
movements are much smaller than those obtained by means of numerical model,
since the model does not take into account dissipation, wave irregularity (in fact
the regular wave induces larger movements) and non-linearity.9
Figure 8. Results in terms of transmission
1
lo w te nsio n
0 .9 typical tensio n
high tension
0 .8 p ile s
0 .7
0 .6
Hsr/Hsi
0 .5
0 .4
0 .3
0 .2
0 .1
0
0 0 .5 1 1.5 2
T p inc /T n33
Figure 9. Results in terms of reflection
Figure 10. Results in terms of displacements (RAO - Response Amplitude Operator)10
Maximum loads on chains (Figure 11), as well as on piles (Figure 12) are
seen to increase more than proportionally with incident wave height and with
incident wave period.
4,0
Tp=0.58s y = 90x - 2
3,5 Tp=0.72s
Tp=0.87s
3,0 Tp=1.00s
Tp=1.15s y = 70x - 1
2,5
Qmax [kg]
y = 50x - 1
2,0
1,5
1,0 y = 52x - 1
0,5
0,0
0 0,01 0,02 0,03 0,04 0,05 0,06 0,07
H1/3,I [m]
Figure 11. Maximum loads (chain system), function of incident wave height and period
Figure 12. Maximum loads (pile system), function of incident wave height and period
DISCUSSION ON THE RESULTS
Influence of the mooring system
Dissipation is seen to increase for larger wave steepness and for periods closer
to the natural period (Figure 13 and 14). These effects are certainly to be
expected. In fact, the higher the wave steepness, the larger the horizontal
acceleration of the fluid particles, and therefore the larger the velocity
difference between fluid and structure, which reasonably cause dissipation. On
the other hand, dissipations are in some way proportional FB movements, which
in turn are larger when the exciting load has a frequency close to the natural
one.11
Figure 13. Dissipation vs incident wave steepness
Figure 14. Dissipation vs incident wave period
Effect of geometry
Tests have been compared to other ones, carried out by the authors on a
different geometry, i.e. with a larger ratio between width and draught.
The curves giving transmission as function of incident wave period are
quite similar for different geometries, if the independent variable is non-
dimensionalized with the natural period of oscillation.12
Effect of pre-tensioning
In Figure 15 the maximum measured loads on the cell, function of the initial
pretension load, for waves with Hs=2.5 cm and different periods is drawn.
As expected, the maximum loads are largely affected by the initial
pretension on chains.
Figure 15. Maximum loads, function of initial pretension, for waves with Hs=2.5 cm
ACKNOWLEDGEMENTS
The support of the Italian Ministry for Research through PRIN2005 program "Tecnologie moderne
per la riduzione dei costi nelle opere di difesa portuali", Prot. 2005084953, is gratefully
acknowledged. The authors also wish to thank INGEMAR S.r.l., for providing precious practical
information on FB design.
REFERENCES
Drimer N., Agnon Y. and Stiassnie M., 1992. A simplified analytical model for a floating breakwater
in water of finite depth. Applied Ocean Research, 14, 33-41.
Fugazza, M and Natale L., 1988. Energy losses and floating breakwater response. Journal of
Waterway Port, Coastal and Ocean Eng. 114, 2, 191-205.
Gobat J.I., and Grosenbaugh M.A., 2001. Dynamics in the touchdown region of catenary moorings,
Int J Offshore Polar. 11, 4, 273-281.
Headland J.R., 1995. Floating breakwaters. In Tsinker G.P. Marine Structures Engineering:
specialised applications. Chapman & Hall ed., 367-411.
Martinelli L. and Ruol P., 2006. 2D Model of Floating Breakwater Dynamics under Linear and
Nonlinear Waves, Proc. 2nd Comsol User Conference, 14 Nov., Milano (electronic format).
Martinelli L., Zanuttigh B., Ruol P., 2007. Effect of layout on floating breakwater performance:
results of wave basin experiments . Proc. Coastal Structures '07.
McCartney, B., 1985. Floating Breakwater Design. Journal of Waterway Port, Coastal and Ocean
Eng. 111, 2, 304-318.
Oliver J.G, Aristaghes P., Cederwall K., Davidson D.D, De Graaf F.F.M., Thackery M. and Torum
A., 1994. Floating Breakwaters—A practical guide for design and construction. In: Report no.
13, PIANC, Supplement to Bullettin 85, 1-52.
Triantafyllou M. S., 1994. Cable mechanics for moored floating systems, in Behaviour of Offshore
Structure, 2, C. Chryssostomidis (ed.), Elsevier, 57–78.You can also read
