Wave Flume Investigation on Different Mooring

8/11/2019 Wave Flume Investigation on Different Mooring

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WAVE FLUME INVESTIGATION ON DIFFERENT MOORINGSYSTEMS FOR FLOATING BREAKWATERS

Piero Ruol1, Luca Martinelli

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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 throughoutthese events. Yet, there is little literature on the assessment of forces acting

1IMAGE, University of Padova, Via Ognissanti 39, 35129 -Padova, Italy, Fax 0498277988, [email protected], University of Bologna, Viale Risorgimento 2, 40136 - Bologna, Italy, Fax 051 6448346,

[email protected]


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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 facilityThe 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 modelThe 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 tothe 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(around gravity

center)

Freeboard Height ofcenter ofgravity

Height ofcenter ofbuoyancy

Distance betweenmetacenter and

center of buoyancy

16.0 kg 0.17 kg m2 50 mm +4.6 mm -3.4 mm 80 mm


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Mooring characteristicsAs 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=MghM=12.6 N m/rad ; K'33_idr= gLc 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-1KP, whereP=[1 hG0; 0 1 0; 0 0 1].

Figure 2. Position of the chains at rest


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Tab. 2. Characteristics of the chain mooring systems for the 3 different pretensions

Low pretension Typical pre-tension High pretension

Longchains

1-2

Shortchains

3-4

Longchains

1-2

Shortchains

3-4

Longchains

1-2

Shortchains

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 gravityLow 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 systemWave gauges: 8 resistance type wave gauges (WGs) were used to measure the

wave field. Their position is given in Figures 3. WGs 14 are used to measure

incident and reflected waves, WGs 48 to measure transmission, WGs 47 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.


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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 conditionsOne 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%.


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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 1.00


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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 modelSimulations are carried out by means of a classical FE model, presented in

details in Martinelli & Ruol (2006). The model solves the scattered andradiated 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 thedifferent 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 frequenciesIn 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 excitedsway, 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 the


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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: =A sin( 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.

Figure 7 a,b. Direct measure of the oscillations artificially induced on the FB

SYNTHESIS OF THE RESULTSResults 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 andlarge 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.

0 2 4 6 8 10-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04Test134

SwayPeriod = 1.45s z=0.12


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Figure 8. Results in terms of transmission

Figure 9. Results in terms of reflection

Figure 10. Results in terms of displacements (RAO - Response Amplitude Operator)

0 0.5 1 1.5 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Tpinc

/Tn33

Hsr/Hsi

low tensiontypical tensionhigh tensionpiles


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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.

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 closerto 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.

y = 52x - 1

y = 50x - 1

y = 70x - 1

y = 90x - 2

0,0

0,5

1,0

1,5

2,0

2,5

3,0

3,5

4,0

0 0,01 0,02 0,03 0,04 0,05 0,06 0,07

H1/3,I[m]

Qmax[kg]

Tp=0.58s

Tp=0.72s

Tp=0.87s

Tp=1.00s

Tp=1.15s


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Figure 13. Dissipation vs incident wave steepness

Figure 14. Dissipation vs incident wave period

Effect of geometryTests 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.


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Effect of pre-tensioningIn 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

ACKNOWLEDGEMENTSThe 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.

REFERENCESDrimer 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 OceanEng. 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 BreakwatersA 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, 5778.

Wave Flume Investigation on Different Mooring

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