Mooring Line Dynamics Volume III, Phase II, Part I, Correlation study: Analysis, Report VM-V-5-III

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MaT

SNetherlands

Marine Technological Research

7 ₇

MOORING LINE DYNAMICS Phase II - Part I

Correlation study: Analysis

MaTS report VM-V-5 III

November 1984

L

Netherlands Industrial Council for Oceanology

P1984-1

-VOL.3

Industriele Raad voor de Oceanologie

Marien Technologisch Speurwerk

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The Netherlands Industrial Council for Oceanology (IRO) and its Marine Technological Research (MaTS)

From the start in the early sixties Dutch industry was involved in the development of the oil and gas resources of the North Sea. The first platforms on the southern part of the UK Continental Shelf were

constructed and installed by the Dutch. From then on the Dutch industry has been building up its name and reputation in all activities related to

design, construction and installation of equipment for exploration and development of oil and gas.

Soon the need was felt for a co-ordinating body to further the _interests of the Dutch offshore industry.

To this end the Netherlands Industrial Council for Oceanology (IRO) was founded in 1971. In this context the term oceanology referred to coastal engineering, underwater technology, sea-mining, shipbuilding, energy

production, equipment manufacture, offshore supply, fishery and recreation and related advisory and supervisory activities amongst which pollution control.

The activities of IRO were, however, _{soon focussing on the production of} oil and gas offshore. By now some 250 companies involved in

above-mentioned activities have become member of IRO. Through the years the IRO has grown to the following set of tasks:

it forms a platform for all people involved in offshore activities _in the Netherlands;

it provides information on offshore activities in the world. One of the channels of information is formed by the 'IRO-Journal' a weekly which gives a short overview of up-to-date information;

it provides information on its members to interested parties. Amongst others the IRO is present on the main offshore exhibitions in the world representing its 240 members. Furthermore IRO publishes the Netherlands Offshore Catalogue, in which it gives descriptions of its member

companies and their activities;

it takes care of contacts with government authorities, taking _{a seat in} scientific committees and other consultative bodies;

it stimulates and draws attention to new possibilities in _{the field of} oceanology which might become of economical importance;

it co-ordinates combined efforts of groups of several _{companies to} operate on foreign markets;

it initiates, co-ordinates and desseminates results of applied _research in the offshore field through its Marine Technological Research (MaTS) efforts.

MaTS projects are jointly financed by government and industry. They are meant to raise the standard of Dutch offshore technology and they are aimed at satisfying the need for knowledge on middle long _{term. It is the} responsibility of the MaTS organisation to sort out strategic research

fields within the offshore context and to develop relevant projects in these fields; futhermore to promote and manage these projects and to disseminate the results.

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c\17

c.svL_1 e Di

Netherlands Ship Mode! Basin

The VVageningeniEde Laboratories of Maritime Research Institute Netherlands

(MARIN)

2. HaacFeeg: P.O. Bor a 673C AA Wageningen.

The Ne;heriands

Telephone + 31 8370 93911. Teiex 45148 nsmb n1 Ede Laboralory. 10. Niels 53-irs1raa 6716 AM Ede Teleb,.one + 31 8383 37177

7

Report No. 45064-3RD

MOORING LINE DYNAMICS

Phase II Part 1

Correlation Study: Analysis

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Report No. 45064-3-RD

MOORING LINE DYNAMICS

Phase II - Part 1

Correlation Study: Analysis

N.S.M.B. Order No. Z 45064

Ordered by: Industriele Raad voor de Oceanologie Marien Technologisch Speurwerk (MaTS)

Project VM-V-5

Postbus 215 2600 AE DELFT

Reported by: Ir H.J.J. van den Boom

Approved by: Dr Ir G. van Oortmerssen

HOEDs

Netherlands Ship Model Basin

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-1-Report No. 45064-3-RD CONTENTS _Page INTRODUCTION 3 MODEL TESTS ₄ SIMULATIONS 7 DISCUSSION ₉ CONCLUSIONS ₁₆ NOMENCLATURE ₁₈ Photographs ₁₉ Tables (6) Figures (33)

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E 73

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-2-Report No. 45064-3-RD

1. INTRODUCTION

As part of the MaTS research program, MARIN performed an extensive

investigation into the "Dynamics of mooring lines". _{This project}

comprised the development of a computer program named DYNLINE for the prediction of the dynamic behaviour of anchor chains and steel wires due to upper-end oscillations. The _{first phase of this study,}

viz, the development of the mathematical model, _{is discussed in}

MARIN Report No. 45064-2-RD.

The present report describes the results of phase II; a correlation study on harmonic oscillation model tests and DYNLINE simulations. The test program comprised water depths _{of 75, 150, 300 and 608} _m. The mooring lines investigated were single component 76 mm and 152

mm chains, 76 mm steel wire and a 76 _{mm chain-wire combi-line. In}

total eleven combinations of mooring lines _{and water depths were}

subject of study. A review of these situations _{is given in Table 1.}

For each situation five frequencies _{of horizontal oscillation in}

the range of the wave frequencies were applied. For several situa-tions various amplitudes of horizontal oscillasitua-tions as well as ver-tical oscillations were part of the _{test program.}

In addition to the measurements of _{upper-end and lower-end line}

forces, _{the motions of the line at} _{one marked position were}

re-corded by underwater video.

All data concerning the configurations of the test program and the relevant results of the experimental _{and numerical tests are} pre-sented separately in part 2 of this report (Report No. 45064-4-RD) entitled: "MOORING LINE _{DYNAMICS, Phase II - Part 2,} _Correlation Study: Data Report"

HOE

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2. MODEL TESTS

The tests for 75, 150, and 300 m water depth were carried out in

the Basin for Unconventional Maritime Structures at a scale of

1:19, 1:38 and 1:76, respectively. The dimensions of this basin are 220 m x 4 m with a water depth of 3.98 m. The tests for 608 m water depth were performed in MARIN's Vacuum Towing Tank, _{measuring 240 m}

x 18 m x 8 m, _{at a scale of 1:76. The depressurizing options of}

this facility were not utilized during this _{test program. All tests} were carried out in accordance with Froude's law of similitude.

A special mechanical oscillator (shown by _{photographs on page 19)}

was used to enforce sinusoidal motions at the upper-end _{of the}

line. This device was built of a steel frame connected to a driving shaft by means of three worm-gear transmissions. _{Each frame}

connec-tion was free to rotate in the vertical _{plane of the frame but}

could be fixed to the frame with _{respect to the horizontal motions} (outer gears) and vertical translatory _{motions (centre gear). The}

stroke of each gear was adjusted by

_{means of a high accuracy}

spindle. The frequency of oscillation was adjusted by the number of revolutions of an electromotor which _{was connected to the central} shaft by means of a non-slip nylon belt. _{A guiding system prevented} transverse motions of the steel frame.

Although this test set-up enables arbitrary two-dimensional ellip-tical motions, only pure sinusoidal horizontal and verellip-tical

oscil-lations were generated in this test program.

The oscillator was firmly connected to the towing carriage, above the basin, parallel to the side walls of the basin. The upper-end of the mooring line was connected to the oscillator frame by means

of a roller type bearing with _{a 2-component strain gauge force}

transducer in it's centre (see photographs on page 19). The _centre

of the force transducer _{was approximately 3 cm above the basin's}

water level.

HOEM

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Report No. 45064-3RD

HOMM

5

The anchor-end of the line was connected to _{a tank-fixed space}

frame in the 4 m deep tank and to a heavy weight in the _{8 m deep}

tank. During all tests the line was parallel to the tank wall at a distance of approximately 1.5 m (4 m basin) and 8 m (8 m tank) from the nearest tank wall.

For the present test program of the _{same model chains were used as}

tested in phase I. The particulars of these chains are listed in

Table 2 while a photograph is presented in _{Report No. 45062-2-RD.} The 76 mm steel wire was geometrically scaled with respect to its

diameter. By use of _flexible 1 x 19 steel model wires the

elasticity however was not _{correctly scaled as indicated in Table}

2. _{The line length to water depth ratio} _{amounted to} ₇ _{for all}

situations except for situation No. 11 _{where a ratio of} 5 was

applied.

Prior to the testing all model _{lines were "statically"}

pre-ten-sioned up to a high percentage of _{their breaking} _strengths.

Following this static loading, each _{line was subjected to} artifi-cial ageing by means of high frequency-large stroke oscillations in the test set-up. This loading is aimed at removing plastic deforma-tions and hysteresis elongation effects known to be linked to new

chains and steel wires.

After this procedure the required _{initial tension To (at the} _mean upper-end position) was adjusted by moving the towing carriage. At the correct tension the carriage was fixed to the tank by means of pneumatic break devices. Pre-tensions of approximately 30 per cent of the breaking load were adjusted in order to include the mean and low frequency excursions of the _{upper-end of the line due to the} motions of a floating structure. Since _{the test program contained} geometrically similar situations (Table 1) _{some information on the} effect of pre-tension could be _{extracted from the test results by} means of scaling. After the pre-tension (To) _{was adjusted and the}

carriage fixed, the maximum quasi-static tensions (T0+) were measured by applying the maximum excursions _(stroke).

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KOMM:

-6-During all tests, which had a duration of approximately 300 _seconds

at full scale, _{the upper-end vertical and horizontal line force} components and the tension at the anchor point were measured. The oscillatory motion of the upper-end was measured by means of a po-tentiometer device. After preliminary on-line statistical _analysis and an inspection on Ultra-Violet paper charts, the oscillation and the forces were recorded on magnetic tape at a sampling rate of 25 Hz (model scale) for further analysis.

During all tests underwater video recordings _{were made of a line} mark located at approximately 2.23 _{m (model scale) from the}

upper-end of the line. For this purpose _{a video camera was positioned}

athwart of this mark at a distance of approximately _{2.0 m (model}

scale). In order to quantify the recorded motions a wire grid with

a mesh width of 0.15 m was placed parallel to the line _{at a}

dis-tance of approximately 0.30 m (model scale).

The system of co-ordinates used is given in Figure 1.

Neglecting the transient starting phenomena, _{the recorded tension}

records were used to derive the maximum dynamic _{tension (T+). To}

this end the average value of _{some 20 tension peaks was taken.}

Plots of the measured records _{are given in Figures 16 through 121} in Part 2 of this report.

For all tests the so-called "dynamic amplification _{factor" defined} as the ratio of the maximum tension in the real dynamic _situation (T+), to the maximum quasi-static tension corresponding to the same maximum excursion in the dynamic case (To+)

A review of all tests and the ensuing _{results are presented in}

Tables 4, 5 and 6. For each configuration the _{dynamic tension} am-plifications are plotted on the basis of the frequency of oscilla-tion in Figures 21 through 33.

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3. SIMULATIONS

For all situations tested in the model basins, time domain computa-tions were carried out by means of the program DYNLINE.

The static line configuration at the pre-tension _{adjusted in the}

basin, required by DYNLINE, was computed _{by MARIN's computer} pro-gram FLEX3D. This program allows arbitrary line _{components and}

three-dimensional line loading to be considered and generates posi-tion and tension at each required posiposi-tion _{along the line.}

The line discretizations chosen as input for DYNLINE are presented together with the line characteristics in Figures 2 through 20. It

should be noted that the line _{mass, underwater weight, volumetric}

diameter and elasticity were scaled from the _{model values}

deter-mined experimentally (Table 2).

For each configuration a numerical quasi-static analysis was

carried out using DYNLINE by applying _{a low frequency upper-end}

oscillation. Assuming negligible dynamic tension effects, this

pro-cedure was used to verify the input of _{DYNLINE and to derive the}

numerical pre-tension and maximum quasi- static _tension.

The integration time step was adjusted to a value which provided

numerical stability at a maximum of 25 _{Newton-Raphson iterations at} each time step and a tension criterion _{of 1 per cent. In this way} time steps of 0.1 and 0.2 seconds were used for the lower frequen-cies and small amplitudes in case of the chain configurations. For the other situations the time step had to be reduced to 0.01 _{s for} severe steel wire dynamics.

The sea floor spring stiffness used _{corresponded to a static}

de-flection of 0.10 m for the lower water depths up to 0.50 m for 608

m. _{These seafloor springs contained} _{a critical damping term in}

order to prevent bottom impact _resonances.

HOHL1

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HOMM

Time record plots of the forced oscillation, the end-tensions _and

the motions at the "video-mark" node are presented in Part 2 of

this report for the oscillation frequency of 1.0 rad/s.

It should be noted that the plotting routine utilized _{a sampling}

rate equal to the DYNLINE integration time step, whereas the model test results have been plotted at a sampling rate of 25 Hz divided by the model scale squared according to Froude's _{law of similitude.}

As already noticed in Report No. 45064-2-RD, _{the computed tension}

records contain in general high frequency _{parasitical components}

due to the line discretization. Therefore the maximum dynamic ten-sion was derived from the low-pass filtered _{upper-end tension for} those situations where parasitical _{components were observed. Time} record plots of these filtered tensions are included in Part 2 of

this report.

Similar to the experimental procedure, _{dynamic amplification} fac-tors (T+/T0 +) were derived from the _{numerical results (Tables 4,} ₅ and 6) and are presented in the Figures _{21 through 33.}

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4. DISCUSSION

Chains

In the water depth of 75 m for both the 76 mm and 152 mm chains a

good agreement was found between _{experimental and numerical}

re-sults. The time record correlations _{are affected by some high} fre-quency parasitical tensions due to snap-loads _{occurring in the} nu-merical model when the line has been slack. The tension peaks,

how-ever, show a perfect agreement as illustrated by _{Figures 23a and}

23b in _{Part 2. The dynamic amplification factor} _{increased rapidly} for frequencies of oscillation larger than 0.5 rad/s. It should be

noted, however, that the stroke of oscillation was kept constant at

all frequencies. Hence for the higher _{frequency region this}

re-sulted in unrealistic _excitations. _Nevertheless _the _agreement

between DYNLINE and model test _{results was reasonable. For the}

highest frequencies _{some overpredictions as well as underprediction}

was found.

In 150 m water depth the agreement _{between the measured and}

compu-ted tensions was less satisfactory _{for the 76 mm chain. In this}

situation a clear underprediction (10 _{to 25 per cent) was given by}

DYNLINE for all amplitudes of oscillation _{in both the horizontal}

and vertical mode. The largest _{differences were found in the} _drag dominated region (Figure 24). _{Even for conditions yielding nearly} sinusoidal tension records _{(no slackness) these} _{differences were} found (Figure 34 in Part 2). _{For the large amplitudes of} oscilla-tion the measured tension records showed a typical peak _enhancement while the numerical results are characterized by broad global peaks

with several secondary oscillations superimposed which were however removed by low-pass filtering (Figure 38 and 45 in Part 2).

-No explanation could be given for the differences in dynamic ampli-fications. Since these discrepances are observed in the drag domi-nated region, one _{may suspect the drag modelling to fail.}

On the

HOMM

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-9-Report No. 45064-3RD

HOU

10

other hand however it should be pointed _{out that the same model}

test set-up was used for situation No. _{8 which provided a good}

agreement between model test and numerical results.

The amplitude dependency of the dynamic _{effects was similar in}

model tests and numerical model (Figure _{24). When comparing} hori-zontal and vertical oscillation results, _{it may be concluded that}

for the vertical mode the dynamic _{effects are slightly less and}

shifted to higher frequencies. The line _{discretization (16 nodes)}

for the 76 mm chain

_{was also used for situation No.} ₅ _{(152 mm}

chain). These simulations resulted in a perfect deterministic agreement with the measured tensions for _{all amplitudes of}

oscil-lation (Figure 26). The increase in amplitude of excitation resulted in an increase of maximum dynamic amplification which oc-curred at lower frequencies of oscillation. _{The reduction of} dynam-ic effects at high frequencies, _{due to the reduction of global line} motions, is clearly indicated by Figure 26. The model test results for the large strokes (Figure 65 in _{Part 2) show that, the start of} each tension peak after slackness is _{the low frequency equivalent} of the high frequency oscillatory numerical results. From the same

records it can be concluded that the maximum tension amplitude is almost equal for both line ends. _{Besides the "harmonic" components,}

the measured tension records _{also contained some low frequency}

effects, possibly due to higher modes of line motion or

three-di-mensional motions. Such effects _{were not found in long duration}

simulations.

Since situation No. 5 basically describes the same geometrical con-figuration as situation _{No. 1, some information on the effect of} pre-tension on the dynamic behaviour of the line is also included in this test program. Scaling the results of situation _{No. 1 by a} factor 2 for the motions and consequently by 8 for tensions and

1//2 for the _frequencies of _oscillation, _dynamic _{amplification} factors _{for situation No.} 5 were derived _for _{a pre-tension of}

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the 152 mm chain breaking load. In this taut condition, _{with only}

200 m (out of 1050 m) line at the _{sea floor, the dynamic effects}

were slightly higher when compared with the 5000 kN initial _tension (Figure 26). It should be noted, however, that the maximum quasi-static tension (T0+) _{amounted to approximately 16,000 kN which}

almost equals the breaking strength of the full scale _chain.

For the deep water situations No. _{7 and 8 (300 m) both the 76} _mm and 152 mm chain resulted in broad tension peaks. Slackness in the line occurred at the upper-end during a fraction of each oscilla-tion period but longer so at the lower-end. _{For both situations a} perfect deterministic agreement between measurements and computa-tions was found (Figures 29 and 30). _{In the numerical results,} sec-ondary tension components at the tension peaks caused a tension

in-crease up to approximately 10 per cent which _{was removed by low}

pass filtering. Some discrepancies at the higher frequencies _{may be}

due to (3 _{dimensional) higher modes of motions and} _{test set-up}

vibrations.

As situation No. 8 is geometrically similar _{to situation No. 4, the} results of the latter configuration were also scaled to situation No. 8 in order to investigate the influence of pre-tension (Figure 30). The same conclusions drawn from the situations No. 1 and 5 can be deduced there.

In general terms the agreement between _{experimental and numerical} results is good for all chain-water depth combinations with the

ex-ception of situation No. 4. _{At a pre-tension of 30 per cent of} _the breaking strength, the chains _{show important dynamic effects in} _the drag dominated frequency region (0.50 _{- 0.30 rad/s). At high} fre-quencies of oscillation extremely _{large dynamic amplifications of} tension were observed, but it is emphasized here that the amplitude of oscillation was unrealistically large regarding the motions of present-day moored floating structures.

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_HOE41E3

-12-On the basis of Figure 26, _{a strong dependency of dynamic tensions} on the amplitude of oscillation can be concluded. It should be not-ed, however, that this effect may originate from the strongly non-linear static load-excursion relationship _{of this configuration.}

The results of situations No. _{1 and 4 were scaled to} _{compare with}

those of configurations of No. _{5 and 8 respectively, and} _{it was}

found that the dynamic _{amplification does not strongly}

depend on the "pre-tension" (at 30 and _{60 per cent of the breaking} _strength)

in these cases.

The dynamic effects _{seem to reduce with an increase of}

water depth.

Knowing that tangential upper-end motions dominate the dynamic

fects, this apparent reduction can be explained by geometrical

ef-fects and the increase of _{constant tension by the weight of}

the free hanging chain.

The 152 mm chain exhibited _{lower dynamic amplifications}

in 75 m of water when compared with the 76 mm chain, but a strong enhancement for 150 m and almost equal _{values for 300 m.}

Steel wires

As already stated in Section 2, the 76 mm steel wire mooring line was not correctly to scale with respect to the line elasticity. _The

elasticity of the model wires _used, _{corresponded to full scale}

lines with a stiffness which _{is 10 to 60 times the actual values in} use for aged offshore mooring lines (see _{Table 2). The results} ob-tained from model tests _{and DYNLINE simulations}

can therefore not

be considered as _{realistic but should be} _used

for correlation

purposes only.

Furthermore it should be _{noted that the "pre-tension"} _{used for the} steel wire differed from the chain values for practical

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HObiE3

-13-For the 75 m water depth (situation No. 3) _{a pre-tension of 420 kN} was adjusted. In this situation the 525 _{m long line was completely} free from the sea floor. These _{tests yielded smooth tension}

peaks

with long periods of slackness _{even at low frequencies of} oscilla-tion. This means that the line _{"flies" in the water under the} in-fluence of inertia (gravity) and drag only, as was clearly observed during the model tests.

A good agreement with the DYNLINE results is shown by Figure 23. It

appeared that the dynamic effects grew rapidly with increasing fre-quencies but reduced again at frefre-quencies _{above 1.0 rad/s.}

In situation No. 6 (150 m water depth, pre-tension 811 kN) the dy-namic amplification started _{at low frequencies of oscillation} _and increased 4 up to 7 at its maximum. _{Figure 27 shows these results,} illustrated a reduction of the dynamic _{ratio with increased stroke.} The absolute magnitude of maximum tensions, however, increased with

the stroke but not as much as _{the maximum quasi-static values.}

Though the differences for _{the smaller amplitude} _{are significant,} DYNLINE provided reasonable _{results for the larger amplitudes.}

The

differences in this trend _{may be explained by the small shift in} the initial condition and _{the strong non-linearity of the}

static

load-displacement curve. Configuration 6 _{was also subjected to}

vertical oscillations (Figure 28).

Figure 31 summarizes the _{results for situation No.} _{9. The effects} observed in situation No. _{6 were more pronounced here. Evaluating}

the discrepancies between _{numerical and experimental} _{results it}

should be noted that the static load of the model wire is extremely non-linear due to the large material stiffness. Comparing the ex-perimental quasi-static tensions _{with those obtained_from} _DYNLINE,

it can be concluded that _{the material stiffness} _{may be one of the} explanations for the differences _{found, since the bending}

stiffness

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HOEI3

-14-Since the full scale material elasticity and pre-tension _{was not}

kept constant for all test situations no general conclusions _with respect to the effects of water depth and pre-tension _{can be drawn.} Also a comparison with mooring chains cannot be made. Taking _into account that the differences between model tests and numerical

re-sults decrease with reduction of the material elasticity _{of the}

model wire (Figures 31, 27 and 23 respectively), it may be expected that for realistic material elasticities DYNLINE will provide _valid

results.

Combi-lines

Composite lines built up from 76 _{mm chain (lower half) and 76 mm} wire (upper half) were tested in water depths of 300 m (situation No. 10) and 608 m (situation No. 11).

Both situations were tested at a scale of 1:76. _{Hence, during the} model tests of 1 mm chain and 1 _{mm wire of equal length was used.} It should be noted that at full scale the steel wire dominates the elasticity of such lines while in the model tests the wire section hardly contributed to the line elongation. The static configuration for these situations featured long _{on-bottom line sections as shown} by Figures 19 and 20. Using total line lengths of 2100 m and 3040 m

for 300 m and 608 m water depth respectively, _{80 per cent of the}

chain was on the sea floor in both static _{configurations.}

The tests at both water depths _{provided nearly the same results}

when comparing the tension records _{(Figures 112 and 118 in Part 2)} and the dynamic amplification ratios _{(Figures 32 and 33). In} par-ticular, situation No. 10 yielded dynamic _{tension contributions at} low frequencies of oscillation as demonstrated by extra model tests and simulations for 0.13 and 0.25 rad/s. _{The dynamic amplification}

of tension is almost constant for frequencies above _{0.50 rad/s}

(Figures 32 and 33). The _{test results were slightly overpredicted} by DYNLINE for situation No. 10 and confirmed _{for situation No. 11.}

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HOMM

-15-The numerical tension records showed the usual high _frequency

os-cillation at the start of each tensioning after slackness. _Some

tension variations at these points were also observed in the mea-sured records. The simulated tension peaks showed also _additional

frequency components which were suspected to be due to numerical

effects and use of low-pass filtering a perfect agreement with the experimental records was found.

When compared to the single component steel wires and chains, the

combi-lines featured extra tension amplification in _{the low}

fre-quency region but a clear reduction of dynamic effects at higher

frequencies. As stated before, the dynamic tension effects are

mainly due to tangential upper-end oscillation, therefore the

initial vertical upper-end line angle should be taken into account

when evaluating the differences between _{the results of different}

configurations. Vertical components of upper-end motion may contribute significantly in _{configurations} _with _large _4,-values

(Figure 1).

Motions recorded by underwater video

A good qualitative agreement was found between _{the motions recorded}

by video and corresponding node motions _{computed by DYNLINE. The}

amplitudes of motion appeared to exceed the computed values by some 5 to 10 per cent, but this may be due to the distance between the line and the wire grid and the direction of the video which was not completely perpendicular to the mooring line.

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5. CONCLUSIONS

From the deterministic correlation between _the _results _{of the}

harmonic oscillation model tests and mathematical simulations for

eleven combinations of different water depths and types of mooring lines, the following conclusions can be drawn:

The computer program DYNLINE provides _{accurate tension records}

due to harmonic upper-end line oscillations.

Frequency independent (average) _{hydrodynamic coefficients}

ob-tained from model tests can be used to describe the fluid reac-tive forces on the line.

The "Dynamic amplification ratio" for tension _{as defined in the}

present study strongly depends on non-linearity _{of the static}

load-excursion relationship of _{the mooring line and should}

therefore be treated with care.

Dynamic amplification of tension _{may be considerable especially} for combinations of high amplitudes and high frequencies of oscillation.

The influence of the direction of motion on the dynamic tension strongly depends on the configuration. Keeping _{in mind that} in-line upper-end oscillations will _{dominate the dynamic behaviour} of the line, it is preferable _{to define the motions in terms of} "tangential" and "normal" rather than vertical _{and horizontal}

di-rections.

The ultimate amplification of tension _{strongly depends on the}

motion characteristics of the floating structure at higher fre-quencies (0.5 - 1.5 rad/s).

RD3

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l6-Report No. 45064-3-RD

- Chain-wire combi-lines exhibited dynamic amplification even at

low frequencies of oscillation (0.25 - 0.50 rad/s).

Wageningen, November 1984. NETHERLANDS SHIP MODEL BASIN

Dr Ir M.W.C. Oosterveld

Head Research and Development Division

AGvD/gt

HOHM

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NOMENCLATURE

HO13

B = width

BS = breaking strength

D = diameter

dc = volumetric diameter

EA = product of line elasticity and cross-section _area

FX = horizontal upper-end force component

FZ = vertical upper-end force component

FX-A = tension at anchor point

L = length

M = mass

S = stroke T = tension

To = initial tension or "pre-tension"

T +₀ _{= maximum quasi-static tension} T+ = maximum dynamic tension

W = weigth

A _{= model scale}

= vertical line angle in rad

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Report No. 45064-3-RD

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-19-Report No. 45064-3-RD

Mooring Line Dynamics

REVIEW OF SITUATION No. 1 TO 11

NOTE: _{* Horizontal and vertical oscillations}

° Situation No. 4 corresponds _{to situation No. 8 by scaling} Situation No. _{1 corresponds to situation No. 5 by scaling}

Table 1

Water depth 75 m A = 19 Water depth 150 m A = 38 Water depth 300 m A = 76 Water depth 608 m A = 76 Chain D = 0.076 m Situation 10 Situation 4*0 Situation 7 -Chain D = 0.152 m ---Situation 2 Situation 5° Situation 8° Steel wire D = 0.076 m Situation 3 Situation 6* Situation 9 Combi-line D = 0.076 m Situation 10 Situation 11

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Report 45064-3-RD

PARTICULARS OF ANCHOR CHAINS Chain type: DIN 766 (D = 0.076 m)

PARTICULARS OF STEEL WIRES

(D = 0.076 m)

HOUM

Table 2

Model chains Prototype chain

o BS = 4.38*106 N - EA = 0.694*10- N D B L M W d EA A _M _W , d EA_a mm mm mm kg/m N/m inc N*105 _kg/m _N/m _mc N*10-1.0 4.2 7.9 0.021 0.177 0.0019 0.03 76 124 1043 0.144 1.19 2.0 6.8 12.0 0.080 0.690 0.0036 0.11 38 119 1021 0.137 0.60 4.0 14.2 22.8 _0.338 _{2.374 0.0076} _7.00 ₁₉ ₁₂₅ ₁₀₆₃ 0.144 4.90 8.0 26.9 40.1 1.383 11.801 0.0151 22.00 9.5 128 1092 0.144 1.93

Model wires Prototype wire

8 EA = 3.2*10S N - 4.4*10 N _ D mm M kg/m W N/m dcm EA 5 N*10 A m kg/m W N/m dcm EA N*1010 1.0 _0.00401 _0.034 _0.001 _0.5 76 23.2 204 0.076 2.3 2.0 _0.0164 _0.144 _0.002 _2.3 38 24.3 213 0.076 1.3 4.0 0.0608 0.540 0.004 5.1 19 22.5 199 0.076 0.36

(25)

DYNLINE INPUT DATA

Static deflection of sea floor (depend on water depth)

Time increment (depend _{on situation)}

Starting time

Duration of simulation

HOMM

0.10 - 0.50 m

0.01 - 0.20 s

2 oscillations 5 oscillations

Table 3

Line discretization _{according to Figures 2}

- 20

Line data _{according to Table 2}

Normal added inertia coefficient _1.60

Tangential added inertia coefficient _0.20

Normal drag coefficient _1.30

Tangential drag coefficient _0.40

(26)

Report No. 45064-3-RD

REVIEW OF THE TESTS AND THE RESULTS

K2HT131

_{Table 4}

Oscillation Model test _DYNLINE

Situ-at ion Test No. Fre-quency LA) Stroke s Quasi-static Dynamic Dynamic ratio Quasi-static Dynamic Dynamic ratio No. in rad/s in m T0 in kN T + 0 in kN T+ in kN T+ T 0 in kN T + 0 in kN T+ in kN T+ T + 0 T +₀ 1 6654 0.51

2.0

₁₂₅₉ ₁₉₉₅ 2720 1.36 1280 2000 2818 1.41 6658

0.76

₃₆₇₀ _1.84 ₄₀₄₀ 2.02 6655 1.01 ₅₄₆₀ _2.74 ₅₄₁₆ _2.71 6656 1.26 ₇₀₄₀ _3.53 7417 3.71 6657 1.50 ₈₁₆₀ _4.09 ₈₉₄₉ _4.47 2 6682 0.52 1.5 5095 7040 7040 1.00 5040 6936 7101 1.02 6685 0.76 ₈₆₄₀ _1.23 ₈₄₂₁ 1.21 6683

0.99

₁₁₂₀₀ _1.59 ₁₀₈₃₅ _1.56 6684 1.23 ₁₆₈₈₀ _2.40 ₁₅₂₂₂ _2.19 6686 1.45 ₂₁₄₄₀ _3.05 ₁₉₇₇₅ _2.85 3 6790 0.35

2.0

₄₂₀ ₂₈₉₀ ₃₀₄₀ _1.05 ₃₇₆ 2834

-

-6785

0.50

₃₅₂₀ _1.22 ₃₆₆₉ _1.29 6786 0.75 ₄₁₈₀ _1.45 ₄₅₄₂ _1.60 6788

0.89

₄₃₈₀ _1.52 ₄₈₈₀ _1.72 6787

0.99

₄₅₂₀ _1.56 ₅₁₁₇ _1.81 6791 1.25

_-

₅₀₀₀ _1.76 6789 1.47 ₄₈₀₀ _1.66 ₃₇₀₀ 1.31 4 6710 0.52

2.0

1324 1535 1960 1.28 1319 1482 1754 1.18 6711 0.77 ₂₄₂₀ _1.58 ₂₀₅₅ 1.39 6712 1.02 ₂₈₀₀ _1.82 2244 1.51 6713 1.26 ₃₀₂₀ _1.97 ₂₃₆₂ 1.59 6714 1.50 ₃₁₀₀ _2.02 ₂₅₉₅ 1.75 4 ₆₆₉₇ _0.51

_4.0

₁₃₂₄ ₁₇₉₂ 3000 1.67 1319 1688 2459 1.46 6698 0.75 ₃₇₈₀ _2.14 2983 1.77 6699 0.97 ₄₁₄₀ _2.31 ₃₂₉₄ 1.95 6700 1.22 ₄₂₂₀ _2.35 3422 2.03 6701 1.46 ₄₀₀₀ _2.23 ₃₇₁₄ 2.20 6702 1.92 ₃₉₆₀ _2.21 3718 2.20 4 6704₆₇₀₅ 0.51_0.76

6.0

1324 2082 4160 2.00 1319 1937 3278 1.69 4960 2.38 ₃₉₁₃ _2.02 6706 1.01 ₅₂₃₀ _2.51 _ 4029 2.08 6707 1.24 ₅₀₀₀ _2.40 4527 2.34 6708 1.47 ₄₈₄₀ _2.32 ₄₇₄₅ 2.45 4 ₆₇₁₆ _0.51

_4.0

₁₃₆₉ ₁₄₆₃ ₁₈₄₀ _1.26 1396 1505 1806 _1.20 6717 0.77 ₂₄₀₀ _1.64 ₂₁₇₁ 1.44 VER- 6718 1.01 ₂₈₆₀ _1.95 ₂₃₆₅ _1.57 TICAL 6719 1.26 ₃₁₄₀ _2.15 ₂₄₁₁ 1.60 6720 1.49 ₃₁₈₀ _2.17 ₂₄₃₅ _1.62

(27)

Report No. 45064-3-RD

* Low-pass filtered

DD

Table 5

Situ-Test Fre- Stroke Quasi- Dynamic Dynamic Quasi- _Dynamic Dynamic

ation quency static ratio static ratio

No. w S No. in T0 T +0 T+ T+ _T0 T +0 T+ T+ T0+ _To+ rad/s in m in kN in kN in kN in kN in kN in kN 5 6668 0.51 2.0 5012 5880 6400 1.09 5110 5845 6312 1.08 6672

0.76

8000 1.36 ₈₁₃₀ _1.39 6669 1.01 10290 1.75 9454 1.62 6670 1.25 14240 2.42 13673 2.34 6671 1.48 ₂₃₀₄₀ _3.92 ₂₁₆₀₀ _3.70* 5 6663 0.51

4.0

5012 6725 9600 1.43 5110 6753 10157 1.50 6667

0.76

14320 2.13 14747 2.18 6664 1.01 ₂₇₆₀₀

_4.10

₂₈₀₀₀ _4.15* 6665 1.25 40160 5.97 40800 6.04* 6666 1.48 ₄₂₄₀₀ _6.30 ₃₈₈₀₀

_5.75'

5 6673 0.51

6.0

5012 8140 15760 1.94 5110 8098 16754 2.07 6676

0.76

28960 3.56 27500 3.40* 6674 1.00 ₄₉₂₀₀ _6.04 ₅₀₄₀₀ _6.22* 6675 1.25 55600 6.83 55100

6.81'

6677 1.47 ₅₄₅₀₀ _6.70 ₄₄₈₀₀

_5.53'

6678 1.91 ₄₅₄₄₀ _5.58

_-

-6 6773

0.25

2.0

811 1240 2200 1.77 799 1215

-

-6768 0.51 ₄₁₈₀ _3.37 ₄₃₀₀ _3.54 6769 0.76 ₅₃₆₀ _4.32 ₆₂₃₅ _5.13 6770 1.00 6040 4.87 7544 6.21 6771 1.25 ₆₄₂₀ _5.18 ₈₆₀₀ _7.08 6772 _1.48 ₆₆₀₀ _5.32 9000 7.41 6 6767 0.25 3.0 811 2022 4160 2.06

-

-6762 0.51 7180 3.55 _ _ 6763

0.76

8520 4.21

-

-6764 1.00 ₉₂₀₀ _4.55

_-

-6765 1.25 ₉₄₄₀ _4.67

_-

-6766 1.46 ₉₆₄₀ _4.77

_-

-6 6761

0.25

3.5 811 2797 5040 1.80 799 3680

-

-6756 0.50 ₈₃₈₀ _3.00 ₁₁₀₅₀ _3.00 6757

0.76

₉₈₀₀ _3.50 ₁₃₃₀₀ _3.61 6758 0.99 ₁₀₆₀₀ _3.79 _ 14270 3.88 6759 1.24 ₁₀₆₅₀ _3.81 ₁₅₄₄₀ _4.20 6760 1.46 ₁₀₇₀₀ _3.83 _- -6 ₆₇₈₀ _0.25 _2.0 ₈₄₂ ₈₈₅ ₉₄₀ _1.06 830 875 - -6775 0.51 1160 _1.31 ₁₁₂₀ _1.28 VER- 6776 _0.76 ₁₄₂₀ _1.60 1440 1.65 TICAL 6777 _1.00 ₁₆₈₀ _1.90 1820

2.08

6778 1.25 ₂₀₀₀ _2.26 ₂₂₂₇ _2.55 6779 1.48 ₂₃₅₀ _2.66 ₃₀₀₀ _3,43

(28)

* Low-pass filtered

Situ-ation Test Fre-quency Stroke Quasi-static Dynamic Dynamic ratio Quasi-static Dynamic Dynamic ratio No. U) S No. in T0 T +0 T+ T+ T₀ T +₀ T+ T+ T0+ _To+ rad/s in m in kN in kN in kN _{in kN in kN} _{in kN} 7 6729₆₇₃₀ 0.51

4.0

1346 1460 2040 1.40 1330 1428 1970 1.38 0.76 ₂₆₄₀ _1.81 ₂₅₂₈ _1.77 6731 1.00 ₃₃₀₀

_2.26

₂₉₀₀ _2.03* 6732 1.23 ₃₃₅₀ _2.33 ₃₀₀₀ 2.10* 6733 1.46 ₃₁₄₀

_2.15

₂₅₀₀ _1.75* 8 6723

0.51

4.0

4972 5472 6800 1.24 4985 5360 6438 1.20 6724 0.75 ₈₉₆₀ _1.64 ₈₁₅₂ _1.52 6725

0.99

₁₂₄₀₀

_2.27

₁₁₆₀₀ _2.16* 6726 1.21 ₁₄₄₀₀ _2.63 ₁₂₂₀₀ _2.27* 6727 1.44 ₁₄₀₀₀

_2.56

₁₁₂₀₀ _2.09* 9 ₆₇₃₅ _0.51

_4.0

₁₃₅₁ ₁₆₉₄ ₈₀₀₀ _4.72 1335 1770 11440

6.46

6736 0.75 ₉₁₀₀ _5.37

_-

-6737 1.00 ₉₃₅₀ _5.51 ₁₄₆₀₀ _8.25 6738 1.22 ₉₃₀₀ _5.49

_-

-6739 1.46 ₈₉₁₀

_5.26

₁₅₅₀₀

_8.76

10 6754₆₇₅₃ 0.13

4.0

1245 1763 2040 1.16 1240 1716 1915 1.15 0.25 ₂₈₆₀ _1.62 ₂₆₆₃ _1.60 6748 0.49 ₃₅₀₀ _1.99 ₃₆₈₄ _2.21 6749 0.73 ₃₇₆₀

_2.13

₃₉₀₀

_2.30*

6750 0.97 ₃₉₂₀ _2.22 ₄₀₀₀ _2.33* 6751 1.20 ₃₈₆₀

_2.19

₄₃₀₀ _2.51* 6752 1.43 3740 _2:12 ₃₉₀₀

_2.27*

11 113010₁₁₃₀₁₁

0.25

4.1

1298 1480 2060 1.39 1250 1475 2080 1.41 0.49 2840 _1.92 ₂₈₉₆ _1.96 113014 0.73 ₃₂₈₀

_2.22

₃₃₀₀ 2.24* 113015 0.96 ₃₄₄₀ _2.32 ₃₃₃₀ _2.25* 113016 1.19 ₃₃₈₀

_2.28

₃₂₀₀

_2.17*

113017 1.41 ₃₁₆₀

_2.14

3200

2.17*

113018 1.69 ₂₇₀₀ _1.82

_-

(29)

Report No. 45064-3-RD

MODEL TEST SET-UP AND DEFINITIONS

Z

HOHM,

Fig.

1

(30)

Report No. 45064-3-RD

SITUATION No. 1 Water depth Chain diameter Chain length Oscillation Sx Quasi-static T0 Quasi-static T0+ 0

HOEM

75.0 0.076 m 525.0 2.0 1259.0 kN 1995.0 kN Fig. 2 13 99.8 m _{416.3 m}

(31)

Report No. 45064-3-RD

/

///A\\\\\\\\\w////7//<\\

SITUATION No. 2 Water depth 75.0 Chain diameter _{0.152 m} Chain length 525.0 Oscillation Sx 1.5 Quasi-static T0 5095.0 kN Quasi-static T0+ : 7040.0 kN Lk'1'

M113

1 3 123.1 m

392.9 m

Video mark

Fig. 3

13

(32)

1

/ ///A\\\\\\\\\V/ ///// /,<\\

SITUATION No. 3

Water depth _75.0

Steel wire diameter : 0.076 in

Steel wire length _525.0 Oscillation Sx 2.0 Quasi-static T0 420.0 kN Quasi-static T0+ 2890.0 kN

HOE13

Fig. ,4

12

Video mark

1

(33)

Report No.

4 50 6 4- 3-RD

SITUATION No. 4 Water depth 150.0 in Chain diameter 0.076 in Chain length 1050.0 Oscillation Sx 2.0 Quasi-static T0 1324.0 kN Quasi-static T0+ 1535.0 kN

HOMDs

Fig. 5

16

464.3 m

(34)

1

6

464.3 m

SITUATION No. 4 Water depth _150.0 _m Chain diameter : 0.076 m Chain length _1050.0 in Oscillation Sx 4.0 in Quasi-static T0 : 1324.0 kN Quasi-static T0+ 1792.0 kN

HOWE)

Fig. 6

16

562.4 in

Video mark

(35)

Report No. 45064-3-RD

SITUATION No. 4

Water depth : 150.0 in

Chain diameter 0.076 in

HOREM

Fig. 7

16 Chain length : 1050.0 in Oscillation Sx : 6.0 in Quasi-static T0 1324.0 kN Quasi-static T0+ : 2082.0 kN 464.3 m 562.4 m

(36)

Report No. 45064-3-RD

1

///

\\\\ \

SITUATION No. 4 Water depth 150.0 in Chain diameter 0.076 in Chain length 1050.0 Oscillation Sz 4.0 Quasi-static T0 1369.0 kN Quasi-static To+ : _1463.0 _kN

HOHM

Fig. 8

16 6

\\\\\\\\(e////////

\\\\

_\\V////

464.3 m 562.4 in

(37)

A

Report No. 45064-3-RD

1

SITUATION No. 5 Water depth _150.0 Chain diameter _{0.152 m} Chain length _1050.0 Oscillation Sx 2.0 Quasi-static To : 5012.0 kN Quasi-static T0+ _5880.0 _kN 6

HOM

559.9 m Video mark Fig. 9 16 464.1 m

///11'.

_{\\\ \,\ W/")11/./W/>/7 4\\}

_\

1

(38)

Report No. 45064-3-RD

1

6

\\'' \\'.\\K\7/././

_{7///i74\\\\\\\}

SITUATION No. 5

Water depth _150.0 in

Chain diameter : 0.152 in

HOW:3

Fig. 10

16 Video mark

/

//,

\

464.1 m 559.9 m Chain length _1050.0 in Oscillation Sx : 4.0 in Quasi-static T0 : 5012.0 kN Quasi-static T0+ : 6725.0 _kN

(39)

A

Report No. 45064-3-RD

SITUATION No. 5 Water depth _150.0 _m Chain diameter _{0.152 m} Chain length : 1050.0 m Oscillation Sx : 6.0 m Quasi-static T : 5012.0 kN 0 Quasi-static T0+ : 8140.0 kN

Fig. 11 16

HOhi

D) e_g) 464.1 m 559.9 m

(40)

Report No. 45064-3-RD

HOME3

Fig. 12

13

SITUATION No. ₆

Water depth : 150.0 m

Steel wire diameter : 0.076 m

Steel wire length : 1050.0 m

Oscillation Sx : 2.0 m Quasi-static To : 811.0 kN Quasi-static T0+ : 1240.0 kN 200.0 m _{836.0 m}

(41)

Report No. 45064-3-RD

SITUATION No. 6

Water depth _150.0 _m Steel wire diameter _{0.076 m} Steel wire length : 1050.0 m

Oscillation

Sx 3.0 m

Quasi-static

T0 : 811.0 kN

Quasi-static T0+ : 2022.0 kN

Fig. 13

13

(42)

/ ///,A\\\\\\W(///

SITUATION No. 6

Water depth _150.0 _in Steel wire diameter _{0.076 in} Steel wire length : 1050.0 _in

Oscillation Sx 3.5 in Quasi-static T0 : 811.0 kN Quasi-static T0+ : 2797.0 kN

HOED

200.0 in

836.0 in

Video mark

Fig. 14

(43)

Report No. 45064-3-RD

SITUATION No. 6

Steel wire diameter : 0.076 m

Steel wire length _1050.0 _m Oscillation Sz 2.0 m Quasi-static To : 842.0 kN Quasi-static T0+ : 885.0 kN

HOUL3

Fig. 15

13

(44)

Report No. 45064-3-RD

SITUATION No. 7

Chain diameter : 0.076 m

Fig. 16

17 Chain length : 2100.0 m Oscillation Sx : 4.0 m Quasi-static T0 : 1346.0 kN Quasi-static T0+ : 1460.0 kN

(45)

Report No. 45064-3-RD

HOED

Fig. 17

17 SITUATION No. Water depth Chain diameter Chain length Oscillation Sx Quasi-static T 0 Quasi-static T0+ : 8 300.0 0.152 m 2100.0 4.0 4972.0 kN 5472.0 kN

(46)

Report No. 45064-3-RD

SITUATION No. 9

Water depth _300.0 _m Steel wire diameter _{0.076 m} Steel wire length : 2100.0 m

Oscillation

Sx 4.0

Quasi-static To : 1351.0 kN

Quasi-static T0+ : 1694.0 kN

HORE

Fig. 18

13

(47)

1

Report No. 45064-3-RD

830.6 m

Chain diameter : 0.076 m

Wire diameter : 0.076 m

HOREM

7

///

.\\\.\\\\W / ///

/ ///

_\\\

t////\

2060.3 m Video mark Fig. 19 17 // SITUATION No. 10 Water depth : 300.0 m

Total line length : 2100.0 m

Chain (lower part) : 1050.0 m

Wire (upper part) : 1050.0 m

Oscillation

Sx : 4.0 m

Quasi-static T

0 : 1245.0 kN

(48)

Report No. 45064-3-RD

SITUATION No. 11

Water depth : 608.0

Total line length : 3040.0

Chain (lower part) : 1520.0

Wire (upper part) : 1520.0 m

Chain diameter _{0.076 m} Wire diameter _0.076 _m Oscillation Sx 4.1 m Quasi-static T0 : 1298.0 kN Quasi-static T0-1- : 1480.0 kN

HOEM

Fig. 20

18

(49)

Report No. 45064-3RD

7.5

5.0

2.5

DYNAMIC RATIO

Situation No. 1

W in rad/s

HOM,

Fig. 21

DYNLINE _Measured _Oscillation

0

_{S = 2.0}

_m

0.5 _1.0

(50)

Report No. 45064-3-RD

7.5

5.0

2.5

0

DYNLINE Measured _Oscillation

0

_{S = 1.5}

_m

0 Mooring Line Dynamics

DYNAMIC RATIO

Situation No. 2

Hnin

Fig. 22

0 _0.5

1 . 0

15

(51)

Report No. 45064-3-RD

7.5

5.0

2.5

DYNLINE

DYNAMIC RATIO Situation No. 3 Measured _Oscillation 0 _{S = 2.0 m} w in rad/s

HOMII3

Fig. 23

0.5 _1.0

(52)

Report No. 45064-3RD

7.5

5.0

2.5

DYNAMIC RATIO

Situation No. 4

Fig. 24 DYNLINE _Measured 0 a 0 Oscillation S =

2.0

m S = 4.0 m S = 6.0 m - --, ..---I'' ---

-

---A---

C - --o a

- ---o

---_-_-_aLt _ ____ tic

--

4,

..../-

-- --

-0.5

_Jo

1 . 5 w in rad/s

(53)

Report No. 45064-3-RD

7.5

5.0

2.5

0

DYNAMIC RATIO

Situation No. 4 - _{Vertical oscillation}

L) in rad/s

:HOH

Fig. 25

0

_0.5

(54)

Report No. 45064-3-RD

7.5

5.0

2.5

0

DYNAMIC RATIO

Situation No. 5

OH73

_{Fig. 26}

W in rad/s DYNLINE _Measured 0 A 0 A Oscillation S = 2.0 m S = 4.0 m S = 6.0 m S = 4.0 in (From situation

-- T0=

5012 -T0 = 10072 No. 1) kN kN

---//

,,,.

Z

cl,

\

0 A

A

/I

/

//

/

,/

....

\

N. /

/

/''1

/

// 0

//

,

//1(

I/ ,/

,/

/

,,e4

.../.2'1/

.

///4S/

1' ...,

/

.

...--- ... --0.5 _1.0

15

(55)

Report No. 45064-3-RD

7.5

5.0

2.5

0

DYNAMIC RATIO

Situation No. 6

U) in rad/s

HOU

Fig. 27

DYNLINE _Measured 0 Oscillation S = 2.0 m S =

3.5

m - A . ... ...r. ... ... ...

/

__..z ...1 ... ...

IV

a.... ...

/

_ 0

_0.5

_1.0 1.5

(56)

7.5

5.0

2.5

0

DYNAMIC RATIO

Situation No. 6 - _{Vertical oscillation}

Report No. 45064-3-RD

TNE75- _{Fig. 28}

0

_0.5

1.0 _1.5

W in rad/s

DYNLINE Measured Oscillation

(57)

Report No. 45064-3-RD

4.0

7.5

5.0

2.5

0

DYNAMIC RATIO

Situation No. 7

0 _{S = 4.0 m}

0 0

Ki0a113

Fig. 29

0

_0.5

1.0

₁₅

(58)

7.5

5.0

2.5

0

DYNAMIC RATIO

Situation No. 8

w in rad/s

0 _{S = 4.0 m} _T0=

4772 kN S = 4.0 m

T0 = 10592 kN (From situation No. 4)

----0

-r..--__________..,

-Report No. 45064-3-RD

OM]

_{Fig. 30}

0 _0.5

(59)

Report No. 45064-3-RD

7.5 5.0

2.5

0 W in rad/s

DYNAMIC RATIO

Situation No. 9

Fig. 31 DYNLINE 0 Measured Oscillation 0 _{S = 4.0 m} 0 ₀ 0 0 1.5 1.0

0.5

(60)

+0

7.5

5.0

2.5

0

DYNAMIC RATIO

Situation No. 10

0 S = 4.0 m

0 0 0

_

Report No. 45064-3RD

L'MS DU I

_{Fig. 32}

0

05

1.0 1.5

(61)

7.5

5.0

2.5

0

DYNAMIC RATIO

Situation No. 11

0 _{S = 4.1 m}

HOEMI

Fig. 33

0 _0.5

1.0