WJ DEN HELD and R W BOS
Gusto Engineering B.V., The Netherlands
ABSTRACT
The paper deals with the loads on, and the strength of, the elevated legs of a jack-up rig during wet towage.
To ensure the safety of a towage, classificatIon societies and other bodies have issued rules and regulations for calculating the strength of jack-up legs. As far as the inertial portion of the leg loads
is concerned, these rules and regulations prescribe fixed criteria based on the linear motional
behaviour of existing, relatively small rigs. Frequently, however, an option is afforded whereby leg loading may be determined by model testing.During the design of a large jack-up rig for the North Sea, it was decided that model tests should be carried out, the expectation being that the results, translated into leg loads, would produce some
latitude in comparison with the existing fixed criteria. In particular, it was anticipated that the
motions of the rig would prove to be substantially less than was assumed by the fixed criteria, by reason of its relatively long natural periods and the limiting effects of non-linear phenomena such as flooding of the deck and viscous damping.A model test programme was set up, in which the certifying authority and classification society for the rig were involved, and a range of sea states was defined, in which the tests had to be performed. To approach the problem directly, it was decided to measure the accelerations in the legs and from these to calculate inertial leg loads by straightforward methods. Because of its direct approach, the method presented could, it was felt, serve as an example for dealing with simliar problems in the future.
Analysis of the results led to some interesting conclusions which reflect the non-linearity of the rig's motional behaviour.
NOTATION
H113 Significant wave height.
1max Maximum wave height. Mres Resulting bending moment. M, Bending moment in x-direction.
Bending moment in y-direction.
N Number of oscillations. ii Acceleration in x-direction.
Acceleration in y-direction. Acceleration in z-direction. Angle of wave incidence.
Second International Symposium on Ocean Engineering and Ship Handling 1983, Swedish Maritime Research Centre SSPA,
P.O. Box 24 001, S-40022 Gothenburg
AUG. 1983
Lab. y.
Scheepsbouwkuncle
VARCHLEF
Technische Hogeschool
MEASUREMENT OF WET TOWAGE LEG LOADING Delfi
,
ON A MODEL OF A LARGE JACK-UP RIG
/
INTRODUCTION
A jack-up rig can stand on the sea floor or float in the water. ThE jack-up concept combines the
immobility in waves of a bottom-supported structure with the ease of transport of a floating
structure. Because of this "dual nature", there are two principal design conditions for a jack-up rig, the standing condition and the transit or transport condition.It is the intention that a rig of this type should spend most of its life in the jacked-up position, and for this reason the standing condition is of primary importance from the point of view of leg design. But it is also necessary to ensure that the legs possess adequate strength to withstand all loads which occur when the rig is moved from one location to another. This may be by wet towage, in which case the rig floats on its own pontoon, or by dry towage, when it is placed on a barge or other vessel. This paper deals with the leg load and leg strength for the wet towage of a jack-up rig.
1. EXISTING CRITERIA 1.1 General
Classification societies and other regulatory bodies have laid down rules pertaining to the strength of jack-up legs in the transit condition, and these must be complied with in order to obtain the necessary
certificates and to satisfy insurance underwriters that the risks during the transport of a rig are
acceptable.
The criteria set out in the rules and regulations are aimed at ensuring that towages are safe. They must therefore cover the maximum probable leg loads in a variety of weather types and related sea states for various types of jack-up rig.
Bearing in mind the number of jack-up rigs and the period which has elapsed since the first ones were constructed, it will be obvious that the operating experience can only be expressed in terms of a few thousand rig years. This, however, covers both the operating and transit conditions, and since a rig spends only a small part of its life under tow, or being mobilized for towage or made ready after
towage, the experience of rigs in the transit condition is only a fraction of the total time and is
certainly not adequate to permit statistical analysis.The criteria, therefore, are often empirical; they also appear to be somewhat arbitrary. Considering their general nature, they may be quite appropriate for some rig types, while for others they may lead to overdesign.
1.2 Explanation of existing criteria
A summary of the existing wet towage leg load criteria is given in Table 1. For more detailed
information, the specific rules and regulations issued by the agencies should be consulted.
The criteria require that the leg strength be determined by applying prescribed loads to the legs; the stresses originating from those loads may not exceed certain levels.
The leg load to be considered consists of: inertial load
gravity load
wind load and
shockload.
In calculating the inertial portion of the leg load, a harmonic rolling or pitching motion of the rig about an arbitrary point, with a prescribed amplitude and period, must generally be assumed. The type of rig transport, which may be a location towage or an ocean towage, determines the numerical value of the amplitude and period to be used in the calculation. The fixed criterion of amplitude and period seems to be generally appropriate: "The units which have complied with it have had few structural problems. Those which have failed to meet it have on occasions suffered leg damage in rough weather". /1/
TABLE i - Simplified overview of existing wet towage leg load criteria.
ABS Inertial bending moment from motion 6 degrees at natural period plus 120% of gravity moment.
DNV
GL
lACS
Inertial load from motion 6 degrees at natural period plus 120% of gravity load.
120% of inertial load from motion 15 degrees at 10 seconds plus 120% of static load plus wind load. Bending moment depending upon a.o. stability moment.
Inertial bending moment from motion 6 degrees at natural period plus 120% of gravity moment.
LR Inertial bending moment from motion 10 degrees at 10 sec. plus wind bending moment plus 125% of gravity bending moment.
NDA Loads resulting from motion 10 degrees at 10 seconds plus 20% shockload.
RINA Inertial bending moment from motion 6 degrees at natural period plus 120% of gravity moment.
Bending moment equal to 120% Only for ocean transit. of sum of inertial moment and
gravity moment. Minimum criterion is 15 degrees at 10 seconds.
Inertial gravity and wind moment resulting from most severe anti-cipated environmental condition. Alternatively inertial bending moment from motion 15 degrees at
10 seconds plus 120% of gravity moment.
Not explicitly mentioned.
Only for ocean transit.
Not explicitly mentioned.
Only for ocean transit.
No fixed criteria. Inertial Not explicitly gravity and wind moment resulting mentioned. from most severe environmental
conditions as envisaged. Loads resulting from motion
20 degrees at 10 seconds plus
20% shockload.
Inertial, gravity plus wind moments resulting from most severe anticipated
environ-mental condition. Alternatively inertial bending moment from
motion 15 degrees at 10 seconds plus 120% of gravity moment.
Both for location and ocean transit.
Only for ocean transit.
195
Agency Location transit Ocean transit Loads derived
from model tests
BV Calculate inertial and gravity load created by motions under wave and wind action.
Alternatively static forces due to gravity for an angle of inclina-tion derived from stability.
Not only for the inertial leg load, but also for the gravity and wind load some agencies prescribe fixed criteria. Others however, consider- the leg load computed on the basis of motion adequate to allow for gravity and wind load. In such case these loads may be ignored for the purpose of the calculation. In some cases it is necessary to add the shock load, which is usually a percentage of the inertial load. However, if, prior to a towage, special precautions are taken, such as placing wedges between the legs and guides, the shockload can be omitted in the calculations.
From Table I it should be noted that the amplitude and period prescribed for a location transit result in a lighter leg load than would follow from the ocean transit criterion. The reason for this is that a location transit is defined as being less risky, sincè it would be carried out in reasonable weather conditions, or could be stopped if the weather threatened to deteriorate.
Further examination of the table reveals that almost every agency has its own specific criteria. While there may be conformity in terms of the amplitude and period, the criteria differ in that in some cases they refer to load, and in others only to bending moment. There are also differences in the types and amounts of additional load to be applied.
Besides the fixed criteria, most of the agencies include options which permit the investigation of alternative ways of obtaining similar levels of safety - for example, by means of model tests or theoretical calculations.
2. BACKGROUND TO, AND PURPOSE OF, THE MODEL TESTS
Application of the fixed criteria for determining the leg load which can be expected during an ocean transit of a jack-up rig sometimes yields a load of such magnitude that the resulting stresses in certain leg members would exceed the maximum permissible levels. Where this occurs, measures must be taken to bring the stresses within allowable limits. These measures can vary from leg reinforcement to reducing the extent by which the leg projects above the upper guide, either by removing the top section of the leg or by lowering the leg.
All these measures, however, are far from attractive to the owner or operator of a rig.
Reinforcement of the legs does not always produce the desired result. Removal of the top sections must be carried out in sheltered waters, and requires a powerful crane or specially designed top section skidding devices. The sections are normally transported on the deck of the rig pontoon, but this necessitates the removal of deck obstacles, and in any case the deck must be strong enough to support the heavy leg sections. The sections can also be transported on a barge, but the cost of this, and an additional tug to tow it, adds greatly to the expense. The third option, lowering the legs in the guides, results in increased towing resistance, which implies a longer towing time or, if this is not acceptable, a need to increase the number of tugs. In either case, additional costs are involved. From the points of view of the designer/builder of the rig and its owner or operator, it would be ideal if towage could be carried out with the full leg length while making no concessions in terms of safety. During the design of a large North Sea class jack-up rig (Figure 1), calculations based on the ocean transit criteria laid down by Noble, Denton and Associates (NDA) showed that the leg length had to be reduced quite extensively. It was felt, however, that the existing criteria were too severe for a rig of this size. In particular, it was anticipated that the rig would have a longer resonance period, and consequently smoother motions, than the smaller units upon which the criteria were based. Moreover it was expected that non-linear phenomena would restrict motion amplitudes. The pontoon of the North Sea rig has sharp edges, which are favourable to inotional damping, and the freeboard is relatively small, with the result that the. deck is flooded in heavy seas.
Because of above-mentioned reasons it was decided to carry out model tests.
The basic purpose of the model tests was to determine the ultimate elevated leg length at which ocean towage of the rig could be undertaken while maintaining the safety standards envisaged in the rules and regulations. As the final outcome of the calculations based on the model tests had to be approved, both Lloyd's Register (LR) and NDA, (the classification society and regulatory body, respectively, for the rig in question), were involved in the selection of the sea states and the analysis of the test results.
3. MODEL TEST PROGRAMME
The test programme was such as to cover the maximum leg load ever likely to be encountered during
wet towage of the rig. As indicated in the criteria laid down by the agencies, the ocean transit
condition is the decisive factor in determining leg strength. This condition was therefore considered to be the most important for the purpose of the tests. However, in order to obtain a fuller insight into the motional behaviour of the rig, and to complete the test series, a number of tests covering the location transit condition were also run.The contrast between the two conditions stems not only from the difference in sea states, but also from differences in the load condition of the rig, i.e. varying draught and radius of gyration.
Figure 2 shows a picture of the model. The test arrangement is shown in Figure 3.
The motions in all six degrees of freedom were measured during the tests. The data obtained were, of course, sufficient to determine the inertial portion of the leg loads, but assumptions stilt had to be made concerning, for example, the roll and pitch point position, and the period of the motion. To obviate different interpretations of the test results, a more direct approach was chosen in measuring the acceleration in the most heavily loaded leg. From the measurements thus obtained, the inertial leg load can be calculated by straightforward methods.
Because of their importance for the whole test programme, first of all the natural periods of the roll and pitch motion have been determined for the location and ocean transit condition and for the condition with the top leg sections on deck.
3.1 Location transit condition
As stated caller, the location transit condition is of relatively minor importance for leg loads and in view of this factonly one sea state was considered. The chosen spectrum was of the fetch-limited 3ONSWAP type and had a significant wave height of 5,0
m and a peak period of
8,5 sec. This represents the maximum sea state likely to be encountered during a towage which, owing to technical problems, may last more than 12 hours. This 12-hour limit is usually embodied in the definition of the location transit condition.3.2 Ocean transit condition
As the ocean transit condition was considered to be decisive in determining the leg strength, and in view of the anticipated non-linear motional behaviour of the rig, it was decided that ocean transit tests should be carried out in a series of sea state spectra with increasing periods and wave heights, and for different headings of the rig with respect to the waves.
The spectra for these tests had to represent realistic, fully developed sea state conditions in the open ocean, and for this reason the two-parameter Pierson-Moscowitz equation was chosen. The spectral parameters of wave height and period were chosen from the well-known table of Wilbur Marks /2/ for sea states resulting from wind velocities ranging from Beaufort7 to 9. With these velocities the NDA
requirement 13/ was fulfilled to cover a 10-year return period oceanic storm. At the same time it was ascertained that the spectral peak periods were sufficiently close to the rig's natural periods for roll and pitch to cover resonance situations.
-Table 2 gives an overview of all the considered sea states.
TABLE 2 - Sea states for model testing.
197
Condition Spectrum type H113 (m) Tpeak
Location transit ONSWAP 5,0 8,5
Ocean transit Pierson-Moscowitz 6,7 12,1
9,1 12,9
11,3 14,9
Sea states corresponding to more severe meteorological conditions were not included in the tests. In such conditions, greater wave heights would, of course, occur, but the wave period would become longer. The rig would then start to follow the wave slope, and surge and sway would become more important than roll and pitch. The inertial leg loads, it was anticipated, would consequently decrease. As will be shown, the test results confirmed this expectation.
In addition to the tests in the above-mentioned sea states, a number were carried out in regular waves of resonance period and with a height/length ratio of 1:40, simulating an ocean transit in swell. In order to establish correlation factors for differences in motional behaviour between the 100% leg length condition and the shortened-leg condition, some of the tests were repeated with the upper sections of the legs stowed on deck (Figure 4). No significant differences in motional behaviour in the two conditions were anticipated.
4. TEST RESULTS
During the tests, all measured signals were rendered visible on a chart recorder for the purpose of inspection and simultaneously recorded in digital form on magnetic tape. They were subsequently analysed to obtain mean, significant and maximum values, standard deviations, zero-crossing period
and number of oscillations.
Calculation of the theoretical maximum wave height from the significant value, using Rayleigh distribution factors, and comparison of the result with the maximum wave height as measured during the tests, reaffirmed the validity of the linear theory for wave height extrapolations (Figure 5). Analysis of the statistical values of the measured motions - especially roll and pitch, which were so relevant to this test programme - showed that the linear relationship between motion amplitude and wave height, which is so often assumed in ship motion theory, did not hold good for the rig in question at relative large wave heights. This is illustrated by the curves in Figures 6 and 7. The roll and pitch amplitudes at first increase linearly with increasing wave height, but beyond a certain point they tend to remain constant.
Looking at the ratio of maximum to significant amplitude, it appears that with increasing wave height the ratio becomes equal to one. Such is illustrated in Figure 8 for the pitch motion. This can be explained by the fact that, at a given moment, the motions are physically constrained by flooding of the deck of the rig at a specific roll or pitch angle.
Although motional data are of value in obtaining a sound understanding of the behaviour of the rig, they did not constitude the. basic aim of the test programme. As stated, a shorter path was chosen, the leg loads being directly derived from measured accelerations.. To this end, the accelerations in the legs were measured at two points and in two directions. At the suggestion of Lloyd's, the results were elaborated to produce so-called equivalent accelerations:
s. .5
j1m(z)z {x;
} dz
fm(z)z dz
where m (z) is the mass distribution along the leg.
is the acceleration in x-direction at deck level.
x2 is the acceleration in x-direction at. distance 1 over the deck.
With the aid of these equivalent accelerations, it is possible to calculate bending moments in legs whose mass distribution differs from those used in the tests. This is often the case in the various preliminary design stages when the mass and its distribution along the leg is still subject to alteration. This approach, however, applies only if it can be assumed that the difference in mass distribution does not influence the motional behaviour of the rig.
The leg bending moments in the x- and y-directions were directly computed from the maximum
values of the equivalent accelerations in the respective directions. It should be noted that the
measured accelerations contain not only contributions from roll and pitch motions, but also surge, sway and gravitational components. The leg bending moments in the y- and x-directions are shown in Figures 9 and 10. Like the pitch and roll motion amplitudes, the bending moments initially increase as the wave height increases, and then stabilize or even decrease.The resulting leg bending moment (Figure 11) has been computed from the equivalent accelerations in the x- and y-directions, account being taken of phase differences between the accelerations. This
resulting moment displays the same characteristics as the individual leg bending moments.
The maximum leg bending moment during the tests occurred in the front leg and for a bow quartering wave direction.
Together with other loads, this bending moment formed the input for a finite element strength calculation.
STRENGTH CALCULATION
A finite element method computer programme was used for the strength calculation. Forthe purpose of this calculation the leg was three-dimensionally modelled (Figure 12). The model was loaded by a bending moment, a horizontal force and a vertical force.
The bending moment was the sum of the maximum inertial bending moment derived from the measurements and the wind bending moment.
The horizontal force consisted of an inertial portion and a wind load portion. The vertical force equalled the weight of the leg.
The bending moment and the forces were properly distributed over the leg at the guide and pinion positions (Figure 13).
The strength calculation resulted in stresses in all members of the leg. The stresses-were all below the yield stress of the material.
The for ocean towage allowed leg length was at the end only determined by punching shear criteria arid allowable stress levels.
For this specific rig design, it was agreed with the certifying authorities that for ocean towage only the utmost top section of the legs must be removed. The length of the top sections to be removed was
only one third of the length that should be removed if the fixed Criteria
were applied. There issufficient space on deck to store those sections and the section weight is such that
no extra reinforcements of the deck had to be provided. It may therefore be concluded that applying model test criteria instead of the fixed criteria was fully justified.CONCLUDING REMARKS
For many types of jack-up rigs the fixed leg strength criteria have shown to be quite appropriate. Considering, however, the motional behaviour of big jack-up rig types, the
use of results from a
carefully prepared model test programme may lead to a lighter construction or a longer allowed leg length for transit conditions.With respect to the strength criteria applied in conjunction with model test results, it is felt that the subject of punching shear requires further investigation especially with chords and braceswhich are comparable in diameter.
ACKNOWLEDGEMENT
The authors acknowledge the kind permission given to them by the management of Gusto Engineering to write and publish this paper.
Authors also wish to express their gratitude to Noble, Denton and Associates Ltd., to Lloyd's Register of Shipping and to the SSPA staff for their valuable contribution in the discussions on the subject.
REFERENCES
/1/
Ridehalgh, I. and A.3. Edwards."Design Operation and Towage of 3ack-Up Rigs".
RINA Offshore Engineering Croup meeting dated February 18, 1982.
/2/
Wilbur Marks.Table of Wind and Sea Scale for fully arisen sea. David Taylor model basin, 1956.
/3/
Self-Elevating Units. Proposed criteria for operations and towages.Report 0002/NDI/3R of Noble, Denton and Associates Ltd., London, ist May, 1981.
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