THE INFLUENCE OF WAVE FORCES ON THE DESIGN OF OFFSHORE STRUCTURES FOR THE OIL INDUSTRY
H.J. ZUNDERDORP
PAPER 14
Koninklijke I Shell ExploratiE" en Produktie Laboratorium, Rijswijk ZH, The Netherlands
1. INTRODUCTION
Until after the second World War, the ocean was regarded by the oil industry only as a cheap means of transportation. Before the war some timber structures very close to the shoreline had been constructed, but drilling for oil on the continental shelf did not really start until 1947, when the first steel platform was erected in 20 ft. of water in the Gulf of Mexico. In the following twenty years, rapid progress took place not only in the number of constructed platforms, but also in the water depths in which these structures were placed. In 1955, 100'was reached, 200' in 1959, 285! in 1965 and in 1967 a platform was placed in 340' of water. This is certainly not the end. Platforms for 600' of water are technically feasible and are already on the drawing boards.
For exploration drilling, movable structures are preferred and these units have been constructed in great' variety - jack-up units with from three to ten legs and submersible units, all still bottom supported when drilling. Floating units have also been developed - boat-shaped vessels, barges, catamarans and finally the semi-submersibles. Anyone who follows the patent literature will find a continuous stream of inventions in this field.
The designer of these structures is confronted with the problem of constructing them in such a way that they are able to withstand without significant damage the loads imposed by the environmental conditions, By "environmental conditionstl we generally mean waves, winds and currents, but icefloes and earthquakes can also be included. In this paper we will limit ourselves mainly to wave forces.
In the first place the design limits have to be established, which means that we have to determine the maximum stresses to which the structure will be exposed. As regards the waves, we need the help of an oceanographer to predict the II1aximum wave height for the area in which the structure is to be placed, At the same time a policy decision has to be made, for, as we all know, the probability that a certain wave height will be exceeded increases with time. For this reason, we first have to decide on the risk factor we are prepared to accept. In the oil industry it is common to accept the so-called 100 year wave as the design wave. That means a wave with a probability of occurrence of once in a hundred years. Of course, we can never
predict when this wave or an even higher one will occur. Statistics show that the encounter probability E, during a lifetime L for a return period T 1 can be derived
from:- ...
E"
a-Ct,-i>
-**
So when we design a structure with an expected lifetime of 20 years for a wave with a return period of 100 years, the probability that this wave will be encountered during this lifetime is
l-(l-l~O
)20 = 16% and this in fact is also the risk we are willing to accept.Most structures are designed only for such maximum stresses, on the as-sumption that, if they can withstand these, they can withstand all others too. This belief is based on experiencE'; gRined in the Gulf of, Mexico, the birthplace of all offshore engineering techniques. Here hurricanes producing enormous waves alternate with very calm seas.
For more exposed areas, such as the North Sea, a se80nd design criterion has to be taken into account - the lifetime of the structure under loads less than the maximum. In some cases, structures have succumbed to so-called low-cycle fatigue: material failure due to the repeated imposition of loads less than the maximum permissible.
In the following a short description will be given of the techniques used in offshore engineering. Perhaps this will give a rather pessimistic or even negative impression. This is not the intention, however. To date a large number of structures have been designed and in general they have performed satisfactorily. The number of failures is small, and only a small percentage of these is due to design faults. In this respect one can say that the offshore industry as a whole has done very welL When criticisms of methods or theories are made in this paper it should be re-membered that the only purpose of this is to underline the difficulties the designer encounters in his day-to-day work and the problems with which he is faced when he is required to design yet larger structures for use in still deeper water.
The offshore industry is expanding rapidly and those working in this field have to meet the challenge that the demands on structures are becoming more and more stringent. To justify these structures economically, the designer has to approach the "optimum design" and this in turn only becomes possible if he can use more refined methods and theories. It is the need for these refinements that will be outlined in the following sections, and it i8 here that the offshore designer joins forces with colleagues working in the hydraulic and other laboratories.
II. FIXED PLATFORMS
Normally the forces resulting from a two-dimensional regular wave are used for the design. Much criticism of this procedure is heard, for in reality waves are neither unidirectional nor regular. This is true, but the use of such a "design wa ven
can be justified in various ways.
It is the task of the engineer to design the structure in such a way that it can fulfil its intended purpose and to do this in the quickest and easiest way. The use of idealised conditions simplifies the necessary calculations tremendously and speeds up the design. So the use of such idealised waves is justified as long as the calculated forces are equal to or higher than those ever met with in reality under the specified conditions. The calculated forces must however, be "realistic", since, if the values chos.en for the forces to be withstood are too high, the design will become unecono-mical. It is strange that although many hundreds of structures have been designed on these principles, very little effort has been made to check the underlying assumptions. To calculate the ·forces resulting from regular waves, the Morrison equation is generally used:
F ..
f&.C~.fJ.
L
iii.IV/.
V""
7(.~, :"H.Q(~.I'.
; ;
-This equation was suggested by Morrison et all) in ... 1951. To solve this equation one 4as to know the velocities
V
and the acceleration~i
of the fluid particles and the drag and mass coefficients CD and em'The water-particle velocities and accelerations are calculated with the aid of theories concerning unijirectional regular waves. The choice of the best wave theory is still a matter on which offshore engineer s disagree. In Shell, the choice of the wave theory depends on the magnitude of two dimensionless parameters d/gT2 or H/gT2, d being the water depth, H the wave height and T the wave period. The theories used include: a modified solitary. a shallow water, Airy, Stokes-Struik third order, Stokes fifth order, Chappelear's numerical and a highest wave theory. The majority of waves used as design waves lie within the range of applicability of the Stokes fifth order or Chappelear's numerical theory.
The drag and inertia coefficients must also be determined. A method proposed by Wiege12) has been used to analyse a large quantity of storm-wave data. According to the two-dimensional wave theories, horizontal acceleration is zero at the time the crest of the wave passes the pile, so at that time the total force on the pile is determined by the drag term only. On the other hand when the wave surface passes the still-water line, the horizontal velocity is zero and the wave force is contributed by the inertia term.
A large number of storm waves have been analysed with the Wiegel method .. There is a large spread in the coefficients so computed. Variations in drag coeffi-cients ranging from 0.05 to 1. 6 and variations in inertia coefficients ranging from
0.1 to 3.4 are found under seemingly similar conditions. It was also found that the drag coefficient decreases with increasing wave height and increasing wave period and also increases with distance below water level. No correlation with the Reynolds number was found. There are reasons for believing that the inertia coefficient is a function of the distance from the sea floor. A number of factors have contributed to these, at first sight, somewhat discouraging results.
In the first place the water particle velocities and accelerations are calculated with the aid of an appropritate wave theory for the measured wave height and wave period. In reality, however, a regular two-dimensional wave has never been present: the measured wave force has always been due to a complete spectrum of waves,
**
approaching from various directions. Current velocity is also measured. It certainly does not go without saying that the same drag coefficient is applicable for arectilinear flow as for an oscillatory flow. Moreover, it is permissible to wonder whether some element of error is not inherent to the Morrison equation. It does not, for example, take into account the dependence of the coefficients on the wave fre-quency, w, although in other fields of engineering (aeronautics, naval architecture) this dependence is known to be very important. Wiege1 3) draws our attention to the formation of eddies, resulting in an oscillating flow with high Reynolds number,
which is quite different from rectilinear flow with a high Reynolds number, especially when the pile diameter is not small with respect to the wave height.
As the water depths for which the platforms are intended become greater, the designs show a tendency to use piles of larger diameters. This being so, the
problems just mentioned become more important and in our view more research is required.
One may wonder whether it is necessary to use an equation like Morrison's, No designer, in fact, is interested in water-particle velocities and accelerations requiring large computer programmes to calcutate them.
It may be possible that a transfer function can be given, directly relating the wave force to parameters depending on wave height, wa78 period, water depth, pile diameter and distance to the surface. For large-diameter piles where the drag term only makes a small contribution to the wave force and scale effects are consequently small, such transfer functions can perhaps be derived from the results of model tests.
Such transfer functions would also be of great value in dealing with irregular waves. Hitherto the designer was only little interested in irregular waves., since his
Knowing the transfer function as described above, one can easily calculate the spectral density of the wave force when the spectral density of the sea surface is known. Although measured wave spectra are available only for certain areas, theore-tical wave spectra can replace them (Neumann, Fisher and Roll, Philips, Pierson). One can also calculate the transfer function starting from Morrison! s equation. This is done by Borgmann (1968). The problem here is that the use of transfer functions assumes that the sy.§tem is linear and that the superposition principle is valid. Because the term V /. V appears in the drag term of Morrison's equation, these conditions are not fulfilled. A linear approximation of the drag term is allowable at any rate for large diameter piles. Such a process is described by Penzien4). Still, one has to keep in mind th2.t by using spectral analysis theories, one treats the
problem on a statistical basis, thereby losing the phase relations between wave profile and wave forces. Consequently, for de5igning the size of members this approach is less suitable than the design wave approach.
ill. FLOATING PLATFORMS
The same problems as those described for fixed platforms are also encountered with floating platforms. Wave force calculations are complicated by the fact that the body itself moves so wave velocities and accelerations have to be compensated for the velocities and accelerations of the platform. The motion itself, however, is caused by the wave forces, so this problem can only be solved by an iterative process. The problem becomes even more complicated because there is mutual interference on the part of the members.
Semisubmersible units are mainly composed of large-diameter tubulars. This enables us to determine the motions and exciting forces by model experiments, without large errors due to scale effects.
Normally we determine transfer functions for the motion giving the relation between motion and wave height as a function of the frequency, as well in amplitude relation as in phase relation.
In principle there are two ways in which this relationship can be determined. **In the first way, the floating body is subjected to the waves and both the motions and
the waves are measured. This can be done for both regular and irregular waves. The irregular wave can be given as the superposition of a large number of regular waves
eoe.
r ::
,,:r
E
~.
('OS(t..Ji\'t
.,.tt;.)
I
For the heave motion we now may write
in which /
far!v,,}/
is the real part of the transfer function, or amplitude operator. The mean square of the wave amplitude over a long period in the frequency band between~Me{"" equals 4J.,.d.:J£.
Ii
rd(w}
w
-We know that this is equal co the spectral density
~Htic.J
;:',. (4)).d", ='
f-
;I ,.a(foI)In the same way we find as the mean square of the heave response
So the heave amplitude operator can be calculated as
/ fa
(fAJI/
=
1f&1e.J/.fJI~
a,.
frr
tt.JJ.1ll1ttJ
**
The second approach by which the transfer function can be calculated is by solving the differential equation of motion. The general equation for a body moving through a fluid is:m (I-a) § - bs - cs
=
Fin which s = a vector, indicating the displacement
s
=
first time derivate of that vector § == second""
"
m == mas s of the body
a == added mass term coefficient b = damping coefficient
c = restoring force coefficient
"
F = sum of all external-forces acting upon the body.
The coefficients a, band c can be determined by a forced oscillating technique in still water. The wave forces are measured on a restrained model vessel.
The transfer function can now be calculated as
in which F is the wave force and H the wave height.
The fIgure is a:l amplitude calculator for heave, calculated in this way. To predict the heave motion, an irregular sea is used. For this sea, with a significant wave height of 8.65 m and a significant period of 11.54 seconds, a Neumann
spectrum is used. From the resulting heave spectrum, it follows that the significant heave motion will be 2.54 m and the maximum heave motion 1. 86 x 2.54
=
4.72 m.IV. CONCLUSI0N
Hitherto offshore structures have been mainly designed by using regular wave
*'
theories. The methods used yield acceptable results as 10j'lg as the ratio of wave height to diameter of tubulars is large/. For large-diameter tubulars, the validity of the methods is doubtful and further research on wave forces is required.For the design of fixed structures in deep water and uf floating bodies, dynamic effects have to be taken into account and this can only be c.one by considering irregu-lar waves. In these studies model experiments will be necessary on a irregu-large scale.
It is for this reason that those of us who are engaged in offshore work are delighted with these beautiful new facilities here at the Waterloopkundig Laboratorium.
References
1. Morrison,Johnson, O'Brien, Exp. studies on Forces on Piles, Proc. 4th Conf. on Coastal Eng. Berkeley, Cal. (1954).
2. Wiegel, R. L .. Oceanographical engineering, Prentice-Hall, 1964. 3. Wiegel,R. L. ,Wave forces.
Course for desfgn and analysis of offshore drilling structures, Berkeley, September 1968.
4. Penzien, J., Notes on non-determinstic analysis.
Course for design and analysis of offshore drilling structures, Berkeley. September 1968.
5. Zunderdorp, H.J., & Buitenhek, M., Oscillator techniques at the shipbuilding laboratory. Report 111.
Shipbuilding Laboratory of the Technological University, Delft.
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