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Non-Linearity Aspects in the Design of Submarine Pipelines
Atd. Civiele Techniek
TH
Delftir. M.L. Fernandez
juni 1981 nr. 138102
Non- Linearity Aspects in the Design of Submarine Pipelines
Prepared for The ~981 European Seminar Offshore Oil and Gas Pipeline Technology, London, February 1981
By: M,L. Fernandez
Department of Civil Engineering Delft University of Technology
The 1981 European·seminar
Offshore Oil and Gas Pipeline Technology
London, February 1981
Non-Linearity Aspects in the Design of Submarine Pipelines
by Mario L. Fernandez
*
INTRODUCTION
"As far as the propositions of mathematics refer to reality, they are not certain •.. and as far as they are certain, they do not refer to reality". A.E.
An arbitrary att~mpt has been made to classify and discuss some
non-linearity aspects related to design, construction and operation of submarine pipelines.
Non-linearities usually interrelate and take part of a comprehensive design, making difficult to quantify their individual influence or sensitivity within the general project. For example, geometric non-linearity on marine pipelines is a very important aspects for design, with diTect implications to material non-linearity and other phenomena. Codes of practice and engineers to achieve simplicity without compromise in safety, credibility and economy may evaluate how far a situation or design may be linearized or schematized. Probable to give the basis for common usage or. quasi-quantitative or/and qualitative methods.
With more and more offshore activity the importance and interest for a better understanding and solution to problems found in a limited number·
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-of submarine pipelines have increased. Such problems: pipe protection against impact loads, creep and pipe stability, scour, pipe settlement, soil liquefaction, pipe spans and vibrations, pipe restrains, fatigue
(concrete weight and steel pipe), corrosion~ buckling (prevention; occurence; repairs)., welds, construction methods (delays, tie-ins,
maintenance, etc.), ecological effects (marine grown, pipe leakage, etc.), etc.. Some of these problems may be related to neglected or ignored
non~linearities.
We may classify or study non-linearities on offshore projects in two levels: a general and a specific, for our case, submarine pipelines. With no pretentions, the general level of non-linearities for an offshore project may .be seen as follows:
1. External influence, environment
2. Internal influence, design criteria.and boundary conditions 3. Simulation model, tools for solution and design
External influence to the offshore project. Non-linearities may additionally be affected by the following conditions:
- Recording, meters and process of measurements
- Forecasting, process technique, quantity and quality of information - Linearization and schematization of data (use of constants)
Sometimes, either from lack of information or with the intention to simplify a problem, we may tend to forget the complexity of the sea, and probable introduce an error or mislead into the design. Some of the non-linearities with external influence are:
Variation of water.properties with increase of depth; currents at sea, velocity profile distribution and separation of boundary layer,
classification and. source of current velocities; seabed configuration, soil classification and properties, sediment transport, etc.
The internal influence or definition of the problem is of foremost importance in the analysis of an offshore project to obtain a correct
solution. Non-linearities may be affected by the following conditions:
- Schematization of the physical problem - Quality of information or data
- Linearization of pipe material properties.
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-Without the proper boundary conditions and representation of the physical problem the solution may not reflect the original phenomena. For example, even with the best of the intentions in (6), the presented results do not reflect an offshore pipeline during laying. By failing to define the physical problem, on this paper (6) are violated almost entirely the four principles or conclusions presented to define the installation of
pipelines by the laybarge method .at the 111980 European Seminar - Offshore
Oil and Gas Pipeline Technology", paper "Theory and Practice of Deepwater Pipe Laying". However, the results in (6) may be seen as an interesting "qualitative" analysis and contribution to understand the importance and influence on design of non-linear elasticity.
Simulation Model, tools for solution and design. The interest in offshore may be measured by the increased amount of publications on different offshore subjects.in- addition to the growing activities, new developments and research programs. Better understanding and·. improvements on design and offshore phenomena may be. seen fromphysicaLand mathematical model results.
From the literature we can learn of development of new techniques and often., is found and published the importance of ·terms earlier regarded as small, linear or constant, probable for simplicity they were
neglected or linearized. In the process of simulation different non-linearities may be linearized:
- Type of physical or mathematical model - Methodology, approach of solution
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-From mathematical models a recent and important contribution to the design and understanding of submarine pipelines is the use of Theory of Rods (1). With the help of rod theories (8) geometric non-linearities of submarine pipelines may be clearly studied. With accuracy and simplicity, which can not be done for a great number of non-linear technical theories, large deflection and twist (material and geometric torsion, often
neglected in the literature) are considered, further the physical problem can include three-dimensional non-linear elasticity, well defined
hydrostatic loads and any boundary condition. Geometric non-linearity in submarine pipelines may be found:
- During laying operation with a lay barge, overbend and sagbend - Tie-ins, including second-end connection
~ Suspended risers, OTEC, production, etc. - Tow techniques, etc.
Sometimes mathematical models may have neglected some basic non-linear
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principles, so do physical models (2). Euler number (E
=
pv ) hardly has pbeen taken into.account to simulate deep water conditions (hydrostatic pressure). For example, most hydrodynamic and morphologic parametel:'s used for design and analysis of pipe stability, resting on the seabed, may have not been checked unde~ deep water conditions.
The purpose. of this paper is to discuss some specific aspects related to
non~linearities in submarine pipelines, but as we have discussed, they
are close related to general offshore non-linearities.
Keeping that in mind, non-linearities in submarine pipelines may be classified as follows:
1. Seawater properties. Only external influence.
2. Pipe stability at seabed. Interna·l influence and simulation. 3. Pipe installation. Internal influence and simulation.
Non-linearities in seawater properties, regardless recording and forecast technique, are mainly influenced by the water depths:
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-a. Density, salinity and electrical conductivity b. Temperature gradient
c. Viscosity. Function of sea. temperature and hydrostatic pressure (water depth), e.g. At 5°C in 100m water depth there is a non-linear
increase of 50% in seawater viscosity.
Pipe stability at seabed. The analysis normally is based on design
parameters, mostly from models and some prototype measurements. Hence, it is very important to analyse the recording or origin of these design parameters (from field or/and laboratory conditions). Non-linearities to take into consideration are:
a. Currents, velocity profile and classification: ocean streams, tidal currents,. wind drift currents and orbital velocity from waves. From pipe stability, we may consider:
- Steady currents, important_in vortex shedding - Unsteady currents (including their forecast)
- Special currents, .from: swell, hurricanes, tsunamis, etc.
b. Boundary.layer separation, probable,.from the seabed and from the
pipeline.~ After considering the effects from:
- Seabed texture and configuration - Pipeline .characteristics
c. Seabed configuration and soil propel:'ties, related to pipe stability, characteristics and hydrodynamic forces:
~ Pipe settlement - Burial and trenching
- Sediment transport, sand waves and scour - Liquefaction (waves and earthquakes)
- Pipe spans .. Vortex shedding, pipe fatigue (incl. concrete) and resonance.
Pipe Installation, Lay Barge _Method and Tow Techniques. The more important aspects to be always considered are the geometric non-linearity (large deflection
&
twist) and the external hydrostatic pressure. Situations where non-linearities may be found are:- 6
-a. Lay Barge Method.
a.l. Overbend. Probable, including non~linear elasticity and static/ dynamic loading.
a.2. Sagbend. Validity of small and large deflection theory. Buckling. a.3 •. Seabed. Installation. and operational stresses. Influence of soil
restrains and geometric non-linearity. b. Tow Techniques·, . for more information see ( 3) • b.l. During tow. Analysis and control.
b.2. Final positioning. Tie-ins and second-end connections. Installation and operating conditions.
REFERENCES
1. Antman, S. S • .., "Theory o:f Rods 11, Encyclopedia of Physics , Vol. IIa/2, Springer-Verlag, 1972, pp. 641-703.
2. Bourguignon, G. P. and Van de Velde, P .A. , 11Waterbouwkundige Constructies, bijzondere onderwerpen", Afd. Civiele Techniek, T.H.-Delft, mei 1976.
3.· Fernandez, M.L., ."Tow Techniques for Marine Pipeline Installation", ASME paper No. 81-Pet-30, presented at the ETCE, Houston, 1981.
4. Graham, D.S. and Machemehl, J.L., "Appropriate Force Coefficients for · Ocean Pipelines", ASME paper. No. 80-Pet-61.
5. Holthuijsen~.L.J., "Methoden voor Golfvoorspelling", T.A.W., Nederland
1980.
6. Kimura, T., Idogaki, S., Takada, K. and Fujita, Y., "Experimental and Analytical Studies of the Elastoplastic Behavior of Offshore Pipelines During Laying", OTC paper No. 3737, 1980.
7. Kolkman,. p, A., "Development of Vibration-Free Gate Design: Learning from Experience and Theory'', IAHR/IUTAM Symposium, Karlsruhe, Sept. 1979.
8. Konuk, I. , "Solution of Two- Point Boundary Value Problems Associated with Submarine Pipelines", University of Southampton, PhD Thesis, submitted Jan. 1981.
9. Maier~ G., Andreuzzi, F., Giannessi, F., Jurina, L. and Taddei,
f.,
"Unilaterial Contact, Elastoplasticity and Complementarity with Reference to Offshore Pipeline Design", Computer Methods in Applied Mechanics and Engineering, Vol. 17/18, North Holland, 1979, pp. 469-495.
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-10. Schlichting, H., "Boundary-Layer Theory", McGraw Hill, 7th ed., 1979.
11. "Snelheidsveld in golven, Inve'ntarisatie van metingen in model en natuur", TOW/Delft Hydraulics Laboratory, Aug. 1980.
12. Verruijt. A., "De losse grondslagen van stabiliteitsberekeningen in de geotechniek, studiebijeenkomst, Stabiliteit van Taluds, T.H.-Delft, Feb. 1980.
