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Offshore Engineering
P Vannucci
To cite this version:
P Vannucci. Offshore Engineering. Master. Université de Versailles Saint Quentin en Yvelines, France. 2008. �cel-01529018�
Master SPI DSME - Dimensionnement
des Structures Mécaniques dans leur
Environnement
2èmeAnnée
Cours Mécanique pour l’Industrie du Pétrole Part 2: Offshore Engineering
P. Vannucci 2 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Foreword
This course on Offshore Engineering is a basic course serving as an
introduction to the problems concerning design and construction of offshore platforms, normally used in oil industry.
So, some topics will be considered in this course, namely the
principal ones that concern the structural design of an offshore platform; some other topics, like for instance marine installation procedures, corrosion protection, facilities and plants engineering will not be considered here.
The course is addressed to undergraduate students having already
a good knowledge in structural engineering and fluid mechanics.
3 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr Chapter 1: Introduction 7 General considerations
Platform functions and types Historical background
Design process
Standards and regulations
Chapter 2: Design actions 65
Types of loads Operational loadings Deformation loads Accidental loads Environmental loadings Storm selection Wind forces Ice forces Snow loads Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Content
Current forces Marine growth Earthquake actionsDesign load combinations
Chapter 3: Hydrodynamics of wave forces 140
The actions of a fluid on an immerged body Inertial force: the added mass
The drag force
Wave theories
Slender and large bodies
First order wave action on a slender body
The case of a moving body
Second order wave action on a slender body
First order wave action on a large body
The Mc Camy and Fuchs solution
5 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Content
The simplified Garrett solution The Ogilvie solution
Second order wave action on large bodies
Something about the case of multiple bodies Oscillating large bodies
Wave slamming
Vortex shedding
Numerical methods for the wave action
The spectral method in wave forces calculation
Chapter 4: Dynamical considerations 373
Introduction
Response to regular waves
Response to an impulsive force
Response to irregular waves: the spectral analysis
The wave force spectrum
6 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr Bibliography
The most part of information, figures and diagrams of this course,
where not explicitly indicated, have been taken from the following sources.
Books
T. Sarpkaya & Isaacson: Mechanics of wave forces on offshore
structures. Van Nostrand, 1981.
B. Mc Clelland & M. D. Reifel (Eds.): Planning and design of fixed
offshore platforms. Van Nostrand, 1986.
O. C. Zienkiewicz, R. W. Lewis & K. G. Stagg (Eds.): Numerical
methods in offshore engineering. J. Wiley, 1978.
M. G. Hallam, N. J. Heaf & L. R. Wotton (Eds.): Dynamics of marine
structures. Report UR8 – CIRIA, 1978.
Internet sites
http://www.kuleuven.ac.be/bwk/materials/Teaching/master/wg15a/l0200 .htm
http://www.nts.no/norsok http://www.offshore.tudelft.nl/
7 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Introduction
Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .frContent
General considerations 9 Platform functions and types 10
Historical background 48
Design process 52
9 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
General considerations
Offshore engineering is a branch of civil engineering involved with
the construction of sea structures, far form the coast.
Such structures are normally called platforms. They are usually
employed in oil industry, but there are also platforms for broadcasting, navigational lighting, radar surveillance, space operations, oceanographic research and so on.
The general design requirements for an offshore platform are similar
to any industrial structure; the first step in the design is to develop a concept of the structure based on its functional requirements, environmental restraints and construction method. The function of an offshore platform is to provide a secure working support, so the platform must be structurally adequate to withstand both operational and environmental loading; in addition, it must be practical to construct and economically feasible.
Nevertheless, due to their characteristics, to environmental and
geographic aspects, to the construction procedures, offshore platforms are very peculiar structures, and several unusual aspects must be taken into account in its design phase: environmental loadings, construction phases, economic aspects, linked to the type, construction procedure and date and to the installation site.
10 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Platform functions and types
During the last five decades, several types of offshore platforms
haves been designed and used; this variety of platform types is due to different factors: technological and scientific progress, economical factors, need to exploit deeper natural reservoirs, ecological constraints.
A possible, of course incomplete, classification is the following one.
jack up
semi-submersible drilling ship Mobile offshore platforms
TLP
free standing tower guyed tower spar tower compliant concrete gravity steel gravity steel jacket steel tower rigid Fixed offshore platforms
11 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Fixed offshore platforms are normally used for production, while
mobile platforms are almost exclusively used for exploration and drilling phases.
The difference between fixed and compliant platforms is in the way
they face environmental (namely wind and wave) lateral actions.
As its name clearly indicates, a fixed platform is a traditional
structure, in the sense that its deformation under lateral loads is small, but it is located into the sea water.
Unlike fixed, compliant platforms are designed to move under lateral
forces, so that the effects of these forces are mitigated. The trade-off in a compliant platform is between excursion amplitude and restraining force.
Compliant platforms are used in deep water, where the stiffness of a
fixed platform decreases while its cost increases, and they are the only technical solution in very deep waters (> 500 m).
The fluid-structure interaction is a capital aspect in platform design,
but it assumes a biggest role in the case of a compliant platform.
Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Platform functions and types
General scheme of offshore platforms in relation with water depth.
ww
w.
mms
.gov
jacket jack-up
13 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Platform functions and types
Steel jacket: it is the most
classical and widely used offshore platform. A typical jacket is shown in the figure.
It is composed of three
principal parts: the deck, carrying the topsides (living quarters, drilling derrick, consumables, facilities, helideck, flare etc.), the jacket itself and the foundation piles.
Steel jackets are normally
used in shallow to moderate deep waters (from 20 to 100 m), but they have been used up to 500 m of water. 14 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Platform functions and types
If not too big, jackets are built in a
dock and then charged onto a barge by a crane. Large jackets are built on one side, directly on a barge or on rails to be the skidded onto a barge.
An important characteristic of a
jacket is a small floatability: in fact, legs are not plugged, as they are the templates for the piles, and the braces are normally too small to ensure the necessary buoyancy. So, a barge is needed to carry them to the field, where the jacket is put into water by a crane, for small jackets, or directly skidded or rolled off the barge (launching
operation) for large jackets. ww
w. of fs hor e-te chnol ogy .c om ww w. of fs hor e-te chnol ogy .c om
15 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
In the first case, the design phase
must take into consideration the lifting phase, while in the second cases a complete analysis of the launching phase must be done, in order to asses the transient stress distribution and to control the actual behaviour of the jacket during the transportation and the launching phases, namely if an additional buoyancy is needed and if the jacket touch the sea bottom during launching.
Numerical investigations are normally
used to simulate these phases, which considerably condition the design of a steel jacket. In the next pages,
these phases are outlined. ww
w. of fs hor e-te chnol ogy .c om Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Platform functions and types
Launching phases of a steel jacket.
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17 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Platform functions and types
Two pictures of a jacket installed by a crane and of the mating of a
deck and a jacket.
ww w. of fs hor e-te chnol ogy .c om ww w. of fs hor e-te chnol ogy .c om 18 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Platform functions and types
The construction phases of a jacket. 1: construction in a coast yard;
2: transportation by barge on the oil field;
3: launching of the jacket.
w ww. of fs ho re-t ec hn ol og y. co m w ww. of fs ho re-t ec hn ol og y. co m www .o ff sh ore-t ec hnol ogy .c om www .o ff sh ore-t ec hnol ogy .c om www .d or is -e ng in ee rin g. com www .d or is -e ng in ee rin g. com 1 2 3
19 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Another characteristic of steel jackets is the foundation system: as
previously said, piles are directly inserted into the legs and they directly support the deck. Sometimes, especially for larger platforms, additional skirt piles are necessary. Once the piles driven, they are grouted into the legs to join them to the platform.
Once the piles installed and grouted, the deck is placed at the top of
the jacket by a crane. Normally, all the installments and facilities are already installed onto the deck before its mating with the deck.
ww w. st ru ct ur ae. de ww w. ri g zone. co m Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Platform functions and types
Steel tower: it is a large jacket where
the piles cannot be inserted in the legs mainly for economical reasons.
In fact, too long piles are too
expensive. So, when the platform is located in deep waters, the jacket becomes very heavy and the piles cannot be as long as the legs. They become skirt piles inserted in sleeves around the outside of the legs.
In this way, the legs are plugged and
normally sufficient to ensure the buoyancy: the jacket does not need a barge to be carried on the site, as it floats (eventually with auxiliary buoyancy) and can be towed. This is very convenient both for economical and construction aspects.
They exist tower structures installed in
21 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Platform functions and types
Some relevant achievements of jacketed structures.
22 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Platform functions and types
Steel gravity platforms: this type of structure, rarely used, uses its
own weight to counter the lateral actions due to wind and waves that tend to overturn the platform: the weight is used as a stabilizing force.
Nevertheless, the real reason for using gravity platforms is the
nature of the soil: when it is of solid rock, it is impossible to drive piles into it, so the gravity solution is the only possible one.
Normally, gravity platforms are concrete platforms, but in some
cases a steel solution can be adopted, in relation with several factors, mainly economic considerations.
Normally, the structure has a certain number of large tanks, flooded
by water or by crude oil, to ballast the platform and provide the necessary weight to counter overturning lateral forces.
These tanks, in the transportation phase, provide the necessary
buoyancy.
An important feature of all the gravity platforms is that they can be
23 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
The Maureen Alpha platform is a steel
gravity platform with a weight of 112000 t, height of 241 m.
It has been installed in 1983 in the
North Sea; in 2001 it has been removed and replaced on another oil field.
ww w. par os ci ent ifi c. com ww w. te cnomar e. it ww w. raeng. or g. uk Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Platform functions and types
Loanga platform
(Nigeria): it is a steel gravity platform, with inclined risers to optimize the exploitation of the field.
25 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Platform functions and types
Concrete gravity platforms: they are the hugest and most
impressive structures ever built.
In this platforms, the steel structure supporting the deck is totally or
partially replaced by a concrete structure of large dimensions.
ww w. ogp. or g. uk ww w. ogp. or g. uk 26 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Platform functions and types
Concrete gravity platforms are used when some particular
circumstances are present:
economical factors: in some cases, the construction of a very large
concrete structure can be cheaper than the construction of a steel structure;
ecological factors: a concrete platform can be very huge, so as to
concentrate onboard some industrial treatments of the crude and to allow a great stocking capacity in the ballast cells;
construction conditions: the pile driving operation for a steel jacket
needs usually 5 to 10 days; in the North Sea it is rare to have such a period of fine weather; the installation in the oil field of a concrete gravity platform, complete with its deck, requires a shorter period (1 to 2 days);
decommissioning aspects: concrete gravity platforms can be
decommissioned and eventually re-used;
soil conditions: when the soil is made of rock it is impossible to drive
piles into it: the gravity solution is then the only one possible;
geographical conditions: the presence of calm and deep waters not far
27 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr ww w. ogp. or g. uk
The above factors have often been determinant in the choice of this
kind of platforms in the North Sea.
Nevertheless, rather recently concrete gravity platforms have been
commissioned in other parts of the world (East Russia, Philippines and so on).
These structures can reach a height of 400 m and weigh more than
800000 t. Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Platform functions and types
29 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Platform functions and types
Source: www.ogp.org.uk 30 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Platform functions and types
It is important to understand the construction phases of this kind of
platforms: the fundamental aspect is the Archimedes' force.
In fact, the concrete substructure is built onshore, in a dock under
the sea level.
Once the base is ready, the dock is flooded and the base floats; it is
then towed in deeper but calm waters, where the construction of the substructure continues on the floating base.
ww w. si r-rober t-mc al pi ne. co m ww w. of fs hor e-te chnol ogy .c om
31 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Once the substructure ready, it is towed in sufficiently deep and
calm waters (a fiord gives the optimal conditions) for the mating operation: the deck, carried by two barges with all the topsides, is mated to the concrete substructure just by an operation of ballasting and deballasting the concrete substructure with water.
All these operations are outlined in the following scheme.
Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Platform functions and types
Malampaya concrete gravity platform (Philippines; the first concrete
gravity platform in Asia): all the construction phases.
1. construction in a dock under the sea level
2. construction of the towers 3. flooding of the dock: the platforms is ready
33 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Platform functions and types
Source: www.arup.com
4. towing of the concrete substructure
ww w. mal a mpa ya. co m 6. mating
5. ballasting of the concrete substructure
7. the final platform
34 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Platform functions and types
The disaster of Sleipner A: this platform produces oil and gas in
the North Sea in a water depth of 82 m. The first concrete base structure for Sleipner A sprang a leak and sank under a controlled ballasting operation during preparation for deck mating in Gandsfjorden outside Stavanger, Norway on 23 August 1991.
The loss was caused by a failure in a cell wall, resulting in a serious
crack and a leakage that the pumps were not able to cope with. The wall failed as a result of a combination of a serious error in the
finite element analysis and insufficient anchorage of the reinforcement in a critical zone.
A better idea of what was involved can be obtained from the photos
in the following page. The top deck weighs 57,000 t, and provides accommodation for about 200 people and support for drilling equipment weighing about 40,000 t.
When the first model sank in August 1991, the crash caused a
seismic event registering 3° on the Richter scale, and left nothing but a pile of debris at 220 m of depth. The failure involved a total economic loss of about $700 million.
35 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
The post accident investigation traced the error to inaccurate finite
element approximation of the linear elastic model of the cells (using the popular finite element program NASTRAN). The shear stresses were underestimated by 47%, leading to insufficient design. In particular, certain concrete walls were not thick enough. More careful finite element analysis, made after the accident, predicted that failure would occur with this design at a depth of 62 m, which matches well with the actual occurrence at 65 m.
Source: http://www.ima.umn.edu/~arnold/disasters/sleipner.html ww w. im a. umn. edu ww w. im a. umn. edu Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Platform functions and types
Free standing towers: they are classical towers but so slender that
their structural behavior is that of a compliant structure: large sway displacements and high oscillating period.
Baldpate: the highest, freestanding compliant structure in the world.
Characteristics:
water depth: 501 m;
sway response cycle: 30 s; lateral displacement: 3 m;
cross section: 42.6 x 42.6 m (bottom),
27.4 x 27.4 m (top);
weight of the tower:
28900 t;
weight of deck and
topsides: 2700 t; foundation: 12 piles driven for 130 m. ww w. of fs hor e-te chnol ogy .c om w. of fs hor e-te chnol ogy .c om
37 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Platform functions and types
Guyed towers: these compliant platforms are composed by a
slender jacket, normally pin-joined at its base, whose vertical stable position is ensured by the buoyancy of the structure itself and by a series of mooring catenary lines.
The structure can oscillate under the lateral actions, the restoring
force being provided by the buoyancy and the mooring lines. The clump weights provide additional restraining forces in case of storm, when they are lifted off the seafloor.
These platforms are used for water depth in the range 200-600 m,
and they can be re-used.
38 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Platform functions and types
SPAR towers: these platforms are composed by a large steel tube
as substructure directly supporting the deck and topsides.
The tube is ballasted so as its floating stable equilibrium position is
vertical (including topsides), and moored by tensioned risers and by mooring lines (catenaries).
On the lateral surface of the large vertical cylinder there are
helicoids, installed to counter vortex-shedding.
39 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr www.offshore-technology.com
TLP (Tension Leg Platforms): they are floating structures
anchored to the seafloor by a series of vertical tendons (tethers) pre-tensioned by extra-buoyancy. The tethers are made by steel pipes.
A TLP is composed by 4 principal parts: the foundation template, the
tethers, the hull and the deck.
Some TLPs (e. g. Heidrun) have a concrete hull.
TLP are very large structures, able to host
great payloads. So, they are used for great fields and can host some refining processes and have a good storage capacity.
TLP can be used from 150 m of water depth
on, and theoretically there is no limit of water depth for their use.
The restoring force is given by extra
buoyancy; this is obtained deballasting the TLP hull once the tethers installed.
TLPs can be re-used. Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Platform functions and types
The constructing phases of a TLP are similar to those of a concrete
gravity platform, and are sketched in the figure.
a: construction of the hull in a dock; b: towing the hull to the mating site; c: towing the deck to the mating site; d: mating;
e: tethers positioning;
f: deballasting for tensioning the tethers.
ww w. of fs hor e-te chnol ogy .c om www.rigzone.com
41 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Platform functions and types
TLPs have known a wide diffusion all over
the world in the last decade. The water depth, in 20 years, has been multiplied by a factor of ten. ww w. of fs hor e-te chnol ogy .c om 88450 290610 66225 106000 16602 displacement (t) 26018 35380 30000 4170 topsides weight (t) 20321 21772 43700 1950 hull's weight (t) 110 x 110 87,6 x 103,1 100 x 100 55 x55 dimension (m) 54 column height (m) 26 24 22,6 24,4 12,2 diam. col. (m) 1158 345 872 395 536 water depth (m) Ursa Heidrun Auger Snorre Jolliet 88450 290610 66225 106000 16602 displacement (t) 26018 35380 30000 4170 topsides weight (t) 20321 21772 43700 1950 hull's weight (t) 110 x 110 87,6 x 103,1 100 x 100 55 x55 dimension (m) 54 column height (m) 26 24 22,6 24,4 12,2 diam. col. (m) 1158 345 872 395 536 water depth (m) Ursa Heidrun Auger Snorre Jolliet 42 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Platform functions and types
Some pictures of TLPs (source: Atlantia Offshore LTD).
Snorre Magnolia
Marlin Heidrun
43 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Recently, a new TLP concept has been developed: it is that known
as mini TLP.
In this solution, only one column is present, just as in the case of
spare towers.
The column is anchored to the
seafloor by pretensioned tethers that are fixed at the end of three pontoons at the bottom of the cylinder.
These TLP have a less payload
capacity, and are normally used for deep water small fields.
ww w. of fs hor e-te chnol ogy .c om www .o ff sho re -t e chnol og y. co m www .o ff sho re -t e chnol og y. co m Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Platform functions and types
Drilling ships: like all the mobile systems, drilling ships are used
mostly for the drilling phase, but they can be used, at least temporarily, also as FPS (Floating Production System).
A drilling ship is, as its name indicates, a common ship equipped
with a drilling system (a derrick tower).
It is maintained in its position by a system of mooring catenaries,
eventually assisted by servo-motors and GPS positioning.
ww w. of fs hor e-te chnol ogy .c om
45 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Platform functions and types
Semi-submersibles: as their name indicates, these are special
ships, normally composed of two pontoons, some columns and a deck. The deck is equipped for all the drilling operations.
A semi-submersible is a complete platform, that can navigate as it is
furnished of motors. Once in place, its positioning is provided by a system of catenaries normally controlled by a GPS system.
Recently a concrete semi-submersible
has been constructed.
ww w. dor is -eng ineer ing. co m ww w. of fs hor e-te chnol ogy .c om www.doris-engineering.com www.doris-engineering.com 46 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Platform functions and types
Jack-ups: these are special mobile platforms,
normally used for the drilling operations.
They are triangular barges, completely
equipped for the drilling operations and disposing of three truss legs.
ww w. of fs hor e-te chnol ogy .c om ht tp :// communi ty .w ebs hot s. co m/ al bum/ 126570186 Z W QFUs
These legs can be lifted
or lowered by motors. When the legs are lifted, the jack-up can navigate just as a common ship. Once arrived on the field, the jack-up lowers the legs so as to be fixed in the drilling place and it lifts itself at the right height above the sea level.
http :// co m m u ni ty .w eb sh ot s.c o m /phot o/ 126570 186 ht tp ://c om m u ni ty .web shots.c om /phot o/ 1265701 86
47 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
In this course, only fixed platforms will be considered, as the case of
mobile platforms concerns much more naval engineering.
Nevertheless, several considerations which will be made in the
following, such as dynamic response, wind and wave force analysis and so on, concern as well mobile platforms, namely jack ups.
ww w. of fs hor e-te chnol ogy .c om Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Historical background
1896. Summerland, California: the first oil and gas operations over
water, with wells drilled from piers extending from shore.
1909 or 1910. Ferry Lake, Louisiana: wells drilled using a wood
deck erected on a platform supported by cypress trunks driven as piling.
1924 and after. Lake Maracaibo, Venezuela: wells drilled from
wooden platforms supported on timber pilings.
1930s: the oil industry moves into the marsh and swamplands of
South Louisiana, and then, as a natural extension, into shallow waters of the Gulf of Mexico, using existing technology for timber structures.
1937. Gulf of Mexico: the first platform close to shore; it is a
traditional timber-pile structure.
1945. Gulf of Mexico: Magnolia Petroleum Company builds a
wooden structure in about 6 m of water and drills the first offshore well remote from shore.
49 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Historical background
1947. Gulf of Mexico: the first steel platform is installed out of sight
of land, in 6 m of water by Superior Oil Company, and another in 5.4 m of water by the Kerr McGee-Phillips-Stanolind group. These early steel platforms were fabricated entirely offshore. They were supported by a large number of small steel pilings (40-60) driven in varying directions and to varying depths. After the pilings were driven, horizontal pipe braces were laid out on the construction barge and cut to fit.
1948. The first prefabricated substructure sections assembled on
the site.
The first steel platform (1947).
1950. The first onshore fabrication
of unitized substructures, referred to as templates or jackets. The steel jacket was placed on the ocean floor, where it acted as a template for the steel piles that were driven through its tubular legs. 50 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Historical background
1955 to 1978. The water depth for steel jacket platform construction
passes from about 30 to 311.8 m: a progression of ten times in 20 years.
1973. North sea: the first concrete gravity platform, Ekofisk, is
installed in 70 m of water.
1983. Gulf of Mexico: Exxon installs the first guyed tower, Lena, in
304 m of water.
1984. North Sea: Conoco installs Hutton, the first TLP, in 147 m of
water, used as a drilling and production platform.
1991. Bullwinkle, the highest rigid steel jacket is installed in 412 m of
water.
1995. The highest concrete platform is installed in 330 m of water. 1998. Baldpate, the highest steel jacket, is installed in 501 m of
water: it is a compliant free standing platform.
1999. A TLP is installed for the first time in more than 1000 m of
water: Ursa, in 1158 m of water, in the Gulf of Mexico.
51 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr 1998; 501 1984; 147 1991; 412 1978; 311,8 1965; 68,5 1955; 30 1947; 6 1976; 258,6 1975; 144 1997; 980 1994; 872 1989; 536 1996; 894 1999; 1158 2004; 1311 2005; 1425 1977; 151 1993; 250 1989; 217 1973; 70 1995; 330 0 200 400 600 800 1000 1200 1400 1600 1940 1950 1960 1970 1980 1990 2000 2010 Year W a te r dept h ( m ) Jackets TLP Concrete Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Design process
The design of an offshore platform is a very complex process, as
several different aspects must be taken into account.
Normally, in a preliminary phase data concerning the industrial
activity, the construction facilities, the environmental conditions must be collected.
These data concern the payload, that is the total weight, surface and
distribution of the topsides facilities, installments and plants; all this, of course, depends on the kind of industrial activity of the platform (see hereafter).
Then, the environmental and geographic conditions must be known;
the design storm must be selected and the characteristic wave determined, which is fundamental to assess the wave lateral forces on the platform.
The wind characteristics must also be determined, in order to
evaluate the maximum horizontal force acting on the superstructure.
The soil stratigraphy must also be known, which is capital for
53 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Design process
In fact, the number and length of piles, which are in connection with
soil properties and stratigraphy but also with the platform dimensions and with the amount of horizontal actions, can affect greatly the design of the platform. Moreover, the existence of bad soil layers or of solid rock can suggest, and eventually impose, the choice of a gravity platform.
The construction phases must always be taken into account during
the design process. In fact, small jackets and decks are lifted and installed by cranes, and so these phases must be considered and submitted to structural calculation, as very different from the normal conditions the jacket and the deck are designed for.
Greater jackets are skidded onto barges and then launched into the
sea, eventually with the aid of a crane or of floating units. Also these phases must be carefully considered and analyzed, as very different from the usual situation of the jacket.
54 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Design process
Finally, the transitory phase of pile driving must be studied: during
this phase, the jacket must not overturn under the action of moderate waves.
In the design phase, the corrosion aspects and the marine growth
must be considered: for the first problem, an additional thickness of the steel members is used (normally 5 mm), and also the use of sacrificial anodes, while for the latter an extra thickness (about 50 mm) is taken into account to calculate the wave action and the total immersed weight.
Another important factor is time: it is always important to construct
the platform in as less time as possible, for evident economical reasons, and this can affect considerably the structural choices and the construction phases.
For rigid structures installed in water depths to about 100 m, static
analyses are normally adequate, because these structures are sufficiently stiff, so that dynamic effect can be safely ignored.
55 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Unlike this case, that is in deeper water and anyway for any situation
in which the fundamental period of the structure exceeds 3 sec (compliant structures), the effect of cyclic platform motion caused by wave action becomes an important factor and must be carefully analyzed: the fluid-structure interaction becomes an important problem and must be properly taken into account in the design phase.
Usually, a preliminary design is done, taken into consideration a
cardinal rule in offshore engineering: the onshore work must be maximized and the offshore work minimized, and this for economical reasons.
This preliminary design is useful to obtain the overall dimensions of
the platform, the number of piles and so on.
Once this preliminary design done and approved, a detailed design
is done, in which all the structural parts are studied and calculated in detail. Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Design process
In this phase, also the exact construction
sequence is attentively considered and taken into consideration in the structural calculations.
The knowledge of the climatic and geographic
data allows to determine some fundamental dimensions of the structure.
In fact, once the LAT (Lowest Astronomical
Tide) and the design wave known, the height h of the jacket can be determined:
Here, a is the wave amplitude, tmax is the
maximum tide and ag is the so-called air-gap, a safety height, normally 0.5 m.
Actually, no point of the deck must be
positioned under the height h, and this to put all the installments off the wave action.
ag a t LAT h= + max + + ag a LAT tmax
57 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Design process
The most important parameter, however, in the design phase is the
economical aspect: this point conditions very much the choice of the structure type.
In the figure, it is shown a comparison of the relative cost trends for
different platform types, for mild-sea (e.g. the Gulf of Mexico) and for extreme-sea conditions (e.g. the North Sea).
It is apparent that the cost of bottom-supported platforms increases
rather quickly with the water depth: beyond a certain water depth, these are no more cost-effective.
58 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Standards and regulations
The offshore installments must be safe to protect the human,
marine, and coastal environments, and to preserve the very considerable investments of time and resources involved.
It is the purpose of this section to identify the methods by which
responsible parties seek assurance of the structural integrity of offshore platforms.
Until the late 1960s, structural integrity in the U.S. offshore industry
was largely the responsibility of the designers, who worked to a variety of standards drawn from coastal and onshore engineering experience.
The first published design standard for fixed offshore platforms was
issued in 1969 by the American Petroleum Institute (API).
Actually, the structural integrity can be checked through one of three
similar, but different, procedures known as verification, certification, and classification, having the characteristic that each is carried out by specialist organizations independent of both the owner and the designer.
59 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
The object of quality assurance procedures is to verify that the best
available technical and environmental knowledge has been applied during the phases of design, construction, installation, and operation of an offshore platform.
Classification is a quality assurance service provided by one of the
private organizations known as classification societies, and begins during the design phase of a structure.
Criteria for classification are the society’s published standards,
known as rules or guides. The procedure begins with submittal of engineering calculations, specifications and fabrication drawings so that the society can verify compliance of the design with the rules.
During the subsequent phases of construction, installation, and
operation, surveys are conducted as necessary to ensure complete and continuing adherence to standards.
The classification procedure includes periodic inspections and
special damage surveys to ensure that integrity and serviceability are maintained throughout the life of the installation.
Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Standards and regulations
Well-known classification societies include the American Bureau of
Shipping, Det Norske Veritas (Norway) and Lloyd’s Register of Shipping (U.K.).
These and other societies have expanded their scope of services
beyond the traditional classification of vessels of commerce to encompass many other types of marine structures, including offshore structures.
Certification is a quality assurance procedure under which the
owner or a government mandates adherence to specified standards or rules for design or construction and requires verification of compliance by one of a limited number of authorized certification agents.
While an authorized certification agent may apply the standards of
its own organization in the process of evaluation, the standards specified by the owner or government having jurisdiction prevail in cases of conflict.
61 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Standards and regulations
Examples of assuring structural integrity by certification are the
procedures adopted by the U. K. and by Norway.
In the U.K. regulations stipulate that a fixed offshore structure must
be certified by American Bureau of Shipping, Det Norske Veritas (Norway), Lloyd’s Register of Shipping (U.K.), Bureau Veritas (France), Germanischer Lloyd (Germany) or Halcrow Ewbank and Associates Certification Group (U. K.).
The U.K. regulations make it clear that the owner has the
responsibility for sound design and construction as well as adequate maintenance of the offshore installation.
Norwegian regulations specify only the Norwegian Petroleum
Directorate (NPD) as the approval agency, but NPD customarily contracts with independent review agencies to confirm compliance with its rules. The owner carries responsibility for assuring structural integrity. 62 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Standards and regulations
Verification is the procedure used in the U.S. to assure structural
integrity of offshore platforms. It is administered by the government under the Platform Verification Program.
In the USA, verification is mandatory for a new platform and for
major modifications to an existing platform if any of the following conditions will exist:
it is installed in water deeper than 120 m; it has a natural period greater than 3 s;
it is installed in an area having unstable bottom conditions; it is installed in a frontier area;
it uses an unusual design concept in comparison to typical installations
in the region.
In 1979, a study conducted in the USA revealed that in the Gulf of
Mexico, over 32000 platform years of service had been accumulated with 37 platforms lost.
63 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Of these, 34 losses were due to overloading from hurricane waves,
and 3 losses occurred because of hurricane wave loading combined with wave-induced motion of unstable sea-floor deposits. This represents a failure rate of 0.1 percent annually.
By 1984, five years after the period covered by the above statistics,
approximately 14000 platform years of service had been added without further losses.
Present offshore technology, standards, and regulations provide
adequate safety of fixed offshore structures against general collapse.
The general knowledge about this topic has spread rapidly all over
the world and at present all the countries have similar and equivalent rules. Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Nevertheless, there are some rules that are considered as reference
norms:
API RP 2A - Recommended Practice for planning, designing,
constructing fixed offshore platforms. In the following of this course, if not specified differently, API norms are intended to be used (abridged in API);
Det Norske Veritas – Rules for the design, construction and inspection
of off-shore structures (abridged in the following with DNV);
British Standard 6235 – Code of practice for fixed offshore structures
(abridged in the following with BS);
DOE – Offshore installations: guidance on design and construction;
German norms.
NTS: Norsok Standard – Actions and action effects (abridged in the
following with NTS – Norwegian Technology Standards, or Norsok Standard).
65 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Chapter 2
Design actions
66 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .frContent
Types of loads 67 Operational loadings 68 Deformation loads 77 Accidental loads 79 Environmental loadings 81 Storm selection 82 Wind forces 99 Ice forces 114 Snow loads 127 Current forces 128 Marine growth 131 Earthquake actions 13367 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
As for any other type of structures, loads acting upon an offshore
platform can be divided into two different main classes:
permanent (dead) loads;
variables (live) loads.
In turn, these two classes can be divided into several subclasses of
loads:
Permanent loads are composed of structural loads, operational dead
loads, deformation and hydrostatic permanent loads.
Variable loads are composed of operational live loads, environmental
loads, accidental loads, variable hydrostatic and deformation loads.
Structural load: it is the self weight of the structure constituting the
platform; hence, it is a result of the design process.
Hydrostatic loads: they are the buoyancy of some submerged
members, buoyancy that, for a part of it, can be also variable as a function of the immersion (depending upon tides and waves). It must be remarked that hydrostatic loads are essential in floating structures, as they give the global stiffness of the structure.
Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Operational loadings
Operational loadings: they are all the loadings which are inherent
to the proper use and functions of the platform.
So, each technical equipment onboard the platform (production and
process moduli, but also the appurtenances, i.e. the boat landing, the helideck, the cranes, the flare boom and so on) and each bulk material and technical pieces (e.g. drilling tubes) used onboard for different purposes are operational loads.
Usually, operational loadings are divided into:
topsides;
consumables;
human weights.
Topsides: it is the whole system hosted by the platform, normally by
the deck: process units, pumps, generators, drilling units, cranes, helideck, flare, living quarters, bridges, boat landing and so on. Topsides are permanent loads.
69 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Operational loadings
Consumables: it is the weight of all the items and liquids that must
be stored onboard for production, treatment and so on: fuel (diesel or gas condensate), potable water, waste treatment, corrosion inhibitors, lubricants, drilling tubulars, drilling mud, chemicals for various treatments and so on.
Human weights: it is the weight of the personnel onboard; it is often
already considered in the weight of the living quarters.
In the design process, all these weights are input data.
In fact, once the production capabilities decided, the designers are
able to decide what goes onboard and its dimensions.
Normally, topsides facilities, like for instance living quarters or
process units, are pre-assembled and standardized items.
So, once decided the number and type of items to be used, the
designer is able to know the topsides weights and dimensions, and following the norms concerning mutual distances of units, to decide the deck: arrangement and dimensions.
70 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Operational loadings
It must be recalled that pre-fabricated units or pre-designed items
(like a helideck) apply generally speaking a complex load to the platform structure.
For instance, the action applied by a flare to the deck of the platform
consists not only of vertical loads, but of all the loads applied by the truss of the flare, which can have also horizontal components.
In addition, the loads given by a modulus are not, in general,
uniformly distributed, but they are applied in some singular precise points, which support the topside weights: of course, this affects the deck design.
However, in a first design phase, some average uniform loads can
be used for pre-dimensioning: from 2 t/m² for usual platforms up to 4 t/m² for North sea platforms.
A more rigorous method is to utilize the following figures to obtain
topside weights and deck areas. The data in these figures are from installed platforms.
71 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Topsides weight as a function of production rate.
Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Deck area as a function of production rate.
73 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Actually, once the deck arrangement chosen, all operating loads are
usually given by the operator and the equipment manufacturers.
An example of detailed operational loads is given in the following
table.
Operational loadings
Loads to be taken into account (kN/m2) For portions of the structure For the structure as a
whole Zone considered Flooring and
joints components Other
Process zone (around wells and large-scale machines) 5 5 2.5
Drilling zone 5 5 2.5
Catwalks and walking platforms (except emergency exits) 3 2.5 1
Stairways (except emergency exits) 4 3 0
Module roofing 2 1.5 1
Emergency exits 5 5 0
STORAGE Storage floors - heavy
Storage floors - light
18 9 12 6 8 4 Delivery zone 10 10 5 Non-attributed area 6 4 3 74 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr Notes:
In the process and drilling zone, for loads on a portion of the structure,
the load must be accumulated with a point load equal to the weight of the heaviest part likely to be removed, with a minimum value of 5 kN.
Point loads are assumed as being applied to a 0,3m x 0,3m surface.
In the absence of specific data from the manufacturer, and at an
early design stage, the following values are recommended in BS norms:
crew quarters and passageways: 3,2 KN/m2;
working areas: 8,5 KN/m2; storage areas: γ H KN/m2;
with
γ is the specific weight of stored materials, not to be taken less than
6,87KN/m3;
H is the storage height (m).
75 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
The Norwegian NTS in Norsok Standard gives the following average
accidental (i.e. variable) loads for the deck design:
Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
The design is intended to be divided into three parts:
Local design: design of deck plates and stiffeners;
Primary design: design of deck beams and beam-columns;
Global design: design of deck main structure (and substructure).
Notes:
Wheel actions to be added to distributed actions where relevant. (Wheel
actions can normally be considered acting on an area of 0.3 x 0.3 m).
Point actions to be applied on an area 0.1 x 0.1 m, and at the most
severe position, but not added to wheel actions or distributed actions.
The distributed load q is to be evaluated for each case. Storage areas
for cement, wet or dry mud should be the maximum of 13 kN/m² and
ρgH, where H is the storage height in m. Laydown areas are not
normally to be designed for less than 15 kN/m².
The factor f is the min of 1.0 and (0.5 + 3/A0.5), where A is the action
area in m².
Global action cases should be established based upon “worst case”,
representative variable action combinations, complying with the limiting global criteria to the structure.
77 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Deformation loads
Deformation loads: they are all the loads produced by an imposed
state of strain on the structure.
Such imposed states of strain can be produced by temperature
differences, ground settlements, pre-stressed states.
In the case of temperature differences, they are typical variable
deformation loads, with different periods (daily, annual).
In hyperstatic structures, temperature differences produce stress
states that can be very important.
To be recalled that the submerged part of the platform is at an
almost constant temperature, while the emerged part can be subjected to very important temperature excursions, generally varying with time and place.
In addition, some structural parts are subjected to temperature
differences produced by the production processes: the most representative case is that of risers, with the external temperature equal to that of the sea and the internal one typical of oil produced, normally rather high.
78 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Another example is that of submerged tanks in gravity platform: the
tank can be filled in with water or with oil or gas, and they have different temperatures.
Pre-stressed states are used in concrete platforms for preventing
from concrete cracks.
In TLP, the tethers are highly pre-stressed by the extra buoyancy of
the hull, which gives the global stiffness of the platform.
Of course, this pre-stress affects also the stress distribution in the
hull.
Ground settlements often occur during reservoir exploitation.
If they are not uniform, they induce stresses in hyperstatic
structures.
79 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Accidental loads: they are caused by wrong operations or by
events not considered in the normal operations of the platforms, such as explosions, impacts, fires and so on.
The most important accidental loads for a platform are those caused
by impact, that produce impulsive forces.
These impulsive forces can arise during some transient operations,
and the most important are those that arise during the landing of helicopters and during the mooring of vessels to the platform.
BS norms consider two situations for helicopter landing: heavy and
emergency.
For the first case, the impact load is equal to 1.5 times the maximum
take-off weight, whilst for the second case this factor is 2.5. In both cases, a horizontal load applied at the points of impact and equal to half the maximum take-off weight must be taken into account.
NTS give some more detailed conditions for the analysis of impact
during helicopter landing, making a distinction between the local forces and the global forces.
Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
For vessel mooring, design impact forces, to be applied at the boat
landing but also to other less favorable parts, should be computed for the largest ship foreseen for the platform, at a velocity corresponding to operational speed.
BS norms, for instance, consider for the minimum design impact that
generated by a vessel of 2500 tons with a velocity of 0.5 m/s.
The added mass must be considered (i.e. DNV norms prescribe an
added mass of 40% for sideways collisions and of 10% for stern or bow impacts).
All the kinetic energy of the ship must be absorbed by the fender, or,
for the zones out of the boat landing, the platform must be able to withstand without major damages (only local damages are allowed) to the same impacts.
When deeper investigations are not conducted, the impact zone
goes from 10 m under the LAT to 13 m above the LAT.
Other accidental loads often considered are those produced by the
fall of objects.
81 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Environmental loadings
Environment gives different kinds of actions on offshore platforms:
wave forces; wind forces; ice forces; snow loads; current forces; marine growth; earthquake actions.
We will briefly consider in the following these loadings, leaving to the
next chapter the hydrodynamics of wave forces, the most important environmental action on offshore structures.
The most part of the environmental loadings depends upon
meteorological conditions.
So, before considering the different actions, we deal in the next
section with the procedure to select a design storm.
82 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Storm selection
There is a relation between the frequency and the intensity of the
events that a structure may experience. Such a relation is qualitatively sketched in the figure.
The structure is designed to withstand some extreme event SD,
which has a frequency fD. The choice of the event is made so that
83 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
during the lifetime L of the structure is reasonably small. This is called the encounter probability and represents one of several ways to characterize environmental risk.
Usually a designer should consider three types of events:
those causing fatigue effects;
those that may interfere with normal operations;
those that may produce the failure or a severe damage of the structure.
Each category requires a different type of data and statistical
analysis for resolution of the associated problems.
Considered as random process, a storm must be statistically
described.
Actually, the physical elements of a storm (e.g. the wave height or
the wind velocity) are described, using the recorded meteorological data, by some distribution laws, particularly suited to describe extreme events, such the occurrence of a storm of great intensity.
The random wave variables, usually recorded and processed, are
defined in the following figure.
Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
Storm selection
85 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
If a suitable convention is adopted, the random sea shown in the
previous figure can be described in terms of wave height (H) and period (T).
In engineering applications the usual definition of wave height is the
maximum surface elevation difference between successive up-crossings of still water level.
This leads to the definition of zero-crossing period Tz.
Longuet-Higgins (1952) has shown that, for certain conditions the
cumulative distribution of wave height is approximated by the Rayleigh distribution:
ση=: standard deviation of η(t) (see previous figure).
Storm selection
.
1
)
(
2 2 8ση He
H
P
−−
=
→
=
− 2 2 8 24
)
(
ση ησ
He
H
H
p
86 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr A measure often used of the random wave field is the significant
wave height, HS.
Hsis taken as H1/3, the expected value of the highest one-third of the
waves in a sample.
For the case of the Rayleigh distribution, it can be shown that:
H1/3= 4ση.
The expected value of the maximum wave height Hmax in a sample
of N waves is given by:
Usually, designers switch at this point from a probabilistic to a
deterministic approach: they introduce a regular train of waves
where the wave height is taken as equal to Hsor Hmax.
Storm selection
. ln 2 2 3 1 N H Hmax =87 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
So, in this deterministic approach the statistics of waves is used only
to obtain a wave height for a regular sea state.
However, in this approach there is the problem of the selection of a
wave period to be associated with the wave height.
This point, concerning the choice of the wave period, will be treated
after.
The probabilistic models developed thus far relate to short-term
stationary conditions.
They must be developed for the prediction of the expected
maximum wave height, the design wave, over a long-term period such as 50 or 100 years (the centennial wave).
The long-term wave height distribution is, usually, based on
one-year’s data and its extrapolation to a return-period of 50 or 100 years is made using the Weibull or Gumbel distribution, which are typical probability laws of extreme values.
Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
The Weibull probability law is
α: scale parameter, α>0; γ: shape parameter, γ>0;
η: location parameter, H≥η;
The values of the mode µ, mean m, median M and standard
deviation σ of the distribution are given by:
Γ is the gamma function:
.
1
)
(
)
(
1 γ γ α η α η γα
η
α
γ
− − − − −−
=
→
−
=
H He
H
P
e
H
H
p
Storm selection
( )
ln2 , 1 2 1 1 . , 1 1 , 1 1 2 1 1 + Γ − + Γ = + = + Γ + = − + =γ
γ
α
σ
α
η
γ
α
η
γ
α
η
µ
γ γ M m . ) ( 0 1∫
∞ − − = Γ x e ttx dt89 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
The Gumbel probability law is
µ : location parameter; it corresponds to the mode of the distribution;
β : scale parameter:
σ : standard deviation of the distribution.
The values of the mean m and of the median M are given
respectively by
Both the Weibull and the Gumbel distribution of the maximum wave
height can be derived from an histogram of the recorded daily highest waves in one year.
.
)
(
1
)
(
β µ β µ β µβ
− − − − − − − −=
→
=
H H e e He
H
P
e
e
H
p
Storm selection
; 7797 . 0 6σ σ π β = ≅ . 2858 . 0 , 45 . 0σ
µ
σ
µ
+ = + = M m 90 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr In the figure, the probability density function and the cumulate
probability function for the case of Weibull (for η=0) and Gumbel
distribution sharing the same mode (µ= 5 m) and median (M= 5.73
m); the curves do not fit the same recorded histogram.
p(H) P(H) H(m) H(m) Gumbel Gumbel Weibull Weibull
Storm selection
91 Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr
The probability distribution used to fit the wave height data is used to
select the design wave.
This is usually done choosing a return period TR: it is the average
time interval between successive events of the design wave being equalled or exceeded:
So, once TR fixed, P(H) is known and by the distribution of wave
height, the design wave is obtained.
For instance, for the case of a Gumbel distribution with mean m and
standard deviation σ, it is easy to find that the design wave has the
height
.
1
1
)
(
)
(
1
1
R RT
H
P
H
P
T
→
=
−
−
=
.
1
ln
ln
7797
.
0
45
.
0
−
−
−
=
R RT
T
m
H
σ
σ
Cop yri gh t P . Vannucci – U VSQ pao lo .v annucci@ m ec a. uv sq .fr This value of H will be, in the average, equalled or exceeded once in
a period equal to TR.
So, for TR= 50 years, it is:
Instead, for TR=100 years, it is:
For instance, for the case of the Gumbel distribution sketched in the
previous figures (m= 6,15 m, σ = 2.565 m) it is H50= 12,8 m and
H100= 14,2 m. This means, for instance, that waves with a height
equal to or greater than 14,2 m are waited once in a century.
For instance, in the Adriatic Sea H100= 13 m, while in the North Sea
H100= 26 m.