Response and strength analysis of jack-up platforms

(1)

p1983

Lab.

V.

_{Scheepsbouwkundl}

HIEF

_hlis

esponse and strength analysis of jack-up

piatisf

che Hogeschool

Delft

By

Jonas Odland, Dr. ing., Statoil*

* This paper was written while the author was an

employee of Det norske Veritas. ABSTRACT:

The paper deals with design criteria for jack-up platforms. Based on

simple descriptions of the environmental conditions, methods for ana-lysis of loads and platform response are described. General methods are mentioned, but it is emphazed on simple methods which may be suitable for feasibility studies, concept evaluations and general parametric stud-ies. Strength criteria are discussed on a general basis, but it is

emphas-ized on criteria which are relevant for the most important structural

members, or members which are typical for jack-up platforms. This in-cludes a very simple method for fatigue damage evaluation.

Keywords: Jack-up, response analysis, strength criteria, fatigue.

1. INTRODUCTION

1.1 Description of the platform concept

Jack-up platforms have been in use since about 1955. This type of platform has become a standard tool for operations in shallow water, generally less than 100 meters depth. Jack-up platforms are very stable dur-ing operation as they rest on the sea bottom, and are not subjected to any heaving motion.

Modern jack-up platforms have three or four legs.

The legs are normally vertical, but special designs

with slightly tilted legs have been developed for better stability. The legs are either designed as tubulars with

circular or square cross section, or as lattice

struc-tures with triangular or square cross section.

There are basically two different concepts for bot-tom 'support. Most jack-up platforms have separate legs with, and in some cases without, special footings (spud. cans). Alternatively all legs are connected to a large steel mat, designed to prevent eiccessive penet-ration where the sea bottom consists of soft clay.

A drilling slot may be cut into one side of the deck, but for other platforms the derrick may be cantilev-ered over the side.

1.2 Special features

For safety evaluation of the platform conceptual de-sign it is of extreme importance to give full attention to each particular design condition, namely:

Transit Installation Operation Retrieval

Norwegian Maritime Research

No. 4/1982 .

2

Jonas Odland

Design analyses tend to emphasize on the opera-tional condition, while statistics show that most ac-cidents occur during transit, installation and retrivel. A jack-up platform is designed with independent

unbraced legs, and is therefore rather flexible. The

transverse stiffness is typically an order of magnitude less that the stiffness of a corresponding jacket

struc-ture. In some connections a jack-up platform may

thus be considered as semi-compliant. However, the

important consequence of low stiffness is that dy namic effects have to be taken into consideration. For deeper waters and for areas with severe wave

conditions, it may be necessary to design for increas-ed stiffness in order to avoid fatigue problems.

A jack-up platform is a mobile unit, but it has

narrow limits for operation. The design conditions are stated in the certificates of the platform.

How-ever, in many cases the environmental conditions on one specific location are more or less incomparable

with the original assumptions. Quick methods for

evaluation of an existing platform's suitability for a new location are frequently needed.

2. ENVIRONMENTAL CONDITIONS 2.1 Design considerations

The suitability of a jack-up platform for a given

lo-cation is entirely determined by the environmental

conditions on that location.

(2)

spe-cific environmental conditions of one location, or for one or more environmental conditions not necessarily related to any specific location.

The environmental conditions are described by a

set of parameters for definition of: Waves Current Wind Temperature Water depth Bottom condition 2.2 Waves

The most

significant environmental loads for

jack-up platforms are those induced by wave action.

In order to establish the maximum response, the

characteristics of waves have to be described in de-tail.

The description of waves is related to the method chosen for the response analysis, see Ch. 4.1.

Deterministic methods are most frequently used in

the design analysis of jack-up platforms. The sea

state is then represented by regular waves defined by the parameters:

Wave height, H Wave period, T

The reference wave height for a specific location is

the 100 year wave, H100, defined as the maximum wave with a return period equal to .100 years. For

unrestricted service the 100 year wave may be taken as (1):

Him = 32 metres

There is no unique relation between wave height and wave period. However, an average relation which has been used by VERITAS for the North Sea is:

T-1,0 124

H

k 4,1

1

where H is in metres and T in seconds.

In order to ensure a sufficiently accurate calcula-tion of the maximum response, it may be necessary to

investigate a range of wave periods. However, it is

normally not necessary to investigate periods longer

than 18 seconds. There is also a limitation of wave

steepness. Wave steepness is defined by:

=

2n

H

S

g T2

The wave steepness need not be taken greater than

the 100 year wave steepness, which may be taken as

(2):

(2-1)

(2-2)

3

S/00 =

(2-3)

where H100 is in metres and T in seconds. The relation between wave height and wave period according to these principles is shown in Fig. 1.

Fig. 1. Design wave height versus period.

Stochastic analysis methods are used when a re-presentation of the irregular nature of the sea is es-sential. A specific sea state is then described by a

wave energy spectrum which is characterized by the following parameters:

Significant wave height, Hs

Average zero-up-crossing period, Tz

The probability of occurrence of a specific sea

state defined by Hs and Tz is usually indicated in a

wave scatter diagram, see Fig. 2.

For fagitue analyses where long term effects are

essential, the wave scatter diagram is divided into a finite number of sea states; each with a certain

pro--32

No. 4/1982

32

(3)

15

PROBABILITY

IN

PARTS PER

Amos

THOUSAND

5

EXPECTED ZERO-CROSSING WAVE PERIOD

Fig. 2. Wave scatter diagram. bability of occurrence.

For extreme response analysis, only sea states

comprising waves of extreme height or extreme

steepness need to be considered.

The most probable largest wave height in a specific sea state of a certain duration is:

H. = Hs N.forIN

(2-4)

where N is the number o$ cycles in the sea state.

The duration of a storm is of the order of a few

hours, and the number of cycles will normally be of order 10'. Consequently:

H ,1,85 Hs

(2-5)

The significant wave height need therefore not be taken greater than 0,55 H100.

The steepness of a specific sea state is defined by:

2

Ss =

7 H

s

(2-6)

g Tz2

The sea steepness need not to be taken greater than

the 100 year sea steepness, which may be taken as,

(1), (2):

No. 4/1982 10 15 4

11/10

, Tz< 6

S,=

2/15 Tz/180 , 6 < Tz< 12

(2-7)

1/15

,12T

The 100 year return period is used as the basis for

extreme load analysis. For other types of analyses,

different return periods may be used, (1).

In connection with fatigue analysis a return period equal to the required fatigue life is used as the basis

for wave load analysis. The required fatigue life is

normally 20 years.

In connection with accidental loads or damage conditions a return period of 1 year is taken as the

basis for wave load analysis.

The maximum wave height corresponding to a

specific return period may be obtained from a wave height exceedance diagram. If wave height exceed-ance data are plotted in a log/linear diagram, the re-sulting curve will in many cases be a straight line, see Fig. 3.

1 EXEEEDANCE PER 0O YEARS.

10-7 10 10 10 10 107

NUMBER OF ECEEDANCE PER YEAR

Fig. 3. Height exceedance diagram.

Such results are obtained for areas with a

homo-genous wave climate. Other results may be obtained for areas where the climate is characterized by long

periods with calm weather interrupted by heavy

storms of short duration, (3), (4).

When the individual waves have been defined,

wave particle motions may be calculated by use of an

appropriate wave theory. In connection with

deter-ministic response analysis Stoke's 5th order theory is

often recommended. However, the linear (Airy)

theory is sufficiently accurate for most purposes, provided the wave forces are calculated for the ac-tually submerged portion of the legs. In connection

with stochastic response analysis, linear (Airy) theory should always be used. For conditions where the li-near theory is inaccurate it is recommended that the wave spectrum is modified rather than the wave the-ory.

(4)

In stochastic wave load analysis the effect of wave shortcrestedness may easily be included by

introduc-ing a wave energy spreadintroduc-ing function. Normally a cosine-square directional distribution function is

recommended, (4).

Calculation of wave crest elevation in connection

with the air gap requirement, see Ch. 7.3, should

always be based on higher order wave theory. There-suit of such calculations may be found in (1) and (3).

2.3. Current

The effect of current in the absence of waves is

normally not very important. However, in

combina-tion with waves a comparatively small change in current velocity may cause an important change in

total load.

According to (1) the current profile may be taken as:

Vc = VT + V w h. z

(2-8)

where

VT _{Tidal current}

V_w Wind generated current at the still water

level

h. Reference depth for wind generated current (h.= 50 m)

Distance from the still water level

(positive downwards)

Although the tidal current velocity can be measur-ed in the absence of waves, and the wind generatmeasur-ed current velocity can be calculated, the resulting

cur-rent velocity in the extreme storm condition is a

rather uncertain quantity. Errors in the estimation of current velocity are often considered to represent one

of the most important uncertainties in the load

ana-lysis.

According to (1) the wind generated current may

be taken as:

vvv = 0,017 vR

(2-9)

where vR is the reference wind velocity as defined in Ch. 2.4.

It is normally assumed that waves and current are coincident in direction.

2.4. Wind

The reference wind velocity, vR, is defined as the wind velocity averaged over one minute (sustained

wind), 10 m above the still water level.

For unrestricted operation vR need normally not

be taken larger than 55 m/s, (1).

The wind velocity as a function of height above the still water level may, according to (1) be taken as:

5

Norwegian Maritime Research No. 4/1982

V =

(2-10)

0

where

z Height of load point above the still water

level

z.

Reference height (z. = 10 m).

It is normally assumed that wind and waves are

coincident in direction.

2.5. Water depth

The water depth is an important parameter in the

calculation of wave and current loads. The required

leg length depends primarily on the water depth,

which therefore is a vital parameter for the

evalua-tion of a jack-up's suitability for a given locaevalua-tion. Definitions:

The tidal range is defined as the range between the highest astronomical tide (HAT) and the

lo-west astronomical tide (LAT).

Mean water level (MWL) is defined as the mean

level between the highest astronomical tide and

the lowest astronomical tide.

The storm surge

includes wind-induced and

pressure-induced effects.

The still water level (SWL) is defined as the.

highest astronomical tide including storm surge. The reference water depth (h) to be used for vari-ous calculations is the distance between the sea bed and the still water level (SWL).

2.6. Bottom conditions

The bottom conditions have to be considered in the following contexts:

The overturning stability depends on the stability of the foundation

The leg bending moments depend on the

bot-tom restraint

The overall stiffness and consequently the na-tural period of the platform depends on the

bot-tom restraint

The response at

resonance depends on the

damping which depends on the bottom conditions

The air gap depends on the penetration depth

at great water depths.

A detailed treatment of bottom conditions can

only be carried out in connection with one specific

location. However, at the design stage it may be

rel-evant to take into account some degree of bottom

restraint. For such purposes a spring stiffness may be determined as indicated in Ch. 4.4. The calculation of a spring stiffness has to be based on information on

shear modulus, G, and Poisson's ratio, v. The

se-lected design values should be stated in the certifica-tes of the platform for evaluation for each new loca-tion. Values that have been used for certain areas of the North Sea are:

(5)

0 = 15,000 kN/m2, P = 0,3

3. LOAD ANALYSIS 3.1. Load categories

Functional loads are loads which are a

necessary

consequence of the structure's existence, use and

treatment.

Environmental loads are loads which are not a

necessary consequence of the structure's existence, use and treatment. Such loads are all directly or

in-directly due to environmental actions.

Accidental loads are loads which may occur as a

result of accident or exceptional conditions.

Only the environmental load analysis is considered here. Functional loads have to be defined specifically for each design. Accidental loads are briefly menti-oned in Ch. 7.4.

3.2. Wave loads

Wave loads on jack-up legs may normally be cal-culated by use of the Morison equation. The hori-zontal force per unit length of a homogenous leg is

then given by:

F = Fc + Fi

_(3-1)

where 1 FD

=ecD

₂ D vI v1 Drag force

F1 = e C/a A _{Inertia force}

e _{Density of liquid}

Horizontal component of fluid acceleration Horizontal component of flow velocity

Cross sectional area of the leg (For a cir-cular cylindrical leg, A = D2/4). D _{Cross sectional dimension perpendicular to}

the flow direction (For a circular cylindr-ical leg, D is the diameter).

CD - Drag (shape) coefficient

C1 _{Inertia (mass) coefficient}

The liquid particle velocity and acceleration in

re-gular waves should be calculated according

to

re-cognized wave theories, taking into account the sig-nificance of shallow water and sur face elevation. (If the cylinder is moving, the equation is to be modified as indicated in Ch. 4.1).

3.3. Current loads

Current loads on jack-up legs may normally be cal-culated from the drag term in the Morison equation. .

The current velocity as a function of depth _{below the}

still water level may be determined in _accordance

with Ch. 2.3.

An explicit expression for the total current load in the absence of waves is given i Appendix A.

a

V

A

No. 4/1982

6

Due to the non-linearity of drag forces it is not

acceptable to calculate separately drag forces due to

waves and current, and subsequently add the two li-nearly. In general the current velocity is to be added to the liquid particle velocity in the waves. The drag

force is then calculated for the resulting velocity.

However, if the drag forces due to wave and current

have been calculated separately, an indication of

their combined effect may be obtained in accordance with Appendix A.

3.4. Wind loads

Wind forces and pressures on members above thesea surface may normally be considered as steady loads. The wind forces have to be calculated for each of

the different directions of environmental loads that

are considered. The calculations are carried out by

dividing the windexposed structure into its indi-vidual parts.

The wind force acting on one part is: Fw = e cD D v2 cos2

2

where

CD- Drag (chape) coefficient as defined in (1). D Cross sectional dimension perpendicular to

the wind direction (For a circular cylindr-ical member D is the diameter).

v _{Design vind velocity as defined in Ch. 2.4.}

p _{Angle between the wind direction and the} cross sectional plane of the member.

e

Density of air ( e = 1,225 kg/m3 for dry

air).

For calculation of the wind force acting on the ex-posed part of a lattice leg, the parameters CD and D

may be replaced by CDE and DE according to Ch.

3.5.

3.5. Idealization of lattice legs

Hydrodynamic loads on a lattice leg may be obtained either from a direct analysis of the complete structure using an appropriate computer program, or from a

simplified analysis of an «equivalent» cylindrical leg. For a simplified analysis it is necessary to determine the equivalent cylinder diameter and the correspond-ing hydrodynamic coefficients.

The equivalent inertia coefficient may be chosen like:

CIE = 2,0

_(3-3)

The equivalent diameter is then determined by:

'4 V

DE -

B

(3-4)

S

(6)

here

VB = A, / Total volume of one bay Cross sectional area of member i

1 _{Length of member i}

Length of one bay

Indicates summation over all members in

one bay

The equivalent drag coefficient is givenby:

CDE CDEi

where

CDEi

= (sin2 j

+ cos2 f3 sin2 a )3/2 CD,

7.

Fig. 4. Flow through a lattice leg.

CoR=Co t cos be

C0 = Drag coefficient for a smooth

cylinder with diameter D

A a ₂

Fig. 5. Drag coefficient for chord with racks.

The submerged portion of the legs varies as the

wave passes.

Second-order bending due to axial loading

re-duces the effective transverse stiffness.

The interaction

leg/hull and the

interaction leg/sea bottom are non-linear.

However, a number of options for simplification

of the analysis are indicated in Fig. 6. The main con-siderations are:

No.4/1982 CD, _{Drag coefficient of member i}

Di Diameter of member i

a Angle which determines the flow di-rection, See Fig. 4.

a Angle which determines the

inclina-tion of diagonal members, see Fig.

4.

Based on experience it is generally accepted that

drag coefficients as for smooth elements may be used in combination with a traditional, deterministic

res-ponse analysis. By turning to a more refined sto-chastic response analysis an inherent safety is lost, and all phases and parameters like the drag

coef-ficients should be reconsidered before accepting the load reduction (1). For a cylindrical chord with racks, the drag coefficient is given in Fig. 5.

4. RESPONSE ANALYSIS

4.1. Global analysis for the elevated condition

A realistic response analysis for a jack-up platform in the elevated condition represents considerable

dif-ficulties. Ideally the response analysis should

auto-matically account for:

Dymanic response The fundamental mode of

large jack-up platforms corresponds to a natural

per-iod in the range 5-7 seconds. This means that

dy-namic effects are significant and have to be account-ed for.

Stochastic response The most significant

en-vironmental loads are those induced by wave action. The irregularity of the sea can only be simulated by use of a stochastic wave model.

Non-linear response Equations governing the

response of a jack-up platform are non-linear for

several reasons:

The more refined wave theories are non-linear.

The drag term in the Morison equation is

non-linear

Current loading interacts with wave loading

and introduces non-zero mean loading

(3-5)

D111

(7)

where a Cd cf Cm DETERMINISTIC NONLINEAR DYNAMIC DETERMINISTIC NONLINEAR STATIC DETERMINISTIC LINEAR STATIC STOCHASTIC LINEAR DYNAMIC STOCHASTIC LJNEAR STATIC

Fig. 6. Options for cimplification of response

ana-lysis.

Dynamic versus static analysis

Stochastic versus deterministic analysis Non-linedr versus linear analysis.

Thedynamic equation

of

equilibrium is considered for illustration:

mF+ci+kr=F

(4-1)

= cd(v-1)1 v

+ cfa + cm(aF)

Mass Damping, c = c(r) Stiffness, k = k(r) Displacement Acceleration of fluid Velocity of fluid Drag force coefficient

Froude-Kryloff force coefficient Added mass

Method A is the most comprehensive of the meth-ods. In principle it is possible to account for all of the special effects mentioned above. A random load his-tory is generated from a wave energy spectum by use

of Monte Carlo simulation technique. The

non-li-near equations of equilibrium may then be

establish-ed and solvestablish-ed by time integration. It is possible to

include simultaneously the effects of wind, waves and current. However, the method is expensive, and there are some uncertainties with respect to the

interpreta-Norwegian Maritime Research No. 4/1982

8

tion of results, particularly for the extrapolation to

extremes from simulated records.

Method B is similar to method A except that only regular waves are considered. Fluid velocity and

ac-celeration are determined from the most accurate

wave theory, and the non-linear equations of equili-brium are solved by time integration. The method is well suited for extreme response analysis, but not for rigorous fatigue analysis.

Method C is based on a linearization of the equa-tion of equilibrium which may then be rearranged as: (m + cm) + ( c1 + ccll) r + kir = F1

(4-2)

where = cdiv + cia = Cf + Cm CcH

=

cd(v ---- _)ref Cd

Acr (v

IT Alternative 1 Alternative 2 Linearized damping and stiffness

There are two alternative methods for linearization of the drag term. In alternative 1 the linearization is

based on a reference relative velocity, (v _Oref evaluated for waves of a predetermined steepness.

This steepness may be frequency dependent, see Eq.

2-1.

In alternative 2 the linerization is based on the

standard deviation, o_(v ₀₅ of the relative velocity. Alternative 1 has the most straightforward physical interpretation, and by this method it is also possible to calculate the drag force for finite wave heights and

thus account for the effect of a variable submerged

volume.

The linearized equation of equilibrium is solved in the frequency domain by use of the standard method

for linear stochastic analysis. This method rests on the assumption that the response spectrum in ques-tion can be represented by the product of a transfer

function of the response squared and the wave spec-trum. The most probable largest response is

comput-ed on the basis of information inherent in the

res-ponse spectrum. The procedure may be used in

com-bination with the normal mode approach which in

the case of a jack-up platform may be very cost

ef-ficient. However, there are also obvious disadvanta-ges of the method:

Linearization of drag forces introduces

uncer-tainties

The estimation of total damping is uncertain

The effect of current cannot be included

con-sistently, see Appendix A.

Extrapolation to extremes is uncertain, especially due to the linerization

(8)

Instantaneous load distributions are difficult to

obtain

Several of the disadvantages mentioned here apply mainly to extreme response analysis. The method is

considered as a suitable approach for fatigue

ana-lysis, where the randomness of the sea is essential. Method D is equivalent to method B for very stiff

platforms, for which dynamic effects are insigni-ficant. The analysis is considerably

simplified-be-cause the equation of equilibrium is reduced to:

kr = Fs

_(4-3)

where

Fs = cdv Iv I + cia

However, jack-up platforms are often so flexible that it is not appropriate to neglect the dynamic ef-fects. It has been found that the dynamic response

may be simulated quite accurately if the load is

mul-tiplied by the dynamic amplification factor (DAF) for a single degree of freedom system, se Ch.4.6.

However, in very short waves the leg forces may act

in different directions. In such cases only that

por-tion of the load which causes deflecpor-tions coinciding

with the fundamental mode of the platform have to

be multiplied by DAF.

Method E is equivalent to method C for very stiff

platforms, for which dynamic effects are insigni-ficant. However, jack-up platforms are so flexible that it is not possible to neglect dynamic effects. It

has been found that the dynamic response may be si-mulated quite accurately if the transfer functions are

multiplied by the dynamic amplification

factor

(DAF) for a single degree of freedom system, see

method D.

Method F is the most simple of all methods, and in

general a number of important effects are ignored.

However, as discussed in connection with the other

methods it is often possible to account for special

effects by simple modifications. In many cases meth-od F may be mmeth-odified in such a way that the accuracy is not significantly reduced in comparison with meth-od B. The main advantage of the methmeth-od is that it is

easy to establish instantaneous load distributions,

and it is possible to work with very large and detailed structural models.

Conclusions: A rigorous analysis corresponding to

method A is possible for special investigations, but expensive. Deterministic methods may be used for

extreme response analysis. Dynamic effects and

non-linear effects should be accounted for, but this may be done by approximate modifications of a li-near/static analysis. Stochastic methods should be used for fatigue analysis. However, it may be suf-ficient to carry out a simplified fatigue analysis ac-cording to Ch. 6.4, either as a preliminary study, or

to see if more refined analysis are necessary. In that case a detetministic response analysis is sufficient.

9

4.2 Global analysis for the transit condition

In the transit condition the legs are fully elevated and

supported as cantilevers in the hull. Any rolling or pitching .motion in combination with wind induces

large bending moments in the legs and large reaction

forces in jackhouses and supporting hull structure. Consequently the critical areas in the transit

condi-tion are:

Lower part of legs Jackhouses

Leg guides and supporting hull structures

In addition to the leg forces, the hull is exposed to sea pressure.

In general the legs are designed for static forces and inertia forces resulting from the motions in the most severe environmental transit conditions,

com-bined with wind forces resulting from the maximum wind velocity. Wave motions may be obtained either from model tests or from computations. It should be

emphasized, however, that a general wave motions

computer program should be applied with great care. The proportions of a jack-up hull are so unusual that

it will normally be necessary to apply a program

which may account for three-dimensional effects. In addition the wave motion response will be influenced by non-linear effects such as:

non-linear damping water on deck

bottom out of water

Because the most severe motions are dominated by rolling or pitching at the natural period, the damping

is essential for calculation of the maximum roll or

pitch amplitudes. Non-linearities in the restoring

forces and moments may on the other hand be

res-ponsible for shift in the natural period.

In lieu of more accurate analysis it is possible to

re-sort to a simplified analysis procedure described in (1). According to this procedure it is sufficient to

consider the following loads:

Inertia forces corresponding to a specified

ampli-tude of roll or pitch motion at the natural period

of the platform.

Static

forces corresponding to the maximum

inclination of the legs due to rolling and pitching.

Wind forces corresponding to a specified wind

velocity.

The effect of heave, surge and sway are implicity

accounted for by use of a specified load factor,

Y = 1.2. The application of the load factor is

desc-ribed in (1).

For calculation of leg forces it is assumed that roll or pitch motion can be described by:

2 7r t

=19₀ sin

To

(4-4)

(9)

where

Time variable

To Natural period of roll or pitch

0 0 Ampilitude of roll or pitch

The axis of rotation is assumed to be located in the water plane, see Fig. 7.

The acceleration of a concentrated mass located at a distance r from the axis of rotation is then:

Tr. 2 t

a =

or sin To where

(27)2

e

Transverse and longitudinal forces per unit length of the leg may then be established.

The transverse forces are: FTs static force, FTD inertia force and Fw wind force, see Fig. 7. The longitudinal forces are: FLs static force and FLD inertia force, see Fig. 7.

Fig. 7. Jack-up platform in transit.

The leg bending moment, shear force and axial force may be obtained in a straightforward way by

applying these distributed loads to a structural model. of the leg, supported in the hull. However, since only the maximum leg section forces and moments at the intersection with the hull are of real interest, the

re-quired information may be obtained by integration

of the load intensities over the leg length.

Na. 4/1982

(4-5)

10

Approximate, explicit formulae are given in

Ap-pendix A. Bending moment and shear force

distribu-tions may then be established according to Fig. 8.

The coefficient 13 is explained in Ch. 4.3.

REACTIONS:

LOWER GUIDES, RL=(1-p)P

UPPER GUIDES, Ru =RL+Q,,

Fig. 8. Bending moment and shear force

distribu-tions in transit. 4.3 Leg-hull interaction

The most highly loaded part of a jack-up leg is

normally the portion located between upper and

lo-wer guides where the leg loads are transferred into

the hull. The leg-hull interaction depends very much

on the actual design concept. In principal the leg

bending moment is

reacted partly by horizontal

forces from the guides and partly by vertical forces from the jacking mechanisms. The fraction (fi' ) of the bending moment which is reacted by vertical

forces in the jacking mechanisms may vary

consider-ably from one design to another. The value of 0

depends primarily on how the jacking mechanisms

are supported by the hull.

The most important effect of the coefficient 13 is

its influence on the leg shear force between upper and lower guides, see Fig. 8. This shear force is very

im-portant, in particular for lattice legs, where large

overall shear forces produce large axial forces in the brace members. It can also be shown that the value of

fl may have a significant effect on the lowest natural frequencies.

Resilient mounted jacking mechanisms will deflect due to loading. In the extreme case with thick shock pads where the deflections may be considerable, the

(10)

jacking mechanisms will only react the axial leg

for-ce, while the guides have to react the bending

mo-ment and the shear force. This is important not only for design of the legs, but also for design of the jack-houses.

Jacking mechanisms fixed to the hull will tend to

absorb directly almost all of the axial forces in the

chords. However, due to local flexibilities a certain amount of the bending moment will have to be

react-ed by guide forces. In general this amount will be

small, and the jacking mechanisms (with locking de-vices) have to be designed not only for the axial leg force, but also for most of the bending moment.

For analysis of the global response it may normally be assumed that the stiffness of the hull structure is infinitely high compared to the stiffness of the legs.

The jacking mechanisms may be represented by a

rotational spring. If this rotational spring stiffness is ki the coefficient ti is approximately given by:

a =

where

AQ Shear area of leg, see Ch.4.5

d Distance between upper and lower guides

1

+ d G AQ

(4-6)

Fig. 9. The spring coefficient Kj.

For illustration it is shown in Fig. 9 how the rota-tional spring stiffness may be determined for a sim-plified two-dimensional structure. .

In the case of resilient mounted jacking mecha-nisms it should be noticed that only compressive

forces can be transferred through the shock pads. 4.4 Leg bottom interaction

There are basically two different foundation concepts for jack-ups:

The mat foundation with large dimensions to

which all legs are connected. The mat is designed

to prevent excessive penetration where the sea

11

bottom consists of soft clay.

Separate legs with or without special footings

(spud-cans).

Only the second concept requires special consid-eration in this connection.

The large diameter of many spud tank designs

implies that the sea bed may provide a considerable degree of rotational restraint for the legs.

For the global response analysis, the sea bed may be represented by a rotational spring. In lieu of more accurate analysis the rotational spring stiffness may be taken as (3), (5):

80r02

3(1-1,)

where

Shear modulus of soil Poisson's ratio of soil Radius of spud-can

The expression for ksgiven above is only valid if

the penetration is sufficient, and not if the jack-up is

standing on the tips of the spud cans, on a very hard bottom.

4.5 Leg stiffness

The leg stiffness has to be determined for the global response analysis. In particular the leg stiffness is

es-sential for the calculation of second order bending

effects and dynamic structural response.

The stiffness of a cylindrical jack-up leg is

char-acterized by the beam properties. A Cross section area

AQ

-- Shear area

I Moment of inertia

Torsional moment of inertia

The stiffness of a lattice leg may be determined

either from a direct analysis of the complete structure by use of an appropriate computer program, or from a simplified analysis of an equivalent cylindrical leg. The key parameter for the evaluation of the equi-valent cylindrical leg is the «equiequi-valent shear area» of a two-dimensional lattice structure, see Fig. 10.

Stiffness parameters for legs with three

or four

chords, are given in Fig. 11. An important feature of such legs is that the stiffness is the same for all

direc-tions. However, this is not the case for legs with

racks on only two of the chords.

In practical cases it may be difficult to represent the complete leg by one beam element. This is be-cause the stiffness normally varies over the length.

The stiffness is closely related to the steel weight, and a typical steel weight distribution of a jack-up leg is shown in Fig. 12.

The overall stiffness or flexibility of jack-up legs

IT

(4-7)

'Norwegian Maritime Research No: 4/1982

(11)

Fig. 10. Equivalent shear area for two-dimensional lattice staructures.

12

Equivalent shear area

(1 + v)sh2

AD A

AQ 7--: d3 s3 2

x

+ 3 Ac

:

(1 + v)sh2

A _

A

IIPF;RIP

h Q d3 . h3 S3 + AD

8 Av + 12 Ac

s

+osh2

ce

A

AQ = d3 s3 4 AD . 12 Ac

....77..

A0.

( 1 + v ) s h2

ADv

1,1,11

d3 h3 S3

2 AD + 2A

4. 12 Ac V. . 1G h AQ =

48(1 + v)Ic, (d)

C

S2 (I +

--I

I

Q) "li

S g ,

(12)

Fig. 11. Equivalent section properties of three-dimensional lattice legs.

13

No. 4/1982

/

A = 3 Aci

3 A

A0y = AQ, =

1- cli

1y = 1 z = 2-Aci1 h2ri IT =

i

AQi h2

\

AQi

\

III

ilk ci

A = 4 Aci

Aciy = AQz = 2 AQj

= I, = Aci h2

IT = AQI h2 , , A Qj I 46....- y I I VT ft

0 Aci

AQj

,

A = 4 Aci

AQy = AQ2 = 2 AQj

ly = Iz = ACi h2 IT = AQj h2

\\

_\

\

_\

\

/3

\

0 /

/

(13)

so depends on the boundary conditions. A

simplif-ied model which accounts for the most important

effects is shown in Fig. 13. This model is subjected to a transverse load, P. The corresponding shear force and bending moment distributions are shown in the figure. The transverse overall stiffness is given by:

0 2 t 6

TONS/METER

8

Fig. 12. Typical steel weight distribution ofa leg.

Fig. 13. Leg stiffness model.

where 1 k fB fQ fB _{Bending flexibility} fQ Shear flexibility

No. 4/1982 where 13

_[1

3 P i d

fB=

3E1 2

1+ P

1+ ti/

=G1

r

a I Q GAQ L

1+ p 'cl

where a /kJ:4i A00 i = I

fl(1

3 -111-÷ -10)2)]

AQ0 I0, Average shear area and moment of

inertia of the portion of the leg located

between upper and lower guides AQ' I Average shear area and momeng of

inertia of the portion of the leg which is

below the lower guides

Coefficient which determines the

fraction of the leg bending moment

which is reacted by vertical forces Coefficient which determines the leg bending moment at the bottom

The coefficients jI. and ii may be directly estimat-ed basestimat-ed on previous experience, or determinestimat-ed from:

1 = 1 + G A00 Wk.,

2. d

2 aEI

I +

T'7 + / d G A0

P =

_{2 E I} I + _ks/

kj Rotational spring stiffness of the jacking

mechanisms, see Ch. 4.3.

k s _{Rotational spring stiffness at the bottom,}

see Ch. 4.4

Alternatively the overall transverse stiffness may be expressed by:

k =

3E1

CP

The Euler load of one leg is given by: 7[2E1

Pp=

_{(K 02}

(4-11)

(4-12)

(4-8b)

(4-8)

C

1 3i ÷

3 E I 11+ a 2 1

+p

1 + p

12GAQ\

(4-13)

where K is an effective length factor which may be With reference to Fig. 13 fB and fQmay be taken as: taken as:

14

(4-9)

(14)

4.6 Dynamic characteristics

Amplification of stresses due to dynamic structural response does normally not represent a serious pro-blem for extreme loading conditions. This is because the frequency of the extreme waves is normally much lower than the lowest natural frequencies. However,

the effect of dynamic amplification may be

signi-ficant for the evaluation of fatigue strength, because the frequently occurring waves may have frequencies

corresponding to the lowest natural frequencies of

the structure.

-It is well established that dynamic effects of struc-tures like jack-up platforms may be closely approx-imated by multiplying the static response by the dy-namic amplification factor, DAF, for a single degree of freedom system:

DAF

where

To Natural period

T Period of variable load (Wave period) Damping ratio

For the elevated condition it is normally found

that the three lowest natural frequencies correspond to the following motions:

Longitudinal displacement (surge) Transverse displacement (sway) Torsional rotation (yaw)

For the transit condition the lowest natural fre-quencies correspond to bending deflection of each

individual leg.

The natural period is the inverse value of the na-tural frequency:

To = f1 = 2 ir me

ke

where

f

Natural frequency

ke Effective stiffness of one leg

m Effective mass related to one leg

The effective stiffness depends on several

par-ameters which may be difficult to define: Leg stiffness Leg/hull interaction Leg/bottom interaction

_( TT0)2)2

(

TT0 ke k r E

(4-16)

(4-17)

15

k Transverse overall stiffness as defined in

Ch. 4.5

P Axial force in one leg due to the functional loads

PE Euler load as defined in Ch. 4.5.

For the transit condition the effective stiffness

may be taken as:

ke = k

(4-17b)

where k is the transverse overall stiffness determined

with A = 0, and b equal to the distance between

upper guides and the centre of the jacking

mecha-nisms.

The effective mass for the elevated condition may be taken as: me Cl MH ± C2 ML

(4-18)

where Cl for mode 3

= 0,5

0.125 p Number of legs

Distance from the hull's centre of gravity to the centre of the legs

NI

Radius of gyration of the mass

,

with

respect to the vertical axis through the

centre of gravity

p Bottom restaint parameter, see Ch. 4.5.

Because rois normally smaller than r, the natural

frequency corresponding to mode 3

is normally higher than the natural frequency corresponding to

modes 1 and 2.

If the mass of the leg is uniformly distributed, the effective mass for the transit condition may be taken as (3):

ML Mass of the portion of one leg located

above the upper guides.

No. 4/1982

K

= 2 VT

(4-14)

where

For the elevated condition the effective stiffness m = 0,24 ML

(4-19)

may be taken as: _where

MH Total mass of the hull with all equipment

and the portions of the legs located

above the lower guides

ML Mass of the portion of one leg located

be-tween the lower guides and the top of

the spud cans (Added mass included)

for modes 1 and 2

(15)

The damping ratio,

t

, to be used in the evalua-tion of DAF is the modal damping ratio. This is a

quantity which depends on a number of variables. By definition:

C C

cCr 2 IV-1-11c

where m, c and k are coefficients of mass, damping and spring in the equivalent one-degree-of-freedom system.

It should be observed that increases with dec-reasing stiffness. This is

important because the

stiffness of jack-up platforms may be an order of magnitue less than the stiffness of a corresponding

jacket.

The total damping coefficient c includes structural damping, hydrodynamic damping and soil damping. All of these contributions are difficult to determine, and none of them should be neglected.

The structural damping includes damping in gui-des, shock pads, locking devices and jacking me-chanisms which means that the structural damp-ing is design dependent.

The soil damping depends on spud can design

and bottom conditions which means that the soil

damping will be design dependent and site

de-pendent

The hydrodynamic damping depends on

leg

structure, drag coefficient and relative water par-ticle velocity. This means that the hydrodynamic damping is not only design dependent, but it also depends on sea conditions and marine growth. It is thus obvious that it is very difficult to select a

representative total damping ratio. Measurements

and numerical simulations have indicated the follow-ing magnitudes:

(4-20)

As described in Ch.4.1 it may be necessary to

in-vestigate a range of wave periods in order to deter-mine the extreme response. If this range comprises the natural period of the platform, the simple

de-terministic approach where dynamic effects are taken into account by the DAF, may be unreasonably con-servative. This is essentially due to the shape of the

transfer function which is characterized by a sharp

peak at the natural period. This peak is narrow

compared to the width of a realistic wave energy spectrum. Only a fraction of the wave energy will then correspond to this peak. In a determinstic

ap-proach the total wave energy is concentrated at one specific wave period, and if this period is taken equal to the natural period, the response will be very severe (resonance).

16

The value of the dynamic amplification factor at

resonance is governed by the damping ratio, t : (DAF)R = 1

t

(4-21)

In order to account for the effect of irregular sea, a «stochastic dynamic amplification factor» is

defined: SDAF

2 t ST

1

where t

_STis an apparent damping ratio.

In this connection it may be assumed that the

transfer function around resonance may be written

as:

TR = C DAF

.

(4-22)

where C is the static response. Consequently:

j C2 DAP S (w) th.4.)

SDAP

(4-23)

J C2 (o.)) d

where S (w) is the wave energy spectrum.

A parametric study based on the

Pierson-Mosko-witz wave spectrum showed that the SDAF has a

maximum when the peak of the wave spectrum is

approximately equal to the natural period. The

SDAF was found to be rather insensitive to varia-tions in the natural period for the range 5-10

sec-onds. The following approximate relation was

ob-tained:

t ST = 0.75 0.65

(4-24)

For the most interesting range this expression may be simplified as:

t ST

2 t

(4-25)

This result is exclusive of the effect of shortcres-tedness, see Ch. 2.2.

4.7 Bottom impact on legs

In the installation and retrieval conditions, a leg may be subjected to an impact force from the sea bottom, due to the jack-up's motions in waves, see Fig. 14.

The impact force due to a roll or pitch motion may be calculated by use of a simplified method based on the following conservative assumptions:

Only one leg touches the bottom

The lower end of the leg is stopped immediately when the leg touches the bottom

The bottom is infinitely rigid

The rotational energy of the jack-up must then be absorbed by the leg, and the impact force is given by: Structural damping:

1-3%

Soil damping:

0-2%

.

Hydrodynamic damping:

3-5%

Total damping:

4-10%

(16)

where

Fig. 14. Bottom impact on legs.

k Overall transverse stiffness

4.5

Im Mass moment of inertia

with respect to roll or pitch T Period of roll or pitch

Amplitude of roll or pitch

(4-26)

of the leg, Ch.

of the jack-up

motion

4.8 Local response of legs

The distribution of shear forces and bending

mo-ments over the length of the legs is obtained from the global response analysis. In addition it is necessary to

calculate the local distribution of stresses over the cross section, and in particular in areas where large

forces are introduced.

The stress distribution in tubular legs may be de-termined from simple beam theory, combined with stress concentration factors when appropriate. For

local areas where large forces, such as reactions from guides or jacking mechanisms are introduced, it may be necessary to resort to finite element analysis.

The local distribution of forces and bending

mo-ments in lattice legs is usually determined from com-puter analysis of a space frame model. Eccentricity of

members in joints has to be accounted for. Peak

stresses (hot spot stresses) in the joints are only need-ed for the fatigue analysis. For approximate analysis some simple relations are given in (6).

The introduction of guide reactions in lattice legs has to be considered in detail. Two aspects should be considered:

17

Bending of the chord member due to a

con-centrated load

Local deformation of the chord wall which is in contact with the guide

The bending action of the chord member may

nor-mally be analysed by use of simple methods. How-ever, the analysis of the chord wall may require so-phisticated computer simulations, considering the

interaction between guide and chord wall.

The introduction of jacking mechanism reactions has to be considered in detail. In cases where only a

one-sided rack is used, see Fig. 15, the horizontal

component of the reaction has to be transmitted

through the chord and bracing structure into the rack on the opposite chord. Since the horizontal reaction component may be very large, high bending stresses

in the chords and high compressive stresses in the

bracing will occur.

-In cases where opposed racks are used, see Fig. 15

Fig. 15. Jacking mechanism reactions.

the horizontal components are readily taken by

compression of the individual racks, involving no

bending of the chords or compression of the bracing.

For the analysis of a portion of a lattice, leg, it is

normally allowable to neglect the effect of loads

dis-tributed over the length of the individual members,

(6).

5. STATIC STRENGTH ANALYSIS 5.1 Strength criteria

In the static strength analysis the following modes of failure are to be considered:

Excessive yielding Buckling

Brittle fracture

(17)

The possibility for excessive yielding has to be. considered for most structural members. The yield

check may be omitted only if it is obvious that other criteria will be governing.

In general it is recommended that the yield analysis

is based on nominal stresses derived from elastic theory. This principle has two important

implica-tions:

Local yielding due to a stress concentration may be accepted. The effect of stress concentrations is only considered in the fatigue analysis.

Full advantage is not always taken of the real

load carrying capacity. However, it is allowable according to (1) to use ultimate strength analysis in special cases.

The possibility for buckling has to be considered'

for all slender structural members. When buckling is

a governing mode of failure, it is essential that

ge-ometric imperfections are kept within specifed limits. The possibility for brittle fracture is considered in connection with the selection of grade of material to

be used, and is therefore normally not treated as an

explicit design criterion. 5.2 Global strength

of

legs

A jack-up leg is designed for the combined action of axial load and bending moment. The failure criterion

is:

a

cr

1,0 (5-1)

where

aa Axial stress due to design loading

a

b Bending stress due to design loading

a_bo Bending stress due to a bending moment Mo = P eo

aCr Critical stress as defined in Ch. 5.3.

PE Euler load as defined in Ch.4.5

P Average axial leg load due to functional loads

Maximum horizontal offset of the

plat-form, including initial out-of-straightness of legs and inclinations as

shown in Fig. 16. (Design specifica-tion).

5.3 Local strength

of

legs

The local strength of legs may be evaluated using the

general strength criteria referred to in Ch. 5.1. The

governing criterion will always depend on the actual design.

Tubular legs are designed as stiffened plate or shell structures. The critical stress, oa., referred to in Ch.

5.2 is the value of the axial stress at which local

fai-lure will occur. Such legs are normally proportioned

and stiffened in such a way that local buckling of

18

eo -Horizontal offset

e, -Out- of -straightness

e, -Hull leg clearances e, -Heel of platform

Fig. 16. Horizontal offset

of

platform.

plates and stiffeners is excluded. The critical stress

will then be determined by the yield criterion as:

acr = (5-2)

where axand aeare the actual values of the axial

stress component and the von Mises equivalent

stress, respectively.

However, it will always be neccessary to verify that local buckling is not possible.

The local strength of lattice legs depends on:

Strength of individual members considered as

bars.

Strength of joints.

Local strength of members subjected to

reac-tions from guides and jacking mechanisms. The critical stress, a cr, referred to in Ch. 5.2 is

equal to the critical axial stress of the chord,

consid-ered as a column or a beam-column. The effective

length factor for chord members should never be ta-ken less than:

K = 1,0 (5-3)

In most cases it is found that the column slender-ness of chord members is so low that buckling is ex-cluded. The critical stress may then be taken as:

acr aF ab

(5-4)

where a b is the axial stress due to local bending of

the chord.

The strength of bracing members may be evaluated

(18)

using the general buckling criteria for

beam-co-lumns. The effective length factor for bracing mem-bers may be taken as:

EXAMPLE:

1

GA = 1,0

>1.(.--.0 7 GB=0,3

Fig. 17. Evaluation of the effective length factor, K. However, a more accurate value may be obtained by use of the diagram shown in Fig. 17. Having de-termined GA and GBfor end A and end B of the

brac-ing member under consideration, K is obtained by

constructing a straight line between the appropriate

points on the scales for GA and GB . The general

definition of GA and GB is given in (7) and (8).

However, for in-plane buckling of horizontal and

diagonal bracing members in a jack-up leg, see Fig. 18 the following values are found:

= 1,0

G= 15 (.R...1) (,)

[1.

R

3

where

1 - Length of bracing member

r - Radius of bracing member

t - Wall thickness of bracing member

R - Radius of chord member

T - Wall thickness of chord member

Design recommendations and strength criteria for simple tubular joints may be found in (6) and (9).

19

Fig. 18. Buckling of bracing members. 6. FATIGUE ANALYSIS

6.1. Design considerations

Fatigue has not been considered as a very important problem for jack-up platforms. The reason for this is that most units in the past have been used in sheltered

and calm areas with shallow water and that the

members. subjected to high dynamic loads are not the

same from location to location. Compared to fixed platforms, jack-up platforms also have the

advant-age that members subjected to fatigue damadvant-age may be regularly inspected and repaired.

For different reasons fatigue may be found to be

more important for future designs, and this has to be considered at the design stage:

Jack-up platforms are used in areas with more

severe sea conditions. This means that the wave

loads which are most important in connection

with fatigue, become more dominanting.

Jack-up platforms are used in areas with

dee-per water. This may lead to more flexible

struc-tures which means that the dynamic amplification of stresses will increase.

In order to meet the requirements for more

severe sea states and deeper water, the strength of the legs must be increased. Due to different

con-siderations regarding the transit condition, it is

essential that the leg weight is minimized. This

leads to the use of high strength steels. The design allowable stresses then increase, and the possibil-ity for fatigue failure increases.

Jack-up platforms may be used as fixed

plat-forms for longer periods. The special advantages of a mobile unit may then be lost.

6.2 Stochastic fatigue analysis

In fatigue analysis it is the stress range that is needed, and not the total stress. This means that the effect of wind and current in many cases may be disregarded

without introducing large errors. The linear

sto-chastic method, see Ch. 4.1, is then a very relevant

Norwegian Maritime Research No. 4/1982 K 0,8

(5-5)

GA cs, .0 50.0 t, 10.0-i - 1.0 50.0 10.0 5.0- 5.0 4.0 3.0 - 0.9 3.0 2.0- 2.0 --- 0.8 1.0 1.0 0.8 - 0.8 0.7 - 0.7 0.6 -0.5 7 0.7 0.6 as 0.4 - 0.4 0.3 - 0.3 0.2 - --- 0.6 02 0.1 0.1 o -0.5 0

(5-6)

-

0,01](1,5 r/R - 2.35)

(19)

method.

Rather than using discrete waves, the various sea states may be described by wave spectra, and all fre-quency components in the sea state are represented. The long term distribution of waves may be described

by a set of wave spectra, with varying significant wave height, period and probability of occurrence.

By combining these spectra with the transfer function for member end stresses, which may have been

cal-culated considering dynamic behaviour of the plat-form, the probability distribution of stress

fluctua-tions for each sea state is obtained. The total fatigue

damage is thereafter arrived at by summing up the

contribution from each sea state, taking into account their probability of occurrence.

Due to the non-linearity of drag forces, the

dy-namic effect of current may in some cases be signi-ficant. In such cases the linear stochastic method of analysis should be modified. One possible method is to increase the wave loads by use of a modification factor as indicated in Appendix A.

6.3 Simplified fatigue evaluation

Considering the idealized expressions for fatigue damage and fatigue life given in Appendix B, it is

obvious that the accuracy of a fatigue analysis is

ex-tremely sensitive to errors in the estimation of the

long term stress distribution, see also (10).

Investigations have shown that even larger

un-certainties are associated with the derivation and se-lection of S-N curve for each particular case, (11).

On this background it is obvious that even the

most sophisticated fatigue analyses will be associated with considerable uncertainties. If one or more of the significant parameters are given only by approximate

values, a simplified fatigue analysis based on con-servative assumptions may be the most reasonable

approach.

A simplified fatigue evaluation is based on the

idealized equations given in Appendix B.For practical use the following parameters are needed:

The stress range A a 0 with return period equal

to 20 years, or the corresponding stress amplitude

amp .= 6 a 0/2).

The weibull parameter (h) which is associated

with the shape of the long term distribution. The stress range ( A a 0) refers to hot spot stresses,

which means that the corresponding nominal stress range has to be multiplied by an appropriate stress

concentration factor.

The nominal stress range may normally be

deter-mined from the response analysis required for the extreme load analysis. In addition it is necessary to

distinguish between the static part and the cyclic

part of the stresses. In this connection the interaction between wave and current loads must be considered, see Ch. 3.3.

The hot spot stress range is then obtained by use of an appropriate stress concentration factor, see (6).

No. 4/1982

20

The Weibull parameter (h) determines the shape of the long term distribution as shown in Fig. 19.

Hma.

a =

Hma. + a1/a2

(6-2)

The dynamic amplification factor is defined in Ch.

4.6. By use of the average relation between wave

height and wave period, given in (2-1), it is possible to determine the shape of the long term distribution. The result of a number of computations is shown in Fig. 20. The parameter h is given as a function of lo-ad combination, a, and natural period, To. The total damping ratio was assumed to be 8 percent, but the results were not very sensitive to variations between 5

and 10 percent. In many cases the calculated long

term distributions could not be fitted by any Weibull

-8 -7

6

-5 -3 -2 -1

'a Q Fig. 19. Long term stress distributions described by

Weilbull distributions.

It may often be assumed that the long term dis-tribution of wave heights can be represented by a

Weibull distribution with h = 1,0, see Ch. 2.2. In accordance with the previously described load and response analyses, it is assumed that the dynamic stress is related to the wave height like:

a = (a1 H + a2H2) . DAF

(6-1)

where

-Wave height

DAF Dynamic amplification factor al, a2 Stress coefficients

The first term in this equation represents that

por-tion of the dynamic stress which is proporpor-tional to

the wave height (inertia forces and drag forces result-ing from the wave/current interaction).

The second term in this equation represents that

portion of the dynamic stress which is proportional to the square of wave height (drag forces).

The ratio between the wave drag force induced

stress and the total dynamic stress at maximum wave height is defined by:

(20)

distribution. In such cases h defines the Weibull

dis-tribution which would lead to the same fatigue da-mage prediction in combination with a typical S-N curve with k = 3.

Similar curves have recently been shown in (12).

An evaluation of sensitivity with respect to natural

period and dampind may be found in (13).

1.4 1.2 0.8 0.6 0.4 0.2 0 0 0.1 0.2 0.3 To/TmAx

Fig. 20. The Weibull parameter h. 7. OTHER DESIGN CRITERIA 7.1 Overturning stability analysis

A jack-up in an elevated condition is exposed to en-vironmental loads (wind, waves and current) which

contribute to a resulting overturning moment, Mo The functional loads (gravity loads) contribute to a

resulting

stabilizing moment, M. Safety against

overturning requires that:

The stabilizing moment is greater than the over-turning moment.

The foundation (sea bed) is stable.

The operating condition is characterized by such a

distribution of functional loads that the stabilizing

moment is as large as possible.

When the ,environmental loads increase to a certain level, it is necessary to change mode, from the

operat-ing condition to the survival condition. The change

of mode may involve extensive and time consuming

operations. It is therefore essential that the criteria and the procedures for change of mode are clearly

stated.

The stabilizing moment due to functional loads is

ealculated with respect to the assumed axis of

rota-tion.

21.

For jack-ups with separate footings (spud cans)

the axis of rotation is assumed to be a horizontal axis

intersecting the axes of two of the legs. It is further

assumed that the vertical position of the axis of rota-tion is at the bottom of the footing.

Any possible stabilizing effect of non-uniform soil reaction on separate leg footings is normally neglect-ed in the overturning stability analysis.

The overturning moment due to wind, waves and current is calculated with respect to the assumed axis of rotation.

The calculation of overturning moment should ac-count for the following effects:

Dynamic amplification of the combined wave/

current load effect.

Amplification of the total moment due to

sec-ond order leg bending effects.

If the calculation is based on a linear static

res-ponse analysis, these effects may be approximately accounted for by use of amplification factors applied as follows:

(7-1)

e P + MWD Mm

. CWm MCWa MO =7. 1 P / PE where

DAF Dynamic amplification factor

Average axial leg load due to

func-tional loads

Euler load of one leg

Overturning moment due to wind

Mean value of overturning moment due to the combined effect of waves

and current

MCWa Amplitude of overturning moment due to the combined effect of waves and current

eo

Maximum horizontal offset of the

platform, see Fig. 16.

Number of legs 7.2 Foundation stability

Problems concerning the foundation stability are

re-lated to design of legs and leg footings or mat, and

soil conditions.

Legs with separate footings (spud cans) may

pe-netrate the sea bed to a considerable depth. However, deep penetration in itself represents no hazard. The

risk is the possibility for a sudden and unexpected

penetration. The design philosophy is that the

foot-ings shall be preloaded to the same vertical load as the maximum combined effect of functional loads

and extreme environmental loads.

During preloading, a sudden penetration of one

leg may lead to excessive tilt and damage to legs

and jacking mechanisms. The presence of sand

layers or crusts over soft clays is considered res-ponsible for such accidents.

During extreme storm conditions, the

founda-Norwegian Maritime Research

No. 4/1982 0.0

.0010

illill1111111111111114r r

0.8 10 TOTAL DAMPING : 8% T MAX=1.0+4.1 Hitx 0,4 0.5 06 PE' MWD Mrvm

(21)

tion will have to react both vertical and horizontal loads. The bearing capacity of soil under

combin-ed horizontal and vertical loading may be signi-ficantly smaller than in the case of pure vertical loading as simulated by the preloading. Uncer-tainties regarding the bearing capacity are also

due to dynamic loading being responsible for

rocking of the footings, associated with

non-uniform soil reaction.

A mat foundation will normally have a very small

penetration even in a soft clay. In stiff clays and

sand, the unevenness of the sea bed may lead to non-uniform distribution of soil reaction, and the contact with the sea bed may be limited. In an extreme case,

this may lead to rocking of the mat under dynamic

loading.

For mat foundations, there are in principle two fai-lure modes:

Sliding of the mat over the surface of the sea bed or along a shallow failure surface directly under the skirts due to horizontal forces.

Overturning due to insufficient bearing

capac-ity under the most stressed edge of the mat caused

by horizontal forces and overturning moment

combined with the weight of the jack-up and the wave pressure on the sea bed.

The effect of repeated loading on sands and clays may be significant and lead to a strength reduction of

order 30-40% for clay and even more for loose

sand, (14).

7.3 Air gap

The air gap is defined as the clear distance between

the hull structure and the maximum wave crest

el-evation. According to (1) the air gap is not to be less than 10 per cent of the combined astronimical tide, storm surge and wave crest elevation above the mean water level (MWL), see Ch. 2.5. However, the air gap is not required to be greater than 1,2 m.

For deep water locations the air gap requirement is

vital for the evaluation of the jack-up's suitability.

In this connection it is very important that the leg pe-netrations are predictable, (15).

7.4 Accidental loads

In the safety evaluation of a platform concept, ac-cidental loads are to identified and taken into

con-sideration. In general such considerations lead to re-commendation of structures of a certain robustness

or ductility. This may be in contrast to a general

preferance for weight optimized structures.

It has been established that the most important

accidental load for a jack-up platform is the impact

from a ship collision. Such an impact load is most

likely to cause local damage to one of the legs only, but the possibility for progressive collapse and over-turning should also be considered.

The overall transverse stiffness of a jack-up plat-form is rather small, normally an order of magnitude

No. 4/1982

22

smaller than the stiffness of a corresponding jacket

structure.

Because a ship collision is a hypothetical event, it is allowable to use very simplified methods of analysis: A simple two-degree-of-freedom system is consider-ed appropriate, see Fig. 21.

Fig. 21. Model for impact analysis.

Under the assumption that kJ_ > > kG it is found that the maximum interaction force between ship and platform is:

mski. ( 5S 5 P) = v

₁₁

+ m /m

P

(7-2)

S

The maximum global load effect is:

PG = kG Sp v where 1 kL mskG

m /M

_P _S

(7-3)

Uks + l/kp

ks Stiffness of ship

kp Local stiffness of platform leg

kG Overall transverse stiffness of platform mp Mass of platform

ms Mass of ship

v Ship velocity before collision

The values kG and mp should be evaluated with

due consideration of ship/platform configuration. The value of Pi, will in the first place be decisive for the extent of local damage, while PG will be deci-sive for the risk of overturning.

7.5 Damage condition

For a jack-up leg of sufficient robustness a credible accidental load as described in Ch. 7.4 will not lead to any significant damage. However, for very slender lattice legs it may be found that one chord element is damage and made inefficient. According to (1) a