Response of fixed offshore platforms to wave and current loading

including soil–structure interaction

Yasser E. Mostafaa, M. Hesham El Naggarb,*

aGeotechnical Engineer, Golder Associates, Burmnaby, B.C., CanadabAssociate Professor and Research Director, Geotechnical Research Centre, Faculty of Engineering,

The University of Western Ontario, London, Ontario, Canada N6A 5B9

Accepted 17 November 2003

Abstract

Fixed offshore platforms supported by pile foundations are required to resist dynamic lateral loading due to wave forces. The response of a

jacket offshore tower is affected by the flexibility and nonlinear behaviour of the supporting piles. For offshore towers supported by clusters

of piles, the response to environmental loads is strongly affected by the pile–soil–pile interaction. In the present study, the response of fixed

offshore platforms supported by clusters of piles is investigated. The soil resistance to the pile movement is modelled using dynamic p–y

curves and t –z curves to account for soil nonlinearity and energy dissipation through radiation damping. The load transfer curves for a single

pile have been modified to account for the group effect. The wave forces on the tower members and the tower response are calculated in the

time domain using a finite element package (ASAS). Several parameters affecting the dynamic characteristics of the platform and the

platform response have been investigated.

q 2004 Elsevier Ltd. All rights reserved.

1. Introduction

Foundation piles have a significant effect on the response

of fixed offshore structures. Bea [1] performed a series of

static push-over analyses on a fixed offshore platform and

found that the first nine nonlinear events were concentrated

in the foundation piles. Mitwally and Novak [2] used a

linear analysis to account for the effect of foundation

flexibility including pile–soil–pile interaction on the

response of offshore structures to random wave loading.

El Naggar and Novak [3] considered foundation nonlinear-

ity using an equivalent linear approach. This paper describes

an efficient approach to model the response of pile groups

supporting a jacket structure to transient loading. The

method employs the concepts of dynamic p–y curves and

dynamic p-multipliers, t –z curves and q–z curves to model

the soil reactions to pile movement. Mostafa and El Naggar

[4] have established dynamic p-multipliers to relate the

dynamic load transfer curves of a pile in a group to the

dynamic load transfer curves for a single pile. The dynamic

p-multipliers were found to vary with the spacing between

piles, soil type, peak amplitude of loading and the

angle between the line connecting any two piles and

the direction of loading [4]. Several parameters such as the

foundation flexibility, dynamic soil resistance, pile–soil–

pile interaction, soil stiffness, and platform deck mass that

affect the dynamic characteristics of the platform and the

platform response to wave and current loading have been

investigated.

2. Platform description

The platform considered in this study is the ‘Kvitebjørn’

platform shown in Fig. 1. It is currently under construction

in the Norwegian section of the North Sea. Water depth at

the site is 190 m and the substructure is a piled steel jacket.

The Kvitebjørn substructure has four legs supported by

vertical steel piles grouped symmetrically around each

corner leg. Due to weight limitations for the offshore lift, the

jacket is fabricated, towed to the site and lift-installed as two

separate structural units. The upper part of the structure is

connected to the lower part through a traditional grouted

0267-7261/$ - see front matter q 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.soildyn.2003.11.008

Soil Dynamics and Earthquake Engineering 24 (2004) 357–368

www.elsevier.com/locate/soildyn

* Corresponding author. Tel.: þ1-519-661-4219; fax: þ1-519-661-.

E-mail addresses: naggar@uwo.ca (M.H. El Naggar); ymostafa@uwo.

ca (Y.E. Mostafa).

connection and extends to approximately 25 m above the

mean sea level (MSL). The jacket’s lower part is

approximately 45 m high and is connected to the pile

foundation. The structure is levelled using four levelling

piles and is permanently fixed on sixteen piles driven to

about 90 m penetration depth.

The weights of the upper and lower parts of the structure

are approximately 73,000 and 45,000 kN, respectively. The

total weight of the foundation is 53,000 kN and the total

weight of the platform is 171,200 kN. The structure is

designed to support a maximum operating topside weight of

225,000 kN. The lower part is square shaped with base

dimensions 50 m £ 50 m, is approximately 45 m high and

has vertical corner legs. The top part extends from

approximately El. 2145 to El. þ8 m and has a constant

batter on all sides with square dimensions at the bottom of

50 m £ 50 m to square dimensions at the top of

25 m £ 25 m. The jacket is flared on two sides to meet the

interface dimension of 22.5 m £ 30 m towards the topside at

El. 21.2 m. These dimensions are held constant from El.

21.2 m to the topside interface elevation of 24.1 m. All

elevations are relative to MSL. The jacket is supported on

16 piles with a diameter of 2.438 m arranged in symmetrical

groups of four piles per corner leg. Each corner leg has an

additional pile with a diameter of 1.372 m to be used for

levelling.

3. Environmental data

The environmental data are based on STATOIL specifica-

tions ‘Metocean Design Criteria for Kvitebjørn’ and are

provided by Aker Engineering AS [5,6]. The maximum

directional wave heights for the 100-year return period are

given in Table 1, including the mean wave period along with

the 90% interval. The current associated with the 100-year

return period design wave height is given in Table 2. No

associated wind has been specified. The thickness of marine

Fig. 1. Three-dimensional view of the platform.

Table 1

Design waves versus return period

Return period

(year)

Wave height

(m)

Height above

MSL (m)

Wave period (s)

Mean value 90% interval

1 22.0 12.8 13.8 12.2–15.5

10 25.3 14.2 14.6 13.0–16.4

100 28.5 16.1 15.3 13.6–17.1

10,000 36.0 20.4 17.1 15.1–19.1

Table 2

Values for associated current

Depth below sea-level (m) Current speed (cm/s)

0 50

25 50

50 50

75 46

100 42

125 39

150 36

175 32

190 29

Y.E. Mostafa, M.H. El Naggar / Soil Dynamics and Earthquake Engineering 24 (2004) 357–368358

growth is considered to be 20 mm below El. þ2 m. The

roughness due to marine growth is taken into consideration

when determining the coefficients in Morison’s equation for

wave forces. The average dry density of the marine growth

material is considered to be 1300 kg/m3. Morison’s equation

[7] is used together with the API wave force guidelines [8] to

generate the hydrodynamic forces. Drag and inertia coeffi-

cients are assumed to be 0.7 and 2.0, respectively, and the

wave kinematics are calculated using the Stokes fifth-order

wave theory.

Table 3

General soil layering

Soil unit Depth (m) Soil description

A 0–7.5 Very soft to soft silty, sandy clay

B 7.5–32 Sandy, clayey silt

C 32–47 Very stiff to hard silty clay

D 47–52 Very dense fine sand

E 52–125.5 Very stiff to hard clay

F .125.5 Very hard clay

Fig. 2. (a) Plan showing the pile arrangement in platform leg A-1. (b) Cross-section of the main piles and levelling piles.

Y.E. Mostafa, M.H. El Naggar / Soil Dynamics and Earthquake Engineering 24 (2004) 357–368 359

4. Geotechnical information

4.1. Soil profile

The soil profile at the tower site consists of a layer of very

soft to soft silty clay 7.5 m thick underlain by a layer of

sandy, clayey silt that extends to a depth of 32 m below the

seabed level. This layer is underlain by a number of layers

of very stiff to hard clay that extend to the end of the

borehole at a level of 85 m below the seabed level. The

foundation design is based on the soil data shown in Table 3

[6]. The results from the cone penetration tests (CPTs) show

that a thin sand layer exists at the surface of the seabed in

some of the borings. Therefore, local scour of 0.5 m is

adopted. No global scour is included in the design. The basis

for the assumption is the water depth at the Kvitebjørn

jacket location [5,6].

4.2. Foundation design

The jacket is supported on 16 main piles arranged in

symmetrical groups of four piles per corner leg. The pile

diameter ðdÞ is 2.438 m and its penetration depth is about

85 m. The pile spacing ðSÞ centre to centre is 8.4 m (i.e.

S=d ¼ 3:44). Four levelling piles also support the jacket, one

in each corner leg. The levelling piles have a diameter of

1.372 m and a penetration depth of about 49 m. The piles in

each group are fixed to a rigid cap. Fig. 2a shows a plan of

the piles arrangement and Fig. 2b shows longitudinal

sections for the main piles and the levelling piles illustrating

the variation of the piles’ thicknesses along their length.

5. Modelling soil reactions

The soil resistance to the pile movement is modelled

using p–y curves and t –z curves for lateral and axial

loading, respectively.

5.1. p–y curves for a single pile

The soil response to lateral loading is nonlinear. To

model this nonlinearity, pile deformation can be related to

soil resistance through nonlinear transfer curves (p–y

curves). Static p–y curves for a single pile can be

established using the API guidelines [8].

Fig. 3. (a) Static and dynamic p–y curves, (b) dynamic p-multipliers, (c) p–y curves for a single pile and a pile in a group and (d) t –z curves for single pile and a

pile in a group.

Y.E. Mostafa, M.H. El Naggar / Soil Dynamics and Earthquake Engineering 24 (2004) 357–368360

The dynamic p–y curves for a single isolated pile are

calculated using the equation proposed by El Naggar and

Bentley [9] as

Pd ¼Psa

yþ i

Ps ba20 þ ka0

vy

d

� �n� �

y

0BB@

1CCAy ð1Þ

where Pd is the dynamic soil reaction at depth x (N/m), Ps is

the static soil reaction obtained from the static p–y curve at

depth x (N/m), a0 is the dimensionless frequency ¼ vd=Vs;

v is the frequency of loading (rad/s), d is the pile diameter

(m), y is the lateral pile deflection at depth x (m), and a

(a ¼ 1 in this analysis), b; k; and n are constants that

depend on the soil type [9]. Fig. 3a shows typical static and

dynamic p–y curves. The dynamic soil resistance is

modelled using a series of springs and dashpots whose

nonlinear stiffness and nonlinear damping constants are

established using Eq. (1), and are given by

knl ¼Psa

yand cnl ¼

Ps ba20 þka0

vy

d

� �n� �

vyð2Þ

5.2. p–y curves for pile groups

Mostafa and El Naggar [4] present a method for

calculating dynamic p–y curves for a pile in a group. In

this method, the dynamic p–y curves for a single isolated

pile are modified using an appropriate p-multiplier ðPmÞ to

calculate the dynamic p–y curves for a pile in a group. The

p-multiplier depends mainly on the pile spacing to diameter

ratio ðS=dÞ and the pile head displacement to diameter ratio

ðy=dÞ: Using the p-multipliers, the soil model will include

only the dynamic p–y curves for individual piles, but it also

accounts for the group effect. The dynamic soil reaction at a

certain depth for a pile in a group, Pg; is given by

Pg ¼ PmPd ð3Þ

where Pm is the p-multiplier and Pd is the dynamic soil

reaction at the same depth for an isolated single pile. Fig. 3b

shows a chart for p-multipliers for piles installed in clay and

Fig. 3c shows dynamic p–y curves for a single pile and a

pile in a group.

The ratio S=d for the main piles of the Kvitebjørn Platform

is 3.44. The levelling pile (pile 5 in Fig. 2a) is closer to pile 3,

with a spacing S=d ¼ 2.35 m. The value of Pm ¼ 0:7 for piles

1, 2, and 4, and the value of Pm ¼ 0:55 for piles 3 and 5 are

established from charts presented in Ref. [4].

5.3. t –z curves and q–z curves for a single pile

The vertical soil resistance along the pile shaft and at the

pile toe is a function of the level and rate of loading. The soil

resistance to the vertical movement of the pile is modelled

using axial shear transfer functions that depend on local pile

deflection (t –z curves). The soil resistance at the pile toe is

modelled using q–z curves.

Various empirical and theoretical methods are available

for developing t –z curves. Coyle and Reese [10] present

empirical t –z curves that are based on the results of model

and full-scale pile load tests. Additional t –z curves for clays

and sands are provided by Vijayvergiya [11] and Reese and

O’Neill [12]. Theoretical curves described by Kraft et al.

[13] may also be used. In this paper, t –z curves are

constructed using the recommendations given by API [8].

Bea [14] stated that the dynamic axial soil resistance to

pile movement due to wave loading and earthquakes (rate

effect) is in the range of 1.2–1.8. Briaud and Garland [15]

propose a method to predict the behaviour of single piles in

cohesive soil subjected to vertical loads applied at various

rates. They state that the gain in pile capacity can be given

by the following equation:

Qu1

Qu2

¼t2t1

� �n

ð4Þ

in which Qu1 and Qu2 are the ultimate pile capacities

reached in times to failure t1 and t2, respectively, and n is

a viscous exponent that varies from 0.02 for stiff clay to 0.10

Fig. 4. Model for soil resistance along the pile shaft and at the pile toe.

Y.E. Mostafa, M.H. El Naggar / Soil Dynamics and Earthquake Engineering 24 (2004) 357–368 361

for soft clay. Briaud and Garland [15] state that for values of

n within the mentioned range, the pile capacity will be

1.21–2.60 times the static capacity. In this paper, the t

values in the dynamic t –z curves are taken to be 1.6 times

the t values in static t –z curves.

5.4. t –z curves and q–z curves for pile groups

Pile–soil–pile interaction causes an increase in the

settlement of the pile group, redistribution of pile stresses

and loads [16,17]. Poulos and Davis [17] present charts for

the interaction factors for piles under axial static loading.

Kaynia and Kausel [18] extend the static interaction factors

approach to dynamic loading. They present dynamic

interaction factors in the form of charts as a function of

the dimensionless frequency a0 ¼ vd=Vs: For S=d ¼ 3:44

and a0 < 0:01; the interaction factor is evaluated from Ref.

[18] and is found to be 0.5, meaning that the interaction

increases the vertical displacement of a pile in the group to

twice that of a single isolated pile subjected to the same

average load per pile in the group. Therefore, the t –z curves

along the pile shaft are adjusted using a z-multiplier, zm; to

account for the interaction effect. The displacement zg for

a pile in a group is then calculated as follows:

zg ¼ zmz ð5Þ

Fig. 3d shows a sketch for the t –z curve for single piles and

a pile group.

Fig. 5. Effect of foundation flexibility on the top nodal tower response: (a) displacement, (b) velocity and (c) acceleration.

Y.E. Mostafa, M.H. El Naggar / Soil Dynamics and Earthquake Engineering 24 (2004) 357–368362

6. Finite element analysis

The structural members of the Kvitebjørn Platform and

the foundation piles are modelled using space frame elements

in the commercial software ASAS-NL. The space frame

element has two nodes, one at each end and each with six

degrees of freedom, three translations and three rotations.

This paper considers the response of the platform to

transient loading due to waves and currents. The loads

considered are due to the extreme wave case with a wave

height of 28.5 m and a wave period of 15.3 s and the

associated current. The direction of the waves is assumed to

be 1808 (i.e. the direction of the Z-axis of the platform).

The soil resistance along the pile shaft is modelled using

sets of lateral and vertical springs whose constants are

evaluated using p–y curves and t –z curves as described

above. The soil is discretized into 34 layers, each layer

2.5 m thick (about one pile diameter). A pair of lateral

springs (one on each side of the pile) and a vertical spring

represent the horizontal and vertical soil resistance in each

layer as shown in Fig. 4. A q–z curve is used to model the

pile tip resistance.

7. Dynamic characteristics of the tower

The deck mass is assumed to be 23,000,000 kg and the

structural damping ratio is assumed to be 2% for all the

results presented in this section. The hydrodynamic damping

derived from the motion of the tower in the water is taken into

Fig. 6. Effect of pile–soil–pile interaction on the top nodal response: (a) displacement, (b) velocity and (c) acceleration.

Y.E. Mostafa, M.H. El Naggar / Soil Dynamics and Earthquake Engineering 24 (2004) 357–368 363

consideration when applying the Morison equation. Free

vibration analysis is performed to evaluate the natural

periods and the mode shapes of the tower.

The first two modes are the most important modes. The

first mode is the lateral translation along the X-direction and

the second mode is lateral translation along the Z-direction.

The first four natural periods are 3.8, 3.7, 2 and 1.23 s.

The free vibration analysis shows that the foundation

flexibility increases the first natural period of the platform

slightly (4.12 s), shifting it closer to the period of wave

loading.

8. Platform response to wave and current loading

As in Section 7, the maximum operating topside mass of

23,000,000 kg is considered for all the results presented.

Dynamic soil resistance and pile–soil–pile interaction are

considered unless otherwise stated.

8.1. Effect of foundation flexibility

The flexibility of the foundation affects the response of

the tower to wave loading. To investigate the effect of

foundation flexibility on the response of the tower, two

cases were considered: a fixed base and a flexible

foundation with soil resistance modelled using dynamic

p–y curves, t –z curves, and q–z curves. The results are

shown in Fig. 5. Fig. 5a shows that the top nodal

displacement for the case of a fixed tower is about one

half that of the top nodal displacement for the case of

a flexible foundation. Fig. 5b and c shows that the

foundation flexibility increases the top nodal velocity and

acceleration.

8.2. Effect of pile–soil–pile interaction

Pile – soil– pile interaction significantly affects the

response of pile groups and the overall response of the

platform. The dynamic soil resistance is modelled using

dynamic p–y curves, t –z curves and q–z curves for single

piles when ignoring group effect. To account for pile–soil–

pile interaction, p-multipliers are used to adjust the dynamic

p–y curves for a single isolated pile as mentioned above. A

value of 0.7 is used for piles 1, 2, and 4 and a value of 0.55 is

used for piles 3 and 5. An average z-multiplier of two is used

to adjust the t –z curves to account for the pile–soil–pile

interaction in the vertical direction.

Fig. 6 shows the time histories of the top nodal displace-

ment, velocity and acceleration. It shows that the pile–soil–

pile interaction increases the top nodal displacement, velocity,

and acceleration by about 15% in comparison with the case of

no interaction. Fig. 7 shows the response of piles 1, 3, and 5

when the pile–soil–pile interaction is considered. The figure

reveals that the displacement of pile 3 is greater than that for

piles 1 and 5. However, the rotation of pile 5 along the top 10 m

of the pile shaft is greater than that for piles 1 and 3.

Fig. 8 shows the envelope of axial force, shear force and

bending moment along the shaft of pile 1. It is noted that

the pile–soil–pile interaction has a significant effect on

the stresses along the pile shaft. The maximum values of

axial force, shear force, and bending moment increased by

about 50, 45, and 115%, respectively, due to pile interaction.

The maximum bending moment with interaction considered

occurs at a depth equal to 12.5 m while the maximum

bending moment with no interaction occurs at a depth equal

to 15 m (i.e. the interaction slightly shifts the location of

maximum bending moment by about a value of one pile

diameter). It is important in the design of offshore piles to

Fig. 7. Effect of pile–soil–pile interaction on the response along the shaft of different piles: (a) horizontal displacement and (b) rotation.

Y.E. Mostafa, M.H. El Naggar / Soil Dynamics and Earthquake Engineering 24 (2004) 357–368364

determine the location of maximum bending moment

because the pile diameter or the pile wall thickness can be

reduced below locations of maximum stresses.

Fig. 9 shows the stresses along piles 1, 3, and 5 when the

pile–soil–pile interaction is considered. The bending

moment and shear force for pile 1 are greater than for piles

3 and 5, but the axial force for pile 3 is greater than that for

pile 1. The unequal distribution of the load between the piles

and the difference in pile rigidity are attributed to the pile

interaction and the arrangement of the piles in the group.

8.3. Effect of dynamic soil resistance

Static p–y and t –z curves are widely used in the design of

offshore piles. However, the dynamic resistance of the soil

may differ substantially from the static case, especially for

the extreme cases of storms and earthquakes. The effect of the

dynamic soil resistance is investigated here. It should be

noted that the group effect (i.e. pile–soil–pile interaction) is

considered for both dynamic and static soil resistance.

Static p–y curves are modelled using nonlinear springs

and dynamic p–y curves are modelled using nonlinear

springs and nonlinear dashpots. The nonlinear stiffness of

the springs along the pile shaft is determined using the API

recommendations [7], while the nonlinear damping constant

of the dashpots is determined from Eq. (2).

Fig. 10 shows the effect of dynamic soil resistance on the

displacement and rotation along the tower length. It is noted

that the dynamic soil resistance significantly decreases the

response of the tower. Fig. 11a and b reveals that the dynamic

Fig. 8. Effect of pile–soil–pile interaction on the stresses along the pile shaft: (a) axial force, (b) shear force and (c) bending moment.

Fig. 9. Effect of pile–soil–pile interaction on piles 1, 3, and 5: (a) axial force, (b) shear force and (c) bending moment.

Y.E. Mostafa, M.H. El Naggar / Soil Dynamics and Earthquake Engineering 24 (2004) 357–368 365

soil resistance decreases the maximum pile head displace-

ment and rotation by about 70 and 80%, respectively. Fig. 12

shows the envelope of the stresses along the pile length. The

calculated axial force, shear force and bending moment

decrease by a ratio of 10, 50, and 60%, respectively, when the

soil dynamic resistance is accounted for.

8.4. Effect of properties of top soil layers

Two soil profiles are considered to investigate the effect

of a variety of properties for the top soil layers. The first

profile is shown in Table 3 and the second is the same, but

with two clay layers: a clay layer in the top 7.5 m with

cu ¼ 5 kPa, 150 ¼ 0:025 and a clay layer from depth ¼ 7.5

to 32 m with cu ¼ 40 kPa, 150 ¼ 0:015: Dynamic soil

resistance and pile–soil–pile interaction are considered in

both cases.

The weak soil profile results in an increase in the

response along the tower height by about 30%. The pile

displacement and rotation along the shaft increase by about

135 and 40%, respectively, when the weak soil layers

are considered as shown in Fig. 13. The results show that

the reduced soil strength of the top soil layer results in a

decrease in the pile shear force and bending moment and the

location of maximum bending moment is shifted down-

wards by about 5 m.

Fig. 10. Effect of dynamic soil resistance on the response along the tower length: (a) displacement and (b) rotation.

Fig. 11. Effect of dynamic soil resistance on the response along the pile length: (a) displacement and (b) rotation.

Y.E. Mostafa, M.H. El Naggar / Soil Dynamics and Earthquake Engineering 24 (2004) 357–368366

9. Conclusions

This paper reports on a parametric study carried out to

investigate the effect of different parameters on the response

of a fixed offshore platform subjected to transient loading

due to extreme wave and current loading. The soil resistance

is modelled using p–y and t –z curves. p- and z-multipliers

are used to account for the pile–soil–pile interaction in a

simplified way. The following conclusions are drawn:

1. The foundation flexibility increases the natural period

of the platform.

2. The foundation flexibility results in a significant increase

in the response of the offshore tower. The foundation

flexibility also increases the velocity and acceleration at

the top node of the tower.

3. Pile–soil–pile interaction increases the response along

the offshore tower height and along the pile length. It

alters the response of the tower base and the velocity and

acceleration of the top node of the tower. Also, it has

a significant effect on the stresses along the pile shaft

especially the bending moment, one of the most

important parameters in the design. Therefore, it must

be considered when designing closely spaced pile

foundations, as in the case considered here.

4. The dynamic soil resistance decreases the response of the

tower and the supporting piles. It decreases the stresses at

the tower base and the stresses along the pile shafts.

Fig. 12. Effect of dynamic soil resistance on the stresses along the pile shaft: (a) axial force, (b) shear force and (c) bending moment.

Y.E. Mostafa, M.H. El Naggar / Soil Dynamics and Earthquake Engineering 24 (2004) 357–368 367

Therefore, the static soil resistance normally used in

the design of offshore piles leads to substantial over-

estimation of the design of the whole platform.

5. The properties of the top soil layers have an important

effect on the response of the tower and supporting piles.

A decrease in the resistance of the upper soil layers

results in an increase in the response at the tower base

and along the pile shaft and a decrease in the shear

force and bending moment along the pile shaft. The

location of the maximum bending moment changes with

a change in soil resistance.

Acknowledgements

The authors wish to thank Dr Torstein Alm of Aker

Kvaerner for providing the first author with the data for the

Kvitebjørn Platform used in this study. Also, the authors

would like to thank Mr Paul Schofield (Century of

Dynamics) for making the ASAS-NL software available

to them at a reduced price.

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Fig. 13. Effect of soil stiffness on the response along the pile length: (a) displacement and (b) rotation.

Y.E. Mostafa, M.H. El Naggar / Soil Dynamics and Earthquake Engineering 24 (2004) 357–368368