Response of fixed offshore platforms to wave and current loading including soil – structure interaction Yasser E. Mostafa a , M. Hesham El Naggar b, * a Geotechnical Engineer, Golder Associates, Burmnaby, B.C., Canada b Associate 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.: þ 1-519-661-4219; fax: þ1-519-661-. E-mail addresses: [email protected] (M.H. El Naggar); ymostafa@uwo. ca (Y.E. Mostafa).
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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
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