Response of Fixed Offshore Platforms To Wave and Current Loading Including Soil-Structure Interaction

 

Soil Dynamics and Earthquake Engineering 24 (2004) 357–368 www.elsevier.com/locate/soildyn

Response of fixed offshore platforms to wave and current loading including soil–structure interaction Yasser E. Mostafaa, M. Hesham El Naggarb,* a

Geotechnical Engineer, Golder Associates, Burmnaby, B.C., Canada  Associate Professor and Research Director, Geotechnical Research Centre, Faculty of Engineering Engineering,, The University of Western Ontario, London, Ontario, Canada N6A 5B9

b

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 loads is strongly affected affected by the pile pile– – soil– soil – pile interaction. In the present study, the re response sponse 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

 p-multipliers were found to vary with the spacing between

Foundation piles have a significant effect on the response [1] performed  performed a series of  of fixed offshore structures. Bea   [1]

pile piles, s, so soil il ty type pe,, pe peak ak am ampl plit itud udee of lo loadi ading ng an and d th thee angl anglee betw betwee een n th thee line line conn connect ectin ing g any any two two pi pile less and and the direction of loading [4] loading  [4].. Several parameters such as the

static push-over analyses on a fixed offshore platform and found that the first nine nonlinear events were concentrated in the foundation foundation pile piles. s. Mitwally Mitwally and Novak   [2]   used a linear linear ana analys lysis is to accoun accountt for the effec effectt of fou founda ndatio tion n flexibi flex ibilit lity y inc includ luding ing pil pile– e– soil– soil– pil pilee int intera eracti ction on on the response resp onse of offsho offshore re structure structuress to rand random om wave loading. El Naggar and Novak   [3] considered [3]  considered foundation nonlinearity using an equivalent linear approach. This paper describes an efficient approach to model the response of pile groups suppor sup portin ting g a jacket jacket str struct ucture ure to transi transient ent loa loadin ding. g. 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 establishe lished d dynamic dynamic   p-mul -multipli tipliers ers to rela relate te the [4]   have estab dynamic load transfer curves of a pile in a group to the dynamic load transfer curves for a single pile. The dynamic *  Corresponding author. Tel.:  þ 1-519-661-4 1-519-661-4219; 219; fax:  þ 1-519-661-. E-mail addresses: [email protected] (M.H. El Naggar); ymostafa@uwo. ca (Y.E. Mostafa). 0267-7261/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.soildyn.2003.11.008

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’ 1.. It is currently under construction platform shown in Fig. in  Fig. 1 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 vertic ver tical al ste steel el piles piles groupe grouped d symmet symmetric ricall ally y around around each 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

 

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Table 1 Design waves versus return period Return period (year)

1 10 100 10,000

Wave height (m)

22.0 25.3 28.5 36.0

Height above MSL (m)

12.8 14.2 16.1 20.4

Wave period (s) Mean value value

90% interval interval

13.8 14.6 15.3 17.1

12.2 – 15.5 13.0 – 16.4 13.6 – 17.1 15.1 – 19.1

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 wei ght of the platfo platform rm is 171,20 171,200 0 kN. The str struct ucture ure is designed to support a maximum operating topside weight of  225,00 225 ,000 0 kN. The lower lower part part is square square shaped shaped with with base base dimensions 50 m   £ 50 m, is approximately 45 m high and has has ve vert rtic ical al co corn rner er legs legs.. Th Thee to top p part part ex exte tend ndss fr from om approximately El.   2 145 to El.   þ 8 m and has a constant batter on all sides with square dimensions at the bottom of  50 m   £   50 m t o s qua quarr e di dim m ens ensii o ons ns at t h hee t o op p 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 21.2 m to the topsid topsidee interf interface ace elevat elevation ion of 24. 24.1 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

Theenvironment Theenvironm ental al data data are bas based ed on STATO STATOIL IL specifi specificacations ‘Metocean ‘Metocean Design Criteria Criteria for Kvitebjørn’ Kvitebjørn’ and are [5,6].. Th Thee maximu maximum m provided provi ded by Aker Engineering Engineering AS   [5,6] directional wave heights for the 100-year return period are given in Table in Table 1, 1, including the me mean an wave period along along with the 90% interval. The current associated with the 100-year 2.. No return period design wave height is given in   Table 2 associated wind has been specified. The thickness of marine Table 2 Values for associated current

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

connection and extends to approximately 25 m above the mean mean se seaa le leve vell (M (MSL SL). ). The The jack jacket et’s ’s lowe lowerr pa part rt is appr approx oxim imat atel ely y 45 m hi high gh and and is conn connect ected ed to the the pile pile foundation. The structure is levelled using four levelling piles and is permanently fixed on sixteen piles driven to about 90 m penetration depth.

Depth below sea-level (m)

Current speed (cm/s)

0 25 50 75 100

50 50 50 46 42

125 150 175 190

39 36 32 29

 

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

Table 3 General soil layering Soil unit

Depth (m)

Soil description

A

0 – 7.5

Very soft to soft silty, sandy clay

B C D E F

7 3.25––4372 47 – 52 52 – 125.5 . 125.5

S Vaenrd yys,ticflfatyoeyhasridlt silty clay Very dense fine sand Very stiff to hard clay Very hard clay

 

 

359

growth is considered to be 20 mm below El.   þ 2 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 use used d togeth together er with with the API wave wave for force ce guidel guideline iness [8] to generate the hydrodynamic forces. Drag and inertia coefficients are assumed to be 0.7 and 2.0, respectively, and the wave kinematics are calculated using the Stokes fifth-order wave theory.

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

 

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4. Geotechnical information

85 m. The pile spacing   ðS Þ  centre to centre is 8.4 m (i.e. ¼  3 :44). Four levelling piles also support the jacket, one S  = d  d  ¼

4.1. Soil profile

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. cap.  Fig. 2a shows 2a  shows a plan of 

The soil profile at the tower site consists of a layer of very soft to clayey soft silty 7.5 m thick underlain layerthe of  sandy, silt clay that extends to a depth of 32by m abelow 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 in  Table 3 [6].. The results from the cone penetration tests (CPTs) show [6] that a thin sand layer exists at the surface of the seabed in somee of the borings. som borings. Therefor Therefore, e, local local sco scour ur of 0.5 m is adopted. No global scour is included in the design. The basis for the assump assumptio tion n is the water dep depth th at the Kvite Kvitebjø bjørn rn  jacket location [5,6] location [5,6]..

g.levelling 2b   shows long itudinal nal the piles pilesforarr arrang angeme ement nt and Fi sections the main piles and  Fig. the pileslongitudi 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 curves and   t – z   curves curves for latera laterall and axial axial loading, respectively. 5.1. 5.1. p – y curves for a single single pile pile

The jacket is supported on 16 main piles arranged in

The soil soil res respon ponse se to latera laterall loadin loading g is nonlin nonlinear ear.. To model this nonlinearity, pile deformation can be related to soil soil res resist istance ance thr throug ough h nonlin nonlinear ear transf transfer er curves curves ( p – y

symmetrical groups of four piles per corner leg. The pile diameter   ðd Þ  is 2.438 m and its penetration depth is about

curves). curve s). Static Static   p – y   curv curves es fo forr a si sing ngle le pi pile le can can be established using the API guidelines  [8]  [8]..

4.2. Foundation design

Fig.3. (a) Static Static and dynamic dynamic p –y  curv  curves, es, (b) dynamic dynamic p-multipliers, (c) p– y curve  curvess fora sin singlepile glepile anda pile pile in a g grou roup p and(d) t –z  cur curvesfor vesfor sin singlepile glepile anda pile in a group.

 

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The dynamic   p – y   curves for a single isolated pile are calculated using the equation proposed by El Naggar and  [9]  as Bentley [9] Bentley

0 B@ P ya



Ps   b a20  þ

s

Pd   ¼

  þ i

 v  y   1 k a d  CA y  y n

0

 

ð1Þ

where P d  is the dynamic soil reaction at depth  x  (N/m), P s  is the static soil reaction obtained from the static  p – y curve at depth  x  (N/m),  a 0  is the dimensionless frequency  ¼  v d  d =    V  Vs  ; v  is   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 thi thiss analys analysis) is),,   b ;   k ;   and   n   are constants that 3a  shows typical static and depend on the soil type [9] type  [9]..  Fig. 3a shows dynamic   p – y   curves curves.. The dyn dynami amicc soil soil res resis istan tance ce is modell mod elled ed using using a ser series ies of spring springss and das dashpo hpots ts whose whose nonlinear nonli near stif stiffness fness and nonlinear nonlinear dampi damping ng constants constants are established using Eq. (1), and are given by Ps a nl ¼ k nl  y



Ps   b a20 þ k a0

and   cnl ¼

 v  y   n

ð2Þ

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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  t – z  curves that are based on the results of model empirical and full-scale pile load tests. Additional t – z curves for clays  and Reese and and sands are provided by Vijayvergiya [11] Vijayvergiya  [11] and O’Neill [12] O’Neill  [12]..  Theoretical curves described by Kraft et al. [13]   may may also also be us used ed.. In th this is pape paper, r,   t – z   curves curves are constructed using the recommendations given by API [8] API  [8].. Bea [14] Bea  [14] stated  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

d 

v  y

 

¼

 t   2

t 1

n

ð4Þ

in whi which ch   Qu1   and   Qu2   are the ultima ultimate te pile pile cap capaci acitie tiess reached in times to failure   t 1   and   t 2 , respectively, and   n  is a viscous exponent that varies from 0.02 for stiff clay to 0.10

5.2 5.2.. p – y cur curves ves for pile group groupss

Mostafa Mosta fa and El Naggar Naggar   [4]   prese present nt a me metho thod d for 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 ð Pm Þ  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  ð S  = d  d Þ  and the pile head displacement to diameter ratio ð y = d  d Þ:  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,  P g ;  is given by Pg   ¼  P m Pd

 

ð3Þ

where   Pm   is the   p-multiplier and   Pd   is the dynamic soil reaction at the same depth for an isolated single pile. Fig. pile.  Fig. 3b shows a chart for  p -multipliers for piles installed in clay and Fig. 3c 3c shows  shows dynamic   p – y  curves for a single pile and a pile in a group. The rat ratio io S  = d d  for the main main piles piles of the Kvi Kviteb tebjør jørn n Pla Platfo tform rm 2a)) isclo isclose serr topile topile 3, is 3. 3.44 44.. Th Thee le leve vell llin ing g pi pile le (pil (pilee 5 in Fig. Fig. 2a ¼  2.3 with wit h a spacin spacing g S  = d d   ¼  2.35 5 m. The The valu valuee of Pm  ¼  0 :7 for for pile piless 1, 2, and 4, and the value of  P  P m  ¼  0 :55 for piles 3 and 5 are established from charts presented in Ref. [4] 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 resistan resi stance ce to the vertical vertical movement of the pile is modelled

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

 

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 state that for values of  for soft clay. Briaud and Garland [15] Garland  [15] state n   within within the mentio mentioned ned ran range, ge, the pil pilee cap capaci acity ty wil willl 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 5.4.. t –z curves curves and q– z curves fo forr pile grou groups ps

Pil Pile– e– soi soil– l– pil pilee int intera eracti ction on cau causes ses an inc increa rease se in the settlement of the pile group, redistribution of pile stresses Davis  [17] present  present charts for and loads [16,17] loads  [16,17].. Poulos and Davis [17] the interaction factors for piles under axial static loading. Kaynia and Kausel [18] Kausel  [18] extend  extend the static interaction factors approa app roach ch to dyn dynami amicc loa loadin ding. g. The They y pre presen sentt dyn dynami amicc

interaction factors in the form of charts as a function of  ¼  3 :44 the dimen dimensionl sionless ess frequency frequency   a0   ¼  v d d  =   V V s  :   For   S  = d d   ¼ and  a 0 0:01;  the interaction factor is evaluated from Ref. [18] [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 ofper a single pile subjected same average load pile inisolated the group. Therefore, theto t –the z curves along the pile shaft are adjusted using a  z -multiplier, z m ;  to account for the interaction effect. The displacement   zg   for a pile in a group is then calculated as follows:  zg  ¼  z m z

 

ð5Þ

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

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

 

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6. Finite element analysis

The structural members of the Kvitebjørn Platform and the found foundationpiles ationpiles are modelled modelled usingspace frameelements in the commercia commerciall software software ASAS-NL 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. Thiss pap Thi paper er consid considers ers the res respon ponse se of the platfo platform rm to tra transi nsient ent loa loadin ding g due to waves waves and cur curren rents. ts. The loads loads considered are due to the extreme wave case with a wave he heig ight ht of 28 28.5 .5 m and and a wave wave peri period od of 15 15.3 .3 s and and the 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 sets of latera laterall and ver vertic tical al spring springss whose whose consta constants nts are

 

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evaluated using   p – y   curves and   t – z   curves as described above. abo ve. The soil is dis discre cretiz tized ed into into 34 lay layers ers,, each each layer layer 2.5 m thick thick (about (about one pile pile diamet diameter) er).. A pai pairr of latera laterall springs (one on each side of the pile) and a vertical spring represent the horizontal and vertical soil resistance in each layertip asresistance. shown in Fig. in  Fig. 4. 4. A  q – z  curve is used to model the pile

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 res result ultss presen presented ted in thi thiss sectio section. n. The hydrod hydrodyna ynamic mic dam dampin ping g deri derive ved d fr fromthe omthe mo moti tion on ofthe to towe werr inthe wa wate terr istaken istaken in into to

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

 

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consideration considera tion when applying applying the Mori Morison son equation. equation. Free vibrat vib ration ion analys analysis is is perfor performed med to eva evalua luate te the nat natura urall 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 -direction and

8.2. Effect of pile–soil–pile interaction

Pile– soil– pile interaction interaction sign significa ificantly ntly affec affects ts the res respon ponse se of pile pile groups groups and the overall overall res respon ponse se of the platform. platf orm. The dynamic dynamic soil resistance resistance is modelled modelled using

8.1. Effect of foundation flexibility

 p – y  curves,  t – z  curves and  q – z  curves for single dynamic 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 6 shows  shows the time histories of the top nodal displacement, velocity and acceleration. It shows that the pile–soil– pile pile interac interactio tion n increas increases es the top nodal nodal displa displacem cement ent,, vel veloci ocity, ty, and accelerat acceleration ion by about about 15% in compariso comparison n with the case of  no interaction. Fig. interaction.  Fig. 7 shows 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 pile piless 1 an and d 5.Howeve 5.However,the r,the ro rota tati tion on ofpile5 alon along g thetop10 m

The flexibility of the foundation affects the response of  the tower to wave wave loa loadin ding. g. To inv invest estiga igate te the eff effect ect of  founda fou ndatio tion n flex flexibi ibilit lity y on the res respon ponse se of the tower, tower, two ca case sess we were re cons consid ider ered ed:: a fixed fixed ba base se an and d a flexi flexibl blee foundatio foun dation n with soil resi resistanc stancee model modelled led usin using g dynamic dynamic  p – y   curves,   t – z   curves, and   q – z   curves. The results are Fig. g. 5a   show showss that that the the top top noda nodall shown sho wn in   Fig. Fig. 5.   Fi displacement for the case of a fixed tower is about one hal halff tha thatt of the top nodal nodal dis displa placem cement ent for the case of  a flexible flexible foundati foundation. on.   Fi Fig. g. 5b an and d c   shows shows that that the foundation flexibility increases the top nodal velocity and acceleration.

of the pile shaft is greater greater than that for piles 1 and 3. Fig. 8 shows 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– soil– pil pilee int intera eracti ction on has a sig signifi nifican cantt ef effec fectt 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 due to pile interaction. The maximum bending moment with interaction considered occu occurs rs at a de dept pth h equa equall to 12 12.5 .5 m whil whilee th thee maxi maximu mum m 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

the second mode is lateral translation -direction. The first four natural periods are 3.8, along 3.7, 2the and Z 1.23 s. The free vibration vibration analysis analysis shows that the foundation 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 23,000,00 0 kg kg is consi considered dered for all the resul results ts pres presented ented.. Dynamic soil resistance and pile–soil–pile interaction are considered unless otherwise stated.

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

 

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365

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.

det determ ermine ine the loc locatio ation n of maximum maximum bend bending ing mom moment ent because the pile diameter or the pile wall thickness can be reduced below locations of maximum stresses. 9 shows  shows the stresses along piles 1, 3, and 5 when the Fig. 9 pil pilee –soil– pil pilee int intera eracti ction on is consid considere ered. d. The bendin bending g moment mome nt 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 curv curves es ar aree wide widely ly us used ed in the the desi design gn of  offshore piles. However, the dynamic resistance of the soil

may differ substantially from the static case, especially for theextreme theextre me cas cases es of sto stormsand rmsand earthq earthquak uakes.The es.The ef effec fectt 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 dynam dynamic ic   p – y   curves curves are mod modell elled ed using using nonlin nonlinear ear springs and nonlinear dashpots. The nonlinear stiffness of  the springs along the pile shaft is determined using the API recommendations [7] recommendations  [7],, while the nonlinear damping constant of the dashpots is determined from Eq. (2). Fig. 10 10 shows  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 and d b rev reveal ealss that that the dyn dynami amicc res respon ponse se of the tower. tower. Fig.11a Fig.11a an

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

 

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

soil resistance decreases the maximum pile head displaceFig.. 12 mentt and rot men rotati ation on by about about 70 and 80% 80%,, res respec pectiv tively ely.. Fig shows the envelope of the stresses along the pile length. The calculated calcu lated axial force, force, shear force and bendi bending ng moment moment decrea dec rease se by a rat ratio io of 10,50, and60%, res respec pectiv tively ely,, whe when n 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 in  Table 3 and 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 Dynamic soi soill to 32 m with with   cu  ¼  40 kPa,   150  ¼  0:015:   Dynamic

resistance and pile–soil–pile interaction are considered in both cases. The The we weak ak so soil il pr profi ofile le re resu sult ltss in an in incr crea ease se in th thee response along the tower height by about 30%. The pile displacement and rotation along the shaft increase by about 135 and 40%, 40%, res respec pectiv tively ely,, when when the wea weak k soil soil layers layers are considered as shown in Fig. in  Fig. 13. 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 locat ion of maximum maximum bending moment is shif shifted ted downwards by about 5 m.

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) 357–368

 

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

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 foundation flexibility flexibility increases increases the natural period of the platform. 2. The foundation flexibilit flexibility y results in a significan significantt 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 es espec pecia iall lly y the bendi bending ng mome moment nt,, one of th thee most most important parameters in the design. Therefore, it must be con consid sidere ered d when when design designing ing clo closel sely y spa spaced ced pil pilee foundations, as in the case considered here. 4. The dynamic soil resistan resistance ce decreases the response of the tower and the supporting piles. It decreases the stresses at the tower base and the str stress esses es alo along ng the pile shafts shafts..

 

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

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

Therefore,, the static Therefore static soil resistance resistance normally normally used in the design of offsho offshore re piles piles leads to substanti substantial al overestimation 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 decrea decrease se in the resistan resistance ce of the upper soil layers layers results in an increase in the response at the tower base and along the pile shaft and a decrease in the shear for force ce and bendin bending g moment moment along along the pile pile sha shaft. ft. 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 forPlatform providing the in first author with the data for the Kvitebjørn used this study. Also, the authors wo woul uld d li like ke to th than ank k Mr Paul Paul Scho Schofie field ld (Cen (Centu tury ry of  Dynamics) Dynam ics) for making making the ASAS-NL ASAS-NL soft software ware available to them at a reduced price.

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