Dynamic behaviour of steel jacket platforms

DYNAMIC DEHAVIOUR OF STEEL JACKET PLATFORMS

by

Rrnosh Prasad Singh

Thosis submittud to tho Indian Instltuto of Toohncilrgy,Uulhi for tho award of tho docau of

DOCTOR OF PHILOSOPH'?

Dopertrnont of hppUod Maahanios, Indian Institute of Tachnoi_ogy,DolhI

Juno 11980

CERTIFIC ATE

This is to certify that the thesis untitled, SiuYNMIc OEHJIOUR OF STEEL J;:CKET PLATFORh1S being submlttuJ by Mr.R.P. Singh to the Indinn Institutu of Technology, Doihi for the award of the dugrE3o of Doctor of Philosophy is a rocord of the honaf'ido research work carriuP out by him. Iir,fl.P1Sinçjh has worked under my

juidancu and suporvision and has fulfilloci the

roquiromuntu for thu submission of this thesis which to my knowledge has roachod the requisite standard.

Thu thosis, or any part thuroof, has not boon submitted to any other University or Institute for the award of any dujrao or diplomu

", Professor

Department of Civil Engçj., IndianIhst1tutu of Technology, Huz KhQS, Now Doihi - 110016

XN

ACKNOWLEDGEMENTS

This thesis was supervised by Professor f,K.Oasu to whom I express my profound sense of gratitude and sincere appreciation for his continuous support and guidenco. His scientific knowledge and maturity in identifying now areas of research work deeply in?luoncd my present work.

I am thankful to the Ministry of education, Government of India for providing me the research

fellowship under Quality Improvement Programme to carry out this study and to Ur.P.G.Mirajgookar, Principal, F(egionel Instituto of Technology, Oamshodpur for

sponsoring mu under the above schema.

Thu author is grateful to Dr J .0 .Chapman, Tuchnicol Diroctor, Wirnpcy Laboratories Limited, Doncansfiold Road, Hayos, I''l1ddlusox, U.K. for making

avajiobla the data of U.P.Fnrtioa field tIED platform.

fly sincere thanks are duo to Ilr,h.K,Join and other finds for , thoir friendship and help.

I wish to thank Mr.N.L,rors for tracing the figures ant Flrs,tJ.Monon for typing this report.

Finally) I must acknewloga the cooperation and assistance extended by my wife and children.

93

ME1STR ACT

Tho objoct of tho prosont work is to study the

dynnmic rosponso characteristics of stool jockot platforms under x'cguLur wovos. Tho structure rincilysod for the

dynamic rosponso is o pluno fraimo vorsion of the Stool jcickot picitform used in the North Sec Fortios Fiold by OP.

Thu structural proportios ossociotcid with tho f'ramos in

thu orthogonal piano arc tokcin into account. Tho soil- piLu, thu pilu—structuro nnd thu structuro—watur intor- octions arc tukon into considorotion.

Thu soil-pilo—structuro system is dividod into two subsys'bcime (i) the soil—pilo subsystem and (ii) the

jackot sutsystam. Each subsystom is cippropriotoly

modullod and the uquntions of motion ciro writton in thu çjonorolizod courdinutos0 in the prosont invosticition Novok's forrriuiutiori has boon odoptod to ovoluato thu impedance functions of thu kilos at their intorfoco with

thu Inq uf thu j uckut p1 ntfrirm • Thu soil is tnkon as Linuorly oastic, isotropic and homounoous,

Using the morlifiud Morison equation tho hydrodynamic forces an the structure oro cOiculcito(1 for the actual

submurjuncu (from the sec bud to the froo vector surfaco) of the momhors; the drag and inortia., coofficionts ciro talon to bo constant. Thu distribution of the hydro- dynomic forcos nInng a structural mombor is nssumud to he

Ij

linoar, The velocities and accoloratjons of the water particles nro calculcatod by using the linear (Iiry)wavo

thoory; its validity is takon to extend upto the foo water surfaço.

Thu solution of thu equations of motion In the goncralizod coordinates has boon obtained by both in the

frequency domain and time domain. The number of

gonorcalizod coordinates needed for occurrito prediction of some of the Important structural responses has been do to r m i nod.

Thu offocte of the foundation flexibility and the fluctuation in the water level on the dynamic response of the platform have boon inuostigatod. The ouors

ossocintod with the drag-torm linearization of the

froquoncy domain analysis is estimated. The timodomain and the froquoncy-domain results are compared with each other and the suitability of the frequency domain analysis for a jacket platform under regular waves is dieOU$SOd

TABLE OF CONTENTS

P age

TITLE PAGE 1

CERTIFICATE 2

ACKNOWLEDGEMENTS 3

ABSTRACT 4

TABLE OF CONTENTS 6

LIST OF FIGURES 10

1. INTRODUCTION AND LITERATURE REVIEW 14

1.1 Literature Review 14

1,1,1 UffshoDo Structural Dynamics

1,1.2 Pilo Foundation 25

1.2 Outline of the Prasont Invastiga- tioris.

1ofara Moe s 32

2. HYDRODYNPJ'IC LOADING 33

2.1 1,invos and Current 30

2,1.1 Wovekinematics 39

2.1.2 Computation of the Ways Length 41 2.2 Use of Modified Morison Equation 42 2.2.1 Fluid Loading on a Tubular Member 42 2.2,2 Fluid Loading 14 ssociatod with 49

Lumpod Volumes and Areas

2.3 Hydrodynamic Loading

in

2.3.1 Nodal Loads for a partially 47 Submerged Tubular Momb©r

2.3.2 Nodal Loads for a Fully Submerged 49

Tubular

2.3,3 Added Mass Matrix 49

2,3,4 Calculation of they Load Voctor{P(t) 50

:3.

rh

P age 2.4 Hydrodynamic Loading in the 52

Frequency Domain Analysis

2.4.1 Linearization of the Drag Force ₅₃ 2.4,2 Hydrodynamic Damping Matrix 55 2.4,3 Fluid Loading Associated with 57

Lumped Volumes and Areas

2.4.4 Nodal Loads for a Partially/Fully 57 Submerged Tubular Member

2.4.5 Added Mass Matrix 58

2.4.6 Calculation of the Load Vector (t) 50

References 59

FOUNDATION XMPZDAiJCES 60

3.1 Soil Stiffness 61

3.1.1 Soil Stiffness in Horizontal ⁶¹ Direction

3.7.2 Soil StjDncss in Vertical 63 Direction

:3,2 Imnpoilancu Functions of the Pile 64

3.2.1

3.2.2 impodanco Functions for Vertical 70 Vibrations

3.2.3 Dynamic Stiffness Matrix of a 72

P110 Hood

Dynomic Stiffness Matrix of a 73 Soil—Pilo Group

Fof'oronoos 74

THE StRUCTUIE 75

4.1 Idealization of the Jacket Platform 75 4.2 Equations of Motion in the Time 76

Domain Analysis

4,2.1 Mass Matrix CM,J 75

4.2.2 Stiffness Matrix

tKT

4.2.3 Damping Matrix (CJ 01

Gonorolizod Coordinates 03 4.2.5 Ruduced Equations of Mct.ion 04

6.

6,

P ay o 4.3 Equations of [lotion n the Fraquoncy 86

Domain Analysis

4.3.1 Noss Matrix MI 87

4.3.2 Stiffness Matrix

EK)

4.3,3 Damping Matrix 07

4,3.4 Reduced Equations of Motion ₀₀

References 90

TIME DOM/IN AND FREQUENCY—DOMAIN SOLUTIONS 91

5.1 Timo—Domain Solutions 91

6.1.1 Solution Algorithm 92

5.1.2 Nodal Rotations 94

5,1.3 E3aso—Shoar and E1aso—Moment 95

5.2 Froqwny—Domajn Solutions 95

5.2,1 Solution Method 96

5.2.2 Nodal Rotations 90

5.2.3 Dose—Shaor and OasO—loront 9 ⁸

References 100

RESULTS IND DISCUSSIONS 101

6.1 Example PrW,1 om 101

6.1.1 Doscription of the Structure 102 6.1.2 Description of thu Pilo Foundation 103 6.1.3 Mode Shapes and Natural Periods of 109

Vibrotion

6,2 Diabota TioIntorsal for the 113 Numerical Solutions

6.2,1 Selection of Timo—Intorval for FO 113 Solutions

6.2.2 Selection of TriiStüp for TO 114 Solutions

6.3 E.ff'act of Numbor of Gorioralizod 1.21 Coordinates (ED, TO)

6,4 ED \Jorsus TO Solutions 122

6. ^/,1 Drag—Tor Linuorzation 128 6.4.2 Effect of Overall Appr-oxlriiatiana 129

MacJo in tho ED bi.nalsi

9

6.5 Response Characteristics under ₁₃₀

ME

Different Wave Loading

6.5.1 Response under 10ft

-

6,5,1.1 Gonoralized Loading 130

6.6.1,2 Structural Response 132 13.5,1.2,1 Effect,, of Variable Subniergonco(with 133

Foundation Flexibility F 2)

6.5.1.2.2 Effect of Foundation Flexibility 134 (with Variable Submergence)

6,5.2 Response Under 10ft * 10 sec Waves 145 6.5,2.1 Generalized Loading 145 65,2,2 Structural Response 146 6.5.2,2.1 Effoot of Variable Submergence (with 146

Foundation Flexibility F 2)

6,5,2,2.2 Effect of Foundation FluxIbj.ity 147 (with Variable Submergence)

6,5,3 Response Under 25 ?t-'7 sac Waves 157 6.5.3.1 Generalized Loading 157 6,5.3,2 Structural Response, 150 6.5.3,2.1 Effoct of Variable Submergence (with 150

Foundation Flexibility F2)

6,5.4 Response Under 50 ft-.10 sac Waves 165 6.5,4.1 GonorLizod Loading 165 6.5.4.2 Structural Thsponsu 166 6.6.4.2.1 Effuct of Variable Submnorenco (with 1137

Foundation Flexibility F2)

6.5.4.2.2 Effect of Foundation Flexibility 1136 (with Variable Submergence)

"ofuroncos 179

7, CONCLUSIONS AND REC0iiflENDTIONS FOR FUTURE WORK 160

7.1 Conclusions 180

7,2 Recommendations for Future Work 101

Roforoncos 104

Appendix P- Sti?fnoss Matrix of a Member 105 Connoctod with thu Rigid Dock

1ppcindix 0- Generalized Stiffness Damping 100 and Mess Matrices of xamplo Problem Appendix C- Structural Stiff'rioss and Damping 194

Matrices of Foundation