Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Geotechnical considerations for offshore gravity type structures with emphasis on foundation stability.. 1982

You don't seem to have a PDF reader installed, try download the pdf

Item Metadata

Download

Media
UBC_1982_A7 G33.pdf
UBC_1982_A7 G33.pdf [ 10.44MB ]
Metadata
JSON: 1.0062594.json
JSON-LD: 1.0062594+ld.json
RDF/XML (Pretty): 1.0062594.xml
RDF/JSON: 1.0062594+rdf.json
Turtle: 1.0062594+rdf-turtle.txt
N-Triples: 1.0062594+rdf-ntriples.txt
Citation
1.0062594.ris

Full Text

GEOTECHNICAL CONSIDERATIONS FOR OFFSHORE GRAVITY TYPE STRUCTURES WITH EMPHASIS ON FOUNDATION STABILITY UNDER STORM WAVE LOADING by THOMAS C. GAARD S., The U n i v e r s i t y of C a l i f o r n i a , D a v i s , 197 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF CIVIL ENGINEERING We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1982 O Thomas C. Gaard, 1982 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. I t i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of Cl^\ ^ ^ ^ . , 1 ^ The University of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date 32/ ^ J z. % DE-6 (3/81) 1 1 ABSTRACT A thorough d i s c u s s i o n of o f f s h o r e g r a v i t y type s t r u c t u r e s p r e s e n t l y being used, or c o n s i d e r e d f o r use i n the near f u t u r e by the o i l i n d u s t r y , i s presented, along with a b r i e f summary of the major types of s t r u c t u r e s now used o f f s h o r e . F a c t o r s a f f e c t i n g the s t a b i l i t y of o f f s h o r e g r a v i t y type s t r u c t u r e s are d i s c u s s e d , from the e v a l u a t i o n of a s u i t a b l e s i t e and the s e l e c t i o n of s o i l parameters, through i n s t a l l a t i o n and short-term foundation s a f e t y . A case study of the E k o f i s k tank i s i n c l u d e d t o show how g e o t e c h n i c a l concepts are a p p l i e d o f f s h o r e . A thorough d e s c r i p t i o n of wave l o a d i n g on o f f s h o r e g r a v i t y s t r u c t u r e s i s presented, i n c l u d i n g a d i s c u s s i o n on how the design storm i s used i n g e o t e c h n i c a l a n a l y s e s . E x i s t i n g s t a b i l i t y methods are reviewed. The m e r i t s and shortcomings of each method are d i s c u s s e d with r e s p e c t t o t h e i r a p p l i c a t i o n o f f s h o r e . Procedures f o r a n a l y z i n g the s t a b i l i t y of o f f s h o r e g r a v i t y type s t r u c t u r e s s u b j e c t e d t o storm wave l o a d i n g are developed based on the method of s l i c e s . Both Janbu's (1973) G e n e r a l i z e d Procedure of S l i c e s and Sarma's (1973) method are adapted f o r o f f s h o r e a n a l y s e s . The l a t t e r method i s mo d i f i e d to perform pseudo-three-dimensional a n a l y s e s . A computer program GRAVSTAB developed f o r t h i s purpose i s d e s c r i b e d and a p p l i e d to s e v e r a l example problems. The v e r s a t i l i t y of the method of a n a l y s i s i s demonstrated and r e s u l t s a re compared w i t h e x i s t i n g methods. i i i TABLE OF CONTENTS ABSTRACT i i TABLE OF CONTENTS .' i i i LIST OF TABLES v i LIST OF FIGURES v i i ACKNOWLEDGEMENTS x NOMENCLATURE x i CHAPTER 1 : INTRODUCTION 1 CHAPTER 2 : THE OFFSHORE GRAVITY TYPE STRUCTURE 11 2.1 General C h a r a c t e r i s t i c s 11 2.2 P l a t f o r m s For General O f f s h o r e Development 14 2.2.1 Concrete Platforms 15 2.2.2 S t e e l P l a t forms 18 2.2.3 H y b r i d P l a t f o r m s 23 2.3 P l a t f o r m s For A r c t i c Development 25 2.4 Deep Water Platforms And Other S t r u c t u r e s 27 2.5 Sources Of New P l a t f o r m Technology 30 CHAPTER 3 : DESIGN, CONSTRUCTION AND INSTALLATION 31 3.1 P r e l i m i n a r y C o n s i d e r a t i o n s 31 3.1.1 Sources Of Loading 31 3.1.1.1 Environmental Loads 31 3.1.1.2 O p e r a t i o n a l Loads 32 3.1.2 Environmental. Design Parameters 33 3.1.3 S i t e S e l e c t i o n And S o i l I n v e s t i g a t i o n s 34 3.1.4 S e l e c t i o n Of S o i l Parameters For Design 42 3.2 P l a t f o r m Design 46 i v 3.2.1 Hydrodynamic Analyses 46 3.2.2 G e o t e c h n i c a l Analyses 47 3.2.3 S t r u c t u r a l Requirements And Analyses 55 3.3 P l a t f o r m C o n s t r u c t i o n 57 3.4 P l a t f o r m I n s t a l l a t i o n 59 3.5 P l a t f o r m Instrumentation 63 CHAPTER 4. : THE EKOFISK TANK - A CASE STUDY 67 CHAPTER 5 : CHARACTERISTICS OF WAVE LOADING 93 5.1 Ocean Waves 93 5.1.1 The Wave Climate 93 5.1.2 Wave Th e o r i e s 94 5.1.3 R e s u l t s Of L i n e a r Wave Theory 97 5.2 C h a r a c t e r i z i n g The Wave System 97 5.2.1 O b t a i n i n g The Design Storm 100 5.2.1.1 S t a t i s t i c a l D e s c r i p t i o n 100 5.2.1.2 G e o t e c h n i c a l E q u i v a l e n t 101 5.2.2 A p p l i c a t i o n Of The Design Storm 102 5.3 Wave Loads On The Foundation System 104 5.3.1 Wave Forces A c t i n g On*The S t r u c t u r e 104 5.3.2 Wave Forces A c t i n g On The Foundation 108 5.4 E f f e c t Of C y c l i c Loading On The Foundation System ...109 CHAPTER 6 : PROCEDURES FOR ANALYZING THE STABILITY OF OFFSHORE GRAVITY TYPE STRUCTURES 115 6.1 Fundamental C o n s i d e r a t i o n s 115 6.2 M o d e l l i n g The Wav e - S t r u c t u r e - S o i l System 120 6.3 Loading A p p l i e d To The Foundation 126 6.4 A v a i l a b l e S t a b i l i t y Methods 128 6.4.1 C l a s s i c a l Bearing C a p a c i t y Approach 128 V 6.4.2 Other Bearing C a p a c i t y Formulations 136 6.4.3 NGI S l i p Surface Method 140 6.4.4 Method Of S l i c e s 144 6.4.5 F i n i t e Element Analyses 144 6.4.6 Model T e s t s 150 6.5 Summary 152 CHAPTER 7 : APPLICATION OF THE METHOD OF SLICES TO OFFSHORE GRAVITY STRUCTURE FOUNDATIONS 154 7.1 The Method Of S l i c e s 156 7.2 Loading A p p l i e d To The Foundation 158 7.3 Treatment Of The A p p l i e d H o r i z o n t a l Force 160 7.4 M o d i f i e d Janbu Method 161 7.4.1 Assumptions 161 7.4.2 D e r i v a t i o n Of E q u i l i b r i u m Equations .161 7.4.3 Working Formulas • 164 7.5 M o d i f i e d Sarma Method 167 7.5.1 Assumptions 169 7.5.2 D e r i v a t i o n Of E q u i l i b r i u m Equations 170 7.5.3 Working Formulas 173 CHAPTER 8 : EXAMPLES AND APPPLICATION OF ANALYSES 175 8.1 D e s c r i p t i o n Of Computer Procedure 175 8.2 Example 1 - A M u l t i - l a y e r e d Cohesive Deposit 177 8.3 Example 2 - A Co h e s i o n l e s s D e p o s i t : E k o f i s k Tank ....183 CHAPTER 9 : SUMMARY AND CONCLUSIONS 189 REFERENCES 194 LIST OF TABLES Table I - Comparison of F i x e d O f f s h o r e Platforms 16 Table II - North Sea Concrete G r a v i t y Platforms 19 Table I I I - G r a v i t y Platforms i n Other P a r t s of the World .. 20 Table IV - Environmental Design C r i t e r i a f o r Some Of f s h o r e Areas 35 Table V - G e o t e c h n i c a l Concerns f o r O f f s h o r e G r a v i t y Type Pl a t f o r m s 48 Table VI - Example of the Accumulated E f f e c t of a 100-year Storm 85 Table VII - Some R e s u l t s of L i n e a r Wave Theory 99 Table VIII - Comparison of E x i s t i n g S t a b i l i t y Analyses 153 Table IX - Geometry and Loading Data f o r Example 1 177 Table X - Comparison of Computed S a f e t y F a c t o r s f o r Example 1 179 Table XI - C o e f f i c i e n t s f o r E s t i m a t i n g Undrained Strength from T r i a x i a l Compression Data 182 Table XII - E f f e c t of Shear Zone Re p r e s e n t a t i o n on the Safety F a c t o r 184 Table XIII - Geometry and Loading Data f o r Example 2 185 Table XIV - E f f e c t of A-parameter on the Saf e t y F a c t o r 188 v i i LIST OF FIGURES F i g u r e 1.1 - S t e e l Jacketed Platforms 2 Fi g u r e 1.2 - Mobile Platforms 2 Fi g u r e 1.3 - The E k o f i s k Tank 5 Fi g u r e 2.1 - Components of an Off s h o r e G r a v i t y Type P l a t f o r m 13 Fi g u r e 2.2 - North Sea Concrete G r a v i t y Type O f f s h o r e Platforms 18 Fi g u r e 2.3 - Tecnomare S t e e l G r a v i t y Type O f f s h o r e P l a t f o r m 22 Fi g u r e 2.4 - Hybrid G r a v i t y Type Of f s h o r e P l a t f o r m s 24 Fi g u r e 2.5 - A r c t i c P l a t f o r m Designs 27 Fi g u r e 2.6 - Proposed Deep-water Platforms 29 Fi g u r e 3.1 - Loads A c t i n g on an Off s h o r e S t r u c t u r e 32 F i g u r e 3.2 - Plan of Survey L i n e s - G r i d : L o c a l Transverse , Mercator Spheroid 37 Fi g u r e 3.3 - T y p i c a l S o i l P r o f i l e as I d e n t i f i e d by Borehole, Cone P e n t r a t i o n Test and Gamma Ray Logging 43 Fi g u r e 3.4 - Comparison of Shear Strength Values from Sample T e s t i n g and from CPT 45 Fi g u r e 3.5 - P o s s i b l e F a i l u r e Modes f o r an O f f s h o r e G r a v i t y S t r u c t u r e Foundation 50 Fi g u r e 3.6 - P o s s i b l e Modes of S l i d i n g F a i l u r e 51 Fi g u r e 3.7 - S t a b i l i t y Diagram f o r a Raft Foundation 53 Fi g u r e 3.8 - I n s t a l l a t i o n Sequence f o r a G r a v i t y P l a t f o r m .. 60 Fi g u r e 3.9 - D e t a i l of CONDEEP Base S t r u c t u r e 61 F i g u r e 3.10 - Maximum Dome Contact Pressures Observed During I n s t a l l a t i o n of the " B e r y l A" CONDEEP 64 Fi g u r e 4.1 - D e t a i l of the E k o f i s k Tank Bottom 69 Fi g u r e 4.2 - Loads on the E k o f i s k Tank f o r the 100-Year Wave 71 v i i i F i g u r e 4.3 - Design Storm Data f o r the E k o f i s k F i e l d 71 F i g u r e 4.4 - T y p i c a l G e o t e c h n i c a l P r o f i l e from E k o f i s k F i e l d 72 F i g u r e 4.5 - Shear Strength Data from E k o f i s k 72 F i g u r e 4.6 - P r e d i c t e d Rocking Displacements f o r the E k o f i s k Tank 76 F i g u r e 4.7 - Load-Settlement Curve f o r E k o f i s k Tank 76 F i g u r e 4.8 - E k o f i s k Settlement Data R e l a t i n g Submerged P l a t f o r m Weight and Storm Wave Data i n the E a r l y Months A f t e r I n s t a l l a t i o n 79 F i g u r e 4.9 - Settlement Data f o r E k o f i s k Tank During E a r l y Storms 79 F i g u r e 4.10 - L o c a t i o n of Pressure Gauges and Piezometers Beneath E k o f i s k Tank 82 F i g u r e 4.11 - Pore Pressures Observed Under E k o f i s k Tank During the F i r s t Major Storm 82 F i g u r e 4.12 - Pore Pressure Rise per Cy c l e Observed i n Undrained Simple Shear with C y c l i c Loading f o r Samples Prepared with R e l a t i v e D e n s i t i e s of 80% 85 Fi g u r e 4.13 - T h e o r e t i c a l P r e d i c t i o n of the Pore Water Pressure D i s t r i b u t i o n Beneath the E k o f i s k Tank f o r R e l a t i v e D e n s i t i e s of 77% and 85% .... 90 F i g u r e 4.14 - Most C r i t i c a l F a i l u r e Surface Found i n S t a b i l i t y A n a l y s i s of E k o f i s k Tank f o r Wave Loads A p p l i e d Under Undrained C o n d i t i o n s 92 F i g u r e 5.1 - Regions of V a l i d i t y f o r V a r i o u s Wave The o r i e s . 98 F i g u r e 5.2 - P r o f i l e of an A i r y Wave 99 F i g u r e 5.3 - Forces A c t i n g on the Foundation of an Off s h o r e G r a v i t y S t r u c t u r e 105 F i g u r e 5.4 - T y p i c a l Design Storm Re p r e s e n t a t i o n Used i n Ge o t e c h n i c a l E n g i n e e r i n g 107 F i g u r e 5.5 - S t r e s s Path f o r a Foundation Element with P a r t i a l Drainage Subjected to Storm Wave Loading i l l F i g u r e 6.1 - E f f e c t i v e S t r e s s e s i n S o i l f o r S t i l l Water C o n d i t i o n s ( i . e . No Wave Loads) 118 F i g u r e 6.2 - D e f i n i t i o n Sketch of E f f e c t i v e Foundation 122 F i g u r e 6.3 - Transformation of Loads, to Foundation Base ....123 F i g u r e 6.4 - T h e o r e t i c a l Rupture Sur f a c e Geometry 129 F i g u r e 6.5 - Comparison of D i f f e r e n t Proposals f o r the Value of Nr 132 F i g u r e 6.6 - Geometry of Rupture Surface Used f o r an E f f e c t i v e S t r e s s Bearing Capacity S o l u t i o n ....138 F i g u r e 6.7 - Geometry of S l i d i n g Body Used by NGI ..141 F i g u r e 6.8 - Geometry of Bearing F a i l u r e Surface Used i n the NGI S l i p Surface Method 141 F i g u r e 6.9 - Comparison of Two- and Three-Dimensional D i s t o r t e d F i n i t e Element Meshes f o r an I n c l i n e d and E c c e n t r i c Load 148 F i g u r e 6.10 - E f f e c t of Load E c c e n t r i c i t y on E f f e c t i v e Bearing Area as E v a l u a t e d Using the F i n i t e Element 149 F i g u r e 7.1 - Repres e n t a t i o n of A n a l y s i s by the Method of S l i c e s 155 F i g u r e 7.2 - Geometry and Forces on a (Janbu) S l i c e 162 F i g u r e 7.3 - Curve Used f o r E v a l u a t i n g the Sa f e t y Factor ...169 F i g u r e 7.4 - Geometry and Forces on a (Sarma) S l i c e 171 F i g u r e 7.5 - T y p i c a l (Sarma) S l i c e Showing Side Forces 171 F i g u r e 8.1 - Shear St r e n g t h P r o f i l e f o r Example 1 178 F i g u r e 8.2 - C r i t i c a l Shear Surfaces f o r Example 1 as Evaluated by D i f f e r e n t S t a b i l i t y Methods 180 F i g u r e 8.3 - Zones of Shear on the P o t e n t i a l F a i l u r e Surface and Relevant Laboratory T e s t s 182 F i g u r e 8.4 - C r i t i c a l Shear Surface f o r Example 1 Found from Computer Program GRAVSTAB 184 F i g u r e 8.5 - D i s t r i b u t i o n of Pore Water Pressures i n Foundation S o i l Used i n Example 2 185 F i g u r e 8.6 - C r i t i c a l Shear Surface f o r Example 2 188 X ACKNOWLEDGEMENTS The author wishes to thank h i s a d v i s o r , P r o f e s s o r W.D. Liam F i n n f o r h i s t e c h n i c a l guidance and v a l u a b l e suggestions to improve the p r e s e n t a t i o n of t h i s t h e s i s . Dr. Yogi Vaid's comments throughout the t e x t were a l s o h e l p f u l i n packaging the f i n a l product. He would a l s o l i k e t o thank h i s a d v i s o r and Dr. M. de S t . Q. Isaacson f o r s t i m u l a t i n g h i s i n t e r e s t i n many aspec t s of o f f s h o r e e n g i n e e r i n g - a f i e l d which the author intends to pursue wholeheartedly. Thanks are a l s o due Dr. P.M. Byrne f o r many v a l u a b l e d i s c u s s i o n s regarding t h e o r e t i c a l aspects of s t a b i l i t y analyses among other t h i n g s . The program r o u t i n e i n GRAVSTAB used f o r a p p l y i n g Sarma's method to o f f s h o r e p l a t f o r m s i s an e x t e n s i o n of an e a r l i e r program STESL by K.W. Lee and W.D. Liam F i n n f o r the a n a l y s i s of the s t a b i l i t y of underwater s l o p e s . Funding f o r the computer s t u d i e s was p r o v i d e d by the N a t i o n a l Research C o u n c i l under grant No.1498 to P r o f e s s o r F i n n . T h i s a s s i s t a n c e was a p p r e c i a t e d . Permission to reproduce many of the f i g u r e s used in t h i s t h e s i s was k i n d l y granted by numerous people. To a l l my f r i e n d s i n Vancouver who made my l a s t two years worth more than an education (and bearable) you are not f o r g o t t e n . A f i n a l thanks to Dr. Isaacson f o r g i v i n g me an i n t e r e s t i n g job at t h i s u n i v e r s i t y that does not r e q u i r e a s u i t to be worn (ever) or a shave more than twice a week. x i NOMENCLATURE B 0 - e q u i v a l e n t foundation width B - e f f e c t i v e foundation width L 0 - e q u i v a l e n t foundation l e n g t h A 0 - p l a t f o r m base area D 0 - s k i r t depth below mudline fl' - e f f e c t i v e u n i t weight of s o i l P H - h o r i z o n t a l wave loa d on p l a t f o r m Pv - v e r t i c a l p l a t f o r m l o a d at s e a f l o o r APV - v e r t i c a l wave loa d on p l a t f o r m M - moment at s e a f l o o r Ap, - wave pressure on s e a f l o o r at t a i l end of p l a t f o r m Ap 2 - wave pressure on s e a f l o o r at nose end of p l a t f o r m PA - a c t i v e s o i l f o r c e on nose of foundation P p - p a s s i v e s o i l f o r c e on t a i l of foundation P w - water pressure f o r c e on t a i l of foundation Ps - shearing r e s i s t a n c e on s i d e s of foundation Pj - shearing r e s i s t a n c e on s o i l - s o i l i n t e r f a c e s at s i d e s V B T - v e r t i c a l l o a d at foundation base V B ~ V B T P e r u n ^ f c width H B T - h o r i z o n t a l l o a d at foundation base H B ~ H B T P e r u n i t width M f e T - moment a p p l i e d at foundation base h, - moment arm f o r a c t i v e or water pressure f o r c e h 2 - moment arm f o r p a s s i v e s o i l f o r c e x i i h 3 - moment arm f o r she a r i n g r e s i s t a n c e on foundation s i d e s e - e c c e n t r i c i t y H E T - h o r i z o n t a l f o r c e a p p l i e d to e f f e c t i v e area H E - H E T per u n i t width H S T - h o r i z o n t a l f o r c e a p p l i e d to s l i d i n g s u r f a c e H s - H S T per u n i t width F s - maximum shear r e s i s t a n c e a v a i l a b l e from s l i d i n g s u r f a c e per u n i t width g - l o a d i n c l i n a t i o n f a c t o r a - normal s t r e s s o" - e f f e c t i v e normal s t r e s s tr, - major p r i n c i p a l s t r e s s 0"3 - minor p r i n c i p a l s t r e s s u - t o t a l pore water pressure u s - s t a t i c pore water pressure u c - pore water pressure due to c y c l i c e f f e c t s Au - pore water pressure due to dynamic wave pressure z - depth below mudline A - pore water pressure parameter 0 - f r i c t i o n angle or m o b i l i z e d f r i c t i o n angle c - cohesion or m o b i l i z e d cohesion tan0 - f r i c t i o n a l r e s i s t a n c e or m o b i l i z e d f r i c t i o n r e s i s t a n c e c' - cohesion i n terms of e f f e c t i v e s t r e s s tan0' - f r i c t i o n a l r e s i s t a n c e i n terms of e f f e c t i v e s t r e s s F - f a c t o r of s a f e t y a p p l i e d to s t r e n g t h parameters c u - undrained shear s t r e n g t h - shear s t r e n g t h T - shear s t r e s s x i i i Qo - u l t i m a t e bearing c a p a c i t y q 0 - u l t i m a t e bearing p r e s s u r e q' - surcharge N - bearing c a p a c i t y f a c t o r f o r f r i c t i o n N - bearing c a p a c i t y f a c t o r f o r cohesion N - bearing c a p a c i t y f a c t o r f o r surcharge s- - bearing c a p a c i t y shape i n f l u e n c e f a c t o r s d- - bearing c a p a c i t y depth i n f l u e n c e f a c t o r s i - - bearing c a p a c i t y l o a d i n c l i n a t i o n i n f l u e n c e f a c t o r s {, - s l i c e number otj - angle made by top of i - t h s l i c e with h o r i z o n t a l ^ t - angle made by base of i - t h s l i c e with h o r i z o n t a l b^ - width of i - t h s l i c e xt- - x-c o o r d i n a t e of midpoint of top of i - t h s l i c e yt| - y - c o o r d i n a t e of midpoint of top of i - t h s l i c e xb^ - x-c o o r d i n a t e of midpoint of base of i - t h s l i c e yb^ - y - c o o r d i n a t e of midpoint of base of i - t h s l i c e xg^ - x-coor d i n a t e of c e n t r o i d of i - t h s l i c e yg^ - y - c o o r d i n a t e of c e n t r o i d of i - t h s l i c e xs- - x-coor d i n a t e of po i n t of a p p l i c a t i o n of s i d e f o r c e s f o r i - t h s l i c e y s c ~ y - c o o r d i n a t e of p o i n t of a p p l i c a t i o n of s i d e f o r c e s f o r i - t h s l i c e h ^ - height of i - t h s l i c e - v e r t i c a l o f f s e t of t h r u s t f o r c e s f o r i - t h s l i c e Ah£ - d i s t a n c e between base and l i n e of t h r u s t f o r i - t h s l i c e FV{, - v e r t i c a l f o r c e on top of i - t h s l i c e FT(. - t o t a l v e r t i c a l load on top of i - t h s l i c e FH: - h o r i z o n t a l f o r c e on top of i - t h s l i c e x i v FN-, - normal f o r c e on top of i - t h s l i c e F T C - t a n g e n t i a l f o r c e on top of i - t h s l i c e US^ - pore water f o r c e on base of i - t h s l i c e s s L - shear f o r c e on one s i d e of i - t h s l i c e x 2 - normal f o r c e on base of i - t h s l i c e N ; - e f f e c t i v e normal f o r c e on base of i - t h s l i c e Si - shear f o r c e on base of i - t h s l i c e E'v - l a t e r a l t h r u s t a p p l i e d t o i - t h s l i c e T'v - v e r t i c a l shear f o r c e at x=xj Q'v - assumed v e r t i c a l shear f o r c e at x=xj v; - v e r t i c a l r e s u l t a n t on base of i - t h s l i c e H ; - h o r i z o n t a l r e s u l t a n t on base of i - t h s l i c e wt - t o t a l s a t u r a t e d weight of i - t h s l i c e w;' - e f f e c t i v e weight of i - t h s l i c e UH; - r e s u l t a n t water f o r c e at x=xj - pore water pressure at base of i - t h s l i c e - normal s t r e s s on base of i - t h s l i c e - shear s t r e s s on base of i - t h s l i c e - shear s t r e n g t h at base of i - t h s l i c e - a v a i l a b l e cohesion on base of i - t h s l i c e tan0 'j - a v a i l a b l e f r i c t i o n a l r e s i s t a n c e on base of i -•th s l i c e = 1 - m o b i l i z e d cohesion on base of i - t h s l i c e tan0'^ - m o b i l i z e d f r i c t i o n a l r e s i s t a n c e on base of i - th s l i c e r t. - f a c t o r of s a f e t y on i n t e r s l i c e face f o r i -th s l i c e K - a c c e l e r a t i o n c o e f f i c i e n t as a f r a c t i o n of g r a v i t y X - v e r t i c a l shear f o r c e m u l t i p l i e r - K f o r a given f a c t o r of s a f e t y V CHAPTER 1 INTRODUCTION The i n c r e a s e i n g l o b a l energy consumption and the p r e v a i l i n g g e o p o l i t i c a l c l i m a t e i n the world have had d i s a s t r o u s e f f e c t s on the cost and a v a i l a b i l i t y of petroleum to most consumers. T h i s , along with the western world's d e s i r e to be energy s e l f - s u f f i c i e n t , has l e d to the development of energy re s o u r c e s which were p r e v i o u s l y c o n s i d e r e d to be uneconomical. In an e f f o r t to meet the goals of energy s e l f - s u f f i c i e n c y and (indeed) a v a i l a b i l i t y , o i l companies have in recent years been i n c r e a s i n g t h e i r e x p l o i t a t i o n of the vast r e s e r v e s of o i l and gas that e x i s t beneath the c o n t i n e n t a l shelves of the world's oceans. As c o n s u l t a n t s to the o i l companies, engineers are r e q u i r e d to (1) provide the t e c h n i c a l input necessary f o r the implementation of hydrocarbon recovery schemes, and (2) to develop r e l i a b l e methods f o r the design, a n a l y s i s , and i n s t a l l a t i o n of the necessary o f f s h o r e s t r u c t u r e s . O f f s h o r e p l a t f o r m s have been i n e x i s t e n c e s i n c e the 1920s when o i l was d i s c o v e r e d at Lake Maracaibo, Venezuela. These s t r u c t u r e s , u s u a l l y made of con c r e t e and p i l e d i n t o the s o f t nearshore sediments, were crude by today's standards but are important i n that they c o n s t i t u t e d the beginning of the o f f s h o r e o i l i n d u s t r y (Bjerrum, 1973). The f i r s t "deep-water" f i x e d p l a t f o r m s c o n s t r u c t e d were the s t e e l j a c k e t or template type s t r u c t u r e s , s i m i l a r to those shown in f i g u r e 1.1 used i n the Gulf of Mexico, of which some s e v e r a l hundred have been b u i l t B) SELF-FLOATER A) CONVENTIONAL TYPE F i g u r e 1.1 - S t e e l j a c k e t e d o f f s h o r e p l a t f o r m s ( A f t e r McPhee and Reeves, 1975) 3 there s i n c e the 1960s. These p l a t f o r m s are a l s o f a m i l i a r s i g h t s i n other p a r t s of the world, namely: Lake Maracaibo, the P e r s i a n G u l f , the North Sea, the Java Sea, the Gulf of Guinea, o f f s h o r e C a l i f o r n i a , and to a l e s s e r extent, other l o c a t i o n s (Martin and Shaw, 1974). Semi-submersible and jackup type e x p l o r a t o r y d r i l l i n g r i g s such as the ones shown i n f i g u r e 1.2 are a l s o i n widespread use throughout the world. In 1969, when the P h i l l i p s Petroleum Company d i s c o v e r e d the f i r s t commercial o i l f i e l d (the E k o f i s k f i e l d ) i n the northern North Sea, engineers were faced with some new and d i f f i c u l t problems when d e s i g n i n g the necessary s t r u c t u r e s f o r the development of t h i s f i e l d . Because of the extreme h o s t i l i t y of the northern North Sea (24 meter high waves at t h i s l o c a t i o n ) and the lack of nearby harbors (the c l o s e s t being n e a r l y 320 k i l o m e t e r s away) the need arose f o r a pro d u c t i o n p l a t f o r m i n c l o s e p r o x i m i t y to the d r i l l i n g p l a t f o r m s (which were to be of the c o n v e n t i o n a l j a c k e t type) which c o u l d f u n c t i o n as a storage f a c i l i t y i n poor weather when tanker l o a d i n g would-be impossible (Bjerrum, 1973). From t h i s need came the f i r s t o f f s h o r e g r a v i t y type p r o d u c t i o n p l a t f o r m ; t h i s i s the famed E k o f i s k tank designed by the C. G. D o r i s Company of France. The tank i s shown being towed from the Norwegian coast to i t s home i n the northern North Sea i n f i g u r e 1.3. I n t e r e s t i n g r a v i t y type p r o d u c t i o n p l a t f o r m s has i n c r e a s e d s t e a d i l y s i n c e 1973 when the E k o f i s k tank was i n s t a l l e d , p r i m a r i l y because of the short i n s t a l l a t i o n time r e q u i r e d f o r a g r a v i t y type s t r u c t u r e (no p i l i n g necessary i n the u n p r e d i c t a b l e North Sea) and the s u c c e s s f u l o p e r a t i o n of the E k o f i s k tank 4 F i g u r e 1.3 - The E k o f i s k tank (See f o l l o w i n g page) (Reproduced with p e r m i s s i o n of the Royal I n s t i t u t e of Naval A r c h i t e c t s , London.)  6 si n c e i n s t a l l a t i o n , i n c l u d i n g a good performance through a major storm (90% of the design storm) which occ u r r e d s i x months a f t e r i t was i n s t a l l e d (Marion, 1974). More than twenty other g r a v i t y p l a t f o r m s have been i n s t a l l e d to date i n the North Sea and other areas of the world (Waagaard, 1977). The E k o f i s k tank was the f i r s t o f f s h o r e g r a v i t y type p l a t f o r m but not the f i r s t g r a v i t y type s t r u c t u r e used o f f s h o r e . G r a v i t y type l i g h t towers had been used e x t e n s i v e l y i n Sweden f o r many years p r i o r to 1973 i n shallower, nearshore waters, u s u a l l y 20 meters deep or l e s s (Stubbs, 1975). The Royal Sovereign l i g h t tower i n the E n g l i s h Channel i s perhaps a more f a m i l i a r example' of a pre-1973 g r a v i t y type s t r u c t u r e . These are r e l a t i v e l y s m a l l s t r u c t u r e s which r e q u i r e d few new design concepts, and c o n s t r u c t i o n and i n s t a l l a t i o n techniques at the time that they were i n s t a l l e d . The i n s t a l l a t i o n of the E k o f i s k tank, however, was a milestone i n e n g i n e e r i n g design and marked a new era f o r o f f s h o r e g r a v i t y s t r u c t u r e s . T h i s tank r e q u i r e d many new design procedures, c o n s t r u c t i o n methods, and i n s t a l l a t i o n techniques that had to be developed s p e c i f i c a l l y f o r these purposes (Bjerrum, 1973; Gerwick and Hognstad, 1973; Marion, 1974). In recent y e a r s , North American engineers have been p l a y i n g an i n c r e a s i n g r o l e i n the development of o f f s h o r e g r a v i t y s t r u c t u r e technology, although few are f o r m a l l y t r a i n e d i n the are a . With i n c r e a s i n g e x p l o r a t i o n and u t i l i z a t i o n of o i l and gas resources o f f the North American c o a s t , the need f o r g e o t e c h n i c a l engineers with a good working knowledge of o f f s h o r e e n g i n e e r i n g w i l l undoubtedly i n c r e a s e on t h i s c o n t i n e n t . 7 The purposes of t h i s t h e s i s are t h r e e f o l d : (1) to introduce the g e o t e c h n i c a l engineer to the f i e l d of o f f s h o r e e n g i n e e r i n g , s p e c i f i c a l l y , to f a m i l i a r i z e him with the s p e c i a l problems a s s o c i a t e d with g r a v i t y s t r u c t u r e s , (2) to present an overview of e x i s t i n g s t a b i l i t y methods a p p l i c a b l e to o f f s h o r e g r a v i t y type s t r u c t u r e s , and (3) to develop an a l t e r n a t i v e procedure f o r a n a l y z i n g the s t a b i l i t y of an o f f s h o r e g r a v i t y s t r u c t u r e s u b j e c t e d to storm wave l o a d i n g . T h i s t h e s i s may be d i v i d e d i n t o two s e c t i o n s . Chapters 2-5 dea l with the f i r s t c o n s i d e r a t i o n , a general background i n o f f s h o r e e n g i n e e r i n g . The second p a r t of t h i s t h e s i s , Chapters 6-8, i s concerned wholly with the t o p i c of foundation s t a b i l i t y under storm wave l o a d i n g . The p r e l i m i n a r y chapters serve a dual purpose. F i r s t , they serve to gi v e the reader u n f a m i l i a r with o f f s h o r e e n g i n e e r i n g a good working knowledge of o f f s h o r e g r a v i t y s t r u c t u r e s . Secondly, they p r o v i d e him with an a p p r e c i a t i o n of the o f f s h o r e environment and the s p e c i a l design and i n s t a l l a t i o n requirements f o r g r a v i t y type s t r u c t u r e s . T h i s i s necessary so that the foundation analyses may be viewed i n p e r s p e c t i v e . The aim of the s e c t i o n on foundation s t a b i l i t y under storm wave l o a d i n g i s to present an overview of the s t a b i l i t y methods p r e s e n t l y a v a i l a b l e f o r performing such analyses and to demonstrate the need f o r and then develop a simple, p r a c t i c a l a l t e r n a t i v e method f o r e f f e c t i v e s t r e s s a n a l y s e s . Chapter 2 serves as an i n t r o d u c t i o n to o f f s h o r e g r a v i t y type s t r u c t u r e s . The ge n e r a l c h a r a c t e r i s t i c s of a g r a v i t y 8 s t r u c t u r e are d e s c r i b e d and the major types of p l a t f o r m s are d i s c u s s e d i n some d e t a i l . Chapter 3 i s concerned with the design, c o n s t r u c t i o n , and i n s t a l l a t i o n requirements f o r these s t r u c t u r e s . F i r s t , the sources of l o a d i n g i n the o f f s h o r e environment are o u t l i n e d . Next, the s i t e s e l e c t i o n , the o f f s h o r e s i t e i n v e s t i g a t i o n and the s e l e c t i o n of g e o t e c h n i c a l s o i l parameters i s d i s c u s s e d i n depth. P l a t f o r m design requirements (hydrodynamic, s t r u c t u r a l , and g e o t e c h n i c a l ) , c o n s t r u c t i o n techniques and i n s t a l l a t i o n procedures are then d e l i n e a t e d . A short s e c t i o n on p l a t f o r m i n s t r u m e n t a t i o n f i n i s h e s o f f t h i s c h a pter. Chapter 4 presents a g e o t e c h n i c a l case study of the E k o f i s k tank. T h i s chapter serves the purposes of demonstrating how g e o t e c h n i c a l analyses are a p p l i e d o f f s h o r e and how performance o b s e r v a t i o n s may be used as a check on design assumptions and p r e d i c t i o n s . Chapter 5, the f i n a l chapter i n the f i r s t p a r t of t h i s t h e s i s , d e a l s with wave l o a d i n g on g r a v i t y p l a t f o r m s . A b r i e f d i s c u s s i o n of the wave c l i m a t e i s given and the mode l l i n g of ocean waves by wave t h e o r i e s and s t a t i s t i c a l means i s d i s c u s s e d . The g e o t e c h n i c a l e q u i v a l e n t of the s t a t i s t i c a l design storm, that which i s used f o r c y c l i c l o a d i n g s t u d i e s and to determine the maximum l o a d , i s given p a r t i c u l a r a t t e n t i o n . F i n a l l y , the c h a r a c t e r i s t i c s of wave l o a d i n g on the foundation system are d i s c u s s e d as they p e r t a i n t o foundation a n a l y s e s . T h i s chapter a l s o serves as an i n t r o d u c t i o n to the next s e c t i o n . Chapter 6 presents the q u a n t i t a t i v e aspects of wave l o a d i n g on the foundation system. Methods of determining p l a t f o r m 9 s t a b i l i t y under storm wave l o a d i n g are then d i s c u s s e d ; the m e r i t s and shortcomings of each method when a p p l i e d to the o f f s h o r e g r a v i t y s t r u c t u r e are emphasized. I t becomes c l e a r that there are two fundamental a n a l y t i c a l l i n e s of approach to the problem: bearing c a p a c i t y theory and the f i n i t e element method. A simple to use l i m i t e q u i l i b r i u m method f o r t o t a l s t r e s s a n a l y s e s of c l a y foundations c a l l e d the NGI (Norwegian G e o t e c h n i c a l I n s t i t u t e ) s l i p s u r f a c e method i s d e s c r i b e d i n d e t a i l . In Chapter 7 an a l t e r n a t i v e method of a n a l y s i s based on the method of s l i c e s i s presented. T h i s method i s along the l i n e s of the NGI method. I t i s a pseudo-three-dimensional e f f e c t i v e s t r e s s method based on Sarma's (1973) method of s l i c e s . Sarma's method of s l i c e s i s not w e l l known among p r a c t i c i n g engineers and hence Janbu's (1973) method of s l i c e s i s a l s o adapted to perform a g r a v i t y s t r u c t u r e s t a b i l i t y a n a l y s i s , although only i n two dimensions. T h i s was done so that e x i s t i n g slope s t a b i l i t y programs may be mo d i f i e d to perform some of the analyses and a l s o to i n s t a l l f a i t h i n the use of Sarma's s l i c e method. In Chapter 8 a computer program GRAVSTAB developed to perform these analyses i s d e s c r i b e d and s e v e r a l example problems are worked. The a p p l i c a t i o n of the method to both a t o t a l s t r e s s a n a l y s i s and an e f f e c t i v e s t r e s s a n a l y s i s i s made. The v e r s a t i l i t y of the method i s shown. T h i s method i s of great p r a c t i c a l v alue f o r working these types of problems. The d i s c u s s i o n of g r a v i t y s t r u c t u r e s presented h e r e i n , although p r i m a r i l y concerned with p l a t f o r m s , i s g e n e r a l l y a p p l i c a b l e t o a l l l a r g e g r a v i t y type o f f s h o r e s t r u c t u r e s . The 10 a n a l y t i c a l procedures d i s c u s s e d and developed i n t h i s t h e s i s are a p p l i c a b l e to any o f f s h o r e s t r u c t u r e with a m o n o l i t h i c g r a v i t y type base, whether i t i s a p l a t f o r m , l i g h t tower, f l a r e s t r u c t u r e or other f a c i l i t y . 1 1A f l a r e s t r u c t u r e i s used f o r burning o f f excess gases, p r i m a r i l y methane, produced along with o i l from a w e l l . 11 CHAPTER 2 THE OFFSHORE GRAVITY TYPE STRUCTURE The f o l l o w i n g d i s c u s s i o n of o f f s h o r e g r a v i t y type s t r u c t u r e s i n c l u d e s a l l the major types of g r a v i t y s t r u c t u r e s p r e s e n t l y i n use and those which are being s e r i o u s l y c o n s i d e r e d by the . o i l i n d u s t r y f o r use throughout the world i n the near f u t u r e . 2.1 General C h a r a c t e r i s t i c s A g r a v i t y type s t r u c t u r e r e s t s d i r e c t l y on the seabed and has no subsurface foundation other than shallow s k i r t s and r i b s which portrude through the upper sediments to t r a n s f e r the h o r i z o n t a l component of the d i s t u r b i n g f o r c e to deeper, stronger s u b s o i l s . In areas where the s u r f i c i a l sediments have adequate s t r e n g t h to prevent s l i d i n g or the r a f t foundation i s excavated, s k i r t s or r i b s may not be present (Huntemann et a l , 1979). S k i r t s have the added f e a t u r e s of p r o v i d i n g scour p r o t e c t i o n from c u r r e n t s and wave induced water motions and c o n t a i n i n g grout which i s used d u r i n g i n s t a l l a t i o n . They are t h e r e f o r e u s u a l l y necessary u n l e s s the foundation has been excavated. To prevent s l i d i n g at the base of the s t r u c t u r e or a shear f a i l u r e beneath the s t r u c t u r e , a v e r t i c a l f o r c e on the foundation must be maintained i n some p r o p o r t i o n to the maximum h o r i z o n t a l l o a d . T h i s i s accomplished by u s i n g a s t r u c t u r e of ample weight with respect to the h o r i z o n t a l f o r c e s expected - hence the name g r a v i t y s t r u c t u r e . 12 There are g e n e r a l l y three d i s t i n c t p a r t s of a l a r g e g r a v i t y p l a t f o r m : the base c a i s s o n , the towers, and the deck. A t y p i c a l North Sea concrete g r a v i t y p l a t f o r m i s shown i n f i g u r e 2.1. Other g r a v i t y p l a t f o r m s , although somewhat d i f f e r e n t , have many of the same f e a t u r e s as the one shown. The deck i s used as a work area and o f t e n houses l i v i n g q u a r t e r s f o r the men who s e r v i c e the p l a t f o r m equipment. The s p e c i f i c equipment on the deck depends on the exact use of the p l a t f o r m . F a c i l i t i e s f o r f r e s h water storage and other p l a t f o r m requirements are o f t e n housed i n the towers. The w e l l r i s e r s may a l s o be contained w i t h i n the l e g s . 2 The base c a i s s o n i s used d u r i n g i n s t a l l a t i o n as a buoyancy chamber; the c a i s s o n i s made up of a number of c e l l s ( e i t h e r outwardly apparent as with the p l a t f o r m shown i n f i g u r e 2.1, or compartmented w i t h i n the c a i s s o n as with the E k o f i s k tank shown i n f i g u r e 1.3) which are used to s y s t e m a t i c a l l y b a l l a s t the s t r u c t u r e . The s k i r t s are d r i v e n i n t o the foundation s o i l and the s t r u c t u r e i s f i r m l y seated by i n c r e a s i n g the b a l l a s t . The c e l l s are used as both b a l l a s t tanks and o i l storage f a c i l i t i e s when the s t r u c t u r e i s o p e r a t i o n a l . These p l a t f o r m s are g e n e r a l l y massive s t r u c t u r e s , p a r t i c u l a r l y those p l a t f o r m s designed f o r the North Sea. The l a r g e s t of the North Sea g i a n t s , a D o r i s type s t r u c t u r e p l a c e d i n the U. K.'s N i n i a n f i e l d i n 1978, weighed 600,000 tons 2 R i s e r s are pipes through which crude o i l flows out from the w e l l and up to the p l a t f o r m i n to be processed, pumped, or s t o r e d . 13 F i g u r e 2.1 - Components of an o f f s h o r e g r a v i t y type p l a t f o r m (Adapted from K l i t z , 1980) 14 (Steven, 1981a). T h i s p l a t f o r m i s t a l l e r than a 50 s t o r y b u i l d i n g from the base to the deck (not i n c l u d i n g the deck equipment) and n e a r l y as wide at the base. A Sea Tank type s t r u c t u r e a l s o p l a c e d i n U. K. waters i n 1978 holds the depth r e c o r d f o r a g r a v i t y p l a t f o r m - 152 meters (Furnes, 1978). Other g r a v i t y p l a t f o r m s i n the North Sea are n e a r l y as l a r g e , and although the p l a t f o r m s i n other o f f s h o r e areas are a p p r e c i a b l y s m a l l e r , they are s t i l l very l a r g e indeed. C l e a r l y these are enormous s t r u c t u r e s with unusual design and c o n s t r u c t i o n requirements. 2.2 P l a t f o r m s f o r General O f f s h o r e Development S t e e l j a c k e t e d s t r u c t u r e s and g r a v i t y p l a t f o r m s form the core of s t r u c t u r e s p r e s e n t l y used i n o f f s h o r e hydrocarbon r e c o v e r y . 3 The j a c k e t e d s t r u c t u r e s are much more numerous. G e n e r a l l y , the s t e e l j a c k e t e d s t r u c t u r e , and the g r a v i t y s t r u c t u r e s d i s c u s s e d i n the f o l l o w i n g s u b s e c t i o n s , w i l l not be used i n water depths g r e a t e r than about 250 to 300 meters. In deeper water, other types of s t r u c t u r e s w i l l be used. 3 A j a c k e t e d s t r u c t u r e was s u c c e s s f u l l y p l a c e d in 312 meters of water i n the Gulf of Mexico i n 1980 (Morrison, 1980a). The i n s t a l l a t i o n of t h i s type of s t r u c t u r e i n water of that depth i s not seen as a t r e n d f o r the f u t u r e . The use of t h i s type of s t r u c t u r e was economically j u s t i f i e d s i n c e the p r i o r i t y was a l a r g e number of w e l l s which t h i s p l a t f o r m , with i t s l a r g e base area, was a b l e to p r o v i d e (Morrison, 1980b). S e v e r a l other j a c k e t e d p l a t f o r m s i n s i m i l a r water depths are planned f o r use i n the Santa Barbara channel. A l t e r n a t i v e p l a t f o r m designs such as those d i s c u s s e d i n s e c t i o n 2.4 are not f u l l y developed y e t . 15 2.2.1 Concrete Platforms The c o n c r e t e ( r e i n f o r c e d and p r e s t r e s s e d ) g r a v i t y type p l a t f o r m was designed to meet s p e c i f i c requirements f o r the development of the E k o f i s k f i e l d i n the North Sea. S t e e l j a c k e t e d p l a t f o r m s , the o n l y f i x e d o f f s h o r e p l a t f o r m s e x i s t i n g at t h a t time, c o u l d not be m o d i f i e d to i n c l u d e the r e q u i r e d amount of storage. T h i s requirement f o r storage was the primary reason that the g r a v i t y type p l a t f o r m was developed and remains as an important f a c t o r when choosing between s t e e l j a c k e t e d and g r a v i t y type s t r u c t u r e s f o r f i e l d development. I t should be remembered that the g r a v i t y s t r u c t u r e i s an a l t e r n a t i v e to the s t e e l j a c k e t e d p l a t f o r m , not a replacement f o r i t . The two p l a t f o r m types are q u i t e d i f f e r e n t and g e n e r a l l y a p p l i c a b l e to d i f f e r e n t design and p r o d u c t i o n c o n s i d e r a t i o n s . A b r i e f comparison of the concrete g r a v i t y type p l a t f o r m and the s t e e l j a c k e t e d p l a t f o r m , the two most common types of ( l a r g e ) f i x e d o f f s h o r e s t r u c t u r e s , i s presented in Table I. Concrete was the f i r s t m a t e r i a l used f o r b u i l d i n g g r a v i t y type pl a t f o r m s and remains the most common f o r a v a r i e t y of reasons, some being: c o n s t r u c t i o n techniques r e q u i r e l e s s s k i l l e d labor than steelwork, the a v a i l a b i l i t y of concrete i s g e n e r a l l y b e t t e r than that of high grade s t r u c t u r a l s t e e l s , and c o n c r e t e i s more c o r r o s i o n r e s i s t a n t and has a longer f a t i g u e l i f e than s t e e l i n the marine environment (Stubbs, 1975). The l a t t e r two reasons are very important s i n c e maintenance i s expensive and r e p a i r s are d i f f i c u l t , i f even p o s s i b l e , o f f s h o r e ( B i l l i n g t o n , 1979). 16 Table I Comparison of F i x e d O f f s h o r e Platforms STEEL JACKETED PLATFORM CONCRETE GRAVITY PLATFORM ADVANTAGES -Much i n d u s t r y experience - G e n e r a l l y cheaper f o r m i l d environments -Design l e s s s i t e - s p e c i f i c -More f l e x i b l e to changes d u r i n g f a b r i c a t i o n -Good f o r areas with deep s o f t sediments ADVANTAGES -Requires l i t t l e s p e c i a l i z e d l a b o r -Greater p r o d u c t i o n c a p a c i t y -Easy to i n c o r p o r a t e storage -Short i n s t a l l a t i o n time -Larger deck -Almost complete at tow-out f o r e a r l y p r o d u c t i o n s t a r t -Longer f a t i g u e l i f e -More c o r r o s i o n r e s i s t a n t DISADVANTAGES -Requires very s k i l l e d l a b o r -Long, c o s t l y i n s t a l l a t i o n s -Hard to pr o v i d e storage - R e l i e s on the a v a i l a b i l i t y of high-grade s t e e l - D i f f i c u l t to i n s p e c t f o r damage -Need more deep borings -Problems with d r i v i n g l a r g e diameter p i l e s - S h o r t e r f a t i g u e l i f e -Less c o r r o s i o n r e s i s t a n t PISADVANTAGES - I n f l e x i b l e to des i g n / c o n s t , changes-very s i t e s p e c i f i c -Design more c r i t i c a l to s p e c i f i c water depth -Seabed must be r e l a t i v e l y f l a t and l e v e l -Requires good bearing s o i l s -Need good knowledge of shallow sediments Adapted from B e l l (1974). 17 As of 1981, fourteen concrete g r a v i t y type p l a t f o r m s have been i n s t a l l e d i n the North Sea (Furnes, 1978; Steven, 1981b). These p l a t f o r m s are of four d i f f e r e n t types: the D o r i s , Andoc, CONDEEP, and Sea Tank de s i g n s . The D o r i s design i s that of the E k o f i s k tank (shown i n f i g u r e 1.3) and looks somewhat d i f f e r e n t in g eneral appearance than the other North Sea designs shown i n f i g u r e 2.2. Design c o n d i t i o n s , a n a l y s i s techniques, and c o n s t r u c t i o n methods a r e , however, v i r t u a l l y the same f o r a l l these p l a t f o r m s . Each p l a t f o r m type was m o d i f i e d somewhat f o r the s p e c i f i c o n - s i t e design c r i t e r i a : design wave h e i g h t , water depth, and p r o d u c t i o n requirements (storage c a p a c i t y and deck i n s t a l l a t i o n s ) . Hence, the s i z e and shape of each p l a t f o r m i s d i s t i n c t . A summary of these p l a t f o r m s i s given i n Table II along with some of t h e i r important f e a t u r e s . Three concrete g r a v i t y p l a t f o r m s have been b u i l t o f f the coast of B r a z i l (Franco, 1976) and one o f f s h o r e L o u i s i a n a (Huntemann et a l , 1979). These p l a t f o r m s are box-shaped and s i g n i f i c a n t l y s m a l l e r than the p e d e s t a l shaped North Sea g i a n t s . Four s t e e l g r a v i t y type p l a t f o r m s o f f the Congo coast ( L a l l i , 1977), and a f l a r e o f f s h o r e B r a z i l (Burns and D'Amorim, 1977), are the only other l a r g e o f f s h o r e g r a v i t y type s t r u c t u r e s i n the world o u t s i d e of the North Sea. A l i s t of these p l a t f o r m s , a l s o g i v i n g some of t h e i r important f e a t u r e s , i s given i n Table I I I . G r a v i t y p l a t f o r m s made of m a t e r i a l s other than c o n c r e t e are p r i m a r i l y s p e c i a l designs f o r p a r t i c u l a r a p p l i c a t i o n s . T h i s i s e s p e c i a l l y t r u e of the a l l - s t e e l g r a v i t y s t r u c t u r e . A) CONDEEP DESIGN B) SEATANK DESIGN C) ANDOC DESIGN Fig. 2.2 North Sea concrete gravity type offshore platforms (Compiled from Sjoerdsma, 1975a) 00 19 Table II North Sea Concrete G r a v i t y Platforms DESIGN FIELD/ COUNTRY WATER DEPTH DESIGN WAVE BASE WIDTH PURPOSE DATE D o r i s E k o f i s k (Norway) 70 24.0 93 P-S 1973 CONDEEP B e r y l A (U.K.) 120 29.5 100 D-P-S 1975 CONDEEP Brent B (U.K.) 142 30.5 100 D-P-S 1975 D o r i s F r i g g CDP1 (U.K.) 96 29.0 101 D 1975 Sea Tank F r i g g TP1 (U.K.) 104 29.0 72 P 1976 D o r i s F r i g g MP2 (U.K.) 94 29.0 101 B 1976 CONDEEP Brent D (U.K.) 142 . 30.5 100 D-P-S 1976 Andoc Dunl i n A (U.K./Hoi.) 152 30.5 104 D-P-S 1977 CONDEEP S t a t f j o r d A (Norway) 149 30.5 1 10 D-P-S 1 977 CONDEEP F r i g g TCP2 (Norway) 1 04 29.0 100 T-B-P 1 977 D o r i s N i n i a n (U.K.) 139 31.2 140 D-P 1978 Sea Tank Brent C (U.K.) 142 30.5 100 D-P-S 1 978 Sea Tank Cormorant A (U.K.) 152 30.5 100 D-P-S 1978 CONDEEP S t a t f j o r d B (Norway) 144 30.5 152 D-P-S 1981 D = D r i l l i n g P=Production S=Storage T=Treatment B=Booster Note: A l l dimensions are i n meters. Adapted from Furnes (1978). 20 Table I I I G r a v i t y P l a tforms i n Other P a r t s of the World DESIGNER/ CONSTRUCTION FIELD/ COUNTRY WATER DEPTH DESIGN WAVE BASE SIZE PURPOSE DATE Tecnomare ( S t e e l ) Loango (Congo) 89 9.4 3@ 1 8 1 D 1976 Tecnomare ( S t e e l ) Loango (Congo) 89 9.4 3@ 1 8 1 D 1976 Tecnomare ( S t e e l ) Loango (Congo) 89 9.4 3@1 8 1 D 1976 Tecnomare ( S t e e l ) Loango (Congo) 89 9.4 3§18' P 1977 Petrobas (Cone-Box) RGdeNorte ( B r a z i l ) 13 ? 46x53 D-P 1978 Petrobas (Cone-Box) RGdeNorte ( B r a z i l ) 13 ? 46x53 D-P 1978 Petrobas (Cone-Box) RGdeNorte ( B r a z i l ) 13 ? 46x53 D-P 1978 ARCO (Cone-Box) L o u i s i a n a (U.S.A.) 4 ? 23x34 D-P 1978 'This design has three base pads ( t r i p o d ) Note: D = D r i l l i n g P=Production Note: A l l dimensions are i n meters. Note: T h i s l i s t may be incomplete. 21 2.2.2 S t e e l Platforms S t e e l g r a v i t y p l a t f o r m s s i m i l a r to the one shown i n f i g u r e 2.3 were f i r s t i n s t a l l e d o f f the Congo coast in 1976 ( L a l l i , 1977) and are p r e s e n t l y being b u i l t f o r other l o c a t i o n s , i n c l u d i n g one f o r the North Sea (Agostoni et a l , 1980).* These p l a t f o r m s have some unique f e a t u r e s which were developed to s o l v e some s p e c i a l foundation problems. The s t e e l g r a v i t y p l a t f o r m was developed f o r use i n the Loango f i e l d o f f the Congo coast ( L a l l i , 1977), 5 Seabed c o n d i t i o n s there c o n s i s t of a rocky uneven bottom (McPhee and Reeves, 1975) which i s too hard f o r p i l e s to be d r i v e n i n t o and too u n y i e l d i n g l y uneven f o r the base s l a b of a concrete s t r u c t u r e . The only type of s t r u c t u r e that c o u l d be p l a c e d e c o n o m i c a l l y on the rocky seabed and provide the r e q u i r e d amount of storage was a s t e e l - b a s e d g r a v i t y p l a t f o r m on base pads. ( P i l e d r i v i n g i n these sediments would r e q u i r e a l l prebored h o l e s , a lengthy and expensive o p e r a t i o n . ) The Tecnomare p l a t f o r m , with i t s t r i p o d arrangement of l e g s , may be used i n areas where the seabed i s uneven or i n c l i n e d by j a c k i n g up the l e g s to compensate f o r d i f f e r e n c e s i n topography (Offshore "The i n s t a l l a t i o n of t h i s p l a t f o r m has been delayed due to numerous problems, i n c l u d i n g a s t r i k e at the c o n s t r u c t i o n yard. The p l a t f o r m i s not expected to produce before 1983 or 1984 (Steven, 1981c). 5The p l a t f o r m was i n i t i a l l y c o nceived f o r general o f f s h o r e areas and l a t e r f o r c o n s i d e r a t i o n i n the S i c i l i a n channel; however, none of these p l a t f o r m s were ever b u i l t . The p l a t f o r m was f u l l y developed f o r use o f f the Congo coast where i t was f i r s t i n s t a l l e d . 22 F i g u r e 2.3 - Tecnomare s t e e l g r a v i t y type o f f s h o r e p l a t f o r m ( A f t e r L a l l i , 1975) 23 Europe, 1974). Since no h i g h l y s k i l l e d l a b o r f o r c e was a v a i l a b l e i n the Congo, the p l a t f o r m s had to be b u i l t i n Europe and towed the 8500 k i l o m e t e r s to the Congo. Towing speed and s t a b i l i t y requirements c o n t r i b u t e d to the design shape. A s t e e l g r a v i t y p l a t f o r m was chosen f o r the Maureen f i e l d i n the North Sea p r i m a r i l y because of r e s e r v o i r c o n s i d e r a t i o n s ( L a l l i , 1977). The Maureen f i e l d i s a s o - c a l l e d marginal f i e l d , t h a t i s , one which has very l i m i t e d p o t e n t i a l . Since p i p e l i n e s are not economically j u s t i f i e d , storage i s r e q u i r e d . In the event that the f i e l d i s not p r o f i t a b l e , the s t r u c t u r e may be removed and r e l o c a t e d to a comparable s i t e with a minimum of s t r u c t u r a l damage; s t e e l was chosen over c o n c r e t e f o r t h i s reason. U n f o r t u n a t e l y , s t e e l , g r a v i t y p l a t f o r m s s u f f e r from many of the same setbacks as s t e e l j a c k e t e d p l a t f o r m s , p r i m a r i l y s t e e l c o s t and a v a i l a b i l i t y , and the need f o r a h i g h l y s k i l l e d l a b o r f o r c e to b u i l d them. Hence, they w i l l remain as an a l t e r n a t i v e to the concrete s t r u c t u r e , not a replacement f o r i t . 2.2.3 Hybrid Platforms The h y b r i d g r a v i t y p l a t f o r m (Hansen and I n g e r s l e v , 1977; McPhee and Reeves, 1975) c o n s i s t s of a s t e e l space frame mounted on a co n c r e t e r a f t . Two d i f f e r e n t p l a t f o r m designs are shown in f i g u r e 2.4. The h y b r i d i s an attempt to combine the best f e a t u r e s of both the s t e e l j a c k e t e d and c o n c r e t e g r a v i t y s t r u c t u r e s . I t does o f f e r some d i s t i n c t advantages over i t s p a r e n t s , but i t a l s o s u f f e r s from some of the same problems, namely: the need f o r a h i g h l y s k i l l e d l a b o r f o r c e , the 24 F i g u r e 2.4 - H y b r i d g r a v i t y type o f f s h o r e p l a t f o r m s (Compiled from L a l l i , 1975, and McPhee and Reeves, 1975) 25 a v a i l a b i l i t y of high grade s t r u c t u r a l s t e e l , and the requirement that the seabed be r e l a t i v e l y f l a t and l e v e l with adequate bearing s t r e n g t h . The design u t i l i z e s a g r a v i t y base p r i m a r i l y to cut down i n s t a l l a t i o n time and c o s t and a space frame s u p e r s t r u c t u r e to a t t r a c t s m a l l e r wave f o r c e s . Because the s u p e r s t r u c t u r e i s l i g h t e r and the wave loads s m a l l e r than f o r the a l l concrete s t r u c t u r e , the base may be decreased i n s i z e and the o v e r a l l weight reduced by 65% to 75% (McPhee and Reeves, 1975). If bearing s o i l s are weak, the base s i z e may be i n c r e a s e d to a v o i d o v e r s t r e s s i n g the s o i l . Two c o n s t r u c t i o n methods add to the pl a t f o r m ' s f l e x i b i l i t y (Hansen and I n g e r s l e v , 1977). The r a f t may be towed to the s i t e and i n s t a l l e d , then the space frame may be connected and the deck mated, or the components may be b u i l t independently and j o i n e d upon completion at a p r o t e c t e d nearshore l o c a t i o n before tow-out. The f i r s t c o n s t r u c t i o n method allows f o r a g r a v i t y type p l a t f o r m to be used when d r a f t r e s t r i c t i o n s are c r i t i c a l , t hat i s , when no deep water c o n s t r u c t i o n s i t e such as a f j o r d i s l o c a t e d nearby; the r a f t and tower are f l o a t e d out s e p a r a t e l y m a i n t a i n i n g towing s t a b i l i t y with much l e s s d r a f t . The second c o n s t r u c t i o n method may be employed when an e a r l y i n s t a l l a t i o n date i s c r i t i c a l by t a k i n g advantage of the modular c o n s t r u c t i o n . No h y b r i d s t r u c t u r e s have yet been i n s t a l l e d . 2.3 Pl a t f o r m s f o r A r c t i c Development G r a v i t y type p l a t f o r m s have a l s o been designed f o r use i n the A r c t i c . Among these designs are the monocone (Stenning and 26 Schumann, 1979) and m u l t i p l e - l e g s t r u c t u r e (Kliewer and Forbes, 1980), both of which are shown i n f i g u r e 2.5. These s t r u c t u r e s were designed f o r shallow i c e - i n f e s t e d waters of the Beaufort Sea. H o r i z o n t a l i c e loads are reduced by the nature of p l a t f o r m geometry. The s u r f a c e p i e r c i n g c y l i n d r i c a l l e g ( s ) reduce the area exposed to t h i n n e r i c e flows, while the c o n i c a l 5 s e c t i o n s below the su r f a c e are designed to f a i l the t h i c k e r i c e sheets i n f l e x u r e i n s t e a d of compression, thereby g r e a t l y reducing the l a t e r a l loads on the s t r u c t u r e . The m u l t i p l e - l e g s t r u c t u r e i s made of s t e e l , which i s more r e s i s t a n t to i c e s c r a p i n g and gouging than c o n c r e t e . The monocone i s c o n s t r u c t e d of r e i n f o r c e d c o n c r e t e covered with s t e e l armor to r e s i s t damage from moving i c e flows. No pl a t f o r m s of e i t h e r design have yet been i n s t a l l e d . A r t i f i c i a l i s l a n d s are a l s o g r a v i t y type s t r u c t u r e s . S e v e r a l types of a r t i f i c i a l i s l a n d s have been proposed f o r e x p l o r a t o r y d r i l l i n g s t r u c t u r e s i n the Beaufort Sea, i n c l u d i n g the c a i s s o n r e t a i n e d s t r u c t u r e (de Jong and Bruce, 1978) a l s o shown i n f i g u r e 2.5. One of these s t r u c t u r e s was r e c e n t l y completed by Dome Petroleum, L t d . i n the Canadian s e c t o r . These s t r u c t u r e s c o n s i s t of e i g h t s t e e l w a l l s e c t i o n s attached v i a f l e x i b l e j o i n t s that can move under i c e l o a d i n g t o t r a n s f e r the l a r g e h o r i z o n t a l l o a d to the s o i l core - which i s of s u f f i c i e n t s i z e to r e s i s t s h e a r i n g f a i l u r e w i t h i n the i s l a n d . Although the s t r u c t u r e ' s core i s b u i l t of s o i l , not concrete or s t e e l , i t i s fundamentally a g r a v i t y s t r u c t u r e , s i n c e s t a b i l i t y i s achieved by p r o v i d i n g a s u f f i c i e n t v e r t i c a l f o r c e on the foundation (weight) to r e s i s t f a i l u r e from h o r i z o n t a l l o a d i n g . (a) Multiple Leg Gravity Type (b) Monocone (c) Caisson Retained Island F i g u r e 2.5 - A r c t i c p l a t f o r m designs (Compiled from (a) Kliewer and Forbes, 1980, (b) Bercha and Stenning, 1979, and (c) de Jong and Bruce, 1978) 28 2.4 Deep Water Platforms and Other S t r u c t u r e s For water deeper than about 300 meters, the co s t of i n s t a l l i n g g r a v i t y p l a t f o r m s and s t e e l j a c k e t e d s t r u c t u r e s i n c r e a s e s very r a p i d l y . 6 In these waters, a l t e r n a t i v e recovery methods are t h e r e f o r e r e q u i r e d to make hydrocarbon recovery economically a t t r a c t i v e . A number of s t r u c t u r e s have been proposed f o r deep water use i n c l u d i n g the a r t i c u l a t e d column (Moinard, 1979), the guyed tower (Finn et a l , 1979), and the t e n s i o n l e g p l a t f o r m (Falkner and Franks, 1978), a l l which are shown i n f i g u r e 2.6. These s t r u c t u r e s are l i k e l y to be used i n water depths of between 300 and 600 meters (Morrison, 1980b). In deeper water, subsea completion systems (Burkhardt and M i c h i e , 1979) w i l l probably a f f o r d the only economical s o l u t i o n . The a r t i c u l a t e d s t r u c t u r e s , guyed towers, and t e n s i o n l e g pl a t f o r m s are a l s o a p p l i c a b l e to areas with small r e s e r v o i r s of l i m i t e d p o t e n t i a l as w e l l as to purposes other than d r i l l i n g or pr o d u c t i o n p l a t f o r m s , such as: f l a r e s t r u c t u r e s , l i g h t towers, and tanker l o a d i n g t e r m i n a l s where t r a d i t i o n a l designs would be uneconomical. They are designed to be compliant, that i s , they move with the d i s t u r b i n g f o r c e somewhat i n s t e a d of t r y i n g to act r i g i d l y and p r o h i b i t a l l motion. The f o r c e s a c t i n g on the The depth at which these s t r u c t u r e s become uneconomical i s i n f l u e n c e d by s e v e r a l f a c t o r s , namely: the s t a t e of cu r r e n t technology, the a v a i l a b i l i t y of a l t e r n a t i v e recovery methods, the nature and s e v e r i t y of environmental l o a d i n g , and the estimated volume of r e c o v e r a b l e hydrocarbons. T h i s depth was chosen based on c u r r e n t p u b l i c a t i o n s . The economical depth of m o n o l i t h i c g r a v i t y type p l a t f o r m s may be l e s s than t h i s - about 200 meters. 29 (b) Articulated Column (c) Tension-legged Platform (After McPhee and Reeves, 1975) F i g u r e 2.6 - Proposed deep-water p l a t f o r m s 30 s t r u c t u r e are thus reduced and the amount of m a t e r i a l s r e q u i r e d are t h e r e f o r e s i g n i f i c a n t l y l e s s than f o r t r a d i t i o n a l d e s igns. For these s t r u c t u r e s , the g r a v i t y type base may be used as a foundation system (as opposed to the a l t e r n a t i v e c h o i c e , p i l e s ) and they are t h e r e f o r e of i n t e r e s t here. The a r t i c u l a t e d column i s p r e s e n t l y being used f o r f l a r e s t r u c t u r e s i n the North Sea (Sjoerdsma, 1975b) and f o r tanker l o a d i n g t e r m i n a l s i n both the North Sea (Sjoerdsma, 1975b) and o f f s h o r e B r a z i l (Burns and D'Amorim, 1977). However, no d r i l l i n g or p r o d u c t i o n p l a t f o r m s of t h i s design have been b u i l t t o date. The North Sea s t r u c t u r e s are i n water depths of between 106 and 150 meters (Moinard, 1979). 2.5 Sources of New P l a t f o r m Technology For updating t h i s l i s t , the reader i s r e f e r r e d to s e v e r a l of many magazines concerned with o f f s h o r e o i l technology, s p e c i f i c a l l y : Ocean Industry, O f f s h o r e , Offshore Engineer, The O i l and Gas J o u r n a l , and the J o u r n a l of Petroleum Technology. Another good source of i n f o r m a t i o n are the Proceedings of the O f f s h o r e Technology Conference which i s h e l d a n n u a l l y i n Houston, Texas. CHAPTER 3 DESIGN, CONSTRUCTION AND INSTALLATION 31 3.1 P r e l i m i n a r y C o n s i d e r a t i o n s Before a p l a t f o r m can be designed, some assessment of the sources of l o a d i n g f o r the p a r t i c u l a r area must be made, and the necessary environmental and g e o t e c h n i c a l design parameters chosen. 3.1.1 Sources of Loading The sources of l o a d i n g i n an o f f s h o r e environment are numerous and of v a r y i n g degrees of importance at d i f f e r e n t l o c a t i o n s . . G e n e r a l l y , they may be broken i n t o two c a t e g o r i e s : environmental loads and o p e r a t i o n a l l o a d s . F i g u r e 3.1 shows the primary loads that may act on an o f f s h o r e s t r u c t u r e . 3.1.1.1 Environmental Loads Environmental loads are d e f i n e d as loads caused by n a t u r a l phenomena - those over which man has no c o n t r o l . Environmental loads a c t i n g on an o f f s h o r e s t r u c t u r e i n c l u d e (1) the f o r c e s caused by i n t e r a c t i o n between moving f l u i d s and the s t r u c t u r e , such as: wind, waves, c u r r e n t s , or flo w i n g s o i l , (2) f o r c e s due to bodies such as i c e impacting the s t r u c t u r e , (3) s t r e s s e s induced by thermal g r a d i e n t s , and (4) f o r c e s r e s u l t i n g from earthquake induced a c c e l e r a t i o n s i n the s t r u c t u r e . Environmental loads t r a n s m i t t e d to the foundation are g e n e r a l l y i n c l i n e d , e c c e n t r i c , and e i t h e r t r a n s i e n t or c y c l i c i n nature. 32 WIND SERVICE J V A \ ^ W V W EARTHQUAKE F i g u r e 3.1 - Loads a c t i n g on an o f f s h o r e s t r u c t u r e 33 3.1.1.2 O p e r a t i o n a l Loads Loads other than environmental are c l a s s i f i e d as s e r v i c e or o p e r a t i o n a l loads and i n c l u d e those caused by moving equipment and machine v i b r a t i o n s on or w i t h i n the s t r u c t u r e , and those caused by i n t e r a c t i o n with support v e s s e l s , such as: mooring lo a d s , h e l i c o p t e r l a n d i n g s , and p o s s i b l e c o l l i s i o n s with e i t h e r f l y i n g or f l o a t i n g v e s s e l s . These are u s u a l l y minor loads necessary only f o r the design of the deck s t r u c t u r e , with the notable e x c e p t i o n being c o l l i s i o n with a l a r g e s u r f a c e v e s s e l (tanker) under power. A d d i t i o n a l l y , there may be loads imposed on the s t r u c t u r e and i t s foundation by f l u c t u a t i o n s i n o i l storage q u a n t i t y , d e n s i t y , or temperature. These loads may be s i g n i f i c a n t and must be c o n s i d e r e d i n design; both minimum and maximum value s of weight f l u c t u a t i o n s must be s p e c i f i e d f o r foundation d e s i g n . Minimum v a l u e s a f f e c t s t a b i l i t y ( o v e r t u r n i n g ) as do maximum values ( o v e r s t r e s s i n g ) . E c c e n t r i c loads may a l s o be imposed on the foundation by v a r y i n g d i s t r i b u t i o n s of deck equipment and o i l i n the storage tanks. The l a t t e r of these may be s i g n i f i c a n t and must e i t h e r be designed f o r or prevented. 3.1.2 Environmental Design Parameters A f t e r environmental c o n d i t i o n s f o r the chosen area have been i d e n t i f i e d , design parameters must be chosen using a p p r o p r i a t e and acc e p t a b l e methods. T h i s i s u s u a l l y o u t l i n e d by the r e g u l a t o r y agency with j u r i s d i c t i o n i n the case who w i l l o f t e n have t h e i r own standards (Department of Energy (U.K.), 34 1974; Department of the I n t e r i o r (U.S.A), 1979; Det Norske V e r i t a s (Norway), 1977; I n t e r n a t i o n a l e de l a P r e c o n t r a i n t e ( F r a n c e ) , 1977). In some cases, requirements may a l s o be set f o r t h by the underwriter (e.g. Ll o y d ' s R e g i s t e r of Shipping) or the owners, who sometimes use p r o f e s s i o n a l s o c i e t y recommendations such as those of the American Petroleum I n s t i t u t e (1978). A p a r t i a l l i s t i n g of environmental parameters f o r some of the world's o f f s h o r e areas i s given i n Table IV. A quick glance at the t a b l e w i l l show that o f f s h o r e p l a t f o r m s are s u b j e c t e d t o harsh environmental c o n d i t i o n s . The r e s u l t s presented i n the t a b l e are f o r s p e c i f i c l o c a t i o n s w i t h i n the o f f s h o r e areas l i s t e d and may be more or l e s s severe than those at other l o c a t i o n s w i t h i n the area. 3.1.3 S i t e S e l e c t i o n and S o i l I n v e s t i g a t i o n s G r a v i t y type s t r u c t u r e s r e q u i r e a f a i r l y l e v e l s e a f l o o r f r e e of l a r g e boulders and other o b s t r u c t i o n s that may damage the base of the s t r u c t u r e when i t i s i n s t a l l e d , u n l e s s the foundation may be prepared p r i o r to i n s t a l l a t i o n . Foundation p r e p a r a t i o n i s . l i m i t e d to water l e s s than about 70 meters deep - at l e a s t on a grand s c a l e (Gerwick, 1974). Recent advances i n underwater equipment and d i v i n g technology have probably extended t h i s depth somewhat. Surface d e p o s i t s must be somewhat uniform to prevent e x c e s s i v e d i f f e r e n t i a l settlement and, while n e c e s s a r i l y p o s s e s s i n g adequate s t r e n g t h f o r s t a b i l i t y , they must not be so strong as to prevent the p e n e t r a t i o n of s k i r t s d u r i n g i n s t a l l a t i o n i f s k i r t s are adopted i n the d e s i g n . 35 Table IV Environmental Design C r i t e r i a For Some O f f s h o r e Areas AREA WAVE HEIGHT (m) CURRENT SPEED (m/s) TIDAL FLUC. (m) WIND SPEED (m/s) ICE THICK, (m) GROUND ACCEL. (g's) B a l t i m o r e Canyon (Ward et al,'77) 30.0 ? ? - Beaufort Sea (Kliewer+Forbes,'80) 12.5 ? 2.8 1 ? 5.0 ? Georges Banks (Ward et al,'77) 25.2 ? - ? Gulf of Alask a (Augustine et al,'78) (Bea and Akky,'79) 40.5 34.0 ? ? ? ? ? ? - ? 0.41 Gulf of Mexico (Haring+Heideman,'78) (Berman et al,'78) 22.8 26.5 ? 2'.7 2.2 2 ? ? ? - ? ? North Sea (Offsh o r e Europe,'74) 30.5 ? ? 36 3 54" - ? O f f s h o r e B r a z i l (Burns+D'Amorim,'77) 16.0 1 .8 1.9 38 5 - ? O f f s h o r e Congo ( L a l l i , ' 7 7 ) 9.4 ? ? ? ? 'Includes a 0.3 meter lunar t i d e and a 2.5 meter storm surge 2 I n c l u d e s both lunar t i d e and storm surge 3One hour s u s t a i n e d speed "Gust ( s e v e r a l seconds) 5One minute s u s t a i n e d speed 36 Another s i t e requirement i s t h a t the bearing s o i l s have adequate s t r e n g t h to support the s t r u c t u r e throughout i t s o p e r a t i o n a l l i f e ; t h i s i n c l u d e s both s t a b i l i t y under design loads and the e f f e c t s of r e p e t i t i v e l o a d i n g (waves, earthquakes, e t c . ) on the v a r i o u s subsurface d e p o s i t s . A d d i t i o n a l l y , settlement of the s t r u c t u r e due to e l a s t i c displacements, primary and secondary c o n s o l i d a t i o n , and c y c l i c compaction, must be w i t h i n t o l e r a b l e l i m i t s . T h i s i s g e n e r a l l y a s i t e requirement s i n c e l i t t l e m o d i f i c a t i o n may be done to the design of a g r a v i t y type s t r u c t u r e with regards to settlement. These b a s i c concerns are i n v e s t i g a t e d using i n f o r m a t i o n from p r e l i m i n a r y surveys, which i s u s u a l l y enough to determine the adequacy of the s i t e . The s e l e c t i o n of a s i t e f o r an o f f s h o r e p l a t f o r m i s p r i m a r i l y d i c t a t e d by o i l r e s e r v o i r c o n s i d e r a t i o n s . There i s always, however, some l a t i t u d e that can be used to optimize foundation c o n d i t i o n s (de R u i t e r , 1976). The r e s e r v o i r requirements may u s u a l l y be met by i n s t a l l i n g the p l a t f o r m ( s ) w i t h i n a f a i r l y l a r g e area, on the order of s e v e r a l square k i l o m e t e r s or more. A general survey of the s p e c i f i e d area i s conducted to determine the most l i k e l y s i t e s to p l a c e a p l a t f o r m ( s ) . At t h i s time, the type and number of p l a t f o r m s to be p l a c e d are o f t e n unknown. The survey l i n e s and t e s t h o l e s f o r one such survey conducted i n the North Sea are i l l u s t r a t e d i n f i g u r e 3.2. G e o l o g i c a l i n v e s t i g a t i o n s , both r e g i o n a l and s i t e s p e c i f i c , are made of the proposed a r e a . The r e g i o n a l survey i s o f t e n 1 1 1 1 1—: lettooo LEGEND Soo mtfres » f S\J*.-/& vEUEL-i • BoftCHOuE TrtAtK. W I T H T I " PCSITIOWS •* U N I rerJmwnoN TEST *J cXPLeCKTieWWCU. c- F i g u r e 3.2 - Plan of survey l i n e s ( A f t e r O f f s h o r e ' S o i l - g r i d : l o c a l t r a n s v e r s e Mechanics, 1976) 38 made using o n l y p r e s e n t l y a v a i l a b l e d a ta. The h i s t o r y of the area i s i n v e s t i g a t e d , with p a r t i c u l a r a t t e n t i o n p a i d to f a c t o r s such as: the l o c a t i o n of b u r i e d channels, d e l t a i c c l a y s , and t e c t o n i c movements. ' Environmental i n f l u e n c e s are assessed, i n c l u d i n g : r e g i o n a l and l o c a l r a t e s of d e p o s i t i o n , p r o x i m i t y to submarine canyons, and permafrost ( G a r r i s o n and Bea, 1977). O n - s i t e s t u d i e s are made using s p e c i a l l y o u t f i t t e d survey s h i p s , some of which are over one hundred meters i n l e n g t h . The d i s t r i b u t i o n p a t t e r n s of minor s e a f l o o r f e a t u r e s , angles of l o c a l s l o p e s , and water depths i n the proposed area are found from bathymetry. G e o p h y s i c a l seismic surveys are made at the same time as the b a t h y m e t r i c a l s t u d i e s and from the same s h i p . A c o u s t i c a l p r o f i l i n g i s done using e l e c t r o n i c t r a n s d u c e r s which impart an a c o u s t i c a l p u l s e to the water by e i t h e r a sound ( P i n g e r ) , mechanical (Boomer), or spark (Sparker) d i s t u r b a n c e . The r e s u l t i n g a c o u s t i c a l t r a n s m i s s i o n , a f t e r t r a v e l l i n g through the water, reaches the seabed and i s r e f l e c t e d back by the v a r i o u s subsurface s t r a t a . The r e t u r n i n g s i g n a l s are pi c k e d up by hydrophone streamers or a r r a y s (Offshore Europe, 1974). High r e s o l u t i o n (Pinger or Boomer) surveys are used to gather i n f o r m a t i o n on the upper sediments, those l e s s than about 30 meters deep, and low r e s o l u t i o n (Sparker) surveys are conducted to determine the c h a r a c t e r i s t i c s of deeper s t r a t a , although i n somewhat l e s s d e t a i l . Some seabed samples are necessary to pr o v i d e s p e c i f i c g e o t e c h n i c a l knowledge of the upper sediments - those most c r i t i c a l to the design of a g r a v i t y type s t r u c t u r e . Shallow samples are taken with a g r a v i t y c o r e r , v i b r a t o r y sampler, or 39 other sampling d e v i c e . A l t e r n a t i v e l y , cone penetrometers may be used to c h a r a c t e r i z e the s u r f i c i a l sediments, p r o v i d e d some samples are taken f o r c o r r e l a t i o n purposes. At l e a s t one deep b o r i n g (100 to 150 meters) i s r e q u i r e d to provide i n f o r m a t i o n on the sediments w i t h i n the range of i n t e r e s t f o r foundation d e s i g n . The p o s i t i o n s of boreholes and the l o c a t i o n s of other t e s t s should be known a c c u r a t e l y r e l a t i v e to the f u t u r e s t r u c t u r e . T h i s may be accomplished by d e p l o y i n g an a r r a y of transponders on the s e a f l o o r and l o c a t i n g a l l boreholes and other t e s t l o c a t i o n s with r e s p e c t to the transponders. The e l e c t r i c a l s i g n a l s emitted by the transponders allow them to be r e a d i l y l o c a t e d from the s u r f a c e ( M c C l e l l a n d , 1977). A p r e l i m i n a r y s i t e s e l e c t i o n may be made based on data from the aforementioned t e s t s . When a s i t e has been chosen f o r f u r t h e r i n v e s t i g a t i o n , a c a r e f u l l y planned f i e l d program must be developed ( H i t c h i n g s et a l , 1976). The cost of o f f s h o r e i n v e s t i g a t i o n s i s extremely high, on the order of tens of thousands of d o l l a r s per day f o r a l a r g e survey s h i p and crew (Braun, 1974); t h e r e f o r e , the program of t e s t i n g must be thoroughly prepared by the g e o t e c h n i c a l c o n s u l t a n t before the s h i p i s o n - s i t e . A l l g e o t e c h n i c a l t e s t i n g i s performed by the c o n s u l t a n t ' s g e o t e c h n i c a l personnel and other o p e r a t i o n s are su p e r v i s e d by h i s i n s p e c t o r s (de R u i t e r , 1976). Engineers on-board monitor the incoming data c o n t i n u o u s l y to make on-the-spot d e c i s i o n s about the l o c a t i o n and extent of i n - s i t u t e s t s . The base of the p l a t f o r m should f a l l w i t h i n the area i n v e s t i g a t e d i n the f i n a l o n - s i t e survey. The s t r u c t u r e once 40 o n - s i t e can be p o s i t i o n e d only approximately over the proposed s i t e s i n c e i t w i l l be c o n s t a n t l y i n motion under wind, wave, and c u r r e n t e x c i t a t i o n . The expected accuracy i n p o s i t i o n i n g must be e s t a b l i s h e d and w i l l govern the s i z e of the area to be e x p l o r e d . E r r o r margins i n p o s i t i o n i n g of 50 meters are t y p i c a l ( M c C l e l l a n d , 1977). The s i t e i n v e s t i g a t i o n i s conducted from a s h i p which i s s u b j e c t to constant motion, as i s any d r i l l s t r i n g or p i e c e of equipment connected to i t . S p e c i a l equipment has been developed to t r y to compensate f o r t h i s motion ( T a y l o r , 1976), however, complete success has not and w i l l not be achieved. T h e r e f o r e , whenever p o s s i b l e , i n - s i t u t e s t i n g i s done with equipment that r e s t s d i r e c t l y on the s e a f l o o r and r e q u i r e s no r i g i d c onnection to the s u r f a c e v e s s e l , only f l e x i b l e c o n t r o l c a b l e s and h y d r a u l i c l i n e s . The s i t e i n v e s t i g a t i o n , although w e l l planned, does not f o l l o w a s t r i c t course. Information gained from e a r l y t e s t s i s used to determine the need f o r l a t e r t e s t s . T h i s should be kept i n mind when reading the f o l l o w i n g t e x t . The seabed topography i s mapped i n d e t a i l using s i d e scan sonar, which i s good to about 0.5 meters, and submersibles (de R u i t e r , 1976). O b s t a c l e s such as boulders must be a c c u r a t e l y l o c a t e d and t h e i r s i g n i f i c a n c e a s s essed. If they are too l a r g e , the s i t e w i l l not be s u i t a b l e u n l e s s they can be removed. If not,-an a l t e r n a t i v e s i t e may have to be chosen. A number of borings are made to v a r y i n g depths. The number of t e s t s depend on the u n i f o r m i t y of the s o i l p r o f i l e . G e n e r a l l y three to f i v e shallow boreholes (to 30-40 meters) and 41 at l e a s t one deep borehole (to 100-200 meters) are sunk (de R u i t e r , 1976). Three c o r i n g s has been suggested as an a b s o l u t e minimum (George, 1976). Samples are u s u a l l y taken at i n t e r v a l s of 1.0 to 1.5 meters over the f i r s t 15 meters, then l e s s f r e q u e n t l y ( M c C l e l l a n d , 1977). The s o i l s can only be i d e n t i f i e d with c e r t a i n t y where samples are taken s i n c e the d r i l l i n g mud and c u t t i n g s e x i t at the s e a f l o o r (Low, 1975). Samples are u s u a l l y extruded on-board, c l a s s i f i e d , and checked f o r q u a l i t y . Some samples are s e l e c t e d f o r on-board t e s t s , i n c l u d i n g r o u t i n e c l a s s i f i c a t i o n s ( A t t e r b e r g l i m i t s , g r a i n s i z e d i s t r i b u t i o n , e t c . ) and unconfined compression t e s t s , while o t h e r s are prepared f o r the on-shore l a b o r a t o r i e s , where c o n s o l i d a t i o n , t r i a x i a l , and other complex t e s t s are c a r r i e d out. Cone penetrometers are used e x t e n s i v e l y to check the u n i f o r m i t y of shallow d e p o s i t s and to estimate the p e n e t r a t i o n r e s i s t a n c e that w i l l be encountered by the dowels and s k i r t s d u r i n g i n s t a l l a t i o n . 7 They are a l s o used f o r c l a s s i f i c a t i o n purposes and f o r e s t i m a t i n g the undrained s t r e n g t h of c l a y s and r e l a t i v e d e n s i t y of sands. The number of p e n e t r a t i o n t e s t s depends on the u n i f o r m i t y of the s o i l p r o f i l e with f i v e to f i f t e e n being t y p i c a l numbers (de R u i t e r , 1976). A d d i t i o n a l a c o u s t i c a l p r o f i l i n g on a f i n e g r i d may be necessary i f abrupt 'Dowels are c a n t i l e v e r rods which j u t out of the base of the p l a t f o r m 5 m or so. They are used to s t a b i l i z e the s t r u c t u r e and prevent i t from moving while i t i s being b a l l a s t e d and the s k i r t s are being imbedded. 42 changes i n s t r a t i g r a p h y are det e c t e d (de R u i t e r , 1976). A v a l u a b l e q u a l i t a t i v e p i c t u r e i s presented from cone p e n e t r a t i o n logs that may be used to assess the r e l i a b i l i t y of borin g data. Down-the-hole penetrometers may be used i n deeper boreholes to measure the d e n s i t y and shear s t r e n g t h of deeper sediments. Gamma ray l o g g i n g can be done down the boreholes f o r a minor i n c r e a s e i n c o s t . The gamma ray l o g pr o v i d e s a continuous p i c t u r e of the borehole and i s u s e f u l as a q u a l i t a t i v e t o o l showing s t r a t i f i c a t i o n and the presence of cohesive s o i l s . These s o i l s are marked by an in c r e a s e d gamma ray count. Other i n - s i t u t e s t s may be c a r r i e d out i n a d d i t i o n to those mentioned, i n c l u d i n g vane shear t e s t s which are a p p l i c a b l e i n areas with s o f t c l a y s ( M c C l e l l a n d , 1977). 3.1.4 S e l e c t i o n of S o i l Parameters f o r Design Design parameters are chosen based on data from both l a b o r a t o r y and i n - s i t u t e s t s . The borehole p r o f i l e s are i n t e r p r e t e d from cone p e n e t r a t i o n l o g s , gamma ray l o g s , and samples. Samples are used f o r i d e n t i f y i n g the d e p o s i t s and f o r making s i t e - s p e c i f i c penetrometer c o r r e l a t i o n s . The i n - s i t u t e s t s p rovide a continuous p i c t u r e of the p r o f i l e and are important f o r i d e n t i f y i n g i n t e r f a c e s and small s c a l e f e a t u r e s , such as t h i n seams or lenses of v a r y i n g m a t e r i a l i n l a r g e r seemingly uniform l a y e r s , s i n c e a continuous r e c o r d of the d r i l l mud or c u t t i n g s i s not a v a i l a b l e . The r e s u l t s of one such borehole i n t e r p r e t a t i o n are shown i n f i g u r e 3.3. The necessary design parameters are found by usi n g e s t a b l i s h e d l a b o r a t o r y t e s t s and i n - s i t u methods p r o p e r l y 43 10 -H 15 •£ a. O 2 5 3 5 I—40- Soil profII* Fine to medium umd with diell froamentt (dente)- Small tilt fraction Few imotf graved Grey tilty cloy with teoms of fine land and tilty landdtiff fo very stiff) Fine fa medium land (dense) Seomi of silry clay Grey illty clay with teomt of lilt and tilty fine umd(very ttlff) Silly land layer? Silly land layer? Silty fine land with of tilty cloy(dente) Silly clayfoord) Flo.5 TYPICAL SOIL PROFILE AS IDENTIFIED »Y BOREHOLE,CONE PENETRATION TEST AND V RAY LOG F i g u r e 3.3 - T y p i c a l s o i l p r o f i l e as i d e n t i f i e d by borehole, cone p e n t r a t i o n t e s t and gamma ray l o g g i n g ( A f t e r George, 1976) 44 c o r r e l a t e d t o the o f f s h o r e s i t e . Oedometer t e s t s are used to o b t a i n c o n s o l i d a t i o n d a t a . The s t r e s s - s t r a i n c h a r a c t e r i s t i c s of the foundation s o i l s and the e f f e c t i v e shear s t r e n g t h parameters are found from t r i a x i a l t e s t s . Simple shear and d i r e c t shear t e s t i n g may a l s o be done. R e l a t i v e d e n s i t y and modulus values are best determined from i n - s i t u t e s t s , such as the cone penetrometer with the a i d of e m p i r i c a l c o r r e l a t i o n c h a r t s . The modulus value i s p a r t i c u l a r l y s e n s i t i v e to sample d i s t u r b a n c e . When choosing design parameters "one should always be aware of the l i m i t a t i o n s imposed by the c o n d i t i o n s under which i n v e s t i g a t i o n s at sea have to be c a r r i e d out," (de R u i t e r , 1976). O b t a i n i n g the shear s t r e n g t h parameters presents many d i f f i c u l t i e s , some being: - The a b i l i t y to o b t a i n samples of high q u a l i t y - Inherent s c a t t e r i n l a b o r a t o r y data - D e c i d i n g which type of shear t e s t s are a p p l i c a b l e to the problem (Rowe, 1975) - The n a t u r a l v a r i a b i l i t y of o f f s h o r e d e p o s i t s When choosing a p r o f i l e , i t must be remembered that an estimate which i s too c o n s e r v a t i v e may r e s u l t i n m i l l i o n s of d o l l a r s having to be spent to i n c r e a s e the p l a t f o r m s i z e so that a reasonable f a c t o r of s a f e t y a g a i n s t s l i d i n g or b e a r i n g f a i l u r e i s o b t a i n e d , while too l i b e r a l an estimate may r e s u l t i n the complete l o s s of a m u l t i - m i l l i o n d o l l a r investment and many l i v e s . R e s u l t s of both i n - s i t u and l a b o r a t o r y shear t e s t s f o r one p a r t i c u l a r s i t e are presented i n f i g u r e 3.4. The i n t e r p r e t a t i o n 45 CONE RESISTANCE fkPal— 0 500 WOO 1500 2000 2500 0 COHESION c (kPa)—• 4 0 6 0 8 0 1 0 0 CD < I UJ CO I 1 - CL g I F i g u r e 3.4 - Comparison of shear s t r e n g t h values from sample t e s t i n g and from CPT ( A f t e r de R u i t e r , 1976) 46 of t h i s p r o f i l e i s c e r t a i n l y s u b j e c t to pe r s o n a l o p i n i o n s and p r e j u d i c e s . A thorough knowledge of the types of t e s t s and the c o n d i t i o n s under which they were performed i s e s s e n t i a l when making such a d e c i s i o n . The cone penetrometer r e s u l t s p rovide a u s e f u l check on the l a b o r a t o r y data. 3.2 P l a t f o r m Design The b a s i c design c o n s i d e r a t i o n s f o r a g r a v i t y p l a t f o r m are d i s c u s s e d b r i e f l y i n t h i s s e c t i o n . D e t a i l e d d e s c r i p t i o n s of design procedures are beyond the scope of t h i s t h e s i s . The reader i s t h e r e f o r e d i r e c t e d to r e f e r e n c e s i f a deeper study i s r e q u i r e d . 3.2.1 Hydrodynamic Analyses Hydrodynamic analyses are performed p r i m a r i l y to provide the s t r u c t u r a l engineer with i n f o r m a t i o n on the magnitude and nature of wind, c u r r e n t , and wave l o a d s . The pressure d i s t r i b u t i o n s caused by these loads on the s t r u c t u r e , which w i l l vary both s p a t i a l l y and temporally, are r e q u i r e d f o r the design of the v a r i o u s components. The t o t a l f o r c e s a c t i n g on the s t r u c t u r e , found from i n t e g r a t i n g the pressure d i s t r i b u t i o n s with r e s p e c t to the s p a t i a l c o o r d i n a t e s , are r e q u i r e d f o r the design of the foun d a t i o n . The nature of wave l o a d i n g on both the s t r u c t u r e and the foundation system i s d i s c u s s e d i n d e t a i l i n Chapter 5. Wave loads are u s u a l l y by f a r the most important f l u i d loads encountered. Many a n a l y t i c a l procedures have been developed to c a l c u l a t e the f o r c e s due to waves i n t e r a c t i n g with 47 g r a v i t y type s t r u c t u r e s . In a d d i t i o n to t h e o r e t i c a l a n a l y s e s , model t e s t i n g i s o f t e n employed to provide a check on r e s u l t s ( G a r r i s o n , 1977), s i n c e hydrodynamic t h e o r i e s cannot account f o r i r r e g u l a r shapes, i n t e r f e r e n c e e f f e c t s , and other such problems that e x i s t with r e a l s t r u c t u r e s , except by approximate.numerical methods or through the use of e m p i r i c a l c o e f f i c i e n t s (which are u s u a l l y based on l a b o r a t o r y t e s t s on small s c a l e models). A n a l y t i c a l methods are used to c a l c u l a t e the f o r c e s on i n d i v i d u a l members of the s t r u c t u r e , s i n c e m o d e l l i n g these members i n d i v i d u a l l y i s i m p r a c t i c a l . Scour p o t e n t i a l i s i n v e s t i g a t e d using model t e s t s s i n c e no ac c e p t a b l e a n a l y t i c a l t h e o r i e s e x i s t . Even model t e s t s are not very r e l i a b l e due to s c a l e e f f e c t s (Maidl and S c h i l l e r , 1979) and d i f f i c u l t i e s i n mo d e l l i n g the s o i l . However, a v a l u a b l e q u a l i t a t i v e p i c t u r e of the o n - s i t e scour p o t e n t i a l may be drawn from these t e s t s . Model t e s t s are i n v a l u a b l e f o r p r o v i d i n g i n f o r m a t i o n on towing r e s i s t a n c e and motions, f l o a t i n g s t a b i l i t y , damage s t a b i l i t y , and submergence behavior when touching down (Offshore Europe, 1974). For these o p e r a t i o n s , model t e s t s are r e l i e d upon h e a v i l y and are- always i n c o r p o r a t e d i n t o the design procedure. 3.2.2 G e o t e c h n i c a l Analyses A f t e r p r e l i m i n a r y surveys are completed and a d e t a i l e d s i t e i n v e s t i g a t i o n has been c a r r i e d out f o r a p o s s i b l e g r a v i t y p l a t f o r m s i t e , comprehensive g e o t e c h n i c a l analyses begin. These analyses are summarized i n Table V. 48 Table V G e o t e c h n i c a l Concerns For O f f s h o r e G r a v i t y Type Platforms 1) INSTALLATION A) P e n e t r a t i o n r e s i s t a n c e of dowels and s k i r t s B) Pore pressure d i s s i p a t i o n and e x i t of c o n f i n e d water C) Bearing pressure on c e l l s and s l a b D) Grouting procedures 2) CONTACT BETWEEN SEAFLOOR AND STRUCTURE A) Scour around or under s t r u c t u r e B) Reduced area f o r bearing or s l i d i n g r e s i s t a n c e 3) STABILITY UNDER PSEUDOSTATIC LOADS A) S l i d i n g B) Bearing f a i l u r e C) Ov e r t u r n i n g 4) SETTLEMENT A) Immediate e l a s t i c B) Primary c o n s o l i d a t i o n C) Secondary c o n s o l i d a t i o n D) Cumulative storm and/or earthquake e f f e c t s 1) S t r a i n s o f t e n i n g i n c l a y s 2) D e n s i f i c a t i o n due shear s t r e s s r e v e r s a l s i n sand 5) DISPLACEMENTS UNDER PSEUDOSTATIC LOADS A) H o r i z o n t a l displacements B) V e r t i c a l displacements 6) EFFECTS OF CYCLIC LOADING A) Pore pressure r i s e B) Reduction i n shear s t r e n g t h C) Decrease i n s t i f f n e s s D) A s s o c i a t e d problems 1) E x c e s s i v e h o r i z o n t a l displacements 2) Rocking 3) L i q u e f a c t i o n 7) DYNAMIC BEHAVIOUR A) Resonance B) O p e r a t i o n a l requirements 8) INSTRUMENTATION A) I n s t a l l a t i o n B) Performance monitoring 49 The p e n e t r a t i o n r e s i s t a n c e of dowels and s k i r t s r e q u i r e s a good knowledge of the upper sediments, u s u a l l y known from e x t e n s i v e cone penetrometer t e s t i n g . T h i s r e s i s t a n c e , which w i l l vary over the s i t e , may be estimated using the standard bearing c a p a c i t y equations of Meyerhof (1963) or Hansen (1970). The r e s i s t a n c e to dowel or s k i r t d r i v i n g i s e s s e n t i a l l y the u l t i m a t e b e a r i n g c a p a c i t y of the upper sediments. Penetrometer c o r r e l a t i o n c h a r t s may be used to estimate the bearing c a p a c i t y f a c t o r s . The l o c a l c o n t a c t p r e s s u r e s on the base s l a b may be estimated by e l a s t i c i t y theory, p r o v i d e d that the d e t a i l e d topography of the s e a f l o o r i s known (Bjerrum, 1973). G e n e r a l l y , the s l a b i s designed f o r a s p e c i f i e d base p r e s s u r e , s i n c e the topography and d i s t r i b u t i o n of the upper sediments are not p r e c i s e l y known. Other i n s t a l l a t i o n problems w i l l be d i s c u s s e d in a subsequent s e c t i o n on p l a t f o r m i n s t a l l a t i o n procedures. Good c o n t a c t between the s e a f l o o r and the s l a b i s necessary to prevent undermining of the foundation from water motions and to i n s u r e adequate area f o r foundation s t a b i l i t y . T h i s i s achieved by g r o u t i n g underneath the s l a b a f t e r the p l a t f o r m has been imbedded as f a r as p o s s i b l e . Proper g r o u t i n g procedures and composition must be s p e c i f i e d . There are a number of p o s s i b l e f a i l u r e modes f o r an o f f s h o r e g r a v i t y s t r u c t u r e foundation, i n c l u d i n g : h o r i z o n t a l s l i d i n g , b e a r i n g f a i l u r e , r o c k i n g , and l i q u e f a c t i o n . These f a i l u r e modes are shown i n f i g u r e 3.5. The s t a b i l i t y of the p l a t f o r m i s i n v e s t i g a t e d to ins u r e that h o r i z o n t a l s l i d i n g or a deep-seated b e a r i n g f a i l u r e does A) SLIDING B) BEARING CAPACITY Fig. 3.5 Possible failure modes for an offshore gravity structure foundation (Adapted from Hove and Foss, 1974) en o 51 not occur. There are a number of p o s s i b l e mechanisms f o r a h o r i z o n t a l s l i d i n g f a i l u r e that must be c o n s i d e r e d i n order to f i n d the most c r i t i c a l one. These are shown i n f i g u r e 3.6. Bearing f a i l u r e i s i n v e s t i g a t e d u s i n g the b e a r i n g c a p a c i t y formulas of Meyerhof (1963) or Hansen (1970), and f o r c l a y d e p o s i t s , a simple l i m i t e q u i l i b r i u m method c a l l e d the (Norwegian G e o t e c h n i c a l I n s t i t u t e ) s l i p s u r f a c e method ( L a u r i t z s e n and Schjetne, 1976). The simple bearing c a p a c i t y equations g i v e a rough estimate of the bearing s t r e n g t h of foundation s o i l s and are convenient and easy to use. They are not s t r i c t l y a p p l i c a b l e to l a y e r e d d e p o s i t s or the ocean wave or earthquake problems where l o a d i n g c o n d i t i o n s are more complicated than the formulae can account f o r . T h e r e f o r e , f i n i t e element analyses are a l s o performed to p r o v i d e a more d e t a i l e d i n v e s t i g a t i o n of the b e a ring s t a b i l i t y . O v e r t u r n i n g f a i l u r e i s not a problem i f l o a d e c c e n t r i c i t y i s not too h i g h . T h i s p o t e n t i a l problem may be avoided by i n c r e a s i n g the base s i z e i f necessary. A s t a b i l i t y diagram i s shown i n f i g u r e 3.7 to show the b a s i c r e l a t i o n s h i p between v e r t i c a l and h o r i z o n t a l loads as they r e l a t e to foundation s t a b i l i t y . The magnitudes of the l o a d s , of course, depend on the foundation s i z e and the s t r e n g t h of the foundation s o i l s . C a l c u l a t i o n s f o r e l a s t i c and c o n s o l i d a t i o n settlements are s i m i l a r to those which are done f o r any other s t r u c t u r e . Of i n t e r e s t here i s that the depth of i n f l u e n c e , i . e . the s i z e of the s t r e s s bulb, i s s u b s t a n t i a l l y l a r g e r f o r these huge s t r u c t u r e s than f o r most p r o j e c t s on l a n d , and t h e r e f o r e , the corresponding settlements are u s u a l l y g r e a t e r . In a d d i t i o n to 52 (ol PASSIVE WEDGE FAILURE (t» DEEP PASSIVE FAILURE (dl SLIDING FAILURE IN SHALLOW WEAK ZONE WITH WIDELY SPACED SKIRTS 1LIJ11J.IJJ1I.111. ' K ... . . • (.) SLIDING FAILURE IN SHALLOW WEAK ZONE AVOIDED WITH CLOSELY SPACED SKIRTS (f) SLIDING FAILURE IN DEEP WEAK ZONE F i g u r e 3.6 - P o s s i b l e modes of s l i d i n g f a i l u r e ( A f t e r Young et a l , 1975) 53 F i g u r e 3.7 - S t a b i l i t y diagram f o r a r a f t foundation (Adapted from Young et a l , 1975) 0 54 these c a l c u l a t i o n s , some assessment of the e f f e c t of cumulative storm or earthquake l o a d i n g on settlement must be made. Laboratory t e s t s are necessary to determine t h i s i n f l u e n c e and a p p r o p r i a t e procedures must be used to estimate the amount (Andersen, 1976; F i n n et a l , 1977; Lee and A l b a i s a , 1974). C y c l i c l o a d i n g and i t s e f f e c t s on the foundation s o i l s are i n v e s t i g a t e d i n an approximate way. For wave l o a d i n g , where the p e r i o d i s on the order of s e v e r a l seconds or more, p s e u d o s t a t i c a n a l y s e s are performed f o r s t a b i l i t y and displacement c a l c u l a t i o n s . C y c l i c e f f e c t s are modelled by changing the s o i l p r o p e r t i e s to account f o r pore water pressure g e n e r a t i o n . For earthquake l o a d i n g , f u l l dynamic analyses are r e q u i r e d with s u i t a b l e e f f e c t i v e s t r e s s computer programs. Displacements of the s t r u c t u r e under p s e u d o s t a t i c wave loads are estimated using the f i n i t e element method. These displacements i n c l u d e v e r t i c a l , h o r i z o n t a l , and r o c k i n g motions. The r e s u l t s are very s e n s i t i v e to the values chosen for the s o i l parameters. The e f f e c t of c y c l i c l o a d i n g may be i n c o r p o r a t e d here by e s t i m a t i n g the pore water pressure r i s e and d e c r e a s i n g the s o i l s t i f f n e s s and shear s t r e n g t h to account f o r t h i s . L i q u e f a c t i o n p o t e n t i a l i s assessed from l a b o r a t o r y t e s t data e i t h e r d i r e c t l y with c y c l i c t r i a x i a l t e s t s m o d i f i e d to allow f o r p a r t i a l drainage (Lee and Focht, 1975a) or i n d i r e c t l y u s i n g a n a l y t i c a l methods (Rahman et a l , 1977). P r e l i m i n a r y s t u d i e s based on s i m p l i f i e d undrained analyses (Bjerrum, 1973) may be u s e f u l to assess the need f o r more advanced i n v e s t i g a t i o n s , e i t h e r l a b o r a t o r y or a n a l y t i c a l . Most dynamic a n a l y s e s are performed by the s t r u c t u r a l 55 engineer who r e q u i r e s s o i l parameters to model the s t i f f n e s s and damping c h a r a c t e r i s t i c s of the foundation s o i l s . The e v a l u a t i o n of these s o i l parameters i s the job of the s o i l s engineer. Seismic c o n s i d e r a t i o n s have not had a s i g n i f i c a n t i n f l u e n c e on g r a v i t y type s t r u c t u r e s designed to date. However, earthquake e n g i n e e r i n g f o r o f f s h o r e g r a v i t y s t r u c t u r e s i s r e c e i v i n g i n c r e a s i n g a t t e n t i o n as s t r u c t u r e s of t h i s type are being c o n s i d e r e d f o r s e i s m i c a l l y a c t i v e a r e a s . A thorough d i s c u s s i o n of t h i s t o p i c i s beyond the scope of t h i s t h e s i s and the reader t h e r e f o r e i s r e f e r r e d to s e v e r a l p u b l i c a t i o n s that deal with t h i s s u b j e c t , namely: Watt et a l (1978) and Seines (1981). Two design codes may a l s o be r e f e r e n c e d : those of Det Norske V e r i t a s (1977) and the American Petroleum I n s t i t u t e (1978). A f i n a l concern of the g e o t e c h n i c a l engineer i s the requirement f o r monitoring the i n s t a l l a t i o n and subsequent performance of the g r a v i t y p l a t f o r m . T h i s i s covered i n d e t a i l i n a l a t e r s e c t i o n . 3.2.3 S t r u c t u r a l Requirements and Analyses The f i n a l s t r u c t u r a l a n a l y s e s and design may proceed when the environmental loads have been d e f i n e d and the s o i l i n v e s t i g a t i o n s are complete. An important requirement of o f f s h o r e s t r u c t u r a l design i s that the s t r u c t u r e be designed f o r c o n s t r u c t i o n , tow-out, and i n s t a l l a t i o n l o a d s, i n a d d i t i o n to the usual procedure of d e s i g n i n g f o r the maximum f o r c e s expected d u r i n g o p e r a t i o n a l l i f e . The three main components of the s t r u c t u r e : the deck, 56 towers, and base c a i s s o n , have d i s t i n c t design requirements. The deck, which i s u s u a l l y made of s t e e l , must r e s i s t c o r r o s i o n (which i s higher i n the s p l a s h zone than elsewhere) and f a t i g u e f a i l u r e throughout the p l a t f o r m ' s l i f e , which i s u s u a l l y between 20 and 30 y e a r s . The c r i t i c a l p o i n t s i n the design are, however, not the deck but the towers and base s l a b (Sjoerdsma, 1975b). The towers must be designed to prevent implosion under the l a r g e h y d r o s t a t i c f o r c e s due to the s t r u c t u r e ' s deep d r a f t and the a d d i t i o n a l wave induced p r e s s u r e l o a d i n g . The d i f f e r e n t i a l h y d r o s t a t i c pressure a c t i n g at the base of the towers may be l a r g e r d u r i n g the c o n s t r u c t i o n or tow-out phases, when the c e l l s are not f i l l e d with b a l l a s t , than when the p l a t f o r m i s o n - s i t e and o p e r a t i o n a l . T h i s must be i n v e s t i g a t e d to determine the c r i t i c a l design l o a d . The c a i s s o n w i l l a l s o have to r e s i s t implosion from l a r g e d i f f e r e n t i a l h y d r o s t a t i c p r e s s u r e s i f there are c e l l u l a r compartments (as with the p l a t f o r m s shown in f i g u r e 2.2). I t must a l s o be s t r o n g enough to r e s i s t damage from foundation l o a d s . These may be l o c a l l y high due to contact pressure with o b j e c t s such as boulders on the seabed or to the high r e s i s t a n c e of dense sand pockets to deformation d u r i n g i n s t a l l a t i o n . According to one code ( F e d e r a t i o n I n t e r n a t i o n a l e de l a P r e c o n t r a i n t e , 1977), the s l a b must be designed f o r 200 t/m 2 at a l l l o c a t i o n s to account f o r u n c e r t a i n t y i n s o i l i n v e s t i g a t i o n s and p e n e t r a t i o n r e s i s t a n c e and f o r higher values i f dense sand i s found from s o i l i n v e s t i g a t i o n s . T h i s value i s about an order of magnitude hig h e r than the uniform bearing pressure c a l c u l a t e d f o r the s l a b . 57 For the base s l a b , i t i s r e a d i l y apparent that the c r i t i c a l d e s i gn loads are those encountered upon i n s t a l l a t i o n . Other c r i t i c a l design c o n d i t i o n s are not so obvious. For example, the s t e e l g r a v i t y type p l a t f o r m s towed from Europe to the Congo were designed f o r g r e a t e r wave loads expected d u r i n g the tow than they would be s u b j e c t e d to once i n s t a l l e d i n the r e l a t i v e l y calm waters o f f s h o r e the Congo coast ( L a l l i , 1977). The dynamic analyses r e q u i r e d f o r a l a r g e g r a v i t y type s t r u c t u r e are numerous and i n v o l v e d . Since many of the loads a c t i n g on the s t r u c t u r e (wind, waves, and earthquakes) c o n t a i n components of many f r e q u e n c i e s , s p e c t r a l analyses are r e q u i r e d f o r both resonance s t u d i e s and f a t i g u e c a l c u l a t i o n s . In a d d i t i o n to the s i g n a l being random, the s t r u c t u r e w i l l probably not be symmetrical and d i f f e r e n t d i r e c t i o n s of l o a d i n g w i l l have to be i n v e s t i g a t e d . For a more thorough p r e s e n t a t i o n of the s t r u c t u r a l requirements f o r an o f f s h o r e g r a v i t y s t r u c t u r e , the reader i s r e f e r r e d to s e v e r a l papers concerned wholly with t h i s t o p i c (Penzien, 1976; R0ren and Fames, 1976; Waagaard, 1977; Watt, 1979). 3.3 P l a t f o r m C o n s t r u c t i o n Of paramount importance i n the c o n s t r u c t i o n of a l a r g e (concrete) g r a v i t y p l a t f o r m i s the a v a i l a b i l i t y of s u i t a b l e s i t e s f o r dry docks, shallow water c o n s t r u c t i o n areas, and deep water c o n s t r u c t i o n s i t e s . The base s e c t i o n of the p l a t f o r m i s b u i l t i n an excavated 58 dry dock. When the r a f t has been completed and the c a i s s o n w a l l s r a i s e d t o a predetermined h e i g h t , the dry dock i s flo o d e d , the cofferdam removed, and the base s e c t i o n f l o a t e d up and towed out to a shallow water s i t e ( u s u a l l y a nearby or at t a c h e d bay or f j o r d ) where i t i s secured by mooring c a b l e s (Clausen, 1976). Compressed a i r may be used under the foundation t o add buoyancy i f there are problems i n f l o a t i n g i t out of the dry dock ( D e r r i n g t o n , 1977) or to cut excavation c o s t s (Werenskiold, 1977). At the shallow water c o n s t r u c t i o n s i t e the base c a i s s o n i s completed and the towers are e r e c t e d . When the towers are completed, the s t r u c t u r e i s then towed out to a 'deep water c o n s t r u c t i o n area where i t p a r t i a l l y submerged by f l o o d i n g b a l l a s t compartments i n the base s e c t i o n and towers, and then moored. I t i s at t h i s s i t e that the deck i s u s u a l l y mated (Sjoerdsma, 1975b). The deck, which was b u i l t onshore, i s loaded onto two barges (or o l d t a n k e r s ) . These barges are then towed out to where the p l a t f o r m i s and p o s i t i o n e d so that the deck i s over the towers. The p l a t f o r m i s then p a r t i a l l y u n b a l l a s t e d to r a i s e the deck o f f the barges and onto the towers (Clausen, 1976). The s t r u c t u r e , v i r t u a l l y complete, i s now ready f o r tow-out. The t r a n s p o r t of the s t r u c t u r e between the va r i o u s c o n s t r u c t i o n s i t e s and then the tow-out to sea f o r i n s t a l l a t i o n must be c a r e f u l l y planned before c o n s t r u c t i o n begins. There must be adequate bottom c l e a r a n c e and room to maneuver the s t r u c t u r e throughout a l l the towing r o u t e s . These c o n s i d e r a t i o n s are the r e s p o n s i b i l i t y of a maritime c o n s u l t a n t 59 who i s w e l l versed i n these p r a c t i c e s (Werenskiold, 1977). 3.4 P l a t f o r m I n s t a l l a t i o n The p l a t f o r m , being p a r t i a l l y submerged f o r s t a b i l i t y , i s towed out to l o c a t i o n by an a r r a y of tugboats. T h i s i s an extremely d e l i c a t e o p e r a t i o n that must be very w e l l planned and co o r d i n a t e d by the maritime c o n s u l t a n t . The p o s i t i o n i n g and submerging of the s t r u c t u r e i s a l s o h i s r e s p o n s i b i l i t y . Weather f o r e c a s t s are used to choose a s a i l i n g time and are c o n s t a n t l y monitored and updated to ins u r e calm seas f o r the tow-out (Werenskiold, 1977). The s t r u c t u r e once o n - s i t e can be p l a c e d only approximately on l o c a t i o n . Because of the hig h i n e r t i a of such a l a r g e s t r u c t u r e , even when moving very slowly, there w i l l no doubt be some f i n i t e motions at the moment of touchdown, e s p e c i a l l y i f there i s a c u r r e n t present (Watt, 1976). The sea must be r e l a t i v e l y calm at the time of i n s t a l l a t i o n to a v o i d e x c e s s i v e motions of the s t r u c t u r e that may damage the c a i s s o n and i t s appendages. The i n s t a l l a t i o n sequence i s shown i n f i g u r e 3.8. The s t r u c t u r e i s s y s t e m a t i c a l l y b a l l a s t e d once o n - s i t e to stay l e v e l while s i n k i n g . The r a t e of submergence i s c a r e f u l l y monitored so that the s t r u c t u r e does not impact the s e a f l o o r h e a v i l y and damage the bottom s l a b , s k i r t s or r i b s . To a i d i n p l a c i n g the s t r u c t u r e and min i m i z i n g damage to both the s t r u c t u r a l and s o i l components of the foundation, s t e e l dowels which portrude s e v e r a l meters below the s k i r t s are pr o v i d e d . The dowels pen e t r a t e the s e a f l o o r under the weight of the p l a t f o r m as i t s i n k s and pro v i d e r e s i s t a n c e to h o r i z o n t a l motion 60 (c) Skirt driving W) Grouting F i g u r e 3.8 - I n s t a l l a t i o n sequence f o r a g r a v i t y p l a t f o r m (Adapted from Watt, 1976) 61 which c o u l d break o f f the s k i r t s or r i b s or gouge out the foundation s o i l s , i m p a i r i n g s t a b i l i t y under storm c o n d i t i o n s . The base d e t a i l of a CONDEEP type p l a t f o r m i n s t a l l e d i n the North Sea i s shown i n f i g u r e 3.9. As the s t r u c t u r e i s f u r t h e r submerged, the s k i r t s and r i b s p e netrate the foundation s o i l . To keep the s t r u c t u r e v e r t i c a l d u r i n g s k i r t p e n e t r a t i o n i n t o the seabed, which i n general w i l l be i r r e g u l a r due to a s l o p i n g s e a f l o o r and v a r y i n g s o i l c o n d i t i o n s at the s i t e , l a r g e moments may be a p p l i e d to the foundation by b a l l a s t i n g a p p r o p r i a t e c e l l s thereby d r i v i n g the s k i r t s deeper (Clausen, 1976). Care must be taken to allow ample time f o r water entrapped w i t h i n the s k i r t compartments to flow out from underneath the s l a b . I f the p l a t f o r m i s lowered too f a s t , h i g h c u r r e n t v e l o c i t i e s may r e s u l t and cause channels to be eroded underneath the s t r u c t u r e that may l e a d to more e r o s i o n and th r e a t e n the s t a b i l i t y of the p l a t f o r m (Gerwick, 1974) . To i n s u r e good contact between the base s l a b of the s t r u c t u r e and the foundation s o i l s , the space between them i s u s u a l l y grouted u t i l i z i n g a b u i l t - i n p i p i n g system i n the base p r o v i d e d f o r t h i s purpose ( C a l l i s et a l , 1979). Grouting u s u a l l y begins a f t e r a few p o i n t s on the base have touched down. The s t r u c t u r e must be submerged slowly to allow excess grout to flow out from underneath the s t r u c t u r e without damaging the foundation s o i l s or . o v e r s t r e s s i n g the s k i r t s (Watt, 1976). Submersibles may be used to monitor the success of g r o u t i n g o p e r a t i o n s ( C a l l i s et a l , 1979). The base of the s t r u c t u r e i s u s u a l l y instrumented so that 62 k 50jn j F i g u r e 3.9 - D e t a i l of CONDEEP base s t r u c t u r e ( A f t e r Clausen, 1976) 63 d e c i s i o n s can be made d u r i n g i n s t a l l a t i o n about the amount of p e n e t r a t i o n p o s s i b l e . I f e x c e s s i v e pressure i s e x e r t e d on any of the foundation components from e i t h e r pushing o b j e c t s such as boulders i n t o the s e a f l o o r or i n c r e a s e d d r i v i n g r e s i s t a n c e from say a l e n s e of dense sand, the submergence may be h a l t e d and g r o u t i n g to f i l l the i n t e r s k i r t spaces may commence. For one CONDEEP s t r u c t u r e very high p r e s s u r e s were experienced on the base of one c e l l d u r i n g submergence - probably from the high deformation r e s i s t a n c e of a l e n s e of dense sand that was undetected d u r i n g the s o i l i n v e s t i g a t i o n s (Clausen, 1976). The d e c i s i o n t o s t o p d r i v i n g the p l a t f o r m t o prevent s t r u c t u r a l damage to the s l a b was made based on i n f o r m a t i o n from instruments b u i l t i n t o the c a i s s o n . The data a v a i l a b l e from the instrument i n t e r p r e t a t i o n s i s shown in f i g u r e 3.10. A f t e r g r o u t i n g i s completed, some form of scour p r o t e c t i o n may be p l a c e d depending upon l o c a l s o i l c o n d i t i o n s and expected water p a r t i c l e v e l o c i t i e s near the s t r u c t u r e . G r a v e l mats connected to the s t r u c t u r e and r o l l e d out a f t e r i n s t a l l a t i o n i s completed have been used (Offshore Europe, 1974). 3.5 P l a t f o r m Instrumentation Platforms are g e n e r a l l y w e l l instrumented to (1) a i d i n i n s t a l l a t i o n , and (2) to p r o v i d e i n f o r m a t i o n on the performance of the s t r u c t u r e d u r i n g i t s o p e r a t i o n a l l i f e . Although the c o s t of instrumenting the s t r u c t u r e i s high, the money saved i n c o n s t r u c t i o n c o s t s i s more than o f f s e t by t h i s ( M c C l e l l a n d , 1977) s i n c e m a t e r i a l s and l a b o r are reduced by not having to i n c r e a s e dimensions to account f o r u n c e r t a i n t i e s i n i n s t a l l a t i o n 64 « 200 Design Maximum Allowable Value 2? (A S 100 0) E 50 I Expected Maximum Values 10 15 20 Dome Number F i g u r e 3.10 Maximum dome co n t a c t p r e s s u r e s observed dur i n g i n s t a l l a t i o n of the " B e r y l A" CONDEEP ( A f t e r Clausen, 1976) 65 loads ( s o i l r e a c t i o n s ) . Instrumentation f o r measuring p l a t f o r m response p r o v i d e s data f o r f u t u r e design on pore p r e s s u r e r i s e , l a t e r a l displacements, e t c . a f t e r the p l a t f o r m i s i n s t a l l e d . The f o l l o w i n g i n s t r u m e n t a t i o n has been used to monitor the i n s t a l l a t i o n of p l a t f o r m s now on s i t e (DiBagio et a l , 1976): - Wavedata by means of a buoy anchored near the p l a t f o r m - Bottom c l e a r a n c e by means of echo-sounders i n s t a l l e d under the base of the c a i s s o n - D r a f t by ,means of pressure t r a n s d u c e r s mounted near the base - B a l l a s t water l e v e l i n c e l l s and towers by means of pressure t r a n s d u c e r s w i t h i n these compartments - Bending moments and a x i a l f o r c e s i n dowels from s t r a i n gauges - Water pr e s s u r e i n s k i r t compartments beneath the c a i s s o n d u r i n g p e n e t r a t i o n and c o n t a c t g r o u t i n g by means of d i f f e r e n t i a l pressure t r a n s d u c e r s - V e r t i c a l i t y from a b i a x i a l i n c l i n o m e t e r - Base c o n t a c t p r e s s u r e s using e a r t h pressure transducers mounted f l u s h on the s l a b - S t r a i n i n r e i n f o r c i n g s t e e l i n base s l a b s and c e l l w a l l s by means of s t r a i n guages i n the reinforcement - Short term settlement by means of pressure measurements i n a c l o s e d h y d r a u l i c system Other i n s t r u m e n t a t i o n has been used to monitor the performance of these p l a t f o r m s (DiBagio et a l , 1976): - A complete system f o r o c e a n o g r a p h i c a l / m e t e o r o l o g i c a l measurements (wave, t i d e , c u r r e n t , wind and temperature data) - Base c o n t a c t p r e s s u r e s by means of e a r t h pressure t r a n s d u c e r s mounted f l u s h on the s l a b - S t r u c t u r a l s t r a i n at the base of the towers, g i v i n g the moments from wave a c t i o n t r a n s f e r r e d to the foundation, from s t r a i n gauges - L i n e a r a c c e l e r a t i o n s and displacements at the base, at mid- 66 height of the towers, and at deck l e v e l - Angular a c c e l e r a t i o n s and displacements at the base and deck l e v e l s - Long-term h o r i z o n t a l and v e r t i c a l displacements by means of a f l e x i b l e t e l e s c o p i c c a s i n g i n s t a l l e d under the c a i s s o n - Pore p r e s s u r e s i n the foundation s o i l by means of piezometers i n s t a l l e d beneath the p l a t f o r m A computer operated d i g i t a l data a c q u i s i t i o n system i s used to process data as i t i s r e c e i v e d with the computation of b a s i c s t a t i s t i c a l data being processed o n - l i n e and s t o r e d on a magnetic tape (Clausen et a l , 1975). 67 CHAPTER 4 THE EKOFISK TANK - A CASE STUDY The E k o f i s k tank has been the s u b j e c t of numerous papers (Bjerrum, 1973; Braun, 1974; Clausen et a l , 1975; Duncan, 1972; Gerwick and Hognstad, 1973; Lee, 1976; Lee and Focht, 1975a; Lee and Focht, 1975b; Marion, 1974). Being the f i r s t l a r g e o f f s h o r e g r a v i t y s t r u c t u r e i n s t a l l e d , i t n a t u r a l l y r e c e i v e d a l o t of a t t e n t i o n i n the e n g i n e e r i n g community. The E k o f i s k tank i s f a m i l i a r to almost everyone i n v o l v e d i n o f f s h o r e p l a t f o r m design and c o n s t r u c t i o n and has a r e l a t i v e l y l a r g e body of l i t e r a t u r e a s s o c i a t e d with i t . With these p o i n t s i n mind, a d i s c u s s i o n of the E k o f i s k tank would appear to be u s e f u l as a means of p r e s e n t i n g g e o t e c h n i c a l concepts and the a p p l i c a t i o n of t h e o r i e s i n the o f f s h o r e environment. A g e o t e c h n i c a l case study of the tank i s presented h e r e i n . A g e n e r a l d e s c r i p t i o n of the E k o f i s k tank may be found in s e v e r a l sources (Gerwick and Hognstad, 1973; Marion, 1974; Offshore Europe, 1974). The d e t a i l s of the design, c o n s t r u c t i o n , and i n s t a l l a t i o n of t h i s p l a t f o r m are d i s c u s s e d i n depth in these papers and w i l l only be h i g h l i g h t e d here. The tank was b u i l t near Stavanger, Norway, then towed over 400 k i l o m e t e r s from the Norwegian coa s t to the E k o f i s k f i e l d i n the middle of the North Sea where i t was p l a c e d on June 30, 1973. A f t e r being p o s i t i o n e d , the s t r u c t u r e was b a l l a s t e d with water to imbed i t i n the foundation s o i l s . P o s i t i o n i n g e r r o r s were 10 meters o f f t a r g e t and 3°50' out of o r i e n t a t i o n (Marion, 68 1974). The base of the s t r u c t u r e , shown i n d e t a i l i n f i g u r e 4.1, i s covered with 5 cm h i g h c o r r u g a t e d s t e e l p l a t e s and has 40 cm high s k i r t s along the p e r i p h e r y and 40 cm high r i b s underneath the c e n t r a l s t r u c t u r e ; these were provided to o b t a i n f u l l c o n t a c t with the s e a f l o o r s o i l . A f t e r s k i r t d r i v i n g was completed, nylon mats atta c h e d j u s t above the s k i r t s were r o l l e d out by d i v e r s and rocks dumped on them to provide p r o t e c t i o n a g a i n s t scour (Gerwick and Hognstad, 1973). A d d i t i o n a l sand b a l l a s t was added a f t e r placement to achieve a maximum negative buoyancy f o r the tank. The submerged weight of the tank a f t e r t h i s b a l l a s t i n g was 190,000 me t r i c tons (Clausen et a l , 1975). The f i n a l c o s t of the p l a t f o r m i n c l u d i n g i n s t a l l a t i o n was i n excess of $28 m i l l i o n (Offshore Europe, 1974). 8 The s t r u c t u r e i s n e a r l y c i r c u l a r i n p l a n , resembling a square with rounded c o r n e r s , with an approximate diameter of 93 meters. I t i s 90 meters high and r e s t s on the seabed i n 70 meters of water. One m i l l i o n b a r r e l s of crude o i l may be s t o r e d i n the c e n t r a l r e s e r v o i r which i s roughly 45 meters square i n p l a n and 70 meters high; t h i s r e s e r v o i r i s composed of nine lobes f o r maximum s t r u c t u r a l s t r e n g t h (Gerwick and Hognstad, 1973) each with w a l l s n e a r l y one meter t h i c k at the base (Offshore Europe, 1974). Surrounding the r e s e r v o i r i s a p e r f o r a t e d breakwater designed to reduce wave loads on the tank, which extends from about 12 meters above the water s u r f a c e to "This f i g u r e i s i n 1973 U.S. d o l l a r s . 69 F i g u r e 4.1 - D e t a i l of the E k o f i s k tank bottom ( A f t e r Clausen et a l , 1975) 70 the base s l a b where i t i s r i g i d l y a t t a c h e d . The h e a v i l y post- tensioned base s l a b i s 6 meters t h i c k and extends beneath the e n t i r e s t r u c t u r e forming a huge s o l i d r a f t foundation c o v e r i n g an area of 7360 m2 (Offshore Europe, 1974). The buoyant weight of the tank i s now about 190,000 metric tons and i n s t a t i c water e x e r t s an average p r e s s u r e of about 25.8 t/m 2 on the foundation s o i l s . Under wave l o a d i n g , there w i l l be a f l u c t u a t i n g component of the v e r t i c a l s t r e s s which i s on the order of 5% of the s t a t i c p r essure (H0eg, 1976). T h i s f l u c t u a t i n g v e r t i c a l l o a d i s i n phase with the h o r i z o n t a l f o r c e and moment (Schjetne, .1976). For the E k o f i s k tank, the magnitude of the f l u c t u a t i n g v e r t i c a l f o r c e i s about 10,000 metric tons f o r the design wave. Th e r e f o r e , when a n a l y z i n g the foundation f o r design wave c o n d i t i o n s , a v e r t i c a l f o r c e of 200,000 metric tons a c t i n g on the foundation i s used; t h i s corresponds to a uniform v e r t i c a l pressure of about 27.2 t/m 2. For the 100-year design wave, a h o r i z o n t a l f o r c e of about 78,600 m e t r i c tons w i l l a c t on the tank (Bjerrum, 1973). Since t h i s r e s u l t a n t f o r c e w i l l a c t above the s e a f l o o r , a moment w i l l be a p p l i e d to the fou n d a t i o n . The magnitude of t h i s moment i s approximately 2,800,000 ton-meters (Clausen et a l , 1975). The tank i s shown s c h e m a t i c a l l y i n f i g u r e 4.2 with the loads a c t i n g on i t co r r e s p o n d i n g to the 100-year wave. Some design storm data i s shown i n f i g u r e 4.3. Foundation c o n d i t i o n s at the E k o f i s k f i e l d are t y p i c a l of the North Sea: a l t e r n a t i n g l a y e r s of dense sands and h e a v i l y o v e r c o n s o l i d a t e d c l a y s . A t y p i c a l g e o t e c h n i c a l p r o f i l e from the E k o f i s k f i e l d i s shown i n f i g u r e 4.4. The upper 26 meters are 71 ft = 78,6001 ^36m L ^93m- Ja^lOpOOt Pv =19Q000t « X " - S W.L, S70m F i g u r e 4.2 - Loads on the E k o f i s k tank f o r the 100-year wave 5000 WAVES 15 MRS DURATION * & 400 20 40 60 60 FT I I L_ 0 5 <0 IS 20 25 M. WAVE HEIGHT. H F i g u r e 4.3 - Design storm data f o r the E k o f i s k f i e l d ( A f t e r Lee and Focht, 1975a) 72 « -Mm ,j 50 m 100 m 150 ml- • —1 20 m 7C m ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ Sand Cljy Sind F i g u r e 4.4 - ^ j « ^ o t e c h n i c a l ) P r o f i l e f r o . E k o H s k M e l a -Om Sea floor jc-70m UNDRAINED SHEAR STRENGTH (t/m') 11 '° S i " I S " uj uj o in SO 60 Fin* land Stiff sandy clay Fint und Hard clay * i • < • 0 • • > • • UU triaxial • Unconfintd compression test o Pocket penetrometer F i g u r e 4.5 - Shear s t r e n g t h data from E k o f i s k l A r t e r Clausen et a l , 1975) 73 comprised of extremely uniform f i n e sand with a t h i n c l a y seam at about 18 meters below the s e a f l o o r ; the upper few meters have a r e l a t i v e d e n s i t y on the order of 100% (Bjerrum, 1973). T h i s high d e n s i t y i s most probably due to the e f f e c t of c o u n t l e s s waves that have passed overhead s i n c e the sand was d e p o s i t e d (Bjerrum, 1973). Shear s t r e s s e s are induced i n the s o i l from p a s s i n g waves because of the v a r y i n g p r e s s u r e d i s t r i b u t i o n they impose on the s e a f l o o r (Henkel, 1970). These s t r e s s e s c y c l e back and f o r t h and may compact the sand i f they are s u f f i c i e n t l y l a r g e . T h i s i s termed " p r e s h e a r i n g " (Bjerrum, 1973) and has been demonstrated to be an important source of s o i l compaction in the l a b o r a t o r y (Lee and Focht, 1975a). The s t i f f c l a y beneath the sand has an undrained shear s t r e n g t h of about 40 t/m 2 (Bjerrum, 1973). The c l a y seam at 18 meters below the mudline i s s u b s t a n t i a l l y weaker. Some shear s t r e n g t h data i s presented i n f i g u r e 4.5. Foundation s t u d i e s f o r the p l a t f o r m were performed independently by M c C l e l l a n d Engineers, L t d . and the Norwegian G e o t e c h n i c a l I n s t i t u t e . The Norwegian G e o t e c h n i c a l I n s t i t u t e r e p resented Det Norske V e r i t a s , the agency r e s p o n s i b l e f o r approving the p l a t f o r m s a f e t y f o r the Norwegian government, and was r e s p o n s i b l e f o r checking the foundation s a f e t y independently of M c C l e l l a n d ' s f i n d i n g s . There was a great concern about s a f e t y s i n c e an o i l s p i l l of p o s s i b l y one m i l l i o n b a r r e l s would be d i s a s t r o u s (Duncan, 1972). F i n a l approval of the tank r e q u i r e d t h at i t c o u l d not be used f o r o i l storage f o r s e v e r a l months a f t e r i n s t a l l a t i o n ; thus, i f a f a i l u r e o c c u r r e d d u r i n g t h i s p e r i o d , no s p i l l c o u l d take p l a c e (Clausen et a l , 1975). 74 P r e l i m i n a r y s t u d i e s c a r r i e d out at the Norwegian G e o t e c h n i c a l I n s t i t u t e (NGI) were r e p o r t e d by Duncan (1972). F i n i t e element mod e l l i n g of the foundation, t a k i n g i n t o account the n o n l i n e a r behaviour of the s o i l s , was done to p r e d i c t the e l a s t i c settlement of the s t r u c t u r e and the displacements expected under storm wave l o a d i n g . E l a s t i c settlement was estimated t o be about 30 cm f o r the tank due to i t s own weight (Duncan, 1972). Assuming that the lo a d - s e t t l e m e n t curve f o r e l a s t i c settlement i s l i n e a r , t h i s would imply that the s t r u c t u r e would move up and down about 1.5 cm when subjected to the f l u c t u a t i n g v e r t i c a l f o r c e of the design wave. The h o r i z o n t a l displacements of the tank were estimated to be about 15 cm back and f o r t h f o r the design wave (Bjerrum, 1973). Concurrent with these l i n e a r displacements are r o c k i n g motions which r e s u l t from the c y c l i c moment. NGI estimates showed that s u b j e c t to the design wave, one s i d e of the base s l a b would move down 30 cm while the opp o s i t e s i d e would move up about 45 cm. Superimposed on the e l a s t i c settlement due to the p l a t f o r m weight, t h i s would mean that one s i d e would l i f t about 15 cm o f f the sand (Duncan, 1972) r e s u l t i n g i n a p o s s i b l y unstable s i t u a t i o n . Because the p l a t f o r m would almost undoubtedly be subjected to numerous storms before the 100-year design storm would h i t , the tank was expected to s e t t l e from the p r e s h e a r i n g e f f e c t and the sand under the tank to d e n s i f y and become s t i f f e r reducing the motions (Duncan, 1972). T h i s settlement and accompanying i n c r e a s e i n s t i f f n e s s meant that r o c k i n g motions expected f o r the 100-year wave c o u l d be m o d i f i e d 75 from the o r i g i n a l e s t i m a t e s . New ' c a l c u l a t i o n s i n d i c a t e d t hat the base s l a b would move up about 15 cm on one s i d e and down 15 cm on the other (Bjerrum, 1973). T h i s i m p l i e d that the base s l a b would not be l i f t e d o f f the s o i l , and. at a l l times would exert a p o s i t i v e pressure on the foundation (Bjerrum, 1973). R e s u l t s of these s t u d i e s are shown i n f i g u r e 4.6. The NGI f i n i t e element s t u d i e s of displacements i n c l u d e d the e f f e c t of the pore water p r e s s u r e change at the s e a f l o o r due to the passage of waves overhead (Bjerrum, 1973). They d i d not, however, i n c l u d e the e f f e c t s of c y c l i c l o a d i n g on the foundation s o i l s . Rahman et a l (1977) have shown that pore water pressure r a t i o s of about 20% and 8% w i l l occur under the edges and cente r of the tank, r e s p e c t i v e l y , when s u b j e c t e d to the 100-year storm. T h e i r a n a l y s i s i s f o r a r e l a t i v e d e n s i t y of 85%, which i s l e s s than the r e l a t i v e d e n s i t y i n - s i t u , and i n c l u d e s the e f f e c t s of p a r t i a l drainage i n the sand. Although t h e i r r e s u l t s are not s t r i c t l y c o r r e c t , they do show that excess pore water p r e s s u r e s w i l l develop under the tank d u r i n g design storm l o a d s . T h i s has been confirmed from o b s e r v a t i o n s o n - s i t e u sing piezometers and pressure gauges i n s t a l l e d underneath the s t r u c t u r e (Clausen et a l , 1975). Expected r o c k i n g displacements would then be g r e a t e r than r e p o r t e d by Bjerrum (1973) f o r the NGI analyses s i n c e the i n c r e a s e i n pore water pressure under the tank would decrease the s t i f f n e s s of the upper sand l a y e r . Settlement observatons have been r e p o r t e d by Foss (1974) and Clausen et a l (1975). A l o a d - s e t t l e m e n t curve i s shown i n f i g u r e 4.7 f o r the i n s t a l l a t i o n phase of the tank. A f t e r touchdown, the p l a t f o r m was b a l l a s t e d to seat i t f i r m l y on the 76 F i g u r e 4.6 - P r e d i c t e d r o c k i n g displacements f o r the E k o f i s k tank ( A f t e r Duncan, 1972) igure 4.7 - Load-settlement curve f o r E k o f i s k tank ( A f t e r Clausen et a l , 1975) 77 foundation s o i l s . During t h i s time the seabed was being deformed from both e l a s t i c compression and p l a s t i c d i s p lacements. The p l a s t i c displacements corresponded to the p e n e t r a t i o n of short c o n c r e t e s k i r t s and to the f l a t t e n i n g of the s e a f l o o r beneath the s t r u c t u r e ; s i n c e the bearing c a p a c i t y of u n d u l a t i o n s and mounds would be exceeded as the p l a t f o r m seated, these f e a t u r e s were destroyed and the p l a t f o r m s e t t l e d . T h i s "bedding settlement" should correspond to the s k i r t depth f o r a f l a t s e a f l o o r , i n d i c a t i n g f u l l s k i r t p e n e t r a t i o n and base c o n t a c t with the s e a f l o o r . The load-settlement curve became n e a r l y l i n e a r when the submerged weight reached 50,000 tons. The p e n e t r a t i o n of the 40 cm high s k i r t s i n t o the s e a f l o o r at t h i s time was about 35 cm. I t i s important that the l o a d - settlement curve became l i n e a r . T h i s i n d i c a t e d that ( e s s e n t i a l l y ) f u l l c o n t a c t between the base of the s t r u c t u r e and the s e a f l o o r was achieved (Clausen et a l , 1975). If the l i n e a r p o r t i o n of the l o a d - s e t t l e m e n t curve i s e x t r a p o l a t e d back to zero submerged weight and forward to 190,000 tons, the e l a s t i c settlement of the tank due to i t s own weight may be e s t a b l i s h e d . T h i s r e s u l t s i n an e l a s t i c settlement of about 10 cm, s u b s t a n t i a l l y l e s s than the 20 cm p r e d i c t e d by NGI. 9 The d i s c r e p a n c y may be due to the use of s t i f f n e s s parameters i n the f i n i t e element analyses that were 9One should note that Duncan's (1972) r e p o r t e d estimate of 30 cm f o r e l a s t i c settlement of the tank was made before f i n a l d i s c r e p a n c i e s i n the value of s o i l parameters were c l e a r e d up (Lee and Focht, 1975a). T h i s estimate was l a t e r changed to 20 cm (Braun, 1974). 78 not r e a l l y r e p r e s e n t a t i v e of the "undisturbed" s o i l ; s t i f f n e s s parameters were probably chosen much too c o n s e r v a t i v e l y as a consequence of the d i f f i c u l t y and u n c e r t a i n t y a s s o c i a t e d with o f f s h o r e s o i l t e s t i n g and sampling - p a r t i c u l a r l y at that time - a decade ago. Settlement continued to occur a f t e r the p l a t f o r m was i n s t a l l e d . The time h i s t o r y of settlement f o r the f i r s t seven months a f t e r i n s t a l l a t i o n i s shown i n f i g u r e 4.8. Most of the b a l l a s t was added to the tank i n the f i r s t few days a f t e r i t was p l a c e d . The load-settlement curve p r e v i o u s l y d i s c u s s e d was developed f o r t h i s time i n t e r v a l . Settlement i n the e a r l y days of J u l y , 1973, Was due to the e l a s t i c response from i n c r e a s e d submerged weight of the p l a t f o r m as i t was b a l l a s t e d . Settlement i n the f o l l o w i n g months may be a t t r i b u t e d to a v a r i e t y of f a c t o r s , namely: i n c r e a s e d submerged weight of the p l a t f o r m (from more b a l l a s t i n g ) , c o n s o l i d a t i o n i n the c l a y , and wave a c t i o n on the tank. The amount of settlement due to the i n c r e a s e d b a l l a s t load can e a s i l y be estimated from e x t r a p o l a t i n g the load-settlement curve i n f i g u r e 4.7. The o v e r a l l e l a s t i c settlement would be about 10 cm and would not i n c r e a s e a f t e r the tank was f u l l y b a l l a s t e d . At the end of b a l l a s t i n g , settlement was observed to be about 13 cm (see f i g u r e 4.8). Hence, the c o n s o l i d a t i o n and wave induced settlement was on the order of 3 cm up u n t i l the middle of October (when b a l l a s t i n g was t e r m i n a t e d ) . During t h i s time the sea was r e l a t i v e l y calm as seen from the wave data i n the f i g u r e . Note that the wave h e i g h t s shown are the s i g n i f i c a n t wave h e i g h t s (a s t a t i s t i c a l parameter) not the 79 F i g u r e 4.8 - E k o f i s k settlement data r e l a t i n g submerged p l a t f o weight and storm wave data i n the e a r l y months a f t e r i n s t a l l a t i o n ( A f t e r Clausen et a l , 1975) MQ0OO r itqpoo 5 | tOQOOO S KtOOO *1* 1974 F i g u r e 4.9 - Settlement data f o r E k o f i s k tank d u r i n g e a r l y storms ( A f t e r Clausen et a l , 1975) 80 maximum wave h e i g h t s ; these values must be i n c r e a s e d by approximately 80% to f i n d the maximum wave h e i g h t s (Sarpkaya and Isaacson); the exact i n c r e a s e depends on s t a t i s t i c a l data which i s not a v a i l a b l e . In November, the p l a t f o r m was subjected to s e v e r a l major storms. The f i r s t storm h i t on 6 November and a settlement of about 2 cm o c c u r r e d d u r i n g the next few days (Clausen et a l , 1975). On 19 November, the major storm of the year o c c u r r e d . When t h i s storm h i t , the p l a t f o r m i n s t r u m e n t a t i o n was out of s e r v i c e and the wave data was estimated from a nearby weather s h i p , the "Famita" (Foss, 1974). Estimates put the maximum wave height at about 22 meters, or about 90% of the 100-year design wave - t r u l y a s i g n i f i c a n t storm. The p l a t f o r m s e t t l e d about 5 cm d u r i n g the p e r i o d of 16 November to 20 November (Foss, 1974). T o t a l settlement d u r i n g November was about 7 cm, of which most probably o c c u r r e d i n the sand. The dense sand c o n s o l i d a t e d under the a c t i o n of repeated shear s t r e s s r e v e r s a l s (Clausen et a l , 1975). A d e t a i l e d r e c o r d of the November set t l e m e n t s i s shown i n f i g u r e 4 . 9 . A f t e r the storm of 19 November subsided, no d e t e c t a b l e a d d i t i o n a l settlement of the p l a t f o r m occurred f o r the next two months. From mid-December 1973 to J u l y 1974, the p l a t f o r m was observed to s e t t l e another 1-3 cm (Clausen et a l , 1975). T h i s was most l i k e l y due to c o n s o l i d a t i o n i n the c l a y . T o t a l settlement one year a f t e r i n s t a l l a t i o n was approximately 24 cm. T h i s was w i t h i n the 20-40 cm range p r e d i c t e d by NGI (Clausen et a l , 1975). They estimated that the i n i t i a l settlement would be 20 cm, and t h a t another 15 cm would occur over the l i f e of the 81 s t r u c t u r e from storm e f f e c t s (Braun, 1974). U n f o r t u n a t e l y , more recent data i s not a v a i l a b l e to extend the settlement-time curve shown in f i g u r e 4.8. Reported d i f f e r e n t i a l settlement of the p l a t f o r m a f t e r i n s t a l l a t i o n was 13 cm from the northeast (high) to the southwest (Clausen et a l , 1975). ( T h i s , however, may not a l l be settlement s i n c e the s e a f l o o r was uneven and perhaps s l i g h t l y s l o p i n g . ) Although seemingly l a r g e , t h i s corresponds to the p l a t f o r m being o f f v e r t i c a l by only about one-twentieth of a degree. In the twelve months a f t e r i n s t a l l a t i o n , a d d i t i o n a l d i f f e r e n t i a l s e ttlements of about 2 cm i n the east-west and 6 cm i n the north-south d i r e c t i o n s o c c u r r e d (Clausen et a l , 1975). Of i n t e r e s t , perhaps, i s how the settlement data was obtained. S i g h t i n g s were made on a nearby j a c k e t e d p l a t f o r m founded on deep p i l e s . T h i s p l a t f o r m had been p l a c e d more than a year before the E k o f i s k tank and was not expected to s e t t l e n o t i c e a b l y d u r i n g the p e r i o d under c o n s i d e r a t i o n (Foss, 1974). The development of excess pore water p r e s s u r e under the E k o f i s k tank has been the s u b j e c t of s e v e r a l s t u d i e s . F o r t u n a t e l y , some pore water p r e s s u r e data from E k o f i s k i s a v a i l a b l e to compare with t h e o r e t i c a l p r e d i c t i o n s . The p l a t f o r m base was instrumented with seven pressure gauges and the u n d e r l y i n g s o i l with twelve piezometers. A d e s c r i p t i o n of the i n s t a l l a t i o n of piezometers beneath the tank i s given by Clausen et a l (1975). The arrangement of these d e v i c e s i s shown i n f i g u r e 4.10. Data from the storm of 6 November, the f i r s t major storm to h i t the p l a t f o r m , i s shown i n f i g u r e 4.11. S e v e r a l important 82 ® : n rtftrt to gauge no. F i g u r e 4.10 - K ^ a t i ? n n . f f ^ r f S S U r e 9 a u 9 e s and piezometers beneath E k o f i s k tank ( A f t e r Clausen et a l , 1975) i 5 K O < 10 ui in m x a. ui a 20 25 75 SO •5 go \ 9 5 o 0)(T) ®_ Hydrostatic (for wattr dtpth • 67.5 m ) - \ _ LEGEND: _ K 4 th Nov. 1322- uBD _ H 6 th Nov. nSS-uiS. ~ I < {*)•• n rtftrt to gaugt no. - X — ® \ H 8 5 TO 75 W 85 go TORE WATER PRESSURE 11/m'l — U D © 0) ,® rtftrt to 1 gaugt no. o o < in < ui z X *— a. Ui o "5 0 2 ( 6 8 PORE WATER PRESSURE INCREASE It/m') DURING 6. NOV STORM F i g u r e 4.11 - Pore p r e s s u r e s observed under E k o f i s k tank d u r i n g the f i r s t ma-jor storm ( A f t e r Clausen et a l , 1975) 83 o b s e r v a t i o n s may be made. F i r s t of a l l , the pore water p r e s s u r e s i n c r e a s e d d u r i n g the storm at a l l t e s t l o c a t i o n s . Secondly, the maximum pore p r e s s u r e s developed i n the sand occ u r r e d not at the p l a t f o r m base, but some d i s t a n c e below i t . T h i r d l y , pore water pressure i n the c l a y seam was s u b s t a n t i a l l y higher than i n the sand, perhaps i n d i c a t i n g t h at p a r t i a l drainage o c c u r r e d i n the sand. And f i n a l l y , the pore water p r e s s u r e s that developed i n the sand beneath the c l a y seam were s i g n i f i c a n t l y l e s s than those developed i n the sand not f a r above i t . T y p i c a l pore water p r e s s u r e r a t i o s were on the order of 3% to 7% i n the sand. U n f o r t u n a t e l y , the instruments were not working f o r the storm of 19 November, which was n e a r l y as l a r g e as the design storm. C o n s i d e r a b l e c o n s o l i d a t i o n had occ u r r e d i n the sand from p r e v i o u s storms by t h i s time and may have a f f e c t e d the pore pressure response c o n s i d e r a b l y . No other pore water pressure data has been made a v a i l a b l e , and thus no p a r t i c u l a r c o n c l u s i o n s about the e f f e c t s of p r e s h e a r i n g on pore water p r e s s u r e response may be made here. E a r l y t h e o r e t i c a l s t u d i e s of pore water p r e s s u r e generation were r e p o r t e d by Bjerrum (1973). He assumed that the sand c o u l d not d r a i n at a l l over the course of the storm and t h e r e f o r e data from undrained l a b o r a t o r y shear t e s t s was d i r e c t l y a p p l i c a b l e . The dimensions of the s t r u c t u r e are such that f u l l drainage cannot take p l a c e d u r i n g the storm; the amount of drainage, of course, depends on the p e r m e a b i l i t y of the s o i l and len g t h of the drainage path. Hence, h i s assumption of no drainage t a k i n g p l a c e was not unfounded. The amount of pore water p r e s s u r e r i s e f o r a s i n g l e c y c l e i n undrained shear was determined from 84 l a b o r a t o r y t e s t s , the data being shown i n f i g u r e 4.12. By r e p r e s e n t i n g the design storm by the number of waves i n s p e c i f i e d height bands ( i . e . a histogram), the number of shear s t r e s s c y c l e s at a p a r t i c u l a r amplitude may be found s i n c e the wave.forces are known. Knowing the number of c y c l e s a p p l i e d at each shear s t r e s s amplitude, the pore water pressure developed under undrained c o n d i t i o n s may be estimated by summing up the c o n t r i b u t i o n of a l l c y c l e s . T h i s i s demonstrated i n Table VI. Bjerrum (1973) found f o r a r e l a t i v e d e n s i t y of about 90%, a pore water pressure r a t i o of about 31% would be developed beneath the p l a t f o r m , assuming undrained c o n d i t i o n s . T h i s a n a l y s i s , being very simple and c o n s e r v a t i v e , i s good f o r demonstrating whether f u r t h e r a n a l y ses are r e q u i r e d . I t should be noted that no c o n s i d e r a t i o n of the d i s t r i b u t i o n of s t r e s s e s beneath the p l a t f o r m was c o n s i d e r e d i n t h i s a n a l y s i s . The r e s u l t s of more advanced analyses are r e p o r t e d by Lee (1976) and Lee and Focht (1975a). There was some u n c e r t a i n t y with regards to the i n - s i t u r e l a t i v e d e n s i t y (Lee and Focht, 1975a). P r e l i m i n a r y s i t e i n v e s t i g a t i o n s at the E k o f i s k f i e l d made by M c C l e l l a n d Engineers, L t d . suggested that the sand was medium dense to dense with a r e l a t i v e d e n s i t y of about 80%. E a r l y s t u d i e s i n d i c a t e d t h a t the sand under the tank might l i q u e f y under the c y c l i c storm l o a d s . For t h i s reason, an e x t e n s i v e program of c y c l i c t e s t i n g was c a r r i e d out on samples taken from E k o f i s k , and f u r t h e r i n - s i t u t e s t s were performed to b e t t e r d e f i n e the r e l a t i v e d e n s i t y of the sand f o r c o r r e l a t i o n with l a b o r a t o r y t e s t r e s u l t s . The p r e l i m i n a r y t e s t s performed to assess the l i q u e f a c t i o n 85 UvwrBrassl*vct: T / o r ' H ' vi F i g u r e 4.12 - Pore water p r e s s u r e r i s e per c y c l e observed i n undrained simple shear with c y c l i c l o a d i n g f o r samples prepared with r e l a t i v e d e n s i t i e s of 80% ( A f t e r Bjerrum, 1973) Table VI Example of the Accumulated E f f e c t of a 100-year Storm ( A f t e r Bjerrum, 1973) Height of waves: m Number of waves, N O TO 4-8 48S 007 0-006 2-9 8-12 471 012 0013 61 12-16 282 017 0030 8-5 16-20 121 0-22 0 065 7-9 20-24 32 0-26 0150 4-8 24-26 3 0-30 0-300 0-9 Total 1394 311 86 p o t e n t i a l were standard undrained c y c l i c t r i a x i a l t e s t s used f o r earthquake s t u d i e s . Data f o r samples compacted at three r e l a t i v e d e n s i t i e s , 63%, 77%, and 100%, showed that l i q u e f a c t i o n ( d e f i n e d here as when the r a t i o of the excess pore water pressure to the e f f e c t i v e c o n f i n i n g pressure i s equal to u n i t y ) would take p l a c e i n the t e s t s with r e l a t i v e d e n s i t i e s of 63% and 77% when s u b j e c t e d to design storm c y c l i c shear s t r e s s e s (Lee and Focht, 1975a). Since the t e s t s used f o r a s s e s s i n g earthquake l i q u e f a c t i o n p o t e n t i a l are not r e a l l y a p p l i c a b l e to the ocean wave problem where p r e s h e a r i n g w i l l d e n s i f y the sand before design loads occur and p a r t i a l drainage w i l l take p l a c e , a d d i t i o n a l t e s t s were performed to reassess the l i q u e f a c t i o n p o t e n t i a l t a k i n g - these f a c t o r s i n t o account. In t h i s set of t e s t s , samples at d i f f e r e n t r e l a t i v e d e n s i t i e s were sheared i n undrained c y c l i c t r i a x i a l t e s t s at low s t r e s s l e v e l s and then allowed to r e c o n s o l i d a t e , s i m u l a t i n g the e f f e c t s of p r e s h e a r i n g . To i n v e s t i g a t e the b e n e f i c i a l e f f e c t s of p a r t i a l drainage, a l a b o r a t o r y t e s t procedure was developed to model t h i s . T h i s l a b o r a t o r y procedure i s o u t l i n e d by Lee and Focht (1975a). F i r s t , the p e r m e a b i l i t y of the sand was e s t a b l i s h e d and the time p e r i o d f o r 10% c o n s o l i d a t i o n to occur beneath the tank was ev a l u a t e d based on plane (and r a d i a l ) flow c o n d i t i o n s . T h i s time p e r i o d was estimated to be 500 seconds (125 seconds f o r r a d i a l flow) and was converted to an e q u i v a l e n t number of waves f o r the 10% c o n s o l i d a t i o n time p e r i o d , e q u a l l i n g about 50 (12.5 f o r r a d i a l f l o w ) . The samples were then t e s t e d undrained f o r t h i s number of c y c l e s . The pore water pressure r i s e was noted, then the back pressure was i n c r e a s e d to 90% of t h i s amount and 87 the drainage l i n e opened to allow the sample to c o n s o l i d a t e by 10% of i t s excess pore water p r e s s u r e . The drainage l i n e was then c l o s e d and the sample was t e s t e d undrained f o r another 50 (12.5) c y c l e s . T e s t i n g continued i n a s i m i l a r f a s h i o n u n t i l the samples e i t h e r l i q u e f i e d or reached e q u i l i b r i u m . From t h i s type of t e s t i n g , i t was found that a sample compacted to 77% r e l a t i v e d e n s i t y would not l i q u e f y . S h o r t l y a f t e r the second stage of l a b o r a t o r y t e s t s had been completed, data from a d d i t i o n a l cone penetrometer t e s t i n g at the s i t e became a v a i l a b l e . T h i s data i n d i c a t e d that the sand was extremely dense with a r e l a t i v e d e n s i t y of n e a r l y 100% (Lee and Focht, 1975a). A d d i t i o n a l l y , the p e r m e a b i l i t y of the sand was determined to be much lower than what had been found p r e v i o u s l y . A s e r i e s of new t e s t s were performed on the sand compacted to 100% r e l a t i v e d e n s i t y and t e s t e d under c o n d i t i o n s of undrained shear. T e s t s were performed on samples that were both u n c o n s o l i d a t e d and c o n s o l i d a t e d to simulate the e f f e c t s of p r e s h e a r i n g . From these t e s t r e s u l t s , i t was concluded that the sand possessed adequate r e s i s t a n c e to l i q u e f a c t i o n , with the p r e s h e a r i n g of samples adding a d d i t i o n a l c y c l i c s t r e n g t h (Lee and Focht, 1975a). The problem of pore water p r e s s u r e g e n e r a t i o n beneath the tank was i n v e s t i g a t e d a f t e r i n s t a l l a t i o n by Rahman et a l (1977) who formulated the problem mathematically. They represented the s o i l by f i n i t e elements, with l i n e a r . s t r e s s - s t r a i n behaviour, and c o n s i d e r e d the d i s t r i b u t i o n of s t r e s s e s w i t h i n the s o i l mass from both the weight of the tank and the a p p l i e d wave l o a d s . T h e i r method i s formulated as f o l l o w s : The zone of d i r e c t i o n a l 88 randomness of the waves i s assumed to be s u f f i c i e n t l y wide so th a t l o a d i n g on any plane p a s s i n g through the v e r t i c a l a x i s of the p l a t f o r m i s e s s e n t i a l l y the same as a l l the others when time averaged. Hence, the problem can be approximated as being axisymmetric with r e s p e c t to l o a d i n g , and t h e r e f o r e , pore water pr e s s u r e g e n e r a t i o n and d i s s i p a t i o n . The equation f o r r a d i a l and v e r t i c a l c o n s o l i d a t i o n i s then formulated to i n c l u d e a pore water pressure generation term whose parameters are d e f i n e d by data from undrained c y c l i c shear t e s t s . The r i s e i n pore water pr e s s u r e measured i n undrained c y c l i c t r i a x i a l t e s t s i s found f o r d i f f e r e n t c y c l i c shear s t r e s s l e v e l s and curves of number of c y c l e s versus pore water pressure are obtained. The c o e f f i c i e n t s of these curves are used i n the pore water pressure g e n e r a t i o n f u n c t i o n . The time h i s t o r y of l o a d i n g i s approximated by a histogram and the loads are a p p l i e d i n c r e m e n t a l l y to the p l a t f o r m . The storm i s a p p l i e d by time s t e p p i n g as f o l l o w s : a given number of c y c l e s at a c e r t a i n s t r e s s l e v e l (corresponding to an e q u i v a l e n t number of waves of a given height) are a p p l i e d (through the use of the pore water p r e s s u r e g e n e r a t i o n f u n c t i o n ) and the r e s u l t i n g pore water p r e s s u r e s are then allowed to d r a i n f o r an amount of time corresponding to the number of waves. The procedure i s cont i n u e d u n t i l the storm i s over, that i s , when a l l the waves have been represented by the time stepping procedure. R e s u l t s of t h e i r s t u d i e s showed that a l l o w i n g f o r p a r t i a l drainage i s extremely important f o r p r e d i c t i n g the c o r r e c t pore water p r e s s u r e s developed underneath the E k o f i s k p l a t f o r m . They found that i f the foundation sand had a r e l a t i v e d e n s i t y of 77%, 89 l i q u e f a c t i o n would not occur; i n f a c t , maximum pore water p r e s s u r e r a t i o s would be l e s s than about 30% beneath the e n t i r e f o u n d a t i o n . A Bjerrum (1973) type of a n a l y s i s at t h i s r e l a t i v e d e n s i t y would i n d i c a t e t hat the sand would have l i q u e f i e d under the tank (Rahman et a l , 1977). Rahman et a l ' s (1977) type of a n a l y s i s can provide i n f o r m a t i o n on the d i s t r i b u t i o n of pore water p r e s s u r e s beneath the tank. The other methods cannot. Some r e s u l t s of t h e i r s t u d i e s are shown i n f i g u r e 4.13. I t i s of i n t e r e s t to note that maximum pore water p r e s s u r e s are developed under the edges of the p l a t f o r m , not beneath the c e n t e r . T h i s w i l l a f f e c t a l l s t r e s s a n a l y s e s , and i s of p a r t i c u l a r s i g n i f i c a n c e when p r e d i c t i n g r o c k i n g motions. S t a b i l i t y a nalyses were c a r r i e d out f o r the tank to insure s a f e t y under storm wave l o a d i n g . For lac k of b e t t e r methods, the b e a r i n g c a p a c i t y equations of Hansen (1970) were used. S e v e r a l problems were encountered when t r y i n g to apply t h i s well-known bearing c a p a c i t y formula to the E k o f i s k tank (Bjerrum, 1973). F i r s t of a l l , the bearing c a p a c i t y f a c t o r s used i n the equation were determined s e m i - e m p i r i c a l l y f o r model f o o t i n g s of a very small s i z e . When e x t r a p o l a t i n g these r e s u l t s to the E k o f i s k tank with a base dimension of about 93 meters, c o n s i d e r a b l e s c a l e e f f e c t s were induced. The value of the b e a r i n g c a p a c i t y f a c t o r Nr was decreased to take t h i s i n t o account (Bjerrum, 1973). The r e d u c t i o n of Nr with f o o t i n g s i z e may a c t u a l l y be a t t r i b u t e d to a decrease i n the f r i c t i o n angle with an i n c r e a s e i n the mean p r i n c i p a l s t r e s s . Secondly, the i n c l i n e d l o a d f a c t o r proposed by Hansen (1970) had never been used on a foundation with such a high r a t i o of h o r i z o n t a l to 90 1 1 I r 0 , - T T * -i 4 i r> lb * Himry of CajkMstwit liom Timt - hra Dr*85% » , »kf •!0'9C*n/MC F i g u r e 4.13 - T h e o r e t i c a l p r e d i c t i o n of the pore water pressure d i s t r i b u t i o n beneath the E k o f i s k tank f o r r e l a t i v e d e n s i t i e s of 77% and 85% ( A f t e r Rahman et a l 1977) 91 v e r t i c a l f o r c e (about 38%). A thorough review of model t e s t r e s u l t s l e d to the c o n c l u s i o n that the i n c l i n a t i o n f a c t o r of Hansen (1970) was a c c e p t a b l e f o r the high r a t i o of h o r i z o n t a l to v e r t i c a l l o a d (Bjerrum, 1973). T h i s f a c t o r reduced the bearing c a p a c i t y to o n e - f i f t h of i t s value f o r v e r t i c a l l o a d i n g o n l y . F i n a l l y , the b e a r i n g c a p a c i t y of the tank would be i n f l u e n c e d by drainage c o n d i t i o n s . Since the wave f o r c e would go from zero to a maximum value i n one-quarter of a wave l e n g t h (about 4 seconds), v i r t u a l l y no drainage c o u l d occur. T h i s problem of ( e s s e n t i a l l y ) undrained b e a r i n g c a p a c i t y had never been i n v e s t i g a t e d b e fore, s i n c e complete drainage i s u s u a l l y assumed f o r foundations on c o h e s i o n l e s s s o i l (Bjerrum, 1973). To model t h i s , the undrained f r i c t i o n angle found from t r i a x i a l t e s t s , i n c r e a s e d from 34° to 36* to account f o r assumed plane s t r a i n c o n d i t i o n s , was used f o r s t a b i l i t y c a l c u l a t i o n s . A p l a s t i c i t y s o l u t i o n was c a r r i e d out to determine the most c r i t i c a l f a i l u r e s u r f a c e f o r the design loads (Bjerrum, 1973). T h i s a n a l y s i s was q u i t e complicated s i n c e the pore water pr e s s u r e d i s t r i b u t i o n a f f e c t e d the e f f e c t i v e s t r e s s e s which determined the rupture s u r f a c e . A lengthy and d i f f i c u l t i t e r a t i o n procedure was r e q u i r e d to f i n d the rupture s u r f a c e . The r e s u l t of t h i s work i s shown i n f i g u r e 4.14. U n f o r t u n a t e l y , no f a c t o r of s a f e t y was r e p o r t e d . 92 F i g u r e 4.14 93 CHAPTER 5 CHARACTERISTICS OF WAVE LOADING 5.1 Ocean Waves Ocean waves are g e n e r a l l y the most important environmental phenomenon that ocean engineers must d e a l with when de s i g n i n g s t r u c t u r e s f o r the o f f s h o r e environment. Although earthquakes or i c e l o a d i n g may apply the l a r g e s t h o r i z o n t a l f o r c e s on a s t r u c t u r e i n some areas, wave l o a d i n g w i l l nonetheless be an important c o n s i d e r a t i o n and must be i n v e s t i g a t e d . Waves i n the ocean come i n a v a r i e t y of forms, i n c l u d i n g : wind waves, ship-generated waves, tsunamis, and t i d e s . In the open ocean where the water i s s u f f i c i e n t l y deep to prevent s i g n i f i c a n t tsunami s h o a l i n g and t i d e s are not r e s t r i c t e d by narrow passages, wind generated waves w i l l be the most important of these forms with regards to o f f s h o r e s t r u c t u r e d e s i g n . These w i l l be the only ocean waves c o n s i d e r e d i n t h i s t h e s i s . 5.1.1 The Wave Climate .The g e n e r a t i o n of wind waves i s a complex phenomenon where energy from the blowing wind i s t r a n s f e r r e d to water p a r t i c l e s at the a i r - s e a i n t e r f a c e by p r e s s u r e g r a d i e n t s and f r i c t i o n a l f o r c e s which subsequently set the water i n t o motion (Kinsman, 1965). The amount of energy that can be put i n t o a wave system depends on the d u r a t i o n , i n t e n s i t y and d i r e c t i o n of the wind, the f e t c h (the sea d i s t a n c e over which the wind blows), the f r i c t i o n a l r e s i s t a n c e of both the s e a f l o o r and a i r - s e a 94 i n t e r f a c e , and i n t e r n a l energy d i s s i p a t i o n . Wind waves may be c l a s s i f i e d as being e i t h e r sea or s w e l l . The former are s t i l l under the i n f l u e n c e of the generating wind, while the l a t t e r t r a v e l a c r o s s the ocean s u r f a c e v i r t u a l l y u n a f f e c t e d by the wind. E m p i r i c a l c h a r t s have been developed to estimate some c h a r a c t e r i s t i c s of these waves from m e t e o r o l o g i c a l data (e.g. Shore P r o t e c t i o n Manual, 1977). Waves in the ocean are very complex and do not conform to p r e c i s e mathematical m o d e l l i n g . The sea i s c h a r a c t e r i z e d by numerous waveforms of v a r y i n g shape, l e n g t h , h e i g h t , speed, and d i r e c t i o n , a l l superimposed on each other i n an everchanging arrangement. For t h i s reason, the sea i s modelled s t a t i s t i c a l l y u s i ng s p e c t r a to take these f a c t o r s i n t o account. These s p e c t r a are approximations at best, and do not a c t u a l l y d e f i n e a p a r t i c u l a r " s e a - s t a t e " at any time. Very l i m i t e d data i s e x t r a p o l a t e d to o b t a i n the s t a t i s t i c a l p r o p e r t i e s of the wave system. For e n g i n e e r i n g purposes, i t i s u s e f u l to d e s c r i b e the ocean s u r f a c e by a t r a i n of uniform waves of s p e c i f i c height and p e r i o d t r a v e l l i n g i n water of constant depth. T h i s i s the most s i m p l i s t i c model of ocean waves and i s o f t e n adequate for design purposes. Numerous t h e o r i e s have been developed fo r t h i s s i t u a t i o n . 5.1.2 Wave T h e o r i e s A l l the a n a l y t i c a l wave t h e o r i e s make some of the same b a s i c assumptions (McCormick, 1973). They d i f f e r i n the way i n which the governing equations and boundary c o n d i t i o n s are 95 mathematically formulated. Common to a l l are the assumptions that the water i s incompressible and that flow i s i r r o t a t i o n a l (no shear s t r e s s e s at the a i r - s e a i n t e r f a c e or at the s e a f l o o r ) . From p o t e n t i a l flow theory, t h i s i m p l i e s that a v e l o c i t y p o t e n t i a l must e x i s t and s a t i s f y the Laplace e q u a t i o n . T h i s equation i s an e x p r e s s i o n of c o n t i n u i t y f o r i r r o t a t i o n a l flow and r e q u i r e s a number of boundary c o n d i t i o n s to s o l v e i t . These are as f o l l o w s : (1) the bottom i s impermeable, nondeformable, and h o r i z o n t a l - a no flow boundary (seabed boundary c o n d i t i o n ) , (2) the pressure at the a i r - s e a i n t e r f a c e i s constant (dynamic f r e e s u r f a c e boundary c o n d i t i o n ) , and (3) the flow at the a i r - sea i n t e r f a c e i s i n accordance with the geometry and motion of the f r e e s u r f a c e (kinematic f r e e s u r f a c e boundary c o n d i t i o n ) . A d d i t i o n a l l y , s i n c e the v e l o c i t y p o t e n t i a l should be c y c l i c i n nature i t i s assumed to be p e r i o d i c with both s p a t i a l and temporal v a r i a t i o n . A n a l y t i c a l wave t h e o r i e s vary i n complexity and accuracy depending on how they approximate the boundary c o n d i t i o n s . The s i m p l e s t theory f o r ocean waves i s the l i n e a r theory presented by A i r y (1845). He assumed that the p e r i o d i c i t y was s i n u s o i d a l and that the f r e e s u r f a c e boundary c o n d i t i o n s c o u l d be l i n e a r i z e d . With these assumptions, the s o l u t i o n of L a p l a c e ' s equation s u b j e c t e d to the four boundary c o n d i t i o n s r e s u l t s i n the v e l o c i t y p o t e n t i a l having only one term, which depends on the wave p e r i o d and h e i g h t , the s t a t i c water depth, and the depth of a r e f e r e n c e p o i n t below the s t a t i c water l e v e l . I t i s s i n u s o i d a l and p e r i o d i c i n the d i r e c t i o n of propagation with time. From the v e l o c i t y p o t e n t i a l , other equations may be 96 d e r i v e d f o r water p a r t i c l e a c c e l e r a t i o n s , v e l o c i t i e s and displacements, wave induced pressure on the s e a f l o o r , e t c . The computed s u r f a c e waves are known as A i r y waves. Other wave t h e o r i e s commonly used are the higher order Stoke's (1880) t h e o r i e s , p a r t i c u l a r l y the second and f i f t h . The f r e e s u r f a c e boundary c o n d i t i o n s i n these t h e o r i e s are estimated to higher o r d e r s by a p e r t u r b a t i o n p r o c e s s . The r e s u l t i n g v e l o c i t y p o t e n t i a l has the same number of terms as the order of the theory, and i s a s e r i e s approximation. The i n d i v i d u a l terms are s i n u s o i d a l ; however, the waveform, being comprised of d i f f e r e n t s i n u s o i d a l forms superimposed on each other, i s not. These waves are c h a r a c t e r i z e d by steeper c r e s t s and shallower troughs than l i n e a r ( s i n u s o i d a l ) waves. For shallow water, where the bottom s i g n i f i c a n t l y a f f e c t s the t r a v e l l i n g s u r f a c e g r a v i t y wave, the waveform may be approximated by the Jacobian e l l i p t i c a l c o s i n e (cn) f u n c t i o n (Korteweg and De V r i e s , 1895) to any order d e s i r e d . These are the c n o i d a l wave t h e o r i e s . They compare w e l l with wave tank t e s t s i n shallow water, but are complicated and d i f f i c u l t to use (Shore P r o t e c t i o n Manual, 1977). Numerical wave t h e o r i e s have a l s o been developed. Dean's (1965) theory, which i s the best known, i s based on stream f u n c t i o n s i n s t e a d of v e l o c i t y p o t e n t i a l s and r e q u i r e s the use of a computer t o so l v e the equations f o r any given set of wave parameters. I t s use i s l i m i t e d i n e n g i n e e r i n g a p p l i c a t i o n s because the method, due to i t s complexity, cannot be used i n most wave f o r c e t h e o r i e s . The r e g i o n s of v a l i d i t y f o r the best known wave t h e o r i e s 97 are shown i n f i g u r e 5.1. C l e a r l y no one theory can be regarded as being the best f o r a l l a p p l i c a t i o n s . 5.1.3 R e s u l t s of L i n e a r Wave Theory L i n e a r wave theory, besides being the sim p l e s t to use, i s more r e l i a b l e than the other a n a l y t i c a l t h e o r i e s over a g r e a t e r range of c o n d i t i o n s . I t does not s u f f e r from numerical i n s t a b i l i t y as most of the other t h e o r i e s do when a p p l i e d i n reg i o n s beyond t h e i r ( c a l c u l a t e d ) range of v a l i d i t y (Sarpkaya and Isaacson, 1981). For these reasons, i t i s the most widely used wave theory by p r a c t i c i n g e n g i n e e r s . A d d i t i o n a l l y , most wave f o r c e t h e o r i e s assume that the waves may be represented by l i n e a r theory, although the wave l e n g t h used i n the r e s u l t i n g wave f o r c e equations may be computed using another wave theory, u s u a l l y Stoke's f i f t h order theory. L i n e a r theory i s used e x t e n s i v e l y i n s p e c t r a l wave f o r c e c a l c u l a t i o n s (Bea and L a i , 1978). The p r o f i l e of a l i n e a r wave i s shown i n f i g u r e 5.2, and some r e s u l t s of l i n e a r wave theory are presented i n Table V I I . Note that only the wave he i g h t , water depth, and e i t h e r wave l e n g t h or p e r i o d are needed to d e f i n e a l i n e a r wave. T h i s i s a l s o the case f o r other wave t h e o r i e s . The wave le n g t h and p e r i o d are r e l a t e d by the d i s p e r s i o n r e l a t i o n , which i s d e r i v e d from the v e l o c i t y p o t e n t i a l . 5.2 C h a r a c t e r i z i n g the Wave System Since wind waves are random i n nature, they are best d e s c r i b e d s t a t i s t i c a l l y . Approximations may then be made to 98 005• | i i 1 1 r 0.00005' o.OOl 0.002 0.005 0.01 0.02 005 0.1 0.2 d F i g u r e 5.1 Regions of v a l i d i t y f o r v a r i o u s wave t h e o r i e s ( A f t e r Sarpkaya and Isaacson, 1981) 99 Wove s p e e d , c L 5 B z • d d k = 2JT - /L 6 - kx-a)t Wove p e r i o d , T = L / c Sur face e levat ion shown ot t = 0 F i g u r e 5.2 - P r o f i l e of an A i r y Wave ( A f t e r Isaacson, 1980) Table VII Some R e s u l t s of L i n e a r Wave Theory ( A f t e r Sarpkaya and Isaacson, 1981) Velocity potential irH cosh (ks) A *= — sin 6 kTsinh(kd) E H cosh (ks) . m — • sin e 2u> cosh (kd) Dispersion relation c 2 = -y- = f - tanh (kd) k 2 k Surface elevation H T| • — COS e Horizontal particle displacement H cosh (ks) . tB • sin 6 ' 2sinh(kd) Vertical particle displacement H sinh (ks) t • i COS 6 * 2sinh(kd) Horizontal particle velocity nH cosh (ks) u • cos 6 T sinh (kd) Vertical particle velocity irH sinh (ks) . w * — . . „ sin 6 T sinh (kd) Horizontal particle acceleration 8u 2 i r 2 H cosh (ks) — c — . sin 8 8t T 2 sinhftd) Vertical particle acceleration aw 2w 2 H sinh (ks) — * x cos S at T 2 »inh(kd) Pressure 1 „ cosh (ks) p •= -pgz + - p g H — _ _ _ c o s e 2 cosh (kd) Group velocity - 1 Ii 2 k d 1 0 0 2 [ iinh (2kd)J C Average energy density E ^ i p g H 2 100 c h a r a c t e r i z e the wave system i n simpler terms f o r the purposes of foundation d e s i g n . 5.2.1 O b t a i n i n g the Design Storm The design storm i s u s u a l l y found by e x t r a p o l a t i n g data from wave r e c o r d s . T h i s data i s o f t e n rather sparse and must be r e p r e s e n t a t i v e of storm wave c o n d i t i o n s to use the s t a t i s t i c a l methods developed f o r d e f i n i n g the design storm. 5.2.1.1 S t a t i s t i c a l D e s c r i p t i o n The d i s t r i b u t i o n of wave h e i g h t s f o r a p a r t i c u l a r s e a - s t a t e may be c h a r a c t e r i z e d by a R a y l e i g h d i s t r i b u t i o n , assuming that the f r e e s u r f a c e i s Gaussian f o r a s p e c i f i c r e c o r d i n g i n t e r v a l , u s u a l l y 6 hours. The assumption that the f r e e s u r f a c e v a r i a t i o n f o r a p a r t i c u l a r s e a - s t a t e may be represented by a Gaussian d i s t r i b u t i o n corresponds w e l l with o b s e r v a t i o n s . Data from the r e c o r d i n g i n t e r v a l i s assumed to be d e s c r i b e d by a 10 minute sample which i s r e p r e s e n t a t i v e of the 6 hour r e c o r d i n g i n t e r v a l . To d e s c r i b e the v a r i a t i o n of s e a - s t a t e s over the long-term ( y e a r s ) , i t i s convenient t o represent each r e c o r d i n g i n t e r v a l by one s t a t i s t i c a l parameter, the s i g n i f i c a n t wave hei g h t , denoted H s. T h i s i s d e f i n e d as the average height of the one- t h i r d h i g h e s t waves in the wave r e c o r d , i . e . the r e c o r d i n g i n t e r v a l . For any r e c o r d i n g i n t e r v a l the s i g n i f i c a n t wave hei g h t may be computed without much d i f f i c u l t y . ( u s u a l l y by a d i g i t a l computer). A p r o b a b i l i t y d i s t r i b u t i o n may be f i t t e d to the s i g n i f i c a n t wave h e i g h t s from numerous records to estimate the s i g n i f i c a n t 101 wave height f o r some remote event (e.g. the design storm). T h i s i s u s u a l l y done using the extreme value s t a t i s t i c s of Gumbel (1958). The p r o b a b i l i t y of a r a r e event o c c u r r i n g may be found f o r a s p e c i f i e d recurrence i n t e r v a l (e.g. 100 y e a r s ) . Thus, the s i g n i f i c a n t wave height f o r the design storm may be estimated from wave r e c o r d s . The d i s t r i b u t i o n of wave h e i g h t s w i t h i n the design storm may be found using short-term s t a t i s t i c s - the R a y l e i g h d i s t r i b u t i o n . The whole procedure may be repeated to f i n d the d i s t r i b u t i o n of wave p e r i o d s f o r the design storm. The d u r a t i o n of a storm may be days, however, f o r p r a c t i c a l purposes some time l i m i t must be chosen. A design storm of twelve hours i s o f t e n used (Isaacson, 1981). The storm i s assumed to b u i l d u p , peak, and decay d u r i n g t h i s time. The d u r a t i o n of the design storm w i l l a f f e c t the wave s t a t i s t i c s . 5.2.1.2 G e o t e c h n i c a l E q u i v a l e n t For g e o t e c h n i c a l purposes, t h i s type of r e p r e s e n t a t i o n i s not very u s e f u l i n p r a c t i c e . T h e r e f o r e , f o r a s p e c i f i e d design storm, i t i s u s e f u l to transform the s t a t i s t i c a l d i s t r i b u t i o n s of wave h e i g h t s and p e r i o d s i n t o a histogram r e l a t i n g wave h e i g h t s to frequency of occurrence ( i . e . number of waves of some he i g h t ) and a curve d e f i n i n g the wave height - wave p e r i o d r e l a t i o n s h i p . T h i s , i n g e o t e c h n i c a l l i t e r a t u r e , i s known as the "design storm". Because the d i s t r i b u t i o n of wave h e i g h t s d u r i n g a storm i s represented by a Ra y l e i g h d i s t r i b u t i o n , the number of waves i n any p a r t i c u l a r band of h e i g h t s w i l l be known. T h i s i s e a s i l y transformed i n t o a histogram. The histogram c o u l d have as many 102 bands as there are waves i n the storm. T h i s , needless to say, would be i m p r a c t i c a l . G e n e r a l l y f i v e to f i f t e e n d i v i s i o n s i s a c c e p t a b l e , depending on the type of a n a l y s i s to be performed and the accuracy d e s i r e d . Six (Bjerrum, 1973) to s i x t e e n (Lee and Focht, 1975a) d i v i s i o n s have been used f o r pore water pressure g e n e r a t i o n s t u d i e s . The d u r a t i o n of the design storm i s a l s o of i n t e r e s t , s i n c e the amount of pore water pressure d i s s i p a t i o n o c c u r r i n g i n g r a n u l a r d e p o s i t s w i l l be s e n s i t i v e to t h i s . Bjerrum (1973) suggests that the storm may be assumed to b u i l d u p over s i x to nine hours, maintain f u l l - s t o r m c o n d i t i o n s f o r three to nine hours, then subside i n another s i x to nine hours. He used the worst s i x hours of the design storm to analyze the pore water p r e s s u r e b u i l d u p under the E k o f i s k tank. These 6 hours of storm c o n t a i n e d 1394 waves. Lee and Focht (1975a) used a group of 5000 waves to c h a r a c t e r i z e a t h i r t e e n hour storm f o r the E k o f i s k tank. Such a l a r g e group of waves appears to be e x c e s s i v e s i n c e the s m a l l e r waves w i l l have l i t t l e e f f e c t on pore water pressure g e n e r a t i o n . T h i s i s confirmed by Rahman et a l (1977) who used a s i x hour storm to analyze the same problem. They found that e q u i l i b r i u m pore water pressure r a t i o s of a few percent at most were q u i c k l y achieved and maintained at the lower c y c l i c s t r e s s r a t i o s produced from the numerous smal l e r waves. 5.2.2 A p p l i c a t i o n of the Design Storm Using the a c t u a l time h i s t o r y of the storm i s i m p r a c t i c a l . T h e r e f o r e , the g e o t e c h n i c a l design storm approximation may be used. Of primary i n t e r e s t here i s when to apply the maximum 103 wave d u r i n g the design storm to f i n d the most c r i t i c a l c o n d i t i o n f o r s t a b i l i t y . Bjerrum (1973) assumed that i t i s c o n s e r v a t i v e to apply the maximum wave at the end of the design storm when pore water p r e s s u r e s would be the h i g h e s t . Based on an undrained a n a l y s i s of the sand d u r i n g the storm, the pore water p r e s s u r e s would indeed be the hig h e s t at the end of the storm. H i s reasoning with regard to maximum pore water pre s s u r e s c o r r e s p o n d i n g to the c r i t i c a l time to apply the maximum wave i s sound, however, the end of the design storm i s not n e c e s s a r i l y the most c r i t i c a l with respect to s t a b i l i t y . For c o h e s i o n l e s s s o i l s , some drainage w i l l take p l a c e d u r i n g the storm and the maximum pore water pre s s u r e s under the foundation w i l l probably occur at the height of the storm or j u s t t h e r e a f t e r . Rahman et a l (1977) assumed that the storm i s c h a r a c t e r i z e d by smal l e r waves i n c r e a s i n g i n he i g h t to a maximum (the design wave), then d e c r e a s i n g i n a s i m i l a r f a s h i o n , as Bjerrum d i d (1973) and they a p p l i e d the waves to the foundation system with t h i s order i n mind - r e p r e s e n t i n g the time h i s t o r y of l o a d i n g i n an approximate way. They found that f o r the E k o f i s k tank (founded on f i n e sand), the maximum pore water p r e s s u r e s would occur j u s t a f t e r the peak of the storm. For t h i s type of a n a l y s i s , the c r i t i c a l a p p l i c a t i o n of the maximum wave would be j u s t a f t e r the peak of the storm. I n t u i t i v e l y , t h i s seems c o r r e c t f o r foundations on sand. For foundations on c l a y , where no s u b s t a n t i a l drainage can take p l a c e d u r i n g the storm, the usual procedure i s to apply the design wave to the s t r u c t u r e at the end of the storm (Schjetne, 1976). T h i s approach i s c o n s e r v a t i v e , but not unduly so, at l e a s t f o r s t i f f c l a y s 104 (Andersen et a l , 1976). 5.3 Wave Loads on the Foundation System Wave loads on the foundation system c o n s i s t of the f o r c e s exerted on the s t r u c t u r e and t r a n s f e r r e d to the s o i l by the r a f t and the p r e s s u r e on the exposed seabed due to t r a v e l l i n g s u r f a c e g r a v i t y waves. Both must be c o n s i d e r e d when d e s i g n i n g the found a t i o n . Because the p e r i o d of wind waves i s on the order of two to twenty seconds, f o r c e s on the foundation may be co n s i d e r e d to a c t p s e u d o s t a t i c a l l y f o r s t r e s s a n a l y s i s . The e f f e c t s of c y c l i c l o a d i n g on the s o i l should be modelled a p p r o p r i a t e l y . The loads a c t i n g on the foundation of a g r a v i t y s t r u c t u r e s u b j e c t e d to wave a c t i o n and the r e s u l t i n g s o i l r e a c t i o n s are shown i n f i g u r e 5.3. 5.3.1 Wave Forces A c t i n g on the S t r u c t u r e Wave loads a c t i n g on the s t r u c t u r e are found using formulas d e r i v e d from p o t e n t i a l flow theory with e m p i r i c a l c o e f f i c i e n t s . There are two b a s i c methods f o r f i n d i n g wave f o r c e s on s t r u c t u r e s : the design wave method and the s p e c t r a l a n a l y s i s method. In the s p e c t r a l method, f o r c e s are d e f i n e d s t a t i s t i c a l l y , whereas i n the design wave method, f o r c e s are t r e a t e d d e t e r m i n i s t i c a l l y . When waves propagate past a s t r u c t u r e , f o r c e s are exe r t e d on i t from both f r i c t i o n a l and i n e r t i a l e f f e c t s caused by the moving f l u i d . The former component i s h i g h l y n o n l i n e a r while the l a t t e r i s not (Morison, 1950). I f the l a t e r a l dimension of Figure 5.3 Forces acting on the foundation of an offshore gravity structure 106 a s t r u c t u r e i s s i g n i f i c a n t compared to the wave l e n g t h (20% or more), the water p a r t i c l e motions and waveform are g r e a t l y d i s t u r b e d by the presence of the body as the wave passes; t h i s must be taken i n t o account when p r e d i c t i n g the wave loads a c t i n g on the body (MacCamy and Fuchs, 1954). D i f f r a c t i o n theory was developed f o r t h i s purpose (MacCamy and Fuchs, 1954) and may now be a p p l i e d to l a r g e volume s t r u c t u r e s of a r b i t r a r y shape such as g r a v i t y p l a t f o r m s ( G a r r i s o n , 1979; Hogben et a l , 1977). L i n e a r d i f f r a c t i o n theory (developed f o r A i r y waves) i s p r e s e n t l y used for both d e t e r m i n i s t i c and p r o b a b i l i s t i c wave f o r c e c a l c u l a t i o n s f o r g r a v i t y p l a t f o r m s (Isaacson, 1980). In the d i f f r a c t i o n regime, the drag component i s small and may be ne g l e c t e d , l e a v i n g only the i n e r t i a l component. The i n e r t i a l f o r c e on a v e r t i c a l s u r f a c e p i e r c i n g c y l i n d e r computed from l i n e a r d i f f r a c t i o n theory i s represented by a s i n g l e term f o r a given wave and v a r i e s s i n u s o i d a l l y i n time (MacCamy and Fuchs, 1954). For the g e o t e c h n i c a l engineer, the s i g n i f i c a n c e of t h i s i s that the o v e r a l l wave f o r c e s on a g r a v i t y s t r u c t u r e w i l l vary n e a r l y s i n u s o i d a l l y i n time. Although the wave f o r c e s w i l l d i f f e r f o r d i f f e r e n t waves i n the storm, i n d i v i d u a l wave f o r c e s may be d e f i n e d completely by a magnitude, o s c i l l a t o r y p e r i o d , phase angle, and frequency of occurrence. For g e o t e c h n i c a l purposes, the phase angle i s unimportant except when f i n d i n g the design p r e s s u r e on the seabed c o r r e s p o n d i n g to the maximum wave. The design storm may then be transformed from a wave h e i g h t — frequency of occurrence histogram, f o r the given wave h e i g h t — wave p e r i o d curve, to one of f o r c e - - f r e q u e n c y of occurrence. T h i s r e p r e s e n t a t i o n i s shown i n f i g u r e 5.4. The v a r i a t i o n of O 5 10 15 20 25 30 0 1 2 3 4 5 6 Wave Height (m) Time (hrs) (c) Hor izontal force--wave parameter re la t ionsh ip (d) Time h is to ry of wave forces Figure 5.4 - Typical design storm representat ion used In geotechnical engineering o -j 108 c y c l i c "shear s t r e s s e s d u r i n g the storm may be be found i n the same way once the h o r i z o n t a l f o r c e s are d e f i n e d . 5.3.2 Wave Forces A c t i n g on the Foundation For any given wave, the r e s u l t a n t v e r t i c a l and h o r i z o n t a l f o r c e s may be computed from d i f f r a c t i o n theory. The wave f o r c e s a c t i n g on the foundation are the same as the wave f o r c e s a c t i n g on the s t r u c t u r e , however, a moment must be a p p l i e d to the foundation to account f o r the r e s u l t a n t h o r i z o n t a l f o r c e a c t i n g some height above the seabed. The f o r c e s a c t i n g on that p a r t of the seabed not under the r a f t are due to the weight of the o v e r l y i n g body of water and the i n f l u e n c e of pa s s i n g waves. The pressure at any l o c a t i o n on the s e a f l o o r i s composed of a steady and a f l u c t u a t i n g component. The steady component i s uniform over the s e a f l o o r (assuming that the water depth does not change) and i s nothing more than the normal h y d r o s t a t i c p r e s s u r e . The f l u c t u a t i n g component i s the dynamic pressure due to p a r t i c l e a c c e l e r a t i o n s i n the wave and at the s e a f l o o r i s very n e a r l y equal to the h y d r o s t a t i c p ressure due to the weight of a column of water d i s p l a c e d from the s t a t i c water l e v e l as the wave passes. Any a p p r o p r i a t e wave theory may be used to f i n d the seabed pressure d i s t r i b u t i o n ; the f l u c t u a t i n g component w i l l be of n e a r l y the same form as the f r e e s u r f a c e . L i n e a r theory i s commonly used and the r e s u l t i n g s e a f l o o r ( c y c l i c ) p ressure d i s t r i b u t i o n i s s i n u s o i d a l . The steady component i s uniform everywhere, and t h e r e f o r e i s of no s i g n i f i c a n c e s i n c e i t a f f e c t s n e i t h e r the e f f e c t i v e 109 s t r e s s e s or the s t r e s s g r a d i e n t s i n the s o i l . The f l u c t u a t i n g component i s of i n t e r e s t f o r two reasons, namely: (1) i t does not a c t u n i f o r m l y over the s e a f l o o r at any given time and must t h e r e f o r e be c o n s i d e r e d as an e x t e r n a l load, and (2) i t induces s t r e s s g r a d i e n t s which produce c y c l i c shear s t r e s s e s i n the s o i l . When f i n d i n g the pressure d i s t r i b u t i o n corresponding to the design wave, the phasing of the wave f o r c e s must be c o n s i d e r e d . The s e a f l o o r p r e s s u r e s near the p l a t f o r m w i l l be l e s s than the pressure amplitude. The maximum f o r c e s a c t i n g on a p l a t f o r m u s u a l l y occur when the nodal p o i n t s of the waveform are near the pla t f o r m ' s v e r t i c a l a x i s , i . e . when the waveform passes through the s t i l l water l e v e l near the p l a t f o r m ' s v e r t i c a l a x i s . For long ( l a r g e ) waves, t h i s means that the pressure curve has a node somewhere over the r a f t and that the maximum pres s u r e s on the seabed due to the wave w i l l be some d i s t a n c e from the edge of the p l a t f o r m (approximately one-quarter of a wavelength away from the v e r t i c a l a x i s of the p l a t f o r m ) . 5.4 E f f e c t of C y c l i c Loading on the Foundation System The e f f e c t s of c y c l i c l o a d i n g on the s o i l must be taken i n t o account f o r a l l s t r e s s a n a l y s e s . Such e f f e c t s i n f l u e n c e the s a f e t y of the p l a t f o r m with r e s p e c t to f a i l u r e ( s l i d i n g , b e a r i n g , r o c k i n g , l i q u e f a c t i o n or o t h e r w i s e ) , as w e l l as the p l a t f o r m motions dur i n g storm l o a d i n g and long-term e f f e c t s such as s e t t l e m e n t . Using a storm histogram s i m i l a r to the one shown i n f i g u r e 5.4(d) to represent the time h i s t o r y of l o a d i n g , the 110 s t r e s s path f o r an element beneath a sand foundation may look l i k e that which i s shown ( u n i d i r e c t i o n a l l y ) i n f i g u r e 5.5. T h i s r e p r e s e n t a t i o n i s i d e a l i z e d f o r the purposes of i l l u s t r a t i o n . The f i g u r e may be i n t e r p r e t e d as f o l l o w s . The f i r s t histogram band r e p r e s e n t s some number of c y c l e s at one s t r e s s amplitude. T h i s amplitude i s the d i s t a n c e from point "a" to the e f f e c t i v e s t r e s s a x i s . The r e s u l t i n g r e s i d u a l pore water pressure decreases the e f f e c t i v e normal s t r e s s . Hence, movement from p o i n t "a" to "b". The next set of s t r e s s c y c l e s are at a magnitude represented by the d i s t a n c e from p o i n t "c" to the h o r i z o n t a l a x i s . Pore water p r e s s u r e reduces the e f f e c t i v e normal s t r e s s to p o i n t "d". The s t r e s s path shown i n the f i g u r e does not show the f u l l path, i . e . the re t u r n to the h o r i z o n t a l a x i s (zero shear s t r e s s ) f o r each set of c y c l e s i s not shown. T h i s was l e f t out to c l e a r l y i l l u s t r a t e the e f f e c t s of c y c l i c l o a d i n g on a foundation element. S i m i l a r l y , the path continues as the c y c l i c s t r e s s amplitude i n c r e a s e s to a maximum corresponding to the design wave, then decreases. Note that excess pore water p r e s s u r e s e x i s t i n the foundation element throughout the storm. Much data i s a v a i l a b l e f o r sand t e s t e d under undrained c o n d i t i o n s . T h i s i s due to the i n t e r e s t i n earthquake induced l i q u e f a c t i o n which has a t t r a c t e d scores of r e s e a r c h e r s . P a r t i a l l y d r a i n e d sand behaviour has not been w e l l s t u d i e d , and l i t t l e i n f o r m a t i o n i s a v a i l a b l e on the s u b j e c t . P a r t i a l drainage f o r c o h e s i o n l e s s s o i l s has not been d i r e c t l y modelled i n l a b o r a t o r y shear t e s t s . Instead, modified undrained c y c l i c t r i a x i a l .tests are used (Lee and Focht, 1 975a). 111 EFFECTIVE NORMAL STRESS, U' F i g u r e 5.5 1 12 Pore water pressure g e n e r a t i o n i n undrained shear depends on the c h a r a c t e r i s t i c s of the sand, the magnitude of the s t a t i c shear s t r e s s i n the s o i l before t e s t i n g , and the magnitude and time h i s t o r y of the a p p l i e d c y c l i c shear s t r e s s e s . The amount of pore water pressure g e n e r a t i o n i n undrained shear may be estimated from l a b o r a t o r y t e s t s t hat a p p r o p r i a t e l y model the ocean wave l o a d i n g problem (Lee and Focht, 1975b). E s t i m a t i o n of the pore water p r e s s u r e s developed under an o f f s h o r e g r a v i t y type s t r u c t u r e may be made using (1) l a b o r a t o r y t e s t s such as those d e s c r i b e d by Lee and Focht (1975a) which model p a r t i a l drainage and p r e s h e a r i n g u s i n g m o d i f i e d c y c l i c t r i a x i a l t e s t s , or (2) from numerical methods that model the s o i l by f i n i t e elements and s o l v e the equations of r a d i a l and v e r t i c a l c o n s o l i d a t i o n (Rahman et a l , 1977). Undrained a n a l y s e s i n sand (Bjerrum, 1973) are too c o n s e r v a t i v e and are not a p p r o p r i a t e f o r advanced s t u d i e s . C y c l i c l o a d i n g of c l a y has r e c e n t l y been a s u b j e c t of i n t e n s i v e study (Andersen et a l , 1976; van Eekelen and P o t t s , 1978) as some of the g r a v i t y p l a t f o r m s i n the North Sea are u n d e r l a i n by s u b s t a n t i a l c l a y d e p o s i t s . The r e s u l t s of an e x t e n s i v e study on c l a y behaviour under c y c l i c l o a d i n g were reported by Andersen et a l (1976), and demonstrated s e v e r a l important concepts. F i r s t of a l l , shear s t r a i n may be used i n s t e a d of pore pressure development as a parameter f o r d e s c r i b i n g response to c y c l i c l o a d i n g . C y c l i c shear s t r a i n s are uniquely r e l a t e d t o the e f f e c t i v e s t r e s s and independent of the o v e r c o n s o l i d a t i o n r a t i o or number of c y c l e s . Secondly, the 113 e f f e c t i v e s t r e n g t h parameters c' and tan0' are v i r t u a l l y u n a f f e c t e d by c y c l i c l o a d i n g , but the undrained s t r e n g t h c w i s . T h i r d l y , the undrained s t r e n g t h i s a f u n c t i o n of c y c l i c shear s t r a i n and the number of s t r e s s c y c l e s a p p l i e d . And f i n a l l y , the h i g h e r the o v e r c o n s o l i d a t i o n r a t i o f o r a given c y c l i c s t r e s s r a t i o , the fewer number of c y c l e s are necessary to b r i n g the sample to f a i l u r e . Andersen (1976) developed a method based on the accumulation of c y c l i c shear s t r a i n s to p r e d i c t f a i l u r e from e x c e s s i v e displacements. I t has been found f o r i n s e n s i t i v e c l a y s that i f the a p p l i e d shear s t r e s s l e v e l i s below some c r i t i c a l v a l u e , a s t a t e of non- f a i l u r e e q u i l i b r i u m w i l l be reached where the s t r e s s - s t r a i n curves f o l l o w c l o s e d h y s t e r e s i s loops with no f u r t h e r i n c r e a s e i n pore water pressure (Sangrey et a l , 1969). If t h i s c r i t i c a l v alue i s exceeded, each l o a d i n g c y c l e w i l l cause a cumulative i n c r e a s e i n pore water pr e s s u r e and displacements which u l t i m a t e l y r e s u l t s i n a shear f a i l u r e . T h i s f a i l u r e w i l l occur at a reduced undrained s t r e n g t h which i s about two-thirds of the value f o r s t a t i c l o a d i n g . T h i s c r i t i c a l c y c l i c shear s t r e s s l e v e l should be determined e x p e r i m e n t a l l y f o r each cohesive d e p o s i t (Bjerrum, 1973). C o n s o l i d a t i o n h i s t o r y i s important when a s s e s s i n g the e f f e c t s of c y c l i c l o a d i n g on c l a y . For normally c o n s o l i d a t e d and s l i g h t l y o v e r c o n s o l i d a t e d d e p o s i t s , drainage a f t e r c y c l i c l o a d i n g i m p l i e s c o n s o l i d a t i o n and an i n c r e a s e i n the un.dirained s t r e n g t h . For h e a v i l y o v e r c o n s o l i d a t e d c l a y s , s w e l l i n g may occur a f t e r l o a d i n g i s terminated, with a corresponding r e d u c t i o n i n s t r e n g t h (Schjetne, 1976). The e f f e c t of t h i s on 114 p l a t f o r m s a f e t y i s as f o l l o w s : For foundations on h i g h l y o v e r c o n s o l i d a t e d d e p o s i t s , the s a f e t y of the p l a t f o r m w i l l decrease with subsequent c y c l i c l o a d i n g . The s a f e t y of p l a t f o r m s on normally c o n s o l i d a t e d or s l i g h t l y o v e r c o n s o l i d a t e d s o i l w i l l i n c r e a s e i n time. However, these d e p o s i t s are u s u a l l y u n s u i t e d f o r a g r a v i t y p l a t f o r m s i n c e displacements may be e x c e s s i v e under storm wave l o a d i n g . 115 CHAPTER 6 PROCEDURES FOR ANALYZING THE STABILITY OF OFFSHORE GRAVITY TYPE STRUCTURES 6.1 Fundamental C o n s i d e r a t i o n s The purpose of a s t a b i l i t y a n a l y s i s i s to assess the margin of s a f e t y a g a i n s t an u l t i m a t e foundation f a i l u r e . T h i s margin of s a f e t y may be expressed i n one of two ways: by a loa d s a f e t y f a c t o r or a m a t e r i a l f a c t o r . The lo a d s a f e t y f a c t o r i s d e f i n e d as the r a t i o of the load r e q u i r e d to cause an u l t i m a t e f a i l u r e to the design l o a d , when the design s t r e n g t h of the s o i l i s used. The m a t e r i a l s a f e t y f a c t o r i s the amount by which the s t r e n g t h parameters must be reduced to b r i n g the s o i l to a s t a t e of l i m i t i n g e q u i l i b r i u m under the design l o a d s . The degree of s t r e n g t h m o b i l i z a t i o n i n the s o i l i s o f t e n how t h i s l a t t e r r e s u l t i s expressed. The two s a f e t y f a c t o r s w i l l i n general be d i f f e r e n t . Onshore, a s a f e t y f a c t o r of about three i s commonly used to take i n t o account u n c e r t a i n t i e s a s s o c i a t e d with the values of st r e n g t h parameters, ground water c o n d i t i o n s , l o a d i n g c o n d i t i o n s , and the r e l i a b i l i t y of a n a l y t i c a l methods. Of f s h o r e , a much lower s a f e t y f a c t o r i s used and a c o n s i d e r a b l e amount of e f f o r t i s spent i n t r y i n g to b e t t e r d e f i n e the problem than i s commonly done f o r most onshore p r o j e c t s . The use of more r i g o r o u s analyses i s j u s t i f i e d e c o n o m i c a l l y , s i n c e the degree of u n c e r t a i n t y w i l l be l e s s , and t h e r e f o r e , the f a c t o r of s a f e t y may be reduced. For t h i s reason, bearing c a p a c i t y theory 116 i s g e n e r a l l y used only f o r a p r e l i m i n a r y estimate of the adequacy of a s i t e f o r a g r a v i t y type s t r u c t u r e . L i m i t e q u i l i b r i u m methods based on s l i p s u r f a c e s and the f i n i t e element method are u s u a l l y employed. E v a l u a t i o n of the s a f e t y f a c t o r r e q u i r e s three t h i n g s : an e s t i m a t i o n of the shear s t r e n g t h of the s o i l , e s t i m a t i o n of the shear s t r e s s e s i n the s o i l , and the p o s t u l a t i o n of a f a i l u r e mechanism. The shear s t r e n g t h of the s o i l may be d e f i n e d by the Mohr-Coulomb f a i l u r e c r i t e r i a , which i s Tr. = c + a tan0 (6.1) where c and tan0 are the shear s t r e n g t h parameters and C i s the normal s t r e s s on the shear s u r f a c e . In terms of e f f e c t i v e s t r e s s , t h i s equation i s T f= c'+ a'tan0' (6.2) where c' and tan0' are the e f f e c t i v e shear s t r e n g t h parameters and 6" i s the e f f e c t i v e normal s t r e s s , d e f i n e d as cr = <y - u (6.3) where u i s the r e s u l t a n t pore water p r e s s u r e . One should remember that each h a l f wave c y c l e the d i r e c t i o n of l o a d i n g r e v e r s e s . There are, t h e r e f o r e , both shear s t r e s s r e v e r s a l s and p u l s a t i n g v e r t i c a l s t r e s s e s i n the s o i l . Both w i l l a f f e c t the magnitude of the pore water pressure at any time d u r i n g the storm. I t i s convenient to d i s c u s s the pore water pressure i n the s o i l i n terms of i t s v a r i o u s components. The t o t a l pore water p r e s s u r e , u, at any l o c a t i o n i s given by u = u s + u e+ Au (6.4) where u s i s the h y d r o s t a t i c component, u c i s the r e s i d u a l pore 117 water p r e s s u r e due to c y c l i c l o a d i n g at any time d u r i n g the storm, and Au i s that p a r t due to the changes i n the p r i n c i p a l s t r e s s e s . The h y d r o s t a t i c pore water pressure i n the s o i l i s simply u s = ^ d + Y w z (6.5a) where )(w i s the u n i t weight of seawater, d i s the s t i l l water depth, and z i s the depth below the mudline. Note that t h i s term i n c l u d e s the pressure due to the s t a t i c body of water above the mudline. The e f f e c t i v e s t r e s s e s i n the s o i l are, however, not i n f l u e n c e d by the presence of an o v e r l y i n g body of water. T h i s i s i l l u s t r a t e d i n f i g u r e 6.1. T h i s may be taken as u s = V„z ' (6.5b) i f the weight of the o v e r l y i n g body of water i s omitted from a l l c a l c u l a t i o n s . The component of pore water p r e s s u r e i n the s o i l due to changes i n the p r i n c i p a l s t r e s s e s may be determined from (Skempton, 1954) Au = B [ A O" 3 + A (AC, - AC 3 ) ] (6.6) where cr, i s the major p r i n c i p a l s t r e s s , o~3 i s the minor p r i n c i p a l s t r e s s , and A and B are d i m e n s i o n l e s s pore pressure parameters measured i n the l a b o r a t o r y . T h i s component w i l l be a maximum or minimum ( f o r d i l a t i o n ) f o r the design wave. The B - parameter may be taken as u n i t y f o r o f f s h o r e foundation a n a l y s e s . For an e l a s t i c i s o t r o p i c s o i l , the A-parameter i s equal to o n e - t h i r d . T h i s i m p l i e s that the r i s e i n pore water pressure i s equal to the t o t a l s t r e s s increment. For other values of t h i s parameter, the pore water pressure r i s e i s not equal to the t o t a l h y d r o s t a t i c s t r e s s increment. 118 d u n n n i j * I / Z / 1 (i) (2) Us u « l « ( d • D 0 ) 6' - q • ).Do * - Xwd + Hz u « *w(d • x) cr' - Y'z (2) F i g u r e 6.1 - E f f e c t i v e s t r e s s e s i n s o i l f o r s t i l l water c o n d i t i o n s ( i . e . no wave loads) 119 Pore water pre s s u r e s w i t h i n the s o i l mass due to c y c l i c l o a d i n g may be estimated u s i n g (1) data from c y c l i c shear t e s t s with a numerical model such as Rahman et a l ' s (1977) to account f o r c o n s o l i d a t i o n , (2) data from m o d i f i e d c y c l i c t r i a x i a l t e s t s such as those d e s c r i b e d by Lee and Focht (1975a) c o r r e l a t e d with the i n - s i t u s t r e s s e s , or (3) from experience gained through o b s e r v a t i o n s of p l a t f o r m s instrumented f o r performance. A combination of these methods may be used. In a d d i t i o n to the pore water pre s s u r e s generated as a consequence of c y c l i n g loads on the s t r u c t u r e , excess pore water p r e s s u r e s w i l l a l s o be developed i n the s o i l not under (or i n f l u e n c e d by the presence of) the r a f t . S t r e s s g r a d i e n t s are induced i n the seabed from the p r e s s u r e v a r i a t i o n s caused by p a s s i n g waves (Henkel, 1970). If the waves are l a r g e enough and l o a d i n g i s s u s t a i n e d , l i q u e f a c t i o n may occur (Finn and Lee, 1978). A s t a b i l i t y a n a l y s i s f o r a c l a y foundation may o f t e n be performed using a t o t a l s t r e s s a n a l y s i s . The pore water pressure r i s e i n a foundation element w i l l be n e a r l y equal to the t o t a l s p h e r i c a l s t r e s s increment f o r o v e r c o n s o l i d a t e d c l a y . The A-parameter i s c l o s e to o n e - t h i r d f o r these c l a y s (Skempton and Bjerrum, 1957). An e f f e c t i v e s t r e s s a n a l y s i s may a l s o be performed. T h i s method p r e s e n t s two d i f f i c u l t i e s , namely: the pore water pre s s u r e s must be estimated and the e f f e c t i v e shear s t r e n g t h parameters have to be e v a l u a t e d . These parameters must be found from l a b o r a t o r y shear t e s t s which r e q u i r e good q u a l i t y samples. These are o f t e n u n a t t a i n a b l e . A t o t a l s t r e s s a n a l y s i s may be performed without e s t i m a t e s of the pore water p r e s s u r e s 120 or l a b o r a t o r y shear t e s t d a ta. The undrained s t r e n g t h determined from i n - s i t u t e s t s such as the cone penetrometer or vane may be used d i r e c t l y , reduced a p p r o p r i a t e l y f o r the estimated e f f e c t of c y c l i c l o a d i n g ( i . e . s t r a i n s o f t e n i n g ) . T h i s has been the case f o r most North Sea g r a v i t y s t r u c t u r e s founded on c l a y (Schjetne, 1976). I t should be noted that f o r c o h e s i v e s o i l s the pore water- p r e s s u r e s developed w i t h i n the s o i l mass due to the weight of the p l a t f o r m may not have d i s s i p a t e d s u b s t a n t i a l l y by the time that a major storm h i t s the f i e l d . In t h i s case, an e f f e c t i v e s t r e s s a n a l y s i s i s r e q u i r e d and loads l e s s than the design wave loads may be used. A t o t a l s t r e s s a n a l y s i s f o r the design storm l o a d i n g , which may be assumed to h i t the p l a t f o r m at a l a t e r date, may a l s o be performed. Some s o r t of r i s k a n a l y s i s w i l l be r e q u i r e d . For the s t a b i l i t y a n a l y s i s of a foundation on c o h e s i o n l e s s s o i l an e f f e c t i v e s t r e s s a n a l y s i s i s performed. T h i s r e q u i r e s e stimates of the pore water p r e s s u r e s w i t h i n the s o i l mass. Any a p p r o p r i a t e method may be used to estimate these pore water p r e s s u r e s . The f r i c t i o n angle must be determined from l a b o r a t o r y shear t e s t s . Cone p e n e t r a t i o n r e s i s t a n c e can help to e s t a b l i s h the r e l a t i v e d e n s i t y which i s needed f o r i n t e r p r e t i n g the t e s t s . 6.2 M o d e l l i n g the W a v e - S t r u c t u r e - S o i l System Since g r a v i t y p l a t f o r m s never approximate s t r i p f o o t i n g s and r a r e l y r e s t on the seabed without some s o r t of subsurface foundation, i . e . s k i r t s and r i b s , some assumptions r e g a r d i n g 121 geometry must be made so that a n a l y t i c a l techniques may be used. The p l a t f o r m i s u s u a l l y modelled by an " e q u i v a l e n t r e c t a n g u l a r foundation", that i s , one with the same area as the a c t u a l p l a t f o r m base. The " e f f e c t i v e foundation" i s u s u a l l y assumed to be at s k i r t - t i p l e v e l ( L a u r i t z s e n and Schjetne, 1976). T h i s assumption i s good i f f a i l u r e does not extend up i n t o the s k i r t compartments. The s k i r t s should be spaced c l o s e l y enough together to prevent f a i l u r e s of the kinds shown i n f i g u r e s 3.6(a), 3.6(b), and 3.6(d). A d e f i n i t i o n sketch of the e f f e c t i v e foundation i s shown i n f i g u r e 6.2(a) f o r a two- dimensional r e p r e s e n t a t i o n and i n 6.2(b) f o r a three-dimensional one. When mo d e l l i n g the foundation system, i t i s important to i n c l u d e a l l the f o r c e s which act on both the s t r u c t u r e and the seabed adjacent to i t . The p o i n t s of a p p l i c a t i o n of the r e s u l t a n t f o r c e s , or the d i s t r i b u t i o n of p r e s s u r e s , must be e i t h e r known or assumed. The loads a c t i n g at the foundation base are r e q u i r e d f o r a s t a b i l i t y a n a l y s i s . The wave loads, which are s p e c i f i e d at the s e a f l o o r , must be t r a n s m i t t e d to the foundation base by i n c l u d i n g the f o r c e s a c t i n g between the s e a f l o o r and the s k i r t t i p s i n the r e s u l t a n t l o a d . F i g u r e 6.3(a) shows the f o r c e s a c t i n g on the foundation system, and f i g u r e 6.3(b) shows the r e s u l t a n t loads which are used i n a s t a b i l i t y a n a l y s i s . These f o r c e s are d e f i n e d q u a l i t a t i v e l y i n the f o l l o w i n g paragraphs. The v e r t i c a l l o a d a p p l i e d to the e f f e c t i v e foundation, V B T , w i l l c o n s i s t of the buoyant weight of the p l a t f o r m Pv , the f l u c t u a t i n g v e r t i c a l f o r c e due to the wave APV (which w i l l be 122 (b) Three-dimensional r e p r e s e n t a t i o n F i g u r e 6.2 - D e f i n i t i o n sketch of e f f e c t i v e foundation 123 APlX) n r r r r 1 " AP(X) W » V « I I I I I l * R (a) Loads a c t i n g on the p l a t f o r m APOO r r r r r r r AP(X) IffNt/l 1 T 1 ' ' 1 » O I M B T (b) Loads t r a n s f e r r e d t o the foundation base F i g u r e 6.3 - Transformation of loads to foundation base 124 downward f o r design c o n d i t i o n s ) , and the added lo a d from s o i l c o n t a i n e d w i t h i n the s k i r t compartments. V e r t i c a l shear f o r c e s a c t i n g on the p e r i p h e r y of the imbedded foundation may u s u a l l y be ignored. The d i s t r i b u t i o n of v e r t i c a l s t r e s s beneath the r a f t w i l l be nonuniform s i n c e l o a d i n g i s i n c l i n e d and e c c e n t r i c . T h i s i s u s u a l l y taken i n t o account by c o n s i d e r i n g only that area of " the foundation base which i s symmetrical with respect to the r e s u l t a n t v e r t i c a l l o a d . The r e s u l t a n t v e r t i c a l l o a d i s then a p p l i e d c e n t r a l l y on t h i s " e f f e c t i v e area" (Hansen, 1961). The e f f e c t v e area i s represented by BL 0 i n f i g u r e 6.2(b). I t may be determined once the l o a d e c c e n t r i c i t y at the base i s e s t a b l i s h e d . T h i s e c c e n t r i c i t y i s i n i t i a l l y unknown si n c e the moment at the base of the s t r u c t u r e depends on the s o i l f o r c e s a c t i n g between the mudline and s k i r t - t i p l e v e l ; these f o r c e s must be determined from an i t e r a t i o n procedure. However, the moment at base l e v e l may be approximated by choosing reasonable valu e s f o r the s o i l f o r c e s . The e f f e c t i v e area may then be e s t a b l i s h e d . The e f f e c t i v e area w i l l u s u a l l y not be i n f l u e n c e d s i g n i f i c a n t l y by the s o i l f o r c e s , p a r t i c u l a r l y f o r shallow f o u n d a t i o n s . For one-dimensional e c c e n t r i c i t y , that i s , when l o a d i n g i s p a r a l l e l to one s i d e of the e q u i v a l e n t r e c t a n g u l a r base, only one dimension of the e q u i v a l e n t foundation i s reduced. T h i s i s normally the case f o r g r a v i t y s t r u c t u r e s s i n c e they are u s u a l l y of s i m i l a r width and l e n g t h ( i . e . they are approximately r a d i a l l y symmetric). Meyerhof's (1953) " e f f e c t i v e width" p r i n c i p l e i s then used. The h o r i z o n t a l f o r c e which a c t s on the e f f e c t i v e foundation, H R T , i s somewhat more d i f f i c u l t to a s s e s s . T h i s 125 f o r c e i s equal to the r e s u l t a n t of the h o r i z o n t a l wave loa d PH and the h o r i z o n t a l components of a l l the f o r c e s a c t i n g between the mudline and s k i r t - t i p l e v e l : the a c t i v e s o i l f o r c e PA on the t a i l end of the foundation, the p a s s i v e s o i l f o r c e Pp on the nose of the foundation, and shear f o r c e s Ps on the s i d e s of the imbedded base. These f o r c e s must be estimated. G e n e r a l l y , the a c t i v e and p a s s i v e s o i l f o r c e s are assumed t o a c t only h o r i z o n t a l l y . For s t r u c t u r e s with s i g n i f i c a n t p e n e t r a t i o n i n t o the s e a f l o o r , t h i s assumption may not be reasonable. When the a c t i v e s o i l f o r c e i s negat i v e , as f o r c l a y foundations, a t e n s i o n crack i s assumed to e x i s t at the t a i l end of the p l a t f o r m . A water f o r c e , Pw, due to the dynamic wave pressure (which i s not i n e q u i l i b r i u m with the s o i l pore water pressures) a c t s i n any c r a c k . The shear f o r c e s a c t i n g on the s i d e s of the foundat i o n , P s, reduce the h o r i z o n t a l f o r c e a p p l i e d to the foundation base. T h i s r e s i s t a n c e i s not i n c l u d e d f o r a plane s t r a i n a n a l y s i s . The d i s t r i b u t i o n of h o r i z o n t a l f o r c e over the foundation base i s assumed d i f f e r e n t l y i n v a r i o u s s t a b i l i t y t h e o r i e s . The dynamic wave pressure a c t i n g on the seabed, Ap(x), v a r i e s roughly s i n u s o i d a l l y ; the estimated v a r i a t i o n depends on the wave theory used to c a l c u l a t e i t . For the purpose of a g r a v i t y s t r u c t u r e s t a b i l i t y a n a l y s i s , i t i s o f t e n adequate to apply the pressure u n i f o r m l y on e i t h e r end of the r a f t , t a k i n g magnitude and phasing i n t o c o n s i d e r a t i o n , s i n c e the v a r i a t i o n of t h i s p r e s s u r e over a short d i s t a n c e i s u s u a l l y minimal. The dynamic wave pressure w i l l a f f e c t the magnitudes of s o i l f o r c e s a c t i n g on the s t r u c t u r e above s k i r t - t i p l e v e l . 126 The e f f e c t s of c y c l i c l o a d i n g on the foundation s o i l s must be adequately taken i n t o account i n accordance with s e c t i o n s 5.4 and 6.1. The e f f e c t of c o n s o l i d a t i o n h i s t o r y on c l a y and pr e s h e a r i n g i n sand, must be c o n s i d e r e d when choosing s t r e n g t h parameters a p p r o p r i a t e f o r design storm a n a l y s e s . 6.3 Loading A p p l i e d t o the Foundation The v e r t i c a l l o a d at the e f f e c t i v e foundation l e v e l , V 6 1 , i s equal t o the sum of the v e r t i c a l l o a d at the s e a f l o o r and the submerged weight of s o i l w i t h i n the s k i r t compartments. T h i s may be w r i t t e n as V B T = Pv + AP V + ( A 0 D 0 ) i " (6.7) where P v i s the v e r t i c a l p l a t f o r m l o a d i n the absence of environmental l o a d i n g (the buoyant weight of the p l a t f o r m , which i s not constant over the l i f e of the s t r u c t u r e ) , AP V i s the v e r t i c a l l o a d due to environmental l o a d i n g , A 0 i s the area of the e q u i v a l e n t base, D 0 i s the depth of the e f f e c t i v e f o u n d a t i o n , and H' i s the e f f e c t i v e u n i t weight of s o i l . The h o r i z o n t a l l o a d a c t i n g on the foundation base, H B T , i s the r e s u l t a n t of the a p p l i e d environmental l o a d P H and a l l the h o r i z o n t a l f o r c e s a c t i n g on the p l a t f o r m between the s e a f l o o r and s k i r t - t i p l e v e l . T h i s may be expressed as H * T = P H + (P* or P j - P p (6.8) where the a c t i v e s o i l f o r c e i s d e f i n e d by PA = [ ( 0 . 5 r D o 2 + A p , D o ) t a n 2 ( 4 5 ' - 0 / 2 ) - 2 c D o t a n ( 4 5 ' - 0 / 2 ) ] L 0 (6.9) Here, Ap f i s the dynamic wave pr e s s u r e a c t i n g on the seabed at the t a i l end of the p l a t f o r m , 0 i s the m o b i l i z e d f r i c t i o n angle, 127 c i s the m o b i l i z e d cohesion, and L 0 i s the e q u i v a l e n t p l a t f o r m l e n g t h . I f PA i s n e g a t i v e , a water p r e s s u r e f o r c e P w r e p l a c e s i t , g i ven by P w= Ap,D 0L 0 (6.10) The p a s s i v e s o i l f o r c e i s d e f i n e d as P p= [ (0.5 o'D o 2+Ap 2Do)tan 2(45 o+0/2)+2cD otan(45°+0/2)]L 0 (6.11) where Ap 2 i s the dynamic wave pressure a c t i n g on the seabed near the nose of the p l a t f o r m . Note that Ap 2 i s a negative q u a n t i t y . The preceding equations may be used to d e f i n e plane s t r a i n l o a d i n g . T h i s i s done by d i v i d i n g each equation by the e q u i v a l e n t p l a t f o r m l e n g t h L 0 to f i n d the f o r c e per u n i t l e n g t h . For a three-dimensional a n a l y s i s , the aforementioned equations may a l s o be used, with one e x c e p t i o n : s h e a r i n g r e s i s t a n c e on the s i d e s of the foundation must be i n c l u d e d . In t h i s case, Equation (6.8) may be w r i t t e n as H B T = P« + (P A or P w) - P f - Ps (6.12) where the shearing r e s i s t a n c e on the s i d e s of the foundation Ps i s d e f i n e d by Ps = 2 D 0 B 0 ( c + O.5tf'D otan0) (6.13) The moment a p p l i e d at the foundation base, M B 1, i s the r e s u l t a n t of the moment at the s e a f l o o r M, and the moments due to a l l the f o r c e s a c t i n g between the s e a f l o o r and the foundation base. T h i s may be expressed as MfeT= M + P HD 0 + (P A or P w ) h i - P f h 2 - P s h 3 (6.14) where h,, h 2 , and h 3 are moment arms f o r the a p p r o p r i a t e f o r c e s . These may be found from e a r t h pressure theory. The e f f e c t i v e width B may be found once the e c c e n t r i c i t y i s known. T h i s may be w r i t t e n as 128 B = B 0(1 ~ 2e) (6.15) where B 0 i s the e q u i v a l e n t foundation width and the e c c e n t r i - c i t y e i s given by e = ( M B 7 A f c - r ) / B 0 (6.16) 6.4 A v a i l a b l e S t a b i l i t y Methods P r e s e n t l y , there are a number of a n a l y t i c a l or numerical methods which may be used to assess the foundation s t a b i l i t y of a g r a v i t y p l a t f o r m . These a r e : the b e a r i n g c a p a c i t y methods, the NGI s l i p s u r f a c e method, and the f i n i t e element method. C e n t r i f u g e t e s t s may a l s o be performed to i n v e s t i g a t e foundation s t a b i l i t y . These methods are d i s c u s s e d i n depth i n the f o l l o w i n g s e c t i o n s . The problems encountered when a p p l y i n g them to o f f s h o r e g r a v i t y s t r u c t u r e s are emphasized. In the f o l l o w i n g c h a p t e r s , an a l t e r n a t i v e procedure based on the method of s l i c e s i s p resented. 6.4.1 C l a s s i c a l Bearing C a p a c i t y Approach The s t a b i l i t y of shallow foundations i s o f t e n i n v e s t i g a t e d using b e a r i n g c a p a c i t y theory. Computation of the u l t i m a t e load Q 0, or u l t i m a t e bearing p r e s s u r e q 0 , i s based on a s i m p l i f i e d model of an i n f i n i t e l y long r i g i d s t r i p f o o t i n g of width B 0 r e s t i n g i n a homogeneous d e p o s i t of e f f e c t i v e u n i t weight cohesion c, and f r i c t i o n angle 0, at a depth D 0. The f o o t i n g i s loaded with a c e n t r a l v e r t i c a l l o a d Q which i s assumed to produce a uniform pressure q. The adjacent s o i l i s loaded with a uniform surcharge q'. T h i s r e p r e s e n t a t i o n i s shown in f i g u r e 6.4. 129 Q o = q 0 B 0 F i g u r e 6.4 - T h e o r e t i c a l rupture s u r f a c e geometry 130 The bea r i n g c a p a c i t y problem i s represented mathematically by a ra t h e r cumbersome set of p a r t i a l d i f f e r e n t i a l equations. A c l o s e d form a n a l y t i c a l s o l u t i o n has not yet been found, although f o r s p e c i a l cases of t h i s problem, s o l u t i o n s are a v a i l a b l e (e.g. P r a n d t l , 1921). The most widely r e c o g n i z e d s o l u t i o n i s t h a t of Terzaghi (1943). He proposed that the u l t i m a t e b e a r i n g c a p a c i t y be evalu a t e d from q 0 = -„'BN Y+ cN c+ q'N. (6.17) 2 * * where the N-values are known as b e a r i n g c a p a c i t y f a c t o r s . These c o e f f i c i e n t s a r i s e from the p l a s t i c i t y s o l u t i o n . Since N t and N % are c a l c u l a t e d f o r one rupture s u r f a c e and N y f o r another, t h i s equation i s an approximation (Hansen, 1970). The l o c a t i o n of the t h e o r e t i c a l rupture s u r f a c e i s d i f f e r e n t f o r each combination of c, 0, and q'. The equation i s , however, c o n s e r v a t i v e and e r r o r s are g e n e r a l l y l e s s than 20% (Lundgren and Mortensen, 1953). The Terzaghi (1943) s o l u t i o n i s g e n e r a l l y accepted, but the numerical v a l u e s of the bearing c a p a c i t y f a c t o r s to be used i n the equation are not. The bearing c a p a c i t y f a c t o r s a r i s e from the p l a s t i c i t y s o l u t i o n and depend only on the f r i c t i o n angle - f o r a p a r t i c u l a r shape of the assumed rupture s u r f a c e . I t i s t h i s dependence on the shape of the assumed rupture s u r f a c e that g i v e s r i s e t o the many d i f f e r e n t i n t e r p r e t a t i o n s of these f a c t o r s . The v a r i a t i o n s i n the N c- and N^-values f o r d i f f e r e n t s o l u t i o n s may be on the order of a f a c t o r of two, and the 131 d i f f e r e n c e s i n the N^-values may be even more. T h i s discrepancy i s of p a r t i c u l a r i n t e r e s t f o r g r a v i t y s t r u c t u r e s founded on coh e s i o n l e s s s o i l where the f r i c t i o n a l ( f i r s t ) term i n Equation (6.17) i s predominant. Values of Ny as a f u n c t i o n of the f r i c t i o n angle have been compiled by Andersen (1972) from the p u b l i s h e d r e s u l t s of s e v e r a l authors. H i s f i n d i n g s are shown g r a p h i c a l l y i n f i g u r e 6.5. I t i s c l e a r that there i s c o n s i d e r a b l e v a r i a b i l i t y i n the value of Ny f o r a given value of the f r i c t i o n angle depending upon whose r e s u l t s are used. Equation (6.17) i s an approximate t h e o r e t i c a l s o l u t i o n f o r a; very i d e a l i z e d f o u n d a t i o n . Real foundations are never i n f i n i t e i n l e n g t h and l o a d i n g i s o f t e n i n c l i n e d Or e c c e n t r i c or both. For g r a v i t y s t r u c t u r e s , l o a d i n g i s always i n c l i n e d and e c c e n t r i c . E c c e n t r i c i t i e s of 10% and i n c l i n e d l o a d f a c t o r s of 0.2 to 0.4 are common. 1 0 Since an a n a l y t i c a l s o l u t i o n i s not p o s s i b l e except f o r the s i m p l e s t of cases, e m p i r i c a l f a c t o r s have been employed to improve r e s u l t s . To extend T e r z a g h i ' s (1943) s o l u t i o n to i n c l u d e the e f f e c t s of the s h e a r i n g r e s i s t a n c e of the s o i l above the foundation base, i n c l i n e d l o a d i n g , and d i f f e r e n t foundation shapes, Equation (6.17) i s r e w r i t t e n as (Hansen, 1961): q 0 = — V BNy s y d r i y + cNeScd̂ i,. + q ' N ^ d ^ i ^ (6.18) where the s-, d-, and i-parameters are e m p i r i c a l c o e f f i c i e n t s 1 0 T h e i n c l i n e d l o a d f a c t o r , denoted by &, i s the r a t i o of the h o r i z o n t a l to v e r t i c a l l o a d . 132 F i g u r e 6.5 - Comparison of d i f f e r e n t p r o p o s a l s f o r the value of Ny ( A f t e r Andersen, 1972) 133 which represent the e f f e c t s of foundation shape, imbedment depth, and load i n c l i n a t i o n , r e s p e c t i v e l y . These e m p i r i c a l c o e f f i c i e n t s were found using p l a t e l o a d i n g t e s t s by v a r y i n g one parameter (set) at a time and c o r r r e l a t i n g the r e s u l t s to Equation (6.18). Curves were f i t t e d to the data to determine approximate a n a l y t i c a l e x p r e s s i o n s . Equation (6.18) i s the gener a l formula f o r the bearing c a p a c i t y of a r i g i d h o r i z o n t a l f o o t i n g r e s t i n g i n a homogeneous h o r i z o n t a l d e p o s i t and i s the b a s i s of the two most widely used bearing c a p a c i t y t h e o r i e s , those of Meyerhof (1963) and Hansen (1970). The two t h e o r i e s d i f f e r i n t h e i r e s t i m a t i o n of these c o e f f i c i e n t s and the N- v a l u e s . Hansen's (1970) f o r m u l a t i o n i s the method p r e f e r r e d o f f s h o r e . T h i s i s due to s e v e r a l f a c t o r s . The most obvious one i s t h at g r a v i t y s t r u c t u r e technology developed i n Europe where engineers used Hansen's (1961,1970) theory f o r be a r i n g c a p a c i t y problems. A thorough study of t h i s method, f o r a p p l i c a t i o n to c o h e s i o n l e s s d e p o s i t s , was made p r i o r to i n s t a l l a t i o n of the E k o f i s k tank (Bjerrum, 1973). The c o n c l u s i o n drawn from t h i s study was that Hansen's (1970) method w i l l p r o v i d e a c c e p t a b l e r e s u l t s , even f o r l a r g e load i n c l i n a t i o n s , when used f o r the purposes i t was developed f o r . ( i . e . f o r t o t a l s t r e s s analyses of homogeneous d e p o s i t s . ) E c c e n t r i c l o a d i n g i s not t r e a t e d by using e m p i r i c a l c o e f f i c i e n t s . The e f f e c t i v e area approach proposed by Meyerhof (1953) i s used i n s t e a d . A c o n c e n t r i c l o a d i s a p p l i e d to the f o o t i n g on a reduced a r e a . The dimensions of t h i s c e n t r a l l y loaded " e f f e c t i v e a r e a " are then used i n the general bearing 134 c a p a c i t y equation, Equation (6.18). O v e r a l l moment e q u i l i b r i u m i s s a t i s f i e d when using t h i s t echnique. The h o r i z o n t a l f o r c e i s a l s o assumed to a c t only over the e f f e c t i v e a r e a . T h i s method of t r e a t i n g e c c e n t r i c loads i s found to be c o n s e r v a t i v e (Hansen, 1970). For t o t a l s t r e s s analyses of c l a y foundations, s u b s t a n t i a l s l i d i n g r e s i s t a n c e may be m o b i l i z e d on that part of the foundation base o u t s i d e of the e f f e c t i v e a r e a . T h i s r e s i s t a n c e w i l l reduce the h o r i z o n t a l f o r c e a c t i n g on the e f f e c t i v e a r e a ; that f o r c e used i n the bearing c a p a c i t y c a l c u l a t i o n . Since the h o r i z o n t a l f o r c e i s c r i t i c a l i n reducing the u l t i m a t e bearing c a p a c i t y , c o n s i d e r a t i o n of any amount of r e s i s t a n c e that may be m o b i l i z e d o u t s i d e of the e f f e c t i v e area i s extremely important i f undue conservatism i s to be avoided. Bearing c a p a c i t y theory may be m o d i f i e d to take t h i s i n t o account ( L a u r i t z s e n and Schjetne, 1976). The h o r i z o n t a l l o a d taken on the foundation base o u t s i d e of the e f f e c t i v e area i s s u b t r a c t e d from the t o t a l l o a d . T h i s f o r c e may be found using the procedure o u t l i n e d i n the f o l l o w i n g s e c t i o n . The b e a r i n g c a p a c i t y s o l u t i o n s mentioned above assumed that the s o i l was homogeneous, with constant values of the cohesion, f r i c t i o n angle, and e f f e c t i v e u n i t weight. T h i s i s , of course, a great s i m p l i f i c a t i o n , s i n c e r e a l s o i l d e p o s i t s are never homogeneous. Of f s h o r e d e p o s i t s i n p a r t i c u l a r tend to be nonhomogeneous. They are u s u a l l y l a y e r e d and o f t e n c o n s i s t of c l a y interbedded with sand, or v i c e v e r s a . T h i s i s due to the nature of the d e p o s i t i o n a l environment. Meyerhof (1963) proposed that when the aforementioned s o i l p r o p e r t i e s vary 135 w i t h i n the d e p o s i t , average val u e s should be used. T h i s i s reasonable i f the v a r i a t i o n s are s m a l l . Since bearing c a p a c i t y theory i s based on the assumption that c r i t i c a l shear zones develop w i t h i n the s o i l mass, average val u e s w i t h i n the p o t e n t i a l f a i l u r e body should be used i n s t e a d of average values along the p o t e n t i a l f a i l u r e s u r f a c e ( L a u r i t z s e n and Schjetne, 1976). The e v a l u a t i o n of s u i t a b l e s o i l parameters to use i n the a n a l y s i s i s q u i t e s u b j e c t i v e s i n c e the l o c a t i o n of the rupture s u r f a c e i s o f t e n unknown. T h i s problem becomes more c r i t i c a l as l o a d i n c l i n a t i o n i n c r e a s e s and the foundation s o i l s become l e s s homogeneous. For l a y e r e d foundations, f u r t h e r assumptions re g a r d i n g the l o c a t i o n of the shear zones may be made. T h i s problem was addressed by T e r z a g h i and Peck (1948) who developed a crude but u s e f u l procedure f o r t r e a t i n g t h i s type of problem. More recent s o l u t i o n s have been presented by Button (1953) f o r a two-layer cohesi v e d e p o s i t , by Meyerhof (1974) f o r the case of a sand l a y e r over c l a y , and by Davis and Booker (1973) f o r the case where the undrained s t r e n g t h i n c r e a s e s l i n e a r l y with depth. The case where a s o f t l a y e r i s sandwiched between two stronger m a t e r i a l s was i n v e s t i g a t e d by Yamaguchi and T e r a s h i (1971). Other approximate techniques f o r d e a l i n g with m u l t i p l e l a y e r systems have been presented by .Brown and Meyerhof (1969) and Reddy and S r i n i v a s a n (1967), among o t h e r s . These s o l u t i o n s are e x t e n s i o n s of T e r z a g h i ' s (1943) theory. The e x t e n s i o n of b e a r i n g c a p a c i t y theory to l a y e r e d foundations i s q u i t e s u b j e c t i v e and approximate.. F u l l y d r a i n e d c o n d i t i o n s are u s u a l l y assumed f o r a bearing 136 c a p a c i t y a n a l y s i s of sand. T h i s i s not the case f o r a l a r g e o f f s h o r e g r a v i t y s t r u c t u r e on t h i s type of d e p o s i t which i s s u b j e c t e d to storm wave l o a d i n g . To be at a l l u s e f u l , the bearing c a p a c i t y formula should take i n t o account the pore water pres s u r e s developed i n the s o i l . 6.4.2 Other Bearing C a p a c i t y Formulations The f i r s t b e a r i n g c a p a c i t y method formulated to c o n s i d e r wave induced pore water p r e s s u r e s was that developed by Hansen (Bjerrum, 1973). T h i s method was used to assess the s t a b i l i t y of the E k o f i s k tank and was r e p o r t e d i n d e t a i l at a l a t e r date by Hansen (1976). The theory was developed based on the assumuptions that the s o i l i s homogeneous and that a r o t a t i o n a l type of f a i l u r e about a p o i n t "o" below the foundation base w i l l occur (see f i g u r e 4.14). A r i g i d - p l a s t i c f a i l u r e mechanism was assumed and the the pore water p r e s s u r e s induced by the d i l a t a n c y of the sand were i n c l u d e d (Hansen, 1976). In g e n e r a l , the s o l u t i o n to t h i s problem i s very d i f f i c u l t to o b t a i n because the rupture s u r f a c e , which i s found based on the e f f e c t i v e s t r e s s d i s t r i b u t i o n , must f i r s t be computed from an estimated pore water pressure d i s t r i b u t i o n . The computed displacement f i e l d then g i v e s a c o r r e c t e d d i s t r i b u t i o n of pore water p r e s s u r e s . T h i s leads to an extremely complicated i t e r a t i v e s o l u t i o n . R e s i d u a l pore water p r e s s u r e s due to c y c l i c l o a d i n g are not c o n s i d e r e d . T h i s method i s not easy to use and has no advantages over other e f f e c t i v e s t r e s s b e a r i n g c a p a c i t y s o l u t i o n s (e.g. the f o l l o w i n g method). Janbu et a l (1976) developed a two-dimensional bearing 137 c a p a c i t y s o l u t i o n f o r a w e i g h t l e s s s o i l with zero pore water p r e s s u r e . They extended t h i s s o l u t i o n to i n c l u d e s o i l weight and excess pore water p r e s s u r e s i n an approximate way; the f o r c e e q u i l i b r i u m equations d e r i v e d f o r the G e n e r a l i z e d Procedure of S l i c e s (GPS) method (Janbu, 1973) were n u m e r i c a l l y i n t e g r a t e d ; the i n t e g r a t i o n was performed over a bearing c a p a c i t y rupture s u r f a c e s i m i l a r to the one shown in f i g u r e 6.6. The s t r e s s d i s t r i b u t i o n on the assumed rupture s u r f a c e i s found by employing the GPS method. Both the v e r t i c a l and h o r i z o n t a l loads are assumed to a c t on the e f f e c t i v e foundation area. T h i s treatment i s adequate f o r c o h e s i o n l e s s s o i l s . T h e i r r e s u l t i s expressed by a m o d i f i e d bearing c a p a c i t y e q u a t i o n . T h i s i s T = r(o;+ a - u w ) t a n 0 (6 . 19 ) o~v+ a = BN y + (q'+ a)N^- u kN w (6.20) where T i s the average h o r i z o n t a l shear along the base, r i s the r e l a t i v e degree of h o r i z o n t a l shear m o b i l i z a t i o n , tan0 i s the m o b i l i z e d f r i c t i o n a l r e s i s t a n c e , o~v i s the average v e r t i c a l s o i l r e a c t i o n over the base, a i s the a t t r a c t i o n ( c / t a n 0 ) , u f c i s the average pore water pressure along the base, and N H i s a dim e n s i o n l e s s bearing c a p a c i t y f a c t o r . An i t e r a t i v e s o l u t i o n i s r e q u i r e d to determine the s a f e t y f a c t o r s i n c e the s o i l f o r c e s are expressed i n terms of the degree of s t r e n g t h m o b i l i z a t i o n . Curves were developed f o r the bearing c a p a c i t y f a c t o r s which may be used to speed up the s o l u t i o n procedure. A pore water pressure d i s t r i b u t i o n i n the s o i l c o r r e s p o n d i n g to the maximum wave i s assumed based on changes i n 138 F i g u r e 6.6 - Geometry of rupture s u r f a c e used fo r an e f f e c t i v e s t r e s s bearing c a p a c i t y s o l u t i o n 139 the p r i n c i p a l s t r e s s e s over one l o a d i n g c y c l e . The maximum pore water pressure at any l o c a t i o n i s found from Equation (6.6). Cumulative pore water p r e s s u r e s from c y c l i c l o a d i n g are i n c o r p o r a t e d i n t o the a n a l y s i s by using a simple pore water pressure g e n e r a t i o n model. T h i s i s given by where n i s the number of bands i n the design storm histogram, m i s a d i m e n s i o n l e s s pore p r e s s u r e parameter obtained from c y c l i c l o a d t e s t s , and N i s the number of c y c l e s at any s t r e s s l e v e l . Since the concern i s with r e l a t i v e l y small pore water pressure r a t i o s , not l i q u e f a c t i o n , t h i s type of pore water pr e s s u r e model i s used. A pore water p r e s s u r e model such as Seed et a l ' s (1976) a r c s i n e formula i s unnecessary. The pore water p r e s s u r e s on the assumed f a i l u r e s u r f a c e must be found by using an i t e r a t i o n technique, s i n c e the s t r e s s e s and pore pressure parameters depend on the degree of s t r e n g t h m o b i l i z a t i o n i n the s o i l . Another bearing c a p a c i t y f o r m u l a t i o n was developed by Murff and M i l l e r (1977) to analyze the foundation s t a b i l i t y of a g r a v i t y p l a t f o r m . They approximated the set of p a r t i a l d i f f e r e n t i a l equations d e r i v e d f o r c l a s s i c a l b e a r i n g c a p a c i t y p l a s t i c i t y s o l u t i o n . T h i s set of p a r t i a l d i f f e r e n t i a l equations i s s o l v e d n u m e r i c a l l y and a l l o w s more complex boundary c o n d i t i o n s t o be s p e c i f i e d . Hence, f a c t o r s such as i n c l i n e d l o a d i n g and i r r e g u l a r base geometry may be d e a l t with d i r e c t l y , i n s t e a d of by using e m p i r i c a l c o e f f i c i e n t s as other b e aring c a p a c i t y t h e o r i e s do. R e s u l t s are comparable to c l a s s i c a l Afo", - o-3) (6.21) 140 theory and are somewhat c o n s e r v a t i v e . Since the s o l u t i o n i s found n u m e r i c a l l y , s o i l p r o p e r t i e s may vary with depth. The shape of the f a i l u r e s u r f a c e i s n e c e s s a r i l y d e f i n e d mathematically to s o l v e the equations, and t h e r e f o r e , i t i s c o n s t r a i n e d to a f u n c t i o n a l r e p r e s e n t a t i o n such as a l o g a r i t h m i c s p i r a l . T h i s c o n s t r a i n t on shape l i m i t s the u s e f u l n e s s of t h i s method f o r l a y e r e d f o u n d a t i o n s . 6.4.3 NGI S l i p Surface Method A s l i p s u r f a c e method was developed at the Norwegian G e o t e c h n i c a l I n s t i t u t e to i n v e s t i g a t e the s t a b i l i t y of o f f s h o r e g r a v i t y p l a t f o r m s founded on c l a y . D e t a i l s of t h i s method have been r e p o r t e d by L a u r i t z s e n and Schjetne (1976) and Schjetne (1976). An a l t e r n a t i v e approach to the bearing c a p a c i t y f o r m u l a t i o n was d e s i r e d that was simple to use, r e l i a b l e , and a p p l i c a b l e to o f f s h o r e g r a v i t y s t r u c t u r e s founded on l a y e r e d d e p o s i t s . The NGI s l i p s u r f a c e method o f f e r s some d i s t i n c t advantages over b e a r i n g c a p a c i t y theory, namely: complex l o a d i n g can be accomodated somewhat more e a s i l y , the h o r i z o n t a l f o r c e i s a p p l i e d on both the e f f e c t i v e area and n o n - e f f e c t i v e area so that undue conservatism i s avoided, and l a y e r e d foundations may be analyzed d i r e c t l y s i n c e the s o i l p r o p e r t i e s may vary along the p o t e n t i a l f a i l u r e s u r f a c e . T h i s method i s based on an assumed f a i l u r e mechanism with the g e o m e t r i c a l model of the " s l i d i n g body" shown in f i g u r e 6.7. The body has a constant c r o s s s e c t i o n over the p l a t f o r m l e n g t h and i s cut o f f by v e r t i c a l planes at the s i d e s . F i g u r e 6.7 - Geometry of s l i d i n g body used by NGI F i g u r e 6.8 _ Geometry of b e a r i n g f a i l u r e s u r f a c e used i n the NGI s l i p s u r f a c e method ( A f t e r L a u r i t z s e n and Schjetne, 1976) 142 The s u r f a c e of the s l i d i n g body i s broken up i n t o four s e c t i o n s as shown i n f i g u r e 6.8: an a c t i v e s e c t i o n "ab", a f l a t s e c t i o n "be", an i n c l i n e d s e c t i o n "cd", and a pa s s i v e s e c t i o n "de". The i n c l i n e d s e c t i o n "cd" i s d i r e c t l y beneath the e f f e c t i v e a r e a . The r e s i s t a n c e t o s l i d i n g f o r each of these s e c t i o n s i s evaluated under f o r c e e q u i l i b r i u m c o n d i t i o n s . The f a c t o r of s a f e t y i s found from o v e r a l l h o r i z o n t a l f o r c e e q u i l i b r i u m . Only the magnitudes of f o r c e s are c o n s i d e r e d , not the d i s t r i b u t i o n , s i n c e moment e q u i l i b r i u m i s not a p p l i e d to the s l i d i n g body. Inherent i n t h i s method, i s the assumption that the shea r i n g r e s i s t a n c e at the s o i l - s o i l i n t e r f a c e s on the side areas w i l l reduce the h o r i z o n t a l f o r c e a c t i n g on the base. T h i s r e s i s t a n c e i s assumed to a c t h o r i z o n t a l l y . Hence, Equation (6.12) may be r e w r i t t e n to i n c l u d e t h i s r e s i s t a n c e : H B , = P H + < P A or P w) - P p - P & - P t (6.22) where Px i s d e f i n e d as P 3 = 0.4(2cA s) (6.23) Here, c i s the average cohesion and A s i s one s i d e area (shown in f i g u r e 6.8 as " c e f d " ) . The c o e f f i c i e n t i s used to account fo r the f a c t that the p o s t u l a t e d f a i l u r e mechanism i s not the c o r r e c t one. I f the s o i l d i d indeed f a i l , there would be s i g n i f i c a n t d i f f e r e n c e s between the assumed v e r t i c a l plane s u r f a c e s on the foundation s i d e s and the a c t u a l f a i l u r e geometry. A plane s t r a i n a n a l y s i s i s e s s e n t i a l l y being modified to do a pseudo-three-dimensional one. The 0.4 value was chosen to make the f a c t o r of s a f e t y agree with Hansen's (1970) 143 f o r m u l a t i o n f o r a homogeneous d e p o s i t , which was m o d i f i e d to reduce the h o r i z o n t a l f o r c e a c t i n g on the e f f e c t i v e a r ea. The h o r i z o n t a l f o r c e taken along the f l a t or s l i d i n g s e c t i o n "be" of the foundation base i s found from H „ = c ( B 0 - B ) L 0 (6.24) T h i s i s a m o b i l i z e d f o r c e with the f a c t o r ( B 0 - B ) L 0 being nothing more than the area of the s l i d i n g s u r f a c e . The h o r i z o n t a l f o r c e a p p l i e d t o the e f f e c t i v e area may then be found from H E, = HftT - H S T (6.25) The NGI s l i p s u r f a c e method i s r e l a t i v e l y simple to use. To f i n d the c r i t i c a l s l i p s u r f a c e , the angle °c i s incremented in steps and the minimum f a c t o r of s a f e t y i s e s t a b l i s h e d . ' The a n a l y s i s may be done by hand, although use of a small computer program w i l l speed up the a n a l y s i s c o n s i d e r a b l y , e s p e c i a l l y when there are a number of l a y e r s . For l a y e r e d foundations, the NGI s l i p s u r f a c e method u s u a l l y p r e d i c t s a lower s a f e t y f a c t o r than the b e a r i n g c a p a c i t y formulas. T h i s s a f e t y f a c t o r should be used i n p r e f e r e n c e to the bearing c a p a c i t y r e s u l t . The geometry of the s l i p s u r f a c e i s f i x e d , only the angle changes; the p a s s i v e zone i s always at 45° with respect to the h o r i z o n t a l . The s l i p s u r f a c e i s c o n s t r a i n e d to the shape shown in f i g u r e 6.8. The s l i p s u r f a c e used i n c a l c u l a t i o n s r e a l l y has a sharp corner where the p a s s i v e wedge s t a r t s . T h i s i s not shown i n the f i g u r e . For l a y e r e d foundations, average s o i l p r o p e r t i e s along the s l i p s u r f a c e are used. A t h i n seam of weak m a t e r i a l w i l l t h e r e f o r e be represented only by a s l i g h t decrease i n the average cohesion computed on the p o t e n t i a l f a i l u r e s u r f a c e . T h i s w i l l have a minimal e f f e c t on the computed f a c t o r 144 of s a f e t y and d i s c r e t i o n must be used when i n t e r p r e t i n g r e s u l t s . The p o s s i b i l i t y of a deep s l i d i n g type of f a i l u r e , such as that shown i n f i g u r e 3 . 6 ( f ) , o c c u r r i n g , cannot be p r o p e r l y assessed. The NGI s l i p s u r f a c e method may only be used f o r t o t a l s t r e s s a n a l y ses of c l a y f o u n d a t i o n s . A d i r e c t e x t e n s i o n of t h i s method to an e f f e c t i v e s t r e s s a n a l y s i s i s not p o s s i b l e . Since the d i s t r i b u t i o n of shear and normal s t r e s s e s along a p o t e n t i a l f a i l u r e s u r f a c e i s not c o n s i d e r e d w i t h i n any of the four shear zones, the i n c l u s i o n of s t r e s s dependent f r i c t i o n a l r e s i s t a n c e and pore water p r e s s u r e s would be exceedingly crude. The method of s l i c e s c o u l d be used f o r extending the NGI s l i p s u r f a c e approach to t r e a t these types of problems. 6.4.4 Method of S l i c e s T h i s technique has been mentioned f o r o f f s h o r e g r a v i t y s t r u c t u r e s t a b i l i t y a n a l y s es ( E i d e , 1974; H0eg, 1976; L a u r i t z s e n and Schjetne, 1976; Young et a l , 1975), although no compre- hensive treatment has yet been r e p o r t e d . None of the a v a i l a b l e s l i c e methods are d i r e c t l y a p p l i c a b l e to o f f s h o r e g r a v i t y s t r u c t u r e s i n t h e i r present forms. T h i s technique w i l l be adapted so that i t may be used f o r o f f s h o r e s t a b i l i t y analyses i n the f o l l o w i n g c h a pter. 6.4.5 F i n i t e Element Analyses The f i n i t e element method may be used to assess foundation s t a b i l i t y (Broughton, 1975; Prev0st et a l , 1981a; Vaughan et a l , 1976; Z i e n k i e w i c z et a l , 1979), although i t i s used p r i m a r i l y f o r displacement c a l c u l a t i o n s . T h i s i s a powerful technique 145 that can e a s i l y d e a l with complex l o a d i n g and v a r i a b l e s o i l p r o p e r t i e s . A s t r e s s - s t r a i n model i s used, which i s more r e a l i s t i c than the r i g i d , p e r f e c t l y p l a s t i c r e p r e s e n t a t i o n used i n the b e a r i n g c a p a c i t y and l i m i t e q u i l i b r i u m methods to b e t t e r model true s o i l behaviour. The s t r e s s - s t r a i n models used i n f i n i t e element analyses vary widely. The f i n i t e element method i s b a s i c a l l y an extension of matrix s t r u c t u r a l a n a l y s i s techniques which s o l v e the equations of e q u i l i b r i u m f o r a set of s t r u c t u r a l members. The s o i l i s d i s c r e t i z e d i n t o "elements" and the force-displacement equations are w r i t t e n f o r the set of s o i l elements. The n o n l i n e a r , a n i s o t r o p i c , e l a s t o p l a s t i c , path-dependent s t r e s s - s t r a i n p r o p e r t i e s of the s o i l may be modelled i n f i n i t e element an a l y s e s by using a p p r o p r i a t e c o n s t i t u t i v e r e l a t i o n s (Prev0st et a l , 1981a). C y c l i c l o a d i n g i s t r e a t e d by using a q u a s i - s t a t i c approach. The r e s u l t s of f i n i t e element analyses are very dependent on the assumed c o n s t i t u t i v e r e l a t i o n s used as i n p u t . Because s o i l s t i f f n e s s parameters are r e q u i r e d to perform the a n a l y s e s , f i n i t e element s t u d i e s are g e n e r a l l y done only a f t e r the d e t a i l e d s i t e i n v e s t i g a t i o n has been c a r r i e d out. A h i g h degree of u n c e r t a i n t y i s always a s s o c i a t e d with the i n - s i t u s t i f f n e s s parameters measured f o r o f f s h o r e d e p o s i t s . In the f i n i t e element method, the a p p l i e d loads are incremented to stepwise approximate the s t r e s s - s t r a i n curve. I f l o a d i n g i s c a r r i e d out f a r enough, some s o i l elements w i l l reach s t r e s s l e v e l s high enough to " f a i l " , that i s , they can no longer support an i n c r e a s e d l o a d . Since they are c o n f i n e d by other elements t h a t have not reached a c r i t i c a l f a i l u r e s t r e s s l e v e l , 146 l a r g e displacements of the f a i l e d elements cannot occur; f a i l u r e i s l o c a l i z e d . A p r o g r e s s i v e f a i l u r e w i l l occur as more elements f a i l under an i n c r e a s i n g l o a d . E v e n t u a l l y , no more load can be added without e x c e s s i v e displacements (and l o a d t r a n s f e r ) w i t h i n much of the s o i l mass; t h i s corresponds to a t o t a l f a i l u r e . The u l t i m a t e bearing c a p a c i t y , or a p p l i e d v e r t i c a l l o a d at f a i l u r e , i s w e l l d e f i n e d f o r dense sands and i n s e n s i t i v e c l a y s , but f o r loose sands and s e n s i t i v e c l a y s i t i s not ( V e s i c , 1975). F o r t u n a t e l y , o f f s h o r e g r a v i t y s t r u c t u r e s are u s u a l l y founded on the former type of d e p o s i t s where f i n i t e element analyses can g e n e r a l l y d i s t i n g u i s h a t o t a l b e a r i n g f a i l u r e . E x c e s s i v e displacements may occur r a t h e r suddenly upon a p p l i c a t i o n of the c r i t i c a l l o a d increment. The r a t i o of the f a i l u r e load to the design l o a d w i l l d e f i n e the l o a d s a f e t y f a c t o r s i n c e the design s o i l s t r e n g t h i s used i n the a n a l y s i s . C o n s i d e r a b l e experience i s r e q u i r e d to i n t e r p r e t r e s u l t s from f i n i t e element a n a l y s e s . Prev0st et a l (1981a) performed an e x t e n s i v e s e r i e s of f i n i t e element a n a l y s e s . They compared t h e i r r e s u l t s with c e n t r i f u g e t e s t data f o r a model f o o t i n g on p l a s t i c s i l t (Prev0st et a l , 1981b) where the l o a d was i n c r e a s e d m o n o t o n i c a l l y to f a i l u r e . Both two- and t h r e e - d i m e n s i o n a l analyses were performed; the former assumed plane s t r a i n c o n d i t i o n s , while the l a t t e r modelled the foundation as a c i r c u l a r f o o t i n g with t h r e e - d i m e n s i o n a l c o n s t i t u t i v e r e l a t i o n s . The t h r e e - d i m e n s i o n a l a n a l y s i s was found to adequately p r e d i c t displacements at the f a i l u r e s t a t e and loads observed i n the model t e s t . The two-dimensional r e s u l t s were found to be c o n s i s t e n t with the experimental data. The (exaggerated) 147 d i s t o r t e d meshes f o r both two- and t h r e e - d i m e n s i o n a l analyses at s i m i l a r l o a d i n c l i n a t i o n s and e c c e n t r i c i t i e s are shown i n f i g u r e 6.9. Note that the displacement p a t t e r n s are s i m i l a r . Prev0st et a l (1981a) concluded that although two-dimensional f i n i t e element s t u d i e s cannot "provide exact q u a n t i t a t i v e i n f o r m a t i o n about the behaviour of the s o i l - s t r u c t u r e system, they would s t i l l p r o v i d e u s e f u l answers r e g a r d i n g r e l a t i v e magnitudes of loads and displacements." T h i s would imply that the plane s t r a i n assumption f o r foundation a n a l y s i s may be adequate i n many ca s e s . The e f f e c t of l o a d e c c e n t r i c i t y was s t u d i e d using the two- dimensional model. Some r e s u l t s are shown i n f i g u r e 6.10. I t i s c l e a r l y e v ident t h a t the e f f e c t i v e b e a r i n g area reduces with i n c r e a s i n g e c c e n t r i c i t y . In f a c t , the e f f e c t i v e bearing area appears to be very n e a r l y equal to the e f f e c t i v e area d e f i n e d by Equation (6.15) f o r plane s t r a i n l o a d i n g . Two-dimensional f i n i t e element methods cannot be adapted to perform a pseudo-three-dimensional a n a l y s i s l i k e , the NGI s l i p s u r f a c e method. That i s , s h e a r i n g r e s i s t a n c e at the s o i l - s o i l i n t e r f a c e s on the s i d e s of the p o t e n t i a l f a i l u r e body cannot be i n c l u d e d i n the element e q u i l i b r i u m e q u a t i o n s . A complete t h r e e - d i m e n s i o n a l a n a l y s i s can model t h i s , but i s exceedingly expensive to perform. Since many s o i l parameters are s t r e s s dependent, i t e r a t i o n techniques must be used to achieve s t r e s s c o m p a t a b i l i t y . T h i s requirement f o r many i t e r a t i o n s with a l a r g e set of simultaneous equations means that use of a computer with a l a r g e memory i s mandatory. I t a l s o leads to the high c o s t of running these 148 (a) Two-dimensional — It s y w i l F _ ' ' ' / I I \ \ S _ . (b) Three-dimensional F i g u r e 6.9 Comparison of two- and three-dimensional d i s t o r t e d f i n i t e element meshes f o r an i n c l i n e d and e c c e n t r i c l o a d ( A f t e r Prevost et a l , 1981a) 149 F i g u r e 6.10 E f f e c t of lo a d e c c e n t r i c i t y on e f f e c t i v e b e a r i n g area as e v a l u a t e d u s i n g the f i n i t e element method ( A f t e r Prevost et a l , 1981a) 150 types of computer programs. For a m u l t i m i l l i o n d o l l a r p l a t f o r m , t h i s may be of l i t t l e s i g n i f i c a n c e . However, f o r smaller s t r u c t u r e s , computer c o s t s can be an important c o n s i d e r a t i o n . Many engineers are u n w i l l i n g to base t h e i r d e c i s i o n s s o l e l y on f i n i t e element a n a l y s e s . T h i s may be due to a d i s t r u s t of the c o n s t i t u t i v e r e l a t i o n s used to model s o i l behaviour or the numerical techniques employed i n s o l v i n g the equations. A high degree of u n c e r t a i n t y a s s o c i a t e d with the e s t i m a t i o n of s t i f f n e s s parameters i s a l s o an important f a c t o r . 6.4.6 Model Te s t s Model t e s t i n g f o r s t a b i l i t y problems i s done using c e n t r i f u g e t e s t s (Andersen et a l , 1979; Heijnen, 1981; Prev0st et a l , 1981b; Rowe, 1975; Rowe et a l , 1976). A small model foundation i s p l a c e d on a c a r e f u l l y c o n s t r u c t e d s o i l p r o f i l e i n a bucket which i s then mounted on an arm connected t o a c e n t r a l s h a f t and spun. The deadweight bearing pressure i s d e r i v e d from the r e s u l t i n g c e n t r i f u g a l f o r c e s . A h o r i z o n t a l l o a d may be a p p l i e d t o the model by means of a jack or c y c l i c loads may be imposed on the model by us i n g a d i s p l a c e m e n t - c o n t r o l l e d servo- h y d r a u l i c a c t u a t o r (Andersen et a l , 1979). For t e s t s with c y c l i c l o a d i n g , water can be put on the s o i l s u r f a c e to apply a back p r e s s u r e ; t h i s may be necessary to prevent c a v i t a t i o n which w i l l not occur i n the f i e l d under high h y d r o s t a t i c p r e s s u r e s . I r r e g u l a r p l a t f o r m geometry i s e a s i l y accounted f o r i n c e n t r i f u g e t e s t s s i n c e a s t r u c t u r a l model of any shape may be made. C e n t r i f u g e t e s t s do not s u f f e r from one of the major problems that other model t e s t s do: the i n a b i l i t y to simulate 151 h i g h s t r e s s e s r e s u l t i n g from g r a v i t a t i o n a l loads i n the p r o t o t y p e . These t e s t s are an attempt to p r e d i c t foundation behaviour without much of the s u b j e c t i v e n e s s of numerical techniques. They do r e q u i r e f i e l d and l a b o r a t o r y t e s t data to d e f i n e the i n - s i t u s o i l p r o p e r t i e s . V a r i a b l e s o i l p r o p e r t i e s are modelled by b u i l d i n g a s o i l p r o f i l e with d i f f e r e n t l a y e r s using s o i l from the t e s t s i t e to c o n t r o l f a c t o r s such as p a r t i c l e s i z e and f a b r i c . C l a y s are remolded and c o n s o l i d a t e d to the s p e c i f i e d o v e r c o n s o l i d a t i o n r a t i o . The more nonuniform the s o i l p r o f i l e i s i n - s i t u , the harder i t i s to model. G e n e r a l l y , a few l a y e r s at most are used. Not only do the s o i l p r o f i l e and l o a d i n g h i s t o r y have to be r e p r e s e n t a t i v e of the p r o t o t y p e , so do the pore water p r e s s u r e s . For c o h e s i o n l e s s s o i l s where s u b s t a n t i a l drainage may take p l a c e i n the model, i n - s i t u c o n s o l i d a t i o n i s modelled by s c a l i n g the time f a c t o r . T h i s i s u s u a l l y done by using pore f l u i d s much more v i s c o u s than water. If s i m i l a r i t y requirements between the model and prototype are s a t i s f i e d , then the v a r i o u s f a c t o r s i n f l u e n c i n g the t e s t do not have to be d i s t i n g u i s h e d s e p a r a t e l y (Heijnen, 1981). For example, the s t r e s s e s w i t h i n the s o i l mass do not have to be determined, s i n c e they are not used i n s e t t i n g up the t e s t . In numerical s t u d i e s , s t r e s s e s are computed using parameters o b t a i n e d from l a b o r a t o r y shear t e s t s . The s t r e s s e s e x i s t i n g i n the c e n t r i f u g e model s o i l are s i m i l a r to those i n the prototype s o i l i f the s o i l p r o f i l e s and l o a d i n g are the same. C e n t r i f u g e t e s t s , l i k e f i n i t e element s t u d i e s , f i n d the l o a d s a f e t y f a c t o r and provide i n f o r m a t i o n on displacement and f a i l u r e modes. 152 C e n t r i f u g e t e s t s have been used to i n v e s t i g a t e the foundation s t a b i l i t y of e x i s t i n g p l a t f o r m s (Rowe, 1975) and f o r t h e o r e t i c a l s t u d i e s (Andersen et a l , 1979; Prev0st et a l , 1981b), but they have not yet been used i n d e s i g n . T h i s w i l l l i k e l y change i n the f u t u r e as t e s t i n g procedures improve (Heijnen, 1981). The major drawback of - c e n t r i f u g e t e s t i n g i s that i t i s time consuming, expensive, and can be conducted at a l i m i t e d number of f a c i l i t i e s . 6.5 Summary A summary of the e x i s t i n g s t a b i l i t y methods a p p l i c a b l e to o f f s h o r e g r a v i t y s t r u c t u r e s i s given i n Table V I I I . I t i s q u i t e e v i d e n t that there are two d i s t i n c t c l a s s e s of a n a l y s e s : the r e l a t i v e l y simple bearing c a p a c i t y f o r m u l a t i o n s and the NGI s l i p s u r f a c e method, and the more s o p h i s t i c a t e d analyses which c o n s i d e r more r e a l i s t i c s t r e s s - s t r a i n behaviour. There i s p r e s e n t l y no a n a l y t i c a l a l t e r n a t i v e to the crude bearing c a p a c i t y approach or the NGI s l i p s u r f a c e method except the f i n i t e element method. A simple e f f e c t i v e s t r e s s method i s needed which can adequately t r e a t both l a y e r e d foundations and complex l o a d i n g . In the f o l l o w i n g c h a p t e r s , such a technique, based on the method of s l i c e s , i s presented. Table VIII - Comparison of Ex is t ing S t a b i l i t y Methods METHOD ADVANTAGES DISADVANTAGES .. AR1NG CAPACITY THEORY (CLASSICAL) -SIMPLE TO USE -SUITABLE FOR HAND CALCULATIONS -EASY TO PERFORM PARAMETER STUDIES -DOES NOT CONSIDER STRESS-STRAIN BEHAVIOUR -BASED ON FIXED GEOMETRY OF RUPTURE SURFACE -CANNOT TREAT COMPLEX LOADING CONDITIONS -LIMITED TO TOTAL STRESS ANALYSES -NOT GOOD FOR LAYERED FOUNDATIONS -SUBJECTIVITY OF BEARING CAPACITY FACTORS NGI SLIP SURFACE METHOD -RELATIVELY EASY TO USE -SUITABLE FOR HAND CALCULATIONS -APPLICABLE TO LAYERED FOUNDATIONS -EASY TO PERFORM PARAMETER STUDIES -DOES NOT CONSIDER STRESS-STRAIN BEHAVIOUR -BASED ON FIXED GEOMETRY OF FAILURE SURFACE -ONLY FOR TOTAL STRESS ANALYSES OF CLAY -DOES NOT CONSIDER DISTRIBUTION OF LOADS -PROBLEMS WITH THIN SEAMS FINITE ELEMENT METHOD (TWO-DIMENSIONAL) -CONSIDERS STRESS-STRAIN BEHAVIOUR -CAN ACCOMODATE IRREGULAR GEOMETRY -APPLICABLE TO LAYERED FOUNDATIONS -CAN STUDY SOIL-STRUCTURE INTERACTION -POSSIBLE TO STUDY PROGRESSIVE FAILURE -PROVIDES INFORMATION ON FAILURE MODES -CANNOT STUDY THREE-DIMENSIONAL EFFECTS -REQUIRES MANY SOIL PARAMETERS AS INPUT -MUCH DATA PREPARATION REQUIRED -EXPENSIVE ANALYSES -REQUIRES THE USE OF A LARGE COMPUTER CENTRIFUGE MODEL TESTING -MODELS STRESS-STRAIN BEHAVIOUR -CAN ACCOMODATE IRREGULAR GEOMETRY -APPLICABLE TO LAYERED FOUNDATIONS -TRUE THREE-DIMENSIONAL ANALYSIS -PROVIDES INFORMATION ON FAILURE MODES -EXTENSIVE PREPARATION REQUIRED -REQUIRES SPECIALLY TRAINED PERSONNEL -REQUIRES SOIL FROM FIELD SITE -EXPENSIVE ANALYSES -LIMITED TO FACILITIES WITH CENTRIFUGES Ul 150 types of computer programs. For a m u l t i m i l l i o n d o l l a r p l a t f o r m , t h i s may be of l i t t l e s i g n i f i c a n c e . However, f o r smaller s t r u c t u r e s , computer c o s t s can be an important c o n s i d e r a t i o n . Many engineers are u n w i l l i n g to base t h e i r d e c i s i o n s s o l e l y on f i n i t e element a n a l y s e s . T h i s may be due to a d i s t r u s t of the c o n s t i t u t i v e r e l a t i o n s used to model s o i l behaviour or the numerical techniques employed i n s o l v i n g the equations. A high degree of u n c e r t a i n t y a s s o c i a t e d with the e s t i m a t i o n of s t i f f n e s s parameters i s a l s o an important f a c t o r . 6.4.6 Model Te s t s Model t e s t i n g f o r s t a b i l i t y problems i s done using c e n t r i f u g e t e s t s (Andersen et a l , 1979; Heijnen, 1981; Prev0st et a l , 1981b; Rowe, 1975; Rowe et a l , 1976). A small model foundation i s p l a c e d on a c a r e f u l l y c o n s t r u c t e d s o i l p r o f i l e i n a bucket which i s then mounted on an arm connected to a c e n t r a l s h a f t and spun. The deadweight bearing pressure i s d e r i v e d from the r e s u l t i n g c e n t r i f u g a l f o r c e s . A h o r i z o n t a l l o a d may be a p p l i e d t o the model by means of a jack or c y c l i c loads may be imposed on the model by us i n g a d i s p l a c e m e n t - c o n t r o l l e d servo- h y d r a u l i c a c t u a t o r (Andersen et a l , 1979). For t e s t s with c y c l i c l o a d i n g , water can be put on the s o i l s u r f a c e to apply a back p r e s s u r e ; t h i s may be necessary to prevent c a v i t a t i o n which w i l l not occur i n the f i e l d under high h y d r o s t a t i c p r e s s u r e s . I r r e g u l a r p l a t f o r m geometry i s e a s i l y accounted f o r i n c e n t r i f u g e t e s t s s i n c e a s t r u c t u r a l model of any shape may be made. C e n t r i f u g e t e s t s do not s u f f e r from one of the major problems that other model t e s t s do: the i n a b i l i t y to simulate 151 h i g h s t r e s s e s r e s u l t i n g from g r a v i t a t i o n a l loads i n the p r o t o t y p e . These t e s t s are an attempt to p r e d i c t foundation behaviour without much of the s u b j e c t i v e n e s s of numerical techniques. They do r e q u i r e f i e l d and l a b o r a t o r y t e s t data to d e f i n e the i n - s i t u s o i l p r o p e r t i e s . V a r i a b l e s o i l p r o p e r t i e s are modelled by b u i l d i n g a s o i l p r o f i l e with d i f f e r e n t l a y e r s using s o i l from the t e s t s i t e to c o n t r o l f a c t o r s such as p a r t i c l e s i z e and f a b r i c . C l a y s are remolded and c o n s o l i d a t e d to the s p e c i f i e d o v e r c o n s o l i d a t i o n r a t i o . The more nonuniform the s o i l p r o f i l e i s i n - s i t u , the harder i t i s to model. G e n e r a l l y , a few l a y e r s at most are used. Not only do the s o i l p r o f i l e and l o a d i n g h i s t o r y have to be r e p r e s e n t a t i v e of the p r o t o t y p e , so do the pore water p r e s s u r e s . For c o h e s i o n l e s s s o i l s where s u b s t a n t i a l drainage may take p l a c e i n the model, i n - s i t u c o n s o l i d a t i o n i s modelled by s c a l i n g the time f a c t o r . T h i s i s u s u a l l y done by using pore f l u i d s much more v i s c o u s than water. If s i m i l a r i t y requirements between the model and prototype are s a t i s f i e d , then the v a r i o u s f a c t o r s i n f l u e n c i n g the t e s t do not have to be d i s t i n g u i s h e d s e p a r a t e l y (Heijnen, 1981). For example, the s t r e s s e s w i t h i n the s o i l mass do not have to be determined, s i n c e they are not used i n s e t t i n g up the t e s t . In numerical s t u d i e s , s t r e s s e s are computed using parameters obt a i n e d from l a b o r a t o r y shear t e s t s . The s t r e s s e s e x i s t i n g i n the c e n t r i f u g e model s o i l are s i m i l a r to those i n the prototype s o i l i f the s o i l p r o f i l e s and l o a d i n g are the same. C e n t r i f u g e t e s t s , l i k e f i n i t e element s t u d i e s , f i n d the load s a f e t y f a c t o r and provide i n f o r m a t i o n on displacement and f a i l u r e modes. 152 C e n t r i f u g e t e s t s have been used to i n v e s t i g a t e the foundation s t a b i l i t y of e x i s t i n g p l a t f o r m s (Rowe, 1975) and f o r t h e o r e t i c a l s t u d i e s (Andersen et a l , 1979; Prev0st et a l , 1981b), but they have not yet been used i n d e s i g n . T h i s w i l l l i k e l y change i n the f u t u r e as t e s t i n g procedures improve (Heijnen, 1981). The major drawback of - c e n t r i f u g e t e s t i n g i s that i t i s time consuming, expensive, and can be conducted at a l i m i t e d number of f a c i l i t i e s . 6.5 Summary A summary of the e x i s t i n g s t a b i l i t y methods a p p l i c a b l e to o f f s h o r e g r a v i t y s t r u c t u r e s i s given i n Table V I I I . I t i s q u i t e e v i d e n t that there are two d i s t i n c t c l a s s e s of a n a l y s e s : the r e l a t i v e l y simple bearing c a p a c i t y f o r m u l a t i o n s and the NGI s l i p s u r f a c e method, and the more s o p h i s t i c a t e d analyses which c o n s i d e r more r e a l i s t i c s t r e s s - s t r a i n behaviour. There i s p r e s e n t l y no a n a l y t i c a l a l t e r n a t i v e to the crude bearing c a p a c i t y approach or the NGI s l i p s u r f a c e method except the f i n i t e element method. A simple e f f e c t i v e s t r e s s method i s needed which can adequately t r e a t both l a y e r e d foundations and complex l o a d i n g . In the f o l l o w i n g c h a p t e r s , such a technique, based on the method of s l i c e s , i s presented. Table VIII - Comparison of Ex is t ing S t a b i l i t y Methods METHOD ADVANTAGES DISADVANTAGES ....AR1NG CAPACITY THEORY (CLASSICAL) -SIMPLE TO USE -SUITABLE FOR HAND CALCULATIONS -EASY TO PERFORM PARAMETER STUDIES -DOES NOT CONSIDER STRESS-STRAIN BEHAVIOUR -BASED ON FIXED GEOMETRY OF RUPTURE SURFACE -CANNOT TREAT COMPLEX LOADING CONDITIONS -LIMITED TO TOTAL STRESS ANALYSES -NOT GOOD FOR LAYERED FOUNDATIONS -SUBJECTIVITY OF BEARING CAPACITY FACTORS NGI SLIP SURFACE METHOD -RELATIVELY EASY TO USE -SUITABLE FOR HAND CALCULATIONS -APPLICABLE TO LAYERED FOUNDATIONS -EASY TO PERFORM PARAMETER STUDIES -DOES NOT CONSIDER STRESS-STRAIN BEHAVIOUR -BASED ON FIXED GEOMETRY OF FAILURE SURFACE -ONLY FOR TOTAL STRESS ANALYSES OF CLAY -DDES NOT CONSIDER DISTRIBUTION OF LOADS -PROBLEMS WITH THIN SEAMS FINITE ELEMENT METHOD (TWO-DIMENSIONAL) -CONSIDERS STRESS-STRAIN BEHAVIOUR -CAN ACCOMODATE IRREGULAR GEOMETRY -APPLICABLE TO LAYERED FOUNDATIONS -CAN STUDY SOIL-STRUCTURE INTERACTION -POSSIBLE TO STUDY PROGRESSIVE FAILURE -PROVIDES INFORMATION ON FAILURE MODES -CANNOT STUDY THREE-DIMENSIONAL EFFECTS -REQUIRES MANY SOIL PARAMETERS AS INPUT -MUCH DATA PREPARATION REQUIRED -EXPENSIVE ANALYSES -REQUIRES THE USE OF A LARGE COMPUTER CENTRIFUGE MODEL TESTING -MODELS STRESS-STRAIN BEHAVIOUR -CAN ACCOMODATE IRREGULAR GEOMETRY -APPLICABLE TO LAYERED FOUNDATIONS -TRUE THREE-DIMENSIONAL ANALYSIS -PROVIDES INFORMATION ON FAILURE MODES -EXTENSIVE PREPARATION REQUIRED -REQUIRES SPECIALLY TRAINED PERSONNEL -REQUIRES SOIL FROM FIELD SITE -EXPENSIVE ANALYSES -LIMITED TO FACILITIES WITH CENTRIFUGES 154 CHAPTER 7 APPLICATION OF THE METHOD OF SLICES TO OFFSHORE GRAVITY STRUCTURE FOUNDATIONS In t h i s chapter the method of s l i c e s equations are modified so that they may be used to analyze the foundation s t a b i l i t y of an o f f s h o r e g r a v i t y s t r u c t u r e s u b j e c t e d to storm wave l o a d i n g . A pseudo-three-dimensional technique not u n l i k e t h a t used i n the NGI s l i p s u r f a c e method i s i n c l u d e d i n the a n a l y s i s . A pore water pr e s s u r e model based on changes i n the p r i n c i p a l s t r e s s e s i s used to account f o r wave induced pore water p r e s s u r e s . Use of t h i s model with the method of s l i c e s i s d e s c r i b e d i n the f o l l o w i n g c h apter. The method developed h e r e i n i s a l s o u s e f u l f o r a n a l y z i n g c l a y foundations f o r a deep s l i d i n g type of f a i l u r e . In these cases b e a r i n g c a p a c i t y theory and the NGI s l i p s u r f a c e method are i n a p p l i c a b l e . The method d e r i v e d from Sarma's (1973) method of s l i c e s i s not d i f f i c u l t to understand or complex to use and i s of s i g n i f i c a n t p r a c t i c a l v a l u e . A t y p i c a l r e p r e s e n t a t i o n of the problem by the method of s l i c e s i s shown in f i g u r e 7.1. The f a i l u r e model used i s s i m i l a r to the one used by NGI, that which was shown in, f i g u r e 6.7. The only d i f f e r e n c e i s that the shear s u r f a c e may take on a d i f f e r e n t shape ( i . e . i t i s not c o n s t r a i n e d to shape shown i n f i g u r e 6.8 - s t r a i g h t l i n e s d e f i n i n g the i n c l i n e d and p a s s i v e s e c t i o n s . ) I t i s convenient to l a b e l the two p a r t s on the s t r u c t u r e base; the f l a t s e c t i o n "ab" w i l l be r e f e r r e d to as the s l i d i n g s e c t i o n , while the p o r t i o n "be" w i l l be termed the 154 CHAPTER 7 APPLICATION OF THE METHOD OF SLICES TO OFFSHORE GRAVITY STRUCTURE FOUNDATIONS In t h i s chapter the method of s l i c e s equations are m o d i f i e d so t h a t they may be used t o analyze the foundation s t a b i l i t y of an o f f s h o r e g r a v i t y s t r u c t u r e s u b j e c t e d to storm wave l o a d i n g . A pseudo-three-dimensional technique not u n l i k e t h a t used i n the NGI s l i p s u r f a c e method i s i n c l u d e d i n the a n a l y s i s . A pore water pressure model based on changes i n the p r i n c i p a l s t r e s s e s i s used to account f o r wave induced pore water p r e s s u r e s . Use of t h i s model with the method of s l i c e s i s d e s c r i b e d i n the f o l l o w i n g chapter. The method developed h e r e i n i s a l s o u s e f u l f o r a n a l y z i n g c l a y foundations f o r a deep s l i d i n g type of f a i l u r e . In these cases b e a ring c a p a c i t y theory and the NGI s l i p s u r f a c e method are i n a p p l i c a b l e . The method d e r i v e d from Sarma's (1973) method of s l i c e s i s not d i f f i c u l t to understand or complex to use and i s of s i g n i f i c a n t p r a c t i c a l v a l u e . A t y p i c a l r e p r e s e n t a t i o n of the problem by the method of s l i c e s i s shown in f i g u r e 7.1. The f a i l u r e model used i s s i m i l a r to the one used by NGI, that which was shown in f i g u r e 6.7. The only d i f f e r e n c e i s that the shear s u r f a c e may take on a d i f f e r e n t shape ( i . e . i t i s not c o n s t r a i n e d to shape shown i n f i g u r e 6.8 - s t r a i g h t l i n e s d e f i n i n g the i n c l i n e d and p a s s i v e s e c t i o n s . ) I t i s convenient to l a b e l the two p a r t s on the s t r u c t u r e base; the f l a t s e c t i o n "ab" w i l l be r e f e r r e d to as the s l i d i n g s e c t i o n , while the p o r t i o n "be" w i l l be termed the Figure7.1 Representation of stability analysis by the method of slices 0 1 0 1 156 e f f e c t i v e a r e a . Two d i f f e r e n t procedures are developed. The f i r s t method i s an a d a p t a t i o n of Janbu's (1973) G e n e r a l i z e d Procedure of S l i c e s . T h i s method was chosen because i t i s a p p l i c a b l e to s l i p s u r f a c e s of a r b i t r a r y shape and because i t i s f a m i l i a r to most foundation engineers. Adaptation of t h i s method to a pseudo- th r e e - d i m e n s i o n a l i s not e a s i l y made due to the way i n which the equations are d e r i v e d . An a l t e r n a t i v e method based on Sarma's (1973) f o r m u l a t i o n i s presented. T h i s method i s e a s i l y adapted to perform a pseudo-three-dimensional a n a l y s i s . Sarma's (1973) method of s l i c e s i s not w e l l known among p r a c t i c i n g engineers. At a f i r s t glance, the method may appear to be an awkward approach to the s t a b i l i t y problem. However, a more thorough study w i l l show that the method i s i n f a c t q u i t e l o g i c a l and extremely v e r s a t i l e . The s l i c e equations are d e r i v e d i n general form, that i s , they are independent of the assumptions r e g a r d i n g e x t e r n a l l o a d i n g . When s p e c i f i c problems are analyzed, f u r t h e r assumptions are made, reg a r d i n g f o r i n s t a n c e : the load d i s t r i b u t i o n on the foundation base, the pore water p r e s s u r e s i n the s o i l , the d i s t r i b u t i o n of s o i l parameters with both depth and h o r i z o n t a l p o s i t i o n , and the shape of a p o t e n t i a l f a i l u r e s u r f a c e . These f a c t o r s w i l l vary with the type of problem to be analyzed, and hence, v e r s a t i l i t y i s maintained. 7.1 The Method of S l i c e s The method of s l i c e s i s a l i m i t e q u i l i b r i u m a n a l y s i s which t r e a t s the s o i l as a r i g i d p l a s t i c m a t e r i a l . The degree of 157 s a f e t y a g a i n s t an u l t i m a t e foundation f a i l u r e i s expressed as F = T|/T (7.1) where F = the f a c t o r of s a f e t y , the shear s t r e n g t h along some shear s u r f a c e , and ^ = the shear s t r e s s along the same shear s u r f a c e . The purpose of a s t a b i l i t y a n a l y s i s i s to f i n d the minimum value of F corresponding to the most c r i t i c a l s t a b i l i t y c o n d i t i o n . The d e t e r m i n a t i o n of the f a c t o r of s a f e t y a g a i n s t an u l t i m a t e foundation f a i l u r e r e q u i r e s estimates of (1) the shear s t r e n g t h of the s o i l along the most c r i t i c a l shear s u r f a c e , (2) the shear s t r e s s along t h i s s u r f a c e , and (3) the l o c a t i o n of t h i s s u r f a c e . The f o l l o w i n g s e c t i o n s w i l l concern themselves with f i n d i n g the shear s t r e s s e s on a shear s u r f a c e and d e r i v i n g e x p r e s s i o n s f o r the f a c t o r of s a f e t y . Since the shear s t r e n g t h and shear s t r e s s w i l l vary along the shear s u r f a c e , the s o i l i s broken up i n t o s l i c e s . The shear s t r e n g t h may vary from s l i c e to s l i c e as w i l l the shear s t r e s s on the base of each s l i c e . If the f a c t o r of s a f e t y i s assumed to be constant along the e n t i r e shear s u r f a c e , then Equation (7.1) w i l l be a weighted average f o r the f a c t o r of s a f e t y , or F = - l ^ ( a ; ) (7.2) n L-i where the a-t's are weighting parameters that depend on s l i c e geometry and l o a d i n g and n i s the number of s l i c e s . The i n d i v i d u a l r a t i o s of shear s t r e n g t h to shear s t r e s s may be examined to see i f the r a t i o anywhere exceeds u n i t y . T h i s i s not v a l i d s i n c e the shear s t r e s s cannot exceed the a v a i l a b l e s t r e n g t h . L o c a l o v e r s t r e s s i n g w i t h i n the p o t e n t i a l f a i l u r e body 158 may be examined by comparing the shear s t r e n g t h s to shear s t r e s s e s along the s l i c e i n t e r f a c e s . Equations w i l l be developed to check i f the f a i l u r e c o n d i t i o n i s v i o l a t e d w i t h i n the p o t e n t i a l f a i l u r e body. The shear s t r e n g t h may be d e f i n e d by the Mohr-Coulomb f a i l u r e c r i t e r i a , which i n terms of e f f e c t i v e s t r e s s i s (Equation 6.2) *tj= c'+ C7'tan0' (7.3) Equation (7.1) e s s e n t i a l l y d e f i n e s a s t a t e of l i m i t e q u i l i b r i u m . T h i s equation may be rearranged to d e f i n e the average shear s t r e s s i n terms of the shear s t r e n g t h . T h i s i s simply *t = ^ ( 1 / F ) • (7.4) where 1/F i s the degree of s t r e n g t h m o b i l i z e d i n the s o i l . T h i s i s constant f o r any shear s u r f a c e . I n t r o d u c i n g Equation (7.3) i n t o (7.4) y i e l d s the m o b i l i z e d or e q u i l i b r i u m shear s t r e s s on the shear s u r f a c e f o r each s l i c e . T h i s i s ~ C L = C'+ 6Jtan0; (7.5) where c^= c'/F, and (7.6a) tan0i= tan0'-/F (7.6b) These are the m o b i l i z e d s t r e n g t h parameters. 7.2 Loading A p p l i e d to the Foundation The v e r t i c a l load at the s e a f l o o r i s i n c r e a s e d by the e f f e c t i v e weight of s o i l w i t h i n the s k i r t compartments when a p p l i e d at the foundation base. T h i s may be w r i t t e n as • Vtvr= P v + A P v + (BoDoLo)*' (7.7) The v e r t i c a l l o a d a p p l i e d to the foundation base per u n i t width 159 as used i n the method of s l i c e s i s simply v * = V ^ / L o (7.8) The h o r i z o n t a l l o a d a c t i n g on the foundation base i s the r e s u l t a n t of the a p p l i e d environmental load P H and a l l the s o i l f o r c e s a c t i n g on the p l a t f o r m between the s e a f l o o r and s k i r t - t i p l e v e l . T h i s may be expressed as (Equation 6.12) H M = P H + (P A or P w) - P f - P s (7.9) where P A , P w, P f , and P t are d e f i n e d by equations (6.9), (6.10), (6.11) and (6.13), r e s p e c t i v e l y . These equations are summarized here f o r r e f e r e n c e purposes. P A= [ (O.5^'Do 2+Ap 1D o)tan 2(45'-0/2)-2cD otan(45 ,-0/2) ] L 0 (7.10) P w= Ap^oLo (7.11) P P= [(0.5*'D o 2+Ap 2D o)tan 2(45°+0/2)+2cD otan(45'+0/2)]L 0 (7.12) P s= 2 D 0 B 0 ( c + O.5-i-'Dotan0) (7.13) The h o r i z o n t a l f o r c e per u n i t width a p p l i e d to the foundation base i s H f t = H a T / L 0 (7.14) The moment a p p l i e d at the foundation base i s the r e s u l t a n t of the moment at the s e a f l o o r and the moments due to a l l the f o r c e s a c t i n g between the s e a f l o o r and the foundation base. T h i s may be expressed as (Equation 6.14) M a T= M + P HD 0 + (P A or P w ) h , - P p h 2 - P s h 3 (7.15) I t i s u s e f u l to use the concept of e f f e c t i v e area when t r e a t i n g the d i s t r i b u t i o n of the h o r i z o n t a l f o r c e on the foundation base. Since there i s only s i n g l e e c c e n t r i c i t y on the e q u i v a l e n t foundation base, the e f f e c t i v e width i s a l l that i s r e q u i r e d . T h i s i s d e f i n e d as (Equation 6.15) B = B 0(1 - 2e) (7.16) 160 with the e c c e n t r i c i t y being given by (Equation 6.16) e = (7.17) Bo 7.3 Treatment of the A p p l i e d H o r i z o n t a l Force The h o r i z o n t a l f o r c e a p p l i e d at the foundation base may be separated i n t o two p a r t s : that which a c t s on the s l i d i n g s u r f a c e "ab" and that which a c t s over the e f f e c t i v e area "be". T h i s may be w r i t t e n simply as H B T= H S T+ H E T (7.18) where H S 1 i s the f o r c e taken by the s l i d i n g s u r f a c e "ab", and H n i s the f o r c e taken by the e f f e c t i v e area "be". Equation (7 . 18 ) may be w r i t t e n as H B = H s + H E (7.19) per u n i t width. The h o r i z o n t a l f o r c e taken by the s l i d i n g s u r f a c e per u n i t width i s given by H s = \(c + o"tan0)dx (7.20) The h o r i z o n t a l f o r c e taken by the e f f e c t i v e area per u n i t width may be found by i n s e r t i n g Equation (7.20) i n t o (7.19) and r e a r r a n g i n g . T h i s y i e l d s f h H E = Hft - \(c + O"tan0)dx (7.21) The h o r i z o n t a l f o r c e taken by any s l i c e may be found from FH L= H e(b t/B) (7.22) where b t i s the width of a s l i c e . Combining equations (7.21) and (7.22) y i e l d s FH-t = [ H B - \ ( c + o"'tan0)dx] (b :/B) (7.23) 161 7.4 M o d i f i e d Janbu Method The a p p l i c a t i o n of Janbu's (1973) G e n e r a l i z e d Procedure of S l i c e s (GPS) method to the a n a l y s i s of o f f s h o r e g r a v i t y s t r u c t u r e foundations r e q u i r e s some m o d i f i c a t i o n s . B a s i c a l l y , what i s r e q u i r e d i s the i n c l u s i o n of h o r i z o n t a l f o r c e s a c t i n g on the tops of the s l i c e s (everywhere in the equations) and the d e t e r m i n a t i o n of the magnitudes of these f o r c e s . They are i n i t i a l l y unknown s i n c e the f o r c e taken o u t s i d e the e f f e c t i v e area on the s l i d i n g s u r f a c e "ab" i s expressed i n terms of the degree of s t r e n g t h m o b i l i z e d i n the s o i l . An i t e r a t i o n procedure must be used to e s t a b l i s h the h o r i z o n t a l f o r c e a p p l i e d to the e f f e c t i v e area, and hence to the s l i c e s . The d e r i v a t i o n presented below f o l l o w s that given by Janbu (1973) as c l o s e l y as i s p o s s i b l e so that a comparison between the two s e t s of equations may be made and so that e x i s t i n g slope s t a b i l i t y programs can be e a s i l y m o d i f i e d . 7.4.1 Assumptions Janbu's (1973) G e n e r a l i z e d Procedure of S l i c e s i s founded on the f o l l o w i n g assumptions: A - Plane s t r a i n c o n d i t i o n s apply. B - The p o s i t i o n of the l i n e of t h r u s t f o r the normal i n t e r s l i c e f o r c e s i s assumed to be known. C - The normal f o r c e on the base i s assumed to act where the the t o t a l r e s u l t a n t v e r t i c a l f o r c e i n t e r s e c t s the base. 7.4.2 D e r i v a t i o n of E q u i l i b r i u m Equations The f o l l o w i n g equations i n c l u d e a l l the f o r c e s a c t i n g on the s l i c e shown in f i g u r e 7.2. The g e o m e t r i c a l v a r i a b l e s and FV, * S.W.L. FH, F i g u r e 7.2 - Geometry and f o r c e s on a (Janbu) s l i c e 163 f o r c e s f o r any s l i c e are d e f i n e d i n the f i g u r e . These equations were developed f o r the l o a d i n g d e f i n e d i n s e c t i o n s 7.2 and 7.3 and f o r the model shown i n f i g u r e 7.1. The equations f o r the v e r t i c a l and h o r i z o n t a l e q u i l i b r i u m of a s l i c e are FT-fc + AT- = N-cosoi + S Lsinc,; (7.24) AEi - FHi = N^sinc; - S-cosc;, (7.25) where FT L = FV t + W, (7.26) AT; = T ( t + 1 ) - T ( i ) (7.27) AE-, = E(L + 1 )-E(L)„ (7.28) Moment e q u i l i b r i u m about the assumed p o i n t of a p p l i c a t i o n of N- (mid-base) y i e l d s E-Ay; " AE-Ah ; + T ; b; + FH-.h; = 6 (7.29) Note that T-'bi-and E^-Ay,; are couples and t h a t terms of second order have been n e g l e c t e d . T h i s equation may be rearranged to f i n d the i n t e r s l i c e shear f o r c e T-, namely, T- = -E'tan6 c + Ah i (AE - /b ̂  ) - h-^FH^b - J (7.30) where tan6; = A y c / b t (7.31) For o v e r a l l v e r t i c a l e q u i l i b r i u m , the t o t a l v e r t i c a l r e s u l t a n t on the shear s u r f a c e must be equal to the weight of the body plus the boundary loads a p p l i e d to the s o i l mass. If • v-t i s the t o t a l v e r t i c a l r e s u l t a n t on the base of a s l i c e , then E [ V t ] = Z [ F T ; ] (7.32) From equation (7.24) note that V-L = NjCOSo-t + S j s i n a ; = FTZ + AT; (7.33) I n t r o d u c i n g t h i s equation i n t o (7.32) y i e l d s l [ A T r ] = 0 (7.34) O v e r a l l h o r i z o n t a l e q u i l i b r i u m r e q u i r e s that the t o t a l 164 h o r i z o n t a l r e s u l t a n t on the shear s u r f a c e be i n e q u i l i b r i u m with the h o r i z o n t a l boundary f o r c e s . I f i s the t o t a l h o r i z o n t a l r e s u l t a n t on the base of a s l i c e , then E[H-j = H e (7.35) From equation (7.25) i t may be w r i t t e n that H; = N - s i n c ; - S^OSc^ = AE z - FH-t (7.36) I n t r o d u c i n g t h i s equation i n t o (7.35) y i e l d s I[AE - J = 0 (7.37) n o t i n g from Equation (7.22) that E[FH r] = H e 7.4.3 Working Formulas The complete set of b a s i c equations which must be s a t i s f i e d f o r each s l i c e i s T i = c; + (cr L-u- t )tan0,; (7.38) o-t = PP C + TT i - " C j t a n o i (7.39) AE = FH ; + (PP ; +TT- Jb-^tano; - T ; b : ( 1 +tan 2 at ) (7.40) T ; = -E- ttan6! + Ah c (dE c/db c ) - h ; ( d F H £ / d b j ) (7.41) where i s the shear s t r e s s , c ; the cohesion, 6"; the normal s t r e s s , Ui the pore water p r e s s u r e , and tan0j the f r i c t i o n a l r e s i s t a n c e on the base of a s l i c e . A d d i t i o n a l l y , PP-,, = FT-t /b-t , and (7.42) TT t = AT ; /b ; (7.43) Note that Equation (7.38) d e f i n e s the s t a t e of l i m i t e q u i l i b r i u m , that (7.39) i s the equation f o r v e r t i c a l e q u i l i b r i u m of a s l i c e , and t h a t (7.40) i s one equation f o r both v e r t i c a l and h o r i z o n t a l s l i c e e q u i l i b r i u m . Moment e q u i l i b r i u m f o r a s l i c e of i n f i n i t e s i m a l width i s d e f i n e d by Equation (7.41 ). 165 The requirement f o r o v e r a l l h o r i z o n t a l e q u i l i b r i u m , from Equations (7.19) and (7.37) may be w r i t t e n as I[AE;;] = H 6 - H s - H t (7.44) T h i s may a l s o be w r i t t e n as E[AE r] = H s + E[FHj] - H e (7.45) I n s e r t i n g Equation (7.40) i n t o (7.45) and r e a r r a n g i n g , y i e l d s l [ F H l + (PP i +TTL ) b ; t a n c x ] - E[*t ;b f ( 1+tan 2a r) ] = H B- H s- E[FH- ] (7.46) The maximum h o r i z o n t a l r e s i s t a n c e a v a i l a b l e from the s l i d i n g s u r f a c e per u n i t width may be expressed as F s = \ ( c ' + cr'tan0')dx = ( H S ) F (7.47) I n t r o d u c i n g = ~C$:/F and (7.47) i n t o (7.46) and s o l v i n g f o r F y i e l d s E[ t r . b ; ( 1+tan 2a ;) ] + F. F = - (7.48) E[ (PP- t+TT-)b rtano- t ] + H B I n t r o d u c i n g Equation (7.39) i n t o (7.38) g i v e s a general e x p r e s s i o n f o r the shear s t r e n g t h , which i s T 4 . = c'- + (PP r+TT c - u £ - v X - t a n o r ) t a n 0 V (7.49) I n t r o d u c i n g = ^ ; / F i n t o the above e x p r e s s i o n and s o l v i n g f o r T^; y i e l d s c ',- + (PP- +TT- -u-L) tan0 '- T 4 . = - ^ i ' ' (7.50) 1 + (1/F)tan0'; tano c The average f a c t o r of s a f e t y f o r the general case i s found by using Equation (7.48) with T 4 ;. d e f i n e d by Equation (7.50). For s i m p l i c i t y , s e v e r a l a b b r e v i a t e d terms, are used to d e f i n e ' the f a c t o r of s a f e t y . For each s l i c e the f o l l o w i n g a b b r e v i a t i o n s w i l l be used: 166 BZ = ( P P j + T T C ) b i t a n a - (7.51) AX = T$ :b.( 1+tan 2 o- t ) (7.52) By i n s e r t i n g Equations (7.51) and (7.52) i n t o (7.48), the formula f o r the average f a c t o r of. s a f e t y i s reduced to E [ A X ] + F. F = (7.53) E [ B r ] + H s By i n t r o d u c i n g Equation (7.50) i n t o (7.52) the A z term f o r each s l i c e can be c a l c u l a t e d i n three steps as f o l l o w s : A ;' = [cL + ( P P J + T T J - u r ) t a n 0 i ]b- (7.54) 1 + (1/F)tan0' t- tano^ NA = (7.55) 1 + t a n 2 a t A = A '/NA (7.56) The A and B values depend on the i n t e r s l i c e shear f o r c e which i n t urn depends on the f a c t o r of s a f e t y . Hence, the need f o r an i t e r a t i o n technique a r i s e s . The s t r e s s e s on the shear s u r f a c e may be c a l c u l a t e d as f o l l o w s : T; = — = (7.57) F F - { ( 1 + t a n 2 o : ) b c ] and V; = PP : + TT t - T t t a n a c . (7.58) i n accordance with Equation (7.39). The i n t e r s l i c e f o r c e s may be found as f o l l o w s : Introduce Equations (7.51) and (7.52) i n t o (7.40) to f i n d AE i = FHj.+ B : - A r/F (7.59) Summing the AE values f o r each s l i c e g i v e s r i s e t o E C = E[AE :] (7.60) The v e r t i c a l shear f o r c e T-t, i s given by (Equation 7.41) 167 T t = -E-ttan6-t + Ah-t (dE^/dbj) - h- (dFH[/db\) (7.61) A l l of the preceding equations must be s a t i s f i e d simultaneously by an i t e r a t i o n procedure. The average f a c t o r of s a f e t y on a s l i c e i n t e r f a c e i s found from c ' j h ; + (E;-UH c)tan0' c = (7.62) T t where UH-t i s the water p r e s s u r e f o r c e on the s l i c e i n t e r f a c e i n q u e s t i o n . For a t h e o r e t i c a l l y c o r r e c t s o l u t i o n , F'~ must be g r e a t e r than F. Note that average s o i l p r o p e r t i e s are used here. 7.5 M o d i f i e d Sarma Method Sarma's (1973) approach to d e r i v i n g a s l i c e method d i f f e r s s u b s t a n t i a l l y from the other s l i c e methods a p p l i c a b l e to s l i p s u r f a c e s of a r b i t r a r y shape: those of Janbu (1973), and Morgenstern and P r i c e (1965). These methods s o l v e the s l i c e e q u i l i b r i u m equations and f i n d the f a c t o r of s a f e t y by changing the value of the f o r c e s on the shear s u r f a c e u n t i l s l i c e e q u i l i b r i u m i s s a t i s f i e d . Since these f o r c e s are expressed i n terms of the f a c t o r of s a f e t y , which i s i n i t i a l l y unknown, an i t e r a t i o n procedure i s r e q u i r e d . Sarma (1973) a l s o s o l v e s the s l i c e e q u i l i b r i u m equations, but i n a d i f f e r e n t way. A d e s t a b i l i z i n g f o r c e i s introduced i n t o the e q u i l i b r i u m equations f o r each s l i c e . T h i s f o r c e i s equal to the product of the a c c e l e r a t i o n c o e f f i c i e n t K and the s l i c e weight - a pseudo-earthquake f o r c e . A f a c t o r of s a f e t y i s assumed and the f o r c e s which depend on the degree of s t r e n g t h 168 m o b i l i z a t i o n i n the s o i l are expressed i n terms of the l i m i t e q u i l i b r i u m parameters. The a n a l y s i s i s performed for s e v e r a l v a l u e s of the f a c t o r of s a f e t y . Since the s o l u t i o n r e q u i r e s no numerical i t e r a t i o n s f o r the f a c t o r of s a f e t y , only d i s t i n c t c a l c u l a t i o n s , there i s no p o s s i b i l i t y of numerical i n s t a b i l i t y . T h i s f a c t o r can be i n v a l u a b l e at times when the other s l i c e methods p r o v i d e no reasonable answer. The s o l u t i o n f o r any p a r t i c u l a r shear s u r f a c e i s found when the a c c e l e r a t i o n c o e f f i c i e n t i s equal to zero f o r some value of the f a c t o r of s a f e t y . A curve of F vs. K may be drawn as shown i n f i g u r e 7.3. The " s t a t i c " f a c t o r of s a f e t y may then be p i c k e d o f f the curve. In the case of an earthquake s t a b i l i t y a n a l y s i s , the s o l u t i o n i s found when the a c c e l e r a t i o n c o e f f i c i e n t i s equal to some s p e c i f i e d v a l u e . A d i s t r i b u t i o n of the d e s t a b i l i z i n g f o r c e w i t h i n the s o i l mass may be assumed f o r t h i s type of work. Sarma's (1973) approach has been adopted f o r o f f s h o r e s t a b i l i t y a n a l y s e s at the U n i v e r s i t y of B r i t i s h Columbia. Finn and Lee (1978) m o d i f i e d t h i s method to analyze the s t a b i l i t y ^ of underwater s l o p e s s u b j e c t e d to s e i s m i c l o a d i n g . A pore water pressure gener a t i o n model was i n c l u d e d i n the a n a l y s i s and the number of c y c l e s to f a i l u r e was found f o r undrained l o a d i n g . F u r t h e r work i n t h i s area i s p r e s e n t l y (1982) being done. Sarma's (1973) method i s d e r i v e d i n such a way that many m o d i f i c a t i o n s may e a s i l y be made. A pseudo-three-dimensional a n a l y s i s may be made by i n c l u d i n g the f o r c e s a c t i n g on the s i d e areas (see f i g u r e 6.2(b)) i n the s l i c e e q u i l i b r i u m equations. 169 * 0-7 8 •12 to * 0 Si*of/c factor of safety 2 Factor of safety , F F i g u r e 7.3 - Curve used f o r e v a l u a t i n g the s a f e t y f a c t o r ( A f t e r F i nn and Lee, 1978) 170 7.5.1 Assumptions The fundamental assumptions on which t h i s s l i c e method i s based a r e : A - Plane s t r a i n c o n d i t i o n s a p p l y . B - The p o i n t of a p p l i c a t i o n of the normal f o r c e a c t i n g on the base of each s l i c e i s assumed to be known. C - The r e l a t i v e magnitudes of the i n t e r s l i c e shear f o r c e s are assumed to be known. A d d i t i o n a l l y , f o r a pseudo-three-dimensional a n a l y s i s D - The magnitudes and p o s i t i o n s of the s i d e f o r c e s on each s l i c e are assumed to be known. 7.5.2 D e r i v a t i o n of E q u i l i b r i u m Equations The f o l l o w i n g equations i n c l u d e a l l the f o r c e s a c t i n g on the s l i c e shown i n f i g u r e s 7.4 and 7.5. The geo m e t r i c a l v a r i a b l e s and f o r c e s f o r any s l i c e are d e f i n e d i n f i g u r e 7.4. The f o r c e s a c t i n g on the s i d e areas are i n c l u d e d i n the s l i c e e q u i l i b r i u m equations as m o b i l i z e d f o r c e s a c t i n g p a r a l l e l to the base. For any s l i c e t h i s f o r c e may be d e f i n e d as SS-L = [ 2 ( b E ) ( y t l - y b : ) ( c + cr'tan0)]/L o (7.63) Note that t h i s f o r c e i s expressed i n terms of i t s e q u i v a l e n t magnitude per u n i t l e n g t h . The e f f e c t i v e normal s t r e s s may be computed from e a r t h pressure theory. For v e r t i c a l and h o r i z o n t a l e q u i l i b r i u m of a s l i c e NjCOSG;: + StSinc- t = W; - AT; + F N - C O S 0 ; + F S j s i n p ; - SScsino; S ; ; C O S c c - Njisino; = KWC + AE X - F N ; s i n 0 r + FS ; C O S P j - S S c C O S O ; The l i m i t i n g e q u i l i b r i u m c o n d i t i o n may be d e f i n e d by (7.64) (7.65) 171 F i g u r e 7 .5 - T y p i c a l (Sarma) s l i c e showing s i d e f o r c e s 172 Sz = (N'c tan0'- + c'-t b- tsecc; )/F (7.66) T h i s equation may be w r i t t e n as Sc = N'£ tan0-t + Cibisecai (7.67) by u s i n g the m o b i l i z e d s t r e n g t h parameters. The e f f e c t i v e normal f o r c e can be c a l c u l a t e d as N'-t = N- - US : (7.68) where US-L i s the f o r c e due to pore water p r e s s u r e on the base of any s l i c e due to pore water p r e s s u r e . T h i s i s simply USt = U x b c s e c c j (7.69) Equations (7.64) and (7.65) can be used to s o l v e f o r N-t and T j , namely, N; = (W t-AT : )coscc " (KW;+AE C)sinoj + FN fcos(«i-p t) - FS;sin(o ;-» K ) (7.70) S-t = (W;-AT;;) s i n a ; + (KW t + AE r ) c OS a : + FN- tsin(o- t-pj ) + FS rcos(o£-0 r ) - S S : (7.71) These equations together with (7.68) can be s u b s t i t u t e d i n t o (7.67) t o o b t a i n AT-tan(0- t-oj ) + AE- = BB C - KW- (7.72) where BB;; = (W£-USj )tan(0--a j) + [ c r b £ seca t-cos0 i+FN csin(0--a.+p I ) -FS;COs(0j-o;+*j ) + S S j C O S 0 £ ] s e c ( 0 £ - a - ) (7.73) Equation (7.72) i s s i m p l i f i e d by summing both s i d e s of the e q u a t i o n . Note that E [ A E t ] = E(n+1) - E(1) = 0 (7.74) s i n c e both E(n+1) and E(1) equal ze r o . Hence, [ (AT t)tan(0;-o- t) ] = E[BB-J - E[KW C] (7.75) Equation (7.75) i s t h e r e f o r e one equation which s a t i s f i e s both v e r t i c a l and h o r i z o n t a l e q u i l i b r i u m f o r a l l s l i c e s . A second 173 equation i s obtained i f moment e q u i l i b r i u m of the whole s l i d i n g body about the o r i g i n i s c o n s i d e r e d . [ (Nj ; C o s o;+Sjsinc c)xbc ] - E[ (-N£ sinctj+S tcoso- )ybt- ] - E [ ( W : ) x g : ] + E[(KW t-)yg-J - E[FN E ( x t c c o s * c +ytt- s i n * . ) ] - E[FS ; ( x t : s i n p £ - y t - c o s $ r ) ] + E[SSj ( x s t s i n c c -ys- tcosa £) ] = 0 (7.76) T h i s equation may be combined with Equations (7.64), (7.65), and (7.72) to e l i m i n a t e N-t, Sj , and AEj, r e s u l t i n g i n I [ W f t x b j - x g j ) ] + E[KW ryg T] - E[BB ;yb t-] + E [ FNj s i n * - (yb c - y t £ ) ] + EtSSiCOSo^yb.-ys^) ] - E[FSt-cos<»t (yb £-yt- ) ] = [ (ATj; { x b i - y b c t a n ( 0 i - o i ; ) } ] (7.77) 7.5.3 Working Formulas The d i s t r i b u t i o n of the i n t e r s l i c e shear f o r c e s i s assumed so that T c = X-Qj or AT; = X.-DQj; (7.78) The Q-t v a l u e s may be found as f o l l o w s : Q. = [(E t-UH t;)tan0 , £ + c ' c h ^ ] f ( x ) (7.79) where f ( x ) i s a d i s t r i b u t i o n parameter. T h i s may be taken as u n i t y s i n c e i t g i v e s a c c e p t a b l e r e s u l t s (Sarma, 1973). E^ may be expressed as E t = K;(0.5 h t 2 + QSjh-) (7.80) where QS; i s the average surcharge above any s l i c e i n t e r f a c e , i s given by Sarma (1973) as 1 - s i n ( 2 o l - 0 ' f )[ ( 1 - 2 R t t ) s i n 0 , ' u / h-)cos0V ] K-t = (7.81) 1 + sin(2o;-0'^ ) s i n 0 ' ; R* i s the r a t i o of excess pore water pressure to v e r t i c a l s t r e s s and i s taken as an average v a l u e . The s t r e n g t h parameters may 174 a l s o be taken as average v a l u e s . Sarma (1973) d i s c u s s e s i n d e t a i l how to o b t a i n the Q- v a l u e s . Upon s u b s t i t u t i n g Equation (7.78) i n t o (7.75) and (7.77) the f o l l o w i n g equations are obtained- S1 • X + S2-K = S3 (7 .82) S4- X - S5-K = S6 (7 .83) jre S1 t h r u S6 are d e f i n e d as f o l l o w s : SI = E[DQ ttan(0 i-o' l)] (7 .84) S2 = E[W-J (7 .85) S3 = I[BB t ] (7 .86) S4 = E[DQ t{xbi;-yb :tan(0 t-c {)} ] (7 .87) S5 = l [ W i y b f ] (7 .88) S6 = E [ F N ; ( y b £ - y t c ) s i n * ,] - E[FSt- ( y b - - y t c Jcos*;; ] + E[SS;(yb t-ys- t)cosac] - EtBB-.yg;;] (7 .89) The i n t e r s l i c e f o r c e s and the f o r c e s a c t i n g on the base can be found using the e q u i l i b r i u m equations d e r i v e d i n the preceding s e c t i o n once K and > are known. The average f a c t o r of s a f e t y on a s l i c e i n t e r f a c e i s found from c' c hj + (Ei-UHc )tan0V F\ = (7.90) CHAPTER 8 EXAMPLES AND APPPLICATION OF ANALYSES 175 8.1 D e s c r i p t i o n of Computer Procedure A computer program GRAVSTAB was developed to perform the analyses d e s c r i b e d i n the preceding chapter. A thorough d e s c r i p t i o n of the program may be found i n the program documentation which i s a v a i l a b l e through the S o i l Dynamics Group at the U n i v e r s i t y of B r i t i s h Columbia. A b r i e f d e s c r i p t i o n of the program w i l l be given here. The r o u t i n e f o r the mo d i f i e d Sarma a n a l y s i s was taken from the program STESL (Lee and F i n n , 1978) and m o d i f i e d f o r a g r a v i t y s t r u c t u r e s t a b i l i t y a n a l y s i s . The r o u t i n e used to perform a m o d i f i e d Janbu a n a l y s i s was w r i t t e n by the author; the equations d e r i v e d i n the preceding chapter were used. T h i s r o u t i n e (and the Sarma r o u t i n e as wel l ) was t e s t e d with numerous example problems, i n c l u d i n g those given i n the papers by Janbu (1973) and Finn and Lee (1978) to e l i m i n a t e any programming e r r o r s . The two s l i c e methods agree very c l o s e l y f o r slope analyses and f o r foundation analyses of cohesive d e p o s i t s . T h i s i s not the case f o r foundation a n a l y s e s of c o h e s i o n l e s s d e p o s i t s . I t was found t h a t the s t r e s s e s computed at the base of each s l i c e from Janbu's (1973) method d i d not form a smooth curve over the s l i p s u r f a c e . There i s some i n s t a b i l i t y a s s o c i a t e d with t h i s . In f a c t , Janbu's (1973) method o f t e n d i d not p r o v i d e an answer f o r these problems. The s o l u t i o n was very unstable and d i v e r g e n t . 176 The loads used i n an a n a l y s i s are found from the equations i n s e c t i o n s 7.2 and 7.3. These loads, which are expressed i n terms of the m o b i l i z e d s t r e n g t h , are found i t e r a t i v e l y . As a f i r s t approximation the e f f e c t i v e foundation width i s assumed to be constant i n any a n a l y s i s . Although the e f f e c t i v e width i s i n i t i a l l y unknown, i t may be estimated by assuming a reasonable f a c t o r of s a f e t y which when used i n the a p p r o p r i a t e equations y i e l d s a numerical value f o r the e f f e c t i v e width. The v a r i a t i o n of the e f f e c t i v e foundation width with the s a f e t y f a c t o r i s minimal and i n most cases may be ignored. The s o i l data may be input i n one of two ways: l a y e r by l a y e r , or s l i c e by s l i c e . The former method r e q u i r e s l e s s data input and lends i t s e l f w e l l to i n v e s t i g a t i n g d i f f e r e n t p o t e n t i a l s l i p s u r f a c e s i n m u l t i - l a y e r e d d e p o s i t s s i n c e the s t r e n g t h parameters w i l l be a u t o m a t i c a l l y c a l c u l a t e d f o r each s l i c e every time a new s l i p s u r f a c e i s chosen. To a i d i n f i n d i n g the c r i t i c a l shear s u r f a c e , a simple rerun c o n t r o l o p t i o n may be used (as many times as d e s i r e d ) . The s l i c e c o o r d i n a t e s on the shear s u r f a c e (between the two end c o o r d i n a t e s "b" and "d" shown in f i g u r e 7.1) may be incremented by a given percentage of t h e i r c u r r e n t v a l u e s to vary the p o s i t i o n of the s l i p s u r f a c e . Hence, the depth c o o r d i n a t e s f o r any shape of shear s u r f a c e need to be input only once s i n c e they may be moved up and down between the two end v a l u e s to l o c a t e the c r i t i c a l p o s i t i o n of the shear s u r f a c e f o r that p a r t i c u l a r shape. The c r i t i c a l shear s u r f a c e may thus be found approximately with a minimum amount of e f f o r t s i n c e only a few shapes (that i s , shear s u r f a c e c o o r d i n a t e s e t s ) 177 need to be s p e c i f i e d . Pore water p r e s s u r e s may be taken as being h y d r o s t a t i c or they may be input i n d i v i d u a l l y f o r each s l i c e . The l a t t e r method i s used f o r an e f f e c t i v e s t r e s s a n a l y s i s ; only the excess pore water p r e s s u r e s need to be i n p u t . For a three-dimensional a n a l y s i s , the pore water p r e s s u r e s on the s i d e s of the s l i c e s are a l s o r e q u i r e d . I t i s o f t e n adequate to use the h y d r o s t a t i c pore water p r e s s u r e s here s i n c e t h i s type of a n a l y s i s i s q u i t e approximate. The s t r e s s e s computed on the base of each s l i c e are standard output f o r GRAVSTAB. They may be examined to see i f o v e r s t r e s s i n g occurs anywhere. These s t r e s s e s may a l s o be used i n an e f f e c t i v e s t r e s s a n a l y s i s t o estimate the instantaneous pore water p r e s s u r e s assuming that the pore water pressure d i s t r i b u t i o n due to the short-term ( i . e . undrained) wave l o a d i n g may be found based on Equation (6.6). T h i s i s demonstrated f o r Example 2. 8.2 Example 1 - A M u l t i - l a y e r e d Cohesive Deposit The f i r s t example problem to be analyzed i s a CONDEEP type s t r u c t u r e founded on a nonhomogeneous cohesiv e d e p o s i t . T h i s problem was taken from L a u r i t z s e n and Schjetne (1976) and represents, an • a c t u a l o f f s h o r e p l a t f o r m i n the North Sea. The r e q u i r e d geometry and l o a d i n g data i s given i n Table IX. The a c t u a l p l a t f o r m base i s n e a r l y c i r c u l a r with a diameter of approximately 100 meters. The shear s t r e n g t h p r o f i l e i s shown in f i g u r e 8.1. One p r o f i l e i s that given by L a u r i t z s e n and Schjetne (1976). The other i s an approximation of t h i s p r o f i l e Table IX Geometry and Loading Data f o r Example 4 Equivalent P l a t f o r m Length, L 0 68.3 m Equivalent P l a t f o r m Width, B 0 68.3 m E f f e c t i v e Foundation Depth, D 0 3.5 m T o t a l V e r t i c a l Load, Pv + APW 187,000 t H o r i z o n t a l Wave Load, PH 49,100 t Moment at S e a f l o o r , M 2,240,000 t-m Dynamic Wave Pressure, Ap, 3.5 t/mJ Dynamic Wave Pressure, Ap 2 -3.5 t/m* Unit Weight of S o i l , V 2.0 t / m 3 Figure 8.1 - Shear s t r e n g t h p r o f i l e f o r Example 1 179 u s i n g l a y e r s with d i f f e r e n t undrained s t r e n g t h s . The l a t t e r p r o f i l e was used f o r the s l i c e a n a l y s e s d i s c u s s e d below. The procedure used to search f o r the most c r i t i c a l shear s u r f a c e i s as f o l l o w s : A f i r s t estimate of the c r i t i c a l shear s u r f a c e i s made using the NGI s l i p s u r f a c e method. A computer program SLIPSURF was w r i t t e n f o r t h i s purpose. The c r i t i c a l s l i p s u r f a c e found i n t h i s way i s then rounded o f f at the sharp corner and the shape i s a l t e r e d s e v e r a l times. As d e s c r i b e d b e f o r e , each shear s u r f a c e shape which i s input i s moved up and down to f i n d the minimum value of the f a c t o r of s a f e t y . By using j u s t a few d i f f e r e n t geometries f o r the shear s u r f a c e , the g e n e r a l shape of the c r i t i c a l shear s u r f a c e may be estimated. More i t e r a t i o n s based on i n f o r m a t i o n provided by the e a r l y runs may be done i f g r e a t e r accuracy i s d e s i r e d . The c r i t i c a l shear s u r f a c e s e v a l u a t e d by a number of methods are shown in f i g u r e 8.2. The corresponding s a f e t y f a c t o r s are given i n Table X. The angle which the b e a r i n g c a p a c i t y rupture s u r f a c e makes with the h o r i z o n t a l may be determined approximately ( L a u r i t z s e n and Schjetne, 1976). For t h i s example problem the s a f e t y f a c t o r s determined by the NGI s l i p s u r f a c e method and the procedures developed i n t h i s t h e s i s agree q u i t e w e l l . The s l i c e methods p r e d i c t a s l i g h t l y lower f a c t o r of s a f e t y . T h i s i s i n p a r t due to the p o s i t i o n of the c r i t i c a l s l i p s u r f a c e determined by the two methods; the c r i t i c a l s l i p s u r f a c e determined by the method of s l i c e s passes through more of the weak zone. For most t o t a l s t r e s s analyses of c o h e s i v e foundations, the NGI s l i p method i s adequate. However, i f a t h i n l a y e r of very weak m a t e r i a l e x i s t s w i t h i n the s t r a t a , then the NGI method i s of 180 Table X Comparison of Computed Safety F a c t o r s f o r Example 1 CALCULATED SAFETY FACTOR METHOD OF ANALYSIS Plane S t r a i n B/L = 0 A c t u a l Case B/L = 1 Hansen's (1970) Formula, m o d i f i e d 2 . 1 5 1 2.35 1 Meyerhof's (1963) Formula, m o d i f i e d 2. 17 1 2.49 1 NGI S l i p Surface Method 2.00 1 2 . 1 5 1 M o d i f i e d Janbu Method of S l i c e s 1 .92 - M o d i f i e d Sarma Method of S l i c e s 1 .93 2.06 'From L a u r i t z s e n and Schjetne (1976) Method of SI Ices NGI S l i p Surface Method Hansen Bearing Capacity Theory F i g u r e 8.2 - C r i t i c a l shear s u r f a c e s f o r Example 1 as e v a l u a t e d by d i f f e r e n t s t a b i l i t y methods 181 l i t t l e use i n a s s e s s i n g the p l a t f o r m s t a b i l i t y . I t i s a l s o important t o note that the i n c r e a s e i n the s a f e t y f a c t o r f o r the pseudo-three-dimensional analyses i s n e a r l y i d e n t i c a l f o r both the NGI method and the procedure developed i n t h i s t h e s i s based on Sarma's method. In the f o r e g o i n g a n a l y s e s , the undrained s t r e n g t h was assumed to be constant with h o r i z o n t a l p o s i t i o n . Since the s t r e s s c o n d i t i o n s w i l l vary c o n s i d e r a b l y along a p o t e n t i a l f a i l u r e s u r f a c e , the use of l a b o r a t o r y shear t e s t r e s u l t s which r e f l e c t the d i f f e r e n t s t a t e s of s t r e s s may be a p p r o p r i a t e . There are four d i s t i n c t s t a t e s of s t r e s s e x i s t i n g w i t h i n the s o i l mass. These are shown i n f i g u r e 8.3. The undrained shear s t r e n g t h may be found by using the s t r e s s path method (Lambe, 1967). Laboratory samples are s u b j e c t e d t o the estimated i n - s i t u and t o t a l s t r e s s e s that they w i l l be s u b j e c t e d to i n the f i e l d . The r e s u l t i n g undrained shear s t r e n g t h s determined i n t h i s way may then be used d i r e c t l y i n a s t a b i l i t y a n a l y s i s . Since there i s o f t e n a l a c k or absence of good q u a l i t y samples, a l l the t e s t s shown i n f i g u r e 8.3 may not always be performed. In these cases, the undrained s t r e n g t h estimated from i n - s i t u t e s t s may be r e l a t e d to the standard or t r i a x i a l compression v a l u e . The other shear s t r e n g t h s may be taken as v a r i o u s percentages of t h i s v a l u e . Some p o s s i b l e v a l u e s f o r these c o e f f i c i e n t s are given i n Table XI. The shear s t r e n g t h p r o f i l e must then be represented by both depth and h o r i z o n t a l v a r i a t i o n s . Assuming t h a t a l a y e r e d p r o f i l e may be used, the s t r e n g t h v a r i a t i o n with h o r i z o n t a l p o s i t i o n may e a s i l y be i n c o r p o r a t e d i n t o the numerical technique 182 Table XI C o e f f i c i e n t s f o r E s t i m a t i n g Undrained Strength from T r i a x i a l Compression Data SHEAR TEST x C,, D i r e c t Shear T r i a x i a l E xtension T r i a x i a l Compression 0.75 0.50 1 .00 1 \ 11 ACTIVE - ZONE - T PASSIVE | TRIAXIAL f - F i g u r e 8.3 - Zones of shear on the p o t e n t i a l f a i l u r e s u r f a c e and r e l e v a n t l a b o r a t o r y t e s t s (Adapted from K j e k s t a d and Lunne, 1979) 183 by u s i n g the t r i a x i a l compression val u e s m u l t i p l i e d by the a p p r o p r i a t e c o e f f i c i e n t s i n the v a r i o u s shear zones. Another s t a b i l i t y a n a l y s i s was performed using these new values f o r the undrained s t r e n g t h . The c r i t i c a l shear s u r f a c e found using t h i s new p r o f i l e was almost i d e n t i c a l to the one found f o r the o r i g i n a l p r o f i l e . R e s u l t s of t h i s study are r e p o r t e d i n Table X I I . The use of the shear zone concept f o r s p e c i f y i n g the s t r e n g t h along the f a i l u r e s u r f a c e i s a matter which has not yet been r e s o l v e d . I t i s important to note that reducing the s a f e t y f a c t o r by such a s u b s t a n t i a l amount has a tremendous e f f e c t on the c o s t of the p l a t f o r m s i n c e the base s i z e must be i n c r e a s e d to reduce the average b e a r i n g p r e s s u r e . T h i s c o s t i n c r e a s e may be on the order of many m i l l i o n s of d o l l a r s . The c r i t i c a l shear s u r f a c e found f o r the aforementioned an a l y s e s i s shown i n f i g u r e 8.4. T h i s type of p l o t i s standard output of GRAVSTAB and i s u s e f u l f o r examining the l o c a t i o n of t h i s s u r f a c e with r e s p e c t to d i f f e r e n t s t r a t a . ( I t i s a l s o u s e f u l f o r l o c a t i n g t h i s s u r f a c e . ) Note the l e n g t h of that part of the s u r f a c e which runs through the weaker l a y e r s . 8.3 Example 2 - A C o h e s i o n l e s s D e p o s i t ; E k o f i s k Tank The second example problem to be analyzed i s the E k o f i s k tank. The r e q u i r e d geometry and l o a d i n g data i s given i n Table X I I I . The d i s t r i b u t i o n of r e s i d u a l pore water pressures due to c y c l i c l o a d i n g i s given i n f i g u r e 8.5. T h i s d i s t r i b u t i o n was developed based on o b s e r v a t i o n s r e p o r t e d by Clausen et a l (1975); these pore water p r e s s u r e s were shown i n f i g u r e 4.11. The contours drawn on the f i g u r e are based on Rahman et a l ' s Table XII E f f e c t of Shear Zone Repres e n t a t i o n on the S a f e t y F a c t o r STRENGTH PROFILE USED COMPUTED SAFETY FACTOR Regular Strengths Shear Zone Strengths 1 .93 1 .62 WflHPLf 1 - COUDfFP STRUCTURE 03.30 Q N. FEB. 02. 1062 2-0 ANALYSIS »PLANE STRAIN) PLATFORN BRSE I 0 F i g u r e 8.4 - C r i t i c a l shear s u r f a c e f o r Example 1 found from computer program GRAVSTAB Table XIII Geometry and Loading Data f o r Example 2 E q u i v a l e n t P l a t f o r m Length, L 0 85.8 m E q u i v a l e n t P l a t f o r m Width, B 0 85.8 m E f f e c t i v e Foundation Depth, D 0 0.4 m Bouyant P l a t f o r m Weight, Pv 190,000 t V e r t i c a l Wave Load, APW 10,000 t H o r i z o n t a l Wave Load, P H 78,600 t Moment at S e a f l o o r , M 2,800,000 t-m Dynamic Wave Pressure, Ap,« 3.0 t/m 2 Dynamic Wave Pressure, Ap 2 -3.0 t/m2 U n i t Weight of S o i l , K 2.0 t/m» F i g u r e 8.5 - D i s t r i b u t i o n of pore water p r e s s u r e s i n foundation s o i l used i n Example 2 186 (1977) work. The most d i f f i c u l t p a r t of t h i s a n a l y s i s i s e s t i m a t i n g the instantaneous pore water pre s s u r e s due to the c y c l i n g l o a d s . These were found based on Equation (6.6), which i s AU = A0"3 + A (ACT, - ACT3) (9.1) The method of s l i c e s may be used to f i n d the changes i n the p r i n c i p a l s t r e s s e s . The procedure used to determine the p r i n c i p a l s t r e s s e s i s as f o l l o w s : A s l i p s u r f a c e i s analyzed and the f a c t o r of s a f e t y corresponding to Au=0 i s found. The same s l i p s u r f a c e i s then analyzed without the wave loads, i . e . the v e r t i c a l p l a t f o r m load o n l y . T h i s l o a d i s now assumed to act over the t o t a l foundation a r e a . The "no l o a d " f a c t o r of s a f e t y i s then e s t a b l i s h e d . The s t r e s s e s at the base of each s l i c e are then determined from the e q u i l i b r i u m equations d e r i v e d i n the p r e v i o u s chapter. T h i s procedure has been set up i n GRAVSTAB. Only the A-parameter i s r e q u i r e d as input f o r any s l i p s u r f a c e . The p r i n c i p a l s t r e s s e s and pore water pressure changes for the instantaneous wave loads are then computed and the new s a f e t y f a c t o r i s determined. The p r i n c i p a l s t r e s s e s may be evaluated from cr, = cr+ [(1 - cos2*)/sin<*] (9.2) o 3 = 6- [(1 + c o s 2 * ) / s i n * ] (9.3) where * i s d e f i n e d by ot = 4 5 ° + 0 / 2 (9 . 4 ) Here 0 i s the m o b i l i z e d f r i c t i o n angle. T h i s w i l l be d i f f e r e n t f o r each case. For the no-load a n a l y s i s t h i s value w i l l be very low. The c r i t i c a l s l i p s u r f a c e found f o r the tank i s shown i n 187 f i g u r e 8.6. Only the r e s i d u a l pore water p r e s s u r e s due to c y c l i c l o a d i n g were used and pore water p r e s s u r e s a s s o c i a t e d with t o t a l s t r e s s increments were n e g l e c t e d ( i . e . Au=0). T h i s i s f e l t t o be c o n s e r v a t i v e s i n c e the dense E k o f i s k sand would probably d i l a t e and c r e a t e negative pore water p r e s s u r e s i n much of the s o i l mass duri n g l o a d i n g . The value of the A-parameter has a marked e f f e c t on the computed f a c t o r of s a f e t y . For the s l i p s u r f a c e shown in the f i g u r e , four v a l u e s of the A-parameter were chosen between 0.0 and -0.33. The l a t t e r value corresponds to a dense sand at f a i l u r e . The s a f e t y f a c t o r s computed with these d i f f e r e n t values are shown i n Table IX. For t h i s problem, the i n c r e a s e i n the s a f e t y f a c t o r due to added r e s i s t a n c e from the s i d e areas was minimal. For sand foundations with shallow f a i l u r e mechanisms t h i s w i l l g e n e r a l l y be the case. For deeper f a i l u r e mechanisms which occur i n c o h e s i v e foundations, the added r e s i s t a n c e can i n c r e a s e the s a f e t y f a c t o r s u b s t a n t i a l l y . T h i s was shown i n the t o t a l s t r e s s a n a l y s i s i n Example 1 and would a l s o show up i n an e f f e c t i v e s t r e s s a n a l y s i s of the same foun d a t i o n . 188 Table XIV E f f e c t of A-parameter on the Safety Factor VALUE OF A-PARAMETER COMPUTED SAFETY FACTOR -0.33 1.77 -0.20 1.61 Au-0 1.51 -0.10 1 .49 0.00 1.37 i D M U 1 - « C •na PA. m m « urn nr.. ' a u J J J J J J J l l V '1* i. i. A h . k . ^ H c j M . ^ i u JM i u Figure 8.6 - C r i t i c a l shear surface f o r Example 2 found from computer program GRAVSTAB 189 CHAPTER 9 SUMMARY AND CONCLUSIONS Of f s h o r e g r a v i t y s t r u c t u r e s have a b r i g h t f u t u r e i n o f f s h o r e development schemes. They o f f e r the advantage of being n e a r l y complete at tow-out, thereby minimizing i n s t a l l a t i o n time. T h i s i s p a r t i c u l a r l y important i n h o s t i l e environments such as the northern North Sea where c o n v e n t i o n a l s t e e l j a c k e t e d s t r u c t u r e s present a s u b s t a n t i a l r i s k i n terms of short-term s a f e t y . I t a l s o allows f o r an e a r l i e r p r o d u c t i o n s t a r t . By nature of t h e i r d e sign, these s t r u c t u r e s i n c o r p o r a t e storage and prov i d e a l a r g e deck area which i s necessary f o r pro d u c t i o n equipment. T h i s i s a s i g n i f i c a n t advantage f o r marginal f i e l d r ecovery or f o r l o c a t i o n s o f f s h o r e where p i p e l i n e s are not eco n o m i c a l l y j u s t i f i e d . O f f s h o r e e n g i n e e r i n g p r e s e n t s many c h a l l e n g e s f o r the g e o t e c h n i c a l s p e c i a l i s t . Although o f f s h o r e e n g i n e e r i n g has e x i s t e d f o r many years, only r e c e n t l y has hydrocarbon e x p l o r a t i o n moved i n t o deeper waters where the design of major s t r u c t u r e s has c o n s i s t e n t l y r e q u i r e d an advancement of the s t a t e of the a r t i n not only g e o t e c h n i c a l e n g i n e e r i n g but a l s o i n s t r u c t u r a l , hydrodynamic, and oceanographical e n g i n e e r i n g . The development of new techniques and design p h i l o s o p h i e s i n a l l of these f i e l d s r e q u i r e s that the g e o t e c h n i c a l engineer be f a m i l i a r with them s i n c e he must p l a y a key r o l e i n g r a v i t y s t r u c t u r e d e s i g n . Instrumentation has :' p r o v i d e d some u s e f u l data f o r 190 p r e d i c t i n g the magnitudes of s e t t l e m e n t s expected f o r a l a r g e g r a v i t y s t r u c t u r e . However, the a v a i l a b i l i t y of t h i s data i s l i m i t e d and most engineers w i l l have to design f u t u r e s t r u c t u r e s based on what i s " p u b l i c a l l y known". P u b l i s h e d data f o r the E k o f i s k tank demonstrates that p l a t f o r m settlement i s d i f f i c u l t to a s s e s s . More recent data i s a v a i l a b l e f o r other p l a t f o r m s which con f i r m s t h i s r e s u l t . S ince settlement due to c y c l i c e f f e c t s i s an important c o n s i d e r a t i o n , some assessment must be made. P r e s e n t l y , the e v a l u a t i o n of c y c l i c s e t t l e m e n t s f o r o f f s h o r e g r a v i t y type s t r u c t u r e s i s made using very s i m p l i s t i c models. C y c l i c settlement a n a l y s i s f o r o f f s h o r e g r a v i t y type s t r u c t u r e s i s an area which r e q u i r e s a c o n s i d e r a b l e amount of r e s e a r c h . Cooperation among those i n d i v i d u a l s and c o r p o r a t i o n s i n v o l v e d i n t h i s r e s e a r c h would g r e a t l y a c c e l e r a t e progress i n t h i s a r e a . S t a b i l i t y i s the other p r i n c i p a l problem that g e o t e c h n i c a l engineers must d e a l with. T h i s i s a complex problem which must be viewed i n p e r s p e c t i v e . The procedures d i s c u s s e d and developed w i t h i n t h i s t h e s i s may only be used i f c e r t a i n c r i t e r i a are met. For example, f u l l c o n t a c t i s u s u a l l y assumed; t h i s c r i t i c a l assumption must be v e r i f i e d by instrument data. Instrumentation i s used to p r o v i d e i n f o r m a t i o n on the s t r e s s d i s t r i b u t i o n over the s l a b and a l s o the d i s t r i b u t i o n of pore water p r e s s u r e s w i t h i n the s o i l mass. The e v a l u a t i o n of r e s i d u a l pore water p r e s s u r e s due to c y c l i c l o a d i n g by t h e o r e t i c a l methods i s by no means r e l i a b l e . In f a c t , s u b s t a n t i a l d i s c r e p a n c i e s e x i s t between t h e o r e t i c a l estimates and o n - s i t e o b s e r v a t i o n s . 191 E s t i m a t i o n of the s t a b i l i t y of a g r a v i t y type s t r u c t u r e i s p r e s e n t l y assessed by u s i n g bearing c a p a c i t y theory, the f i n i t e element method, or the NGI s l i p s u r f a c e method f o r c l a y f o u n d a t i o n s . Bearing c a p a c i t y theory i s of l i m i t e d value f o r use i n o f f s h o r e analyses p r i m a r i l y because of the i n a b i l i t y to (1) t r e a t adequately complex l o a d i n g , (2) analyze l a y e r e d foundations, and (3) perform e f f e c t i v e s t r e s s a n a l y s e s . Extensions of c l a s s i c a l theory have been proposed to d e a l with the l a t t e r problem, however, these t h e o r i e s are of l i m i t e d v a l u e . The NGI s l i p s u r f a c e method i s an improvement over bearing c a p a c i t y theory, however, t h i s method i s only a p p l i c a b l e to t o t a l s t r e s s a n a l y ses of cohesiv e d e p o s i t s . The f i n i t e element method may a l s o be used t o assess p l a t f o r m s t a b i l i t y . The most s e r i o u s problems a s s o c i a t e d with t h i s method are that the s o i l s t i f f n e s s parameters need to be known a c c u r a t e l y and the assumed c o n s t i t u t i v e r e l a t i o n s be reasonable f o r the s o i l a n alyzed. Both of these f a c t o r s must be c o n s i d e r e d i n the l i g h t of the r e l i a b i l i t y of o f f s h o r e s o i l i n v e s t i g a t i o n s . An a l t e r n a t i v e approach to the bearing c a p a c i t y and f i n i t e element methods was presented. T h i s procedure i s based on the method of s l i c e s . Two methods were d e r i v e d . Janbu's (1973) method, which i s w e l l known to most foundation engineers, was extended to t r e a t g r a v i t y s t r u c t u r e problems i n two dimensions. A pseudo-three-dimensional a n a l y s i s procedure was not developed w i t h i n t h i s framework. An a l t e r n a t i v e technique, based on Sarma's (1973) method of s l i c e s was developed. Three- dimensional e f f e c t s were e a s i l y i n c o r p o r a t e d i n t o Sarma's (1973) 192 method. T h i s method i s a l s o n u m e r i c a l l y s t a b l e which makes a s o l u t i o n p o s s i b l e f o r any problem by using the method of s l i c e s . The a n a l y s i s procedures developed in t h i s t h e s i s were a p p l i e d to two example problems - one on a l a y e r e d cohesive d e p o s i t and one on c o h e s i o n l e s s s o i l . The f i r s t example i l l u s t r a t e d how a t o t a l s t r e s s a n a l y s i s c o u l d be performed. R e s u l t s were compared with e x i s t i n g methods and shown to be good. The pseudo-three-dimensional a n a l y s i s suggests that the s a f e t y f a c t o r can be i n c r e a s e d by about s i x percent due to the added r e s i s t a n c e from the s i d e a r e a s . T h i s r e s u l t agrees w e l l with the NGI s l i p s u r f a c e method. The NGI method prov i d e s reasonable r e s u l t s f o r cohesive foundations without t h i n weak seams. For the problem analyzed, the method of s l i c e s i s shown to g i v e a lower f a c t o r of s a f e t y , although not s u b s t a n t i a l l y lower f o r t h i s p r o f i l e . For other p r o f i l e s the d i f f e r e n c e may be g r e a t e r . The values of the undrained s t r e n g t h chosen along the s l i p s u r f a c e have a pronounced e f f e c t on the computed s a f e t y f a c t o r . The use of the shear zone concept reduces the s a f e t y f a c t o r c o n s i d e r a b l y . An e f f e c t i v e s t r e s s a n a l y s i s was a l s o performed. The c r i t i c a l p a r t of t h i s a n a l y s i s was the d e t e r m i n a t i o n of the instantaneous pore water p r e s s u r e s due to the wave lo a d s . The method of s l i c e s was used to p r e d i c t these pore water pre s s u r e s based on changes in the p r i n c i p a l s t r e s s e s . T h i s procedure was incorporated' i n t o the computer program GRAVSTAB. The value of the A-parameter has a s i g n i f i c a n t e f f e c t on the pore water p r e s s u r e s developed and hence the f a c t o r of s a f e t y computed. For a dense sand, such as E k o f i s k sand, where d i l a t i o n w i l l 193 occur, the s t a b i l i t y w i l l i n c r e a s e s i n c e the pore water pr e s s u r e s on the s l i p s u r f a c e w i l l be l e s s . The procedures developed i n t h i s t h e s i s were shown to p r o v i d e reasonable answers to o f f s h o r e g r a v i t y s t r u c t u r e s t a b i l i t y problems. The procedure based on Sarma's (1973) method of s l i c e s i s p r e f e r r e d s i n c e i t can provide i n f o r m a t i o n on t h r e e - d i m e n s i o n a l e f f e c t s and does not s u f f e r from numerical i n s t a b i l i t y . T h i s method, which i s easy to use and a p p l i c a b l e to a wide range of problems, i s suggested as a means of e s t i m a t i n g o f f s h o r e g r a v i t y s t r u c t u r e s t a b i l i t y under storm wave l o a d i n g . $SIGNOFF 194 REFERENCES 0 1. Agostoni, A l b e r t o ; Di T e l i a , Vincenzo; Guone, Enzo; and S e b a s t i a n i , Gaetano. (1980): "TSG - I n t e g r a t e d Storage P l a t f o r m f o r E a r l y P r o d u c t i o n i n the North Sea." T w e l f t h Annual O f f s h o r e Technology Conference, Houston, Proceedings, Vol.4, pp.245-260. 2. A i r y , G. B. (1845): "On T i d e s and Waves." Encyclopedia M e t r o p o l i t a n a , London, pp.241-396. 3. American Petroleum I n s t i t u t e . (1978): API Recommended. P r a c t i c e f o r Planning, Designing and C o n s t r u c t i n g F i x e d O f f s h o r e S t r u c t u r e s , API/RP2A; 9th Ed., D a l l a s . 4. Andersen, K. H. (1972): "Bearing C a p a c i t y of Shallow Foundations on C o h e s i o n l e s s S o i l s . " Norwegian G e o t e c h n i c a l I n s t i t u t e , I n t e r n a l Report 51404-1. 5. Anderson, Knut H. (1976): "Behavior of Clay Subjected to Undrained C y c l i c Loading." I n t e r n a t i o n a l Conference on the Behavior of O f f s h o r e S t r u c t u r e s , Oslo, Proceedings, Vol.1, pp.392-403. 6. Andersen, K. H.; Brown, S. F.; Foss, I.; P o o l , J . H.; and Rosenbrand, W. F. (1976): " E f f e c t of C y c l i c Loading On Clay Behavior." Norwegian G e o t e c h n i c a l I n s t i t u t e , No.113, pp.1- 6. 7. Andersen, K. H.; Seines, P. B.; Rowe, P. W.; and C r a i g , W. H. (1979): " P r e d i c t i o n and Observation of a Model G r a v i t y P l a t f o r m on Drammen C l a y . " Second I n t e r n a t i o n a l Conference on the Behavior of O f f s h o r e S t r u c t u r e s , London, Proceedings, Vol.1, pp.427-446. 8. Augustine, F. E., Maxwell, F. D., and Lazanoff, S. M. (1978): "Extreme Wave Heights i n the Gulf of A l a s k a . " Tenth Annual O f f s h o r e Technology Conference, Houston, Proceedings, Vol.3, pp.1551 -1562. 9. Bea, R. G., and Akky, M. R. (1979): "Seismic, Oceanogra- p h i c , and R e l i a b i l i t y C o n s i d e r a t i o n s i n O f f s h o r e P l a t f o r m Design." E l e v e n t h Annual O f f s h o r e Technology Conference, Houston, Proceedings, Vol.4, pp.2251-2262. 10. Bea, R. G., and L a i , N. W. (1978): "Hydrodynamic Loading on O f f s h o r e P l a t f o r m s . " Tenth Annual O f f s h o r e Technology Conference, Houston, Proceedings, V o l . 1 , pp.155-168. 11. B e l l , W. E. (1974): "The Equipment Requirements for O i l and Gas i n the North Sea." O f f s h o r e Europe, 2nd Ed., Bucks, England: S c i e n t i f i c Surveys (Offshore) L t d . , pp.27-36. 195 12. Bercha, F. G., and Stenning, D. G. (1979): " A r c t i c O f f shore Deepwater I c e - S t r u c t u r e I n t e r a c t i o n . " E l e v e n t h Annual O f f s h o r e Technology Conference, Houston, Proceedings, Vol.4, pp.2377-2386. 13. Berman, M. Y., Blenkarn, K. A., and Dixon, D. A. (1978): "The V e r t i c a l l y Moored P l a t f o r m , f o r Deepwater D r i l l i n g and P r o d u c t i o n . " Tenth Annual O f f s h o r e Technology Conference, Houston, Proceedings, V o l . 1 , pp.55-64. 14. B i l l i n g t o n , C. J . (1979): "The Underwater Repair of Concrete O f f s h o r e S t r u c t u r e s . " E l e v e n t h Annual Offshore Technology Conference, Houston, Proceedings, Vol.2, pp.927- 938. 15. Bjerrum, L. (1973): " G e o t e c h n i c a l Problems Involved i n Foundations of S t r u c t u r e s i n the North Sea." Geotechnique, Vol.23, No.3, pp.319-358. 16. Braun, W i l l i M. (1974): " E k o f i s k Settlements and the Steady Sealab." Ground E n g i n e e r i n g , V o l . 7 , No.4, pp.47-49. 17. Broughton, P e t e r . (1975): "Offshore G r a v i t y Based O i l P r o d u c t i o n P l a t f o r m I n t e r a c t i o n with the Sea Bed." Seventh Annual O f f s h o r e Technology Conference, Houston, Proceedings, Vol.3, pp.387-398. 18. Brown, J . D., and Meyerhof, G. G. (1969): "Experimental Study of Bearing C a p a c i t y i n Layered C l a y s . " Seventh I n t e r n a t i o n a l Conference on S o i l Mechanics and Foundation E n g i n e e r i n g , Mexico C i t y , Proceedings, Vol.2, pp.45-51. 19. Burkhardt, J . A., and M i c h i e , T. W. (1979): "Submerged Pro d u c t i o n System--A F i n a l Report." E l e v e n t h Annual O f f s h o r e Technology Conference, Houston, Proceedings, Vol.2, pp.801-806. 20. Burns, G. E., and D'Amorim, G. D. (1977): "Bouyant Towers f o r Phase I Development of Garoupa F i e l d . " N i n t h Annual O f f s h o r e Technology Conference, Houston, Proceedings, Vol.2, pp.177-184. 21. Button, S. J . (1953): "The Bearing C a p a c i t y of Footings on a Two-layer Cohesive S u b s o i l . " T h i r d I n t e r n a t i o n a l Conference on S o i l Mechanics and Foundation E n g i n e e r i n g , Z u r i c h , Proceedings, Vol.1, pp.332-335. 22. C a l l i s , C ; Knox, C ; Sutton, D.; and Wiley, S. ( 1979): "An Assessment of G r o u t i n g M a t e r i a l s , Placement Methods, and M o n i t o r i n g Equipment f o r O f f s h o r e S t r u c t u r e s . " Eleventh Annual O f f s h o r e Technology Conference, Houston, Proceedings, Vol.4, pp.2755-2764. 196 23. Clausen, C a r l J . Frimann. (1976): "The CONDEEP S t o r y . " O f f s h o r e S o i l Mechanics, Eds. P h i l l i p George and David Wood, Cambridge: Cambridge U n i v e r s i t y E n g i n e e r i n g Department, pp.256-270. 24. Clausen, C. J . F.; DiBagio, E.; Duncan, J . M.; and Andersen, K. H. (1975): "Observed Behavior of the E k o f i s k O i l Storage Tank Foundation." Seventh Annual O f f s h o r e Technology Conference, Houston, Proceedings, V o l . 3 , pp.399- 413. 25. Davis, E. H., and Booker, J . R. (1973): "The E f f e c t of I n c r e a s i n g Strength with Depth on the Bearing C a p a c i t y of C l a y s . " Geotechnique, Vol.23, No.4, pp.551-563. 26. Dean, R. G. (1965): "Stream F u n c t i o n R e p r e s e n t a t i o n of N o n l i n e a r Ocean Waves." J o u r n a l of the Geophysical Research, Vol.70, No.18. 27. Department of Energy. (1974): Guidance on the Design and C o n s t r u c t i o n of O f f - s h o r e I n s t a l l a t i o n s , London. 28. Department of the I n t e r i o r , U.S.G.S. (1979): Approval Procedure f o r I n s t a l l a t i o n and Operation of P l a t f o r m s , F i x e d and Mobile S t r u c t u r e s , and A r t i f i c i a l I s l a n d s , esp. PCS, Order 8, Washington. :29. D e r r i n g t o n , J . A. (1977): " C o n s t r u c t i o n of the McAlpine/Sea Tank G r a v i t y Platforms at Ardyne P o i n t , A r g y l l . " Design and C o n s t r u c t i o n of O f f s h o r e S t r u c t u r e s , London: I n s t i t u t e of C i v i l E ngineers, Proceedings, pp.121-130. 30. Det Norske V e r i t a s . (1977): Rules f o r the Design Construc- t i o n and I n s p e c t i o n of F i x e d O f f s h o r e S t r u c t u r e s , Oslo. 31. DiBagio, Elmo, M y r v o l l , Frank, and Hansen, Svein Borg. (1976): "Instrumentation of G r a v i t y Platforms f o r Performance Obse r v a t i o n s . " I n t e r n a t i o n a l Conference on the Behavior of O f f s h o r e S t r u c t u r e s , Oslo, Proceedings, V o l . 1 , pp.516-527. 32. Duncan, J . M. (1972): "Foundation Study f o r North Sea O i l Tank." Norwegian G e o t e c h n i c a l I n s t i t u t e , No.92, pp.13-18. 33. E i d e , Ove T. (1974): "Marine S o i l Mechanics." Norwegian G e o t e c h n i c a l I n s t i t u t e , No.103, pp.1-20. 34. F a l k n e r , C. B., and Franks, N. S. (1978): "Production Techniques from Tension Legged P l a t f o r m s . " Tenth Annual O f f s h o r e Technology Conference, Houston, Proceedings, Vol.4, pp.2079-2086. 197 35. F e d e r a t i o n I n t e r n a t i o n a l e de l a P r e c o n t r a i n t e . (1977): Recommendations f o r the Design of Concrete Sea S t r u c t u r e s , 3rd Ed., Slough. 36. F i n n , L. D., W a r d e l l , J . B., and L o f t i n , T. D. (1979): "The Guyed Tower as a P l a t f o r m f o r In t e g r a t e d D r i l l i n g and Produ c t i o n O p e r a t i o n s . " J o u r n a l of Petroleum Technology, Vol.31, No.12, pp.1531-1537. 37. F i n n , W. D. Liam and Lee, Michael K. W. (1978): " S e a f l o o r S t a b i l i t y Under Seismic and Wave Loading." ASCE Sp r i n g Conference, Boston, S p e c i a l t y Session on S o i l Mechanics i n the Marine Environment. 38. F i n n , W. D. Liam, Lee, Kwok W., and M a r t i n , Geoffrey R. (1977): "An E f f e c t i v e S t r e s s Model f o r L i q u e f a c t i o n . " J o u r n a l of the G e o t e c h n i c a l E n g i n e e r i n g D i v i s i o n , ASCE, Proceedings, Vol.103, N 0 . G T 6 , pp.517-533. 39. Foss, I v a r . (1974): " D i s c u s s i o n — S e t t l e m e n t Observations of the E k o f i s k O i l Storage Tank i n the North Sea." B r i t i s h G e o t e c h n i c a l S o c i e t y Settlement Conference, Cambridge U n i v e r s i t y , U n i t e d Kingdom, Proceedings, pp.674-676. 40. Franco, A l v a r o . (1976): "Offshore B r a z i l due Concrete P l a t f o r m s . " O i l and Gas J o u r n a l , Vol.74, No.18, pp.153-159. 41. Furnes, 0. (1978): "Overview of Of f s h o r e O i l Industry with Emphasis on the North Sea." Le c t u r e s on Of f s h o r e E n g i n e e r i n g , Combined Proceedings of a One-Day Conference Plus E i g h t Weekly Seminars, Aalborg U n i v e r s i t y Center, Aalborg, Denmark. 42. G a r r i s o n , C. J . (1977): "Wave Loads on North Sea G r a v i t y P l a t f o r m s : A Comparison of Theory and Experiment." N i n t h Annual O f f s h o r e Technology Conference, Houston, Proceedings, V o l . 1 , pp.513-524. 43. G a r r i s o n , C. J . (1979): "Hydrodynamic Loading of Of f s h o r e S t r u c t u r e s . Three Dimensional Source D i s t r i b u t i o n Methods." Numerical Methods i n Of f s h o r e E n g i n e e r i n g , Ed. 0. C. Zien - k i e w i c z , New York: John Wiley and Sons, Inc., pp.87-140. 44. G a r r i s o n , L. E., and Bea, R. G. (1977): "Bottom S t a b i l i t y as a F a c t o r i n P l a t f o r m S i t i n g and Design." Ninth Annual O f f s h o r e Technology Conference, Houston, Proceedings, V o l . 3 , pp.127-134. 45. George, P. J . (1976): "Notes on S i t e I n v e s t i g a t i o n with Respect to the Design of O f f s h o r e S t r u c t u r e s . " O f f shore S o i l Mechanics, Eds. P h i l l i p George and David Wood, Cambridge: Cambridge U n i v e r s i t y E n g i n e e r i n g Department, pp.101-116. 198 46. Gerwick, Ben C , J r . (1974): " P r e p a r a t i o n s of Foundations f o r Concrete Caisson Sea S t r u c t u r e s . " S i x t h Annual O f f s h o r e Technology Conference, Houston, Proceedings, V o l . 1 , pp.119- 130. 47. Gerwick, B. C , and Hognstad, E. (1973): "Concrete O i l Storage Tank Placed on North Sea F l o o r . " C i v i l E n g i n e e r i n g , ASCE, Vol.43, No.8, pp.81-85. 48. Gumbel, Emil J u l i u s . (1958): S t a t i s t i c s of Extremes, New York: Columbia U n i v e r s i t y P r e s s , 375 p. 49. Hansen, Bent. (1976): "Modes of F a i l u r e Under I n c l i n e d E c c e n t r i c Loads." I n t e r n a t i o n a l Conference on the Behavior of O f f s h o r e S t r u c t u r e s , Oslo, Proceedings, V o l . 1 , pp.488- 500. 50. Hansen, F. J . , and I n g e r s l e v , L. C. F. (1977): "The Case f o r a H y b r i d . " Design and C o n s t r u c t i o n of Offshore S t r u c t u r e s , London: I n s t i t u t e of C i v i l Engineers, Proceedings, pp.135-141. 51. Hansen, J . B. (1961): "A General Theory f o r Bearing C a p a c i t y . " The Danish G e o t e c h n i c a l I n s t i t u t e , Copenhagen, B u l l e t i n No.11, pp.38-46. 52. Hansen, J . B. (1970): "A Revised and Extended Formula f o r Bearing C a p a c i t y . " The Danish G e o t e c h n i c a l I n s t i t u t e , Copenhagen, B u l l e t i n No.28, pp.5-11. 53. Haring, R. E., and Heideman, J.C. (1978): "Gulf of Mexico Rare Wave Return P e r i o d s . " Tenth Annual O f f s h o r e Technology Conference, Houston, Proceedings, Vol.3, pp.1537-1550. 54. Heijnen, W. J . (1981): "The Use of P h y s i c a l Models i n Solv- ing O f f s h o r e G e o t e c h n i c a l Problems." O f f s h o r e S t r u c t u r e s : The Use of P h y s i c a l Models i n T h e i r Design, Eds. G. S. T. Armer and F. K. Garas, L a n c a s t e r : The C o n s t r u c t i o n Press, pp.263-272. 55. Henkel, D. J . (1970): "The Role of Waves i n Causing Sub- marine L a n d s l i d e s . " Geotechnique, Vol.20, No.1, pp.75-80. 56. H i t c h i n g s , Gordon A., Bradshaw, Heath, and L a b i o s a , Thomas D. (1976): "The P l a n n i n g and E x e c u t i o n of O f f s h o r e S i t e I n v e s t i g a t i o n s f o r a North Sea G r a v i t y P l a t f o r m . " E i g h t h Annual O f f s h o r e Technology Conference, Houston, Proceedings, V o l . 1 , pp.61-74. 57. H0eg, Kaare. (1976): "Foundation E n g i n e e r i n g f o r Fixed O f f s h o r e S t r u c t u r e s . " I n t e r n a t i o n a l Conference on the Behavior of O f f s h o r e S t r u c t u r e s , Oslo, Proceedings, Vol.1, pp.39-69. 199 58. Hogben, N.; M i l l e r , B. L.; S e a r l e , J . W.; and Ward, G. (1977): " E s t i m a t i o n of F l u i d Loading on Offshore S t r u c t u r e s . " I n s t i t u t e of C i v i l Engineers, London, Proceedings, Vol.63, Part 2, pp.515-562. 59. Hove, Knut and Foss, I v a r . (1974): " Q u a l i t y Assurance f o r O f f s h o r e Concrete G r a v i t y S t r u c t u r e s . " S i x t h Annual O f f s h o r e Technology Conference, Houston, Proceedings, Vol.2, pp.829-842. 60. Huntemann, J . E., A n a s t a s i o , F. L., J r . , and Deshazar, W. A. (1979): "Concrete G r a v i t y P l a t f o r m i n Shallow O f f s h o r e L o u i s i a n a Water." E l e v e n t h Annual Offshore Technology Conference, Houston, Proceedings, Vol.2, pp.1003-1008. 61. Isaacson, M. de S t . Q. (1980): "Wave Forces i n the D i f f r a c t i o n Regime--A Review." Coastal/Ocean E n g i n e e r i n g Report, Department of C i v i l E n g i n e e r i n g , U n i v e r s i t y of B r i t i s h Columbia. 62. Isaacson, M. de S t . Q. (1981): P r i v a t e Communication. 6 3 . Janbu, Nilmar. (1973): "Slope S t a b i l i t y Computations." Embankment-Dam E n g i n e e r i n g , Casagrande Volume, Eds. R. C. H i r s c h f i e l d and S. J . Poulos. New York: John Wiley and Sons, Inc., pp.45-86. 64. Janbu, Nilmar, Grande, L a r s , and Eggareide, Rare. (1976): " E f f e c t i v e S t r e s s S t a b i l i t y A n a l y s i s f o r G r a v i t y S t r u c t u r e s . " I n t e r n a t i o n a l Conference on the Behavior of O f f s h o r e S t r u c t u r e s , Oslo, Proceedings, V o l . 1 , pp.449-466. 65. de Jong, J . J . A., and Bruce, J . C. (1978): "Design and C o n s t r u c t i o n of a Caisson Retained I s l a n d D r i l l i n g P l a t f o r m f o r the Beaufort Sea." Tenth Annual O f f s h o r e Technology Conference, Houston, Proceedings, Vol.4, pp.2111-2120. 66. Kinsman, B. (1965): Wind Waves, t h e i r Generation and Propa- g a t i o n on the Ocean Surface, Englewood C l i f f s , N. J . : P r e n t i c e - H a l l , 676 p. 6 7 . K j e k s t a d , O., and Lunne, T. (1979): " S o i l Parameters Used fo r Design of G r a v i t y P l a t f o r m s i n the North Sea." Second I n t e r n a t i o n a l Conference on the Behavior of Offshore S t r u c t u r e s , London, Proceedings, Vol.1, pp.175-192. 68. K l i e w e r , Raymond M., and Forbes, Graeme S. (1980): "A F i x e d P l a t f o r m P r o v i d i n g an I n t e g r a t e d Deck on a M u l t i p l e Leg Ice R e s i s t a n t S u b s t r u c t u r e . " T w e l f t h Annual O f f s h o r e Technology Conference, Houston, Proceedings, Vol.4, pp.315-324. 200 69. K l i t z , J . Kenneth. (1980): North Sea O i l : Resource Require- ments f o r Development of the U.K. S e c t o r , Oxford: Pergammon Press, 260 p. 70. Korteweg, D. J . , and De V r i e s , G. (1895): "On the Change of Form of Long Waves Advancing i n a Rectangular Channel, and on a New Type of Long S t a t i o n a r y Wave." P h i l o s o p h i c a l Magazine, 5th S e r i e s , pp.422-443. 71. L a l l i , D. (1975): " D i s c u s s i o n . " O f f - s h o r e S t r u c t u r e s , London: I n s t i t u t e of C i v i l Engineers, Proceedings, pp.92- 93. 72. L a l l i , D. (1977): "Design, C o n s t r u c t i o n and I n s t a l l a t i o n of the Loango S t e e l G r a v i t y P l a t f o r m s . " Design and C o n s t r u c t i o n of O f f s h o r e S t r u c t u r e s , London: I n s t i t u t e of C i v i l E ngineers, Proceedings, pp.31-38. 73. Lambe, T. W. (1967): " S t r e s s Path Method." J o u r n a l of the S o i l Mechanics and Foundation D i v i s i o n , ASCE, Proceedings, Vol.93, NO.SM6, pp.309-317. 74. L a u r i t z s e n , R o l f , and Schjetne, Knut. (1976): " S t a b i l i t y C a l c u l a t i o n s f o r O f f s h o r e G r a v i t y S t r u c t u r e s . " E i g h t h Annual O f f s h o r e Technology Conference, Houston, Proceedings, V o l . 1 , pp.76-82. 75. Lee, Kenneth L. (1976): " P r e d i c t e d and Measured Pore Pressures i n the E k o f i s k Tank Foundation." I n t e r n a t i o n a l Conference on the Behavior of O f f s h o r e S t r u c t u r e s , Oslo, Proceedings, Vol.2, pp.384-398. 76. Lee, K. L., and A l b a i s a , A. (1974): "Earthquake Induced Settlements i n S a t u r a t e d Sands." J o u r n a l of the G e o t e c h n i c a l E n g i n e e r i n g D i v i s i o n , ASCE, Proceedings, Vol.100, NO.GT4, pp.387-406. 77. Lee, Kenneth L., and Focht, John A., J r . (1975a): "Lique- f a c t i o n P o t e n t i a l at E k o f i s k Tank i n North Sea." J o u r n a l of the G e o t e c h n i c a l E n g i n e e r i n g D i v i s i o n , ASCE, Proceedings, Vol.101, NO.GT1, pp.1-18. 78. Lee, Kenneth L., and Focht, John A., J r . (1975b): " C y c l i c T e s t i n g of S o i l f o r Ocean Wave Loading Problems." Seventh Annual O f f s h o r e Technology Conference, Houston, Proceedings, V o l . 1 , pp.343-354. 79. Lee, K. W., and F i n n , W. D. Liam. (1978): "STESL - A Compu- t e r Program f o r S t a t i c and Earthquake Analyses of Underwater Slopes." S o i l Dynamics Group, U n i v e r s i t y of B r i t i s h Columbia. 201 80. Low, E. (1975): "Foundations f o r G r a v i t y Type Of f - s h o r e D r i l l i n g / P r o d u c t i o n P l a t f o r m s . " O f f - s h o r e S t r u c t u r e s , London: I n s t i t u t e of C i v i l E ngineers, Proceedings, pp.27- 35. 81. Lundgren, H., and Mortensen, K. (1953): "Determination by the Theory of P l a s t i c i t y of the Bearing C a p a c i t y of Continuous Footings on Sand." T h i r d I n t e r n a t i o n a l Conference on S o i l Mechanics and Foundation E n g i n e e r i n g , Z u r i c h , Proceedings, V o l . 1 , pp.409-412. 82. MacCamy, R. C , and Fuchs, R. A. (1954): "Wave Forces on P i l e s : A D i f f r a c t i o n Theory." U. S. Army Corps of Engineers, Beach E r o s i o n Board, T e c h n i c a l Memo No.69, Washington. 83. M c C l e l l a n d , B. (1977): " G e o t e c h n i c a l Problems i n Ocean E n g i n e e r i n g . " Ninth I n t e r n a t i o n a l Conference on S o i l Mechanics and Foundation E n g i n e e r i n g , Tokyo, Proceedings, Panel D i s c u s s i o n , S p e c i a l t y Session 7, pp.513-523. 84. McCormick, M. E. (1973): Ocean E n g i n e e r i n g Wave Mechanics, New York: John Wiley and Sons, Inc., 179 p. 85. McPhee, W. S., and Reeves, S. J . (1975): " D r i l l i n g and P r o d u c t i o n Platforms f o r the O i l I n d u s t r y . " O f f - s h o r e S t r u c t u r e s , London: I n s t i t u t e of C i v i l Engineers, Proceedings, pp.189-196. 86. M a i d l , B., and S c h i l l e r , W. (1979): " T e s t i n g and Exper- iences of D i f f e r e n t Scour P r o t e c t i o n Technologies i n the North Sea." Eleventh Annual O f f s h o r e Technology Conference, Houston, Proceedings, V o l . 2 , pp.981-988. 87. Marion, H. A. (1974): " E k o f i s k Storage Tank." Symposium on Ocean E n g i n e e r i n g , Teddington: The Royal I n s t i t u t e of Naval A r c h i t e c t s , Proceedings, pp.83-90. 88. M a r t i n , M. R., and Shaw, L. K. (1974): "A Decade of North Sea P l a t f o r m s . " Symposium on Ocean E n g i n e e r i n g , Teddington: The Royal I n s t i t u t e of Naval A r c h i t e c t s , Proceedings, pp.73-82. 89. Meyerhof, G. G. (1953): "The Bearing C a p a c i t y of Foun- d a t i o n s Under E c c e n t r i c and I n c l i n e d Loads." T h i r d I n t e r n a t i o n a l Conference on S o i l Mechanics and Foundation E n g i n e e r i n g , Z u r i c h , Proceedings, V o l . 1 , pp.440-445. 90. Meyerhof, G. G. (1963): "Some Recent Research on the Bearing C a p a c i t y of Foundations." Canadian G e o t e c h n i c a l J o u r n a l , V o l . 1 , No.1, pp.16-26. 202 91. Meyerhof, G. G. (1974): "Ultimate Bearing C a p a c i t y of Fo o t i n g s on Sand Layer O v e r l y i n g C l a y . " Canadian G e o t e c h n i c a l J o u r n a l , Vol.1'1, No.2, pp.223-229. 92. Moinard, M. (1979): "Deep Sea Prod u c t i o n Use of A r t i c u l a t e d Columns." Symposium on New Technologies f o r E x p l o r a t i o n and E x p l o i t a t i o n of O i l and Gas Resources, London: Graham and Trotman L i m i t e d , Proceedings, Vol.2, pp.1010-1033. 93. Morgenstern, N. R., and P r i c e , V. E. (1965): "The A n a l y s i s of the S t a b i l i t y of General S l i p S u r f a c e s . " Geotechnique, Vol.15, No.1, pp.79-93. 94. Morison, J . R. (1950): "The Force E x e r t e d by Surface Waves on P i l e s . " Petroleum T r a n s a c t i o n s , TP 2846, pp.149-154. 95. M o r r i s o n , A l l e n . (1980a): "Cognac: World's T a l l e s t O i l P l a t f o r m . " C i v i l E n g i n e e r i n g , «Vol.50, No.6, pp.55-57. 96. Morrison, A l l e n . (1980b): "U.S. O f f s h o r e Future: New Techniques, Deeper Water, But Where's the O i l ? . " C i v i l E n g i n e e r i n g , Vol.50, No.6, pp.58-59. 97. Murff, J . D., and M i l l e r , T. W. (1977): " S t a b i l i t y of O f f - shore G r a v i t y S t r u c t u r e Foundations by the Upper Bound Method." Ninth Annual O f f s h o r e Technology Conference, Houston, Proceedings, Vol.3, pp.147-154. 98. Of f s h o r e Europe, 2nd Ed. (1974): Bucks, England: S c i e n t i f i c Surveys (Offshore) L t d . 99. O f f s h o r e S o i l Mechanic's. (1976): Eds. P h i l l i p George and David Wood, Cambridge: Cambridge U n i v e r s i t y E n g i n e e r i n g Department, pg.431. 100. Penzien, Joseph. (1976): " S t r u c t u r a l Dynamics of F i x e d O f f - shore S t r u c t u r e s . " I n t e r n a t i o n a l Conference on the Behavior of O f f s h o r e S t r u c t u r e s , Oslo, Proceedings, V o l . 1 , pp.581- 592. 101. P r a n d t l , L. (1921): "Uber d i e E i n d r i g u n g F e s t i g k e i t (Harte) P l a s t i s c h e r B a u s t o f f e und d i e F e s t i g k e i t von Schneiden." Z i e t s c h r i f t Fur Angewandte Mathematic und Mechanic, V o l . 1 , pp.15-20. 102. Prev0st, Jean. H., Cuny, Bernard., and S c o t t , Ronald F. (1981a): "Offshore G r a v i t y S t r u c t u r e s : C e n t r i f u g a l M o d e l l i n g . " J o u r n a l of the G e o t e c h n i c a l E n g i n e e r i n g D i v i s i o n , ASCE, Proceedings, Vol.107, No.GT2, pp.125-141. 103. Prev0st, Jean. H., Cuny, Bernard., Hughes, Thomas. J . R., and S c o t t , Ronald F. (1981b): "Offshore G r a v i t y S t r u c t u r e s : A n a l y s i s . " J o u r n a l of the G e o t e c h n i c a l E n g i n e e r i n g D i v i s i o n , ASCE, Proceedings, Vol.107, No.GT2, pp.143-165. 203 104. Rahman, M. S., Seed, H. B., and Booker, J . R. (1977): "Pore Pressure Generation Under O f f s h o r e G r a v i t y S t r u c t u r e s . " J o u r n a l of the G e o t e c h n i c a l E n g i n e e r i n g D i v i s i o n , ASCE, Proceedings, Vol.103, No.GT12, pp.1419-1436. 105. Ranney, W i l l i a m M. (1979): O f f s h o r e O i l Technology—Recent Developments. Park Ridge, N. J . : Noyes Data C o r p o r a t i o n , 399 p. 106. Reddy, A. S., and S r i n i v a s a n , R. J . (1967): "Bearing C a p a c i t y of F o o t i n g s on Layered C l a y s . " J o u r n a l of the S o i l Mechanics and Foundation D i v i s i o n , ASCE, Proceedings, Vol.93, NO.SM2, pp.83-99. 107. R0ren, E. M. Q., and Fames, 0. (1976): "Behavior of S t r u c t u r e s and S t r u c t u r a l Design." I n t e r n a t i o n a l Conference on the Behavior of O f f s h o r e S t r u c t u r e s , O s l o , Proceedings, V o l . 1 , pp.70-112. 108. Rowe, P. W. (1975): "Displacement and F a i l u r e Modes of Model O f f s h o r e G r a v i t y Platforms Founded on C l a y . " O f f s h o r e Europe Conference '75, Aberdeen, Scot l a n d , pp.218.1-16. 109. Rowe, P. W., C r a i g , W. H., and P r o c t o r , D. C. (1976): "Model S t u d i e s of O f f s h o r e G r a v i t y S t r u c t u r e s Founded on C l a y . " I n t e r n a t i o n a l Conference on the Behavior of O f f s h o r e S t r u c t u r e s , Oslo, Proceedings, V o l . 1 , pp.439-448. 110. de R u i t e r , J . (1976): "North Sea S i t e I n v e s t i g a t i o n s — T h e Role of the G e o t e c h n i c a l C o n s u l t a n t . " O f f s h o r e S o i l Mechanics, Eds. P h i l l i p George and David Wood, Cambridge: Cambridge U n i v e r s i t y E n g i n e e r i n g Department, pp.61-78. 111. Sangrey, D. A., Henkel, D. J . , and E s r i g , M. I. (1969): "The E f f e c t i v e S t r e s s Response of Saturated Clay S o i l to Repeated Loading." Canadian G e o t e c h n i c a l J o u r n a l , Vol.6, No.3, pp.241-252. 112. Sarma, S. K. (1973): " S t a b i l i t y A n a l y s i s of Embankments and Slopes." Geotechnique, Vol.23, No.3, pp.423-433. 113. Sarpkaya, T., and Isaacson, M. de St. Q. (1981): Mechanics of Wave Forces on O f f s h o r e S t r u c t u r e s , New York: Van Nos- t r a n d Reinhold, 651 p~. 114. Schjetne, Knut. (1976): "Foundation E n g i n e e r i n g f o r G r a v i t y S t r u c t u r e s i n the- North Sea." Norwegian G e o t e c h n i c a l I n s t i t u t e , No.113, pp.23-33. 115. Seed, H. Bolton, M a r t i n , P h i l l i p e P., and Lysmer, John. (1976): "Pore Water Pressure Changes During S o i l L i q u e f a c t i o n . " J o u r n a l of the G e o t e c h n i c a l E n g i n e e r i n g D i v i s i o n , ASCE, Proceedings, Vol.102, No.GT4, pp.323-346. 204 116. Seines, P. B. (1981): "Offshore Earthquake T e c h n o l o g y — F i r s t P a r t . " ASCE F a l l Conference, S t . L o u i s , Proceedings, pp.81 7-823. 117. Shore P r o t e c t i o n Manual, 3rd Ed. (1977): 3 V o l . , U. S. Army C o a s t a l Engineering Research Center, Washington: United S t a t e s Government P r i n t i n g O f f i c e . 118. Sjoerdsma, G. W. (1975a): "General A p p r a i s a l of Of f - s h o r e G r a v i t y S t r u c t u r e s . " O f f - s h o r e S t r u c t u r e s , London: I n s t i t u t e of C i v i l E ngineers, Proceedings, pp.61-66. 119. Sjoerdsma, G. W. (1975b): " D i s c u s s i o n - Ses s i o n G." O f f - shore S t r u c t u r e s , London: I n s t i t u t e of C i v i l Engineers, Proceedings, pg.l9B. 120. Skempton, A. W. (1954): "The Pore Pressure C o e f f i c i e n t s A and B." Geotechnique, Vol.4, No.4, .pp.143-147. 121. Skempton, A. W., and Bjerrum, L. (1957): "A C o n t r i b u t i o n to the Settlement A n a l y s i s of Foundations on C l a y . " Geotechnique, Vol.7, pp.168-178. 122. Stenning, D. G., and Schumann, C. G. (1979): " A r c t i c P r o d u c t i o n Monocone." E l e v e n t h Annual O f f s h o r e Technology Conference, Houston, Proceedings, Vol.4, pp.2357-2366. 123. Steven, Robert R. (1981a): "Some O f f s h o r e Feats Set World Standards, Others Set World Records." O f f s h o r e , Vol.41, No.7, pp.70-71. 124. Steven, Robert R. (1981b): "North Sea: S p e c i a l Report, Future B r i g h t f o r Norway P r o d u c t i o n . " O f f s h o r e , Vol.41, No.2, pp.98-104. 125. Steven, Robert R. (1981c): "North Sea: S p e c i a l Report, U.K. Output Slackens Due to Problems." O f f s h o r e , Vol.41, No.2, pp.89-96. 126. Stokes, G. C. (1880): "On the Theory of O s c i l l a t o r y Waves." Mathematical and P h y s i c a l Papers, V o l . 1 , Cambridge: Cambridge U n i v e r s i t y P r e s s . 127. Stubbs, S. B. (1975): "Seabed Foundation C o n s i d e r a t i o n s f o r G r a v i t y S t r u c t u r e s . " O f f - s h o r e S t r u c t u r e s , London: I n s t i t u t e of C i v i l E n gineers, Proceedings, pp.67-74. 128. T a y l o r , K. L. (1976): " P r a c t i c e s Adopted i n North Sea I n v e s t i g a t i o n s . " O f f s h o r e S o i l Mechanics, Eds. P h i l l i p George and David Wood, Cambridge: Cambridge U n i v e r s i t y E n g i n e e r i n g Department, pp.1 17-130. 129. T e r z a g h i , K a r l . (1943): T h e o r e t i c a l S o i l Mechanics, New York: John Wiley and Sons, Inc., 510 p. 205 130. T e r z a g h i , K a r l , and Peck, Ralph B. (1948): S o i l Mechanics i n E n g i n e e r i n g P r a c t i c e , Second E d i t i o n 1966, New York: John Wiley and Sons, Inc., 729 p. 131. van Eekelen, H. A. M., and P o t t s , D. M. (1978): "The Beha- v i o r of Drammen Clay Under C y c l i c Loading." Geotechnique, Vol.28, No.2, pp.173-196. 132. Vaughan, P. R.; Davachi, M. M.; E l Ghamrawy, M. K.; Hamza, M. M.; and Hight, D. W. (1976): " S t a b i l i t y A n a l y s i s of Large G r a v i t y S t r u c t u r e s . " I n t e r n a t i o n a l Conference on the Behavior of O f f s h o r e S t r u c t u r e s , Oslo, Proceedings, Vol.1, pp.467-487. 133. V e s i c , Aleksandar S. (1975): "Bearing C a p a c i t y of Shallow Foundations." Foundation E n g i n e e r i n g Handbook, Eds. Hans F. Winterkorn and Hsai-Yang Fang, New York: Van Nostrand Reinhold Company, pp.121-147. 134. Waagaard, Knut. (1977): "Fatigue of O f f s h o r e Concrete S t r u c t u r e s — D e s i g n and Experimental I n v e s t i g a t i o n s . " N i n t h Annual O f f s h o r e Technology Conference, Houston, Proceedings, Vol.4, pp.341-350. 135. Ward, E. G., Evans, D. J . , and Pompa, J . A. (1977): "Extreme Wave Heights Along the A t l a n t i c Coast of the U n i t e d S t a t e s . " Ninth Annual O f f s h o r e Technology Conference, Houston, Proceedings, Vol.2, pp.315-324. 136. Watt, B. J . (1976): " G r a v i t y S t r u c t u r e s — I n s t a l l a t i o n and Other Problems." O f f s h o r e S o i l Mechanics, Eds. P h i l l i p George and David Wood, Cambridge: Cambridge U n i v e r s i t y E n g i n e e r i n g Department, pp.286-305. 137. Watt, B. J ; Boaz, I. B.; Ruhl, J . A.; S h i p l e y , S. A.; and Ghose, A. (1978): "Earthquake S u r v i v a b i l i t y of Concrete P l a t f o r m s . " Tenth Annual O f f s h o r e Technology Conference, Houston, Proceedings, Vol.2, pp.957-975. 138. Watt, B. J . (1979): "Basic S t r u c t u r a l Systems—A Review of T h e i r Design and A n a l y s i s Requirements." Numerical Methods in O f f s h o r e E n g i n e e r i n g , Ed. 0. C. Z i e n k i e w i c z , New York: John Wiley and Sons, Inc., pp.1-42. 139. Werenskiold, K. (1977): "Maritime Operations R e l a t i v e to C o n s t r u c t i o n of O f f s h o r e S t r u c t u r e s . " Design and C o n s t r u c t i o n of O f f s h o r e S t r u c t u r e s , London: I n s t i t u t e of C i v i l E n gineers, Proceedings, pp.97-105. 140. Yamaguchi, H., and T e r a s h i , M. (1971): "Ultimate Bearing C a p a c i t y of the M u l t i - L a y e r e d Ground, Fourth Asian Regional Conference on S o i l Mechanics and Foundation E n g i n e e r i n g , Proceedings, V o l . 1 , pp.97-105. 206 141. Young, Alan G., K r a f t , L e l a n d M., J r . , and Focht, John A., J r . (1975): " G e o t e c h n i c a l C o n s i d e r a t i o n s i n Foundation Design of O f f s h o r e G r a v i t y S t r u c t u r e s . " Seventh Annual O f f s h o r e Technology Conference, Houston, Proceedings, V o l . 3 , pp.367-386. 142. Z i e n k i e w i c z , 0. C; N o r r i s , V. A.; W i n n i c k i , L. A.; Naylor, D. J . ; and Lewis, R. W. (1979): "A U n i f i e d Approach to the S o i l Mechanics Problems of O f f s h o r e Foundations." Numerical Methods in O f f s h o r e E n g i n e e r i n g , Ed. 0. C. Z i e n k i e w i c z , New York: John Wiley and Sons, Inc., pp.361-411.

Cite

Citation Scheme:

    

Usage Statistics

Country Views Downloads
United States 25 7
United Kingdom 8 0
Germany 7 0
France 6 0
China 1 0
Turkey 1 0
City Views Downloads
Houston 17 0
Unknown 15 0
Borehamwood 7 0
Blacksburg 3 3
Sugar Land 2 2
Redmond 1 2
Sunnyvale 1 0
Beijing 1 0
Ashburn 1 0

{[{ mDataHeader[type] }]} {[{ month[type] }]} {[{ tData[type] }]}

Share

Share to:

Comment

Related Items