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Geotechnical considerations for offshore gravity type structures with emphasis on foundation stability.. Gaard, Thomas C. 1982

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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 ,  Davis,  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  We a c c e p t to  THE  OF C I V I L  this  ENGINEERING  t h e s i s as  the required  standard  UNIVERSITY OF BRITISH April,  O  conforming  COLUMBIA  1982  Thomas C. G a a r d ,  1982  In p r e s e n t i n g  t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of  requirements f o r an advanced degree at the  the  University  of B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make it  f r e e l y a v a i l a b l e f o r reference  and  study.  I further  agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying o f t h i s t h e s i s f o r s c h o l a r l y purposes may department or by h i s or her  be granted by the head o f representatives.  my  It is  understood t h a t copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain  s h a l l not be allowed without my  permission.  Department o f  Cl^\  The  U n i v e r s i t y of B r i t i s h Columbia  1956  Main Mall  Vancouver, Canada V6T 1Y3 Date  DE-6  ^ ^ ^ . , 1 ^  (3/81)  3 2 / ^ J z. %  written  11  ABSTRACT  A  thorough  presently by the  being  discussion  used, or c o n s i d e r e d  the o i l industry, major  of o f f s h o r e  f o r use i n t h e  i s presented, along  t y p e s o f s t r u c t u r e s now u s e d  Factors  g r a v i t y type  affecting  the  structures  near  with a b r i e f  future  summary o f  offshore.  stability  of o f f s h o r e  gravity  type  structures are discussed,  from t h e e v a l u a t i o n  of a s u i t a b l e  site  and  parameters, through  installation  and  A case study of the E k o f i s k  tank  the s e l e c t i o n of s o i l  short-term is  foundation  included  to  offshore. gravity the  A  show  how  thorough  structures  design  safety.  storm  Existing  geotechnical  concepts  d e s c r i p t i o n o f wave l o a d i n g  i s presented,  i s used  offshore are  offshore.  g r a v i t y type  methods  developed  Procedures structures  a r e reviewed.  respect  for analyzing subjected  a n d Sarma's  are  offshore  perform  computer  program  described  and  versatility  of  The  applied method  developed to of  several  for  this  example  analysis  r e s u l t s a r e compared w i t h e x i s t i n g m e t h o d s .  Both  how  is  and  their  loading Janbu's  (1973) method  latter  pseudo-three-dimensional  GRAVSTAB  the  analyses.  to  t o s t o r m wave  Procedure of S l i c e s  to  on  the s t a b i l i t y of  (1973) G e n e r a l i z e d  modified  the  with  of s l i c e s .  for  on  offshore  The m e r i t s  method  adapted  based  on  analyses.  s h o r t c o m i n g s o f e a c h method a r e d i s c u s s e d application  applied  including a discussion  i n geotechnical  stability  are  method  analyses. purpose problems.  demonstrated  is A is The and  iii  TABLE OF CONTENTS  ABSTRACT  i i  TABLE OF CONTENTS  .'  L I S T OF TABLES  vi  L I S T OF FIGURES  v i i  ACKNOWLEDGEMENTS  x  NOMENCLATURE CHAPTER  i i i  xi  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 F o r G e n e r a l O f f s h o r e Development  14  2.2.1  Concrete  Platforms  2.2.2  Steel  2.2.3  Hybrid Platforms  15  Platforms  18 23  2.3  Platforms For A r c t i c  Development  2.4  Deep Water P l a t f o r m s And O t h e r  2.5  Sources  Of New P l a t f o r m T e c h n o l o g y  CHAPTER 3 : DESIGN, CONSTRUCTION 3.1  AND INSTALLATION  Preliminary Considerations  3.1.1  Sources  Loads  3.1.1.2  O p e r a t i o n a l Loads  3.1.2  Environmental. Design  3.1.3  Site  3.1.4  Selection  P l a t f o r m Design  31  31 32 Parameters  And S o i l  Of S o i l  30  31  Environmental  Selection  27  31  Of L o a d i n g  3.1.1.1  3.2  Structures  25  Investigations  Parameters  For Design  33 34 42 46  iv  3.2.1  Hydrodynamic  Analyses  46  3.2.2  Geotechnical  Analyses  47  3.2.3  Structural  R e q u i r e m e n t s And A n a l y s e s  55  3.3  Platform Construction  57  3.4  Platform Installation  59  3.5  Platform  63  Instrumentation  CHAPTER  4. : THE EKOFISK TANK - A CASE STUDY  67  CHAPTER  5 : CHARACTERISTICS OF WAVE LOADING  93  Ocean  93  5.1  Waves  5.1.1  The Wave C l i m a t e  93  5.1.2  Wave T h 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 T h e o r y  97  5.2  C h a r a c t e r i z i n g The Wave System  5.2.1  Obtaining  The D e s i g n  5.2.1.1  Statistical  5.2.1.2  Geotechnical  5.2.2 5.3  97  Storm  100  Description  100  Equivalent  101  A p p l i c a t i o n Of The D e s i g n Wave L o a d s On The F o u n d a t i o n  Storm  102  System  104  5.3.1  Wave F o r c e s  A c t i n g On*The S t r u c t u r e  104  5.3.2  Wave F o r c e s  A c t i n g On The F o u n d a t i o n  108  5.4 CHAPTER  Effect  Of C y c l i c  Loading  On The F o u n d a t i o n  ...109  6 : PROCEDURES FOR ANALYZING THE S T A B I L I T Y OF OFFSHORE  GRAVITY  TYPE STRUCTURES  6.1  Fundamental C o n s i d e r a t i o n s  6.2  Modelling  6.3  Loading  6.4  Available Stability  6.4.1  System  115  The W a v e - S t r u c t u r e - S o i l  System  A p p l i e d To The F o u n d a t i o n  Classical  Bearing  Methods Capacity  115  120 126 128  Approach  128  V  6.4.2  Other Bearing  6.4.3  NGI S l i p S u r f a c e  6.4.4  Method Of S l i c e s  144  6.4.5  Finite  144  6.4.6  Model T e s t s  6.5  Capacity  Formulations  136  Method  140  Element A n a l y s e s  150  Summary  152  CHAPTER 7 : APPLICATION  OF THE METHOD OF S L I C E S TO  OFFSHORE GRAVITY STRUCTURE FOUNDATIONS  154  7.1  The Method Of S l i c e s  156  7.2  Loading Applied  158  7.3  T r e a t m e n t Of The A p p l i e d  7.4  Modified  To The F o u n d a t i o n  Assumptions  7.4.2  Derivation  7.4.3  Working Formulas Modified  160 161 161  Of E q u i l i b r i u m  Equations  .161  •  164  Sarma Method  7.5.1  Assumptions  7.5.2  Derivation  7.5.3  Working Formulas  167 169  Of E q u i l i b r i u m  Equations  Of Computer  8.1  Description  8.2  Example  8.3  Example 2 - A C o h e s i o n l e s s  OF ANALYSES  175  Procedure  1 - A Multi-layered  CHAPTER 9 : SUMMARY  170 173  CHAPTER 8 : EXAMPLES AND APPPLICATION  REFERENCES  Force  J a n b u Method  7.4.1  7.5  Horizontal  AND CONCLUSIONS  175  Cohesive Deposit Deposit:  Ekofisk  177 Tank  ....183 189 194  L I S T OF TABLES  Table  I  - Comparison of F i x e d O f f s h o r e P l a t f o r m s  16  Table  II  - North  19  Table  III  - Gravity Platforms  Table  IV  - Environmental Design O f f s h o r e Areas  Table V T a b l e VI  Sea C o n c r e t e  Gravity Platforms i n Other  P a r t s of the World  Criteria  f o r Some 35  - G e o t e c h n i c a l Concerns Platforms  f o r O f f s h o r e G r a v i t y Type 48  - Example o f t h e A c c u m u l a t e d E f f e c t  of a  100-year  Storm  85  Table VII  - Some R e s u l t s o f L i n e a r Wave T h e o r y  Table VIII  - Comparison of E x i s t i n g  Table  - Geometry and L o a d i n g  IX  Table X T a b l e XI Table XII  Stability  Data  99  Analyses  f o r Example  1  - C o m p a r i s o n o f Computed S a f e t y F a c t o r s f o r Example 1 - 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 C o m p r e s s i o n D a t a - Effect the  .. 20  o f Shear  153 177  179 182  Zone R e p r e s e n t a t i o n on  Safety Factor  Table XIII  - Geometry and L o a d i n g  T a b l e XIV  - Effect  184 Data  f o r Example  2  o f A - p a r a m e t e r on t h e S a f e t y F a c t o r  185 188  vi i  L I S T OF FIGURES  Figure  1.1  - Steel  Figure  1.2  - Mobile  Platforms  2  Figure  1.3  - The E k o f i s k Tank  5  Figure  2.1  - Components o f an O f f s h o r e Platform  Figure  2.2  Jacketed  Platforms  2  Gravity  Type 13  - N o r t h Sea C o n c r e t e G r a v i t y Type  Offshore  Platforms  18  Figure  2.3  - Tecnomare S t e e l G r a v i t y Type O f f s h o r e  Figure  2.4  - Hybrid  G r a v i t y Type O f f s h o r e  Figure  2.5  - Arctic  Platform  Figure  2.6  - P r o p o s e d Deep-water P l a t f o r m s  29  Figure  3.1  - L o a d s A c t i n g on an O f f s h o r e  32  Figure  3.2  Figure  3.3  - Plan of Survey L i n e s - G r i d : L o c a l Transverse , Mercator Spheroid - T y p i c a l S o i l P r o f i l e a s I d e n t i f i e d by B o r e h o l e , Cone P e n t r a t i o n T e s t a n d Gamma Ray L o g g i n g  43  - Comparison o f Shear S t r e n g t h Sample T e s t i n g a n d from CPT  45  Figure Figure  3.4 3.5  Platforms  Structure  27  Structure  Values  37  from  Modes f o r an O f f s h o r e Foundation  Figure  3.6  - P o s s i b l e Modes o f S l i d i n g  Figure  3.7  - Stability  Figure  3.8  - Installation  Figure  3.9  - Detail  Figure  3.10 - Maximum Dome C o n t a c t  Diagram  Failure  f o r a Raft  Sequence  50 51  Foundation  53  for a Gravity Platform  .. 60  o f CONDEEP Base S t r u c t u r e  Installation  22 24  Designs  - Possible Failure Gravity  Platform  Pressures  Observed  61 During  o f t h e " B e r y l A" CONDEEP  Figure  4.1  - Detail  o f t h e E k o f i s k Tank B o t t o m  Figure  4.2  - L o a d s on t h e E k o f i s k Tank Wave  64 69  f o r t h e 100-Year 71  vi i i  Figure  4.3  - Design  Storm Data  f o r the Ekofisk F i e l d  Figure  4.4  - Typical Geotechnical  Profile  from  71  Ekofisk  Field  72  Figure  4.5  - Shear S t r e n g t h  Figure  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 - L o a d - S e t t l e m e n t C u r v e f o r E k o f i s k Tank  76 76  - E k o f i s k S e t t l e m e n t D a t a R e l a t i n g Submerged P l a t f o r m W e i g h t a n d S t o r m Wave D a t a i n t h e E a r l y Months A f t e r I n s t a l l a t i o n  79  - Settlement Storms  79  Figure  4.7  Figure  4.8  Figure Figure Figure Figure  4.9  Data  Data  from E k o f i s k  72  f o r E k o f i s k Tank D u r i n g  Early  4.10 - L o c a t i o n o f P r e s s u r e Gauges a n d P i e z o m e t e r s B e n e a t h E k o f i s k Tank  82  4.11 - P o r e P r e s s u r e s O b s e r v e d Under E k o f i s k Tank D u r i n g t h e F i r s t M a j o r Storm  82  4.12 - P o r e P r e s s u r e R i s e p e r C y c l e O b s e r v e d i n Undrained Simple Shear w i t h C y c l i c L o a d i n g f o r Samples P r e p a r e d w i t h R e l a t i v e D e n s i t i e s o f 80%  85  Figure  4.13 - T h e o r e t i c a l P r e d i c t i o n o f t h e P o r e 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 o f 77% a n d 85% .... 90  Figure  4.14 - Most C r i t i c a l F a i l u r e S u r f a c e Found i n S t a b i l i t y A n a l y s i s o f E k o f i s k Tank f o r Wave L o a d s A p p l i e d Under U n d r a i n e d C o n d i t i o n s  Figure  5.1  - Regions of V a l i d i t y  Figure  5.2  - Profile  Figure  5.3  - F o r c e s A c t i n g on t h e F o u n d a t i o n Offshore Gravity Structure  Figure  Figure  Figure  5.4  5.5  6.1  o f an A i r y  f o rVarious  Wave T h e o r i e s  Wave  92 . 98 99  o f an  - T y p i c a l D e s i g n Storm R e p r e s e n t a t i o n Geotechnical Engineering  105 Used i n 107  - S t r e s s Path f o r a F o u n d a t i o n Element with P a r t i a l D r a i n a g e S u b j e c t e d t o Storm Wave Loading - Effective Stresses in Soil for S t i l l C o n d i t i o n s ( i . e . No Wave L o a d s )  i l l  Water 118  Figure  6.2  - Definition  Figure  6.3  - Transformation  Figure  6.4  - Theoretical  Figure  6.5  - Comparison of D i f f e r e n t V a l u e o f Nr  Figure  6.6  S k e t c h of E f f e c t i v e  o f Loads, t o F o u n d a t i o n  Rupture Surface  Base  Geometry  Proposals  f o r the  Stress Bearing  Used f o r an  Capacity  Solution  6.7  - Geometry o f S l i d i n g  Figure  6.8  Figure  6.9  - Geometry o f B e a r i n g F a i l u r e S u r f a c e U s e d i n t h e NGI S l i p S u r f a c e Method - C o m p a r i s o n o f Two- and T h r e e - D i m e n s i o n a l D i s t o r t e d F i n i t e E l e m e n t 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  Figure  6.10  7.1  Body U s e d by NGI  7.2  - Geometry and F o r c e s  Figure  7.3  - C u r v e Used f o r E v a l u a t i n g  Figure  7.4  - Geometry and F o r c e s  Figure  7.5  - Typical  Figure  8.1  - Shear S t r e n g t h  Figure  8.2  Figure  8.3  - C r i t i c a l S h e a r S u r f a c e s f o r Example 1 a s 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 - Zones of S h e a r on t h e 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  Figure Figure  8.5 8.6  on a  on a  (Sarma) S l i c e Profile  (Janbu) S l i c e the Safety  Factor  (Sarma) S l i c e  Showing S i d e  149  f o r Example  f o r Example  ...169 171 171  1  178  - D i s t r i b u t i o n o f P o r e Water P r e s s u r e s F o u n d a t i o n S o i l Used i n Example 2 Shear Surface  162  Forces  - C r i t i c a l S h e a r S u r f a c e f o r Example 1 Found from Computer P r o g r a m GRAVSTAB  - Critical  148  155  Figure  8.4  141  o f A n a l y s i s by t h e Method o f  Slices  Figure  ....138 ..141  - E f f e c t of L o 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 - Representation  ....123 129  Figure  Figure  122  132  - Geometry o f R u p t u r e S u r f a c e Effective  Foundation  2  180 182 184  in 185 188  X  ACKNOWLEDGEMENTS  The Finn  a u t h o r w i s h e s t o thank h i s a d v i s o r ,  for  improve  his the  comments final Dr.  M.  throughout  de  intends  Byrne  to offshore STESL  by  stability studies grant  of  No.1498  this To  worth  more  interesting worn  -  i s an and  a  final job at  W.D.  to  (ever)  an  Finn.  regarding things.  program  a n a l y s i s of the  under  assistance the  the  computer  Research Council This  due  Sarma's method  for  r e p r o d u c e many of  Dr.  also  earlier  f o r the  National  education  thanks to  of  and  author  among o t h e r  Funding  by  are  for applying  the  i n many  the  discussions  Liam F i n n  the  interest  Thanks  to  Vaid's  advisor  which  analyses  slopes.  by  this  Yogi  his  field  extension  f r i e n d s i n Vancouver an  thank  valuable  kindly granted  than A  to  stability  Permission  a l l my  Liam  suggestions  Dr.  stimulating his  Professor  t h e s i s was  forgotten.  t o be  Lee  to  thesis.  i n GRAVSTAB u s e d  provided  appreciated. in  of  underwater  was  like  for  many  platforms K.W.  valuable  wholeheartedly.  for  routine  this  engineering  aspects  program  and  W.D.  t e x t were a l s o h e l p f u l i n p a c k a g i n g  Isaacson  pursue  theoretical The  the  of  would a l s o  offshore to  P.M.  He  S t . Q.  of  guidance  presentation  product.  aspects  Dr.  technical  Professor  was  f i g u r e s used  numerous p e o p l e . who  made my  (and  bearable)  Isaacson  u n i v e r s i t y that  or a shave more t h a n  last  for  does not  twice  two  you giving  years  are me  require a  a week.  not an suit  xi  NOMENCLATURE  B  - equivalent  0  B  foundation  - effective  foundation  L  0  - equivalent  A  0  - platform  D  0  - skirt  base  length  area  d e p t h below unit  mudline  - effective  P  H  - h o r i z o n t a l wave l o a d  P  v  - vertical  platform  - vertical  wave l o a d  V  width  foundation  fl'  AP  width  weight of s o i l on  load on  platform at seafloor  platform  M  - moment a t s e a f l o o r  Ap,  - wave p r e s s u r e  on s e a f l o o r a t t a i l  Ap  - wave p r e s s u r e  on s e a f l o o r a t nose end o f p l a t f o r m  2  P  A  - active  P  p  - passive  P  w  - water p r e s s u r e  P  s  - shearing  resistance  on s i d e s  Pj  - shearing  resistance  on s o i l - s o i l  V  - vertical  load  V  B T  B  H H  ~ B T  B  M  feT  V  B TP  e r  soil soil  u n  ^  f c  - horizontal ~  H  B TP  e r  force  on nose o f  f o r c e on t a i l  at foundation  foundation  of  f o r c e on t a i l  end of p l a t f o r m  foundation  of  foundation  of  foundation interfaces at sides  base  width load at foundation  base  unit width  - moment a p p l i e d  at foundation  base  h,  - moment arm f o r a c t i v e o r w a t e r p r e s s u r e  h  - moment arm f o r p a s s i v e  2  soil  force  force  xi i  h  3  e  - moment arm f o r s h e a r i n g  E T  - horizontal  H  E  - H  H  S T  - horizontal  H  s  - H  E T  S T  force  per unit  applied  sides  force  per unit  applied  -  a  - normal  o"  - e f f e c t i v e normal  tr,  - major p r i n c i p a l  stress  0"  - minor p r i n c i p a l  stress  u  - total  3  load  to sliding  inclination  available  p o r e water pore water  pressure  u  c  - p o r e water p r e s s u r e due t o c y c l i c  pressure  Au  - p o r e water p r e s s u r e  z  - d e p t h below  A  - p o r e water p r e s s u r e  0  - friction  angle or mobilized  c  - cohesion  or mobilized  tan0  - frictional  c'  - cohesion  tan0'  - frictional  F  - factor  T  effects  due t o dynamic wave p r e s s u r e  mudline parameter  resistance  friction  resistance  shear  strength stress  angle  cohesion or m o b i l i z e d  i n terms of e f f e c t i v e  of safety  - undrained  - shear  surface  stress  - static  shear  from s l i d i n g  stress  s  -  surface  factor  u  u  area  width  - maximum s h e a r r e s i s t a n c e per u n i t w i d t h  s  to effective  width  g  c  on f o u n d a t i o n  - eccentricity  H  F  resistance  friction  stress  i n terms of e f f e c t i v e  applied strength  resistance  to strength  stress  parameters  xi i i  Qo  - ultimate  bearing  capacity  q  - ultimate  bearing  pressure  0  q'  - surcharge  N  - bearing  capacity  factor  N  - bearing  capacity  factor f o r cohesion  N  - bearing  capacity  factor  s-  - bearing  capacity  shape  influence  factors  d-  - bearing  capacity  depth  influence  factors  i-  - bearing  capacity  load  {,  - slice  otj  - a n g l e made by t o p o f i - t h s l i c e  ^  - a n g l e made by base o f i - t h s l i c e  t  for friction  f o r surcharge  inclination  influence  factors  number with  horizontal  with  horizontal  b^  - width of i - t h s l i c e  xt-  - x-coordinate  of midpoint  of t o p of i - t h s l i c e  yt|  - y-coordinate  of midpoint  of t o p of i - t h  xb^  - x-coordinate  of m i d p o i n t  o f base o f i - t h s l i c e  yb^  - y-coordinate  of midpoint  of base o f i - t h  xg^  - x-coordinate  of c e n t r o i d  of i - t h s l i c e  yg^  - y-coordinate  of c e n t r o i d  of i - t h s l i c e  xs-  - x-coordinate i-th slice  of point  of a p p l i c a t i o n of s i d e  forces f o r  y c  ~ y-coordinate i-th slice  of p o i n t  of a p p l i c a t i o n of s i d e  forces f o r  h^  - height  s  slice  slice  of i - t h s l i c e  - vertical  offset  Ah£  - distance  between base a n d l i n e  FV{,  - vertical  f o r c e on t o p o f i - t h s l i c e  FT(.  - total  FH:  - horizontal  vertical  of t h r u s t  load  force  forces  for i-th slice  of t h r u s t  on t o p o f i - t h s l i c e  on t o p o f i - t h s l i c e  for i-th slice  xiv  FN-,  - normal  FT  - tangential  force  on t o p o f i - t h s l i c e  US^  - p o r e water  force  on b a s e o f i - t h s l i c e  ss  - shear force  C  L  force  - normal  on t o p o f i - t h s l i c e  on one  force  side  of i - t h s l i c e  on base o f i - t h s l i c e  N;  - effective  Si  - shear force  E'v  - lateral  'v  - vertical  Q'v  - assumed v e r t i c a l  v;  - vertical  H;  - horizontal  wt  - total  w;'  - effective  w e i g h t of i - t h s l i c e  UH;  - resultant  water  T  normal  force  on b a s e o f i - t h s l i c e  on base o f i - t h s l i c e  thrust  applied  shear f o r c e  resultant  a t x=xj  on b a s e o f i - t h s l i c e  resultant  saturated  to i - t h s l i c e  s h e a r f o r c e a t x=xj  on b a s e o f i - t h s l i c e  w e i g h t of i - t h s l i c e  force  - pore water p r e s s u r e - normal  x 2  a t x=xj  a t base o f i - t h s l i c e  s t r e s s on base o f i - t h s l i c e  - s h e a r s t r e s s on base o f i - t h s l i c e - shear s t r e n g t h a t base of i - t h s l i c e - a v a i l a b l e cohesion t a n 0 'j = 1 tan0'^ r  t.  on base o f i - t h s l i c e  - available  frictional  - mobilized  cohesion  - mobilized  frictional  -  f a c t o r of s a f e t y  K  - acceleration  X  - vertical  on  resistance  slice  on base o f i - t h s l i c e resistance interslice  coefficient  f a c t o r of  on base of i - t h face  f o r i t-h  as a f r a c t i o n  shear f o r c e m u l t i p l i e r  - K f o r a given  on base of i -•th  safety  slice  slice  of g r a v i t y  V  CHAPTER 1 INTRODUCTION  The  increase  prevailing effects  global  geopolitical  on  consumers. energy  in  the  and  availability  a l o n g w i t h the western  self-sufficient,  has  led  r e s o u r c e s w h i c h were p r e v i o u s l y In  an  effort  gas  that  oceans. required  their  exist As to  reliable  the  hydrocarbon methods  for  platforms discovered at  Lake  structures,  usually  of  nearshore  sediments,  important  in that  uneconomical.  self-sufficiency  in recent  shelves  input  recovery the  and  years  of  the  been  world's  necessary schemes,  design,  are  for  and  the  (2)  analysis,  industry  made  were c r u d e  Maracaibo,  to and  piled  by  standards  1973).  today's  similar  of Mexico,  to  those  the  1920s  Venezuela.  c o n c r e t e and  they c o n s t i t u t e d  (Bjerrum,  in existence since  into  These the  soft  but  are  the b e g i n n i n g of the o f f s h o r e The  p l a t f o r m s c o n s t r u c t e d were t h e s t e e l  Gulf  energy  o i l companies, e n g i n e e r s  have been  when o i l was  structures,  of  be  of the n e c e s s a r y o f f s h o r e s t r u c t u r e s .  Offshore  oil  to  o f t h e v a s t r e s e r v e s of o i l and  the c o n t i n e n t a l to  t o most  desire  be  the  disastrous  t o the development  (1) p r o v i d e t h e t e c h n i c a l  installation  world's  o i l c o m p a n i e s have  consultants  of  and  petroleum  considered to  exploitation  beneath  implementation develop  of  t o meet t h e g o a l s o f e n e r g y  (indeed) a v a i l a b i l i t y , increasing  consumption  c l i m a t e i n t h e w o r l d have had  cost  This,  energy  shown  o f w h i c h some s e v e r a l  first jacket  "deep-water" or  in figure hundred  template 1.1  have  fixed type  used  i n the  been  built  A) CONVENTIONAL TYPE Figure  1.1  B) SELF-FLOATER  - Steel jacketed offshore platforms ( A f t e r McPhee and R e e v e s , 1975)  3  there in  s i n c e t h e 1960s.  other  parts  Persian Gulf,  of  These p l a t f o r m s the  the North  world,  Sea,  offshore  California,  and t o a  (Martin  and  1974).  exploratory  Shaw,  drilling  rigs  are a l s o i n widespread In first North  problems  when  development the  lesser  such  northern  North  with  facility  type  harbors  to the d r i l l i n g jacket type)  1973).  From t h i s  production  platform;  designed shown  being North  Interest steadily  platforms  f o r the  this  of  platform i n  were t o be o f  f u n c t i o n as a  l o a d i n g would-be  is  the  of  storage  impossible  offshore  famed  nearly  gravity  Ekofisk  France.  The  tank  tank is  t o i t s home i n t h e  1.3.  type  when  being  (which  need came t h e f i r s t  production the  because of the s h o r t  type  difficult  structures  from t h e N o r w e g i a n c o a s t  in gravity 1973  and  f o r a production  which c o u l d  Sea i n f i g u r e  since  primarily gravity  towed  new  (the c l o s e s t  by t h e C. G. D o r i s Company  northern  North  nearby  i n p o o r w e a t h e r when t a n k e r  (Bjerrum,  some  Sea (24 meter h i g h waves a t t h i s l o c a t i o n )  k i l o m e t e r s away) t h e need a r o s e  conventional  1.2  i n the northern  Because of t h e extreme h o s t i l i t y  320  proximity  figure  type  Company d i s c o v e r e d t h e  necessary  the  the  of  jackup  in  (the Ekofisk f i e l d )  and  close  lack  locations  the world.  Petroleum  the  field.  and  the  of Guinea,  other  a s t h e ones shown  were f a c e d  designing  of t h i s  Sea, the G u l f extent,  use throughout  sights  Lake M a r a c a i b o ,  Semi-submersible  o i l field  Sea, e n g i n e e r s  namely:  the Java  1969, when t h e P h i l l i p s commercial  are also familiar  Ekofisk  tank  installation  s t r u c t u r e (no p i l i n g  Sea) and t h e s u c c e s s f u l  platforms  necessary  operation  of  has i n c r e a s e d  was  time  installed,  required for a  i n the u n p r e d i c t a b l e the  Ekofisk  tank  4  Figure  1.3 - The E k o f i s k t a n k (See f o l l o w i n g page) (Reproduced w i t h p e r m i s s i o n of the Royal I n s t i t u t e of N a v a l A r c h i t e c t s , London.)  6  since  installation,  storm it  including  (90% of t h e d e s i g n  was i n s t a l l e d  areas of the world The  Ekofisk  1974).  t o date  (Waagaard,  1977).  was  platform  but not the f i r s t  Gravity  type  for  light  many y e a r s p r i o r  usually  20  meters  Sovereign  light  familiar  example'  are  relatively  concepts, time  The  offshore  that  had  (Bjerrum, In an  or  less  construction  of  (Stubbs,  Ekofisk  design  geotechnical engineering  in  increasing  type  used o f f s h o r e .  waters, The R o y a l  i s perhaps  type  a  more  structure. few  These  new  design  techniques  at the  and  off  the  for  North  undoubtedly  era  a for  techniques  these  1973; M a r i o n ,  purposes  1974).  e n g i n e e r s have been of  playing  offshore  gravity  few a r e f o r m a l l y t r a i n e d  e x p l o r a t i o n and u t i l i z a t i o n  the  new  installation  development  although  a  was  r e q u i r e d many new d e s i g n  specifically  American  however,  marked  American  e n g i n e e r s w i t h a good w o r k i n g will  gravity  1975).  tank,  and  T h i s tank  developed  role  resources  Sea and o t h e r  nearshore  and i n s t a l l a t i o n  the  structures.  technology,  With  gravity  installed.  engineering  be  after  e x t e n s i v e l y i n Sweden  shallower,  a pre-1973 g r a v i t y  recent years, North  structure  gas  structure  1973; G e r w i c k and H o g n s t a d ,  increasing  area.  in  c o n s t r u c t i o n methods, to  type  s m a l l s t r u c t u r e s which r e q u i r e d  gravity  procedures,  offshore  i n the E n g l i s h Channel  installation in  first  gravity  deep  t h e y were  milestone  the  t o 1973  of  a major  twenty o t h e r  i n the North  t o w e r s had been u s e d  tower  and  that  More t h a n  installed  tank  through  s t o r m ) w h i c h o c c u r r e d s i x months  (Marion,  p l a t f o r m s have been  a good p e r f o r m a n c e  coast,  i n the  of  o i l and  the  need f o r  knowledge o f o f f s h o r e  i n c r e a s e on t h i s  continent.  7  The the  purposes of t h i s  geotechnical  specifically, associated of  to  with  existing  type  engineer  t h e s i s a r e t h r e e f o l d : (1) t o t o the f i e l d  familiarize  him  with  gravity structures,  stability  methods  of o f f s h o r e the  introduce  engineering,  s p e c i a l problems  (2) t o p r e s e n t  an  overview  applicable to offshore  gravity  s t r u c t u r e s , and (3) t o d e v e l o p an a l t e r n a t i v e p r o c e d u r e f o r  analyzing  the  subjected  t o s t o r m wave  This deal  stability  of  an  offshore  the  first  engineering.  C h a p t e r s 6-8,  is  i n t o two s e c t i o n s .  consideration, The  second  concerned wholly  stability  under  s t o r m wave l o a d i n g .  serve  dual  purpose.  a  unfamiliar offshore  with  offshore  First,  installation  is  necessary  that  The a i m o f t h e  under  wave  stability analyses simple,  methods and  to  practical  The they  loading  general of  serve  section  presently  to  on  alternative  the  method  foundation chapters the reader  him w i t h  and t h e s p e c i a l  may  for  an  design  structures.  This  be v i e w e d i n  foundation  present  need  thesis,  knowledge o f  they p r o v i d e  available  demonstrate  this  to give  analyses  2-5  background i n  preliminary  f o r g r a v i t y type  is  Chapters  a good w o r k i n g  the foundation  perspective. storm  structure  the t o p i c of  environment  requirements  so  with  Secondly,  of the o f f s h o r e  and  a part  engineering  gravity structures.  appreciation  gravity  loading.  t h e s i s may be d i v i d e d  with  offshore  stability  an o v e r v i e w o f t h e performing  such  f o r and t h e n d e v e l o p a for  effective  stress  analyses. Chapter type  2  structures.  serves The  as  an  general  introduction to offshore characteristics  of  a  gravity gravity  8  structure  are  discussed  i n some  Chapter  Next, the  requirements  and  site  i n the  design  geotechnical), are  instrumentation Chapter tank.  then  soil  analyses  the  are  A short  outlined.  i n v e s t i g a t i o n and is  techniques  and  F i r s t , the  discussed  (hydrodynamic, and  in  structural, installation  s e c t i o n on p l a t f o r m  chapter.  a geotechnical  serves  site  parameters  delineated. off this  construction,  environment  requirements  finishes  This chapter  observations  of p l a t f o r m s a r e  structures.  the offshore  construction  4 presents  geotechnical  these  offshore  selection,  Platform  procedures  types  the design,  for  s e l e c t i o n of g e o t e c h n i c a l  depth.  t h e major  detail.  of l o a d i n g the  and  3 i s concerned with  installation sources  described  case  purposes  study  of  of the E k o f i s k  demonstrating  a r e a p p l i e d o f f s h o r e and how  may be u s e d a s a c h e c k  on  design  how  performance  assumptions  and  predictions. Chapter thesis,  5,  deals  discussion  the  with  of  final  chapter  in  the f i r s t  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 .  the  wave  climate  i s given  that the  geotechnical which  i s used  maximum l o a d ,  characteristics discussed also  as they  serves Chapter  on  the  equivalent  for cyclic  i s given of  of  wave  the  particular loading  foundation  Methods  of  storm,  Finally,  on t h e f o u n d a t i o n analyses.  of  the  system a r e  This  chapter  o f wave  loading  section.  the q u a n t i t a t i v e aspects  system.  brief  s t u d i e s and t o d e t e r m i n e  a s an i n t r o d u c t i o n t o t h e n e x t 6 presents  design  attention.  pertain t o foundation  A  means i s d i s c u s s e d .  statistical  loading  of t h i s  and t h e m o d e l l i n g  o c e a n waves by wave t h e o r i e s and s t a t i s t i c a l The  part  determining  platform  9  stability merits  and  offshore that the  under  storm  shortcomings  gravity  there  stress  loading of  structure  are  each  are  then  method  discussed;  when a p p l i e d  emphasized.  It  the to the  becomes  clear  a r e two f u n d a m e n t a l a n a l y t i c a l l i n e s o f a p p r o a c h t o  problem: bearing  method.  wave  A  capacity  simple  to  use  a n a l y s e s of c l a y  Geotechnical  theory limit  and  the  equilibrium  foundations c a l l e d  Institute)  slip  finite  surface  method  the  NGI  method  element for total  (Norwegian  i s described  in  detail. In  Chapter  7 an a l t e r n a t i v e method o f a n a l y s i s  method o f s l i c e s of  the  i s presented.  NGI method.  This  and  hence  i s not w e l l  Janbu's  perform a g r a v i t y two d i m e n s i o n s . programs also  (1973)  structure This  be  known  among  method o f s l i c e s stability  was done so t h a t  modified  to perform  e x i s t i n g slope  8  computer  worked.  stress  The  analysis  versatility practical  of  value  program  i s described  application  the  a n d an e f f e c t i v e s t r e s s the  method  f o r working  The d i s c u s s i o n  of  although  primarily  applicable  to a l l large  i s shown. these  gravity  concerned gravity  GRAVSTAB  and s e v e r a l  of  stability  some o f t h e a n a l y s e s and  In  these analyses  adapted t o  although only i n  i n t h e u s e o f Sarma's s l i c e  a  Sarma's engineers  i s also  analysis,  lines  effective  practicing  faith  Chapter  the  (1973) method o f s l i c e s .  to i n s t a l l  perform are  may  i s along  I t i s a pseudo-three-dimensional  s t r e s s method b a s e d on Sarma's method o f s l i c e s  method  b a s e d on t h e  developed  to  example p r o b l e m s  method  analysis This  method.  t o both a  total  is  made.  The  method  i s of  great  types of problems. structures with  presented  platforms,  type o f f s h o r e  is  herein, generally  structures.  The  10  analytical  p r o c e d u r e s d i s c u s s e d and  applicable type  1  to  base,  any  offshore  whether  it  structure  is  facility.  developed  a  in this  thesis  are  with a m o n o l i t h i c g r a v i t y  platform,  light  tower,  structure  or other  A flare primarily  structure i s used for burning off excess methane, p r o d u c e d a l o n g w i t h o i l f r o m a w e l l .  flare  1  gases,  11  CHAPTER 2 THE  The  following  structures presently by  OFFSHORE GRAVITY TYPE STRUCTURE  discussion  includes  a l l t h e major  i n use and t h o s e  the . o i l  of  industry  offshore  gravity  types of g r a v i t y  type  structures  which a r e being  seriously  considered  f o r use throughout  the world  i n the near  future.  2.1  General  Characteristics  A gravity has  type  no s u b s u r f a c e  which p o r t r u d e horizontal  t o prevent  or r i b s  Skirts  have  from  through  In a r e a s  skirts  which  usually To  is  necessary prevent  failure  sliding be  added  used  ample w e i g h t  load. with  shallow  force  or the r a f t present  induced during  water  sediments  have  foundation  motions  installation.  a  et  structure.  ribs the  stronger adequate  and  a l ,  1979).  protection containing  They a r e t h e r e f o r e excavated.  vertical  or a  force  i n some p r o p o r t i o n t o t h e  respect to the  and  i s excavated,  a t t h e base of the s t r u c t u r e structure,  and  transfer  t o deeper,  (Huntemann  This i s accomplished  hence t h e name g r a v i t y  skirts  to  u n l e s s t h e f o u n d a t i o n h a s been  the  seabed  f e a t u r e s of p r o v i d i n g scour  f o u n d a t i o n must be m a i n t a i n e d horizontal  on t h e  sediments  where t h e s u r f i c i a l  sliding  beneath  upper  than  of the d i s t u r b i n g  c u r r e n t s and wave  grout  the  may n o t the  rests directly  foundation other  component  subsoils. strength  structure  shear on  the  maximum  by u s i n g a s t r u c t u r e o f  horizontal  forces  expected  -  12  There a r e g e n e r a l l y platform: North  t h e base c a i s s o n ,  Sea  concrete  t h e same The  features  deck  is  quarters  f o r t h e men  specific  equipment  platform.  also  up  who  caisson used  service the  A  typical  have  many  and o f t e n  platform  houses  equipment.  use o f t h e  and o t h e r  i n the towers.  platform  The base c a i s s o n  i s used  a s a b u o y a n c y chamber; t h e c a i s s o n  i s made  the l e g s .  2  The  The  risers  within  ( e i t h e r outwardly apparent  f i g u r e 2.1,  systematically  tank  or  soil  seated  by  ballast  t a n k s and o i l s t o r a g e  with  the  within  the  1.3) w h i c h  are  the s t r u c t u r e . and  the b a l l a s t .  as  compartmented  shown i n f i g u r e  ballast  i n t o the foundation increasing  storage  living  well  as with the E k o f i s k  to  driven  a s a work a r e a  housed  o f a number o f c e l l s in  gravity  i s shown i n f i g u r e 2.1.  somewhat d i f f e r e n t ,  f o r f r e s h water  installation  shown  platform  on t h e deck d e p e n d s on t h e e x a c t  Facilities  platform  of a l a r g e  t h e t o w e r s , and t h e d e c k .  although  used  be c o n t a i n e d  during  parts  a s t h e one shown.  requirements are often may  distinct  gravity  Other g r a v i t y platforms, of  three  the  structure  The c e l l s  facilities  The s k i r t s a r e is  firmly  a r e used a s both  when t h e  structure  is  operational. These  are  generally  particularly  those platforms  largest  t h e N o r t h Sea g i a n t s ,  in  2  platforms  of  t h e U. K.'s  Ninian  field  designed  in  massive  f o r the  a Doris 1978,  type  structures,  North  Sea.  structure  weighed  600,000  The placed tons  R i s e r s a r e p i p e s t h r o u g h w h i c h c r u d e o i l f l o w s o u t from t h e w e l l and up t o t h e p l a t f o r m i n t o be p r o c e s s e d , pumped, o r s t o r e d .  13  Figure  2.1  - Components o f an o f f s h o r e g r a v i t y t y p e platform ( A d a p t e d from K l i t z , 1980)  14  (Steven,  1981a).  building  from the  equipment) structure record  and  This base t o nearly  also placed  for  a  and  although  core  of  recovery.  they  are  (not  at  waters -  the  still  including  i n 1978  N o r t h Sea in  than  base.  152  A Sea holds  meters are  other very  structures  for General  jacketed  Offshore  s t r u c t u r e s and presently  jacketed  Generally,  the  steel  structures  discussed  story  the  deck  Tank  type depth  (Furnes,  1978).  as  offshore  large  a 50  the  nearly  with  large,  areas  indeed.  unusual  are  Clearly  design  and  form  the  jacketed i n the  types  Development gravity  used  structures  i n water depths g r e a t e r  deeper water, other  3  K.  i n the  The  used  wide  platforms  structures 3  deck  taller  requirements.  Platforms Steel  is  platform  enormous  construction  2.2  the  smaller,  are  as  gravity  gravity platforms  these  the  i n U.  Other  appreciably  platform  of  in  platforms offshore  are  structure,  much  hydrocarbon  more numerous.  and  the  following subsections, than about  250  structures will  t o 300 be  will  gravity not  meters.  be In  used.  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 i n 312 meters of water in the Gulf of M e x i c o i n 1980 ( M o r r i s o n , 1980a). The i n s t a l l a t i o n o f t h i s t y p e of s t r u c t u r e i n water of t h a t d e p t h i s not s e e n a s a t r e n d f o r t h e f u t u r e . The use of this type of structure was economically j u s t i f i e d s i n c e t h e p r i o r i t y was a l a r g e number of w e l l s w h i c h t h i s p l a t f o r m , w i t h i t s l a r g e base area, was able to provide ( M o r r i s o n , 1980b). Several 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 d e p t h s a r e p l a n n e d for use in the Santa Barbara c h a n n e l . A l t e r n a t i v e p l a t f o r m designs such as t h o s e d i s c u s s e d i n s e c t i o n 2.4 a r e not f u l l y d e v e l o p e d y e t .  15  2.2.1  Concrete The  concrete  platform  was  development jacketed at  Platforms  designed  to  of  Ekofisk  the  platforms,  that  time,  amount of  storage.  that  as  important  gravity  the  type  It  should  i t .  the  be  modified  requirement  steel  two  was  (large)  platforms include was  the Steel  existing  the  required  the  primary  d e v e l o p e d and  between s t e e l  the  gravity platform, are  different  comparison  fixed  for  N o r t h Sea.  for storage  types  jacketed  to  type  remains  jacketed  and  development.  jacketed  to  steel  the  field  platform  platform  the  not  remembered t h a t  A brief  Table  in  fixed offshore  applicable  of  field  gravity  requirements  only  for  considerations.  types  specific  f a c t o r when c h o o s i n g  be  The  and  prestressed)  g r a v i t y type platform  to  generally  and  meet  This  structures  alternative for  the  could  reason an  (reinforced  of  not  quite  the  a  an  replacement  and  concrete the  is  different  design  platform,  offshore  structure  two  structures,  and  production gravity most  type  common  i s presented  in  I. C o n c r e t e was  type  platforms  reasons,  some  skilled  better  concrete  is  life  steel  two  e x p e n s i v e and (Billington,  that  of  for  are  techniques  gravity  grade  of  has  concrete  a longer  (Stubbs,  is and  fatigue  1975).  s i n c e maintenance  i f even p o s s i b l e ,  of  less  structural steels,  important  difficult,  require  availability  r e s i s t a n t and  very  building  most common f o r a v a r i e t y  the  high  used  marine environment  r e p a i r s are 1979).  the  construction  corrosion  i n the  reasons  material  steelwork,  than  more  first  remains  than  generally  latter  and being:  labor  than  the  The is  offshore  16  Table I Comparison  of F i x e d Offshore  STEEL JACKETED PLATFORM  Platforms  CONCRETE GRAVITY  ADVANTAGES  ADVANTAGES -Much i n d u s t r y  experience  - G e n e r a l l y cheaper environments -Design  less  -Requires labor  little  -Greater p r o d u c t i o n c a p a c i t y  site-specific  -Good f o r a r e a s w i t h s o f t sediments  -Easy  to incorporate storage  -Short -Larger  installation deck  -Almost c o m p l e t e a t tow-out for early production start fatigue  -More c o r r o s i o n DISADVANTAGES  -Long, c o s t l y  skilled  labor  - I n f l e x i b l e to design/const, changes-very s i t e s p e c i f i c  storage  - D e s i g n more c r i t i c a l t o s p e c i f i c water depth - S e a b e d must be f l a t and l e v e l  -Difficult damage  -Requires  to inspect f o r  -Need more deep  fatigue  large  life  corrosion  resistant  from  (1974).  Bell  relatively  good b e a r i n g  -Need good knowledge o f shallow sediments  borings  -Problems with d r i v i n g diameter piles  Adapted  resistant  PISADVANTAGES  - R e l i e s on t h e a v a i l a b i l i t y of h i g h - g r a d e steel  -Less  life  installations  -Hard t o p r o v i d e  -Shorter  time  deep  -Longer  very  specialized  for mild  -More f l e x i b l e t o c h a n g e s during fabrication  -Requires  PLATFORM  soils  17  As been  of  1981, f o u r t e e n c o n c r e t e  installed  These  i n the North  platforms  Sea ( F u r n e s ,  are of four d i f f e r e n t  CONDEEP,  a n d Sea Tank d e s i g n s .  Ekofisk  tank  in  general  figure  the  Design  specific and  distinct. with  A  of  requirements  Hence, t h e s i z e summary  of  some o f t h e i r  Three c o n c r e t e coast  Brazil  Four  steel  these  gravity (Franco,  smaller gravity  1976)  and  the p e d e s t a l  type  platforms  Gravity  important  i s given  designs  especially  t r u e of the a l l - s t e e l  is  (Burns  A list  are  box-shaped  and  Sea g i a n t s . (Lalli,  and  D'Amorim,  type  s t r u c t u r e s i n the  of these  for particular  o f f the  offshore Louisiana  p l a t f o r m s made o f m a t e r i a l s o t h e r  special  water  i n Table II  built  features, i s given  primarily  somewhat f o r  o f f t h e Congo c o a s t  large offshore gravity  some o f t h e i r  fora l l  platform  shaped N o r t h  are  giving  same  in and  wave h e i g h t ,  one  platforms  Sea.  the  have been  than  o u t s i d e of the North  shown  features.  offshore Brazil  the only other  different  ( s t o r a g e c a p a c i t y and deck  platforms  platforms  These  design  the  techniques,  was m o d i f i e d  1977), and a f l a r e  world  Sea d e s i g n s  a n d shape o f e a c h  important  (Huntemann e t a l , 1979). significantly  criteria:  1981b).  i s that of  somewhat  analysis  Each p l a t f o r m type  production  installations).  along  conditions,  have  t h e D o r i s , Andoc,  The D o r i s d e s i g n 1.3) and l o o k s  platforms  Steven,  types:  the other North  on-site design  type  1978;  methods a r e , however, v i r t u a l l y  platforms.  depth,  in figure  appearance than  construction these  (shown  2.2.  gravity  1977),  platforms,  also  i n Table I I I .  than  concrete are  applications.  gravity structure.  This i s  A) CONDEEP DESIGN  B) SEATANK DESIGN  C) ANDOC DESIGN  Fig. 2.2 North S e a concrete gravity type offshore platforms (Compiled  from S j o e r d s m a ,  1975a) 00  19  Table II N o r t h Sea C o n c r e t e G r a v i t y DESIGN  FIELD/ COUNTRY  Doris  Ekofisk (Norway)  CONDEEP  WATER DEPTH  DESIGN WAVE  Platforms BASE WIDTH  PURPOSE  DATE  70  24.0  93  P-S  1973  Beryl A (U.K.)  120  29.5  100  D-P-S  1975  CONDEEP  Brent B (U.K.)  142  30.5  100  D-P-S  1975  Doris  F r i g g CDP1 (U.K.)  96  29.0  101  D  1975  Sea  F r i g g TP1 (U.K.)  104  29.0  72  P  1976  Doris  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  Dunlin A (U.K./Hoi.)  152  30.5  104  D-P-S  1977  CONDEEP  Statfjord (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  Doris  Ninian (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  Statfjord (Norway)  144  30.5  152  D-P-S  1981  Tank  CONDEEP  D=Drilling  A  B  P=Production  S=Storage  Note: A l l dimensions a r e i n meters.  T=Treatment Adapted  B=Booster  from F u r n e s  (1978).  20  Table I I I Gravity  Platforms  i n Other Parts  of the World  PURPOSE  DATE  3@ 1 8  1  D  1976  9.4  3@ 1 8  D  1976  89  9.4  3@1 8  D  1976  Loango (Congo)  89  9.4  3§18'  P  1977  Petrobas (Cone-Box)  RGdeNorte (Brazil)  13  ?  46x53  D-P  1978  Petrobas (Cone-Box)  RGdeNorte (Brazil)  13  ?  46x53  D-P  1978  Petrobas (Cone-Box)  RGdeNorte (Brazil)  13  ?  46x53  D-P  1978  ARCO (Cone-Box)  Louisiana (U.S.A.)  4  ?  23x34  D-P  1978  FIELD/ COUNTRY  Tecnomare (Steel)  Loango (Congo)  89  9.4  Tecnomare (Steel)  Loango (Congo)  89  Tecnomare (Steel)  Loango (Congo)  Tecnomare (Steel)  'This  design  has t h r e e  Note: D = D r i l l i n g  WATER DEPTH  DESIGN WAVE  DESIGNER/ CONSTRUCTION  base pads  (tripod)  P=Production  Note: A l l dimensions a r e i n meters.  Note: T h i s  list  may be i n c o m p l e t e .  BASE SIZE  1  1  21  2.2.2  Steel Steel  figure  gravity  2.3  (Lalli,  Platforms  were  1977)  including  first  and  one  platforms  installed  f o r the North  some s p e c i a l The  Loango  steel field  conditions Reeves, too  gravity  there which  unyieldingly  structure.  The  economically  on  of  storage  (Pile  was  driving  holes,  a  platform,  only the  areas  where t h e  legs  to  for  in  these and  its seabed  compensate  the of  (Lalli,  1976  These  developed  f o r use 1977),  uneven b o t t o m t o be  base  slab  provide  gravity  expensive  the  platform  to  Seabed  5  (McPhee  driven of  i n the  into  a  and and  concrete placed  r e q u i r e d amount on  base  pads.  would r e q u i r e a l l p r e b o r e d operation.)  arrangement  i s uneven o r for  were  in  locations,  s t r u c t u r e t h a t c o u l d be  sediments  tripod  in  e t a l , 1980).*  developed  for p i l e s  s e a b e d and  a steel-based  lengthy with  rocky  was  of a r o c k y  type  for other  which  coast  i s too hard uneven  shown  problems.  Congo  consist  one  t h e Congo c o a s t  (Agostoni  platform  the  the  built  features  foundation  off  1975)  Sea  to  off  are p r e s e n t l y being  p l a t f o r m s have some u n i q u e solve  similar  of  inclined  differences  in  The  l e g s , may by  Tecnomare be  jacking  topography  used i n up  the  (Offshore  "The i n s t a l l a t i o n of this platform 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 y a r d . The p l a t f o r m i s not e x p e c t e d t o produce before 1983 or 1984 (Steven, 1981c).  5  T h e p l a t f o r m was i n i t i a l l y c o n c e i v e d f o r g e n e r a l o f f s h o r e areas and later for c o n s i d e r a t i o n i n t h e S i c i l i a n c h a n n e l ; however, none of t h e s e p l a t f o r m s were e v e r b u i l t . The p l a t f o r m was fully d e v e l o p e d f o r use off the Congo coast where i t was first installed.  22  Figure  2.3 - Tecnomare s t e e l g r a v i t y t y p e o f f s h o r e (After L a l l i , 1975)  platform  23  Europe,  1974).  available and  stability  in  requirements  the North  that are  Sea  i s , one  event  skilled  p l a t f o r m was  primarily The  t o be  w h i c h has  the  very  i s not  structural  damage;  steel  f o r t h e Maureen  is  profitable,  r e l o c a t e d to a comparable was  site  chosen  speed  marginal  field,  pipelines  required.  In  the  s t r u c t u r e may  with  over  field  considerations  Since  the  and  shape.  potential.  removed and  was  i n Europe  Towing  reservoir  storage  force  built  is a so-called  limited  justified,  field  chosen  because of  Maureen f i e l d  economically that  had  labor  c o n t r i b u t e d t o the d e s i g n  gravity  1977).  not  highly  8500 k i l o m e t e r s t o t h e Congo.  steel  (Lalli,  no  i n t h e Congo, t h e p l a t f o r m s  towed t h e  A  Since  a  minimum  concrete  for  be of this  reason. Unfortunately,  steel, gravity  the  same  as  cost  and  setbacks  availability,  steel and  the  to b u i l d  them.  to the  concrete  s t r u c t u r e , not  2.2.3  Hybrid  on  figure  2.4.  features  of  structures. parents, namely:  but the  from many  for a highly will  skilled  r e m a i n as  a replacement  an  of  steel labor  alternative  for i t .  Platforms  Reeves,  a concrete  need  Hence, t h e y  hybrid gravity  McPhee and  suffer  jacketed platforms, primarily  force  The  platforms  1975)  raft. The  Two  the does  different is  for  an  steel offer  i t also suffers need  (Hansen  and  c o n s i s t s of a s t e e l  hybrid  both It  platform  a  space  platform designs attempt  jacketed  to  f r o m some  of  skilled  1977;  frame mounted are  shown i n  combine t h e  and  some d i s t i n c t  highly  Ingerslev,  concrete  best  gravity  advantages over i t s the  same  labor  problems, force,  the  24  Figure  2.4  - Hybrid 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 R e e v e s , 1975)  25  availability that  of high  t h e s e a b e d be  bearing  relatively  steel,  flat  and  and t h e r e q u i r e m e n t  level  with  design  installation attract  utilizes  a g r a v i t y base p r i m a r i l y t o c u t down  t i m e and c o s t a n d a s p a c e  smaller  lighter  wave  forces.  and t h e wave l o a d s  structure,  the  base  may  soils  overstressing  frame  Because  smaller  than  (McPhee  superstructure  the  in size  and  a l l concrete  and t h e o v e r a l l  Reeves,  1975).  a r e weak, t h e base s i z e may be i n c r e a s e d  (Hansen a n d I n g e r s l e v ,  1977).  and  the  installed,  then  The r a f t  space  that  upon c o m p l e t i o n The f i r s t  platform  be  built  at a protected  the r a f t  construction  method may be employed when an critical  by  construction.  No h y b r i d  2.3  for Arctic  Platforms Gravity  the  Arctic.  type  these  out  early  advantage  of  s t r u c t u r e s have y e t been  gravity  separately The s e c o n d installation  the  modular  installed.  Development  platforms  Among  before  are c r i t i c a l ,  much l e s s d r a f t .  taking  a  and  such as a f j o r d i s  floated  towing  is  with  for  restrictions  and tower a r e  stability  location  allows  maintaining  date  independently  nearshore  c o n s t r u c t i o n method  t o be u s e d when d r a f t  nearby;  flexibility  may be towed t o t h e s i t e  i s , when no deep water c o n s t r u c t i o n s i t e  located  to avoid  frame may be c o n n e c t e d and t h e  deck mated, o r t h e components may  tow-out.  If  the s o i l .  Two c o n s t r u c t i o n methods a d d t o t h e p l a t f o r m ' s  joined  to  the s u p e r s t r u c t u r e i s for  be d e c r e a s e d  r e d u c e d by 65% t o 75%  bearing  type  adequate  strength.  The  weight  grade s t r u c t u r a l  have a l s o been d e s i g n e d  designs  for  use  a r e t h e monocone ( S t e n n i n g  in and  26  Schumann, 1980),  1979) a n d m u l t i p l e - l e g  f o r shallow  Horizontal  geometry. area  i c e loads  The  exposed  surface  to thinner  piercing cylindrical i c e flows,  flexure  of  lateral  loads  The  monocone steel  to  ice  scraping  to  of  resist  Artificial  flexible  the  the t h i c k e r  sections  5  i c e sheets i n reducing the  from  also  consist that  horizontal to resist  load  failure  gravity sufficient  (weight) t o r e s i s t  failure  The  covered  with  flows.  type  have  wall  been p r o p o s e d f o r Sea,  within  - which  structure, vertical  since force  from h o r i z o n t a l  These  attached v i a  to transfer  the  i s of s u f f i c i e n t Although the  or s t e e l ,  stability on  recently  sector.  the i s l a n d .  not concrete  including 1978) a l s o  was  sections  i c e loading core  No  structures.  structures  steel  of s o i l ,  concrete.  (de J o n g a n d B r u c e ,  these  to the s o i l  i s built  a a  eight  more  installed.  gravity  c a n move under  shearing  core  fundamentally  of  is  ice  i n the Beaufort  structure of  than  moving  islands  which  concrete  have y e t been are  One  gouging  reinforced  structures  2.5.  joints  providing  Beaufort  reduce the  conical  by Dome P e t r o l e u m , L t d . i n t h e C a n a d i a n  structure's  by  leg(s)  thereby g r e a t l y  and  artificial  retained  in figure  structures  size  of  drilling  caisson  large  islands  types  completed  the  i s made o f s t e e l ,  damage  p l a t f o r m s of e i t h e r design  shown  to f a i l  structure  i s constructed  exploratory  structures  on t h e s t r u c t u r e .  armor  Several  while  compression,  multiple-leg  resistant  of  Forbes,  a r e r e d u c e d by t h e n a t u r e o f p l a t f o r m  are designed  instead  and  These  i c e - i n f e s t e d waters  below t h e s u r f a c e  the  (Kliewer  b o t h o f w h i c h a r e shown i n f i g u r e 2.5.  were d e s i g n e d Sea.  structure  the  loading.  i t is  i s achieved foundation  (a) Multiple Leg Gravity Type  (b) Monocone  (c) Caisson Retained Island  Figure  2.5 - A r c t i c p l a t f o r m d e s i g n s ( C o m p i l e d from (a) K l i e w e r and F o r b e s , 1980, (b) B e r c h a and S t e n n i n g , 1979, and ( c ) de J o n g and B r u c e , 1978)  28  2.4  Deep Water P l a t f o r m s a n d O t h e r For  water  installing  deeper  gravity  are  economically  (Moinard,  1979),  water In  depths  deeper  Michie, The  A  t h e guyed  2.6. of  tower  subsea  1979) w i l l  and  as w e l l  platforms,  tanker loading  uneconomical.  completion  They  and  structures  structures  have  a l , 1979), 1978),  systems  column the  a l l which a r e t o be u s e d  in  1980b).  (Burkhardt  economical  towers,  been  and  (Morrison,  and  to areas with small  and  solution.  tension  leg  reservoirs  of  as t o purposes other than d r i l l i n g or structures,  t e r m i n a l s where t r a d i t i o n a l  light  force  somewhat  a l l motion.  instead The  towers,  d e s i g n s would  a r e d e s i g n e d t o be c o m p l i a n t , t h a t  prohibit  recovery  the a r t i c u l a t e d  the only  such a s : f l a r e  move w i t h t h e d i s t u r b i n g rigidly  of  and F r a n k s ,  guyed  cost of  alternative  structures are l i k e l y  structures,  potential  production  jacketed  (Finn et  probably a f f o r d  the  make h y d r o c a r b o n r e c o v e r y  use i n c l u d i n g  (Falkner These  to  number  platforms are also applicable limited  steel  meters,  between 300 a n d 600 m e t e r s  water,  articulated  and  required  water  l e g platform  shown i n f i g u r e  300  In t h e s e waters,  attractive.  f o r deep  tension  6  therefore  proposed  about  platforms  increases very r a p i d l y . methods  than  Structures  is,  of t r y i n g  forces acting  be  they  to act on t h e  The depth a t which these structures become u n e c o n o m i c a l 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 state of current technology, the a v a i l a b i l i t y o f a l t e r n a t i v e r e c o v e r y methods, the n a t u r e and s e v e r i t y of environmental loading, and t h e estimated volume of r e c o v e r a b l e h y d r o c a r b o n s . T h i s d e p t h was c h o s e n b a s e d on c u r r e n t p u b l i c a t i o n s . The e c o n o m i c a l depth of monolithic g r a v i t y t y p e p l a t f o r m s may be l e s s t h a n t h i s - a b o u t 200 m e t e r s .  29  (b) Articulated Column  (c) Tension-legged Platform ( A f t e r McPhee and Reeves,  Figure  2.6 - P r o p o s e d d e e p - w a t e r p l a t f o r m s  1975)  30  structure are For  a r e t h u s r e d u c e d and  therefore  these s t r u c t u r e s ,  foundation and  system  loading  in  of  The  106  and  Sources  many  and  Another Offshore Houston,  (Burns  North  used  choice,  as  piles)  being  Sea  used  for  1975b) and  (Sjoerdsma,  D'Amorim,  1977).  flare  for tanker 1975b)  magazines  (Moinard,  list,  the  concerned  However,  s o u r c e of  Technology Texas.  are  i n water  no  built  depths  of  1979).  reader with  and  the  is referred  offshore  Ocean I n d u s t r y , O f f s h o r e ,  Journal,  good  structures  and  P l a t f o r m Technology  updating this  Gas  a  here.  (Sjoerdsma,  and  Sea  150 m e t e r s  o f New  specifically: Oil  to the a l t e r n a t i v e  i s presently Sea  be  designs.  o r p r o d u c t i o n p l a t f o r m s o f t h i s d e s i g n have been  date.  For  North  required  for t r a d i t i o n a l  t y p e base may  interest  column  the  Brazil  drilling  between  of  than  t e r m i n a l s i n both the North  offshore  2.5  (as o p p o s e d  articulated  structures  less  the g r a v i t y  they are t h e r e f o r e The  to  significantly  t h e amount of m a t e r i a l s  oil  i n f o r m a t i o n a r e the which  several  technology,  Offshore Engineer,  J o u r n a l of P e t r o l e u m  Conference  to  Technology.  Proceedings is  held  The  of  annually  the in  31  CHAPTER 3 DESIGN, CONSTRUCTION AND  3.1  Preliminary  Considerations  Before a platform sources of loading necessary  INSTALLATION  c a n be d e s i g n e d ,  some a s s e s s m e n t  f o r the p a r t i c u l a r area  environmental  and  of  the  must be made, and t h e  geotechnical  design  parameters  chosen.  3.1.1  Sources of Loading The  sources of  numerous  and  of  loading  varying  locations. . Generally,  in  an  offshore  degrees  of  environmental  loads  primary  t h a t may a c t on an o f f s h o r e  loads  3.1.1.1  Environmental  Environmental  into  loads.  two  Figure  structure.  Loads  loads  are defined  loads  acting  caused  by i n t e r a c t i o n between moving  such  an  offshore  a s : w i n d , waves, c u r r e n t s ,  to bodies induced  such as i c e by  earthquake  induced  Environmental inclined,  thermal  loads  categories: 3.1 shows t h e  as loads  caused  phenomena - t h o s e o v e r w h i c h man h a s no c o n t r o l . on  are  importance a t d i f f e r e n t  t h e y may be b r o k e n  and o p e r a t i o n a l  environment  structure  or flowing  and soil,  the  structure,  gradients,  and  (4) f o r c e s  transmitted  in  (1) t h e f o r c e s the  impacting  accelerations  Environmental  include  fluids  by n a t u r a l  structure,  (2) f o r c e s due (3)  stresses  r e s u l t i n g from  the  to the foundation  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  structure. are generally i n nature.  32  WIND  SERVICE  J V A \ ^ W V W EARTHQUAKE  Figure  3.1  - Loads a c t i n g  on an o f f s h o r e  structure  33  3.1.1.2  Operational  Loads other operational and  than  vibrations  by i n t e r a c t i o n  loads,  or f l o a t i n g  necessary notable  only  on  with  caused  by  as s e r v i c e or  moving  support  vessels,  under  such  as:  i t s foundation or  with a  by  may be l o a d s  fluctuations  temperature.  either  minor  loads  large  surface  vessel  values  affect  imposed on t h e s t r u c t u r e  in  o i l storage  quantity,  These  l o a d s may be s i g n i f i c a n t and  both  minimum a n d maximum v a l u e s o f  i n design;  f l u c t u a t i o n s must be  Minimum  usually  with  o f t h e deck s t r u c t u r e , w i t h t h e  collision  there  be c o n s i d e r e d  weight  are  mooring  power.  Additionally,  density,  These  the design  being  equipment  o r w i t h i n t h e s t r u c t u r e , and those  vessels.  for  exception  (tanker)  must  are c l a s s i f i e d  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  flying  and  environmental  l o a d s and i n c l u d e t h o s e  machine  caused  Loads  specified  stability  for  foundation  (overturning)  design.  a s do maximum  values ( o v e r s t r e s s i n g ) . Eccentric varying tanks. be  distributions The l a t t e r  designed  3.1.2  the often  foundation  by  may be s i g n i f i c a n t  and  must  either  f o r or prevented.  Design  environmental  identified,  appropriate  the  o f deck e q u i p m e n t a n d o i l i n t h e s t o r a g e  of these  Environmental After  been  l o a d s may a l s o be imposed on  design  and a c c e p t a b l e  regulatory have t h e i r  agency  Parameters conditions  for  parameters  must  methods.  with  own s t a n d a r d s  This  the chosen area be  chosen  have using  i s u s u a l l y o u t l i n e d by  jurisdiction (Department  i n the case of  Energy  who  will  (U.K.),  34  1974;  Department  Veritas  of  (Norway),  (France),  the  1977;  1977).  In  by t h e u n d e r w r i t e r  the  owners,  recommendations Institute  the world's  de  l a Precontrainte  requirements  may a l s o be s e t  (e.g. L l o y d ' s R e g i s t e r of Shipping) or  sometimes  such  listing  as  use  those  professional  of  the  of environmental  offshore areas  the table w i l l  harsh  1979; D e t N o r s k e  society  American  Petroleum  (1978).  A partial  at  (U.S.A),  Internationale  some c a s e s ,  forth  who  Interior  environmental for  i s given  show t h a t  are  specific  listed  and may be more  or  i n Table  IV.  for  some  A quick  of  glance  offshore platforms are subjected to  conditions.  table  parameters  The r e s u l t s  locations less  within  severe  presented  i n the  the o f f s h o r e areas  than  those  at  other  l o c a t i o n s w i t h i n the area.  3.1.3  Site  Selection  and S o i l I n v e s t i g a t i o n s  Gravity  type  free  of l a r g e  b o u l d e r s and o t h e r o b s t r u c t i o n s  the  base  of  the  structures  structure  f o u n d a t i o n may be p r e p a r e d preparation at  is.limited  least  on a g r a n d  underwater  equipment  extended  this  depth  uniform  to prevent  require  when  prior  t o water scale and  during  not  be  less  than  1974).  excessive d i f f e r e n t i a l  i f skirts  may  damage  unless the Foundation  70 m e t e r s deep -  Recent  technology  strength  so s t r o n g a s t o p r e v e n t  installation  about  seafloor  advances i n  have  probably  S u r f a c e d e p o s i t s must be somewhat  n e c e s s a r i l y p o s s e s s i n g adequate must  that  installation.  (Gerwick,  somewhat.  level  i t i s installed,  to  diving  a fairly  s e t t l e m e n t and, w h i l e for  stability,  they  the p e n e t r a t i o n of s k i r t s  a r e adopted  i n the d e s i g n .  35  T a b l e IV E n v i r o n m e n t a l D e s i g n C r i t e r i a F o r Some O f f s h o r e A r e a s  GROUND WAVE CURRENT TIDAL WIND ICE HEIGHT FLUC. THICK, ACCEL. SPEED SPEED (m) (m) (m) (g's) (m/s) (m/s)  AREA  B a l t i m o r e Canyon (Ward e t a l , ' 7 7 )  30.0  ?  B e a u f o r t Sea (Kliewer+Forbes,'80)  12.5  ?  G e o r g e s Banks (Ward e t a l , ' 7 7 )  25.2  1  -  ?  5.0  ?  ?  -  ?  Gulf of Alaska (Augustine e t al,'78) (Bea a n d Akky,'79)  40.5 34.0  ? ?  ? ?  G u l f of Mexico (Haring+Heideman,'78) (Berman e t a l , ' 7 8 )  22.8 26.5  ? 2'.7  2.2 ?  N o r t h Sea ( O f f s h o r e Europe,'74)  30.5  ?  ?  36 54"  Offshore B r a z i l (Burns+D'Amorim,'77)  16.0  1 .8  1.9  38  ?  ?  O f f s h o r e Congo (Lalli,'77)  9.4  ' I n c l u d e s a 0.3 meter 2  Includes  both  3  One h o u r  sustained  "Gust 5  2.8  ?  (several  One m i n u t e  lunar  lunar tide  seconds) speed  2  -  ? ?  surge  ? 0.41 ? ?  3  -  ?  5  -  ?  ?  and a 2.5 meter  and storm  speed  sustained  tide  -  ? ?  ?  storm  surge  36  Another adequate  and  etc.)  requirement  strength  operational loads  site  life;  the  on  to  support  this  structure  both  subsurface  of  a  since  gravity  basic  type  concerns  preliminary  are  the  modification  of  dictated  a  by  a  large  kilometers  or more.  conducted  to  be  placed  site  for  one  in  At  made  be  done t o t h e  site design  using  information  from the  for  an  this often  offshore  platform  met  by  area,  on  most  the  unknown.  i n the  used  1976).  the of  order the  likely  t y p e and The  be  to  of  optimize  platform(s)  several  square  specified  area  sites  place  lines  N o r t h Sea  to  platforms and  are  is  reservoir  the  number of  survey  There  The  installing  survey  the  time,  can  is  test  is a to holes  illustrated  3.2.  Geological are  be  such survey conducted  figure  a  These  Ruiter,  A general  determine  are  generally  must  i s u s u a l l y enough t o d e t e r m i n e  (de  usually  fairly  platform(s).  is  o i l reservoir considerations.  conditions  r e q u i r e m e n t s may within  compaction,  settlement.  a l w a y s , however, some l a t i t u d e t h a t foundation  may  cyclic  regards to  investigated which  earthquakes,  site.  selection  primarily  This  structure with  surveys,  a d e q u a c y of The  little  (waves,  design  displacements,  s e c o n d a r y c o n s o l i d a t i o n , and  requirement  under  its  elastic  to  limits.  throughout  Additionally,  p r i m a r y and  tolerable  due  have  deposits.  of  within  structure  soils  stability  settlement  be  bearing  r e p e t i t i v e loading  various the  the  the  includes  e f f e c t s of the  i s that  of  i n v e s t i g a t i o n s , both the  proposed area.  r e g i o n a l and The  regional  site survey  specific, is  often  1  1  1  1  1—:  lettooo  LEGEND Soo mtfres  »  f  *J  Figure  S\J*.-/& vEUEL-i  •  TrtAtK. W I T H T I " PCSITIOWS cXPLeCKTieWWCU.  BoftCHOuE  •* U N I rerJmwnoN TEST c-  3.2 - P l a n o f s u r v e y l i n e s - g r i d : l o c a l t r a n s v e r s e ( A f t e r O f f s h o r e ' S o i l M e c h a n i c s , 1976)  38  made u s i n g o n l y p r e s e n t l y area  i s investigated,  such a s : t h e l o c a t i o n tectonic  regional  submarine canyons, On-site  and l o c a l  and  bathymetry. time  Acoustical impart  pulse  subsurface s t r a t a .  information  streamers  on  the  less  or  Boomer)  upper  sediments,  those  the ship. which  disturbance. through  back  by  the  a r e p i c k e d up 1974).  used  less  of  a sound  travelling  signals  to  than  (Sparker) surveys a r e of deeper  at  by e i t h e r  are  The  angles  t h e same  reflected  surveys  survey  made  or a r r a y s ( O f f s h o r e Europe,  the c h a r a c t e r i s t i c s  strata,  High gather  about  30  conducted  although i n  detail.  Some s e a b e d geotechnical  is  to  area a r e found  (Sparker)  The r e t u r n i n g  m e t e r s deep, a n d low r e s o l u t i o n determine  proximity  transducers  transmission, after and  assessed,  features,  water  (Boomer), o r s p a r k  the seabed  (Pinger  the  and  i n length.  i n the proposed  to  clays,  outfitted  meters  seafloor  the  a n d B e a , 1977).  i s done u s i n g e l e c t r o n i c  acoustical  reaches  resolution  somewhat  of d e p o s i t i o n ,  of  to factors  are  Geophysical seismic surveys are  acoustical  by h y d r o p h o n e  to  influences  one h u n d r e d  minor  paid  deltaic  (Garrison  water depths  profiling  resulting  various  attention  a s t h e b a t h y m e t r i c a l s t u d i e s a n d from  an  the water,  rates  history  a r e made u s i n g s p e c i a l l y  (Pinger), mechanical The  The  channels,  and p e r m a f r o s t  p a t t e r n s of  slopes,  same  of b u r i e d  studies  distribution  from  with p a r t i c u l a r  some o f w h i c h a r e o v e r  local  data.  movements. ' E n v i r o n m e n t a l  including:  ships,  available  samples  knowledge  are of  critical  t o the design of a  samples  are  taken  necessary  the  upper  gravity  with a g r a v i t y  to  provide  sediments  type  specific  - those  structure.  corer, vibratory  most  Shallow  sampler, or  39  other  sampling  device.  used t o c h a r a c t e r i z e samples boring the  are  taken  A l t e r n a t i v e l y , cone p e n e t r o m e t e r s may be the  surficial  sediments,  forcorrelation  purposes.  design. tests  within  The should  the  range  of  other  locations  respect  located  When  site  a  planned  field  survey  must  and  extent The  of tens  be  before  the ship  by  the  allow  (McClelland,  them t o 1977).  data  from  be A the  of  (Hitchings  consultant's  on-board  p e r day f o r a  1974); t h e r e f o r e , t h e p r o g r a m  prepared  by  et  i n v e s t i g a t i o n s i s extremely  i s on-site.  are supervised  of i n - s i t u  investigated  (Braun,  t o make o n - t h e - s p o t  base  The  of thousands of d o l l a r s  thoroughly  Engineers  continuously  to the transponders.  for further investigation, a  of o f f s h o r e  s h i p and crew  operations  1976).  and  p r o g r a m must be d e v e l o p e d  cost  large  other  an a r r a y o f  a l l boreholes  surface  has been c h o s e n  The  performed  locating  future  tests.  on t h e o r d e r  is  foundation  the  by d e p l o y i n g  by t h e t r a n s p o n d e r s the  to  s e l e c t i o n may be made b a s e d on  high,  consultant  with  from  site  1976).  testing  be a c c o m p l i s h e d  s i g n a l s emitted  aforementioned  carefully  may  accurately  and  preliminary  for  relative  known  on t h e s e a f l o o r  readily  i n f o r m a t i o n on  be  transponders  electrical  one d e e p  and t h e l o c a t i o n s o f o t h e r  This  test  interest  some  p o s i t i o n s of boreholes  structure.  of  At l e a s t  (100 t o 150 m e t e r s ) i s r e q u i r e d t o p r o v i d e  sediments  al,  provided  by  the  geotechnical  A l l geotechnical geotechnical  his  inspectors  monitor decisions  the about  testing  personnel  and  (de R u i t e r ,  incoming  data  the  location  within  the area  tests.  the  i n the f i n a l  platform  should  o n - s i t e survey.  fall The  structure  once  40  on-site site  can  positioned  since i t w i l l  current be  be  be  excitation.  established  explored.  The subject  c o n s t a n t l y i n motion The  and  expected  will  E r r o r margins  (McClelland,  in positioning  investigation constant  equipment c o n n e c t e d  success  motion,  has  not  in-situ  rests  the  directly  the  surface  hydraulic The follow used  on  site  and  of t h e a r e a  50 m e t e r s a r e  testing  ship  drillstring  (Taylor, not  course.  be  which  is  good  flexible  too l a r g e ,  the  is  or p i e c e of developed  1976),  however, Therefore,  rigid  control  I f not,-an  well  that  connection  cables  about  their  will  not  planned,  from  tests.  and  alternative  on  three to f i v e  the  0.5  meters,  such  as  site  may  and  is kept  boulders  unless  must  be  If they  are  they  have t o be  boreholes  of  the  scan  submersibles  assessed.  suitable  uniformity  shallow  tests  using side  A number of b o r i n g s a r e made t o v a r y i n g d e p t h s . depend  not  text.  significance be  early  does  T h i s s h o u l d be  i s mapped i n d e t a i l  Obstacles  and  site  although  following  to  1976). located  Generally  be  typical  equipment  r e q u i r e s no  for later  topography  accurately  tests  to  which  achieved.  Information gained  t h e need  seabed  (de R u i t e r ,  of  must  been  i s done w i t h  and  only  a  e q u i p m e n t has  will  investigation,  i n mind when r e a d i n g t h e  removed.  size  from  i s any  Special  seafloor  vessel,  to determine  sonar,  positioning  and  lines.  a strict  The  as  f o r t h i s motion  whenever p o s s i b l e ,  to  proposed  in  of  i s conducted  to i t .  t o t r y t o compensate complete  the  the  under wind, wave,  accuracy  govern  over  1977).  site to  only approximately  soil  can  be  chosen. The  number  profile.  ( t o 30-40 m e t e r s )  and  41  at  least  one  (de R u i t e r ,  deep  1976).  absolute  minimum  intervals  of  less  1.0  drilling  Three  Samples  are  usually  checked  for quality.  tests,  including  grain  size  exit  The  e t c . ) and  triaxial,  and  then  can o n l y  (Low,  1975).  for  and  on-board  (Atterberg  limits, tests,  laboratories,  complex  be the  classified,  unconfined compression  other  an  taken at  since  selected  classifications  as  taken  on-board,  while o t h e r s are prepared f o r the on-shore consolidation,  soils  are  are  sunk  15 m e t e r s ,  a t the s e a f l o o r  Some samples  distribution,  suggested  first  samples  extruded  routine  are  Samples a r e u s u a l l y  1977).  where  cuttings  been  over the  (McClelland,  and  100-200 m e t e r s )  has  1976).  meters  with c e r t a i n t y  mud  (to  corings  (George, t o 1.5  frequently  identified  borehole  t e s t s are  where carried  out. Cone  penetrometers  uniformity  of  resistance  that  during  and  will  density  depends  on  the  7  They  of sands.  are  profiling  also  to  to e s t i m a t e the the used  dowels for  check  the  penetration and  skirts  classification  the u n d r a i n e d s t r e n g t h of c l a y s The  uniformity  being t y p i c a l  acoustical  extensively  be e n c o u n t e r e d by  for estimating  relative  fifteen  used  s h a l l o w d e p o s i t s and  installation.  purposes  are  of  numbers on a f i n e  number the  of  penetration  soil  profile  (de R u i t e r ,  1976).  grid  may  and  tests  with five  to  Additional  be n e c e s s a r y i f a b r u p t  'Dowels a r e cantilever rods which j u t o u t o f t h e base of t h e p l a t f o r m 5 m or so. They a r e u s e d t o stabilize the structure and prevent i t from moving w h i l e i t i s b e i n g b a l l a s t e d and t h e s k i r t s a r e b e i n g imbedded.  42  changes  in  stratigraphy  are detected  (de R u i t e r ,  valuable  qualitative picture  logs  may be u s e d t o a s s e s s t h e r e l i a b i l i t y  that  i spresented  from cone  D o w n - t h e - h o l e p e n e t r o m e t e r s may be u s e d t o measure t h e d e n s i t y Gamma  ray  logging  increase  i ncost.  picture  of  showing These  soils  clays  Selection  ray  and  l o g provides  i s useful  and  interpreted samples. making  the presence  important  of  seemingly  The  a  cohesive  cone  tests.  t o those in  uniform  penetration for  continuous  on  established  areas  with  of  since  i s not  design  laboratory  profiles  of  the  varying  both are  gamma r a y l o g s , a n d  correlations.  and f o r  The i n - s i t u  profile scale  material  a continuous record  available.  and a r e features, in  larger  of the d r i l l  The r e s u l t s o f one s u c h  i n f i g u r e 3.3.  parameters  tests  from  i d e n t i f y i n g the deposits  i n t e r p r e t a t i o n a r e shown necessary  mentioned,  data  borehole  logs,  picture  lenses  layers,  cuttings  Other  Design  based  The  penetrometer  seams o r  soils.  gamma r a y c o u n t .  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 s m a l l  such as t h i n  borehole  a r e chosen  Samples a r e u s e d  provide  or  Parameters for  in-situ  site-specific  continuous  1977).  of S o i l  from  a  as a q u a l i t a t i v e t o o l  t e s t s which a r e a p p l i c a b l e  parameters  laboratory  mud  f o r a minor  and  (McClelland,  boreholes  be done down t h e b o r e h o l e s  gamma  of  data.  sediments.  borehole  vane s h e a r  of boring  deeper  a r e marked by an i n c r e a s e d  Design  tests  The  strength  A  penetration  i n deeper  t e s t s may be c a r r i e d o u t i n a d d i t i o n  including  3.1.4  can  stratification  in-situ  soft  the  and shear  1976).  and  are  in-situ  found methods  by  using properly  43  Soil profII* Fine to medium umd with diell froamentt (dente)-  Small tilt fraction Few imotf graved 10-H  Grey tilty cloy with teoms of fine land and tilty landdtiff fo very stiff)  15 Fine fa medium land (dense) Seomi of silry clay  •£ a. O  2 5  Grey illty clay with teomt of lilt and tilty fine umd(very ttlff)  Silly land layer? Silly land layer? 35  I—40-  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 cone p e n t r a t i o n t e s t G e o r g e , 1976)  a s i d e n t i f i e d by b o r e h o l e , a n d gamma r a y l o g g i n g ( A f t e r  44  correlated obtain the  t o the o f f s h o r e s i t e .  consolidation data.  foundation  are  found  from  t e s t i n g may are  best  with  value  stress-strain  the e f f e c t i v e  triaxial  determined  When c h o o s i n g the  and  tests.  a l s o be done.  penetrometer modulus  soils  The  Oedometer t e s t s  shear  Simple  in-situ  shear  tests,  sensitive  design parameters  limitations  imposed  i n v e s t i g a t i o n s at  sea  "one  by  and  direct  have  to  be  of  shear  modulus  such  as  values the  cone  charts.  The  t o sample d i s t u r b a n c e .  s h o u l d a l w a y s be  the  to  s t r e n g t h parameters  t h e a i d of e m p i r i c a l c o r r e l a t i o n  is particularly  used  characteristics  R e l a t i v e d e n s i t y and  from  are  conditions  carried  aware  under  out,"  of  which  (de R u i t e r ,  1976). Obtaining difficulties, - The -  the  strength  t o o b t a i n samples of h i g h  scatter  shear  natural variability  When  choosing  which  i s t o o c o n s e r v a t i v e may  having  to  reasonable is  a profile,  be  spent  factor  obtained,  complete  loss  presents  many  of  to  t e s t s are  applicable  too  to  the  of o f f s h o r e d e p o s i t s  i t must be  remembered  result  increase  in  liberal  multi-million  t h a t an  millions  an  or  estimate  dollar  estimate  of  the p l a t f o r m s i z e  safety against s l i d i n g  while of a  quality  in laboratory data  - D e c i d i n g w h i c h t y p e of p r o b l e m (Rowe, 1975) - The  parameters  some b e i n g :  ability  Inherent  shear  dollars so t h a t a  bearing may  failure  result  investment  i n the  and  many  lives. Results particular  of both  site  in-situ  are presented  and  l a b o r a t o r y shear  in figure  3.4.  The  tests  for  one  interpretation  45  CONE RESISTANCE 0  500  COHESION c (kPa)—•  fkPal—  WOO 1500 2000 2500  0  40  60  80  100  CD <  IUJ  CO I 1-  CL  g  I  Figure  3.4 - C o m p a r i s o n o f s h e a r s t r e n g t h v a l u e s f r o m sample t e s t i n g and f r o m CPT ( A f t e r de R u i t e r , 1976)  46  of  this profile  prejudices. conditions  i s certainly  subject to  A t h o r o u g h knowledge o f t h e t y p e s under w h i c h t h e y  making s u c h  a decision.  were  Platform The  design reader  opinions  and  o f t e s t s and t h e  is  essential  results  when  provide a  data.  Design  basic design  discussed  performed  The cone p e n e t r o m e t e r  u s e f u l c h e c k on t h e l a b o r a t o r y  3.2  personal  briefly  considerations for a gravity  in this  procedures  are  section. beyond  i s therefore directed  Detailed  the  platform are  descriptions  scope of t h i s  to references  thesis.  i f a deeper  study  of The is  required.  3.2.1  Hydrodynamic Hydrodynamic  the  structural  nature  of  distributions vary of  both the  the in  engineer  with  i n f o r m a t i o n on and  caused  by t h e s e  loads  found  components. from  to  the s p a t i a l  the  to provide  magnitude  loads.  The  a r e r e q u i r e d f o r the  The  total the  and  pressure  on t h e s t r u c t u r e , w h i c h  integrating  will  design  f o r c e s a c t i n g on t h e  pressure  distributions  coordinates, are required f o r the  The n a t u r e  and the f o u n d a t i o n  o f wave  system  loading  i s discussed  on  both  in detail  5.  Wave l o a d s a r e u s u a l l y by encountered.  developed  wave  and t e m p o r a l l y ,  of the f o u n d a t i o n .  structure  loads  performed p r i m a r i l y  current,  various  Chapter  are  wind,  respect  design  analyses  spatially  structure, with  Analyses  to calculate  Many  far  the  analytical  most  important  procedures  fluid  have  been  t h e f o r c e s due t o waves i n t e r a c t i n g  with  47  gravity  type  model t e s t i n g  structures. i s often  (Garrison,  1977), s i n c e  irregular  shapes,  that  In a d d i t i o n  employed  to provide a  hydrodynamic  interference  to theoretical  theories  except  on  laboratory  Analytical  methods  are  individual  members  of  members  used the  to  such  problems  c o e f f i c i e n t s (which on  small  calculate  structure,  scale  the  since  are  models).  forces  modelling  on these  individually i s impractical.  Scour p o t e n t i a l acceptable  i s investigated  analytical theories  very  r e l i a b l e due t o s c a l e  and  difficulties  qualitative  tests.  Model  tests  towing  in  picture  from t h e s e  Europe,  effects  model t e s t s  and  the s o i l .  invaluable motions,  since  Schiller,  However, a  heavily  For and  these  for providing floating  operations,  a r e - always  1979) valuable  s c o u r p o t e n t i a l may be  drawn  information  stability,  and submergence b e h a v i o r when t o u c h i n g down  1974).  no  Even model t e s t s a r e n o t  (Maidl  of the o n - s i t e  and  using  exist.  modelling  are  resistance  stability,  upon  tests  results  by a p p r o x i m a t e . n u m e r i c a l  methods o r t h r o u g h t h e u s e o f e m p i r i c a l based  on  cannot account f o r  e f f e c t s , and o t h e r  e x i s t with r e a l s t r u c t u r e s ,  usually  check  analyses,  on  damage (Offshore  model t e s t s a r e r e l i e d  incorporated  into  the  design  procedure.  3.2.2  Geotechnical After  Analyses  preliminary  s u r v e y s a r e c o m p l e t e d and a d e t a i l e d  investigation  has  platform  comprehensive  site,  been  a n a l y s e s a r e summarized  carried  out  geotechnical  i n T a b l e V.  for  a  possible  analyses begin.  site  gravity These  48  Table  V  G e o t e c h n i c a l C o n c e r n s F o r O f f s h o r e G r a v i t y Type  1)  Platforms  INSTALLATION A) P e n e t r a t i o n r e s i s t a n c e o f d o w e l s and s k i r t s B) P o r e p r e s s u r e d i s s i p a t i o n a n d e x i t o f c o n f i n e d water C) B e a r i n g p r e s s u r e on c e l l s and s l a b D) G r o u t i n g p r o c e d u r e s  2) CONTACT BETWEEN SEAFLOOR AND STRUCTURE A) S c o u r a r o u n d o r under s t r u c t u r e B) Reduced a r e a f o r b e a r i n g o r s l i d i n g r e s i s t a n c e 3) S T A B I L I T Y UNDER PSEUDOSTATIC LOADS A) S l i d i n g B) B e a r i n g f a i l u r e C) O v e r t u r n i n g 4) SETTLEMENT A) Immediate e l a s t i c B) P r i m a r y c o n s o l i d a t i o n C) S e c o n d a r y c o n s o l i d a t i o n D) C u m u l a t i v e s t o r m a n d / o r e a r t h q u a k e effects 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 s h e a r s t r e s s r e v e r s a l s 5) DISPLACEMENTS UNDER PSEUDOSTATIC LOADS A) H o r i z o n t a l d i s p l a c e m e n t s B) V e r t i c a l d i s p l a c e m e n t s 6) EFFECTS OF CYCLIC LOADING A) P o r e p r e s s u r e r i s e B) R e d u c t i o n i n s h e a r s t r e n g t h C) D e c r e a s e i n s t i f f n e s s D) A s s o c i a t e d p r o b l e m s 1) E x c e s s i v e h o r i z o n t a l d i s p l a c e m e n t s 2) R o c k i n g 3) L i q u e f a c t i o n 7) DYNAMIC BEHAVIOUR A) R e s o n a n c e B) O p e r a t i o n a l r e q u i r e m e n t s 8)  INSTRUMENTATION A) I n s t a l l a t i o n B) P e r f o r m a n c e m o n i t o r i n g  i n sand  49  The good  penetration  knowledge  extensive will  The  of  the  upper  cone penetrometer  vary  bearing  r e s i s t a n c e of dowels and s k i r t s  over  the  resistance  ultimate  to  bearing  correlation factors.  testing.  site,  capacity equations  sediments,  dowel  or  skirt  elasticity  pressures  by  topography  o f t h e s e a f l o o r i s known  s l a b i s designed  topography precisely  and  to  been and  offshore sliding, failure The that  for  be  Generally,  pressure,  since  the  sediments a r e not  installation  be  discussed  procedures.  a  gravity bearing  stability.  Proper  This  is  t h e p l a t f o r m has  grouting  procedures  specified.  number structure failure,  of  possible  rocking,  of the p l a t f o r m sliding  failure  foundation,  modes a r e shown i n f i g u r e stability  from water m o t i o n s and  underneath the slab a f t e r  must be  horizontal  may  the d e t a i l e d  problems w i l l  foundation  imbedded a s f a r a s p o s s i b l e .  are  1973).  of the foundation  area  by g r o u t i n g  There  slab  (Bjerrum,  upper  capacity  between t h e s e a f l o o r and t h e s l a b i s n e c e s s a r y  undermining  composition  (1970).  the bearing  that  installation  which  Penetrometer  on t h e b a s e  the  s e c t i o n on p l a t f o r m  i n s u r e adequate  achieved  of  from  i s e s s e n t i a l l y the  sediments.  base  a  the standard  provided  for a specified  Other  Good c o n t a c t prevent  theory,  distribution  known.  in a subsequent  to  driving  c h a r t s may be u s e d t o e s t i m a t e contact  using  (1963) o r Hansen  c a p a c i t y o f t h e upper  The l o c a l  known  resistance,  may be e s t i m a t e d  estimated  the  usually  This  of Meyerhof  requires  modes  including:  and  f o r an  horizontal  liquefaction.  These  3.5. is  investigated  or a deep-seated bearing  to  insure  failure  does  A) SLIDING  B) BEARING CAPACITY  Fig. 3.5 Possible failure modes for an offshore gravity structure foundation ( A d a p t e d from Hove and F o s s ,  1974)  en o  51  not  occur.  T h e r e a r e a number  horizontal find  sliding  t h e most c r i t i c a l Bearing  formulas  failure  of  deposits,  a  and  a  foundation  soils  and  strictly  than  too  high.  the  shown  figure and  stability.  easy  t o use.  foundation  similar  to  interest  here  structures  loads  the  of  which  d e p t h of  are  are  for.  more  Therefore,  to provide  a more  load  eccentricity be  stability  avoided diagram  relate  to  the  between  foundation  foundation  other  depend  land,  and  usually greater.  for  on  soils. are  structure.  i n f l u e n c e , i . e . the larger  by is  c o n s o l i d a t i o n settlements  f o r most p r o j e c t s on are  They  l o a d s , of c o u r s e ,  substantially  settlements  capacity  basic relationship  s t r e n g t h of and  if  a r e done f o r any  i s t h a t the is  A  they  the  method  o c e a n wave or  p r o b l e m may  the as  the  stability.  a problem  show  for e l a s t i c  bulb,  bearing  i f necessary.  to  and  account  potential  magnitudes  size  than  corresponding  This  3.7  those  stress  the  for clay  s t r e n g t h of  conditions  a l s o performed  i s not  horizontal The  are  of  base s i z e  Calculations  the  and  can  capacity  bearing  are convenient  failure  increasing  the  simple  loading  3.6.  surface  bearing  analyses  Overturning  vertical  slip  The  formulae  to  called  the  investigation  in  method  of  where  i n order  and  estimate  the  element  not  (1970),  equilibrium  1976).  a  the b e a r i n g  Hansen  Institute)  rough  problems  complicated  or  for  shown i n f i g u r e  a p p l i c a b l e t o l a y e r e d d e p o s i t s or the  earthquake  is  limit  Schjetne,  give  detailed  (1963)  mechanisms  considered  i s investigated using  simple  equations  finite  These a r e  Geotechnical  (Lauritzsen  possible  t h a t must be  one.  Meyerhof  (Norwegian  not  failure  of  size  these  therefore,  Of of  huge the  In a d d i t i o n t o  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  Figure  3.6 - P o s s i b l e modes o f s l i d i n g ( A f t e r Young e t a l , 1975)  failure  53  Figure  3.7  - S t a b i l i t y diagram f o r a r a f t foundation ( A d a p t e d f r o m Young e t a l , 1975) 0  54  these  calculations,  storm  or  earthquake  Laboratory  (Andersen,  procedures  are  Cyclic  properties  to account  earthquake  loading,  effective  Displacements are  results  the  soil  for  f o r pore full  of  potential  allow  for partial  drainage  using  analytical  methods  based  investigations,  to  either  Most dynamic  soils  are  displacement  analyses  For  are required with  programs. under  finite  pseudostatic  e l e m e n t method. and r o c k i n g  loading  may  water p r e s s u r e  be  rise  s t r e n g t h to account assessed  cyclic  from  triaxial  (Lee and F o c h t , (Rahman  et  undrained  assess  the s o i l  generation.  t o the values chosen  is  with  on s i m p l i f i e d  useful  t h e amount  by c h a n g i n g  horizontal,  of c y c l i c  and s h e a r  directly  and  1974).  and  water p r e s s u r e  sensitive  either  be  influence  estimate  stability  the  e s t i m a t i n g the pore stiffness  made.  F o r wave l o a d i n g , where t h e  structure  using  The e f f e c t  be  on t h e f o u n d a t i o n  dynamic  the  data  may  to  cumulative  o f s e v e r a l s e c o n d s o r more, p s e u d o s t a t i c  include v e r t i c a l ,  Liquefaction  studies  used  s t r e s s computer  are very  parameters. by  be  this  e f f e c t s are modelled  estimated  displacements  here  must  t o determine  must  performed  calculations.  loads  settlement  i n an a p p r o x i m a t e way.  i s on t h e o r d e r  suitable  of  on  l o a d i n g and i t s e f f e c t s  investigated  analyses  of the e f f e c t  1976; F i n n e t a l , 1977; L e e and A l b a i s a ,  Cyclic  The  loading  t e s t s are necessary  appropriate  period  some a s s e s s m e n t  the  These  motions.  f o r the s o i l incorporated  and d e c r e a s i n g for this.  laboratory  test  tests modified to  1975a) o r  a l , 1977).  analyses need  wave  indirectly Preliminary  (Bjerrum,  for  more  1973)  advanced  l a b o r a t o r y or a n a l y t i c a l .  analyses  are  performed  by  the  structural  55  engineer  who r e q u i r e s  soil  p a r a m e t e r s t o model t h e 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 o f t h e f o u n d a t i o n of  these  soil  Seismic on  parameters  earthquake receiving being  discussion the  structures  engineering  for  considered  deal  therefore  with  (1981).  this  Norske  Veritas  to  date.  gravity  active  However,  structures  as s t r u c t u r e s  i s referred to  is  of t h i s type a r e  areas.  A  thorough  several  publications  that  n a m e l y : Watt e t a l (1978) and S e i n e s  c o d e s may a l s o  (1977)  engineer.  i s beyond t h e s c o p e o f t h i s t h e s i s and  subject,  Two d e s i g n  offshore  seismically  of t h i s t o p i c  reader  designed  attention  for  evaluation  have n o t had a s i g n i f i c a n t i n f l u e n c e  type  increasing  The  i s the j o b of the s o i l s  considerations  gravity  soils.  and  the  be r e f e r e n c e d : American  those  Petroleum  of  Det  Institute  (1978). A  final  requirement  concern for  of  the  monitoring  geotechnical  the  installation  performance of t h e g r a v i t y p l a t f o r m . in  a later  3.2.3  subsequent  i s covered  in  detail  section.  final  s t r u c t u r a l a n a l y s e s and d e s i g n  environmental  investigations offshore  usual  during  are  have  been  defined  An  important  complete. i s that  the structure  t o w - o u t , and i n s t a l l a t i o n  procedure  operational  The  loads  s t r u c t u r a l design  construction, the  This  and  i s the  S t r u c t u r a l R e q u i r e m e n t s and A n a l y s e s The  the  engineer  three  of d e s i g n i n g  loads,  f o r t h e maximum  may p r o c e e d when and  the  requirement  soil of  be d e s i g n e d f o r in  addition  forces  to  expected  life.  main  components  of  the  structure:  t h e deck,  56  t o w e r s , and The  base c a i s s o n ,  deck, which  (which  20  i n the  throughout  and  30  the  years.  however, not  distinct  i s u s u a l l y made o f  i s higher  failure  have  the  splash  steel,  life,  critical  deck but  the  must  requirements.  resist  corrosion  zone t h a n e l s e w h e r e ) and  platform's The  design  which  points  t o w e r s and  fatigue  i s u s u a l l y between in  base  the  design  slab  are,  (Sjoerdsma,  1975b). The large the  t o w e r s must be  designed  h y d r o s t a t i c f o r c e s due  t o the  a d d i t i o n a l wave i n d u c e d  hydrostatic larger are  during  not  and  pressure the  filled  the  c o n s t r u c t i o n or  from l a r g e d i f f e r e n t i a l  from  with  la  objects  all  dense sand  about  such as dense  an  pressure  of  be  strong be  sand  and  may  is on-site  determine  a l s o have t o  platforms  on  high  the  (Federation  for  shown  to  damage contact to  than  for in  for higher  the  the  during  designed  investigations. higher  in  Internationale  uncertainty  r e s i s t a n c e and  slab.  i f there  s e a b e d or  s l a b must be  account  magnitude  due  the  resist  enough t o r e s i s t  locally  be cells  pockets to deformation  code  from s o i l  c a l c u l a t e d f o r the  the  boulders  penetration  i s found  order  to  towers  to  the  differential  platform  will  with  t o one  draft  hydrostatic pressures  1977), t h e  locations and  (as  also  According  investigations if  of  caisson  T h e s e may  Precontrainte,  at  2  must  loads.  resistance  installation.  t/m  It  foundation  high  de  compartments  2.2).  pressure  The  under  tow-out p h a s e s , when the  investigated  load.  The  the  T h i s must be  implosion  figure  b a s e of  t h a n when the  design  cellular  loading.  ballast,  critical  are  implosion  s t r u c t u r e ' s deep  pressure  a c t i n g at  with  operational.  to prevent  soil values  This value uniform  200  is  bearing  57  For design  the  loads  critical steel  base s l a b ,  i t i s r e a d i l y apparent  are  encountered  design  conditions  for  greater  t h e y would be  The  are  on  the  components both  addition be  t o be  installed  and  t o the  symmetrical  studies  and  i n the  for  a  example,  Since  than  relatively  calm  gravity  many of  the  earthquakes)  fatigue  random, t h e  Congo were  the  s p e c t r a l analyses  and  the  tow  large  ( w i n d , waves, and  s i g n a l being  For  Other  1977).  involved.  many f r e q u e n c i e s ,  resonance  obvious.  (Lalli,  critical  installation.  expected during  required  numerous  of  so  loads  Congo c o a s t  structure  upon  the  towed f r o m E u r o p e t o t h e  t o once  dynamic a n a l y s e s  structure acting  the  not  wave  subjected  waters o f f s h o r e  not  are  g r a v i t y type platforms  designed  for  those  that  type loads  contain  are  required  calculations.  structure  d i f f e r e n t d i r e c t i o n s of  will  loading  In  probably will  have  investigated. For  a  more  requirements  f o r an  referred  to  (Penzien,  1976;  thorough offshore  several  presentation gravity  papers  R0ren and  of  the  structural  structure,  the  reader  concerned  Fames,  1976;  wholly with Waagaard,  this  1977;  is  topic Watt,  1979).  3.3  Platform Of  paramount  (concrete) sites  Construction  gravity platform  f o r dry  docks,  water c o n s t r u c t i o n The  importance  shallow  in  is  the  the  construction  availability  water c o n s t r u c t i o n  of  of  areas,  a  large  suitable and  deep  sites.  base s e c t i o n o f  the  platform  is built  in  an  excavated  58  dry  dock.  walls  When  raised  the  raft  h a s been c o m p l e t e d a n d t h e c a i s s o n  t o a predetermined height,  t h e d r y dock  t h e c o f f e r d a m removed,  and t h e base s e c t i o n  out  site  t o a s h a l l o w water  f j o r d ) where Compressed if  i t i s secured  (usually  there a r e problems  (Derrington,  1977)  in or  cables  cut  i t out  1976).  t o a d d buoyancy  of  excavation  bay o r  (Clausen,  the foundation  floating  to  up a n d towed  a nearby or a t t a c h e d  by m o o r i n g  a i r may be u s e d under  floated  i s flooded,  the  costs  dry  dock  (Werenskiold,  1977). At  t h e s h a l l o w water c o n s t r u c t i o n  completed  and  completed,  the structure  construction ballast  area  towers  It  (Sjoerdsma,  is  The  o n t o two b a r g e s  site deck,  o u t t o where t h e p l a t f o r m  deck  is  unballasted (Clausen, ready  to raise  1976).  t h e deck  transport  construction  must  towers.  The  was  and  i s usually  built  then mated  onshore,  is  These barges a r e then  i s and p o s i t i o n e d The  water  by f l o o d i n g  towers,  t h e deck  which  a 'deep  platform  is  so  that  then  the  partially  o f f t h e barges and onto t h e towers  structure,  virtually  complete,  i s now  f o r tow-out. The  must  the  and  (or o l d tankers).  towed  over  that  to  submerged  section  is  When t h e t o w e r s a r e  out  i t partially  this  t h e base c a i s s o n  erected. towed  i n t h e base  at  1975b).  are  i s then  where  compartments  moored.  loaded  the  site  be  sites  carefully  of  structure  and t h e n t h e tow-out planned  be a d e q u a t e b o t t o m  structure  the  throughout  between  t o sea f o r  before construction  clearance a l l  and  the  c o n s i d e r a t i o n s a r e the r e s p o n s i b i l i t y  the  room  towing of a  to  various  installation  begins. maneuver  routes.  maritime  There the These  consultant  59  who  i s well  3.4  versed  Platform The  i n these p r a c t i c e s  being  partially  towed o u t t o l o c a t i o n by an  array  d e l i c a t e operation  coordinated  by t h e m a r i t i m e  are  used  The on  location.  finite  there  i s a current  once o n - s i t e  motions  calm  of  stay  monitored  which The  while  the  that  slowly,  and  Weather  the  tow-out  there  1976).  that  the  structure  as i t s i n k s  sequence  structure  and  slab,  will  The  the  the  and p r o v i d e  no d o u b t  sea  be  must  be  to avoid  excessive  caisson  and i t s  b a l l a s t e d once o n - s i t e t o  o f submergence d o e s n o t impact skirts  or r i b s . damage  under  resistance  the  is  carefully  the s e a f l o o r To to  aid in both  steel  below t h e s k i r t s  seafloor  large  i s shown i n f i g u r e 3.8.  minimizing  meters  approximately  of such a  components o f t h e f o u n d a t i o n ,  several  dowels p e n e t r a t e  may damage  The r a t e  only  o f touchdown, e s p e c i a l l y i f  i s systematically  sinking.  and s o i l  portrude  platform  for  inertia  a t the time of i n s t a l l a t i o n  h e a v i l y and damage t h e b o t t o m  structural  an  p l a n n e d and  positioning  seas  high  (Watt,  The i n s t a l l a t i o n  so  placing  is  time and a r e c o n s t a n t l y  c a n be p l a c e d  the  present  structure  level  This  well  The  calm  a t t h e moment  motions of t h e s t r u c t u r e appendages.  must be v e r y  insure  even when moving v e r y  relatively  tugboats.  i s also h i s responsibility.  to  Because  some  The  that  for stability, i s  1977).  structure  structure,  of  t o choose a s a i l i n g  m o n i t o r e d and u p d a t e d (Werenskiold,  submerged  consultant.  submerging of t h e s t r u c t u r e forecasts  1977).  Installation  platform,  extremely  (Werenskiold,  are  the  dowels provided.  weight  to horizontal  of  the  motion  60  (c)  Figure  Skirt driving  3.8  W)  Grouting  - I n s t a l l a t i o n sequence f o r a g r a v i t y ( A d a p t e d f r o m W a t t , 1976)  platform  61  which  could  break  foundation  soils,  The  detail  base  N o r t h Sea As  be  the  impairing of  a  the s t r u c t u r e the  skirt  to  by  skirts  deeper  ample  time  flow  out  too  fast,  into a  c o n d i t i o n s at the s i t e ,  under  To  keep  installed  may  Care  the s l a b .  and be  cells must  entrapped within  may  be  taken  contact  soil  to  the s k i r t  result  to  the the  allow  compartments  and may  is  to  lowered  cause channels  of the p l a t f o r m  good  will  thereby d r i v i n g  erosion  stability  ribs  vertical  applied  that  the  and  varying  I f the p l a t f o r m  velocities  threaten  i n the  i n general  t o be e r o d e d u n d e r n e a t h t h e s t r u c t u r e and  the  conditions.  the s t r u c t u r e  seafloor  appropriate  ( C l a u s e n , 1976).  high current  storm  the seabed, which  l a r g e moments  from underneath  o r gouge o u t  submerged, t h e s k i r t s  sloping  ballasting  f o r water  ribs  3.9.  i s further  penetration due  or  CONDEEP t y p e p l a t f o r m  foundation s o i l .  irregular  foundation  skirts  stability  i s shown i n f i g u r e  penetrate during  off  lead  to  more  (Gerwick,  1974) . To  insure  structure usually  and  The flow  foundation s o i l s ,  grouted u t i l i z i n g  provided usually  the  for  this  s t r u c t u r e must be from  foundation  operations The  may  (Callis  base  a few  or be  points  to  system al,  on t h e base  slab  of  the  the  monitor  in  the  1979).  base  Grouting  have t o u c h e d down.  to allow  structure  .overstressing used  base  t h e s p a c e between them i s  et  slowly  the  the  piping  (Callis  submerged  underneath  soils  Submersibles  a built-in  purpose  begins a f t e r  out  between  excess grout  to  w i t h o u t damaging  the  skirts  (Watt,  the s u c c e s s of  1976). grouting  e t a l , 1979).  of the s t r u c t u r e  i s usually  instrumented  so  that  62  k  Figure  3.9  50jn  - Detail (After  j  o f CONDEEP base Clausen, 1976)  structure  63  decisions  can  penetration of  the  made d u r i n g  possible.  foundation  boulders say  be  a  lense  grouting  If excessive  components  i n t o the  s e a f l o o r or  fill  the  CONDEEP s t r u c t u r e v e r y base  of  one  cell  resistance  undetected  during  decision  to stop  damage  to  the  slab  After may  be  3.5  of  The  i s completed,  depending  from t h e  high  sand  velocities  to the  structure  have been u s e d  installation,  and  (Offshore  conditions  structure.  rolled  1976).  The  structural from  d a t a a v a i l a b l e from  soil  the  was  out  Europe,  the  protection and  expected  Gravel  mats  after installation  is  1974).  Instrumentation are  generally  and  (2)  of  the  of  instrumenting  the  costs  since materials  well  to provide  structure during  construction  near  that  information  some form of  upon l o c a l  and  the  prevent on  from  on  (Clausen,  to  as  one  experienced  dense  based  caisson.  such  For  scour  Platforms  increase  commence.  grouting  Platform  1977)  i n t o the  made  any  halted  3.10.  water p a r t i c l e  completed  be  i n t e r p r e t a t i o n s i s shown i n f i g u r e  placed  connected  were  platform  was  on  objects  may  investigations  the  of  driving resistance  s p a c e s may  lense  amount  i s exerted  submergence  a  soil  driving  the  submergence - p r o b a b l y  of  the  instruments b u i l t instrument  increased  pressures  during  deformation  pressure  interskirt high  about  from e i t h e r p u s h i n g  of dense sand, the  to  installation  instrumented information  i t s operational  structure is and  more labor  dimensions to account  is than are  to on  life.  high,  the  aid  the  money this  by  for uncertainties  not in  in  performance  A l t h o u g h the  o f f s e t by reduced  (1)  saved  cost in  (McClelland, having  to  installation  64  «  200  Design Maximum Allowable Value  2? (A  S 100 0)  E 50  I  Expected  Maximum Values  10 15 20 Dome Number  Figure  3.10  Maximum dome c o n t a c t p r e s s u r e s o b s e r v e d installation o f t h e " B e r y l A" CONDEEP C l a u s e n , 1976)  during (After  65  loads  (soil  response lateral  reactions).  provides data displacements,  The  Instrumentation  f o r future design etc. after  f o r measuring  on p o r e p r e s s u r e  the p l a t f o r m  of p l a t f o r m s  now on s i t e  (DiBagio  - Wavedata by means o f a buoy a n c h o r e d n e a r  rise,  is installed.  f o l l o w i n g i n s t r u m e n t a t i o n h a s been u s e d  installation  platform  t o monitor  the  e t a l , 1976): the platform  - Bottom c l e a r a n c e by means o f e c h o - s o u n d e r s the base of t h e c a i s s o n  installed  - Draft base  mounted n e a r t h e  -  by  ,means  of  pressure  transducers  B a l l a s t water level in cells and towers by p r e s s u r e t r a n s d u c e r s w i t h i n t h e s e compartments  - Bending gauges  moments  and  axial  forces  i n dowels  under  means from  of  strain  - Water p r e s s u r e i n s k i r t compartments beneath the caisson during penetration and c o n t a c t grouting by means o f d i f f e r e n t i a l pressure transducers - Verticality  inclinometer  -  Base c o n t a c t p r e s s u r e s using mounted f l u s h on t h e 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 b a s e s l a b s and c e l l means o f s t r a i n guages i n t h e r e i n f o r c e m e n t  -  Short t e r m s e t t l e m e n t by means o f p r e s s u r e a c l o s e d h y d r a u l i c system  Other of  from a b i a x i a l  earth  i n s t r u m e n t a t i o n h a s been u s e d  these  platforms  - A complete measurements data)  pressure  t o monitor  transducers w a l l s by  measurements i n the  performance  ( D i B a g i o e t a l , 1976): system (wave,  for tide,  oceanographical/meteorological current, wind and t e m p e r a t u r e  -  Base contact pressures t r a n s d u c e r s mounted f l u s h  by means of on t h e s l a b  -  Structural strain a t t h e base of t h e towers, g i v i n g t h e 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 d i s p l a c e m e n t s  earth  pressure  a t the base, a t mid-  66  height  of the towers,  and a t deck  - Angular accelerations deck l e v e l s  and  level  displacements  a t t h e base a n d  - L o n g - t e r m h o r i z o n t a l a n d v e r t i c a l d i s p l a c e m e n t s by means o f 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 t h e c a i s s o n - Pore pressures i n the foundation soil piezometers i n s t a l l e d beneath the p l a t f o r m A  computer  process  data  statistical magnetic  tape  operated  d i g i t a l data  acquisition  as i t i s r e c e i v e d with  the  data  on-line  being  processed  ( C l a u s e n e t a l , 1975).  by  means  system  computation and  of  i s used t o of  stored  basic on  a  67  CHAPTER 4 THE  The  Ekofisk  (Bjerrum,  1973;  G e r w i c k and and  Focht,  gravity  Braun,  Hognstad,  in  to almost  and  has  the  t a n k would  presenting  tank  offshore  depth  the  middle After  water  to  built  the  being  imbed  large  be  1972;  1975a;  large  received  a  lot  of  tank  is  platform of  Lee  offshore  Ekofisk  body  design  literature  i n mind, a d i s c u s s i o n  of  useful  of  the  as  a  means  a p p l i c a t i o n of  A geotechnical  the  and  Ekofisk  case  will  tank may  Hognstad,  The  installation  from t h e  of  to  c o n c e p t s and  1974).  t a n k was  1973.  were  appear  (Gerwick  and  kilometers  first  The  papers  Duncan,  Focht,  in offshore  With these p o i n t s  i n t h e s e p a p e r s and The  the  community.  a relatively  d e s c r i p t i o n of  Europe,  construction,  and  naturally  involved  numerous  theories  study  of  the  found  in  herein.  sources  Offshore  Lee  Being  it  environment.  i s presented  several  400  it.  geotechnical  A general  1974).  of  e t a l , 1975;  1976;  engineering  with  Ekofisk  Lee,  everyone  subject  Clausen  installed,  the  construction  the  1974;  1973;  associated  in  been t h e  1975b; M a r i o n ,  attention  and  t a n k has  structure  familiar  EKOFISK TANK - A CASE STUDY  1973;  details  of  this  only  Marion,  of  platform  be  be  the are  highlighted  North  Sea  positioned,  i t i n the  10 m e t e r s o f f t a r g e t  where  the  i t was  soils.  3 ° 5 0 ' out  of  in  here. towed  Ekofisk placed  s t r u c t u r e was  foundation and  to the  design,  discussed  n e a r S t a v a n g e r , Norway, t h e n Norwegian c o a s t  1974;  on  field  in  June  30,  ballasted  Positioning  orientation  over  with errors  (Marion,  68  1974).  The  figure  4.1,  base  of  the  i s c o v e r e d w i t h 5 cm h i g h  and  has  ribs  underneath the c e n t r a l  obtain was  40 cm  full  high  contact  completed,  rolled  o u t by  protection  divers  et  al,  rocks  was  in  structure with  93 m e t e r s .  final  i s nearly  rounded  of  on  The  40 cm  high  provided skirt  them  to  to  to  driving were  provide  Hognstad,  1973).  achieve  a  submerged w e i g h t o f  190,000 m e t r i c of  in  plates  above t h e s k i r t s  placement  the  tons  platform  $28 m i l l i o n  of  (Clausen including  (Offshore  Europe,  One  reservoir  square  in plan  and  70 m e t e r s  nine  lobes  for  maximum  1973)  (Offshore  perforated  million  high;  barrels  which  is  on  the  seabed  a  in  of c r u d e o i l may roughly  this  reservoir  structural  strength  1974).  resembling  one meter  45  be  meters  i s composed of (Gerwick thick  and  at  the  Surrounding the r e s e r v o i r  is a  b r e a k w a t e r d e s i g n e d t o r e d u c e wave l o a d s on t h e t a n k ,  e x t e n d s from a b o u t  figure  plan,  rests  each w i t h w a l l s n e a r l y Europe,  in  w i t h an a p p r o x i m a t e d i a m e t e r o f  h i g h and  water. central  Hognstad,  circular  corners,  i n the  "This  was  cost  excess  stored  which  after  and  After  and  f o r the tank.  I t i s 90 m e t e r s  70 m e t e r s  base  just  dumped  added  steel  were  soil.  (Gerwick  ballasting  The  these  detail  8  The square  this  was  structure;  scour  buoyancy  1975).  installation 1974).  and  in  the p e r i p h e r y  mats a t t a c h e d  sand b a l l a s t  tank a f t e r  along  shown  corrugated  w i t h the s e a f l o o r  nylon  maximum n e g a t i v e the  skirts  against  Additional  structure,  i s i n 1973  12 m e t e r s above t h e  U.S.  dollars.  water  surface  to  69  Figure  4.1  - Detail (After  of the E k o f i s k tank bottom C l a u s e n e t a l , 1975)  70  the  base  s l a b where i t i s r i g i d l y  tensioned  attached.  base s l a b i s 6 meters t h i c k  entire  structure  forming  an  o f 7360 m  (Offshore Europe,  area The  tons  will on  buoyant weight  and  25.8 t/m  2  in  static  the order  vertical  and  (Schjetne, of  tons  foundation  the  200,000 m e t r i c corresponds For  the  be  resultant  wave  acting  on data  i s shown i t  2,800,000  in figure  This  the h o r i z o n t a l force Ekofisk  tank,  the 10,000  when a n a l y z i n g a  vertical is  of about  the  f o r c e of  used; 27.2  this  t/m . 2  wave, a h o r i z o n t a l f o r c e o f about (Bjerrum,  1973).  The m a g n i t u d e o f t h i s  ton-meters  to  (Clausen  Since  4.2 w i t h  t h e 100-year wave.  the loads  i s shown  is The  acting  Some d e s i g n  storm  4.3.  alternating clays.  will  moment  e t a l , 1975).  c o n d i t i o n s at the E k o f i s k f i e l d  Sea:  field  pressure  schematically in figure  overconsolidated Ekofisk  1976).  f o r c e w i l l a c t above t h e s e a f l o o r , a moment  Foundation North  there  s t r e s s which i s  foundation  w i l l a c t on t h e t a n k  corresponding  i s shown  o f about  f o r c e i s about  conditions, the  metric  loading,  (H0eg,  Therefore,  vertical  the  covering  190,000  wave  the  vertical  on  a p p l i e d t o the f o u n d a t i o n .  tank  For  wave.  100-year d e s i g n  approximately  the  design  tons  Under  pressure  .1976).  to a uniform  78,600 m e t r i c this  soils.  fluctuating  tons  i s now a b o u t  l o a d i s i n phase w i t h  f o r the design for  foundation  component o f t h e v e r t i c a l  fluctuating  magnitude  raft  beneath  w a t e r e x e r t s an a v e r a g e p r e s s u r e  o f 5% o f t h e s t a t i c  moment  extends  1974).  of the tank  be a f l u c t u a t i n g  metric  a huge s o l i d  on t h e f o u n d a t i o n  2  and  The h e a v i l y p o s t -  are  typical  of  l a y e r s o f d e n s e s a n d s and h e a v i l y  A typical in figure  geotechnical p r o f i l e  4.4.  The upper  26  from t h e  meters  are  71  ^93m-  - S W.L,  Ja^lOpOOt ft = 78,6001  S70m P =19Q000t v  ^36m  L  Figure  «X  "  4.2 - L o a d s on t h e E k o f i s k  t a n k f o r t h e 100-year wave  5000 WAVES 15 MRS DURATION  *  &  400  20 I 0  Figure  I 5  40  60  60 FT  L_  <0  IS 20 WAVE HEIGHT. H  25 M.  4.3 - D e s i g n s t o r m d a t a f o r t h e E k o f i s k ( A f t e r L e e and F o c h t , 1975a)  field  72  «  -Mm  •  ,j  —1  20m 7Cm  Sand  50 m  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  Cljy  Sind  100 m  150 ml-  Figure  4.4  - ^j«^otechnical  )  P  r  o f i l e fro.  E  k  oHs  -Om  Sea floor  11 '° S i "  IS"  jc-70m  UNDRAINED SHEAR STRENGTH (t/m')  Fin* land Stiff sandy clay Fint u n d  * i •  Hard clay  •< • 0 • >  •  uj uj o in SO 60  Figure  4.5  •  UU triaxial  • o  Unconfintd compression test Pocket penetrometer  - Shear s t r e n g t h lArter Clausen  d a t a from E k o f i s k e t a l , 1975)  k  Mela  73  comprised at a  of  about  uniform  18 m e t e r s below t h e  relative  high  extremely  d e n s i t y on  density  is  waves t h a t have p a s s e d (Bjerrum,  1973).  of  probably overhead  Shear  sand  seafloor;  the o r d e r  most  fine  the upper  100% due  with a t h i n few  (Bjerrum,  the  s t r e s s e s are  1973).  sand  induced  was  deposited  i n the  soil  waves b e c a u s e of t h e 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  impose  on  back and large. been in  seafloor  f o r t h and This  may  the  compact  i s termed  demonstrated  (Henkel,  stiff  t o be  strength  clay  of a b o u t  an  t/m  Foundation  has 1973).  for  the  Geotechnical  Institute.  approving was of  be  findings.  s i n c e an  disastrous  the  an  compaction  undrained  The  clay  weaker.  shear  seam a t Some  i t c o u l d not  spill  be  was  thus,  c o u l d take  Final used  18  shear  were  performed  the  Norwegian  L t d . and  agency  foundation  of p o s s i b l y  1972).  installation;  p e r i o d , no  the There  o i l spill  (Duncan,  that  months a f t e r this  soil  has  Institute  responsible  for  t h e p l a t f o r m s a f e t y f o r t h e N o r w e g i a n government,  McClelland's  required  of  and  Norwegian G e o t e c h n i c a l  Veritas,  responsible for checking  safety  sufficiently  1973)  platform  by M c C l e l l a n d E n g i n e e r s , The  are  4.5.  independently  Norske  source  sand  in figure  studies  r e p r e s e n t e d Det  i f they  is substantially  i s presented  they  1975a).  (Bjerrum,  2  m e t e r s below t h e m u d l i n e strength data  Focht,  from  These s t r e s s e s c y c l e  (Bjerrum,  important  beneath the 40  sand  "preshearing"  l a b o r a t o r y (Lee and  The  the  1970).  This  of c o u n t l e s s  passing  the  seam  m e t e r s have  t o the e f f e c t  since  clay  a  safety great  one  independently concern  million  approval  and  barrels of  for o i l storage  the  about would tank  for several  if a  failure  occurred  during  place  (Clausen  e t a l , 1975).  74  Preliminary Geotechnical Finite the  studies  Institute  (NGI) were  element m o d e l l i n g  n o n l i n e a r behaviour  elastic  settlement  expected  under to  (Duncan,  1972).  out  of  wave  structure  1973).  vertical  linear,  that  for  linear  from  the  cyclic  the design  s l a b would move down 30 cm w h i l e about  45 cm.  platform  Superimposed  weight,  15 cm o f f t h e unstable  storm  preshearing become  sand  stiffer  settlement  and  for  that  the  wave  moment.  reducing  (Bjerrum, are rocking  NGI  estimates  s i d e would move up  settlement  resulting  the  t h e sand under  accompanying  rocking motions expected  in  platform  t o numerous s t o r m s b e f o r e  the  to  wave, one s i d e o f t h e b a s e  would h i t , t h e t a n k was e x p e c t e d and  weight  wave.  displacements  the opposite  1972)  Because  was  curve  imply  design  on t h e e l a s t i c  (Duncan,  be s u b j e c t e d  effect  settlement  due t o  w o u l d mean t h a t one s i d e w o u l d  situation.  undoubtedly design  this  displacements  1.5 cm when s u b j e c t e d  the  these  to  the  o f t h e t a n k were e s t i m a t e d t o  with  subject  account  predict  the  would  f o r c e of the design  15 cm back and f o r t h  motions which r e s u l t  to  load-settlement  this  h o r i z o n t a l displacements  Concurrent  showed  is  the  w o u l d move up and down a b o u t  about  (1972).  30 cm f o r t h e tank due t o i t s own  structure  be  Norwegian  taking into  Elastic  settlement  The  Duncan  and  loading.  Assuming t h a t  fluctuating  by  was done  elastic  the  the  of the f o u n d a t i o n ,  the  be a b o u t  at  reported  of the s o i l s ,  storm  estimated  carried  motions increase  lift a  the  about  possibly  would  almost  the  100-year  to settle  from t h e  the tank (Duncan,  t o d e n s i f y and 1972).  in stiffness  meant  This that  f o r t h e 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  the  base  slab  estimates. would  15 cm on t h e o t h e r slab  would  not  exert  a positive  NGI  the e f f e c t  soils.  include  the e f f e c t s  respectively,  drainage  strictly  correct,  confirmed gauges  1975).  i n pore  stiffness  Clausen  figure  of c y c l i c  4.7  (Bjerrum,  base would 1973).  4.6. included  loading  Although  pore  water  their  d u r i n g d e s i g n storm  underneath  the  storm. i s less  effects  of  r e s u l t s a r e not water  pressures  loads.  T h i s has  u s i n g p i e z o m e t e r s and  the s t r u c t u r e  (Clausen  r o c k i n g d i s p l a c e m e n t s would t h e n  et  be g r e a t e r  (1973) f o r t h e NGI a n a l y s e s s i n c e t h e  sand  observatons  e t a l (1975).  pressure  o f 85%, w h i c h  excess pore  water p r e s s u r e under  the  They d i d n o t ,  on t h e f o u n d a t i o n  and i n c l u d e s  observations on-site  installed  due  under t h e e d g e s and c e n t e r  density  in-situ,  the tank  from  1973).  when s u b j e c t e d t o t h e 100-year  t h e y do show t h a t  o f t h e upper  for  occur  the sand.  by B j e r r u m  Settlement and  in  Expected  reported  increase the  density  d e v e l o p under  pressure  the  of d i s p l a c e m e n t s  (Bjerrum,  i s for a relative  the r e l a t i v e  than  in figure  studies  20% and 8% w i l l  partial  al,  element  that  and. a t a l l t i m e s  foundation  s t u d i e s a r e shown  analysis  been  the  o f waves o v e r h e a d  o f about  Their  will  This implied  o f f the s o i l ,  p r e s s u r e on  that  o f t h e p o r e w a t e r p r e s s u r e change a t t h e s e a f l o o r  the tank,  than  1973).  indicated  15 cm on one s i d e and down  Rahman e t a l (1977) have shown t h a t  ratios of  (Bjerrum,  finite  to the passage however,  'calculations  move up a b o u t  be l i f t e d  R e s u l t s of these The  New  the  tank  would  decrease  layer.  have  been  r e p o r t e d by F o s s  A load-settlement curve  installation  phase  touchdown, t h e p l a t f o r m was b a l l a s t e d  of  to seat  the  is  (1974)  shown  tank.  i t firmly  in  After on  the  76  Figure  4.6  - P r e d i c t e d r o c k i n g d i s p l a c e m e n t s f o r the E k o f i s k t a n k ( A f t e r Duncan, 1972)  igure  4.7  - Load-settlement curve f o r Ekofisk ( A f t e r C l a u s e n e t a l , 1975)  tank  77  foundation  soils.  deformed  from  both  displacements. penetration the of  "bedding  for  a  flat  nearly  linear  time  was  settlement  about  full  s e a f l o o r was the  extrapolated  weight  may  settlement  stiffness  of by  the  cm  exceeded  elastic  about  NGI.  9  The  parameters  skirts It  of  platform settled.  skirt  curve  reached  into  the  This  depth base  became  50,000  tons.  seafloor t h a t the  load-  indicated  base o f  the  at  that  s t r u c t u r e and  e t a l , 1975). the  settlement  the  the  platform  i s important  load-settlement  submerged  This  weight of  the  may  finite  be  and  in  an  less  than  due  to  curve  forward  t a n k due  results  substantially  discrepancy in  bearing capacity  p e n e t r a t i o n and  (Clausen  10 cm,  of  as  the  skirt  between t h e  established.  flattening  full  linear.  zero  the  t o the  high  portion  to  load-settlement  cm.  contact  to  the  submerged w e i g h t  35  achieved  back  be  40  plastic  corresponded  to  and  being  correspond  The  became  linear  tons,  predicted  be  should  the  the  curve  (essentially)  and  was  and  s t r u c t u r e ; s i n c e the  seafloor.  p e n e t r a t i o n of  190,000  skirts  mounds w o u l d  when  seabed  displacements  f e a t u r e s were d e s t r o y e d  the  the  compression  seafloor, indicating  with  If  plastic  settlement"  contact  time  elastic  beneath the  these  This  this  this  of s h o r t c o n c r e t e  u n d u l a t i o n s and  The  9  The  seafloor  seated,  the  During  to  the  element a n a l y s e s  is to  i t s own elastic  the  20  use  cm of  t h a t were  O n e s h o u l d n o t e t h a t Duncan's (1972) r e p o r t e d e s t i m a t e of 30 cm for elastic 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 t h e v a l u e of s o i l p a r a m e t e r s were cleared up (Lee and Focht, 1975a). This e s t i m a t e was l a t e r c h a n g e d t o 20 cm ( B r a u n , 1974).  78  not  really  r e p r e s e n t a t i v e of  parameters  were  c o n s e q u e n c e of offshore  soil  a decade  probably  testing  and  and  after  ballast  was  placed.  July,  time  history  added t o t h e  occur  of  curve  Was  due  weight  interval.  of  i n the  the  following  -  factors,  platform  ( f r o m more b a l l a s t i n g ) ,  wave a c t i o n on The  the  curve  in  about  10 cm  be  and  ballasted. about  At  wave i n d u c e d  the  significant  The  end  (see  to the  overall  increase  figure  increased ballasted.  attributed  to of  a the and  increased ballast  was  on  the  relatively that heights  the (a  calm  the  elastic after  4.8).  (when b a l l a s t i n g  Note wave  due  of b a l l a s t i n g ,  settlement  sea was  figure.  was  days  c o n s o l i d a t i o n i n the c l a y ,  from e x t r a p o l a t i n g  4.7.  of O c t o b e r the  settlement  would not  13 cm  be  was was  early  namely: i n c r e a s e d submerged w e i g h t  estimated  figure  may  it  discussed  from  it  the  tank.  amount of  easily  as  Most of  i n the  response  was seven  days a f t e r  Settlement  months  of  few  first  4.8.  previously  platform  platform  f o r the  first  t o the e l a s t i c  variety  the  a  with  a t t h a t time  the  i s shown i n f i g u r e  load-settlement time  after  settlement  i n the  1973,  Settlement  time  associated  - particularly  tank  for this  submerged  to  installation  The  developed  middle  stiffness  much t o o c o n s e r v a t i v e l y as uncertainty  sampling  continued  The  months  be  soil;  ago.  installed.  can  "undisturbed"  chosen  the d i f f i c u l t y  Settlement  of  the  load  load-settlement  settlement  the  tank  settlement  was  would  was  be  fully  observed  to  Hence, t h e c o n s o l i d a t i o n and order was as  wave  of  3 cm  up  terminated). seen  the  During  this  from t h e wave d a t a  heights  statistical  until  shown parameter)  are not  in the the  79  Figure  4.8 - E k o f i s k s e t t l e m e n t d a t a r e l a t i n g submerged p l a t f o w e i g h t and s t o r m wave d a t a i n t h e 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 C l a u s e n e t a l , 1975)  MQ0OO  r  itqpoo  5 |  tOQOOO  S  KtOOO  *1*  Figure  1974  4.9 - S e t t l e m e n t d a t a f o r E k o f i s k t a n k d u r i n g s t o r m s ( A f t e r C l a u s e n e t a l , 1975)  early  80  maximum  wave  heights;  approximately Isaacson); is  these  80% t o f i n d  the exact  values  must  be  increased  t h e maximum wave h e i g h t s  (Sarpkaya  i n c r e a s e d e p e n d s on s t a t i s t i c a l  data  and  which  not a v a i l a b l e . In November, t h e p l a t f o r m was  storms. about  The  first  storm  On  When t h i s service ship,  and  the  wave d a t a  wave  a t about -  truly  5 cm d u r i n g 1974).  (Foss,  (Clausen  under  et  al,  settlements After  months.  1975).  A  settlement  to  was most  likely  settlement  settle  the  due  one y e a r  was a b o u t The  to after  They e s t i m a t e d  20 cm, and t h a t a n o t h e r  wave  design about (Foss, 7 cm, o f  dense  sand  shear  stress reversals  record  o f t h e November  4.9. subsided,  1-3 cm  consolidation  detectable  f o r t h e next  1974, t h e  (Clausen  installation  no  platform  in  the  15 cm would o c c u r  Total 24  cm.  (Clausen  et  settlement  over  This  clay.  was a p p r o x i m a t e l y  that the i n i t i a l  two was  e t a l , 1975).  T h i s was w i t h i n t h e 20-40 cm range p r e d i c t e d by NGI 1975).  of  weather  20 November  sand.  1973 t o J u l y  another  out  100-year  of the p l a t f o r m o c c u r r e d  From mid-December  was  p u t t h e maximum  November  19 November  of  occurred.  from a n e a r b y  to  detailed  in figure  t h e storm  observed  in  et a l ,  The p l a t f o r m s e t t l e d  the a c t i o n of repeated  i s shown  additional  during  occurred  (Clausen  90% o f t h e  storm.  major  and a s e t t l e m e n t o f  of the year  Estimates  16 November  settlement  w h i c h most p r o b a b l y consolidated  1974).  of  storm  several  instrumentation  22 m e t e r s , o r a b o u t  the p e r i o d  to  days  was e s t i m a t e d  a significant  Total  few  t h e major  h i t , the p l a t f o r m  the "Famita"  height  the next  19 November,  storm  subjected  h i t on 6 November  2 cm o c c u r r e d d u r i n g  1975).  al,  by  the l i f e  would be of  the  81  structure recent  from  data  storm e f f e c t s  i s not a v a i l a b l e  shown i n f i g u r e Reported  was  13 cm  settlement  since  sloping.)  Although being  degree.  in  founded  on  months  available was  installation a l (1975).  one-twentieth  of a  installation,  1975).  is  how  the  data  a  nearby  and  some  pore  water  with twelve  additional  (Clausen et a l ,  the  The  the  occurred  excess  of p i e z o m e t e r s  to  settlement  was  jacketed  not  pore  expected  of  pressure  a r r a n g e m e n t of  than  settle 1974).  pressure  The  gauges  and  i s g i v e n by  devices  is  is  platform  A description  the tank  the  studies.  from E k o f i s k  predictions.  these  to  several  piezometers.  beneath  platform  (Foss,  data  cm  was  w a t e r p r e s s u r e under  subject  seven  6  been p l a c e d more  under c o n s i d e r a t i o n  with  slightly  and  been  soil  perhaps  i n the e a s t - w e s t  has  instrumented  the  not a l l be  corresponds  o n l y about  t o compare w i t h t h e o r e t i c a l  underlying  figure  this  to  2 cm  tank  of  (high)  however, may  T h i s p l a t f o r m had  d u r i n g the p e r i o d  Fortunately,  base  perhaps,  deep p i l e s .  tank  curve  platform after  uneven and  after  s e t t l e m e n t s o f about  development  Ekofisk  was  by  the  northeast  large,  vertical  b e f o r e the E k o f i s k  The  hit  off  of  (This,  S i g h t i n g s were made on  noticeably  et  seemingly  interest,  obtained.  a year  the  seafloor  the n o r t h - s o u t h d i r e c t i o n s Of  the s e t t l e m e n t - t i m e  settlement  from  the  In t h e t w e l v e  differential  U n f o r t u n a t e l y , more  4.8.  ( C l a u s e n e t a l , 1975).  platform  1974).  to extend  differential  installation southwest  (Braun,  of  the the  Clausen  shown  in  4.10.  Data  from  the storm  the  platform,  of  6 November, t h e  i s shown i n f i g u r e  first  4.11.  major  Several  storm  to  important  82  ® : n rtftrt to gauge no.  Figure  4.10 -  K^ i? n.f ^ f 9 9 s and p i e z o m e t e r s b e n e a t h E k o f i s k t a n k ( A f t e r C l a u s e n e t a l , 1975) a t  n  75  i  \  f  SO  r  S S U r e  •5  go  a u  e  9 5  o  ®_  5  0)(T)  —U  K  D  O <  ui in  o o  10  0)  ©  Hydrostatic  <  in  <  ui z  (for wattr dtpth • 67.5 m ) - \ _  m x  a. a  ,®  LEGEND:  ui  _ K  20  4 th Nov. 1322-  uBD _  I  Ui o  -X—  H 6 th Nov. nSS-uiS. ~  ®\  <  H  {*)•• n r t f t r t to gaugt no.  rtftrt to gaugt no.  25 8  5  TO  75  W  85  TORE WATER PRESSURE 11/m'l  Figure  X a.  *—  go  "5  0  2  (  1  6  PORE WATER PRESSURE INCREASE DURING 6. NOV STORM  8 It/m')  4.11 - P o r e p r e s s u r e s o b s e r v e d under E k o f i s k tank d u r i n g t h e f i r s t ma-jor s t o r m ( A f t e r C l a u s e n e t a l , 1975)  83  observations pressures  may  be  increased  made. during  S e c o n d l y , t h e maximum occurred  not  Thirdly,  than  the  pore  in  sand,  that  significantly above of  developed  less  perhaps  pore water  working the  design  occurred  in  t h e sand  have a f f e c t e d pore water particular water  And  finally,  Unfortunately,  the  seam were  sand  not f a r  were on t h e o r d e r  which  were  was n e a r l y a s  consolidation  by t h i s  p r e s s u r e d a t a h a s been made a v a i l a b l e ,  had  t i m e and may  the pore p r e s s u r e response c o n s i d e r a b l y .  c o n c l u s i o n s about  water  instruments  Considerable  from p r e v i o u s s t o r m s  pore  the clay the  partial  and  No o t h e r thus  no  t h e e f f e c t s o f p r e s h e a r i n g on p o r e  p r e s s u r e r e s p o n s e may be made h e r e . Early  theoretical  were r e p o r t e d not d r a i n  studies  by B j e r r u m  o f p o r e water  (1973).  The  structure  dimensions  course,  of  the  take place during depends  on  the d r a i n a g e p a t h .  the storm;  single  was  t h e amount  cycle  in  undrained  of  of the s o i l  Hence, h i s a s s u m p t i o n The amount  directly  a r e such t h a t  the p e r m e a b i l i t y  p l a c e was n o t u n f o u n d e d . a  t h e sand  could  a t a l l over t h e c o u r s e o f the storm and t h e r e f o r e shear t e s t s  cannot  pressure generation  He assumed t h a t  from u n d r a i n e d l a b o r a t o r y  for  in  sand  below i t .  that  the  pressure ratios  storm.  the  substantially  indicating  f o r t h e s t o r m o f 19 November,  l a r g e as  in  seam was  water  locations.  b u t some d i s t a n c e  i n t h e sand beneath  3% t o 7% i n t h e s a n d .  not  developed  than those developed  i t . Typical  pore  at a l l test  pressure i n the clay  the  a l l , the  storm  base,  d r a i n a g e o c c u r r e d i n the sand. pressures  of  pressures  a t the platform  p o r e water  higher  First  applicable. full  shear  drainage  drainage,  of  and l e n g t h of  o f no d r a i n a g e  o f pore water  data  taking  pressure  rise  was d e t e r m i n e d  from  84  laboratory  tests,  representing specified stress  the  data  design  h e i g h t bands  cycles  wave.forces each  the  storm  shown by  in  the  figure  number  at a p a r t i c u l a r  amplitude  of  may  the pore  contribution  T h i s i s demonstrated  a l l cycles.  water p r e s s u r e r a t i o platform, very  assuming  platform The (1976)  of  and  of about  It  This  of  relative  density  investigations  Early  studies  liquefy  indicated  under  the  with that  e x t e n s i v e program of c y c l i c taken  from  better  d e f i n e the r e l a t i v e  with  Ekofisk,  laboratory The  test  preliminary  a relative the  cyclic  sand  storm testing  and f u r t h e r  that  no  beneath  the  and  Lee  Focht,  at the E k o f i s k that  density  the  field  sand  was  of about  80%.  the  For t h i s  was c a r r i e d  in-situ  density  (Lee  under  loads.  by  was some u n c e r t a i n t y  made by M c C l e l l a n d E n g i n e e r s , L t d . s u g g e s t e d dense  noted  being whether  analyses are reported  regards to the i n - s i t u  to  the  i n Table VI.  stresses  There  dense  up  analysis,  be  (1975a).  medium  summing  analysis.  o f more a d v a n c e d  site  developed  f o r demonstrating  should  distribution  Preliminary  at  beneath the  and F o c h t  1975a).  s i n c e the  31% w o u l d be d e v e l o p e d  undrained c o n d i t i o n s .  the  Lee  shear  90%, a p o r e  was c o n s i d e r e d i n t h i s results  in  d e n s i t y o f about  analyses are required.  consideration  with  for a relative  s i m p l e and c o n s e r v a t i v e , i s good  further  of  water p r e s s u r e  be e s t i m a t e d by  (1973) f o u n d  waves  be f o u n d  under u n d r a i n e d c o n d i t i o n s may  Bjerrum  By  Knowing t h e number o f c y c l e s a p p l i e d  s t r e s s amplitude,  of  4.12.  ( i . e . a h i s t o g r a m ) , t h e number  a r e known.  shear  being  out  tank  might  r e a s o n , an on  samples  t e s t s were p e r f o r m e d  o f t h e sand  for  to  correlation  results. tests  performed  t o assess the l i q u e f a c t i o n  85  UvwrBrassl*vct: T  Figure  4.12  H'  /or' vi  - Pore water p r e s s u r e r i s e p e r c y c l e observed i n undrained simple shear w i t h c y c l i c l o a d i n g f o r s a m p l e s p r e p a r e d w i t h r e l a t i v e d e n s i t i e s o f 80% ( A f t e r B j e r r u m , 1973)  T a b l e VI Example o f t h e A c c u m u l a t e d E f f e c t o f a 100-year ( A f t e r B j e r r u m , 1973)  Height of waves: m 4-8 8-12 12-16 16-20 20-24 24-26 Total  Number of waves, N 48S 471 282 121 32 3 1394  O TO  007 012 017 0-22 0-26 0-30  0-006 0013 0030 0 065 0150 0-300  2-9 61 8-5 7-9 4-8 0-9 311  Storm  86  potential  were s t a n d a r d u n d r a i n e d c y c l i c  earthquake relative  densities,  (defined  here  pressure would  studies.  Data  for  as  when  the  ratio  confining  take p l a c e i n the t e s t s when  and  Focht,  subjected  the ocean before  Since  liquefaction wave p r o b l e m  the  taking-  laboratory laboratory  period  for this then  procedure  procedure  for  10%  based  period  radial for  test  is  was  by  on p l a n e  was  (and  estimated  to  Lee  drainage,  Focht  radial  flow).  number  time p e r i o d ,  The s a m p l e s were t h e n  of c y c l e s .  The p o r e  t h e back p r e s s u r e was  This  and t h e time t h e tank  conditions.  was This  (125 s e c o n d s f o r  equalling tested  a  (1975a).  f l o w ) a n d was c o n v e r t e d t o an e q u i v a l e n t number  t h e 10% c o n s o l i d a t i o n  and t h e n  t o model t h i s .  t o be 500 s e c o n d s  in  of p r e s h e a r i n g .  beneath  flow  s e t of  sheared  levels  was e s t a b l i s h e d  radial)  take p l a c e ,  were  and  occur  sand  liquefaction  partial  developed  outlined  consolidation  of  the  In t h i s  the e f f e c t s  effects  t h e p e r m e a b i l i t y o f t h e sand  evaluated time  the b e n e f i c i a l  applicable to  the  a t low s t r e s s  simulating  unity)  assessing  drainage w i l l  densities  water  o f 63% and  densify  into account.  tests  to  for  reassess  relative  triaxial  pore  s t r e s s e s (Lee  a r e not r e a l l y  to  factors  to reconsolidate,  investigate  First,  these  samples a t d i f f e r e n t  allowed  used  where p r e s h e a r i n g w i l l  potential  cyclic  excess  shear  three  liquefaction  densities  cyclic  tests  potential  t e s t s were p e r f o r m e d  undrained  the  used f o r  at  pressure i s equal  d e s i g n l o a d s o c c u r and p a r t i a l  tests,  compacted  with r e l a t i v e  additional  To  of  t o d e s i g n storm  1975a).  earthquake  samples  tests  63%, 77%, and 100%, showed t h a t  to the e f f e c t i v e  77%  triaxial  of  about  waves  50 (12.5  undrained  water p r e s s u r e r i s e  i n c r e a s e d t o 90% o f t h i s  was  for  noted,  amount  and  87  the  drainage  10%  of  then  line  opened t o a l l o w the  i t s excess pore water p r e s s u r e . closed  and  t h e sample was  (12.5) c y c l e s .  Testing  samples e i t h e r  liquefied  of  testing,  density  i t was  w o u l d not  Shortly completed, site  extremely  or reached  found  that  the  second  Additionally,  A  of  relative  shear.  new  Tests  preshearing. sand  and  Focht, The  tank who  was  by  Their  both  50  until  t o 77%  the type  relative  on  consolidated  to  results,  resistance  samples a d d i n g  that  the  of n e a r l y  been  on  the  sand  i t was  at  the was  (Lee  and  sand  was  previously. compacted  of  were  the  to  undrained  that  simulate  been  sand  100%  found  samples  had  testing  under c o n d i t i o n s  performed  adequate  tests  the p e r m e a b i l i t y of the  both  effects  of  concluded  that  the  to l i q u e f a c t i o n ,  with  the  additional  cyclic  strength  (Lee  1975a). problem  of pore  investigated  after  finite  elements,  water p r e s s u r e g e n e r a t i o n b e n e a t h installation  the weight  method  of the  by Rahman e t a l  mathematically.  They  tank  i s f o r m u l a t e d as  of  stresses within  and  the  (1977)  behaviour,  the  applied  f o l l o w s : The  the  r e p r e s e n t e d the  with l i n e a r . s t r e s s - s t r a i n  c o n s i d e r e d the d i s t r i b u t i o n  from  density  tested  formulated the problem  soil and  and  indicated  t h a n what had  From t h e s e t e s t  of  was  From t h i s  laboratory  were p e r f o r m e d  and  were  possessed  preshearing  tests  density  unconsolidated  fashion  cone penetrometer  T h i s data  t o be much l o w e r  series  line  f o r another  equilibrium.  s t a g e of  dense w i t h a r e l a t i v e  1975a).  undrained  a sample compacted  from a d d i t i o n a l  determined  100%  tested  drainage  liquefy.  after  data  The  continued in a similar  became a v a i l a b l e .  Focht,  sample t o c o n s o l i d a t e by  zone o f  soil  wave  mass  loads.  directional  88  randomness o f t h e waves i s assumed t o be that  loading  on any p l a n e p a s s i n g t h r o u g h  the p l a t f o r m i s e s s e n t i a l l y averaged.  Hence, t h e  axisymmetric pressure and  problem  can  consolidation  i s then  from u n d r a i n e d c y c l i c  p r e s s u r e measured for  different  cycles  generation  by  The  a  follows:  pressure  a  continued  are  then to  until  allowed  the  and  and to  number  the storm  are  the  water radial  defined i n pore is  water  found  The  pressure  loading  loads  are  applied  of c y c l e s  i s extremely  drain  of  waves. that  stepping  showed t h a t  important  i f t h e f o u n d a t i o n sand  resulting for  is  applied by  time  at a certain  pore  of  water water  an amount o f t i m e  The  procedure  is  i s , when a l l t h e waves procedure. allowing  for predicting  underneath  by  water  obtained.  of  is  the  i s over,  studies  water p r e s s u r e s developed that  pore  ( t h r o u g h t h e use o f t h e p o r e  function)  R e s u l t s of t h e i r  found  being  tests  i n the pore  number  have been r e p r e s e n t e d by t h e t i m e  drainage  as  ( c o r r e s p o n d i n g t o an e q u i v a l e n t number o f waves  generation  corresponding  time  and c u r v e s o f number o f  The s t o r m  given  height) are applied  pressures  triaxial  history  histogram  stepping  level  a x i s of  for  are  The r i s e  levels  time  t o the p l a t f o r m .  as  equation  pressure  incrementally  given  tests.  stress  water  function.  so  formulated t o i n c l u d e a pore  of these c u r v e s a r e used  approximated  a  and t h e r e f o r e ,  whose p a r a m e t e r s  shear  shear  pore  the v e r t i c a l  approximated  The  i n undrained c y c l i c  cyclic  versus  coefficients  stress  be  g e n e r a t i o n and d i s s i p a t i o n .  water p r e s s u r e g e n e r a t i o n term data  wide  t h e same a s a l l t h e o t h e r s when  with respect to loading,  vertical  sufficiently  the E k o f i s k  had a r e l a t i v e  for  partial  the c o r r e c t  pore  platform.  They  density  o f 77%,  89  liquefaction pressure  would  ratios  foundation.  not  would  occur; be  A Bjerrum  less  would  the  (Rahman e t a l , 1977).  analysis  can  fact,  maximum  than about  30%  indicate  that  provide  t h e sand would  Rahman e t a l ' s  information  on  results  s t u d i e s a r e shown i n f i g u r e  developed center.  of t h e i r  under This  particular  the  used  bearing account  1973).  For  equations  capacity  First  of a l l ,  of a v e r y s m a l l  an  on  scale  effects  factor  (Bjerrum,  a  Nr  1973).  factor  rocking  to  the  and  to  the  of  induced.  decreased reduction  by Hansen  to  to  insure  methods,  tank  factors f o r model  these  about  take  93  results meters,  v a l u e of  the  this  into  with footing friction  stress.  w i t h such a h i g h r a t i o  used.  Ekofisk  capacity  i n the  (1970)  of  this  The  of Nr  to a decrease  is  apply  semi-empirically  i n t h e mean p r i n c i p a l  foundation  not beneath  When e x t r a p o l a t i n g  was  proposed  are  (1970) were  bearing  dimension  It i s  motions.  trying  formula  pore  cannot.  better  Hansen  when  the  of  of  pressures  f o r t h e tank  lack  of  4.13.  analyses,  out  of  were  The  be a t t r i b u t e d  increase load  size.  tank w i t h a base  capacity  actually  inclined used  stress  were e n c o u n t e r e d  bearing  considerable  with  a l l  water  under  type  methods  platform,  when p r e d i c t i n g  capacity  the E k o f i s k  may  the  i n t h e e q u a t i o n were d e t e r m i n e d  footings to  affect  other  pore  a n a l y s e s were c a r r i e d  problems  (Bjerrum,  of  s t o r m wave l o a d i n g .  bearing  well-known  The  maximum  edges  significance  under  Several  the  will  Stability safety  that  relative  the d i s t r i b u t i o n  Some  note  entire  (1977)  the tank.  to  the  have l i q u e f i e d  p r e s s u r e s beneath  interest  water  beneath  water  of  pore  (1973) t y p e of a n a l y s i s a t t h i s  density tank  in  had  size angle  Secondly, never  the been  of h o r i z o n t a l  to  90  1  1  r  I  0,-TT*  4  -i l b * Himry of  i  r>  CajkMstwit liom  Timt - hra  D*85% r  » , »kf •!0' C*n/MC 9  Figure  4.13 - T h e o r e t i c a l p r e d i c t i o n o f t h e p o r e w a t e r p r e s s u r e d i s t r i b u t i o n beneath t h e 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 o f 77% and 85% ( A f t e r Rahman e t a l 1977)  91  vertical  f o r c e (about  results  led  Hansen  to  38%).  the  (1970) was  acceptable  load  (Bjerrum,  capacity  to  one-fifth  Finally,  the  drainage  conditions.  maximum  4 seconds),  investigated  the  increased  in  before, on  This  pressure  the  The  of  factor  of  this  was  work  s a f e t y was  of h o r i z o n t a l to  reduced  the  a  wave  capacity  for  to  (about  T h i s problem  had  never  of  been  i s u s u a l l y assumed  (Bjerrum, found  from z e r o  length  could occur.  1973).  from  To  model  triaxial  tests,  assumed  plane  strain  calculations. out  design  the  to determine the loads  since effective  A  lengthy  r e q u i r e d to f i n d  i s shown i n f i g u r e reported.  bearing  i n f l u e n c e d by  complicated  surface.  of  tank w o u l d be  carried  affected  rupture  procedure  no  was  factor  loading only.  of  to account  test  for v e r t i c a l  angle  for s t a b i l i t y  quite  iteration result  friction  distribution  determined  ratio  s i n c e complete drainage  s u r f a c e f o r the  was  model  t h e wave f o r c e w o u l d go  bearing  solution  failure  analysis  the  no d r a i n a g e  t o 36*  used  A plasticity critical  i t s value  of  inclination  factor  cohesionless s o i l  f r o m 34° was  high  This  one-quarter  undrained  conditions,  of  undrained  foundations  this,  1973).  Since  virtually  (essentially)  for  f o r the  b e a r i n g c a p a c i t y of  value  review  c o n c l u s i o n t h a t the  vertical  a  A thorough  the 4.14.  (Bjerrum, the  pore  most  1973). water  s t r e s s e s which and rupture  difficult surface.  Unfortunately,  92  Figure  4.14  93  CHAPTER 5 CHARACTERISTICS OF WAVE LOADING  5.1  Ocean  Waves  Ocean  waves a r e g e n e r a l l y  phenomenon  that  structures or  ice  ocean  may  i n some a r e a s ,  important  consideration in  environment.  apply  structure  Waves  important  e n g i n e e r s must d e a l  f o r the o f f s h o r e  loading  t h e most  the l a r g e s t  wave l o a d i n g and must be  environmental  w i t h when  designing  Although  earthquakes  horizontal  f o r c e s on a  will  nonetheless  ocean  t h e o c e a n come i n a v a r i e t y  significant narrow of  the  p a s s a g e s , wind  be t h e o n l y  5.1.1  water  tsunami s h o a l i n g  t h e s e forms w i t h  will  of f o r m s ,  including:  and  is  sufficiently  tides  energy  g e n e r a t e d waves w i l l  regards to offshore  o c e a n waves c o n s i d e r e d  the  generation  not  the  to prevent  restricted  by  be t h e most i m p o r t a n t  structure in this  design.  These  thesis.  o f wind waves i s a complex  from t h e b l o w i n g wind air-sea  interface  i s transferred by p r e s s u r e  f o r c e s which  s u b s e q u e n t l y s e t the water  1965).  amount o f e n e r g y t h a t  depends the  are  deep  In  The Wave C l i m a t e .The  at  where  an  investigated.  w i n d waves, s h i p - g e n e r a t e d waves, t s u n a m i s , and t i d e s . open  be  The  on t h e d u r a t i o n ,  fetch  frictional  (the  sea  resistance  intensity  distance of  both  phenomenon where  to  water  particles  g r a d i e n t s and  frictional  into  motion  (Kinsman,  c a n be p u t i n t o a wave s y s t e m and d i r e c t i o n  of  o v e r w h i c h t h e wind the  seafloor  the  wind,  b l o w s ) , the  and  air-sea  94  interface,  and  classified  as  under  the  travel  across  wind.  internal  being  either  influence the  (e.g.  of  ocean  Empirical  characteristics  energy d i s s i p a t i o n . or  the  generating  these  in  the  very  waveforms of v a r y i n g  direction,  a l l superimposed  arrangement.  For  using  to take  are  spectra  this  approximations  particular  at  extrapolated  to  at  obtain  the  latter by  the  to estimate  some  meteorological  complex and  The  on  sea  each the  do  is  data  other sea  and  any the  not  conform  to  characterized height,  in  speed,  by and  an  everchanging  i s modelled  statistically  f a c t o r s into account.  best,  "sea-state"  still  unaffected  shape, l e n g t h ,  reason, these  are  wind, w h i l e  from  be  1977).  p r e c i s e mathematical modelling. numerous  former  been d e v e l o p e d  waves  ocean a r e  The  virtually  have  Shore P r o t e c t i o n Manual, Waves  swell.  surface  charts of  sea  Wind waves may  do  not  time.  actually  Very  statistical  These  spectra define  limited  data  p r o p e r t i e s of  a is  the  wave  describe  the  system. For ocean  engineering  surface  period  by  a train  travelling  simplistic  purposes, of  it  is  uniform  waves of  i n w a t e r of c o n s t a n t  model of o c e a n waves and  purposes.  useful  Numerous  theories  to  specific  depth.  This  i s o f t e n adequate  have  been  height i s the for  developed  and most  design  for  this  situation.  5.1.2  Wave All  basic which  Theories  the  analytical  assumptions the  wave  (McCormick,  governing  theories  1973).  equations  and  make some of  They d i f f e r boundary  i n the  the way  conditions  same in are  95  mathematically that  the  (no  water  shear  From  flow  must  theory,  exist  and  satisfy  follows:  and h o r i z o n t a l  (1) t h e b o t t o m  sea  surface interface  the  free  it  temporal  (kinematic  assumed  variation.  and a c c u r a c y  to  d e p e n d i n g on  how  velocity  irrotational  flow  conditions to solve i t .  These  for  i s impermeable, (seabed  and  nondeformable,  boundary  is  condition),  constant  (dynamic  (3) t h e f l o w a t t h e a i r -  with  t h e geometry  free  s u r f a c e boundary  be  Analytical  a  This  interface  s i n c e the v e l o c i t y  is  that  seafloor).  equation.  condition),  i s i n accordance  surface  Additionally, nature  boundary  is irrotational  the Laplace  - a no f l o w b o u n d a r y  (2) t h e p r e s s u r e a t t h e a i r - s e a  assumptions  or a t the  implies  i s an e x p r e s s i o n o f c o n t i n u i t y  as  free  interface  this  r e q u i r e s a number o f b o u n d a r y  are  the  i s i n c o m p r e s s i b l e and t h a t f l o w  potential  equation  Common t o a l l a r e  s t r e s s e s a t the a i r - s e a  potential  and  formulated.  and  motion  of  condition).  potential  should  be  cyclic  in  periodic  with both  spatial  and  wave t h e o r i e s v a r y  i n complexity  they  the  approximate  boundary  conditions. The  simplest  presented  by A i r y  sinusoidal be  and  linearized.  Laplace's results depends  theory (1845).  He  that the free With  equation  these  subjected  i n the v e l o c i t y on  f o r o c e a n waves i s t h e l i n e a r assumed t h a t t h e  to  potential  with  time.  conditions could  the  solution  having  only  one  t h e wave p e r i o d and h e i g h t , t h e s t a t i c  i s sinusoidal  and p e r i o d i c  From t h e v e l o c i t y  was  of  the f o u r boundary c o n d i t i o n s  and t h e d e p t h o f a r e f e r e n c e p o i n t below It  periodicity  s u r f a c e boundary assumptions,  theory  i n the  the s t a t i c  direction  potential,  other  of  term,  which  water  depth,  water  level.  propagation  equations  may  be  96  derived  for  water  displacements, computed  free to  higher  orders  by  potential  a  are  different These  the  however,  sinusoidal are  than  linear  For  shallow  travelling  approximated (Korteweg  (Shore  the  i s not.  and s h a l l o w e r  waves.  may  wave,  elliptical  They compare  well  method,  be  function These a r e  with  wave  and d i f f i c u l t  tank t o use  1977).  i s the  the is  (cn)  1895) t o any o r d e r d e s i r e d .  t h e o r i e s have a l s o  solve  waveform  cosine  water, but a r e c o m p l i c a t e d  I t s use  most wave f o r c e  on e a c h o t h e r ,  of  the  gravity  best  i n s t e a d of v e l o c i t y  parameters.  comprised  surface  which  The  being  waveform,  terms  affects  (1965) t h e o r y ,  because  the  of  significantly  wave  to  resulting  w a t e r , where t h e b o t t o m  Numerical  computer  The  The i n d i v i d u a l  (sinusoidal)  P r o t e c t i o n Manual,  functions  The  theories are estimated  c h a r a c t e r i z e d by s t e e p e r c r e s t s  De V r i e s ,  i n shallow  order  and f i f t h .  process.  forms s u p e r i m p o s e d  t h e c n o i d a l wave t h e o r i e s . tests  higher  approximation.  by t h e J a c o b i a n and  e t c . The  h a s t h e same number o f t e r m s a s t h e o r d e r  waves  troughs  the  the second  perturbation  t h e o r y , and i s a s e r i e s sinusoidal;  and  waves.  used  particularly  velocities  on t h e s e a f l o o r ,  s u r f a c e boundary c o n d i t i o n s i n these  are  a  pressure  wave t h e o r i e s commonly  (1880) t h e o r i e s ,  velocity the  wave i n d u c e d  accelerations,  s u r f a c e waves a r e known a s A i r y  Other Stoke's  particle  potentials equations  limited  due  known,  in  been d e v e l o p e d . is  based  on  Dean's stream  and r e q u i r e s t h e use o f  f o r any g i v e n engineering  to i t s complexity,  s e t o f wave applications  cannot  be u s e d i n  theories.  r e g i o n s of v a l i d i t y  f o r the best  known  wave  theories  97  are as  shown i n f i g u r e being  5.1.3  the best  5.1.  Clearly  no one t h e o r y  c a n be  regarded  for a l l applications.  R e s u l t s o f L i n e a r Wave T h e o r y Linear  more  wave t h e o r y , b e s i d e s b e i n g  reliable  range  of  than  the other a n a l y t i c a l  conditions.  instability  as  most  r e g i o n s beyond t h e i r and  Isaacson,  used  wave t h e o r y  wave  the s i m p l e s t t o  It of  does  not  the other  For these  by p r a c t i c i n g  suffer  a greater  from  numerical  t h e o r i e s do when a p p l i e d i n  ( c a l c u l a t e d ) range  1981).  t h e o r i e s over  use, i s  of  reasons,  validity  (Sarpkaya  i t i s t h e most  engineers.  widely  Additionally,  most  f o r c e t h e o r i e s assume t h a t t h e waves may be r e p r e s e n t e d by  linear wave  theory, although force equations  usually  Stoke's  extensively  in  the  may be computed u s i n g a n o t h e r  fifth  in  t h e wave l e n g t h u s e d  order  spectral  theory.  Linear  resulting  wave  theory  wave f o r c e c a l c u l a t i o n s  theory, is  used  (Bea and L a i ,  1978). The some  profile  results  of a l i n e a r  of l i n e a r  wave i s shown  wave t h e o r y  also  or  period  the case  period  f o r other  wave  theories.  The  by t h e d i s p e r s i o n r e l a t i o n ,  from  the v e l o c i t y  5.2  C h a r a c t e r i z i n g t h e Wave S y s t e m  described  depth,  5.2,  and  i n Table V I I .  and  a r e needed t o d e f i n e a l i n e a r  are related  Since  figure  are presented  N o t e t h a t o n l y t h e wave h e i g h t , w a t e r length  in  either  wave.  wave which  wave  This i s  length  and  i s derived  potential.  wind waves  are  statistically.  random  in  nature,  Approximations  may  they then  are  best  be made t o  98  005•  0.00005'  |  i i  1  1  r  o.OOl 0.002 0.005 0.01 0.02  005 0.1  0.2  d  Figure  5.1  R e g i o n s o f v a l i d i t y f o r v a r i o u s wave ( A f t e r S a r p k a y a and I s a a c s o n , 1981)  theories  99  Wove s p e e d , c  L  5 B  Wove p e r i o d , T = L / c Surface elevation shown ot t = 0  Figure  5.2 - P r o f i l e  d  z•d  k = 2JT-/L  6 - kx-a)t  o f an A i r y  Wave  (After  I s a a c s o n , 1980)  Table VII Some R e s u l t s o f L i n e a r Wave T h e o r y ( A f t e r S a r p k a y a a n d I s a a c s o n , 1981)  Velocity potential  Dispersion relation Surface elevation Horizontal particle displacement Vertical particle displacement  irH cosh (ks) A *= — sin 6 kTsinh(kd) EH cosh (ks) . m — • sin e 2u> cosh (kd) c = -y- = f - tanh (kd) k k 2  2  H T| • —  COS e  H cosh (ks) . sin 6 2sinh(kd) H sinh (ks) t• i COS 6 * 2sinh(kd) t '  •  B  nH cosh (ks) cos 6 T sinh (kd)  Horizontal particle velocity  u•  Vertical particle velocity  irH sinh (ks) . w * — . . „ sin 6 T sinh (kd) 8u c 2 i r H cosh (ks) 2  Horizontal particle acceleration  — —. 8t T  Vertical particle acceleration  aw — *  Pressure  sin 8  2 w H sinh (ks) x2 cos S 2  at  T  »inh(kd)  1 „ cosh (ks) p •= -pgz + - p g H — _ _ _ c o s e 2 cosh (kd)  - Ii  2 k d  1  Group velocity 0 0  Average energy density  sinhftd)  2  2 [  E^ipgH  1  iinh (2kd)J 2  C  100  characterize of  t h e wave s y s t e m  foundation  5.2.1  terms f o r  the Design  design  storm  f r o m wave r e c o r d s .  methods d e v e l o p e d  may the  is  u s u a l l y f o u n d by e x t r a p o l a t i n g  This data  i s often  rather  f o r d e f i n i n g the design  Statistical  sparse  distribution  be  c h a r a c t e r i z e d by a R a y l e i g h  free surface 6 hours.  for  particular  distribution recording  To  describe  (years), by  one  third  may  corresponds well  with  H .  highest  height  assumed  variation  i s convenient  in  any  wave  recording  over  each  record,  the  recording  difficulty  from  the  interval. long-term interval  wave  height,  o f t h e one-  i . e . the the  variation  by a 10 m i n u t e  recording  significant  interval much  interval,  Data  t o be d e s c r i b e d  that  by a G a u s s i a n  as the average h e i g h t  may be computed w i t h o u t  digital  observations.  to represent  the  assuming  recording  be r e p r e s e n t e d  the  sea-state  the free surface  sea-states  i s defined  waves  For  of  parameter,  This  s  interval.  recording  significant .(usually  wave by  a  computer).  A probability wave  is  statistical  denoted  statistical  for a particular  i s r e p r e s e n t a t i v e o f t h e 6 hour  i t  the  distribution,  that  sea-state  the  a n d must be  storm.  for a specific  The a s s u m p t i o n  interval  sample w h i c h  o f wave h e i g h t s  i s Gaussian  usually  data  Description  The  a  purposes  Storm  r e p r e s e n t a t i v e o f s t o r m wave c o n d i t i o n s t o use  5.2.1.1  the  design.  Obtaining The  i n simpler  heights  distribution  may  from numerous r e c o r d s  be f i t t e d  to the s i g n i f i c a n t  to estimate  the s i g n i f i c a n t  101  wave h e i g h t is  usually  (1958). for  f o r some remote e v e n t done u s i n g t h e e x t r e m e  The p r o b a b i l i t y  a specified  significant from  storm  Rayleigh find  wave h e i g h t  may be  found  distribution.  twelve  often  is  duration  of t h e d e s i g n  5.2.1.2  Geotechnical  very  storm, of  i t  heights  i s useful  height)  to frequency and  a  relationship. "design  be  estimated  statistics  -  the  may be r e p e a t e d t o  f o r the design  chosen.  decay  will  purposes,  A  storm.  design  1981).  during  affect  this  storm  of  The s t o r m i s  this  t h e wave  periods  time.  The  statistics.  into  defining  of r e p r e s e n t a t i o n i s  for a specified  the s t a t i s t i c a l a  of o c c u r r e n c e  curve  type  Therefore,  to transform  histogram  design  distributions relating  wave  ( i . e . number o f waves o f some the  wave h e i g h t  This, in geotechnical literature,  - wave p e r i o d  i s known a s t h e  storm".  Because t h e d i s t r i b u t i o n represented any  may  Thus, t h e  o f wave h e i g h t s w i t h i n t h e  (Isaacson,  and  in practice.  wave h e i g h t s and  storm  found  Equivalent  geotechnical useful  be  used  storm  Gumbel  may be d a y s , however, f o r p r a c t i c a l  must  assumed t o b u i l d u p , peak,  of  This  o c c u r r i n g may be  short-term  o f wave p e r i o d s  d u r a t i o n of a storm  hours  statistics  The whole p r o c e d u r e  limit  not  using  storm).  ( e . g . 100 y e a r s ) .  f o r the design  p u r p o s e s some t i m e  For  interval  The d i s t r i b u t i o n  the d i s t r i b u t i o n The  value  of a r a r e event  recurrence  wave r e c o r d s .  design  (e.g. the design  by  particular  transformed  o f wave h e i g h t s d u r i n g a s t o r m  a Rayleigh d i s t r i b u t i o n , band o f h e i g h t s w i l l  into  a histogram.  is  t h e number o f waves i n  be known.  The h i s t o g r a m  This  is  easily  c o u l d have a s many  102  b a n d s a s t h e r e a r e waves i n t h e s t o r m . would  be  impractical.  acceptable, and and  the  on  pressure  1975a)  Six  divisions  duration  amount  granular  have  of  pore  water  that  then  the  be  sensitive  s t o r m may  1394  Such  waves.  Lee  a l a r g e group  smaller  waves w i l l  generation.  divisions is be  performed  to sixteen for  This  and  pore  (Lee water  were q u i c k l y  a c h i e v e d and  produced  5.2.2  Application  Therefore, Of  this.  from  tank.  Bjerrum  for  three  the  These  Focht  He  to  nine  used  pore  the  water  6 h o u r s of  storm of  hour  storm  f o r the  o f waves a p p e a r s  t o be  excessive since  effect  Ekofisk  on p o r e water p r e s s u r e  problem.  pressure ratios  They  of a few  m a i n t a i n e d a t the lower  of the D e s i g n  found  that  p e r c e n t a t most cyclic  stress  waves.  of the storm  d e s i g n storm  interest  used a  Storm  time h i s t o r y  the g e o t e c h n i c a l primary  in  (1973)  (1975a) u s e d a g r o u p  t h e numerous s m a l l e r  the a c t u a l  since  occurring  i s c o n f i r m e d by Rahman e t a l (1977) who  p o r e water  ratios  interest,  dissipation  to  a thirteen  s t o r m t o a n a l y z e t h e same  Using  i s a l s o of  s i x to nine hours.  have l i t t l e  equilibrium  used.  used  conditions  the E k o f i s k  5000 waves t o c h a r a c t e r i z e  hour  1973)  of the d e s i g n storm t o a n a l y z e  b u i l d u p under  contained  six  to  say,  be assumed t o b u i l d u p o v e r s i x t o  subside i n another  s i x hours  pressure  the  been  pressure  nine hours, maintain f u l l - s t o r m  tank.  (Bjerrum,  of t h e d e s i g n s t o r m  deposits w i l l  suggests  worst  to f i f t e e n  to  generation studies.  The  hours,  five  needless  the type of a n a l y s i s  accuracy desired.  Focht,  the  depending  Generally  This,  here  is  impractical.  approximation  may  be  i s when t o a p p l y t h e maximum  103  wave d u r i n g t h e d e s i g n  storm  to find  t h e most c r i t i c a l c o n d i t i o n  for  stability.  Bjerrum  to  apply  maximum wave a t t h e e n d o f t h e d e s i g n  pore  the  water  undrained  pressures analysis  indeed  His  with  corresponding sound,  some  occur al  with  will  in a similar  mind  representing  -  approximate fine  after  way.  substantial  drainage  procedure of  sand.  i s to apply the  conservative,  Based  under  storm  storm  but not  on  the  water  is  For  time  storm.  pressures  found  that  will  (the design  Rahman e t by  can take  system w i t h  wave),  then  this  they  order i n  loading  in  For t h i s  type  of  this  foundations  on  so,  1976). at  least  a f t e r the for  where  no  clay,  the usual  structure This for  the  correct  p l a c e d u r i n g t h e storm,  (Schjetne,  just  analysis,  seems  an  (founded  water p r e s s u r e s would occur  t h e d e s i g n wave t o t h e  unduly  smaller  f o r t h e E k o f i s k tank  Intuitively, For  and t h e  d i d (1973) a n d  of  is  probably  thereafter.  history  water  cohesionless  characterized  t o a maximum  an  i s not n e c e s s a r i l y  the foundation or just  when  t h e pore  o f t h e maximum wave would be j u s t  storm.  on  storm  t h e maximum wave  f a s h i o n , as Bjerrum  the  They  foundations  conservative  take p l a c e d u r i n g t h e storm  t h e maximum p o r e  the  pore  t o apply  to the foundation  application  of  maximum  time  t h e peak o f t h e s t o r m .  critical peak  waves  sand),  highest.  respect to s t a b i l i t y .  i n height  the  end  to  water p r e s s u r e s  applied  on  regard  (1977) assumed t h a t t h e s t o r m  decreasing  is  be t h e h i g h e s t a t t h e e n d o f  drainage  increasing  i t  d u r i n g the storm,  a t the h e i g h t of the storm  waves  the  t h e end o f t h e d e s i g n  t h e most c r i t i c a l  maximum p o r e  be  t o the c r i t i c a l  however,  soils,  would  o f t h e sand  p r e s s u r e s would reasoning  (1973) assumed t h a t  at  the  approach stiff  is  clays  104  ( A n d e r s e n e t a l , 1976).  5.3  Wave L o a d s on t h e F o u n d a t i o n Wave  exerted and  loads  on t h e f o u n d a t i o n  system c o n s i s t of the f o r c e s  on t h e s t r u c t u r e and t r a n s f e r r e d t o t h e s o i l  the pressure  gravity  on t h e e x p o s e d  waves.  foundation. two  System  to  Both  effects  be  seconds,  s e a b e d due t o t r a v e l l i n g considered  Because the p e r i o d  twenty  considered  must  cyclic  forces  loading  when  o f w i n d waves on  to act pseudostatically  of  by t h e r a f t  on  the  for the  designing  the  i s on t h e o r d e r foundation  stress  soil  surface  may  be  analysis.  should  of  The  be m o d e l l e d  appropriately. The l o a d s subjected shown  to  a c t i n g on t h e f o u n d a t i o n wave  in figure  5.3.1  acting  on t h e  reactions are  from p o t e n t i a l flow  There  are  two  basic  the design In  the  Structure  on t h e s t r u c t u r e  derived  statistically,  structure  5.3.  Wave l o a d s  method.  gravity  a c t i o n and t h e r e s u l t i n g s o i l  Wave F o r c e s A c t i n g  structures:  of a  theory  methods  with empirical for  wave method spectral  are found using  wave  the  spectral  method,  whereas i n t h e d e s i g n  coefficients.  finding  and  forces  wave  formulas  forces  are  method,  on  analysis defined  forces  are  treated d e t e r m i n i s t i c a l l y . When on  i t from both  moving the  waves  fluid.  latter  propagate past frictional The  a structure,  and i n e r t i a l  f o r m e r component  i s not (Morison,  1950).  forces are  effects i s highly  caused  exerted by  nonlinear  I f the l a t e r a l  the while  dimension  of  Figure 5.3 Forces acting on the foundation of an offshore gravity structure  106  a  structure  i s significant  more), t h e water disturbed  by  t h e body  developed  gravity  for  regime,  theory  only  vertical  the  For  nearly differ  piercing  overall  The  design  and  by a  frequency  t h e phase a n g l e  s t o r m may of  then  occurrence  wave p e r i o d c u r v e ,  may  t o one  representation  is  wave  linear  1954).  of t h i s will  forces  individual  on a  f o r a given  structure  the  is vary will  wave f o r c e s  oscillatory  period,  For geotechnical  except  corresponding  be t r a n s f o r m e d  of  term  occurrence.  histogram,  force  from  the s i g n i f i c a n c e  i s unimportant  used  neglected,  (MacCamy a n d F u c h s ,  magnitude, of  Linear  calculations  be  computed  Although  now  shape s u c h a s  The i n e r t i a l  waves i n t h e s t o r m ,  p r e s s u r e on t h e s e a b e d  frequency  This  i n time  i n time.  for different  angle,  and  component.  was  In the d i f f r a c t i o n  wave f o r c e s on a g r a v i t y  sinusoidally  purposes, design  small  cylinder  sinusoidally  acting  theory  wave f o r c e  i s r e p r e s e n t e d by a s i n g l e  may be d e f i n e d c o m p l e t e l y phase  is  this  waves) i s p r e s e n t l y  1980).  the g e o t e c h n i c a l engineer,  the  greatly  1954) and may  of a r b i t r a r y  for Airy  (Isaacson,  inertial  theory  wave a n d v a r i e s  Diffraction  and p r o b a b i l i s t i c  component  surface  diffraction  are  t h e wave l o a d s  (MacCamy and F u c h s ,  (developed  platforms  the drag  waveform  ( G a r r i s o n , 1979; Hogben e t a l , 1977).  deterministic  leaving  1954).  t o l a r g e volume s t r u c t u r e s  gravity  that  purpose  platforms  both  and  when p r e d i c t i n g  (MacCamy and F u c h s ,  diffraction for  t o t h e wave l e n g t h ( 2 0 % o r  o f t h e body a s t h e wave p a s s e s ;  i n t o account  for this  be a p p l i e d  motions  the presence  must be t a k e n on  particle  compared  when  f i n d i n g the  t o t h e maximum wave.  from  a  wave  height—  f o r t h e g i v e n wave h e i g h t —  force--frequency  shown i n f i g u r e  5.4.  of  occurrence.  The v a r i a t i o n o f  O  5  10  15  Wave Height (c)  Horizontal  20  30  0  (m)  f o r c e - - w a v e parameter  F i g u r e 5.4  25  1  2  3 Time  relationship  (d)  4  5  6  (hrs)  Time h i s t o r y of wave f o r c e s  - T y p i c a l d e s i g n storm r e p r e s e n t a t i o n used In g e o t e c h n i c a l e n g i n e e r i n g  o -j  108  c y c l i c "shear s t r e s s e s  during  t h e s t o r m may be be  same way once t h e h o r i z o n t a l  5.3.2  Wave F o r c e s A c t i n g For  any  given  forces  found  i n the  are defined.  on t h e F o u n d a t i o n  wave, t h e r e s u l t a n t  may be computed  acting  on t h e f o u n d a t i o n a r e t h e same a s t h e wave f o r c e s  the  structure,  foundation  t o account  some h e i g h t The raft the  forces  more t h a n  is  that the  composed  normal  horizontal  t o the  force  acting  body  of  of  a  steady  and  i s uniform  a  water  and  over  fluctuating the  pressure.  due  to water  is  very  the level  nearly  weight  seafloor  fluctuating  be u s e d t o f i n d  surface.  the r e s u l t i n g seafloor  Linear  (cyclic)  accelerations  equal  to  the  o f a c o l u m n o f water  a s t h e wave  t h e f l u c t u a t i n g component w i l l  as the f r e e  The  p r e s s u r e due t o p a r t i c l e  wave t h e o r y may  distribution;  o f t h e s e a b e d n o t under t h e  The p r e s s u r e a t any l o c a t i o n on  hydrostatic  from t h e s t a t i c  form  acting  t h e water d e p t h d o e s n o t c h a n g e ) and i s n o t h i n g  pressure  appropriate  same  forces  must be a p p l i e d  of the o v e r l y i n g  t h e wave and a t t h e s e a f l o o r  displaced  part  waves.  i s t h e dynamic  hydrostatic  and  on t h a t  The s t e a d y component  component in  acting  of p a s s i n g  seafloor  (assuming  moment  f o r the r e s u l t a n t  a r e due t o t h e w e i g h t  component.  a  The wave  above t h e s e a b e d .  influence  the  however,  theory.  and h o r i z o n t a l  forces  on  from d i f f r a c t i o n  vertical  passes.  the seabed be  theory  pressure  of  Any  pressure  nearly  the  i s commonly used distribution  is  sinusoidal. The is  steady  component  o f no s i g n i f i c a n c e s i n c e  i s u n i f o r m e v e r y w h e r e , and i t  affects  neither  the  therefore effective  109  stresses  or  component  i s of i n t e r e s t  f o r two r e a s o n s ,  not  uniformly  t h e s e a f l o o r a t any g i v e n  act  therefore stress  the stress gradients  over  i n the s o i l .  The  namely:  fluctuating  (1)  i t  time  and must  be c o n s i d e r e d a s an e x t e r n a l l o a d , and ( 2 ) i t  gradients  which  produce  cyclic  shear  does  induces  s t r e s s e s i n the  soil. When f i n d i n g design The  wave, t h e p h a s i n g  seafloor  pressure usually  occur  still  long  pressures  amplitude.  platform's the  the pressure  (large)  of  seabed  The  the platform w i l l forces  the p l a t f o r m ' s  this  and t h a t  vertical  t h e maximum  one-quarter  through  axis.  For  curve  has a  pressures  on  of a wavelength  away  a x i s of the p l a t f o r m ) .  Loading  of  on t h e F o u n d a t i o n  cyclic  the  of  the  platform with  rocking, liquefaction  p l a t f o r m motions during  storm  System  l o a d i n g on t h e s o i l  for a l l stress analyses.  as  platform  be some d i s t a n c e from t h e edge  i n t o account  bearing,  a  means t h a t t h e p r e s s u r e  the r a f t  of C y c l i c  safety  on  than t h e  i . e . when t h e waveform p a s s e s  (approximately  effects  considered.  be l e s s  acting  to the  p o i n t s o f t h e waveform a r e near t h e  due t o t h e wave w i l l  the p l a t f o r m  Effect  near  waves,  from t h e v e r t i c a l  5.4  axis,  level  node somewhere o v e r the  near  The maximum  vertical  corresponding  o f t h e wave f o r c e s must be  when t h e n o d a l  water  distribution  Such  respect  must be  effects to f a i l u r e  or otherwise),  as  l o a d i n g and long-term  well  taken  influence (sliding, as  effects  the such  settlement. Using  figure  a  storm  histogram  5.4(d) t o r e p r e s e n t  the  similar time  to  the  history  of  one  shown i n  loading,  the  110  stress like  path  that  for  which  representation The  figure  i s shown  point  the  The n e x t  represented  by  horizontal  axis.  water  stress  does  not  axis  (zero  This  was  loading as  Pore  to point  "d".  path,  shear  stress)  f o r each  left  out t o c l e a r l y  cyclic  stress  excess  water  pore  i s available  conditions.  This  liquefaction  which  little drainage in  drained  information for  laboratory  triaxial  reduces  exist  at  a  "c" to the  the  effective  p a t h shown i n t h e f i g u r e t o the h o r i z o n t a l is  not  the e f f e c t s  increases  to  continues a  decreases.  shown.  of c y c l i c  S i m i l a r l y , the path  then  from  maximum  Note  i n the foundation  that  element  the storm.  Much d a t a  Partially  are  from p o i n t  illustrate  wave,  pressures  pressure  cycles  s e t of c y c l e s  amplitude  t o the design  amplitude.  water  i . e . the return  element.  corresponding  throughout  The s t r e s s  histogram  Hence, movement  stress  pressure  illustration.  stress  pore  distance  show t h e f u l l  on a f o u n d a t i o n  the  the  of  This  "a" t o the e f f e c t i v e  stress.  set  magnitude  a t one  residual  normal  of  look  5.5.  The f i r s t  from p o i n t  resulting  effective  " a " t o "b".  normal  as f o l l o w s .  i s the distance The  f o u n d a t i o n may  purposes  some number o f c y c l e s  axis.  decreases  f o r the  may be i n t e r p r e t e d  amplitude  stress  b e n e a t h a sand  (unidirectionally) in figure  i s idealized  band r e p r e s e n t s This  an e l e m e n t  sand  tested  i s due t o t h e i n t e r e s t has  attracted  sand b e h a v i o u r is  available  cohesionless shear  for  tests.  .tests a r e used  soils  under  i n earthquake  scores  of  h a s n o t been w e l l on  undrained  the  researchers. studied,  subject.  h a s n o t been d i r e c t l y  Instead, modified  ( L e e and F o c h t , 1 9 7 5 a ) .  induced  undrained  and  Partial modelled cyclic  111  EFFECTIVE Figure  5.5  NORMAL  STRESS,  U'  1 12  Pore on  water  pressure generation in undrained  the c h a r a c t e r i s t i c s  shear  stress  time h i s t o r y of  pore  from  tests  such as  model  tests,  by  or  elements  consolidation  in  (Bjerrum,  intensive 1978)  by  extensive  important instead  describing uniquely  of  on  Andersen  pore  related  overconsolidation  the  and  Focht  (1)  under  an  laboratory  cyclic  methods  that  model  s o l v e the e q u a t i o n s of r a d i a l  too  Undrained  conservative  has  clay  recently  and  the and  analyses are  not  al  Eekelen  deposits.  (1976), of  and  number  and  as  Sea  are  of  an  results  loading  s t r a i n may a  Cyclic  s t r e s s and of  Potts,  demonstrated  a l l , shear  loading.  to the e f f e c t i v e  The  under c y c l i c  development  to c y c l i c  or  van  been a s u b j e c t o f  p l a t f o r m s i n the North  behaviour  First  ratio  model  preshearing using modified  gravity  pressure  response  be  1975b).  be made u s i n g  e t a l , 1976;  clay et  s h e a r may  which  clay  the  concepts. of  and  amount  studies.  substantial  study by  of  The  and  (1975a)  are  (Andersen  some  underlain  reported  loading  study  as  Focht,  (Rahman e t a l , 1977).  f o r advanced  Cyclic  stresses.  appropriately  numerical  1973)  the magnitude  water p r e s s u r e s developed  and  (2) from  and  i n undrained  that  (Lee and  drainage  finite  appropriate  shear  s t r u c t u r e may  vertical sand  tests  the pore  type  static  t h o s e d e s c r i b e d by Lee  partial  triaxial soil  gravity  cyclic  problem  of  the magnitude of the  generation  laboratory  Estimation  depends  before testing,  pressure  wave l o a d i n g  offshore  soil  of the a p p l i e d  water  estimated ocean  i n the  of the sand,  shear  be  used for  strains  independent  cycles.  several  parameter shear  were  of  Secondly,  are the the  113  effective  strength  unaffected Thirdly, strain the  cyclic  the  undrained  higher  the  overconsolidation  to  fewer  accumulation  excessive It shear  Andersen  has  been  found  for  equilibrium  on  s t r a i n s to p r e d i c t f a i l u r e  reached  reduced  value  for  level  should  pore  water  undrained static be  from  slightly  failure.  loading.  which This  history loading  is  on  after  reduction  in  This  stress-strain  further  increase  If t h i s a  critical  cumulative  failure  i s about  critical  cyclic  which  will  occur  two-thirds  for  important  clay.  overconsolidated  For  non-  displacements  experimentally  heavily  loading strength  For  an  when normally  deposits,  i m p l i e s c o n s o l i d a t i o n and  strength.  a s t a t e of  cause  and  applied  of  shear  each  the  stress  cohesive  1973).  Consolidation of c y c l i c  no  cycle will  strength  i f the  where t h e  with  pressure  determined  (Bjerrum,  value,  ( S a n g r e y e t a l , 1969).  r e s u l t s i n a shear  occur  stress  (1976) d e v e l o p e d a method b a s e d  h y s t e r e s i s loops  ultimately  loading  finally,  cyclic  necessary  shear  the  be  in  and  for a given  is.  w  to b r i n g  i s exceeded, each l o a d i n g  effects  And  i n s e n s i t i v e clays that  will  follow closed  deposit  c  f u n c t i o n of c y c l i c  i s below some c r i t i c a l  p o r e water p r e s s u r e  a  virtually  strength  applied.  ratio  shear  increase  at  are  displacements.  failure  value  is a  of c y c l e s a r e  of c y c l i c  stress level  curves  tan0'  undrained  stress cycles  number  failure.  and  the  strength  number of  the  c'  but  the  sample  in  loading,  and  ratio,  the  by  parameters  increase  terminated,  (Schjetne,  clays,  with  1976).  in  The  a  the  consolidated  drainage a f t e r  overconsolidated  is  assessing  the  cyclic  un.dirained  swelling  may  corresponding  effect  of  this  on  114  platform  safety  is  overconsolidated decrease  with  platforms  on  soil  will  unsuited excessive  as  follows:  deposits, subsequent  the  For safety  cyclic  normally consolidated  increase for a under  in time.  gravity  of  the  loading. or  slightly  loading.  since  on  highly  platform  will  safety  of  The  overconsolidated  However, t h e s e d e p o s i t s  platform  s t o r m wave  foundations  are  displacements  usually may  be  115  CHAPTER 6 PROCEDURES FOR ANALYZING OFFSHORE GRAVITY  6.1  Fundamental The  of of  as  the  used.  load,  strength result  The l o a d  when  equilibrium  mobilization  the design  factor  under  i n the  i s expressed.  safety  This  factor  t o c a u s e an  margin  the design  soil  is  The two s a f e t y  i s defined  by  which  the s o i l  loads.  often  failure  of the s o i l i s  amount  to bring  safety  ultimate  strength  i s the  p a r a m e t e r s must be r e d u c e d  limiting  failure.  the margin  i n one o f two ways: by a l o a d  required  safety  i s to assess  foundation  factor.  of the l o a d  The m a t e r i a l  strength of  be e x p r e s s e d  design  analysis  an u l t i m a t e  or a material  the r a t i o  to  Considerations  against  s a f e t y may  factor  TYPE STRUCTURES  purpose of a s t a b i l i t y  safety  THE S T A B I L I T Y OF  to a  the state  The d e g r e e o f  how  factors will  this  latter  in general  be  di f ferent. Onshore, a s a f e t y take  i n t o account  strength conditions, Offshore,  f a c t o r of about  uncertainties associated  parameters, and  the  a much l o w e r  ground  water  analyses  s a f e t y may  be r e d u c e d .  will  justified  be l e s s ,  For t h i s  projects.  loading  considerable the problem The  economically,  bearing  of  methods.  define  and t h e r e f o r e ,  reason,  values  analytical  in trying to better  is  used t o  conditions,  i s u s e d and a  factor  done f o r most o n s h o r e  degree of u n c e r t a i n t y  the  safety  than  rigorous  with  of  i s spent  more  i s commonly  reliability  amount o f e f f o r t i s commonly  three  use  of  s i n c e the  the f a c t o r of  capacity  theory  116  is  generally  adequacy  used  of  equilibrium element  a  site  methods  for  for based  method a r e u s u a l l y  Evaluation estimation shear  only  of  a  a  gravity  on  slip  the s a f e t y  mechanism.  in  the  type  of  surfaces  and  Limit  the  finite  criteria,  of the s o i l ,  three  t h i n g s : an  estimation  of  and t h e p o s t u l a t i o n o f a of the s o i l  may  be d e f i n e d  stress,  this  T =  c'+  f  on  the  equation  shear  6" cr  <y -  of  (6.2)  normal  stress, defined  remember t h a t  reverses.  the magnitude  pressure.  There a r e , t h e r e f o r e , stresses  in  o f t h e p o r e water  i s convenient to discuss  i n terms o f i t s v a r i o u s  pressure,  both shear the  pressure  s  u  s  t h e p o r e water  components.  u, a t any l o c a t i o n i s g i v e n  u = u + u + where  as  soil.  stress Both  a t any t i m e  the storm.  It soil  parameters  e a c h h a l f wave c y c l e t h e d i r e c t i o n  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  during  strength  (6.3)  should  affect  shear  u  loading  will  of e f f e c t i v e  a'tan0'  where u i s t h e r e s u l t a n t p o r e w a t e r One  In t e r m s  the  is  i s the e f f e c t i v e =  by t h e  p a r a m e t e r s and C i s  surface.  where c' a n d t a n 0 ' a r e t h e e f f e c t i v e and  failure  (6.1)  where c and t a n 0 a r e t h e s h e a r s t r e n g t h stress  the  which i s  Tr. = c + a t a n 0  normal  the  structure.  factor requires  soil,  The s h e a r s t r e n g t h  Mohr-Coulomb f a i l u r e  estimate  employed.  of the shear s t r e n g t h  stresses  preliminary  e  pressure  The t o t a l  pore  i n the water  by  Au  i s t h e h y d r o s t a t i c component, u  (6.4) c  i s the r e s i d u a l pore  117  water  p r e s s u r e due  storm,  and  Au  to c y c l i c  i s that  loading  part  due  at  any  time  t o the changes  during  i n the  the  principal  stresses. The u  =  s  where  the  )( i s t h e u n i t  weight  w  z  and  includes  is  the  of seawater,  depth  below  t h e p r e s s u r e due The  effective  influenced  This  is illustrated  by  d is  the  the mudline.  to the s t a t i c  stresses  6.1.  T h i s may  water  that  body o f water are,  t h e p r e s e n c e o f an o v e r l y i n g in figure  still Note  i n the s o i l  = V„z  s  i s simply (6.5a)  not  if  p r e s s u r e i n the s o i l  w  mudline.  u  p o r e water  + Y z  ^ d  depth, term  hydrostatic  above  however,  body o f  be t a k e n  water.  as  '  the weight  of the o v e r l y i n g  body o f w a t e r  this  (6.5b) i s o m i t t e d from a l l  calculations. The  component  changes  in  (Skempton, Au  where  the  principal  cr, i s  principal  3  + A (AC,  the  stress,  may  AC  the be  soil  due  determined  to from  be  taken  one-third. i s equal to the  of  this  to the t o t a l  )]  (6.6)  stress,  as  parameter,  for  the  offshore  soil, that  stress  the  minor  will  stress  be a  The  increment.  B-  foundation  A-parameter  the r i s e  the p o r e water  hydrostatic  is  T h i s component  unity  implies  total  3  f o r t h e d e s i g n wave.  isotropic  This  o~  B are d i m e n s i o n l e s s pore p r e s s u r e  (for dilation)  equal  equal  may  i n the l a b o r a t o r y .  F o r an e l a s t i c  to  3  A and  analyses.  values  stresses  principal  and  maximum o r minimum parameter  -  major  p a r a m e t e r s measured  pressure  pressure in  1954)  B[AO"  =  of p o r e water  i n pore  is  water  For  other  pressure rise  i s not  increment.  118  d  unnnij  * I / Z  1  /  (i)  (2)  Us  u  « l«(d  6'  - q •  • ).Do  D ) 0  *  -  u  « *w(d  cr' -  Xwd  + Hz •  x)  Y'z  (2)  Figure  6.1 -  E f f e c t i v e stresses in s o i l for s t i l l w a t e r c o n d i t i o n s ( i . e . no wave l o a d s )  119  Pore water p r e s s u r e s w i t h i n the loading  may  be  estimated  with a numerical  model s u c h  for  consolidation,  such  as  the  those  in-situ  d e s c r i b e d by  observations  pore on  of  or  from  Lee (3)  platforms  and  excess  be  pore  raft.  S t r e s s g r a d i e n t s are  waves  liquefaction  are  may  large  occur  pressure the  using rise  total  The  spherical  Bjerrum,  performed. pore  by  for a clay stress  stress  An  effective  p r e s s u r e s must be  two  analysis.  may  be  estimated  without  estimates  from  1970).  sustained,  may The  be  often pore  nearly  be  water  equal  clays  to  and  the  (Skempton also  namely:  effective  be the  shear  T h e s e p a r a m e t e r s must  w h i c h r e q u i r e good  These are o f t e n u n a t t a i n a b l e . performed  is  difficulties,  tests  samples.  seabed  s t r e s s a n a l y s i s may  be  l a b o r a t o r y shear  presence  for overconsolidated clay.  evaluated.  from  loading  be  1978).  s t r e n g t h p a r a m e t e r s have t o be found  the loads  (Henkel,  i s c l o s e to o n e - t h i r d for these 1957).  to  the  i n the  foundation  increment  T h i s method p r e s e n t s  water  Lee,  A  pressures w i l l also  induced  and  with  through  addition  p a s s i n g waves  enough  total  tests  performance.  In  i n a f o u n d a t i o n element w i l l  A-parameter  and  a  triaxial  ( o r i n f l u e n c e d by  ( F i n n and  A stability analysis performed  under  v a r i a t i o n s caused  tests  account  gained  for  water  of)  the  shear  a s a c o n s e q u e n c e of c y c l i n g  soil  If  cyclic  (1975a) c o r r e l a t e d  used.  i n the  the p r e s s u r e  to  cyclic  experience  developed the  not  Focht  instrumented  o f t h e s e methods may  structure,  from  due  modified c y c l i c  from  water p r e s s u r e s g e n e r a t e d the  (1) d a t a  mass  a s Rahman e t a l ' s (1977) t o  (2) d a t a  stresses,  combination  using  soil  A total  of t h e p o r e  stress water  quality analysis pressures  120  or  laboratory  determined vane  from  may  be  estimated T h i s has  shear  test  in-situ  used  effect  on c l a y  It  should  tests  of  platform  that  a major  stress  loading,  f o r most  penetrometer  ( i . e .strain  North  Sea  or  for  the  softening).  gravity  for cohesive s o i l s  the s o i l  mass due  n o t have d i s s i p a t e d  storm h i t s  the f i e l d .  i s required  be u s e d .  d a t e , may  strength  appropriately  loading  be n o t e d t h a t  may  which  undrained  structures  ( S c h j e t n e , 1976).  analysis  l o a d s may  reduced  cyclic  pressures developed within the  The  s u c h as t h e cone  directly,  been t h e c a s e  founded  data.  A total  may  and  the  In t h i s c a s e ,  water-  weight  substantially  by  an  the  of time  effective  loads less  t h a n t h e d e s i g n wave  stress analysis  f o r the d e s i g n storm  be assumed t o h i t t h e  a l s o be p e r f o r m e d .  to  the pore  Some s o r t  platform of r i s k  at  a  analysis  later will  be  required. For soil  the s t a b i l i t y  an e f f e c t i v e  stress  analysis analysis  e s t i m a t e s of t h e p o r e w a t e r appropriate  method  pressures.  The  may  shear t e s t s .  establish  the r e l a t i v e  the  6.2  i s performed.  pressures within used angle  This  the s o i l  requires mass.  t o e s t i m a t e these pore must  Cone p e n e t r a t i o n density  cohesionless  which  be  determined  resistance  i s needed  for  Any water from  can h e l p t o interpreting  tests.  M o d e l l i n g t h e W a v e - S t r u c t u r e - S o i l System Since  and  be  friction  laboratory  o f a f o u n d a t i o n on  rarely  foundation,  gravity rest  p l a t f o r m s never on  the seabed  i.e. skirts  and  approximate  without  ribs,  some  strip  some s o r t  footings  of s u b s u r f a c e  assumptions  regarding  121  g e o m e t r y must be made so t h a t a n a l y t i c a l  techniques  The  "equivalent  platform  foundation", platform be  at  i s u s u a l l y modelled that  base.  i s , one  The  together  level  i s good  compartments.  The  skirts  3.6(b),  and  effective  foundation  same  area  foundation"  does n o t should  failures  3.6(a),  an  ( L a u r i t z s e n and  i f failure  to prevent  dimensional  the  "effective  skirt-tip  assumption  with  by  of  the  3.6(d).  A  shown  in  is  r e p r e s e n t a t i o n and  be  used.  rectangular  as  the  actual  i s u s u a l l y assumed Schjetne,  extend  be  may  up  into  spaced kinds  shown  i n 6.2(b) f o r a  in  skirt enough figures  sketch  6.2(a)  This  the  closely  definition figure  1976).  to  of  for  the  a  two-  three-dimensional  one. When  modelling  i n c l u d e a l l the seabed  either base are which  or  base by and  6.3(b)  the  The will  skirt  The  fluctuating  the These  i t i s important  the  structure  of  application  of  pressures,  loads a c t i n g at analysis.  The  s e a f l o o r , must be the  tips  forces  in  the the  resultant  and  the  the  of  the  must  be  foundation  wave  loads,  t r a n s m i t t e d to  acting  resultant foundation  loads  between load.  forces are defined  the the  Figure  system,  which are  to  and  used  in a  qualitatively  in  paragraphs.  vertical  consist  both  points  f o r c e s a c t i n g on  analysis.  following  at the  shows  system,  distribution  including  the  6.3(a) shows t h e  stability  the  The  assumed.  specified  foundation  figure  i t .  required for a s t a b i l i t y  are  seafloor  to  f o r c e s , or  known  foundation  f o r c e s w h i c h a c t on  adjacent  resultant  the  of  l o a d a p p l i e d to the the  vertical  buoyant  f o r c e due  effective  weight t o the  of  the  wave AP  V  foundation, platform P (which  v  V , B T  , the  will  be  122  (b) T h r e e - d i m e n s i o n a l  Figure  6.2  - Definition  sketch  representation  of  effective  foundation  123  APlX) W » V «  AP(X)  1"  n r r r r I I I I I  l  *  R  (a) L o a d s a c t i n g  APOO  IffNt/l  rrrrrr  1 T  1  ' '  1  »  (b) L o a d s t r a n s f e r r e d  Figure  6.3  on t h e p l a t f o r m  r  O I  M  B  AP(X)  T  to the foundation  - Transformation  of l o a d s  base  to foundation  base  124  downward  for  contained  within  acting be  on  design  c o n d i t i o n s ) , a n d t h e added  the s k i r t  the periphery  ignored.  compartments.  raft  will  be n o n u n i f o r m  This  i s usually  taken  since  base w h i c h  resultant  load.  c e n t r a l l y on t h i s  effectve  area  i s represented  once  established.  the  This  by B L  only  with  load  that  respect load  (Hansen,  eccentricity  at  to the then  1961).  the  eccentricity is initially  area  is  i n f i g u r e 6.2(b).  0  the  and e c c e n t r i c .  by c o n s i d e r i n g  " e f f e c t i v e area"  usually  beneath  i s inclined  i s symmetrical  soil  forces  may  stress  The r e s u l t a n t v e r t i c a l  applied  determined  loading  from  shear  foundation  vertical  i n t o account  of " t h e f o u n d a t i o n vertical  Vertical  o f t h e imbedded  The d i s t r i b u t i o n o f  load  unknown  The  I t may  be  base  is  since the  moment a t t h e base o f t h e s t r u c t u r e d e p e n d s on t h e  soil  forces  acting  these  forces  between  the  must be d e t e r m i n e d moment values  f o r the s o i l  by  foundations.  For  only  one  This  approximately  foundation,  effective  dimension  ,  of  of  However,  width  symmetric).  area  usually  n o t be  then  for  equivalent  equivalent  and  i s , when  rectangular  structures  length  Meyerhof's  shallow  foundation  for gravity  be  influenced  e c c e n t r i c i t y , that the  the  reasonable  may  particularly  the  the case  of s i m i l a r  radially  R T  will  forces,  t o one s i d e  horizontal H  procedure.  one-dimensional  width" p r i n c i p l e i s then The  The  soil  i s normally  they a r e u s u a l l y  level;  be a p p r o x i m a t e d by c h o o s i n g  forces.  the  is parallel  reduced.  may  The e f f e c t i v e a r e a  significantly  loading  and s k i r t - t i p  from an i t e r a t i o n  a t base l e v e l  established.  base,  mudline  ( i . e . they  is since are  (1953) " e f f e c t i v e  used. force  which  i s somewhat more  acts  on  the  effective  difficult  to  assess.  This  125  force  is  equal  to the r e s u l t a n t  o f t h e h o r i z o n t a l wave l o a d  and  t h e h o r i z o n t a l components o f a l l t h e f o r c e s  acting  the  m u d l i n e and s k i r t - t i p  tail  end  of  the  foundation,  nose o f t h e f o u n d a t i o n , imbedded active  base. and  passive  the  seafloor,  this  soil  force  tension  crack  i s assumed  (which acts  A  P  A  on t h e  the passive  soil  force  P  p  on t h e  is  i n any c r a c k .  to  foundation strain  base.  The s h e a r  This  analysis.  foundation  base  as  exist w  reduce  s  on t h e s i d e s  s  assumed  significant  negative,  force, P ,  water  P ,  P  are  with  of  the  Generally,  the  to  only  act  penetration  at  clay  the  the s o i l  forces  the  for  tail  horizontal  resistance  assumed  of  i s not included  differently  in  a  the  pressure  pressures) of  applied  The d i s t r i b u t i o n o f h o r i z o n t a l  is  end  on t h e s i d e s force  the  foundations,  pore water  acting  into  When  due t o t h e dynamic wave  i s not i n e q u i l i b r i u m with  foundation,  forces  a s s u m p t i o n may n o t be r e a s o n a b l e .  active  platform.  force  forces  For structures  between  soil  f o r c e s must be e s t i m a t e d . soil  H  the a c t i v e  and shear  These  horizontally.  level:  P  for  a  the  to the plane  f o r c e over the  various  stability  theories. The varies the  dynamic  roughly  wave  gravity apply  structure  used  pressure  pressure  dynamic acting  to  stability  acting  on t h e s e a b e d ,  calculate i t . analysis,  uniformly  magnitude and p h a s i n g this  pressure  Ap(x),  s i n u s o i d a l l y ; t h e e s t i m a t e d v a r i a t i o n depends  theory  the  wave  will  For the purpose of a often  adequate  on e i t h e r end o f t h e r a f t ,  into consideration,  over a s h o r t  wave p r e s s u r e  i t is  distance  is  since usually  level.  to  taking  the v a r i a t i o n of minimal.  a f f e c t t h e magnitudes of s o i l  on t h e s t r u c t u r e above s k i r t - t i p  on  The forces  126  The  e f f e c t s of c y c l i c  be a d e q u a t e l y and  6.1.  taken  The  preshearing  i n t o account  effect  Loading Applied The  is  vertical  equal  may be w r i t t e n B T  =  where  P P  v  v  vertical  V  is  the  the  0  within  H  * T  =  P  H  tail  f  level,  V  6 1  ,  skirt  compartments.  This  (6.7) platform  load  ( t h e buoyant weight  due  to environmental  base,  D  of  is  0  load acting  acting  level. (P*  P = [(0.5rD Here, Ap  the  the l i f e  or  where t h e a c t i v e A  analyses.  l o a d a t t h e s e a f l o o r and the  over  forces  +  strength  0  vertical  horizontal  skirt-tip  choosing  at the e f f e c t i v e foundation  r e s u l t a n t of the a p p l i e d  and  the  load  the  the  soil 2  o  P j  -  loading, depth  A  the  weight  of  load  P  effective  soil.  on t h e f o u n d a t i o n  environmental  i s the  V  i s the area of  0  of  AP  which  base, H  H  between  and  B T  , is  a l l the  the s e a f l o o r  may be e x p r e s s e d a s P  +Ap,D )tan  (6.8)  p  force  i s defined 2  o  i s t h e dynamic  the absence of  of the p l a t f o r m ,  on t h e p l a t f o r m  This  in  structure),  a n d H' i s t h e e f f e c t i v e u n i t  horizontal  on c l a y a n d  + (A D )i"  equivalent  The  5.4  t o the Foundation  loading  load  foundation,  must  sections  history  when  storm  soils  as  not constant  the  consolidation  f o r design  of s o i l  + AP  environmental is  i n accordance with  t o t h e sum o f t h e v e r t i c a l  submerged w e i g h t  V  of  on t h e f o u n d a t i o n  i n s a n d , must be c o n s i d e r e d  parameters appropriate  6.3  loading  (45'-0/2)-2cD tan(45'-0/2) ]L o  wave p r e s s u r e  end of the p l a t f o r m ,  by  acting  on t h e  0 i s the mobilized  0  (6.9)  seabed  friction  at  angle,  127  c  is  the  length. it,  mobilized If P  given P=  The  0  P=  force  i s defined  2  2  o  force  replaces  P  w  the  preceding  Note t h a t  e q u a t i o n s may  equivalent  platform  is  done  by  length  L  three-dimensional  a l s o be  used, with  s i d e s of  the  Equation  (6.8)  = P«  BT  o  platform.  This  a  where  the  may or  A  to  0  one  0  - P  the  In  this  s i d e s of  the  the  case,  foundation  P  s  (6.13)  o  the  the  T h i s may + P D H  be 0  h ,  and  T h e s e may  be  found  (P h  effective This  may  the  expressed  +  where h,,  2  moment a t  foundation  f o r c e s a c t i n g between the  known.  r e s i s t a n c e on  + O.5tf'D tan0)  0  to a l l the  The  length.  (6.12)  r e s i s t a n c e on  moment a p p l i e d a t  = M  the  equations  s  of  feT  shearing  by  unit  aforementioned  strain  as - P  f  plane  f o r c e per  near  quantity.  equation  included.  resultant  base.  the  exception: be  each  (6.11)  seabed  i s a negative  2  used to d e f i n e  find  must  the  0  by  = 2D B (c The  w  Ap  dividing  written  P )  shearing  is defined s  be  be  a c t i n g on  a n a l y s i s , the  foundation  (P  +  o  dynamic wave p r e s s u r e  loading.  M  platform  as  2  i s the  2  The  P  a water p r e s s u r e  equivalent  (6.10)  soil  n o s e of  H  i s the  0  0  o  where A p  may  L  [(0.5 'D +Ap Do)tan (45 +0/2)+2cD tan(45°+0/2)]L  p  For  and  by  passive  the  i s negative,  A  Ap,D L  w  cohesion,  be  3  A  or  are  base,  s e a f l o o r M,  s e a f l o o r and  is  B1  the the  moments  the due  foundation  as  P )hi w  - P h f  2  - P h s  moment arms f o r t h e  from e a r t h w i d t h B may written  and  M ,  as  pressure be  (6.14)  3  appropriate  forces.  theory.  f o u n d once t h e  eccentricity  is  128  B = B (1  ~ 2e)  0  where B city  i s the  0  equivalent  e i s given  e =  6.4  (6.15)  f c  t h e NGI  be  are  s u r f a c e method, a l s o be  stability.  These  methods  sections.  offshore gravity  chapters, is  using  Bearing  stability  performed are  finite to  stability  of  element  method.  i n v e s t i g a t e foundation  discussed  in  in  the  when a p p l y i n g  them  emphasized.  procedure  numerical  b e a r i n g c a p a c i t y methods,  problems encountered  of  Capacity  shallow  b a s e d on  depth  In t h e f o l l o w i n g  t h e method of  slices  or  ultimate  in  a  cohesion  c,  and  loaded produce  with  figure  6.4.  rigid  homogeneous d e p o s i t friction  a central  a uniform  uniform  long  angle  surcharge  0,  vertical  pressure q'.  i s often  Computation  bearing pressure  infinitely  resting  Approach  foundations  bearing capacity theory.  model o f an  a  foundation  the  s t r u c t u r e s are  alternative  Classical The  0  The  and  or  presented.  6.4.1  Q,  an  the  These a r e : the  t e s t s may  to  a number o f a n a l y t i c a l  used t o a s s e s s  Centrifuge  following  eccentri-  Methods  platform.  slip  the  (6.16)  there  methods w h i c h may gravity  and  0  Available Stability Presently,  a  width  by  (M A -r)/B B 7  foundation  q. This  of  the  ultimate  q , 0  i s b a s e d on  strip  footing  of e f f e c t i v e  at a depth D . 0  load The  investigated  Q  which  adjacent  soil  representation  a  simplified  of  width  unit  weight  The is  B  footing assumed  i s loaded is  load  shown  0  is to  with in  129  Qo=q B 0  Figure  6.4  0  - T h e o r e t i c a l rupture  surface  geometry  130  The by  bearing  c a p a c i t y problem  i s represented  a r a t h e r cumbersome s e t o f p a r t i a l  closed for  form a n a l y t i c a l  special  cases  (e.g. P r a n d t l , The  0  this  widely  He p r o p o s e d  evaluated  q  of  differential  h a s n o t y e t been  problem,  equations.  found,  solutions  are  A  although available  1921).  most  (1943).  solution  mathematically  recognized that  the  solution  ultimate  i s t h a t of T e r z a g h i  bearing  capacity  be  from  = - „ ' B N + c N + q'N. Y  2  (6.17)  c  *  *  where t h e N - v a l u e s a r e known a s b e a r i n g c a p a c i t y f a c t o r s .  These  coefficients  Since  N  t  and N  %  another,  combination  one  rupture  i s an a p p r o x i m a t i o n  o f c , 0,  rupture  solution.  surface  and N  (Hansen,  1970).  The  different  for  surface  and q ' .  is  The e q u a t i o n than  values  of t h e b e a r i n g  are not.  the  plasticity  for  a particular  factors. solutions  to  (Lundgren  i s g e n e r a l l y accepted, capacity factors  solution  and depend o n l y  shape o f t h e assumed  the  many  be  on  surface.  c  order  of  a factor  from  angle  -  It i s  surface that  interpretations  i n the N - and N^-values the  arise  on t h e f r i c t i o n  rupture  different  but t h e  t o be u s e d i n  The b e a r i n g c a p a c i t y f a c t o r s  The v a r i a t i o n s may  for  i s , however,  20%  d e p e n d e n c e on t h e shape o f t h e assumed r u p t u r e rise  y  1953). (1943) s o l u t i o n  equation  gives  plasticity  Terzaghi  numerical  this  the  and e r r o r s a r e g e n e r a l l y l e s s  Mortensen, The  the  equation  for  of the t h e o r e t i c a l  conservative and  from  are calculated this  location each  arise  for  of these different  o f two, and t h e  131  differences is  of  i n the  N^-values may  particular interest  cohesionless Equation  soil  for  where  friction  the  published  angle  the  considerable  variability  the  angle depending  friction  very  infinite both.  idealized in length  For  gravity  eccentric. 0.2  possible  except  common.  have been e m p l o y e d To of  extend  the  base,  q  0  where  to  inclined  10  y  the  s-,  y  r  i  y  d-,  loading 10%  Since  findings  y  are  that  there  is  for a given  value  of  used.  i n c l i n e d Or is  and an  always  are  for never  eccentric inclined  i n c l i n e d load  factors  analytical solution  o f cases,  empirical  (1943) s o l u t i o n t o o f the  and as  soil  different  is  or and of not  factors  include above  the  the  foundation  foundation  + cNeScd^i,. + q ' N ^ d ^ i ^  and  effects  shapes,  (Hansen, 1961):  i-parameters are  T h e i n c l i n e d load f a c t o r , denoted h o r i z o n t a l to v e r t i c a l load.  1 0  His  foundations  is often  of  resistance loading,  s d  (1972) from  improve r e s u l t s .  (6.17) i s r e w r i t t e n  = — V BN  function of  Andersen  N  of  Real  simplest  Terzaghi's  shearing  Equation  loading  f o r the  a  upon whose r e s u l t s a r e  structures,  are  as  term i n  approximate t h e o r e t i c a l s o l u t i o n  Eccentricities  t o 0.4  by  f o u n d e d on  I t is clear  value  foundation. and  y  authors.  6.5.  discrepancy  (first)  N  V a l u e s of  i n the  (6.17) i s an  Equation a;  frictional  several  i n figure  This  structures  have been c o m p i l e d  r e s u l t s of  graphically  even more.  gravity  (6.17) i s p r e d o m i n a n t .  the  shown  be  by  &,  (6.18)  empirical coefficients  is  the  ratio  o f the  132  Figure  6.5  - Comparison of d i f f e r e n t proposals for t h e v a l u e o f Ny ( A f t e r A n d e r s e n , 1972)  133  which r e p r e s e n t depth,  and  load  coefficients parameter Equation  (set) at  footing  a  analytical  foundation  shape,  respectively.  plate  time  Curves  formula  of  inclination,  (6.18).  general  effects  were f o u n d u s i n g  approximate  basis  the  and  loading  These  fitted  expressions.  f o r the bearing  the  to the data Equation  capacity  the  two  those of Meyerhof  (6.18)  of a r i g i d  differ  in  most w i d e l y u s e d b e a r i n g  (1963) and Hansen  their  estimation  of  results  The  to  i s the  horizontal  and  capacity  (1970).  one  to determine  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 of  empirical  t e s t s by v a r y i n g  corrrelating  were  imbedment  i s the theories,  two  theories  t h e s e c o e f f i c i e n t s and t h e N-  values. Hansen's offshore. is  that  (1970)  This  formulation  is  i s due t o s e v e r a l  gravity structure  the  factors.  method  The most o b v i o u s one  technology developed  e n g i n e e r s u s e d Hansen's  (1961,1970) t h e o r y  problems.  s t u d y o f t h i s method,  A  cohesionless Ekofisk  thorough deposits,  tank  s t u d y was t h a t results, purposes of  was made p r i o r  (Bjerrum, Hansen's  even  for  1973).  large  i t was d e v e l o p e d  homogeneous  for.  to  capacity  f o r a p p l i c a t i o n to  installation  will  of  the  drawn from  this  provide  acceptable  inclinations,  when u s e d  (i.e. for total  stress  f o r the analyses  deposits.)  Eccentric coefficients.  load  i n E u r o p e where  f o r bearing  The c o n c l u s i o n  (1970) method  preferred  loading  is  not  The e f f e c t i v e a r e a  (1953)  is  used  instead.  footing  on a r e d u c e d a r e a .  loaded  "effective  area"  treated  are  using  approach proposed  A concentric The  by  load  dimensions then  used  of  empirical  by  Meyerhof  i s applied this  t o the  centrally  i n the general  bearing  134  capacity is  satisfied  also of  equation,  Equation  when u s i n g  assumed  this  to a c t only  treating eccentric  (6.18).  technique.  over  loads  O v e r a l l moment  equilibrium  The h o r i z o n t a l  the e f f e c t i v e area.  force i s  This  i s f o u n d t o be c o n s e r v a t i v e  method  (Hansen,  1970). For  total  sliding  resistance  foundation will  force  if  is  outside  may be m o d i f i e d  base o u t s i d e  the  the  friction a great  bearing  angle,  take The  this  into  horizontal  the  simplification,  may  capacity  theory  (Lauritzsen  t a k e n on t h e  i s subtracted  be  important  and  foundation  from t h e  total  the procedure o u t l i n e d i n  s o l u t i o n s m e n t i o n e d a b o v e assumed  since  Offshore  the that  the  bearing  that  i s extremely  account  using  Since  the ultimate  Bearing  load  and e f f e c t i v e u n i t real  deposits  They a r e u s u a l l y  interbedded  proposed  of  resistance  calculation.  i s t o be a v o i d e d .  was homogeneous, w i t h c o n s t a n t  of  This  o f any amount o f r e s i s t a n c e  capacity  nonhomogeneous.  nature  part  section.  homogeneous.  clay  substantial  that  i n reducing  f o r c e may be f o u n d  following  soil  critical  of the e f f e c t i v e a r e a  This  The  to  1976).  capacity  of the e f f e c t i v e area  undue c o n s e r v a t i s m  load.  on  of the e f f e c t i v e area.  consideration  Schjetne,  foundations,  mobilized  i n the bearing  force  mobilized  be  of c l a y  t h e h o r i z o n t a l f o r c e a c t i n g on t h e e f f e c t i v e a r e a ;  used  horizontal capacity,  may  base o u t s i d e  reduce  that  s t r e s s analyses  with  weight. soil in  the  of the  This  particular  layered  and o f t e n This  environment.  aforementioned  cohesion,  i s , of c o u r s e ,  deposits  sand, or v i c e v e r s a .  depositional when  values  are tend  never to  consist  be of  i s due t o t h e  Meyerhof soil  that  (1963)  properties  vary  135  within  the  deposit,  reasonable theory  i f the  average values v a r i a t i o n s are  i s b a s e d on  the  within  the  potential  failure  body s h o u l d  the  1976).  The  analysis surface load  soil  be  failure  evaluation  of  i s often  unknown.  inclination  used  the  This  bearing  capacity  shear  values  is  zones  within  i n s t e a d of average  surface  since  used.  critical  average  ( L a u r i t z s e n and  suitable soil  subjective  be Since  that  mass,  potential  is quite  small.  assumption  develop  along  should  values  Schjetne,  p a r a m e t e r s t o use l o c a t i o n of  the  in  the  the  rupture  T h i s p r o b l e m becomes more c r i t i c a l  increases  and  the  foundation  soils  as  become  less  regarding  the  T h i s problem  was  homogeneous. For  layered  location  of  addressed  by  useful  the  cohesive  shear  Terzaghi  procedure  solutions  layer  foundations,  have  where t h e  Peck  by  Meyerhof and  by  Reddy and  strength layer  bearing  of  been  Fully  and  by  increases  is  by  Booker  ( 1 9 6 7 ) , among o t h e r s .  theory  to  theory.  layered  recent  two-layer  of  with  and with  by .Brown and  but  a  sand  (1973) f o r the  between  dealing  (1943)  case  linearly  Yamaguchi  for  More  (1953) f o r a the  sandwiched  presented  Terzaghi's  capacity  subjective  developed a crude  (1974) f o r  investigated  Srinivasan  extensions  (1948) who  D a v i s and  Other approximate techniques have  made.  Button  c a s e where a s o f t  systems  be  been p r e s e n t e d  clay,  was  and  may  t y p e of p r o b l e m .  undrained  materials  zones  for treating this  deposit,  over  f u r t h e r assumptions  depth.  two  The  stronger  Terashi  (1971).  multiple  Meyerhof  case  layer  (1969)  These s o l u t i o n s The  and are  extension  of  foundations  is  quite  u s u a l l y assumed  for a  bearing  approximate..  drained  conditions  are  136  capacity  analysis  offshore  gravity  structure  subjected  t o storm  wave l o a d i n g .  bearing capacity  of sand.  formula  pressures developed  6.4.2  Other The  Hansen  occur  that  dilatancy  and  the  about  (see f i g u r e and  solution  the  rupture  field  water then  pressures. solution. are  not  advantages solutions  was  be  at  a l l  i n t o account  method  a  large  useful,  the pore  the water  to t h i s  used  i s homogeneous and "o"  below t h e  were  water  is  first  gives  corrected  leads  R e s i d u a l pore considered.  Janbu et a l  an  effective  following  (1976)  on  from  of  to  easy  stress  the  rotational will  mechanism by  was the  In g e n e r a l , because  the  effective  an  estimated  displacement pore  complicated  w a t e r p r e s s u r e s due i s not  date on  to obtain  computed  extremely  a  1976).  distribution  T h i s method  other  (e.g. the  to  The  later  induced  based  be computed  distribution.  a  failure  (Hansen,  found  stability  f o u n d a t i o n base  i s very d i f f i c u l t  which  Hansen  based  that  pressures  included  problem  at a  developed  A rigid-plastic  pore  by  to a s s e s s the  soil  must  was  pressure  over  developed  theory  surface,  This  that  reported in d e t a i l  a point  sand  formulated to consider  The  the  stress distribution, pore  capacity  4.14).  the  of the  the  for  soil.  T h i s method was  tank  failure  assumed  case  type of d e p o s i t which i s  To  water p r e s s u r e s was  (1976).  assumuptions type of  i n the  1973).  the E k o f i s k  by  this  should take  bearing  wave i n d u c e d p o r e  of  on  the  Bearing Capacity Formulations  first  (Bjerrum,  T h i s i s not  water  iterative  cyclic t o use  loading  and  bearing  has  no  capacity  method).  developed  a  two-dimensional  bearing  137  capacity  solution  pressure. and  They  for a weightless s o i l extended  e x c e s s p o r e water  equilibrium Slices the  method  integration  was  similar  distribution employing  the  (Janbu,  1973)  the  the GPS  one  method.  bearing  i s adequate  Their equation.  v  where the  rupture Both  surface  i s e x p r e s s e d by a  BN is  y  + (q'+  the degree  the  mobilized  soil  reaction  k  of h o r i z o n t a l  frictional  The  stress  is  found  by  and  horizontal This  soils. bearing  capacity  to  (6.20)  w  shear  resistance,  v  determine  factor.  the s a f e t y  tan0  i s the average  vertical  water  pressure  base,  An  factor  of the degree  t o s p e e d up t h e s o l u t i o n  corresponding  o~  of  r is  mobilization,  p r e s s u r e a l o n g the  C u r v e s were d e v e l o p e d f o r t h e b e a r i n g  pore  shear a l o n g the base,  over the base, a i s the a t t r a c t i o n  a r e e x p r e s s e d i n terms  A  rupture  (6.19)  a)N^- u N  dimensionless bearing capacity  used  of  integrated;  foundation area.  modified  average h o r i z o n t a l  t h e a v e r a g e p o r e water  be  force  Procedure  6.6.  the v e r t i c a l  for cohesionless  the  w  relative  required  way;  r(o;+ a - u ) t a n 0  a = T  weight  This i s  T= o~ +  result  soil  capacity  in figure  l o a d s a r e assumed t o a c t on t h e e f f e c t i v e treatment  water  were n u m e r i c a l l y  shown  assumed  pore  to include  f o r the G e n e r a l i z e d  performed over a  to  on  solution  zero  p r e s s u r e s i n an a p p r o x i m a t e  equations derived  (GPS)  surface  this  with  (c/tan0), and  iterative since  strength  capacity  N  H  u  is  fc  is  solution  the s o i l  is a is  forces  mobilization.  f a c t o r s which  may  procedure. distribution  in  the  soil  t o t h e maximum wave i s assumed b a s e d on c h a n g e s i n  138  Figure  6.6  - Geometry effective  of r u p t u r e surface u s e d f o r an s t r e s s bearing capacity s o l u t i o n  139  the  principal  s t r e s s e s over  water p r e s s u r e  a t any  Cumulative  pore  incorporated  into  pressure  where m  n is  is a  the  number of  the concern  using  ratios,  a  i s given  simple  N  pressure i s the  parameter  i s with  relatively  liquefaction, A pore water  this  histogram,  obtained  small type  pressure  assumed  failure  technique, depend  since  on  the  the  model  water  The  be  as pore  found and  of  by pore  strength  soil.  to  platform.  analyze  They  equations  solution.  the  approximated derived  conditions  to  loading  and  irregular  instead  of  capacity  theories  and  the  using do.  Hence,  b a s e g e o m e t r y may empirical Results  are  of  a  bearing capacity  such  d e a l t with  coefficients  Murff  partial  equations  complex  factors be  of  differential  more  by  stability  set  for c l a s s i c a l  allows  specified.  developed  foundation  T h i s s e t of p a r t i a l  numerically  by  water  such  stresses  degree  (1977)  be  stress  of p o r e  s u r f a c e must  the  from  pore  on  Miller  solved  water  number of c y c l e s a t any  b e a r i n g c a p a c i t y f o r m u l a t i o n was  plasticity  storm  i s unnecessary.  i n the  differential  pore  are  by  Another  gravity  (6.6).  loading  (1976) a r c s i n e f o r m u l a  parameters  mobilization  is  not  iteration  pressure  and  and  model i s u s e d .  an  using  cyclic  bands i n t h e d e s i g n  pore  Since  water p r e s s u r e s  from  Equation  (6.21)  level.  al's  from  maximum p o r e  3  tests,  et  This  The  o- )  load  Seed  found  pressures  model.  cyclic  pressure  is  t h e a n a l y s i s by  dimensionless  pressure  loading cycle.  location  water  generation Afo", -  one  as  comparable  boundary as  inclined directly,  other to  bearing  classical  140  theory  and  are  Since may  vary  the  with  necessarily therefore, as  somewhat  solution  depth.  shape  of  6.4.3  Slip  NGI  spiral.  Surface  surface  Geotechnical  been r e p o r t e d (1976).  by  An  the  soil  failure  to solve  the  properties surface  is  equations,  and  functional representation  c o n s t r a i n t on  for layered  shape  such  limits  the  foundations.  Method method  I n s t i t u t e to  platforms  to a  This  t h i s method  slip  of  mathematically  i t i s constrained  usefulness  gravity  i s found n u m e r i c a l l y ,  The  defined  a logarithmic  A  conservative.  was  i n v e s t i g a t e the  f o u n d e d on  Lauritzsen  alternative  formulation  was  desired  applicable  to  offshore  developed  clay.  and  stability  D e t a i l s of  Schjetne  approach  t h a t was  the to  Norwegian  of  offshore  and  Schjetne  bearing  capacity  use,  structures  the  t h i s method have  (1976)  to  simple  gravity  at  reliable,  f o u n d e d on  and  layered  deposits. The over  NGI  bearing  accomodated applied that be  on  somewhat  more  the  failure body"  planes  easily,  the  at  the the  soil  surface.  mechanism w i t h shown  area  in  the  complex the  and  i s avoided,  since  failure  s e c t i o n over  vertical  namely:  effective  directly  potential  "sliding  method o f f e r s some d i s t i n c t  theory,  undue c o n s e r v a t i s m  assumed  cross  surface  capacity  both  analyzed  the  slip  and  platform sides.  length  can  be  force  is  area  so  foundations  may  non-effective layered  may  method  geometrical  f i g u r e 6.7.  loading  horizontal  properties This  advantages  The  vary  i s b a s e d on model  body has  and  along  is  a  cut  of  an the  constant off  by  Figure  Figure  6.7  6.8  - Geometry o f s l i d i n g  _  body u s e d  by  NGI  Geometry of b e a r i n g f a i l u r e s u r f a c e u s e d i n t h e 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 S c h j e t n e , 1976)  142  The  surface  sections  "be",  section  "de".  an  area.  sections  is of  evaluated  safety  is  Only  distribution,  sliding  inclined  shearing  in  resistance  found  from  method,  at  i s assumed  and  a  overall  B, = H P  passive  of  these  conditions.  The  horizontal  force  are considered,  i s not a p p l i e d  to  force  not  t o the  w  p  acting  - P  &  this - P  that  on t h e b a s e . Hence,  resistance: (6.22)  t  as (6.23)  i s the average cohesion  figure the  correct  6.8 a s " c e f d " ) . fact  one.  significant surfaces geometry.  that I f the  the  A plane  soil  did  analysis  to  make  of  the  sides  do a p s e u d o - t h r e e - d i m e n s i o n a l factor  i s one s i d e a r e a  safety  is  failure  indeed  between  foundation strain  s  The c o e f f i c i e n t  to  the  and A  the p o s t u l a t e d  differences  on  This  Equation  s  c  the  i n t e r f a c e s on t h e s i d e  horizontally.  to include  P  assumption  soil-soil  act  < A or P ) - P  +  i s defined  x  the  the  = 0.4(2cA )  Here,  flat  beneath the  f o r each  equilibrium  is  the h o r i z o n t a l  (6.12) may be r e w r i t t e n  for  force  four  "ab", a  "cd" i s d i r e c t l y  to sliding  under  this  resistance  in  "cd",  s i n c e moment e q u i l i b r i u m  reduce  3  section  section  the magnitudes of f o r c e s  areas w i l l  P  i s b r o k e n up i n t o  body.  Inherent  where P  body  section  The r e s i s t a n c e  equilibrium.  H  sliding  The i n c l i n e d  effective  the  the  a s shown i n f i g u r e 6.8: an a c t i v e  section  factor  of  used  mechanism  fail,  the  one. agree  would  vertical actual  i s essentially  account  i s not the  there  assumed  and  to  (shown  being  be  plane failure modified  The 0.4 v a l u e was c h o s e n with  Hansen's  (1970)  143  formulation  for  a  homogeneous  deposit,  r e d u c e t h e h o r i z o n t a l f o r c e a c t i n g on The section  horizontal "be"  of  the  H„ = c(B -B)L 0  This  applied E  The find  ftT  - H  and  analysis  force with of  the  the  sliding area  0  surface.  may  t h e n be  slip  s u r f a c e method slip  surface,  may  be  done by  s p e e d up  capacity  in preference  the  The  f i g u r e 6.8.  a  sharp  shown  material  will  in  average  surface.  the  slip  safety  This  the  slip  slip  This  of a s m a l l  the  slip  cohesion  surface  45°  only  with  computer when  the  NGI  f a c t o r than should  the  t o the  foundations,  represented  used. only on  have a m i n i m a l e f f e c t  be  angle  respect  wedge s t a r t s .  are  computed  ' The  to  shape  by  the on  This  weak  decrease  potential the  soil  seam of  a slight  has  i s not  average  A thin  the  shown  in calculations really  passive  in  result.  is fixed,  used  layered  safety factor  i s constrained  surface  For  lower  safety  surface  use.  especially  foundations,  capacity  to  established.  use  layered  simple  °c i s i n c r e m e n t e d  is  i s always at  surface  t h e r e f o r e be  will  For  bearing  zone  where  figure.  p r o p e r t i e s along  the  t o the  The  corner  i n the  layers.  passive  in  from  analysis considerably,  formulas.  g e o m e t r y of  horizontal.  nothing  horizontal force  found  angle  hand, a l t h o u g h  the  a number of  of  the  s u r f a c e method u s u a l l y p r e d i c t s a  changes;  The  being  0  is relatively  slip  The  sliding  from  factor (B -B)L  are  used  or  (6.25)  t h e minimum f a c t o r  bearing  flat  i s found  there  the  area.  S T  critical  program w i l l  the  to  (6.24)  effective  NGI the  effective  along  base  modified  0  area  t o the  H, = H  steps  the  taken  foundation  i s a mobilized  more t h a n  To  force  the  w h i c h was  computed  failure factor  144  of The  s a f e t y and  discretion  possibility  stress  NGI  the  3.6(f), slip  used  surface  of  type  method  of  failure,  stress  shear  and  o n l y be  A direct  analysis normal  zones,  the  and of  pore  approach  c o u l d be to t r e a t  Method o f This  slice  adapted the  6.4.5  so t h a t  The stability 1976; for  been  possible.  of the  NGI  this Since  potential  four  frictional  the  total  shear  resistance The  slip  method surface  problems.  Young e t a l , has  1974;  directly  i t may  be  H0eg,  1975),  although  used  Lauritzsen no  None of t h e  applicable forms.  1976;  to This  for offshore  compreavailable  offshore  gravity  technique  will  stability  be  analyses  chapter.  Element  Analyses  e l e m e n t method may  (Broughton,  1975;  be  used  to assess  foundation  P r e v 0 s t e t a l , 1981a; Vaughan e t a l ,  Z i e n k i e w i c z e t a l , 1979), a l t h o u g h displacement  for offshore gravity  y e t been r e p o r t e d .  present  finite  mentioned  (Eide,  their  following  Finite  extending  analyses  are  in  for  exceedingly crude.  t y p e s of  has  1976;  methods  for  that  Slices  treatment  structures  in  these  stability  Schjetne,  hensive  used  technique  structure and  dependent  water p r e s s u r e s w o u l d be  slices  6.4.4  stress  used  stresses along a  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  s u c h as  e x t e n s i o n of  i s not  failure  inclusion  results.  be p r o p e r l y a s s e s s e d .  may  foundations.  effective  distribution  when i n t e r p r e t i n g  o c c u r r i n g , cannot  a n a l y s e s of c l a y  method t o an  be  of a deep s l i d i n g  shown i n f i g u r e The  must  calculations.  This  it  is  used  i s a powerful  primarily technique  145  that  can  easily  properties. realistic in  the  of  with  complex  stress-strain the  bearing  rigid,  soil  and  behaviour.  finite  model  limit The  vary  element  for  a  set  of  are  for  the  anisotropic, properties analyses (Prev0st  the  by  dependent  perform  the  stiffness the  incremented loading stress  levels  elements  an  finite  that  modelled  soil  is  equations nonlinear,  stress-strain finite  is treated  parameters  element  element relations  by  using  element  are  studies are  a  analyses  for offshore  method,  the  "fail", Since  been c a r r i e d  out.  with  reached a c r i t i c a l  the  in-  deposits.  applied  loads  are  curve.  If  elements w i l l  i s , they can  are  to done  stress-strain  that  they  required  as  generally  i s always a s s o c i a t e d  f a r enough, some s o i l  enough t o  have not  The  constitutive  finite  of  equations  The  in  i n v e s t i g a t i o n has  element  load.  in  extension  the  elements.  s t e p w i s e approximate the  increased  better  used  force-displacement  r e s u l t s of  parameters measured  high  used  assumed c o n s t i t u t i v e r e l a t i o n s u s e d  uncertainty  finite to  The  an  which s o l v e  loading  stiffness  i s c a r r i e d out  support  the  be  detailed site  d e g r e e of  In  soil  i s more  models  path-dependent  Cyclic  the  analyses,  a f t e r the  A high  on  soil  representation  basically  appropriate  approach.  Because  situ  is  soil  may  using  input.  only  of  soil  e t a l , 1981a).  quasi-static very  set  which  s t r u c t u r a l members.  elastoplastic,  of  used,  stress-strain  method  i n t o " e l e m e n t s " and  written  is  variable  e q u i l i b r i u m methods t o  s t r u c t u r a l a n a l y s i s techniques  equilibrium  and  widely.  discretized  are  loading  perfectly plastic  capacity  element a n a l y s e s  The matrix  A  than  model t r u e finite  deal  no  longer  by  other  stress  level,  confined failure  reach  146  large displacements is  localized.  fail  increasing load.  added w i t h o u t the  The  but  soil  former  critical  may  load  r e q u i r e d to  et a l  element test  (Prev0st  et  analyses  were  conditions, circular  to  performed;  footing  with  three-dimensional  displacements model t e s t . consistent  for  at The with  the  from  performed They a  where Both  failure  the  latter  finite an  the  and  former  a n a l y s i s was failure  found  the  s t a t e and  experimental  experience  series results  was  of with  plastic  silt  increased  plane  foundation  constitutive to  design  three-dimensional  assumed  modelled  three-dimensional  load  the  analyses.  extensive  on  the  load to  element  footing  can  of  s i n c e the  their  on  Excessive  Considerable  two-  two-dimensional the  the  1975).  analyses  upon a p p l i c a t i o n  of  clays,  (Vesic,  failure.  compared  model  failure.  the  ratio  results  1981b)  while  bearing  l o a d at  u s u a l l y founded  load safety factor  analyses. data  failure.  insensitive  element  i n the a n a l y s i s .  (1981a)  al,  monotonically  The  be  load transfer) within  s t r u c t u r e s are  total  d e f i n e the  interpret  more l o a d c a n  c l a y s i t i s not  r a t h e r suddenly  increment.  centrifuge  The  occur  s t r e n g t h i s used  Prev0st  a  failure  a s more e l e m e n t s  to a t o t a l  of d e p o s i t s where f i n i t e  load w i l l  finite  sensitive  distinguish  displacements  is  (and  occur;  c a p a c i t y , or a p p l i e d v e r t i c a l  offshore gravity  type  generally  soil  occur  E v e n t u a l l y , no  mass; t h i s c o r r e s p o n d s  s a n d s and  Fortunately,  design  will  i s w e l l d e f i n e d f o r d e n s e s a n d s and  for loose  the  elements cannot  excessive displacements  ultimate bearing  failure,  failed  A progressive failure  under an  much of  of t h e  loads observed were  data.  The  as  a  relations.  adequately  results  strain  found  predict in  the  to  be  (exaggerated)  147  distorted similar figure  meshes f o r b o t h load  6.9.  Prev0st  Note  element  information would  effect  clearly  cannot  for  of  Some r e s u l t s  very  In  method.  strain  finite  the  That  three-dimensional  analysis  Since techniques requirement equations mandatory.  are  relative that  a n a l y s i s may  shown i n f i g u r e bearing area  be  bearing  It with area  area d e f i n e d  by  loading.  e l e m e n t methods c a n n o t analysis  like,  failure  equilibrium can  two-  6.10.  reduces  the e f f e c t i v e  s i d e s of t h e p o t e n t i a l element  to  system,  imply  be  adapted  the  NGI  i s , s h e a r i n g r e s i s t a n c e a t the  the  expensive  in  similar.  s t u d i e d u s i n g the  t o the e f f e c t i v e  a pseudo-three-dimensional  included  T h i s would  was  fact,  nearly equal  (6.15) f o r p l a n e  on  in  quantitative  regarding  foundation  load eccentricity  eccentricity.  interfaces  shown  soil-structure  displacements."  at  two-dimensional  exact  answers  e v i d e n t t h a t the e f f e c t i v e  t o be  surface  although  the  useful  are  patterns are  "provide  of  analyses  cases.  Two-dimensional perform  eccentricities  that  assumption  model.  increasing  Equation  three-dimensional  the d i s p l a c e m e n t  provide  strain  dimensional  appears  and  behaviour  l o a d s and  i n many  The  the  still  plane  adequate  is  that  studies  about  m a g n i t u d e s of the  inclinations  and  e t a l (1981a) c o n c l u d e d  finite  they  two-  model t h i s ,  but  is  slip  soil-soil  body c a n n o t  equations.  to  A  be  complete  exceedingly  perform. many s o i l  must be  parameters are  used  to achieve  f o r many i t e r a t i o n s means  that  It also  use  s t r e s s dependent,  stress  compatability.  w i t h a l a r g e s e t of  of a computer w i t h a  l e a d s t o the  high  iteration  cost  of  This  simultaneous  l a r g e memory i s running  these  148  (a) T w o - d i m e n s i o n a l  —  s  It y  wil  F  _ ' ' ' / I I \ \ S _  (b)  Figure  6.9  .  Three-dimensional  C o m p a r i s o n o f two- a n d t h r e e - d i m e n s i o n a l f i n i t e e l e m e n t meshes f o r an i n c l i n e d and l o a d ( A f t e r P r e v o s t e t a l , 1981a)  distorted eccentric  149  Figure  6.10  E f f e c t of l o 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 a r e a a s e v a l u a t e d u s i n g t h e f i n i t e e l e m e n t method ( A f t e r P r e v o s t e t a l , 1981a)  150  types  o f computer p r o g r a m s .  this  may  be  structures,  of  little  finite  the  element a n a l y s e s .  numerical  of  stiffness  parameters  Model Model  shaft the  for  which  resulting  stability  1975;  i s placed  on  hydraulic cyclic  on a c a r e f u l l y  The d e a d w e i g h t  or the A  high  estimation  centrifugal  of  actuator  (Andersen  not occur  i n the f i e l d  Irregular  platform  Centrifuge  since  profile in  to a  central  i s derived  or c y c l i c  loads  For  is  a structural  from  may  with  to apply  a  c a v i t a t i o n which  hydrostatic easily  be  servo-  tests  surface  t o prevent  under h i g h  t e s t s do n o t s u f f e r  other  model  h o r i z o n t a l l o a d may be  a l , 1979).  will  tests  small  a displacement-controlled  et  geometry  using  1981; P r e v 0 s t  soil  pressure A  done  A  constructed  forces.  t h e model by u s i n g  that  is  1976).  bearing  t h i s may be n e c e s s a r y  problems  of  factor.  l o a d i n g , water c a n be p u t on t h e s o i l  centrifuge  the  problems  Rowe e t a l ,  back p r e s s u r e ;  made.  with  t o t h e model by means o f a j a c k  imposed  behaviour  i s t h e n mounted on an arm c o n n e c t e d  and s p u n .  applied  distrust  ( A n d e r s e n e t a l , 1979; H e i j n e n ,  a l , 1981b; Rowe,  a bucket  associated  solely  Tests  tests  foundation  a  i n s o l v i n g the equations.  i s a l s o an i m p o r t a n t  testing  centrifuge et  uncertainty  f o r smaller  decisions  T h i s may be due t o  employed  platform,  consideration.  r e l a t i o n s u s e d t o model s o i l  techniques  degree  However,  a r e u n w i l l i n g t o base t h e i r  constitutive  6.4.6  significance.  computer c o s t s c a n be an i m p o r t a n t  Many e n g i n e e r s on  For a m u l t i m i l l i o n d o l l a r  pressures.  accounted  for in  model o f any shape may be from  one  of  model t e s t s d o : t h e i n a b i l i t y  the  major  to simulate  151  high  stresses  prototype.  These  behaviour  in-situ  Variable profile  the  the  soil  it  is  to  only  do  the  soil  representative  of  the  by  For  take  s c a l i n g the  model.  i n the  time  are not  similarity  satisfied, have  to  profile  then be  than  the  various  stresses within  determined,  since  obtained the  not  stresses  centrifuge  model s o i l  are  soil  like  finite  provide  profiles element  information  on  is  few  soil  test site Clays  so  to are  in-situ,  the  l a y e r s a t most  loading  where  h i s t o r y have  do  the  pore  substantial  consolidation  are to  water  drainage  i s modelled  i s u s u a l l y done by  and  the  using  soil used  (Heijnen,  mass do  not  pore  computed The  s i m i l a r to loading  the and  the  do For  to  be  test.  In  parameters  stresses  the  test  1981).  using  those  are  find  displacement  prototype  have  i n s e t t i n g up  tests.  studies,  model and  i n f l u e n c i n g the  separately  are  shear  tests, and  they are  laboratory  i f the  and  factors  the  from  soil  a  a  water.  distinguished  studies,  to  overconsolidation  profile  r e q u i r e m e n t s between  example, t h e  numerical  fabric.  in-situ  This  building  specified  soils  factor.  by  and  prototype,  model,  f l u i d s much more v i s c o u s If  numerical  t e s t data  from t h e  Generally,  cohesionless  place  laboratory  the  foundation  of  soil  size  to  harder  may  and  modelled  consolidated  more n o n u n i f o r m  pressures.  are  particle  The  be  field  in  to p r e d i c t  subjectiveness  d i f f e r e n t layers using  and  Not  the  properties  ratio.  used.  attempt  loads  properties.  f a c t o r s s u c h as  remolded  of  an  require  soil  soil  with  control  do  gravitational  are  much  They  the  from  tests  without  techniques. define  resulting  existing in  i n the  prototype  same.  Centrifuge  load  safety  failure  modes.  factor  152  Centrifuge foundation  stability  theoretical  that  in  1981).  been  used  e x i s t i n g platforms (Andersen et a l ,  the The  yet  been u s e d  future  as  number of  to  investigate  (Rowe, 1975) 1979;  in  This  m a j o r drawback of - c e n t r i f u g e be  for  et a l ,  procedures  can  the  and  Prev0st  design.  testing  i t i s t i m e c o n s u m i n g , e x p e n s i v e , and  limited  6.5  of  t h e y have not  change  (Heijnen,  have  studies  1981b), but likely  tests  will  improve  testing  is  conducted at  a  facilities.  Summary A  summary of  the  existing stability  offshore  gravity structures  evident  that  relatively surface  simple  method,  consider presently capacity finite  there  are  more  realistic  no  analytical  approach  or  needed  which  complex  loading. the  can  A  the  method of  classes  more  sophisticated  stress-strain alternative NGI  slip  simple  adequately In  distinct  formulations  the  slices,  of  It  and  the  surface  effective  crude  stress  i s presented.  such  the slip  which  There  is  bearing  method e x c e p t  layered  chapters,  NGI  analyses  the  to  is quite  analyses:  behaviour.  to  t r e a t both  following  applicable  in Table VIII.  capacity  the  e l e m e n t method.  b a s e d on  two  bearing and  i s given  methods  the  method  is  foundations  and  a  technique,  Table VIII - Comparison of E x i s t i n g S t a b i l i t y  DISADVANTAGES  ADVANTAGES  METHOD  -DOES NOT CONSIDER STRESS-STRAIN BEHAVIOUR  -SIMPLE TO USE  .. AR1NG CAPACITY THEORY (CLASSICAL)  Methods  -SUITABLE FOR HAND CALCULATIONS  -BASED ON FIXED GEOMETRY OF RUPTURE SURFACE  -EASY TO PERFORM PARAMETER STUDIES  -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  -DOES NOT CONSIDER STRESS-STRAIN BEHAVIOUR  -SUITABLE FOR HAND CALCULATIONS  -BASED ON FIXED GEOMETRY OF FAILURE SURFACE  -APPLICABLE TO LAYERED FOUNDATIONS  -ONLY FOR TOTAL STRESS ANALYSES OF CLAY  -EASY TO PERFORM PARAMETER STUDIES  -DOES NOT CONSIDER DISTRIBUTION OF LOADS -PROBLEMS WITH THIN SEAMS  FINITE ELEMENT METHOD (TWO-DIMENSIONAL)  -CONSIDERS STRESS-STRAIN BEHAVIOUR  -CANNOT STUDY THREE-DIMENSIONAL  -CAN ACCOMODATE IRREGULAR GEOMETRY  -REQUIRES MANY SOIL PARAMETERS AS INPUT  -APPLICABLE TO LAYERED FOUNDATIONS  -MUCH DATA PREPARATION REQUIRED  -CAN STUDY SOIL-STRUCTURE  -EXPENSIVE ANALYSES  INTERACTION  -POSSIBLE TO STUDY PROGRESSIVE FAILURE  EFFECTS  -REQUIRES THE USE OF A LARGE COMPUTER  -PROVIDES INFORMATION ON FAILURE MODES  CENTRIFUGE MODEL TESTING  -MODELS STRESS-STRAIN BEHAVIOUR  -EXTENSIVE PREPARATION REQUIRED  -CAN ACCOMODATE IRREGULAR GEOMETRY  -REQUIRES SPECIALLY TRAINED PERSONNEL  -APPLICABLE TO LAYERED FOUNDATIONS  -REQUIRES SOIL FROM FIELD  -TRUE THREE-DIMENSIONAL  -EXPENSIVE ANALYSES  ANALYSIS  -PROVIDES INFORMATION ON FAILURE MODES  SITE  -LIMITED TO FACILITIES WITH CENTRIFUGES Ul  150  types  o f computer p r o g r a m s .  this  may  be  structures,  of  little  finite  the  numerical  of  6.4.6  uncertainty  parameters  Model Model  shaft the  for  i n s o l v i n g the equations.  associated  which  resulting  stability  1975;  i s placed  on  hydraulic cyclic  Rowe e t a l ,  on a c a r e f u l l y  The d e a d w e i g h t  or the A  high  estimation  centrifugal  of  actuator  (Andersen  will  not occur  i n the f i e l d  Irregular  platform  Centrifuge  since  profile in  to a  central  i s derived  or c y c l i c  loads  For  is  a structural  from  may  with  to apply  a  c a v i t a t i o n which  hydrostatic easily  be  servo-  tests  surface  to prevent  under h i g h  t e s t s do n o t s u f f e r  other  model  h o r i z o n t a l l o a d may be  a l , 1979).  t h i s may be n e c e s s a r y  tests  small  a displacement-controlled  et  geometry  using  1981; P r e v 0 s t  soil  pressure A  done  A  constructed  forces.  t h e model by u s i n g  that  is  1976).  bearing  back p r e s s u r e ;  problems  of  factor.  l o a d i n g , water c a n be p u t on t h e s o i l  centrifuge  the  problems  t o t h e model by means o f a j a c k  imposed  made.  with  i s t h e n mounted on an arm c o n n e c t e d  and spun.  applied  distrust  behaviour  ( A n d e r s e n e t a l , 1979; H e i j n e n ,  a l , 1981b; Rowe,  a bucket  a  solely  Tests  tests  foundation  f o r smaller  decisions  t o model s o i l  i s a l s o an i m p o r t a n t  testing  centrifuge et  employed  platform,  consideration.  T h i s may be due t o  r e l a t i o n s used  techniques  stiffness  However,  a r e u n w i l l i n g t o base t h e i r  element a n a l y s e s .  constitutive  degree  significance.  computer c o s t s c a n be an i m p o r t a n t  Many e n g i n e e r s on  For a m u l t i m i l l i o n d o l l a r  pressures.  accounted  for in  model o f any shape may be from  one  of  model t e s t s do: t h e i n a b i l i t y  the  major  to simulate  151  high  stresses  prototype.  These  behaviour  in-situ  Variable profile  the  properties  are  particle  consolidated  the soil  more n o n u n i f o r m t h e  harder  it  is  to  only  do  the  soil  representative  of  the  pressures. may by  For  take  fluids  not  similarity  satisfied, have  to  then be  the  determined,  since  the  than  various  within  they are  not  stresses  are  finite  provide  and  profiles element  information  on  is  few  so  soil  test site Clays  to are  in-situ,  the  l a y e r s a t most  loading  where  h i s t o r y have  do  the  pore  substantial  consolidation  are to  water  drainage  i s modelled  i s u s u a l l y done by  and  the  separately soil used are  model s o i l  like  to  overconsolidation  profile a  a  using  model and  pore  prototype  f a c t o r s i n f l u e n c i n g the  the  centrifuge  soil  t e s t data  water.  shear  tests, and  This  laboratory  i f the  specified  in-situ  from  soil  fabric.  r e q u i r e m e n t s between  stresses  obtained  soils  distinguished  studies,  and  prototype,  factor.  example, t h e  numerical  profile  model,  much more v i s c o u s  If are  i n the  time  numerical  building  from t h e  Generally,  cohesionless  place  s c a l i n g the  model.  by  soil  size  to  The  be  the  foundation  of  laboratory  modelled  d i f f e r e n t layers using  and  Not  and  in  to p r e d i c t  subjectiveness  field  ratio.  used.  attempt  loads  properties.  f a c t o r s s u c h as  remolded  of  an  require  soil  soil  with  control  do  gravitational  are  much  They  the  from  tests  without  techniques. define  resulting  mass do  not  computed The  s i m i l a r to loading  find  displacement  the  do For  to  be  test.  In  parameters  stresses  the and  the  using  those  are  1981). have  i n s e t t i n g up  tests.  studies,  (Heijnen,  test  existing in  i n the  prototype  same.  Centrifuge  load  safety  failure  modes.  factor  152  Centrifuge foundation  stability  theoretical  that  in  1981).  been  used  (Andersen et a l ,  the The  number of  to  e x i s t i n g platforms  yet  been u s e d  future  as  investigate  (Rowe, 1975) 1979;  in  This  m a j o r drawback of - c e n t r i f u g e be  for  et a l ,  procedures  can  the  and  Prev0st  design.  testing  i t i s t i m e c o n s u m i n g , e x p e n s i v e , and  limited  6.5  of  t h e y have not  change  (Heijnen,  have  studies  1981b), but likely  tests  will  improve  testing  is  conducted at  a  facilities.  Summary A  summary of  the  existing stability  offshore  gravity structures  evident  that  relatively surface  simple  method,  consider presently capacity finite  there  are  realistic  no  analytical  approach  or  e l e m e n t method. which  complex  loading.  b a s e d on  the  can  A  the  method of  classes  more  sophisticated  stress-strain alternative NGI  slip  simple  adequately In  distinct  formulations  the  slices,  of  It  and  the  surface  effective  crude  stress  i s presented.  such  the slip  which  There  is  bearing  method e x c e p t  layered  chapters,  NGI  analyses  the  to  is quite  analyses:  behaviour.  to  t r e a t both  following  applicable  in Table VIII.  capacity  the  more  needed  two  bearing and  i s given  methods  the  method  is  foundations  and  a  technique,  Table VIII - Comparison of  DISADVANTAGES  ADVANTAGES  METHOD  ....AR1NG CAPACITY THEORY (CLASSICAL)  E x i s t i n g S t a b i l i t y Methods  -SIMPLE TO USE  -DOES NOT CONSIDER STRESS-STRAIN BEHAVIOUR  -SUITABLE FOR HAND CALCULATIONS  -BASED ON FIXED GEOMETRY OF RUPTURE SURFACE  -EASY TO PERFORM PARAMETER STUDIES  -CANNOT TREAT COMPLEX LOADING CONDITIONS -LIMITED TO TOTAL STRESS ANALYSES -NOT GOOD FOR LAYERED FOUNDATIONS -SUBJECTIVITY  NGI  SLIP SURFACE METHOD  OF BEARING CAPACITY FACTORS  -RELATIVELY EASY TO USE  -DOES NOT CONSIDER STRESS-STRAIN BEHAVIOUR  -SUITABLE FOR HAND CALCULATIONS  -BASED ON FIXED GEOMETRY OF FAILURE SURFACE  -APPLICABLE TO LAYERED FOUNDATIONS  -ONLY FOR TOTAL STRESS ANALYSES OF CLAY  -EASY TO PERFORM PARAMETER STUDIES  -DDES NOT CONSIDER DISTRIBUTION OF LOADS -PROBLEMS WITH THIN SEAMS  FINITE ELEMENT METHOD (TWO-DIMENSIONAL)  -CONSIDERS STRESS-STRAIN BEHAVIOUR  -CANNOT STUDY THREE-DIMENSIONAL EFFECTS  -CAN ACCOMODATE IRREGULAR GEOMETRY  -REQUIRES MANY SOIL PARAMETERS AS INPUT  -APPLICABLE TO LAYERED FOUNDATIONS  -MUCH DATA PREPARATION REQUIRED  -CAN STUDY SOIL-STRUCTURE  -EXPENSIVE ANALYSES  INTERACTION  -POSSIBLE TO STUDY PROGRESSIVE FAILURE -PROVIDES  CENTRIFUGE MODEL TESTING  -REQUIRES THE USE OF A LARGE COMPUTER  INFORMATION ON FAILURE MODES  -MODELS STRESS-STRAIN BEHAVIOUR  -EXTENSIVE PREPARATION REQUIRED  -CAN ACCOMODATE IRREGULAR GEOMETRY  -REQUIRES SPECIALLY TRAINED PERSONNEL  -APPLICABLE TO LAYERED FOUNDATIONS  -REQUIRES SOIL FROM FIELD SITE  -TRUE THREE-DIMENSIONAL  -EXPENSIVE ANALYSES  -PROVIDES  ANALYSIS  INFORMATION ON FAILURE MODES  -LIMITED TO FACILITIES WITH CENTRIFUGES  154  CHAPTER 7 APPLICATION OF  THE  METHOD OF  SLICES  TO  OFFSHORE GRAVITY STRUCTURE FOUNDATIONS  In so an  this  that  chapter  they  offshore  may  the  be  method of  used  to analyze  slip  surface  water p r e s s u r e is of  used  chapter.  failure. slip  these  cases  (1973)  A typical slices  is  similar  to the  figure take  on  shown  i s of  in  one The  a different  only  sections.)  the  by  NGI,  The  flat  section, while  section the  pore  method  practical  the  was  shear  portion  the  will "be"  NGI from  understand  model u s e d  d e f i n i n g the  "ab"  the  method  be will  shown surface  constrained  to label  of  value.  which the  the  type  and  to  failure  that  in  derived  difficult  The  Use  i s also useful  theory  p r o b l e m by  lines  It i s convenient  the  stresses  sliding  capacity  ( i . e . i t i s not  - straight  in A  described  deep  d i f f e r e n c e i s that  shape  s t r u c t u r e base; the  a  significant of  used  analysis.  herein  of  loading.  principal  is  i s not  f i g u r e 7.1. used  f i g u r e 6.8  sliding  slices  representation  shown  6.7.  in  passive  and  for  inapplicable.  method of  t o use  slices  bearing  wave  p o r e water p r e s s u r e s .  method d e v e l o p e d  foundations  s u r f a c e method a r e  o r complex  the  method o f The  clay  In  Sarma's  the  the  i n the  modified  stability  unlike that  i n the  f o r wave i n d u c e d  are  foundation  not  changes  equations  to storm  is included  model b a s e d on  t h i s model w i t h  for analyzing  technique  method  to account  following  the  gravity structure subjected  A pseudo-three-dimensional NGI  slices  to  parts  r e f e r r e d to be  is in, may  shape  inclined  two  of  termed  and on as the  154  CHAPTER 7 APPLICATION OF  THE  METHOD OF  SLICES  TO  OFFSHORE GRAVITY STRUCTURE FOUNDATIONS  In so an  this  that  chapter  they  may  the  be  method o f  used t o analyze  NGI  slip  surface  water p r e s s u r e is  used  chapter.  analyzing  failure. slip  method of The  clay  In  these  (1973)  o r complex  cases  A typical slices  is  similar  to the  figure take  on  shown  one The  a different  only  sections.)  the  by  NGI,  flat  s e c t i o n , while  The  pore  theory  method  to  the  portion  "be"  NGI from  understand  model used was  shear  d e f i n i n g the the  will  the  method  constrained  label  of  value.  which the  the  type  and  to  failure  that  in  derived  practical  The  Use  is also useful  difficult  s e c t i o n "ab" the  the  stresses  sliding  p r o b l e m by  lines  It i s convenient  A  described  capacity  ( i . e . i t i s not  - straight  in  analysis.  deep  d i f f e r e n c e i s that  shape  s t r u c t u r e base; the  a  significant of  used  principal  is  i s not  f i g u r e 7.1. used  f i g u r e 6.8  sliding  slices  i s of  in  for  bearing  representation  shown  6.7.  in  passive  and  slices  of  loading.  p o r e water p r e s s u r e s .  inapplicable.  method of  t o use  wave  method d e v e l o p e d h e r e i n  foundations  s u r f a c e method a r e  Sarma's  the  the  i n the  modified  stability  unlike that  i n the  f o r wave i n d u c e d  are  foundation  not  changes  equations  to storm  i s included  model b a s e d on  t h i s model w i t h  for  technique  method  to account  following  the  the  offshore gravity structure subjected  A pseudo-three-dimensional  of  slices  be will  in  surface  may  to  shape  parts  r e f e r r e d to be  is  shown  inclined  two  of  termed  and on as the  Figure7.1 Representation of stability analysis by the method of slices  01 01  156  effective Two is  an  area. different  procedures are developed.  adaptation  Slices.  of  Janbu's  T h i s method was  s u r f a c e s of a r b i t r a r y foundation  engineers.  three-dimensional  (1973)  and  i s not e a s i l y  formulation  i t i s applicable  because  i t i s familiar  An  of t h i s  made due  alternative  i s presented.  of  slices  At a f i r s t approach  g l a n c e , the to  study w i l l extremely The they are  i s not w e l l  the  t o t h e way  method b a s e d  T h i s method  show t h a t  may  t h e method  slice  independent When  of  the  the  horizontal  specific made,  on  the  Sarma's  Sarma's  (1973)  position,  These  analyzed,  and h e n c e ,  regarding  and  factors w i l l  The Method o f  be  an  awkward  logical  form,  regarding  are  for  and  that i s , external  analyzed,  instance:  the pore water  of s o i l  further  the  load  pressures in  parameters w i t h both depth  t h e shape  of  a  potential  failure  v a r y w i t h the type of problem  versatility  t o be  i s maintained.  Slices  method o f s l i c e s  the s o i l  in general  problems  distribution  surface.  treats  i n which  adapted  quite  assumptions  on t h e f o u n d a t i o n b a s e ,  The  pseudo-  is easily  to  fact  equations are derived  distribution  7.1  most  However, a more t h o r o u g h  i s in  are  and  appear  problem.  assumptions  soil,  to  versatile.  loading.  the  slip  known among p r a c t i c i n g e n g i n e e r s .  method  stability  to  method t o a  to perform a pseudo-three-dimensional a n a l y s i s . method  method  P r o c e d u r e of  because  Adaptation  equations are derived.  first  (1973) G e n e r a l i z e d  chosen  shape  The  as a r i g i d  is a limit plastic  equilibrium material.  analysis The  which  degree  of  157  safety  a g a i n s t an  ultimate foundation f a i l u r e  i s expressed  as  F = T|/T where  (7.1)  F = the  factor  of  safety,  the  shear  s t r e n g t h a l o n g some s h e a r  ^ = the  shear  s t r e s s a l o n g t h e same s h e a r  The  purpose  of a s t a b i l i t y  of  F  The  d e t e r m i n a t i o n of the  corresponding  to  analysis  of s a f e t y  foundation  failure  of  a l o n g t h e most c r i t i c a l  the s o i l  stress The  along t h i s  following  shear the  factor  of  Since the  shear  on  s u r f a c e , and  on a s h e a r  the  shear  be  (7.1)  may  vary  F  constant will  =  n  (3) t h e  concern  stability against  (1) t h e  themselves  from  slice.  along  shear  i s broken  slice  ultimate  shear s t r e n g t h (2) t h e  of t h i s with  deriving  shear  surface.  finding  the  expressions for  If the  average  stress will  up  to s l i c e  into  shear  f o r the  vary  slices.  as w i l l  factor  the e n t i r e  be a w e i g h t e d  along  The  the shear  of s a f e t y surface, factor  shear stress  is  assumed  then  Equation  of s a f e t y ,  or  l ^ ( a ; )  (7.2)  L-i  are weighting parameters  that  geometry  loading  number  t  individual  and  ratios  examined  to  not  since  strength.  condition.  an  surface,  where t h e a- 's  valid  surface.  t h e minimum v a l u e  location  s u r f a c e and  s t r e n g t h and  the s o i l  t h e base o f e a c h  to  shear  and  safety.  surface,  strength  r e q u i r e s e s t i m a t e s of  sections w i l l  stresses  i s to f i n d  t h e most c r i t i c a l factor  surface,  see  Local  and  of s h e a r i f the  the shear  n  is  the  strength ratio  shear  cannot  within  exceed  on  slice  of s l i c e s . stress  anywhere e x c e e d s u n i t y .  stress  overstressing  to  depend  the  the p o t e n t i a l  may  The be  This i s available  failure  body  158  may  be  examined  stresses  along  developed the  to  by the  slice  check  i f the  potential failure The  shear  failure  the  shear  interfaces. failure  strengths  Equations  to  shear  will  be  condition i s v i o l a t e d within  body.  strength  criteria,  (Equation  comparing  may  be  which  in  defined terms  of  by  the  Mohr-Coulomb  effective  stress  is  6.2)  *tj= c'+  C7'tan0'  Equation  (7.3)  (7.1)  equilibrium.  essentially  This  average shear  equation  defines  may  s t r e s s i n t e r m s of  be  the  a  state  rearranged  shear  of  limit  to define  strength.  the  This  is  simply *t  = ^(1/F)  where is  1/F  •  i s the  constant  into the  (7.4) shear  f o r any  effective applied • The  V  tvr=  v  or  Introducing  soil.  This  Equation  (7.3)  e q u i l i b r i u m shear This  stress  c'/F,  is  and  (7.6a)  tan0'-/F  (7.6b) strength  to the load  at  weight  soil  within  +  A P  vertical  v  of  foundation +  parameters.  Foundation  vertical  the  on  (7.5)  the m o b i l i z e d  at P  surface.  f o r each s l i c e .  Loading Applied The  shear  i n the  6Jtan0;  tan0i=  7.2  strength mobilized  the m o b i l i z e d  surface  c^=  These are  degree of  yields  ~ C L = C'+ where  (7.4)  the  base.  seafloor the  skirt  T h i s may  be  i s increased compartments written  the when  as  (BoDoLo)*'  l o a d a p p l i e d t o the  by  (7.7) foundation  base p e r  unit  width  159  as  used v  *  i n t h e method o f s l i c e s  i s simply  = V^/Lo The  (7.8)  horizontal  resultant  acting  level.  This P  M  acting  of the a p p l i e d  forces  H =  load  between  load  or P ) - P  A  w  w  f  f  - P  (6.11) and ( 6 . 1 3 ) ,  respectively.  here  purposes.  f o r reference  and a l l t h e s o i l  H  and s k i r t - t i p  6.12) (7.9)  by e q u a t i o n s  (6.9),  [ (O.5^'Do +Ap D )tan (45'-0/2)-2cD tan(45 -0/2) ]L  P =  Ap^oLo  P =  [(0.5*'D +Ap D )tan (45°+0/2)+2cD tan(45'+0/2)]L  P =  2D B (c  2  w  o  0  0  (7.11) (7.12)  2  o  s  (7.10)  ,  o  2  P  The  2  1  (6.10),  T h e s e e q u a t i o n s a r e summarized  P = A  i s the  s  are defined  t  P  base  the s e a f l o o r  may be e x p r e s s e d a s ( E q u a t i o n  where P , P , P , and P A  environmental  on t h e p l a t f o r m  + (P  H  on t h e f o u n d a t i o n  2  o  o  0  + O.5-i-'D tan0)  0  (7.13)  o  horizontal  force  per u n i t  width a p p l i e d  to  the  foundation  base i s H  = H  ft  a T  The of  /L  moment  t h e moment  forces This M  (7.14)  0  applied  a t the foundation  at the s e a f l o o r  acting  between  the  a n d t h e moments seafloor  may be e x p r e s s e d a s ( E q u a t i o n a T  = M + P D  It  H  + (P  0  i s useful  treating  the  t o use t h e  distribution  foundation  base.  equivalent  foundation  required.  This  Since  p  due  to  a l l the  and t h e f o u n d a t i o n  - P h  2  s  concept of  there  the  i s only  of  base.  (7.15)  3  effective  horizontal  area  force  as (Equation  width  isall  when  on  single eccentricity  base, the e f f e c t i v e  i s defined  B = B ( 1 - 2e) 0  w  i s the r e s u l t a n t  6.14)  or P ) h , - P h  A  base  the  on t h e  that  is  6.15) (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 The  separated surface This H  =  where  H  S 1  H  n  H per  = H  B  at the foundation  into  parts:  which  two and  S T  + H  H  be f o u n d  "be".  surface  be w r i t t e n  "ab", and "be".  as (7.19)  E  The  = H  E  horizontal i s given  force  taken  by  the  sliding  by (7.20)  t a k e n by t h e e f f e c t i v e a r e a  inserting  This  -  ft  force  by  f H  sliding  as  t a k e n by t h e e f f e c t i v e a r e a  per unit width  rearranging.  The  may  horizontal  may  the  the e f f e c t i v e area  t a k e n by t h e s l i d i n g  the f o r c e  + H  s  over  on  = \ ( c + o"tan0)dx  s  The  simply  i s the force i s  which a c t s  acts  Equation  (7.20)  per u n i t  into  where b  t  (7.19)  and  yields  \(c + O " t a n 0 ) d x force  taken  (7.21)  by any s l i c e may  be f o u n d  FH = H ( b / B ) e  width  h  horizontal L  be  (7.18)  unit width.  surface  that  that  base may  E T  (7.18)  Equation  Force  force applied  be w r i t t e n H  Horizontal  horizontal  "ab"  may B T  of the A p p l i e d  from (7.22)  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- = [ H - \ ( c t  B  + o"'tan0)dx] ( b / B ) :  (7.23)  161  7.4  Modified The  Slices  J a n b u Method  a p p l i c a t i o n of  Janbu's  (GPS)  to  structure  method  foundations  what  i s required  the  tops  of  determination initially area  on  of  the  of  to  the  as  the  sets  stability  closely  as  is possible  be  be  easily  e q u a t i o n s ) and forces.  the  the  They  terms  soil.  on  are  the e f f e c t i v e  An  horizontal  of  the  iteration  force  applied  slices.  follows  that  so  a comparison  that  made and  so  given  that  by  Janbu between  existing  slope  modified.  (1973) G e n e r a l i z e d  following  A - Plane  C - The the  strain  conditions  slice  of  following shown  Slices  is  founded  apply.  the line of thrust for i s assumed t o be known.  n o r m a l f o r c e on t h e base total resultant vertical  Derivation The  P r o c e d u r e of  assumptions:  B - The position of i n t e r s l i c e forces  the  below  Basically,  taken o u t s i d e  the  gravity  forces acting  in  of  Assumptions  the  7.4.2  these  in  hence t o  e q u a t i o n s may  p r o g r a m s can  Janbu's on  of  of  i n the  t o e s t a b l i s h the and  offshore  horizontal  i s expressed  mobilized  used  of  Procedure  modifications.  force  "ab"  derivation presented  (1973) two  the  surface  e f f e c t i v e area,  The  7.4.1  magnitudes  strength  p r o c e d u r e must be  some  (everywhere  since  sliding  analysis  i n c l u s i o n of  slices  unknown  the  degree  the  the  requires  i s the  (1973) G e n e r a l i z e d  Equilibrium equations  i n f i g u r e 7.2.  the  normal  i s assumed t o a c t where the f o r c e i n t e r s e c t s the b a s e .  Equations include The  a l l the  geometrical  forces acting  on  variables  and  *  S.W.L.  FV,  FH,  Figure  7.2  - Geometry and  forces  on  a  (Janbu)  slice  163  forces were and  f o r any  s l i c e are defined  developed  i n the f i g u r e .  f o r the l o a d i n g  f o r t h e model  defined  shown i n f i g u r e  The e q u a t i o n s  These  equations  in sections  7.2  and  7.3  horizontal  equilibrium  7.1.  f o r the v e r t i c a l  and  of a s l i c e a r e FT-  + AT-  = N-cosoi  + S sinc,;  (7.24)  AEi  -  FHi  = N^sinc;  - S-cosc;,  (7.25)  FT  L  fc  where  = FV  AT;  L  + W,  t  (7.26)  = T(t+1)-T(i)  (7.27)  AE-, = E(L + 1 )-E(L)„ Moment  (7.28)  e q u i l i b r i u m a b o u t t h e assumed  point  o f a p p l i c a t i o n o f N-  (mid-base) y i e l d s E-Ay;  " AE-Ah  Note t h a t order find  T - ' b i - a n d E^-Ay,;  have  tan6; For  v-  t  = Ay /b c  on  body p l u s  E[V ]  second  be r e a r r a n g e d t o  namely, (7.30) (7.31)  t  shear  equilibrium,  surface  the boundary l o a d s vertical  must  be e q u a l  applied  resultant  the  total  vertical  t o the weight of  to the s o i l  mass.  on t h e b a s e of a s l i c e ,  (7.24) n o t e  = NjCOSo-  Introducing l[AT ] r  t  this  then  + Sjsina  ;  equation  that = FT  Z  into  + AT;  (7.33)  (7.32) y i e l d s  = 0  Overall  If •  (7.32)  ;  From e q u a t i o n L  e q u a t i o n may  terms of  = Z[FT ]  t  V-  This  f o r c e T-,  vertical  the  i s the t o t a l  (7.29)  + Ah i (AE - /b ^ ) - h - ^ F H ^ b - J  c  overall  resultant  shear  = 6  a r e c o u p l e s and t h a t  been n e g l e c t e d .  = -E'tan6  where  + FH-.h;  ;  the i n t e r s l i c e  T-  the  + T b;  ;  (7.34) horizontal  equilibrium  requires  that  the  total  164  horizontal the  resultant  horizontal  resultant E[H-j From  boundary  forces.  = H  I[AE-J  (7.25) i t may  i s the  total  with  horizontal  then  be w r i t t e n  = AE z -  - S^OSc^  t h i s equation  =  in equilibrium  (7.35)  into  that  FH-  (7.36)  t  (7.35) y i e l d s  0  (7.37)  noting  from E q u a t i o n  7.4.3  Working Formulas  (7.22) t h a t  The c o m p l e t e s e t o f b a s i c  E[FH ] =  H  r  e  e q u a t i o n s w h i c h must be  satisfied  each s l i c e i s Ti  = c; +  o-  = PP  t  AE T  = FH ;  (cr -u- )tan0,; L  - "Cjtanoi  + TTi  C  ;  is Ui  (7.39)  + (PP +TT- Jb-^tano; - T ; b  ;  t  stress,  (7.38)  t  = -E- tan6! + A h  where  the  c  ( 1 +tan a )  (7.40)  2  :  t  (dE /db ) - h (dFH /dbj) c  shear  c  ;  stress, c  on t h e base of a s l i c e .  (7.41)  £  the c o h e s i o n ,  ;  the pore water p r e s s u r e ,  resistance  and  tan0j  6"; t h e n o r m a l  the  frictional  Additionally,  PP-,, = FT- /b- , and  (7.42)  TT  (7.43)  t  t  Note  t  = AT / b  ;  that  Equation  ;  equilibrium, equilibrium vertical for  If  be  e  = N-sinc;  Introducing  for  surface  on t h e b a s e o f a s l i c e ,  equation  H;  on t h e s h e a r  (7.39)  of a s l i c e ,  and  a slice  (7.41 ) .  that  (7.38)  and t h a t  horizontal of  is  slice  infinitesimal  defines the  the  state  equation  of  for  vertical  (7.40) i s one e q u a t i o n equilibrium. width  is  Moment  defined  limit  f o r both  equilibrium by  Equation  165  The  requirement  Equations  for  overall  horizontal  equilibrium,  from  (7.19) and (7.37) may be w r i t t e n a s  I[AE;;] = H T h i s may a l s o E[AE ] = H r  Inserting  - H  6  - H  s  (7.44)  t  be w r i t t e n a s s  + E[FHj] - H  Equation  (7.40) i n t o  l [ F H + (PP +TT ) b t a n c l  i  (7.45)  e  L  ;  (7.45) and r e a r r a n g i n g ,  ] - E[*t b ( 1+tan a ) ] = H -  H -  2  x  ;  f  r  yields  B  E[FH- ]  s  (7.46) The maximum surface F  horizontal  per unit  resistance  available  from  the  sliding  w i d t h may be e x p r e s s e d a s  = \ ( c ' + cr'tan0')dx = ( H ) F  s  (7.47)  S  Introducing  = ~C$ /F and (7.47) i n t o :  (7.46) and s o l v i n g  forF  yields E[ t r . b ; ( 1 + t a n a ) ] + F. 2  ;  F =  E[ (PP- +TT-)b tano- ] + H t  Introducing expression T .= 4  r  t  Equation  B  (7.39)  f o r the shear  c'-  (7.48)  into  strength,  (7.38)  gives  a  which i s  + (PP +TT - u - X - t a n o ) t a n 0 V  (7.49)  v  r  Introducing f o r T^; y i e l d s  c  £  r  = ^;/F  into  general  t h e above e x p r e s s i o n  and s o l v i n g  c ',- + (PP- +TT- -u- ) t a n 0 'L  T .= 4  -^  i  '  1 + (1/F)tan0'; The a v e r a g e f a c t o r using  Equation  simplicity,  '  (7.50) tano  of s a f e t y  (7.48) w i t h  several  factor of s a f e t y . w i l l be u s e d :  c  f o r the general case T . defined 4 ;  abbreviated  by E q u a t i o n  terms, a r e  For each s l i c e  is  used  to  the f o l l o w i n g  found  (7.50).  by For  d e f i n e ' the abbreviations  166  B  (7.52)  2  t  :  inserting  formula  Equations  (7.51)  f o r the average E[A ]  factor  and  (7.52)  of. s a f e t y  into  (7.48),  i s reduced  to  =  (7.53) E[B ]  +  r  By  H  s  introducing Equation  slice  the  + F.  X  F  (7.50) i n t o  c a n be c a l c u l a t e d  A '  =  NA  =  ;  A  (7.52) t h e A  term  z  f o r each  s t e p s as f o l l o w s :  + ( P P J + T T J - u ) t a n 0 i ]b-  1 +  (1/F)tan0' - t a n o ^  (7.54)  r  t  (7.55)  = A  The A  i n three  [cL  1 +  in  (7.51)  i  C  = T$ b.( 1+tan o- )  AX By  (PPj+TT )b tana-  =  Z  t  (7.56)  v a l u e s depend  t u r n depends  The  2  '/NA  and B  iteration  tan a  on  on t h e i n t e r s l i c e  the f a c t o r  technique  arises.  stresses  on  of s a f e t y .  the  shear  shear  Hence,  s u r f a c e may  force  which  t h e need  f o r an  be c a l c u l a t e d  as  follows: T; = —  =  (7.57) F-{(1+tan o )b ]  F  2  :  c  and V; in  = PP  + TT  :  accordance  be  found  (7.40) t o AEi  E  C  t  with  .  c  Equation  (7.39).  as f o l l o w s : Introduce  The  interslice  Equations  (7.51) and  (7.58) forces  may  (7.52)  into  find  = FHj.+  Summing  - T tana  t  t h e AE  B  :  - A /F  (7.59)  r  values  f o r each s l i c e  gives rise  to  = E[AE ]  The v e r t i c a l  (7.60)  :  shear  force  T-t, i s g i v e n  by  (Equation  7.41)  167  T All by  = -E- tan6-  t  t  - h- ( d F H [ / d b \ )  + Ah- ( d E ^ / d b j )  t  t  o f t h e p r e c e d i n g e q u a t i o n s must an  iteration The  be  (7.61)  satisfied  simultaneously  procedure.  average  f a c t o r of  safety  on  a slice  interface  i s found  from c'jh; +  (E;-UH )tan0' c  c  =  (7.62) Tt  where UH-  i s the water p r e s s u r e f o r c e  t  question. greater  For  than  a  F.  theoretically  Note t h a t  on  the  correct  average  slice  interface  s o l u t i o n , F'~  soil  properties  in  must  are  be  used  here.  7.5  Modified  Sarma Method  Sarma's  (1973) a p p r o a c h  substantially surfaces  from  of  Morgenstern  arbitrary  and  equilibrium  the o t h e r  Price  the  (1965).  is  terms of the  f a c t o r of  procedure  Sarma but  is  (1973)  the  equilibrium  equal  to the product  slice  weight and  the  Janbu solve  f a c t o r of  safety  surface forces  is  differs to  slip  (1973),  methods  Since these  solves A  the  the by  and slice  changing  until  slice  are expressed  initially  slice  unknown,  equations  f o r each  of the a c c e l e r a t i o n  forces  equilibrium  destabilizing  - a pseudo-earthquake the  applicable  of  shear  which  method  in an  required.  also  into  those  the  safety,  i n a d i f f e r e n t way.  assumed  on  satisfied.  methods  These  find  forces  equilibrium  iteration  slice  shape:  e q u a t i o n s and  the v a l u e of  to d e r i v i n g a s l i c e  force.  w h i c h d e p e n d on  force  equations,  is  slice.  introduced  This  coefficient K A  factor  the degree  of of  force and safety  is the is  strength  168  mobilization  i n the  equilibrium  parameters.  v a l u e s of  the  numerical  soil  f a c t o r of  iterations  calculations,  there  This  can  factor  coefficient safety. The In  A curve  "static" the  when  of  an  within  soil  Sarma's stability and  Lee  safety  mass may  (1973)  be  (1978) m o d i f i e d  pressure  slopes  generation  number  of  Further  work  Sarma's  cycles in  (1973)  modifications  may  analysis  be  (see  may  may  figure  University  model was to  included  failure area  method  is  e a s i l y be made by  is  was  presently in  made.  A  including  the  slice  7.3.  curve.  solution  equal  to  is  some  work.  for  the  A pore  analysis  (1982) a  Finn  stability^  for undrained  such  offshore  Columbia.  loading.  i n the  found  derived  6 . 2 ( b ) ) i n the  the  British  seismic  of  d e s t a b i l i z i n g force  t h i s method t o a n a l y z e to  o f f the  adopted  of  any  factor  f o r t h i s t y p e of been  for  in figure  picked  the  slice  acceleration  shown  is  distinct  other  the  analysis,  of  has  subjected  this  be  no  instability.  the of  coefficient  assumed  only  solution  when  then  stability  approach the  The  several  requires  t i m e s when t h e  drawn as  distribution  analyses at  underwater  areas  A  safety,  limit  for  numerical  found  be  acceleration  value.  of  answer.  K may  the  solution  f o r some v a l u e  earthquake  the  specified the  F vs.  of  i s performed the  at  is  zero  f a c t o r of  c a s e of  found  invaluable  to  terms  f a c t o r of  possibility  surface  i s equal  Since  the  reasonable  shear  in  analysis  safety. for  be  expressed  The  i s no  methods p r o v i d e no particular  are  water  and  the  loading.  being way  of  that  done. many  pseudo-three-dimensional forces  acting  equilibrium  on  the  side  equations.  169  *  0-7  Si*of/c factor of safety 8  •12 to*  0  2 Factor  of safety , F  F i g u r e 7.3 - C u r v e u s e d f o r e v a l u a t i n g t h e s a f e t y ( A f t e r F i n n a n d L e e , 1978)  factor  170  7.5.1  Assumptions The  f u n d a m e n t a l a s s u m p t i o n s on w h i c h t h i s  slice  method  is  based a r e : A  - Plane  strain  conditions  apply.  B  - The point of a p p l i c a t i o n of the normal f o r c e t h e b a s e o f e a c h s l i c e i s assumed t o be known.  C - The r e l a t i v e m a g n i t u d e s o f t h e a r e assumed t o be known. Additionally,  interslice  f o r a pseudo-three-dimensional  shear  Derivation The  the  following  slice  variables The  in  and f o r c e s acting  equilibrium  L  force  E  this  magnitude  per  computed  from  horizontal NjCOSG;:  l  unit earth  + StSinc-  t  of a  = W;  c  - Njisino;  C  limiting  equilibrium  on  in  figure  7.4.  i n the s l i c e  parallel  to the  as (7.63)  terms  of  its  normal For  equivalent  s t r e s s may vertical  be and  slice FN-COS0;  + AE  X  - SScsino; - FN sin0  + FS;COSPj  The  acting  o  theory.  - AT; +  = KW  be d e f i n e d  in  + FSjsinp; S;;COSc  on e a c h  The g e o m e t r i c a l  acting  The e f f e c t i v e  pressure  equilibrium  7.5.  defined  forces  may  i s expressed length.  forces  areas are included  + cr'tan0)]/L  :  force  and are  equations as m o b i l i z e d this  a l l the  7.4  f o r any s l i c e  = [2(b )(yt -yb )(c  that  include  figures  forces  Equations  on t h e s i d e  F o r any s l i c e  SSNote  equations  shown  forces  base.  of E q u i l i b r i u m  forces  analysis  D - The magnitudes and p o s i t i o n s o f t h e s i d e s l i c e a r e assumed t o be known.  7.5.2  a c t i n g on  condition  ;  -  (7.64)  r  (7.65)  SScCOSO;  may  be d e f i n e d  by  171  Figure  7.5  - Typical  (Sarma) s l i c e  showing s i d e  forces  172  S  =  z  This  = N'  tan0-  £  using  normal  + c'- b - s e c c ; )/F  c  e q u a t i o n may  Sc by  (N' tan0'-  be w r i t t e n  as (7.67)  mobilized  strength  f o r c e c a n be c a l c u l a t e d  N'-  = N-  t  - US  where  US-  of  slice  any  due  parameters.  The  effective  as (7.68)  :  i s t h e f o r c e due  L  (7.66)  t  + Cibisecai  t  the  t  t o pore water p r e s s u r e  t o pore water p r e s s u r e .  This  on  the  i s simply  USt = Uxbcseccj Equations  base  (7.69)  (7.64) and  (7.65) c a n be u s e d t o s o l v e  f o r N-  t  and T j ,  namely, (W -AT )coscc  N; =  t  :  "  (KW;+AE )sinoj C  + FN cos(«i-p ) - FS;sin(o -» ) f  S-  t  =  t  (W -AT;;) s i n a ;  ;  (7.70)  K  + (KW + AE ) c OS a :  ;  t  r  + FN- sin(o- -pj ) + F S c o s ( o £ - 0 ) - S S t  t  These e q u a t i o n s  r  together  with  r  (7.68)  can  (7.71)  :  be  substituted  into  (7.67) t o o b t a i n A T - t a n ( 0 - - o j ) + AE-  = BB  t  C  - KW-  (7.72)  where BB;; =  (W -USj ) t a n ( 0 - - a j) + [ c b s e c a - c o s 0 + F N s i n ( 0 - - a . + p ) £  r  £  t  i  c  I  -FS;COs(0j-o;+*j ) + S S j C O S 0 ] s e c ( 0 - a - ) £  Equation equation.  (7.72) Note  is  simplified  (7.73)  £  by  summing  both  s i d e s of the  that  E [ A E ] = E(n+1) - E ( 1 ) = 0  (7.74)  t  since  b o t h E(n+1) and E ( 1 ) e q u a l  [ (AT )tan(0;-o- ) ] = t  Equation vertical  t  Hence,  E[BB-J - E[KW ]  horizontal  (7.75)  C  (7.75) i s t h e r e f o r e and  zero.  one e q u a t i o n  equilibrium  which  satisfies  for a l l slices.  both  A second  173  equation  i s obtained  body a b o u t  the  i f moment e q u i l i b r i u m of  origin c  £  -  E [ ( W ) x g ] + E[(KW -)yg-J  -  E[FS  ;  whole  sliding  i s considered.  [ ( N j ; C o s o ; + S j s i n c ) x b c ] - E[ (-N :  the  :  sinctj+S c o s o - )yb - ] t  t  - E [ F N ( x t c o s * +yt - s i n * . ) ]  t  E  c  c  t  ( x t s i n p - y t - c o s $ ) ] + E[SSj ( x s s i n c -ys- cosa ) ] = 0 :  £  r  t  c  t  £  (7.76) This  equation  may  be  combined  (7.72) t o e l i m i n a t e N- ,  Sj , and  t  I [Wftxbj-xgj)]  with  Equations  AEj,  (7.64),  resulting  (7.65),  and  in  + E [ K W y g ] - E [ B B y b - ] + E [ FNj s i n * - ( y b - y t ) ] r  T  ;  t  c  £  + E t S S i C O S o ^ y b . - y s ^ ) ] - E[FS -cos<» ( y b - y t - ) ] t  =  i  c  Working The  i  (7.77)  i ;  Formulas  distribution  of  the  interslice  shear  f o r c e s i s assumed  that T  The  = X-Qj  c  Q-  or  AT;  v a l u e s may  t  Q.  =  be  [(E -UH ;)tan0 t  t  = X.-DQj; found , £  as  unity  since  expressed E  t  given  K-  =  t  (7.79)  c  parameter.  T h i s may  results  (Sarma,  be  taken  1973).  E^  as may  as + QSjh-)  2 t  i s the average  is  follows:  i t gives acceptable  = K;(0.5 h  where QS;  (7.78)  +c' h^]f(x)  where f ( x ) i s a d i s t r i b u t i o n  be  £  [ (ATj; { x b - y b t a n ( 0 - o ) } ]  7.5.3  so  t  by  Sarma  (7.80)  surcharge  (1973)  any  slice  interface,  as  1 - s i n ( 2 o - 0 ' f )[ ( 1 - 2 R l  above  t  t  ) s i n 0  ,  '  u  /  h-)cos0V ]  (7.81)  1 + sin(2o;-0'^ )sin0'; R* and  i s the is  ratio taken  of e x c e s s as an  pore water p r e s s u r e  average value.  The  to v e r t i c a l  stress  strength parameters  may  174  also  be  detail  taken as average how  Upon the  values.  t o o b t a i n t h e Qsubstituting  following  Sarma  (1973)  discusses  in  values.  Equation  (7.78) i n t o  (7.75) and  (7.77)  equations are obtained-  S1 • X + S2-K  =  S3  (7 .82)  S4- X - S5-K  =  S6  (7 .83)  j r e S1  thru  S6  a r e d e f i n e d as  follows:  SI  =  E[DQ tan(0 -o' )]  (7 .84)  S2  =  E[W-J  (7 .85)  S3  =  I[BB ]  (7 .86)  S4  =  E[DQ {xbi;-yb tan(0 -c  S5  =  l[Wiybf]  S6  =  E[FN (yb -yt  t  i  l  t  t  ;  :  t  (7 .87)  {)} ]  (7 .88) £  ) s i n * ,] - E[FS - ( y b - - y t Jcos*;; ]  c  t  c  + E [ S S ; ( y b - y s - ) c o s a c ] - EtBB-.yg;;] t  be  The  interslice  found  using  preceding The  f o r c e s and  the  (7 .89)  t  the  equilibrium  section  once K and  average  factor  of  > are safety  forces acting equations  on  t h e base  derived  in  can the  known. on  a slice  interface  i s found  from F\  c' h j + c  =  (Ei-UHc ) t a n 0 V  (7.90)  175  CHAPTER 8 EXAMPLES AND APPPLICATION OF ANALYSES  8.1  D e s c r i p t i o n o f Computer A  computer  analyses  program  described  description  of  documentation  which  at  program  1978) The  and  chapter  was t e s t e d w i t h  eliminate The and  the case  Janbu's  for  found  the  by  in  the S o i l  (Lee  and  structure stability modified  Janbu  (1973)  and  of  Janbu  Finn,  analysis.  analysis  was  d e r i v e d i n the preceding  Finn  including and  those  Lee  given  (1978)  methods a g r e e  There  very c l o s e l y  f o r slope  of c o h e s i v e d e p o s i t s .  analyses  This  i s not  deposits.  a smooth c u r v e  i s some i n s t a b i l i t y  The  solution  was  over  very  an  It slice  a s s o c i a t e d with  (1973) method o f t e n d i d n o t p r o v i d e  problems.  to  errors.  (1973) method d i d n o t form  Janbu's  divergent.  Dynamics G r o u p  t h a t t h e s t r e s s e s computed a t t h e b a s e o f e a c h  surface.  these  program  The r o u t i n e f o r t h e m o d i f i e d  t h e p r o g r a m STESL  a  thorough  description  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  from  fact,  A  A brief  the equations  foundation analyses  found  In  chapter.  numerous example p r o b l e m s ,  two s l i c e  was  slip  through  to perform the  T h i s r o u t i n e ( a n d t h e Sarma r o u t i n e a s w e l l )  any programming  for  from  be  Columbia.  perform  author;  were u s e d .  may  for a gravity  to  the  the papers  program  was t a k e n  was d e v e l o p e d  preceding  be g i v e n h e r e .  modified  by  the  of B r i t i s h  r o u t i n e used  written  GRAVSTAB  i s available  will  Sarma a n a l y s i s  in  the  the U n i v e r s i t y  the  in  Procedure  the this.  answer  unstable  and  176  The in  l o a d s used  sections  7.2  i n an a n a l y s i s a r e and  7.3.  be  approximation  constant  initially factor  of  the e f f e c t i v e  any  analysis.  unknown, i t may  of  yields  in  safety  be  found  minimal  and  The  foundation width Although  layer,  or  foundation width  i n most c a s e s may data  slice  by  input  and  slip  surfaces  may  with  former  multi-layered  used shear in  two  since  may  be  incremented  c o o r d i n a t e s f o r any  o n l y once s i n c e end  end  values for that  t h u s be only a  to  locate  particular  found few  t h e y may  factor  is  ways: l a y e r  since  slice  aid  potential  in  The  and  on  the shown  of  their  surface.  Hence,  s u r f a c e need t o down between  critical  be  "d"  of the  shear  w i t h a minimum amount o f  i s , shear  the  o p t i o n may  a given percentage of the s l i p  every  finding  coordinates  be moved up and  shape.  data  f o r each s l i c e  c o o r d i n a t e s "b" by  less  by  the s t r e n g t h  the c r i t i c a l p o s i t i o n  (that  variation  different  shape of s h e a r  approximately  shapes  two  rerun c o n t r o l  The  v a l u e s t o vary the p o s i t i o n  depth  surface may  7.1)  To  simple  s u r f a c e (between t h e two  current  input  chosen.  a  The  requires  deposits  ( a s many t i m e s as d e s i r e d ) .  figure  the  surface,  of  to i n v e s t i g a t i n g  is  width i s  reasonable  safety  method  surface  shear  to  ignored.  time  critical  width.  the  be a u t o m a t i c a l l y c a l c u l a t e d  slip  i s assumed  i n the a p p r o p r i a t e e q u a t i o n s  parameters w i l l a new  in a  the e f f e c t i v e  i n p u t i n one  The  lends i t s e l f well in  be  be  slice.  equations  As  e s t i m a t e d by a s s u m i n g a  w h i c h when u s e d  soil  the  iteratively.  a n u m e r i c a l v a l u e f o r the e f f e c t i v e  the e f f e c t i v e  from  These l o a d s , which are e x p r e s s e d  terms of the m o b i l i z e d s t r e n g t h , a r e first  found  be the  shear  surface effort  surface coordinate sets)  177  need t o be  specified.  P o r e water p r e s s u r e s may they  may  method pore  be  i s used  be  input  individually  f o r an  effective  the  are a l s o pore  pore  required.  water  as b e i n g  for  hydrostatic  each s l i c e .  stress analysis;  w a t e r p r e s s u r e s need t o be  analysis,  taken  input.  For  w a t e r p r e s s u r e s on  a  the  since this  type  The  latter  the  excess  three-dimensional s i d e s of  I t i s o f t e n a d e q u a t e t o use  p r e s s u r e s here  only  or  the  the  slices  hydrostatic  of a n a l y s i s  is quite  approximate. The  stresses  standard  output  overstressing in pore  an  be  due  found  The  to the on  Equation  of  They may  be  each  to estimate  that  the  also  the  pore  This  are  be  used  instantaneous  water  ( i . e . undrained)  (6.6).  slice  e x a m i n e d t o see i f  T h e s e s t r e s s e s may  short-term  example p r o b l e m  founded  represents,  taken  on  pressure  wave l o a d i n g  i s demonstrated f o r  g e o m e t r y and platform  figure  100  base  One  (1976).  The  analyzed  Lauritzsen  i s a CONDEEP  and  deposit.  Schjetne  loading data is  nearly The  profile other  i s given circular  shear is  i s an  in  type This  (1976)  o f f s h o r e p l a t f o r m i n the North  meters.  8.1.  t o be  Deposit  a nonhomogeneous c o h e s i v e  from  an • a c t u a l  approximately  Schjetne  assuming  base  1 - A M u l t i - l a y e r e d Cohesive  p r o b l e m was  in  GRAVSTAB.  stress analysis  based  first  structure  actual  the  2.  Example  required  on  o c c u r s anywhere.  water p r e s s u r e s  Example  8.2  for  effective  distribution may  computed  Table  and  Sea.  The  IX.  The  with a diameter  strength p r o f i l e that given  approximation  by of  is  of  shown  L a u r i t z s e n and this  profile  T a b l e IX Geometry and L o a d i n g Data f o r Example 4 Equivalent P l a t f o r m Length, L Equivalent P l a t f o r m Width, B  v  H o r i z o n t a l Wave Load, P  W  68.3 m 68.3 m  0  E f f e c t i v e F o u n d a t i o n Depth, D T o t a l V e r t i c a l Load, P + AP  0  0  3.5 m 187,000 t 49,100 t  H  Moment a t S e a f l o o r , M  2,240,000 t-m  Dynamic Wave P r e s s u r e , Ap,  3.5 t/m  Dynamic Wave P r e s s u r e , A p  -3.5 t/m*  U n i t Weight of S o i l , V  2  2.0  J  t/m3  F i g u r e 8.1 - Shear s t r e n g t h p r o f i l e f o r Example 1  179  using  layers  profile  was  The surface surface  used  f o r the  estimate  of  as  follows: A  found  each shear  down  to  using  just  the  find a  few  shape of  iterations done  surfaces  Table  The  way  different the  b a s e d on  accuracy by  a  horizontal  (Lauritzsen  and  Schjetne,  in this  methods p r e d i c t a s l i g h t l y  by  due the  to the two  method of total  methods; t h e  slices  method material  is  adequate.  exists within  safety.  By  surface,  the  be  by  The  and  estimated.  the  early  critical  runs shear in  safety  factors  are  given  in  bearing  capacity  be  the  NGI  rupture  determined  For  this  slip  example p r o b l e m  the  s u r f a c e method and  the  f a c t o r of critical slip  However, strata,  safety.  slip  surface the  a  then  is  determined  the  l a y e r of NGI  slice in  determined  weak z o n e .  thin the  The  This  surface  foundations, if  surface  approximately  t h e s i s agree q u i t e w e l l .  cohesive  the  described  shown  may  the  sharp  are  critical  of  the  methods  p a s s e s t h r o u g h more of  stress analyses  critical  of  lower  p o s i t i o n of  The  i s moved up  may  i s desired.  1976).  f a c t o r s d e t e r m i n e d by  computer  As  shear  provided  shear  A  f a c t o r of  surface  number  which the  the  shear  critical  o f f at  i s input  f o r the  information  the  part  shear  corresponding  procedures developed  rounded  of  geometries  with  safety  value  critical  angle  the  f o r t h i s purpose. i s then  latter  critical  s u r f a c e method.  shape w h i c h  minimum  The  below.  i s a l t e r e d several times.  surface  i f greater  The  X.  makes  shape  evaluated  8.2.  slip  written  in this  the  first  t h e NGI  was  before,  figure  discussed  is  and  be  analyses  most  corner  may  slice  strengths.  f o r the  SLIPSURF  general  undrained  procedure used to s e a r c h  surface  More  different  i s made u s i n g  program slip  with  by  For NGI  most slip  very  method  the  is  weak of  180  Table Comparison  o f Computed  X  Safety  Factors  f o r Example 1  CALCULATED SAFETY METHOD OF Hansen's  (1970) F o r m u l a ,  Meyerhof's NGI  Slip  ANALYSIS  Surface  P l a n e S t r a i n A c t u a l Case B/L = 0 B/L = 1  modified  (1963) F o r m u l a ,  FACTOR  modified  Method  2. 15  2.35  1  2. 17  2.49  1  1  1  2.00  2. 1 5  1  1  Modified  J a n b u Method o f  Slices  1 .92  -  Modified  Sarma Method o f  Slices  1 .93  2.06  'From L a u r i t z s e n and S c h j e t n e  (1976)  Method of  SI Ices  NGI S l i p S u r f a c e  Method  Hansen B e a r i n g C a p a c i t y  Figure  8.2  Theory  - C r i t i c a l s h e a r s u r f a c e s f o r Example 1 a s 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  little  use  important  in  assessing  t o note  that  on  NGI  platform s t a b i l i t y .  the increase i n the safety  pseudo-three-dimensional the  the  analyses i s nearly  method and t h e p r o c e d u r e  It i s also  factor  identical  developed  in this  f o r the  for  thesis  both based  Sarma's method. In t h e  assumed  foregoing  to  be  constant  stress conditions failure  There soil  will  surface,  reflect  analyses,  four  mass. The  stress  vary  distinct  undrained  shear  method  will  be  subjected  shear  s t r e n g t h s determined  of  good q u a l i t y  to  analysis. samples,  not always  be p e r f o r m e d .  estimated  from  triaxial  in-situ  compression  profile  may  position  may  easily  potential  results  which  appropriate.  by  w i t h i n the  using  the  samples  are  stresses  that  The r e s u l t i n g  way may  then  shown  a lack  they  undrained  be u s e d  in  of  this  are given must  variations. the  be r e l a t e d  The o t h e r s h e a r  percentages  used,  a  Laboratory  the f i e l d .  strength p r o f i l e  be  found  and t o t a l  t e s t s may  value.  horizontal  be  Since the  directly  or  figure  absence 8.3  may  In t h e s e c a s e s , t h e u n d r a i n e d s t r e n g t h  f o r these c o e f f i c i e n t s  and  be  a l l the t e s t s  values  depth  may  Since there i s often  as  shear  test  was  8.3.  1967).  in this  taken  The  various  in  along  of s t r e s s e x i s t i n g  in figure  in-situ  strength  position.  shear  stress  states  (Lambe,  t o the estimated  a stability  of  s t r e n g t h may  subjected  in  horizontal considerably  states  T h e s e a r e shown  path  undrained  t h e use o f l a b o r a t o r y  the d i f f e r e n t are  with  the  t o the standard or strengths  value.  be  Some p o s s i b l e  i n Table XI.  then  be r e p r e s e n t e d by  Assuming  strength variation  be i n c o r p o r a t e d i n t o  may  that with  the numerical  a  both  layered  horizontal technique  182  Table  XI  Coefficients for Estimating Undrained S t r e n g t h from T r i a x i a l C o m p r e s s i o n D a t a SHEAR TEST Direct  1  \  Shear  x C,, 0.75  Triaxial  Extension  0.50  Triaxial  Compression  1 .00  11  ACTIVE -  ZONE PASSIVE | TRIAXIAL f -  - T  Figure  8.3  - Zones o f s h e a r on t h e p o t e n t i a l failure 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 ( A d a p t e d f r o m K j e k s t a d and Lunne, 1979)  183  by  using  the  triaxial  appropriate  coefficients  stability  a n a l y s i s was  undrained  strength.  new  profile  original XII.  was  profile.  The  use  strength along  the  the  by  cost  on  of  the  output this  of  8.3  the  this  shear  failure  the p l a t f o r m  to  with  respect  t o note  XIII.  The  This  to c y c l i c developed  (1975); these contours  loading based  on  drawn  on  the  Table  not  the  yet  safety  effect  must be  f o r the  type  on  increased  increase  may  of p l o t  is  the  strata.  Deposit;  and  aforementioned standard  l o c a t i o n of  (It  l e n g t h of  is  also  that  part  weaker l a y e r s .  Ekofisk  Tank  analyzed  is  loading  data  r e s i d u a l pore  i n f i g u r e 8.5.  observations  the  for  in  reducing  Note t h e  the  p o r e water p r e s s u r e s  found  f o r s p e c i f y i n g the  for examining  surface.)  i s given  this  This cost  different  of  found u s i n g  a tremendous  found  is useful  distribution  the  one  base s i z e  s e c o n d example p r o b l e m t o be  Table  for  dollars.  surface  geometry  values  reported  that  pressure.  2 - A Cohesionless  required  are  the  Another  i s a m a t t e r w h i c h has  s i n c e the  to  the  by  zones.  new  zone c o n c e p t  of many m i l l i o n s o f shear  shear  surface  study  surface  average b e a r i n g  GRAVSTAB and  Example  The  The  of  s u r f a c e which runs through  tank.  was  Results  for locating this  The  due  identical  multiplied  these  shear  i s shown i n f i g u r e 8.4.  surface  the  various  almost  critical  of  useful  critical  I t i s important  order  The analyses  the  s u c h a s u b s t a n t i a l amount has  to reduce the be  in  values  performed using  The  of  been r e s o l v e d . factor  compression  reported  were  f i g u r e are  shown  the  i s given  water This by in  b a s e d on  Ekofisk in  pressures  distribution Clausen figure  et a l 4.11.  Rahman e t a l ' s  Table Effect  of S h e a r  Zone R e p r e s e n t a t i o n  STRENGTH PROFILE USED  Regular Shear  Strengths  Zone  XII  Strengths  on  the  Safety Factor  COMPUTED SAFETY FACTOR  1 .93 1 .62  WflHPLf 1 - COUDfFP STRUCTURE 03.30 Q N. FEB. 02. 1062 2-0 ANALYSIS »PLANE STRAIN)  PLATFORN BRSE  I0  Figure  8.4  - C r i t i c a l s h e a r s u r f a c e f o r Example 1 f o u n d from computer p r o g r a m GRAVSTAB  Table Geometry  XIII  and L o a d i n g D a t a  Equivalent  Platform  Length, L  Equivalent  Platform  Width, B  Effective Bouyant Vertical  Weight, P  Wave L o a d , AP  H o r i z o n t a l Wave L o a d ,  v  P  Figure  of S o i l , K  0  0.4 m 190,000 t  78,600 t  H  2,800,000 t-m  Dynamic Wave P r e s s u r e , Ap,«  U n i t Weight  85.8 m  10,000 t  W  Moment a t S e a f l o o r , M  Dynamic Wave P r e s s u r e ,  2  85.8 m  0  F o u n d a t i o n Depth, D  Platform  0  f o r Example  Ap  2  3.0 t/m  2  -3.0 t/m  2  2.0 t/m»  8.5 - D i s t r i b u t i o n o f p o r e w a t e r p r e s s u r e s i n f o u n d a t i o n s o i l u s e d i n Example 2  186  (1977) work. The  most d i f f i c u l t  instantaneous  pore  part  water  T h e s e were f o u n d b a s e d on AU The  = A0"  + A (ACT,  3  method of  slices  may  principal  s t r e s s e s i s as  slip  over  total  previous the  The  principal  factor  is  (6.6),  to  to the  cycling  loads.  which i s  The  from t h e  find  procedure  follows: A  foundation  slip  This  load  determined.  surface  the  the  determine  the  i s analyzed  and  i s now  s t r e s s e s at  the  b a s e of  e q u i l i b r i u m equations  factor  f o r any  t h e n computed and  The  principal  of  act  safety  each s l i c e  been s e t up  are  to  derived  p o r e water p r e s s u r e  same  i . e . the  assumed  load"  input  The  wave l o a d s ,  "no  s t r e s s e s and  in  to  The  i s r e q u i r e d as  wave l o a d s  changes  t o Au=0 i s f o u n d .  without  area.  the  used  T h i s p r o c e d u r e has  A-parameter  instantaneous  used  load only.  chapter.  Only  be The  then e s t a b l i s h e d .  then determined  due  (9.1)  i s then a n a l y z e d  platform  the  Equation  safety corresponding  surface  vertical  is  of  pressures  the  3  stresses.  factor  this analysis i s estimating  - ACT )  principal  the  of  in  are the  i n GRAVSTAB.  slip  surface.  changes the  new  s t r e s s e s may  be  for  the  safety evaluated  from cr,  = cr+  [(1  - cos2*)/sin<*]  (9.2)  o  = 6-  [(1  + cos2*)/sin*]  (9.3)  3  where ot  * i s defined =  45°+  0/2  Here 0 i s the for  by  each case.  (9.4)  mobilized For  the  friction no-load  angle.  This w i l l  analysis this  be  value  different  will  be  very  low. The  critical  slip  surface  found  f o r the  tank  i s shown i n  187  figure  8.6.  cyclic with is  loading  total felt  probably of  Only  the  the were  stress to  be  dilate  soil  residual  pore  used  pore  increments  and  c r e a t e n e g a t i v e pore  a  marked e f f e c t  slip  s u r f a c e shown i n t h e  on  were c h o s e n between 0.0  these  values are  be  the c a s e .  cohesive safety  analysis  The  the  with  shallow  For  deeper  stress analysis  side  The  areas  the  to  This  latter  was  computed  safety factor minimal.  with  resistance  can  shown i n t h e in  to sand  w i l l generally  added  up  due  For  which  foundation.  the  IX.  mechanisms  show  For  corresponds  failure  T h i s was  i n much  A-parameter  value  factors  would  A-parameter  of s a f e t y .  mechanisms t h i s  would a l s o  same  of  factor  safety  failure  the  1 and  of t h e  value  i n c r e a s e i n the  substantially.  i n Example  water p r e s s u r e s  shown i n T a b l e  problem, the  foundations,  factor  ( i . e . Au=0).  f o u r v a l u e s of the  -0.33.  failure.  r e s i s t a n c e from  foundations  figure,  and  at  added  The  t h e computed  t o a d e n s e sand  this  due  water p r e s s u r e s a s s o c i a t e d  were n e g l e c t e d  mass d u r i n g l o a d i n g .  different  pressures  c o n s e r v a t i v e s i n c e t h e d e n s e E k o f i s k sand  has  For  and  water  occur  in  increase  the  total an  stress  effective  188  Table XIV E f f e c t o f A-parameter on t h e S a f e t y  Factor  COMPUTED SAFETY FACTOR  VALUE OF A-PARAMETER  -0.33  1.77  -0.20  1.61  Au-0  1.51  -0.10  1.49  1.37  0.00  i D M U  1-  « C  •na PA. m m « urn  nr..  'auJJJJJJJllV  '1* i.  i.  A h . k . ^ H c j M . ^  iu  JM  iu  F i g u r e 8.6 - C r i t i c a l shear s u r f a c e f o r Example 2 found from computer program GRAVSTAB  189  CHAPTER 9 SUMMARY AND CONCLUSIONS  Offshore  gravity  structures  have  o f f s h o r e development  schemes.  They o f f e r  nearly  tow-out,  thereby  complete  time.  This  at  is  particularly  such as t h e n o r t h e r n structures present safety. nature  It  of t h e i r  provide  recovery  design,  This  or f o r  economically  engineering  geotechnical  specialist.  for  exploration  in  terms  steel of  which  is  necessary  advantage  offshore  where  presents  many  Although  offshore  engineering  recently  has  field  pipelines  a r e not  challenges  f o r the  many  years,  only  art  in  not  only  h y d r o d y n a m i c , and o c e a n o g r a p h i c a l and d e s i g n  o f new t e c h n i q u e s  these  r e q u i r e s that the g e o t e c h n i c a l engineer  them s i n c e he must p l a y a key  role  of  major  of the s t a t e but a l s o i n  engineering.  development  has  hydrocarbon  moved i n t o d e e p e r w a t e r s where t h e d e s i g n  geotechnical engineering  with  By  production  f o r marginal  of  fields  start.  for  r e q u i r e d an advancement  structural,  jacketed  short-term  production  s t r u c t u r e s has c o n s i s t e n t l y the  environments  s t r u c t u r e s i n c o r p o r a t e s t o r a g e and  i s a significant locations  installation  in hostile  f o r an e a r l i e r  these  in  justified.  Offshore  existed  allows  risk  future  the advantage of being  N o r t h Sea where c o n v e n t i o n a l  a l a r g e deck a r e a  equipment.  bright  minimizing  important  a substantial  also  a  The  p h i l o s o p h i e s i n a l l of  in  gravity  be f a m i l i a r structure  design. Instrumentation  h a s :' p r o v i d e d  some  useful  data  for  190  predicting gravity  structure.  limited based  the magnitudes of  and  on  Ekofisk  More r e c e n t d a t a this  Presently,  Cyclic  structures research.  evaluation  area  data  for  of  analysis  among t h o s e  cyclic  the  platforms  due  to  cyclic  must  be  settlements for very  simplistic  for offshore gravity considerable  individuals  r e s e a r c h would g r e a t l y  is  is difficult  other  settlement  which r e q u i r e s a  Cooperation in this  for  s t r u c t u r e s i s made u s i n g  settlement  i s an  Since  data  c o n s i d e r a t i o n , some a s s e s s m e n t  the  type  Published  is available  result.  important  gravity  models.  known".  large  future structures  demonstrates that p l a t f o r m settlement  made.  and  accelerate  type  amount  of  corporations progress  in  area. Stability  engineers be  criteria this  i s the other p r i n c i p a l  must d e a l w i t h .  viewed  developed  in  distribution water  this  a r e met.  critical  For  over  pore  The  example,  i s used  only  full  contact  must be  within water is  slab the  methods  substantial  discrepancies  on-site observations.  by  exist  verified  also  soil  no  be  means  assumed;  instrument on  to  The  and  certain  the  the d i s t r i b u t i o n  mass. due  if  is usually by  must  discussed  used  information  and  pressures  theoretical  that geotechnical  procedures  may  to provide  the  problem  i s a complex p r o b l e m w h i c h  thesis  assumption  pressures  residual  This  perspective.  within  Instrumentation  and  have t o d e s i g n  tank  i s an  this  will  a  of t h i s  is "publically  effects  involved  the a v a i l a b i l i t y  for  what  confirms  offshore  However,  most e n g i n e e r s  to assess. which  settlements expected  data. stress  of  pore  evaluation  cyclic  loading  reliable.  between t h e o r e t i c a l  In  of by  fact,  estimates  191  Estimation presently element  assessed method,  foundations. use (1)  of a g r a v i t y  or  the  NGI  slip  capacity  adequately  Extensions  of  latter  value. bearing  and  (3)  NGI  effective  these  surface  method  element  method  may  The most  s e r i o u s problems a s s o c i a t e d with  soil  stiffness  of  cohesive  a l s o be u s e d  analyzed.  f a c t o r s must  An  Both of these  of o f f s h o r e s o i l  alternative  of  slices.  method, w h i c h extended  are  of  deposits. platform  be r e a s o n a b l e  be c o n s i d e r e d  that  the  Two  investigations.  i s based  methods were d e r i v e d .  gravity  foundation  An  method  of  alternative slices  e f f e c t s were e a s i l y  was  technique,  the  (1973)  engineers,  within  procedure  finite on  Janbu's  was n o t  framework.  soil  i n the l i g h t  analysis  dimensional  finite  are  for  A pseudo-three-dimensional  (1973)  over  stability.  t h i s method  i n two  Sarma's  limited  The  s t r u c t u r e problems  this  with  i s only a p p l i c a b l e  T h i s procedure  i s w e l l known t o most  to treat  to deal  a p p r o a c h t o t h e b e a r i n g c a p a c i t y and  e l e m e n t methods was p r e s e n t e d . method  analyses.  p a r a m e t e r s need t o be known a c c u r a t e l y and relations  the r e l i a b i l i t y  to  layered  i s an improvement  to assess  t h e assumed c o n s t i t u t i v e  of  stress  c a p a c i t y t h e o r y , however, t h i s method analyses  clay  value f o r  analyze  theories  stress  for  inability  t h e o r y have been p r o p o s e d  however, slip  (2)  is  the f i n i t e  method  because of the  to t o t a l  the  structure  i s of l i m i t e d  loading,  perform  classical  problem,  The  complex  surface  theory  i n offshore analyses primarily treat  type  by u s i n g b e a r i n g c a p a c i t y t h e o r y ,  Bearing  foundations,  the  of the s t a b i l i t y  was  dimensions. developed based  developed.  i n c o r p o r a t e d i n t o Sarma's  on  Three(1973)  192  method.  This  solution  method  i s also numerically  p o s s i b l e f o r any  The  analysis  applied  to  deposit  and  procedures  two  example  one  illustrated  p r o b l e m by  on  how  a  cohesionless  soil.  total  good.  The  be  slip  reasonable  results  seams.  the  lower  a  greater.  the  slip  factor. factor  increased  by  first  example  The  surface  method.  for  cohesive  problem analyzed, f a c t o r of  profile. The  be  For  values  performed.  the  NGI  shear  profiles  effect  due  to  the  agrees  well  method  provides  without  method of  undrained  of  shown  result  s a f e t y , although  The  the  This  foundations  other  of  and  six percent  The  the  have a p r o n o u n c e d  use  methods  about  surface  part  instantaneous  of  slices  based  changes  on  stress  this  pore  method of  was  thin  slices  is  shown  difference  s t r e n g t h chosen on  weak  not s u b s t a n t i a l l y  the  zone c o n c e p t  A-parameter  pressures  used  the  computed  reduces  was  also  may along  safety  the  safety  the due  determination to the  to p r e d i c t these principal  performed.  the  wave l o a d s .  The  pore water  stresses.  a  significant hence t h e  such  as  effect  factor  Ekofisk  of  The  of  pressures  T h i s procedure  computer p r o g r a m GRAVSTAB.  has  sand,  was  water p r e s s u r e s  d e v e l o p e d and  dense  analysis  analysis  i n the  i n c o r p o r a t e d ' i n t o the  a  existing  side areas.  effective  critical  For  cohesive  considerably.  An  the  layered  analysis could  from t h e  lower  for this  be  a  were  the  resistance  give  on  thesis  pseudo-three-dimensional a n a l y s i s suggests that  added  to  this  slices.  be  f a c t o r can  For  method of  to  safety  NGI  stress  the in  - one  were compared w i t h  the  developed  problems  Results  with  using  s t a b l e w h i c h makes a  on  The the  safety  value pore  was of  water  computed.  sand, where d i l a t i o n  will  193  occur,  the  pressures  on  The provide  slip  reasonable  method of  slices  wide  estimating loading.  $SIGNOFF  increase  answers The  to  range offshore  method, w h i c h problems,  gravity  in  since  this  water  i s easy  were shown  gravity  based  does not  structure  pore  thesis  i t can  is  the  less.  offshore  since  e f f e c t s and  of  be  procedure  is preferred  This  will  developed  three-dimensional  a  will surface  problems.  instability. to  the  procedures  stability  on  stability  on  structure  Sarma's  provide  suggested stability  (1973)  information  s u f f e r from  t o use  to  numerical  and  applicable  as  a means of  under  s t o r m wave  194  REFERENCES  0  1. A g o s t o n i , 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." Twelfth Annual Offshore Technology Conference, Houston, P r o c e e d i n g s , V o l . 4 , pp.245-260. 2.  A i r y , G. B. ( 1 8 4 5 ) : "On Tides and M e t r o p o l i t a n a , London, pp.241-396.  3. A m e r i c a n Practice Offshore 4.  Waves."  Encyclopedia  Petroleum Institute. (1978): API Recommended. for Planning, Designing and C o n s t r u c t i n g Fixed S t r u c t u r e s , API/RP2A; 9 t h Ed., D a l l a s .  A n d e r s e n , K. H. (1972): "Bearing Capacity of Shallow Foundations on C o h e s i o n l e s s S o i l s . " N o r w e g i a n 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 R e p o r t 51404-1.  5. A n d e r s o n , Knut H. ( 1 9 7 6 ) : " B e h a v i o r o f Clay Subjected to Undrained C y c l i c L o a d i n g . " I n t e r n a t i o n a l C o n f e r e n c e on t h e Behavior of O f f s h o r e S t r u c t u r e s , O s l o , P r o c e e d i n g s , Vol.1, pp.392-403. 6.  A n d e r s e n , K. H.; Brown, S. F.; F o s s , I . ; P o o l , J . H.; and R o s e n b r a n d , W. F. ( 1 9 7 6 ) : " E f f e c t of C y c l i c L o a d i n g On C l a y B e h a v i o r . " N o r w e g i a n G e o t e c h n i c a l I n s t i t u t e , No.113, pp.16.  7.  A n d e r s e n , K. H.; S e i n e s , P. B.; Rowe, P. W.; and Craig, W. H. (1979): " P r e d i c t i o n and Observation of a Model Gravity Platform on Drammen C l a y . " Second I n t e r n a t i o n a l C o n f e r e n c e on t h e B e h a v i o r of O f f s h o r e S t r u c t u r e s , London, P r o c e e d i n g s , V o l . 1 , pp.427-446.  8.  A u g u s t i n e , F. E., M a x w e l l , F. D., and L a z a n o f f , S. M. ( 1 9 7 8 ) : "Extreme Wave H e i g h t s i n t h e G u l f o f A l a s k a . " T e n t h Annual Offshore Technology Conference, Houston, P r o c e e d i n g s , V o l . 3 , pp.1551 -1562.  9.  Bea, R. G., and Akky, M. R. (1979): " S e i s m i c , Oceanograp 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 Platform Design." Eleventh Annual Offshore Technology Conference, H o u s t o n , P r o c e e d i n g s , V o l . 4 , pp.2251-2262.  10.  Bea, R. G., and L a i , N. W. ( 1 9 7 8 ) : "Hydrodynamic L o a d i n g on Offshore Platforms." Tenth Annual Offshore Technology C o n f e r e n c e , H o u s t o n , P r o c e e d i n g s , V o l . 1 , pp.155-168.  11.  B e l l , W. Gas in England:  E. (1974): the North Scientific  "The E q u i p m e n t R e q u i r e m e n t s f o r O i l and S e a . " O f f s h o r e E u r o p e , 2nd Ed., B u c k s , S u r v e y s ( O f f s h o r e ) L t d . , pp.27-36.  195  12.  B e r c h a , F. G., and S t e n n i n g , D. G. ( 1 9 7 9 ) : " A r c t i c O f f s h o r e Deepwater Ice-Structure Interaction." Eleventh Annual Offshore Technology Conference, Houston, Proceedings, V o l . 4 , pp.2377-2386.  13.  Berman, M. Y., B l e n k a r n , K. A., and D i x o n , 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 Production." Tenth Annual O f f s h o r e Technology Conference, H o u s t o n , P r o c e e d i n g s , 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 Offshore Structures." Eleventh Annual O f f s h o r e T e c h n o l o g y C o n f e r e n c e , H o u s t o n , P r o c e e d i n g s , V o l . 2 , pp.927938.  15.  Bjerrum, L. (1973): "Geotechnical Problems Foundations of S t r u c t u r e s i n t h e N o r t h S e a . " V o l . 2 3 , No.3, pp.319-358.  16.  B r a u n , W i l l i M. ( 1 9 7 4 ) : " E k o f i s k S e t t l e m e n t s and t h e S e a l a b . " G r o u n d 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 Gravity Based Oil Production P l a t f o r m I n t e r a c t i o n w i t h t h e Sea Bed." Seventh Annual Offshore Technology Conference, Houston, P r o c e e d i n g s , V o l . 3 , pp.387-398.  18.  Brown, J . D., and M e y e r h o f , G. G. (1969): "Experimental Study of Bearing Capacity in Layered Clays." Seventh International Conference on S o i l M e c h a n i c s and F o u n d a t i o n E n g i n e e r i n g , M e x i c o C i t y , P r o c e e d i n g s , V o l . 2 , pp.45-51.  19.  B u r k h a r d t , J . A., and M i c h i e , T. W. (1979): "Submerged Production System--A Final Report." Eleventh Annual Offshore Technology Conference, Houston, Proceedings, V o l . 2 , pp.801-806.  20.  B u r n s , G. E . , and D'Amorim, G. D. f o r Phase I D e v e l o p m e n t of Garoupa Offshore Technology Conference, V o l . 2 , pp.177-184.  21.  B u t t o n , S. J . ( 1 9 5 3 ) : "The B e a r i n g C a p a c i t y o f F o o t i n g s on a Two-layer Cohesive Subsoil." Third International C o n f e r e n c e on S o i l M e c h a n i c s and Foundation Engineering, Z u r i c h , P r o c e e d i n g s , V o l . 1 , pp.332-335.  22.  C a l l i s , C ; Knox, C ; S u t t o n , D.; and W i l e y , S. ( 1979): "An Assessment of Grouting M a t e r i a l s , P l a c e m e n t Methods, and M o n i t o r i n g Equipment for Offshore Structures." Eleventh Annual Offshore Technology Conference, Houston, P r o c e e d i n g s , V o l . 4 , pp.2755-2764.  Involved in Geotechnique, Steady  ( 1 9 7 7 ) : "Bouyant Towers Field." Ninth Annual Houston, Proceedings,  196  :  23.  Clausen, C a r l J . Frimann. (1976): "The CONDEEP Story." Offshore Soil Mechanics, Eds. Phillip G e o r g e and D a v i d Wood, Cambridge: Cambridge University Engineering D e p a r t m e n t , pp.256-270.  24.  C l a u s e n , C. J . F.; D i B a g i o , E.; Duncan, J . M.; and A n d e r s e n , K. H. ( 1 9 7 5 ) : " O b s e r v e d B e h a v i o r o f the Ekofisk Oil Storage Tank Foundation." Seventh Annual Offshore T e c h n o l o g y C o n f e r e n c e , H o u s t o n , P r o c e e d i n g s , V o l . 3 , pp.399413.  25.  D a v i s , E . H., and B o o k e r , J . R. (1973): "The Effect of Increasing Strength w i t h D e p t h on t h e B e a r i n g C a p a c i t y o f C l a y s . " G e o t e c h n i q u e , V o l . 2 3 , No.4, pp.551-563.  26.  Dean, R. G. (1965): "Stream Function Representation of Nonlinear Ocean Waves." Journal of the Geophysical R e s e a r c h , V o l . 7 0 , No.18.  27.  Department of Energy. (1974): G u i d a n c e on t h e D e s i g n 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 , L o n d o n .  28.  Department of the Interior, U.S.G.S. (1979): Approval Procedure for Installation and O p e r a t i o n of Platforms, F i x e d and M o b i l e 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, O r d e r 8, W a s h i n g t o n .  29.  D e r r i n g t o n , J . A. ( 1 9 7 7 ) : " C o n s t r u c t i o n o f t h e M c A l p i n e / S e a Tank G r a v i t y P l a t f o r m s a t A r d y n e P o i n t , A r g y l l . " D e s i g n 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 , L o n d o n : Institute of C i v i l E n g i n e e r s , P r o c e e d i n g s , pp.121-130.  30.  Det tion  and  Norske V e r i t a s . (1977): Rules f o r the Design C o n s t r u c 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 , O s l o .  31. D i B a g i o , Elmo, M y r v o l l , F r a n k , and Hansen, Svein Borg. (1976): "Instrumentation of Gravity Platforms for P e r f o r m a n c e O b s e r v a t i o n s . " I n t e r n a t i o n a l C o n f e r e n c e 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 , P r o c e e d i n g s , V o l . 1 , pp.516-527. 32.  Duncan, J . M. ( 1 9 7 2 ) : " F o u n d a t i o n S t u d y f o r N o r t h Sea Oil Tank." N o r w e g i a n 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. Geotechnical  34.  F a l k n e r , C. B., and F r a n k s , N. S. (1978): "Production Techniques from Tension Legged P l a t f o r m s . " Tenth Annual Offshore Technology Conference, Houston, Proceedings, V o l . 4 , pp.2079-2086.  (1974): "Marine Soil Mechanics." I n s t i t u t e , No.103, pp.1-20.  Norwegian  197  35.  Federation Internationale de Recommendations f o r t h e D e s i g n 3rd Ed., Slough.  l a Precontrainte. (1977): o f C o n c r e t e Sea S t r u c t u r e s ,  36.  F i n n , L . D., W a r d e l l , J . B., a n d L o f t i n , T. D. ( 1 9 7 9 ) : "The Guyed Tower a s a P l a t f o r m f o r Integrated D r i l l i n g and Production O p e r a t i o n s . " J o u r n a l of Petroleum Technology, V o l . 3 1 , No.12, pp.1531-1537.  37.  F i n n , W. D. L i a m a n d L e e , M i c h a e l K. W. (1978): "Seafloor Stability Under Seismic a n d Wave L o a d i n g . " ASCE S p r i n g C o n f e r e n c e , B o s t o n , S p e c i a l t y S e s s i o n on S o i l M e c h a n i c s in the Marine Environment.  38.  F i n n , W. D. L i a m , L e e , Kwok W., and M a r t i n , G e o f f r e y R. (1977): "An E f f e c t i v e Stress Model for Liquefaction." Journal o f t h e 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, P r o c e e d i n g s , V o l . 1 0 3 , 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 O b s e r v a t i o n s of t h e E k o f i s k O i l S t o r a g e Tank i n t h e N o r t h Sea." B r i t i s h Geotechnical Society Settlement Conference, Cambridge U n i v e r s i t y , U n i t e d Kingdom, P r o c e e d i n g s , 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 a n d Gas J o u r n a l , V o l . 7 4 , No.18, pp.153-159.  41.  F u r n e s , 0. ( 1 9 7 8 ) : "Overview o f O f f s h o r e O i l I n d u s t r y w i t h Emphasis on t h e N o r t h Sea." Lectures on Offshore Engineering, Combined P r o c e e d i n g s o f a One-Day C o n f e r e n c e Plus Eight Weekly Seminars, Aalborg University Center, A a l b o r g , Denmark.  42.  G a r r i s o n , C. J . ( 1 9 7 7 ) : "Wave L o a d s on N o r t h Sea G r a v i t y P l a t f o r m s : A Comparison of Theory and E x p e r i m e n t . " Ninth Annual Offshore Technology Conference, Houston, P r o c e e d i n g s , V o l . 1 , pp.513-524.  43. G a r r i s o n , C. J . ( 1 9 7 9 ) : "Hydrodynamic L o a d i n g of O f f s h o r e S t r u c t u r e s . Three D i m e n s i o n a l Source D i s t r i b u t i o n Methods." N u m e r i c a l Methods i n O f f s h o r e E n g i n e e r i n g , E d . 0. C. Z i e n k i e w i c z , New Y o r k : J o h n W i l e y a n d Sons, I n c . , pp.87-140. 44.  G a r r i s o n , L . E . , a n d Bea, R. G. ( 1 9 7 7 ) : "Bottom Stability as a Factor i n P l a t f o r m S i t i n g and D e s i g n . " N i n t h A n n u a l Offshore Technology Conference, Houston, Proceedings, V o l . 3 , pp.127-134.  45. G e o r g e , P. J . ( 1 9 7 6 ) : "Notes on S i t e I n v e s t i g a t i o n w i t h Respect t o the Design of O f f s h o r e Structures." Offshore Soil Mechanics, Eds. P h i l l i p George and D a v i d Wood, Cambridge: Cambridge University Engineering Department, pp.101-116.  198  46.  G e r w i c k , Ben C , Jr. (1974): " P r e p a r a t i o n s of Foundations f o r C o n c r e t e C a i s s o n Sea S t r u c t u r e s . " S i x t h A n n u a l O f f s h o r e T e c h n o l o g y C o n f e r e n c e , H o u s t o n , P r o c e e d i n g s , V o l . 1 , pp.119130.  47.  G e r w i c k , B. C , and Hognstad, E. (1973): "Concrete Oil S t o r a g e Tank P l a c e d on N o r t h Sea F l o o r . " C i v i l E n g i n e e r i n g , ASCE, V o l . 4 3 , No.8, pp.81-85.  48.  Gumbel, E m i l J u l i u s . (1958): Statistics Y o r k : C o l u m b i a U n i v e r s i t y P r e s s , 375 p.  49.  Hansen, Bent. (1976): "Modes of Failure Eccentric Loads." I n t e r n a t i o n a l Conference of O f f s h o r e S t r u c t u r e s , O s l o , P r o c e e d i n g s , 500.  50.  Hansen, F. J . , and I n g e r s l e v , L. C. F. ( 1 9 7 7 ) : "The Case for a Hybrid." Design and Construction of Offshore Structures, London: Institute of Civil Engineers, P r o c e e d i n g s , pp.135-141.  51.  H a n s e n , J . B. (1961): "A General Capacity." The Danish Geotechnical B u l l e t i n No.11, pp.38-46.  52.  H a n s e n , J . B. ( 1 9 7 0 ) : "A R e v i s e d and E x t e n d e d Formula for Bearing Capacity." The Danish Geotechnical Institute, Copenhagen, B u l l e t i n No.28, pp.5-11.  53.  H a r i n g , R. E., and Heideman, J . C . ( 1 9 7 8 ) : " G u l f of Mexico R a r e Wave R e t u r n P e r i o d s . " T e n t h A n n u a l O f f s h o r e T e c h n o l o g y C o n f e r e n c e , H o u s t o n , P r o c e e d i n g s , V o l . 3 , pp.1537-1550.  54.  H e i j n e n , W. J . ( 1 9 8 1 ) : "The Use of P h y s i c a l M o d e l s i n S o l v ing Offshore 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 M o d e l s i n T h e i r D e s i g n , E d s . G. S. T. Armer and F. K. G a r a s , L a n c a s t e r : The Construction Press, pp.263-272.  55.  H e n k e l , D. J . (1970): "The R o l e of Waves i n C a u s i n g Subm a r i n e L a n d s l i d e s . " G e o t e c h n i q u e , V o l . 2 0 , No.1, pp.75-80.  56.  H i t c h i n g s , Gordon A., Bradshaw, Heath, and Labiosa, 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 Site Investigations for a North Sea Gravity Platform." Eighth Annual Offshore Technology Conference, Houston, P r o c e e d i n g s , V o l . 1 , pp.61-74.  57.  H0eg, K a a r e . (1976): "Foundation Engineering for Fixed Offshore Structures." I n t e r n a t i o n a l Conference on the B e h a v i o r of O f f s h o r e S t r u c t u r e s , O s l o , P r o c e e d i n g s , Vol.1, pp.39-69.  of Extremes, Under on t h e Vol.1,  New  Inclined Behavior pp.488-  Theory for Bearing I n s t i t u t e , Copenhagen,  199  58.  Hogben, N.; M i l l e r , B. L.; S e a r l e , J . W.; and Ward, G. (1977): "Estimation of Fluid Loading on Offshore Structures." Institute of Civil Engineers, London, P r o c e e d i n g s , V o l . 6 3 , P a r t 2, pp.515-562.  59.  Hove, Knut and F o s s , Offshore Concrete Offshore Technology V o l . 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 Gravity Platform in Shallow Offshore Louisiana Water." Eleventh Annual Offshore Technology Conference, Houston, Proceedings, Vol.2, pp.1003-1008.  61.  I s a a c s o n , M. de S t . Q. (1980): "Wave Forces in the D i f f r a c t i o n Regime--A Review." Coastal/Ocean Engineering Report, Department of Civil Engineering, U n i v e r s i t y of British Columbia.  62.  I s a a c s o n , M.  63.  Janbu, N i l m a r . (1973): "Slope Stability 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 . P o u l o s . New Y o r k : John Wiley and Sons, I n c . , pp.45-86.  64.  Janbu, Nilmar, Grande, L a r s , and E g g a r e i d e , R a r e . (1976): "Effective Stress Stability Analysis for Gravity Structures." International Conference on t h e B e h a v i o r of O f f s h o r e S t r u c t u r e s , O s l o , P r o c e e d i n g s , V o l . 1 , pp.449-466.  65.  de J o n g , J . J . A., and B r u c e , J . C. (1978): " D e s i g n and C o n s t r u c t i o n of a C a i s s o n R e t a i n e d 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 B e a u f o r t Sea." Tenth Annual Offshore Technology C o n f e r e n c e , H o u s t o n , P r o c e e d i n g s , V o l . 4 , pp.2111-2120.  66.  Kinsman, B. ( 1 9 6 5 ) : Wind Waves, t h e i r G e n e r a t i o n and g a t i o n on t h e Ocean S u r f a c e , Englewood Cliffs, P r e n t i c e - H a l l , 676 p.  67.  K j e k s t a d , O., and Lunne, T. ( 1 9 7 9 ) : " S o i l Parameters Used for Design o f G r a v i t y P l a t f o r m s i n t h e N o r t h S e a . " Second International Conference on the Behavior of Offshore S t r u c t u r e s , London, P r o c e e d i n g s , V o l . 1 , pp.175-192.  68.  K l i e w e r , Raymond M., and F o r b e s , Graeme S. ( 1 9 8 0 ) : "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 I c e 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 C o n f e r e n c e , H o u s t o n , P r o c e e d i n g s , V o l . 4 , pp.315-324.  de  I v a r . (1974): " Q u a l i t y Assurance for Gravity Structures." Sixth Annual Conference, Houston, Proceedings,  S t . Q.  (1981):  Private  Communication.  PropaN. J . :  200  69.  K l i t z , J . K e n n e t h . ( 1 9 8 0 ) : N o r t h Sea O i l : R e s o u r c e R e q u i r e ments f o r D e v e l o p m e n t of t h e U.K. S e c t o r , O x f o r d : Pergammon P r e s s , 260 p.  70.  K o r t e w e g , D. J . , and De V r i e s , G. ( 1 8 9 5 ) : "On t h e Change of Form o f Long Waves A d v a n c i n g i n a R e c t a n g u l a r C h a n n e l , and on a New Type of Long S t a t i o n a r y Wave." Philosophical M a g a z i n e , 5 t h S e r i e s , pp.422-443.  71.  L a l l i , D. (1975): "Discussion." Off-shore Structures, L o n d o n : I n s t i t u t e of C i v i l E n g i n e e r s , Proceedings, pp.9293.  72.  L a l l i , D. (1977): " D e s i g n , 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 Steel Gravity Platforms." Design and Construction 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 g i n e e r s , P r o c e e d i n g s , pp.31-38.  73.  Lambe, T. W. ( 1 9 6 7 ) : " S t r e s s P a t h M e t h o d . " J o u r n a l of the Soil M e c h a n i c s and F o u n d a t i o n D i v i s i o n , ASCE, P r o c e e d i n g s , V o l . 9 3 , NO.SM6, pp.309-317.  74.  L a u r i t z s e n , R o l f , and S c h j e t n e , Knut. (1976): "Stability Calculations for Offshore Gravity Structures." Eighth Annual Offshore Technology Conference, Houston, P r o c e e d i n g s , V o l . 1 , pp.76-82.  75.  L e e , K e n n e t h L. (1976): " P r e d i c t e d and Measured Pore P r e s s u r e s i n the E k o f i s k Tank Foundation." International Conference on the B e h a v i o r of O f f s h o r e S t r u c t u r e s , O s l o , P r o c e e d i n g s , V o l . 2 , pp.384-398.  76.  L e e , K. L., and A l b a i s a , A. (1974): "Earthquake Induced Settlements in Saturated Sands." Journal of the Geotechnical Engineering Division, ASCE, Proceedings, V o l . 1 0 0 , NO.GT4, pp.387-406.  77.  L e e , K e n n e t h L., and F o c h t , J o h n A., J r . ( 1 9 7 5 a ) : " L i q u e f a c t i o n P o t e n t i a l a t E k o f i s k Tank i n N o r t h S e a . " J o u r n a l o f 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, V o l . 1 0 1 , NO.GT1, pp.1-18.  78.  L e e , K e n n e t h L., and F o c h t , J o h n A., J r . ( 1 9 7 5 b ) : " C y c l i c T e s t i n g of S o i l f o r Ocean Wave L o a d i n g Problems." Seventh Annual Offshore Technology Conference, Houston, P r o c e e d i n g s , V o l . 1 , pp.343-354.  79.  L e e , K. W., and F i n n , W. D. L i a m . ( 1 9 7 8 ) : "STESL - A Computer Program for Static and Earthquake Analyses of Underwater Slopes." Soil Dynamics Group, U n i v e r s i t y of British Columbia.  201  80.  Low, E . ( 1 9 7 5 ) : " F o u n d a t i o n s f o r G r a v i t y Type Off-shore Drilling/Production Platforms." Off-shore Structures, L o n d o n : I n s t i t u t e of C i v i l E n g i n e e r s , Proceedings, pp.2735.  81.  L u n d g r e n , H., and M o r t e n s e n , K. ( 1 9 5 3 ) : " D e t e r m i n a t i o n by the Theory of Plasticity of the Bearing Capacity of Continuous Footings on Sand." Third International C o n f e r e n c e on S o i l M e c h a n i c s and Foundation Engineering, Z u r i c h , P r o c e e d i n g s , V o l . 1 , pp.409-412.  82.  MacCamy, R. C , and F u c h s , R. A. ( 1 9 5 4 ) : "Wave F o r c e s on Piles: A Diffraction Theory." U. S. Army Corps of Engineers, Beach Erosion 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): "Geotechnical Problems in Ocean Engineering." Ninth International Conference on Soil M e c h a n i c s and F o u n d a t i o n E n g i n e e r i n g , Tokyo, Proceedings, P a n e l D i s c u s s i o n , S p e c i a l t y S e s s i o n 7, pp.513-523. 84.  M c C o r m i c k , M. E . ( 1 9 7 3 ) : Ocean E n g i n e e r i n g Wave New Y o r k : J o h n W i l e y and Sons, I n c . , 179 p.  Mechanics,  85.  McPhee, W. S., and R e e v e s , S. J . (1975): "Drilling and Production Platforms for the O i l Industry." Off-shore Structures, London: Institute of Civil Engineers, P r o c e e d i n g s , 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 E x p e r i e n c e s of D i f f e r e n t Scour P r o t e c t i o n Technologies in the North Sea." E l e v e n t h Annual O f f s h o r e Technology Conference, H o u s t o n , P r o c e e d i n g s , V o l . 2 , pp.981-988.  87.  M a r i o n , H. A. ( 1 9 7 4 ) : " E k o f i s k S t o r a g e Tank." Symposium on Ocean E n g i n e e r i n g , T e d d i n g t o n : The R o y a l I n s t i t u t e of N a v a l A r c h i t e c t s , P r o c e e d i n g s , pp.83-90.  88.  M a r t i n , M. R., and Shaw, L. K. ( 1 9 7 4 ) : "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 , T e d d i n g t o n : The Royal Institute of Naval Architects, Proceedings, pp.73-82.  89.  M e y e r h o f , G. G. ( 1 9 5 3 ) : "The Bearing Capacity of Foundations Under Eccentric and Inclined Loads." Third I n t e r n a t i o n a l C o n f e r e n c e on S o i l M e c h a n i c s and Foundation E n g i n e e r i n g , Z u r i c h , P r o c e e d i n g s , V o l . 1 , pp.440-445.  90.  M e y e r h o f , G. G. (1963): "Some Recent Research on the Bearing Capacity of Foundations." Canadian Geotechnical J o u r n a l , V o l . 1 , No.1, pp.16-26.  202  91.  M e y e r h o f , G. G. (1974): "Ultimate Bearing Capacity of Footings on Sand Layer Overlying Clay." 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. M o i n a r d , M. ( 1 9 7 9 ) : "Deep Sea P r o d u c t i o n Use o f A r t i c u l a t e d Columns." Symposium on New T e c h n o l o g i e s f o r E x p l o r a t i o n and Exploitation o f O i l and Gas R e s o u r c e s , L o n d o n : Graham and Trotman L i m i t e d , P r o c e e d i n g s , V o l . 2 , pp.1010-1033. 93.  M o r g e n s t e r n , N. R., and P r i c e , V. E . ( 1 9 6 5 ) : "The Analysis 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, V o l . 1 5 , No.1, pp.79-93.  94. M o r i s o n , J . R. ( 1 9 5 0 ) : "The F o r c e E x e r t e d by S u r f a c e Waves on P i l e s . " P e t r o l e u m T r a n s a c t i o n s , TP 2846, pp.149-154. 95.  Morrison, A l l e n . Platform." C i v i l  (1980a): "Cognac: W o r l d ' s T a l l e s t 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. Offshore Future: Techniques, Deeper Water, But Where's the O i l ? . " E n g i n e e r i n g , V o l . 5 0 , No.6, pp.58-59.  97.  M u r f f , J . D., and M i l l e r , T. W. ( 1 9 7 7 ) : " S t a b i l i t y o f Offshore Gravity Structure Foundations by t h e Upper Bound Method." Ninth Annual Offshore Technology Conference, H o u s t o n , P r o c e e d i n g s , V o l . 3 , pp.147-154.  98. O f f s h o r e E u r o p e , 2nd E d . ( 1 9 7 4 ) : Surveys (Offshore) L t d . 99.  Bucks, England:  Oil New Civil  Scientific  O f f s h o r e S o i l Mechanic's. (1976): E d s . P h i l l i p G e o r g e and D a v i d Wood, Cambridge: Cambridge U n i v e r s i t y Engineering D e p a r t m e n t , pg.431.  100. P e n z i e n , J o s e p h . ( 1 9 7 6 ) : " S t r u c t u r a l D y n a m i c s o f F i x e d 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 C o n f e r e n c e on t h e B e h a v i o r of Offshore S t r u c t u r e s , O s l o , P r o c e e d i n g s , V o l . 1 , pp.581592. 101.  P r a n d t l , L. ( 1 9 2 1 ) : "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." Zietschrift F u r Angewandte M a t h e m a t i c und M e c h a n i c , V o l . 1 , pp.15-20.  102. P r e v 0 s t , J e a n . H., Cuny, B e r n a r d . , and S c o t t , R o n a l d F. (1981a): "Offshore Gravity Structures: Centrifugal Modelling." Journal of the Geotechnical Engineering D i v i s i o n , ASCE, P r o c e e d i n g s , V o l . 1 0 7 , No.GT2, pp.125-141. 103. P r e v 0 s t , J e a n . H., Cuny, B e r n a r d . , Hughes, Thomas. J . R., and S c o t t , R o n a l d F. ( 1 9 8 1 b ) : " 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 : Analysis." Journal of the Geotechnical Engineering D i v i s i o n , ASCE, P r o c e e d i n g s , V o l . 1 0 7 , No.GT2, pp.143-165.  203  104.  Rahman, M. S., Seed, H. B., and B o o k e r , J . R. ( 1 9 7 7 ) : "Pore Pressure Generation Under Offshore Gravity Structures." J o u r n a l of t h e Geotechnical Engineering Division, ASCE, P r o c e e d i n g s , V o l . 1 0 3 , 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 T e c h n o l o g y — R e c e n t D e v e l o p m e n t s . P a r k R i d g e , N. J . : Noyes Data Corporation, 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 L a y e r e d C l a y s . " J o u r n a l of t h e S o i l Mechanics and Foundation Division, ASCE, Proceedings, V o l . 9 3 , NO.SM2, pp.83-99.  107.  R 0 r e n , E. M. Q., and F a m e s , 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 D e s i g n . " I n t e r n a t i o n a l C o n f e r e n c e on t h e B e h a v i o r o f 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 Failure Modes of M o d e l 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 . " O f f s h o r e Europe Conference '75, A b e r d e e n , S c o t 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 Studies 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 C o n f e r e n c e on t h e B e h a v i o r of O f f s h o r e S t r u c t u r e s , O s l o , P r o c e e d i n g s , V o l . 1 , pp.439-448.  110.  de R u i t e r , J . (1976): " N o r t h 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 Geotechnical Consultant." Offshore Soil Mechanics, Eds. P h i l l i p G e o r g e and D a v i d Wood, C a m b r i d g e : Cambridge U n i v e r s i t y E n g i n e e r i n g D e p a r t m e n t , pp.61-78.  111.  S a n g r e y , D. A., H e n k e l , D. J . , and E s r i g , M. I . (1969): "The Effective Stress R e s p o n s e of S a t u r a t e d C l a y S o i l t o Repeated Loading." Canadian Geotechnical Journal, Vol.6, No.3, pp.241-252.  112.  Sarma, S. K. ( 1 9 7 3 ) : " S t a b i l i t y A n a l y s i s of Embankments S l o p e s . " G e o t e c h n i q u e , V o l . 2 3 , No.3, pp.423-433.  113.  S a r p k a y a , T., and I s a a c s o n , M. de S t . Q. ( 1 9 8 1 ) : of Wave F o r c e s on O f f s h o r e S t r u c t u r e s , New Y o r k : t r a n d R e i n h o l d , 651 p~.  114.  S c h j e t n e , Knut. (1976): "Foundation Structures in the- N o r t h Sea." I n s t i t u t e , No.113, pp.23-33.  115.  Seed, H. B o l t o n , M a r t i n , P h i l l i p e P., and Lysmer, John. (1976): "Pore Water Pressure Changes During Soil Liquefaction." Journal of the Geotechnical Engineering D i v i s i o n , ASCE, P r o c e e d i n g s , V o l . 1 0 2 , No.GT4, pp.323-346.  and  Mechanics Van Nos-  Engineering for Gravity Norwegian Geotechnical  204  116.  Seines, P. B. (1981): "Offshore Earthquake F i r s t P a r t . " ASCE F a l l C o n f e r e n c e , S t . L o u i s , pp.81 7-823.  Technology— Proceedings,  117.  S h o r e P r o t e c t i o n M a n u a l , 3 r d E d . ( 1 9 7 7 ) : 3 V o l . , U. S. Army Coastal Engineering Research Center, Washington: U n i t e d S t a t e s Government P r i n t i n g O f f i c e .  118.  S j o e r d s m a , G. W. ( 1 9 7 5 a ) : " G e n e r a l A p p r a i s a l of Off-shore Gravity Structures." Off-shore Structures, London: I n s t i t u t e o f C i v i l E n g i n e e r s , P r o c e e d i n g s , pp.61-66.  119.  S j o e r d s m a , G. W. ( 1 9 7 5 b ) : "Discussion shore Structures, London: Institute Proceedings, pg.l9B.  120.  Skempton, A. W. ( 1 9 5 4 ) : "The P o r e P r e s s u r e Coefficients and B." G e o t e c h n i q u e , V o l . 4 , No.4, .pp.143-147.  121.  Skempton, A. W., a n d B j e r r u m , L . ( 1 9 5 7 ) : "A C o n t r i b u t i o n t o the Settlement Analysis of Foundations on C l a y . " G e o t e c h n i q u e , V o l . 7 , pp.168-178.  122.  S t e n n i n g , D. G., and Schumann, C. G. (1979): "Arctic Production Monocone." E l e v e n t h Annual O f f s h o r e Technology C o n f e r e n c e , H o u s t o n , P r o c e e d i n g s , V o l . 4 , pp.2357-2366.  123.  S t e v e n , R o b e r t R. ( 1 9 8 1 a ) : "Some O f f s h o r e F e a t s Set World Standards, Others S e t World Records." O f f s h o r e , Vol.41, No.7, pp.70-71.  124.  S t e v e n , R o b e r t R. (1981b): Future Bright f o r Norway No.2, pp.98-104.  125.  S t e v e n , R o b e r t R. (1981c): "North Sea: S p e c i a l Report, U.K. O u t p u t Slackens Due t o Problems." O f f s h o r e , Vol.41, No.2, pp.89-96.  126.  S t o k e s , G. C. ( 1 8 8 0 ) : "On t h e T h e o r y o f O s c i l l a t o r y Waves." Mathematical and P h y s i c a l Papers, Vol.1, Cambridge: Cambridge U n i v e r s i t y P r e s s .  127.  S t u b b s , S. B. ( 1 9 7 5 ) : "Seabed F o u n d a t i o n C o n s i d e r a t i o n s f o r Gravity Structures." Off-shore Structures, London: I n s t i t u t e o f C i v i l E n g i n e e r s , P r o c e e d i n g s , pp.67-74.  128.  T a y l o r , K. L . (1976): "Practices Adopted i n N o r t h Sea Investigations." Offshore Soil Mechanics, Eds. Phillip George and D a v i d Wood, Cambridge: Cambridge University E n g i n e e r i n g D e p a r t m e n t , pp.1 17-130.  129.  Terzaghi, Karl. (1943): Theoretical Soil Y o r k : J o h n W i l e y a n d S o n s , I n c . , 510 p .  - S e s s i o n G." Offof C i v i l E n g i n e e r s , A  "North Sea: S p e c i a l Report, Production." Offshore, Vol.41,  Mechanics,  New  205  130.  T e r z a g h i , K a r l , and Peck, R a l p h B. (1948): Soil in Engineering P r a c t i c e , Second Edition 1966, J o h n W i l e y and Sons, I n c . , 729 p.  Mechanics New York:  131.  van E e k e l e n , H. A. M., and P o t t s , D. M. ( 1 9 7 8 ) : "The Behav i o r of Drammen C l a y Under C y c l i c Loading." Geotechnique, V o l . 2 8 , No.2, pp.173-196.  132.  Vaughan, P. R.; D a v a c h i , M. M.; E l Ghamrawy, M. K.; Hamza, M. M.; and H i g h t , D. W. (1976): "Stability 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 C o n f e r e n c e on t h e B e h a v i o r of O f f s h o r e S t r u c t u r e s , O s l o , P r o c e e d i n g s , Vol.1, pp.467-487.  133.  V e s i c , A l e k s a n d a r S. ( 1 9 7 5 ) : " B e a r i n g C a p a c i t y of S h a l l o w F o u n d a t i o n s . " F o u n d a t i o n E n g i n e e r i n g Handbook, E d s . Hans F. W i n t e r k o r n and Hsai-Yang Fang, New York: Van Nostrand R e i n h o l d Company, pp.121-147.  134.  Waagaard, K n u t . (1977): "Fatigue of Offshore Concrete S t r u c t u r e s — D e s i g n and E x p e r i m e n t a l I n v e s t i g a t i o n s . " Ninth Annual Offshore Technology Conference, Houston, P r o c e e d i n g s , V o l . 4 , pp.341-350.  135.  Ward, E . G., E v a n s , D. J . , and Pompa, J . A. (1977): "Extreme Wave H e i g h t s Along the Atlantic C o a s t of t h e United States." Ninth Annual Offshore Technology C o n f e r e n c e , H o u s t o n , P r o c e e d i n g s , V o l . 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." Offshore Soil Mechanics, Eds. Phillip 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 D e p a r t m e n t , pp.286-305.  137.  Watt, B. J ; Boaz, I . B.; R u h l , J . A.; S h i p l e y , Ghose, A. (1978): "Earthquake Survivability P l a t f o r m s . " Tenth Annual Offshore Technology H o u s t o n , P r o c e e d i n g s , V o l . 2 , pp.957-975.  138.  Watt, B. J . ( 1 9 7 9 ) : " B a s i c S t r u c t u r a l S y s t e m s — A Review of T h e i r D e s i g n and A n a l y s i s R e q u i r e m e n t s . " N u m e r i c a l Methods in Offshore Engineering, Ed. 0. C. Z i e n k i e w i c z , New York: J o h n W i l e y and S o n s , I n c . , pp.1-42.  139.  W e r e n s k i o l d , K. ( 1 9 7 7 ) : " M a r i t i m e Operations Construction of Offshore Structures." 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 , L o n d o n : C i v i l E n g i n e e r s , P r o c e e d i n g s , pp.97-105.  140.  Y a m a g u c h i , H., and T e r a s h i , M. (1971): " U l t i m a t e B e a r i n g C a p a c i t y of t h e M u l t i - L a y e r e d G r o u n d , F o u r t h A s i a n R e g i o n a l C o n f e r e n c e on S o i l M e c h a n i c s and Foundation Engineering, P r o c e e d i n g s , V o l . 1 , pp.97-105.  S. A.; and of C o n c r e t e Conference,  Relative Design Institute  to and of  206  141.  Young, A l a n G., K r a f t , L e l a n d M., J r . , and F o c h t , John A., Jr. (1975): "Geotechnical Considerations in Foundation Design of Offshore Gravity S t r u c t u r e s . " Seventh Annual Offshore 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.; N a y l o r , D. J . ; and L e w i s , R. W. ( 1 9 7 9 ) : "A U n i f i e d A p p r o a c h t o the S o i l Mechanics Problems of O f f s h o r e F o u n d a t i o n s . " Numerical M e t h o d s i n 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 Y o r k : J o h n W i l e y and S o n s , I n c . , pp.361-411.  

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