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Porewater pressure response of an artificial island to wave loading Yogendrakumar, Muthucumarasamy 1983

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POREWATER PRESSURE RESPONSE OF AN ARTIFICIAL ISLAND TO WAVE LOADING by MUTHUCUMARASAMY YOGENDRAKUMAR B.Sc(Eng.), U n i v e r s i t y Of Peradeniya, S r i Lanka,  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES CIVIL ENGINEERING DEPARTMENT  We accept t h i s t h e s i s as conforming to the r e q u i r e d  standard  THE UNIVERSITY OF BRITISH COLUMBIA December  ©  1983  MUTHUCUMARASAMY YOGENDRAKUMAR,  1 9 8 3  1 9 8 0  In  presenting  this  thesis  in  partial  fulfilment  of  the  requirements f o r an advanced degree at the U n i v e r s i t y  of  British  Columbia,  I  it  freely  available  for  permission  agree  for  purposes may or  her  that  the  Library  shall  reference  and  study.  I  extensive  be granted by  representatives.  p u b l i c a t i o n of t h i s t h e s i s allowed without my  Department of  written  Civil  January 20,  the Head of my It for  is  agree  Department or  understood  financial  permission.  Engineering  1984  further  that  copying of t h i s t h e s i s f o r s c h o l a r l y  The U n i v e r s i t y of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5  Date:  make  gain  that  by  his  copying or  shall  not  be  Dedicated Appah and  Ammah  ABSTRACT  Plans f o r the f u t u r e development of in  hydrocarbon  the Western Canadian A r c t i c are based  retained  and  Tanker  islands  as  reserves  on the use of Caisson  platforms  for exploration  d r i l l i n g and f u t u r e p r o d u c t i o n . At present, the design of these islands  are  based  on c u r r e n t g e o t e c h n i c a l e n g i n e e r i n g design  procedures. As e x p l o r a t i o n p r o g r e s s e s the  this,  procedures these  A  one  with  account  sophisticated  waters,  based  analytical  t o q u a n t i f y the probable  environmental  loadings.  method  of  The  method  considers  effects  during  wave  The  chief  i s presented f o r  of these i s l a n d s to  both  loading.  response  earthquake.  analysis  the porewater pressure response  loading.  generation  to  more  loads are due to i c e , wave and  computer  determining  requires  the a b i l i t y  islands  environmental  wave  deeper  need f o r secure designs i s indeed necessary. To be a b l e to  achieve  of  towards  dissipation  and  I t a l s o takes  into  o„f the e f f e c t of i n c r e a s i n g porewater p r e s s u r e on  properties.  The  computer  different a r t i f i c i a l  program  was  soil  used t o analyse three  i s l a n d s s u b j e c t e d to d i f f e r e n t p a t t e r n s of  storm waves, each of d u r a t i o n  6  hours.  a n a l y s e s a r e presented and d i s c u s s e d .  The  results  of the  iv  TABLE OF CONTENTS  Page No. DEDICATION  i i  ABSTRACT  i i i  TABLE OF CONTENTS  iv  LIST OF TABLES  viii  LIST OF FIGURES  x  ACKNOWLEDGEMENTS  x iii  CHAPTER 1  1  INTRODUCTION  1.1 Conventional A r t i f i c i a l 1.2 Caisson Retained  Islands  Islands  1 3  1.3 Scope  5  1.4 T h e s i s O u t l i n e  7  CHAPTER 2  GENERAL ASPECTS OF WAVE INDUCED RESIDUAL POREWATER PRESSURES  9  2.1 Introduct ion  9  2.2 Mechanism For Porewater Pressure Generation  9  2.3 D i s s i p a t i o n  E f f e c t s On Wave Induced R e s i d u a l  Porewater Pressure  10  2.4 Wave Induced I n s t a b i l i t y  11  2.5 Review Of A n a l y t i c a l Methods  15  2.5.1 Seed and Rahman Method  15  2.5.2 Siddharthan and Finn Method  17  CHAPTER 3  GENERAL THEORY  19  3.1 Assumptions and I d e a l i z a t i o n s  19  3.1.1 Storm Waves  19  3.1.2 S o i l P r o f i l e and Ocean F l o o r  22  3.2 D e r i v a t i o n  Of Governing Equation  3.3 E s t i m a t i o n  Of Rate Of Porewater  Pressure Generation  22  23  3.4 S o l u t i o n Technique  26  3.5 V a r i a t i o n In Volume C o m p r e s s i b i l i t y  29  3.6 S o i l Moduli V a r i a t i o n  29  3.6.1 M o d i f i c a t i o n Of Bulk Modulus  31  3.6.2 M o d i f i c a t i o n Of Shear Modulus  32  3.7 E s t a b l i s h i n g E q u i v a l e n t 3.8 L i n e a r  CHAPTER 4  Uniform Storm  34  Wave Theory  35  FINITE ELEMENT FORMULATION OF THE PROPOSED METHOD  38  4.1 I n t r o d u c t i o n  38  4.2 Formulation of F i n i t e Element Equations  40  4.2.1 I n t e r p o l a t i o n Function  41  4.2.2 Element Matrix Equation  42  4.2.3 G l o b a l Matrix Equation  47  CHAPTER 5  ISLAND GEOMETRIES AND SOIL PROPERTIES FOR WAVE ANALYSES  50  5.1 I s l a n d C o n f i g u r a t i o n  50  5.2 S p e c i f i e d Storm Waves  55  vi  5.3 S o i l P r o p e r t i e s  56  5.3.1  Basic  S o i l Properties  56  5.3.2  Derived S o i l P r o p e r t i e s  5.3.3  S e l e c t i o n Of I n i t i a l Volume  56  Compressibility 5.4 L i q u e f a c t i o n  CHAPTER 6  59  Strength Curve  66  WAVE INDUCED RESIDUAL POREWATER PRESSURE ANALYSIS  70  6.1 General  70  6.2 Response of Islands on Sand Foundation  70  6.3 Wave Induced Porewater Pressure Of I s l a n d 6.3.1  Response  1 to 6m 6 hour Storm  71  Wave Induced Porewater Pressure Of I s l a n d  Response  1 to 4m 6 hour Storm  85  6.3.2 Comparison Of Performance to the Two D i f f e r e n t Storms 6.4 Wave Induced Porewater Pressure  95 Response  Of I s l a n d 2 6.5 Wave Induced Porewater Pressure  99 Response  Of I s l a n d 3  112  6.6 Summary and Comparison Of R e s u l t s of Analyses on Sand Foundation  122  vi i  CHAPTER 7  EFFECT OF ROCKFILL COVER ON WAVE INDUCED POREWATER PRESSURES  128  7.1 I n t r o d u c t i o n  128  7.2 E f f e c t Of Cover on Porewater Pressure Response Of I s l a n d  1 to 6m 6 hour Storm  7.2.1 E f f e c t Of P e r m e a b i l i t y  of Cover M a t e r i a l  128 141  7.3 E f f e c t Of Cover on Porewater Pressure Response Of I s l a n d  1 to 4m 6 hour Storm  143  7.4 E f f e c t Of Cover on Porewater Pressure Response Of I s l a n d 2  148  7.5 E f f e c t Of Cover on Porewater Pressure Response Of I s l a n d 3  CHAPTER 8  EFFECT OF FOUNDATION CONDITIONS ON POREWATER PRESSURES  8.1 Response Of I s l a n d  CHAPTER 9  REFERENCES  158  1  SUMMARY AND CONCLUSIONS  167 167  172  176  vi i i  LIST OF TABLES  No.  Page No.  5.1 D e t a i l s Of Islands  51  5.2 S p e c i f i e d Storms Of the I s l a n d s  57  5.3 S o i l P r o p e r t i e s  58  Selected  For Wave Analyses  5.4 C o m p r e s s i b i l i t i e s of C o h e s i o n l e s s M a t e r i a l in Given S t r e s s Range For R e l a t i v e D e n s i t i e s  65  6.1 Maximum Porewater Pressure Response At Sections Of I s l a n d  1 At the End of the 6m 6 hour Storm  81  6.2 Maximum Porewater Pressure Response At Sections Of I s l a n d  1 At the End of the 4m 6 hour Storm  6.3 Comparison of Porewater Pressure  91  Response  to Two D i f f e r e n t Storms  96  6.4 Maximum Porewater Pressure Response At Sections Of I s l a n d  2 At the End of the 9m 6 hour Storm  109  6.5 Maximum Porewater Pressure Response At Sections Of I s l a n d  3 At the End of the 12m 6 hour Storm  120  6.6 Drainage C h a r a c t e r i s t i c s Requirement to L i m i t Porewater Pressure R a t i o  to Specified  Levels  For D i f f e r e n t Storms Of Duration 6 Hours. 6.7 P r e d i c t e d  Maximum Depth Of L i q u e f a c t i o n At  C r i t i c a l Locations  For D i f f e r e n t Storms Of  Duration 6 Hours and D i f f e r e n t For  124  I s l a n d s On Sand Foundation.  Permeabilities 125  ix  7.1 E f f e c t Of 1m Coarse Cover On Maximum Porewater Pressure Response  At S e c t i o n s Of I s l a n d  1 At  the End Of 6m 6 hour Storm  138  7.2 E f f e c t Of 1m Coarse Cover On Maximum Porewater Pressure Response  At S e c t i o n s Of I s l a n d  1 At  the End Of 4m 6 hour Storm 7.3  147  E f f e c t Of 1m Coarse Cover On Maximum Porewater Pressure Response  At S e c t i o n s Of I s l a n d 2 At  the End Of 9m 6 hour Storm 7.4  157  E f f e c t Of 1m Coarse Cover On Maximum Porewater Pressure Response  At S e c t i o n s Of I s l a n d  the End Of 12m 6 hour Storm  3 At 166  X  LIST OF FIGURES  No.  Page No.  1.1 Caisson Retained I s l a n d  4  3.1  25  Rate of Porewater Pressure Generation  3.2 Basic Equation and S o l u t i o n Domain  27  3.3  28  L i q u e f a c t i o n Strength Curve  3.4 V a r i a t i o n of Volume C o m p r e s s i b i l i t y With Porewater Pressure R a t i o  30  3.5 Wave Pressure and D e f i n i t i o n s of Terms - L i n e a r Wave Theory 5.1  37  S e c t i o n s of I s l a n d 1 For Wave Induced R e s i d u a l Porewater Pressure Analyses  52  5.2 S e c t i o n s of I s l a n d 2-For Wave Induced R e s i d u a l Porewater Pressure Analyses 5.3  S e c t i o n s of I s l a n d 3 For Wave Induced R e s i d u a l Porewater Pressure Analyses  5.4 Oedometer Test R e s u l t s For a Libyan Sand 5.5  .53  54 61  E f f e c t Of Density On C o m p r e s s i b i l i t y At Low  Excess Porewater Pressure  63  5.6 Volumetric S t r a i n Vs Root V e r t i c a l E f f e c t i v e Stress  67  5.7 L i q u e f a c t i o n Strength Curve Of Sand  69  6.1 Section-AA;J  R e s i d u a l Porewater Pressure  72  Response At the end Of  to  6m 6 hour Storm  78  to 6.7 Section-GG^/  j  xi  6.8 Section-AA; Shear S t r e s s R a t i o D i s t r i b u t i o n At the S t a r t of the 6m 6 hour Storm  80  6.9 Maximum Porewater Pressure Response Of I s l a n d 1 At the End of the 6m 6 hour Storm  83  6.10 Maximum Porewater Pressure Response Of I s l a n d 1 At the End of the 6m 6 hour Storm 6.11 Porewater Pressure Response 6 hour Storm For D i f f e r e n t  84  At the End of 6m Permeabilities  86  6.12 Section-AA;}  R e s i d u a l Porewater Pressure  87  6.13 Section-CC;V  Response At the end Of  88  6.14 Section-DD;J  4m 6 hour Storm  89  6.15 Maximum Porewater Pressure Response Of I s l a n d 1 At the End of the 4m 6 hour Storm  92  6.16 Maximum Porewater Pressure Response Of I s l a n d 1 At the End of the 4m 6 hour Storm 6.17 Porewater Pressure Response 6 hour Storm For D i f f e r e n t  93  At the End of 4m Permeabilities  94  6.18 Time H i s t o r y Of Porewater Pressure At 3m Below I s l a n d Surface At S e c t i o n CC 6.19 Section-PP;^ to  V  6.25 S e c t i o n - W ; J  98  R e s i d u a l Porewater Pressure  100  Response At the end Of  to  9m 6 hour Storm  106  6.26 Section-QQ; Flow Through  Interface  At the End of 9m 6 hour Storm  107  6.27 Maximum Porewater Pressure Response Of I s l a n d 2 At the End of the 9m 6 hour Storm  110  xi i  6.28  Section-HH;! to  6.34  R e s i d u a l Porewater Pressure  ^ Response At the end Of  Section-NN;J  12m  6 hour Storm  113 to 119  6.35 Maximum Porewater Pressure Response Of I s l a n d 3 At 7.1  the End of the 12m 6 hour Storm  Section-AA;1 to  V  E f f e c t Of Cover On Porewater  129  Pressure Response At the end Of  to  6m 6 hour Storm  135  7.7  Section-GG;'  7.8  E f f e c t of Cover on Time H i s t o r y Of Pore Pressure At  7.9  121  3m Below O r i g i n a l  I s l a n d Surface At S e c t i o n CC  140  Section-AA; E f f e c t of Cover P e r m e a b i l i t y on Porewater Pressure Response At the end of 6m 6 hour Storm  142  7.10  Section-AA; )  E f f e c t Of Cover On Porewater  144  7.11  Section-CC;V  Pressure Response At the end Of  to  7.12  Section-DD;J  4m 6 hour Storm  146  7.13  Section-PP;-)  E f f e c t Of Cover On Porewater  149  Pressure Response At the end Of  to  1  7  to  7.19 S e c t i o n - W ; J  9m 6 hour Storm  155  7.20  E f f e c t Of Cover On Porewater  159  Pressure Response At the end Of  to  12m  165  Section-HHn to  S  7.26  Section-NN;J  8.1  Section-AA; R e s i d u a l Porewater Pressure Pesponse At  8.2  the end Of 6m 6 hour Storm  168  Section-CC; R e s i d u a l Porewater Pressure Pesponse At  8.3  6 hour Storm  the end Of 6m 6 hour Storm  Section-AA; Shear S t r e s s R a t i o D i s t r i b u t i o n  169 171  ACKNOWLEDGEMENTS  I would e s p e c i a l l y major  l i k e t o thank P r o f e s s o r W.D.Liam F i n n , my  a d v i s o r , f o r h i s encouraging  throughout  suggestions and support shown  t h i s research.  I am indebted to Dr. M.de St.Q.Isaacson  f o r h i s comments and  d i s c u s s i o n which have enhanced the q u a l i t y of t h i s I am e s p e c i a l l y g r a t e f u l t o love,  patience  t h i s graduate  and  studies.  my  understanding  wife,  Uma,  study. without  whose  I would never have completed  1  CHAPTER 1 INTRODUCTION  1 . 1 Conventional  Artificial  Dramatic drilling ever  Islands  advances  f o r both  have  taken  place  e x p l o r a t i o n and p r o d u c t i o n  proposed  to s u i t  hostile  concrete  of hydrocarbons  and  remote.  gravity  These  include  Of  artificial  structures,submersible  al,1979),bottom-founded floating  methods have  been  o f f s h o r e environments g e n e r a l l y c o n s i d e r e d t o  s t r u c t u r e s such as the 'Monopad'  are  offshore  s i n c e the f i r s t commitment of the o i l i n d u s t r y t o o f f s h o r e  works. Numerous i n n o v a t i v e o f f s h o r e d r i l l i n g  be  in  and  the  islands,  concrete  gravity  'Cone'(Stenning  mobile r i g s and s e v e r a l other  et  types of  rigs. these  the  popular  d e l t a area Canadian  i n n o v a t i v e methods, a r t i f i c i a l  and  the  in  offshore d r i l l i n g  southern  Beaufort  sea  islands  i n the Mackenzie in  the  Western  Arctic.  Artificial platforms  mode  drilling  islands  a r e man-made  for exploration d r i l l i n g .  islands  and  serve as  The c o n v e n t i o n a l a r t i f i c i a l  i s l a n d s can be d i v i d e d i n t o d i f f e r e n t main groups depending the c o n s t r u c t i o n (1)  Islands,known  winter on  techniques. as  i c e islands,  by t r u c k i n g on-land  the sea bed a f t e r  into blocks. completion  Slope of  the  built  g r a v e l s and dumping  during them  removing the i c e by c u t t i n g i t protection island.  i s provided  after  Adequate f r e e board i s  on  2  a l s o provided during  so that these i s l a n d s  summer.  could  be  used  T h i s type of i s l a n d i s s u i t a b l e for  water depths l e s s than 2 to 3 metres. (2) Islands b u i l t wall  consisting  required by  within of  an  sandbags.  for construction  barges  from  underwater  an  The  of the  offshore  retaining  fill  material  i s l a n d i s hauled in borrow  p r o t e c t i o n above the water l e v e l  pit.  i s usually  Slope provided  by a d d i t i o n a l sandbags. (3)  Islands  constructed  material  excavated  offshore  and/or  by  as  hydraulic  suction  fills  with  from  art  dredges  onshore borrow p i t and  pumped as a  s l u r r y through a f l o a t i n g p i p e l i n e d i r e c t l y onto island.  Slope  sacrificial  protection  is  provided  beach surrounding the  The islands, sea,  technical  particularly  suitable  abundance  close  construction  to  power  f i l l i n g material  construction  of  of  filling the and  extent  conventional  material  island  be  location.  i s l a n d w i t h i n the  for c o n s t r u c t i o n during  following  must  pits  the  must  type  artificial  and  Beaufort factors.  available  in  Secondly,enough  equipment must be a v a i l a b l e on  from borrow  the  by the  a  water depths.  i n the o f f s h o r e environment of  i s i n f l u e n c e d to a great  Firstly,  haul  feasibility  by  i s l a n d . This  of i s l a n d i s s u i t a b l e for intermediate  the  to  site  complete  to the  l i m i t e d time a v a i l a b l e  summer season. T h i r d l y , a reasonable  construction  season  be  equipment can  be moved onto the  available  so  i s l a n d in time.  that  drilling  3  The in  cost  deeper  for i s l a n d construction  water  and  m a t e r i a l cannot be  1.2  Caisson The  construction,  of c a i s s o n by  increased  gained  through  material  involved  form the  around 6 to 9 metres and  of  the  case  berm would be c o n s t r u c t e d  caissons 1.1  Figure  would  shows  be  islands b u i l t  the  gravel.  island  b y - s t e e l doors to r e t a i n the  in  of  schematically  a  The  and  are  fill.  The  is fixed,generally deeper  to w i t h i n  f l o a t e d onto a new  concept  onto a p r e v i o u s l y  water,  the  the maximum set  down depth of the water s u r f a c e . Once e x p l o r a t i o n the  of e x i s t i n g  i n t e r i o r by sand and  geometry  experience  r i s e to the  caissons  island  transporting  performance  set down depth of a set of c a i s s o n s  underwater  filling  for  in  i s l a n d s . These are  concrete  b a c k f i l l i n g the  connected at the corners  the  i s l a n d s have given  reuseable  caissons  maximum  filling cost  retained a r t i f i c i a l  berm and  concrete  suitable  locally.  suitable  artificial  ballasting  built  where  m a t e r i a l to the s i t e , coupled with the  confidence  conventional  locations  Islands  of  the  suitable f i l l and  found  Retained  scarcity  at  increases s u b s t a n t i a l l y  is  complete,  l o c a t i o n as a r i n g .  typical  caisson  retained  island. The  caisson  retained  i s l a n d s , a l s o known as CRI  advantage that they r e q u i r e much l e s s q u a n t i t y than c o n v e n t i o n a l subject also  artificial  islands.  to s i g n i f i c a n t e r o s i o n during  offers  the  advantage  that  of f i l l  Further,these  have the material are  not  or a f t e r c o n s t r u c t i o n . It  it  can  be c o n s t r u c t e d  more  4  Figure  1 . 1 ; Caisson Retained I s l a n d ( A f t e r De Jong and Bruce, 19  5  s p e e d i l y . The in  the  above f a c t o r s provide  Beaufort  that  CRI  could  limited  be  and  converted  i s l a n d with a p p r o p r i a t e m o d i f i c a t i o n s and that  it  could  for i t s  use  sea i n the Western Canadian A r c t i c , where the  c o n s t r u c t i o n p e r i o d i s extremely possibility  the a t t r a c t i o n  provide  uncertain. into a  The  production  approvals  and  also  o i l storage w i t h i n c a i s s o n s are added  advantages of the c a i s s o n r e t a i n e d i s l a n d s .  1.3  Scope The  sea  artificial  are  for  d r i l l i n g islands built  the  purpose  t h e r e f o r e , they are, at t h i s Further,  all  of  of  gas  stage,  i s l a n d s that have been c o n s t r u c t e d the  shear  f l o e s of f i r s t proven to be  zone  year and m u l t i - y e a r  once  to wave and  gas  deeper waters, a r t i f i c i a l to  harsher  and  a  will  thousands conditions.  Beaufort and  character.  in shallow  waters  few  recent  more  water depths  the l a n d f a s t i c e from the  pack i c e . These i s l a n d s  are  ice attacks.  o i l e x p l o r a t i o n s progress  d r i l l i n g i s l a n d s w i l l become  towards exposed  o f f s h o r e environments. They w i l l have i n t e r a c t i o n s  with much more mobile i c e packs than encountered they  in  i n intermediate  which separates  resistant  However,  temporary  for  in  o i l explorations  them have been c o n s t r u c t e d  w i t h i n the l a n d f a s t i c e zone, except  on  and  to date  be  exposed  kilometres Therefore,  before.  Also  to open-water fetches of up to s e v e r a l depending  on  wind  direction  deep water i s l a n d s have to be  on the b a s i s of r e v i s e d design procedures,  generally  towards g r e a t e r s t r i n g e n c y , to ensure t h e i r long term  and  ice  designed trending success.  6  One aspect  of  the  more i n t e r e s t i n g and  that  has  to  artificial is  islands  be  given  consideration  i n both deep and  for  the  stability  in  intermediate  the wave induced porewater pressure  implications  perhaps, more important  of  during the  designing water depths  a storm  and  its  i s l a n d . I t has  been  r e a l i s e d that the magnitude of wave induced porewater at  any  location  in berm and  s e a f l o o r depends not  pressure  only on  the  i n t e n s i t y of the storm but a l s o on the contemporaneous r a t e s of generation  and  d i s s i p a t i o n of porewater pressure,  depends on the  l i q u e f a c t i o n , the-drainage  c h a r a c t e r i s t i c s of s o i l In  practice,  based on  the  Generally  most  suitability drawn  and  fill  mainly  material  from  with l e s s than 10%  s u i t a b l e for f i l l  imperatives  f o r berms i s  past  experience.  gravel  in the Beaufort  coupled  material  with  certainly  meet  dredged  an  the  porewater  sea  extremely  for  of the  are accepted  area,  the  to such  economic  limited construction  berm  construction for the  fill.  that  would  Therefore,  i s used, i t i s p o s s i b l e that during pressure  may  build  perhaps even to l i q u e f a c t i o n l e v e l s , causing the s t a b i l i t y  150  to have a good q u a l i t y c o n t r o l  the accepted standard  when l e s s permeable f i l l  silt  m a t e r i a l . However, s c a r c i t y of  p e r i o d make i t almost impossible  storm,  of  sand and/or g r a v e l with an average g r a i n s i z e of  c l e a n sand and  on the  compressibility  deposits.  criteria  microns or g r e a t e r be  and  which i n turn  a  up s u b s t a n t i a l l y , great concern  for  i s l a n d s . It i s a l s o p o s s i b l e that r e s i d u a l  porewater  pressures  after  a  storm  can  cause  reduction  in s t a b i l i t y  of the  i s l a n d . In order  substantial  to handle  these  7  conditions,  a  proper  understanding  pressures d u r i n g and a f t e r a storm  of wave induced  porewater  i s essential.  A part of the study c a r r i e d out i n t h i s t h e s i s i s d i r e c t e d towards f i n d i n g answers t o such above.  potential  B a s i c a l l y , v a r i o u s analyses were conducted  the l e v e l of porewater p r e s s u r e s of  a  problems  typical  artificial  storm. V a r i a t i o n strata  in  comprising  induced at  drilling  berm  mentioned  to e s t a b l i s h  selected  island  configuration,  sections  d u r i n g a moderate variation  in  the s e a f l o o r s o i l p r o f i l e and t h e i r  soil  drainage  and c o m p r e s s i b i l i t y c h a r a c t e r i s t i c s were a l s o c o n s i d e r e d i n the analyses  to  porewater  determine  pressure.  their  A l l wave  analyses were conducted which  was developed  is  modified  a  1979;1982). presented  using  of  important  i n Chapter  induced  the  on  the  porewater  computer  program  by Yogendrakumar, Siddharthan  version  Some  significance  STABW  (Siddharthan  induced pressure STABW3,  and F i n n . I t and  Finn,  elements of the program STABW3 are  3 and 4.  1.4 T h e s i s O u t l i n e Chapter of  wave  2 d i s c u s s e s e x t e n s i v e l y the important  induced  residual  porewater  i n c l u d e the mechanisms of  porewater  dissipation  loading.  review  during  wave  aspects  pressure a n a l y s i s which pressure  It  also  generation  and  contains a brief  of e x i s t i n g a n a l y t i c a l methods f o r the d e t e r m i n a t i o n  of  wave induced porewater p r e s s u r e s . Chapter  3  deals  with the general theory of wave induced  r e s i d u a l porewater pressure a n a l y s i s . The  assumptions  of the  8  theory  are  examined  and the procedures  m o d i f i c a t i o n s i n s o i l p r o p e r t i e s caused  f o r i n c o r p o r a t i n g the  by i n c r e a s i n g porewater  pressures are discussed.  the  The m o t i v a t i o n f o r the development of STABW3  program  formulation  i n v o l v e d are  presented The required  i n Chapter  the f i n i t e element equations 4.  s e l e c t i o n of s o i l parameters and other  Chapter  i n Chapter 6  discusses  porewater  the  pressure  c o n d i t i o n s are presented summary  data  analysis  5. results analysis  c h a r a c t e r i s t i c s . The e f f e c t of r o c k f i l l  The  relevant  f o r wave induced r e s i d u a l porewater pressure  are presented  residual  of  and  i n Chapter  of  wave  induced  for different  drainage  cover  and  foundation  7 and 8 r e s p e c t i v e l y .  and main c o n c l u s i o n s based  the analyses a r e presented  the  i n Chapter  9.  on the r e s u l t s of  9  CHAPTER 2 GENERAL ASPECTS OF WAVE INDUCED RESIDUAL POREWATER PRESSURES  2.1  Introduction The wave induced  result  of  However,  complex  with  respect it  a  porewater  pressure  response  i n t e r a c t i o n between waves and  certain  assumptions  to storm c h a r a c t e r i s t i c s and  and  seafloor  induced  acceptable  porewater  characteristics, to  evaluate  with an accuracy g e n e r a l l y and  i d e a l i z a t i o n s are o f t e n e x t e n s i v e and are d i s c u s s e d i n the  next  2.2  engineering  with  assumptions  Chapter  for  pressures  a  seafloor.  idealizations  i s p o s s i b l e to devise a simple a n a l y t i c a l t o o l  wave  is  purposes.  Such  along with the development of theory.  Mechanism For Porewater Pressure The  mechanism  Generation  that i s r e s p o n s i b l e f o r the g e n e r a t i o n  of r e s i d u a l porewater pressure under the well  understood.  The  waves,  action  of  waves  is  as they pass by, c r e a t e dynamic  wave pressure on the s e a f l o o r . There are numerous wave t h e o r i e s a v a i l a b l e to compute the amplitude of  which  primarily  has on  its wave  own  assumptions  characteristics  r e s e a r c h e r s determine theory  of the pressure and and  wave,  each  applicability  based  water  pressure wave amplitude  depth.  using l i n e a r wave  which assumes the s e a f l o o r to be r i g i d and  impermeable.  Some aspects of the l i n e a r wave theory are presented 3.8.  Most  in Section  T h i s moving harmonic pressure wave on the s e a f l o o r c r e a t e s  shear s t r e s s e s , c y c l i c  i n nature, the magnitude of which depend  10  on the m a t e r i a l p r o p e r t i e s of the u n d e r l y i n g s o i l soil  profile.  pressures i n  These the  cyclic  underlying  volumetric s t r a i n p o t e n t i a l  forming  the  shear s t r e s s e s generate porewater soil  due  to  the  creation  (Martin, Finn and Seed,  of  1975).  2.3 D i s s i p a t i o n E f f e c t s On Wave Induced R e s i d u a l Porewater Pressure Unlike  earthquakes,  storms  s e v e r a l hours. T h e r e f o r e , u n l i k e i n common be  assumption  adopted  analyses.  in  last  much longer, o f t e n  earthquake  analyses,  that an undrained c o n d i t i o n p r e v a i l s cannot  wave  induced  residual  porewater  pressure  The a n a l y s i s assuming undrained c o n d i t i o n s w i l l  to higher porewater p r e s s u r e response than w i l l a c t u a l l y and  as  a r e s u l t undue c o n s e r v a t i s m i n design w i l l  using t h i s approach. To a v o i d t h i s , into  the  account  both  dissipation  as  lead occur  result  i t i s necessary  from  to  take  w e l l as the generation of  porewater p r e s s u r e . The net porewater p r e s s u r e response w i l l be the r e s u l t a n t of the two opposing processes mentioned D i f f u s i o n w i t h i n and drainage out boundary,  constitute  substantial easily.  the  i n those s o i l s  Seed  and  dissipation i n which  Rahman  of  the  effects.  drainage  (1977)  free  have  changes  residual in  draining  These may be  can  take  place  illustrated  s i g n i f i c a n c e of i n c o r p o r a t i n g d i s s i p a t i o n e f f e c t s on induced  above.  the  the wave  porewater p r e s s u r e response. In g e n e r a l , the  porewater  pressure  response  produced  i n c o r p o r a t i n g d i s s i p a t i o n e f f e c t s , w i l l depend p r i m a r i l y on (1) the geometric d e t a i l of the s o i l  profile,  by  11  (2)  the  compressibility  soil  l a y e r s forming the s o i l  2.4 Wave Induced  in  profile.  drilling  character  with  most. The designs of these simple  p e r m e a b i l i t y c h a r a c t e r i s t i c s of  Instability  The a r t i f i c i a l temporary  and  geotechnical  islands design  based  only  design  designs  becomes more  necessary.  the  with  be  and  are  on  fairly As  the need f o r more  production  islands  able to achieve t h i s , one r e q u i r e s  geotechnical  to  engineering  analytical  t o q u a n t i f y the probable  environmental  loadings.  response  The  chief  loads are due to i c e , waves and earthquakes. The  relative  importance  depends  on  the  of the  risk  from  each  of  l o c a t i o n of the i s l a n d . A b r i e f  instability arising current  temporary  the a b i l i t y  islands  environmental  in  To  sophisticated  procedures of  f o r both  date  assessments.  e x p l o r a t i o n progresses towards deeper waters, secure  to  l i v e s of a few years at  i s l a n d s are  engineering  built  this  sources  review of the  from wave l o a d i n g and the methods a v a i l a b l e  engineering  practice  to  handle  wave  related  i n s t a b i l i t y a r e presented h e r e i n . The fall  kinds of i n s t a b i l i t y  that a r i s e from wave l o a d i n g  i n t o two main c a t e g o r i e s . The f i r s t  instantaneous  s t r e s s f i e l d generated  i n t e n s i t y of the  passing  wave  is  one  i s due  to the  by a passing wave. I f the strong  enough,  then  the  e f f e c t i v e s t r e s s e s a s s o c i a t e d with the wave l o a d i n g v i o l a t e the Mohr-Coulomb  failure  y i e l d i n g w i l l occur  criterion  and  consequently  i n the s e a f l o o r or i s l a n d s l o p e .  f a i l i n g or  12  The  other kind of wave induced  cumulative  e f f e c t s of waves  pressures.  The  consequences  pressure are of two related.  If  which  the  types.  create  of  the  The  induced  i n s t a b i l i t y a r i s e s from the  wave  first  porewater  residual induced  type  is  loose  a l l shear  pressures a t t a i n a value  ground  surface  and  stratification,  nature of supported  temporary l o s s of s t r e n g t h may r e s u l t problems.  The  artificial  i s l a n d s are concerned,  subsidence,  most  slides  consequence a r i s i n g somewhat wave  liquefaction, shear  common  resistance  susceptible  but s t i l l  to  of  the  large  slope  of  structures, this  serious  engineering  sand  boils,  excessive  f a i l u r e . The second type of porewater  pressures  is  of major concern. Even i f the  pressures  reduce  in  are  from wave induced  porewater they  soil  form of these problems, as f a r as  and. foundation  l e s s dramatic  induced  then  s t r e n g t h t e m p o r a r i l y . Depending on the  c o n d i t i o n s such as d e n s i t y of s o i l , the  porewater  liquefaction  equal to the i n i t i a l e f f e c t i v e overburden p r e s s u r e , will  porewater  the  do  not  reach  level  of  i n s i t u e f f e c t i v e s t r e s s e s and  soil  so  that  s c a l e deformation  it  becomes  more  under a p a s s i n g l a r g e  wave or g r a v i t y s t r e s s e s . Another pressure  is  possible the  consequence  potential  for  of  residual  porewater  s e t t l e m e n t . The wave  induced  r e s i d u a l porewater pressure w i l l e v e n t u a l l y d i s s i p a t e , at r a t e s d i c t a t e d by the drainage dissipation  characteristics  w i l l be accompanied by a decrease  v o i d s which may be r e f l e c t e d the  of  in  corresponding  the  soil.  This  i n volume of the settlements  at  s u r f a c e . The amount of settlement w i l l depend on the l e v e l  13  of induced porewater p r e s s u r e , the extent of a f f e c t e d zone  and  nature of overburden m a t e r i a l . At  present,  the  analysis  of instantaneous wave induced  porewater pressure  i s best i n v e s t i g a t e d  computer  STAB-MAX  program  coupled e f f e c t i v e coupling  of  stress  (Siddharthan analysis  (1978)  and  Madsen  of  finite  assumed  hydraulic  general  et a l , l 9 7 9 ) . I t i s a  taking  into  account  the  and  deposits  anisotropy.  g e n e r a l i s a t i o n of  of seabed to wave  loading  by  Madsen(l978) provided the base f o r STAB-  MAX. Yamamoto, i n h i s study, deposits  the  the sand s k e l e t o n and pore water i n r e s i s t i n g the  waves. The study of the response Yamamoto  througth  assumed  infinite of  hydraulic depth.  infinite  isotropy  and  On the other hand,  depth  but  included  The computer program STAB-MAX i s thus a  the  Yamamoto-Madsen  solutions  to  layered  s o i l s with h y d r a u l i c a n i s o t r o p y and d e p o s i t s of f i n i t e depth. A limited  field  verification  of the c a p a b i l i t y of STAB-MAX has  been reported by Finn et a l (1982). The computer programs a v a i l a b l e at present residual  porewater  pressure  and  estimating  p o t e n t i a l under wave l o a d i n g are OCEAN1 STABW  (Siddharthan  et  al,l979).  computer program STABW3 i s developed.  In  this  incorporated  in  thesis,  another  particular  program  review  i n c o r p o r a t e d i n these programs i s presented analyses  liquefaction  (Seed et a l , 1977) and  This  i s an extended v e r s i o n of STABW. A b r i e f  The  for predicting  the  of the analyses  i n S e c t i o n 2.5. STAB-MAX, STABW, and  STABW3 are a l l based on the assumption of l e v e l s e a f l o o r . T h e i r a p p l i c a t i o n to g e n t l e slopes may be  acceptable  for practical  14  purposes.  But  as  the  slope  get  steeper  the p r e d i c t i o n of  porewater pressure based on these programs becomes conservative.  The main sources that  are  responsible  conservative  predictions  (i)  drainage from a s l o p i n g s e a f l o o r  greater  increasingly f o r the  of porewater p r e s s u r e s a r e : than from a l e v e l  one ( i i ) the  presence  seafloor  which  of  tend  static  shear  stresses  in  a  sloping  t o r e t a r d the rate of porewater p r e s s u r e  generation. The s t a b i l i t y of a s l o p i n g limiting equilibrium first  to  s e a f l o o r may  be  methods of a n a l y s i s . Henkel  p r o v i d e an a n a l y t i c a l  under a wave l o a d i n g .  H i s method  stress  method.  considers  equilibrium  s t a t e of a  conditions,  taking  gravity  method  circular  slip  surface  f o r t h i s method i s that  nature  associated seafloor  of  considers  the for  i t does not i n c l u d e  the wave loading  with i t which are so  total  limiting undrained  the  true  and the porewater pressure  vital  f o r the  stability  of  slopes.  applicable  to steeper slopes  method i s a m o d i f i c a t i o n include  is a  of the s o i l . The main  Finn and Lee (1979) proposed an e f f e c t i v e analysis  (1970) was the  i n t o account wave p r e s s u r e s on the s e a f l o o r ,  loads and the undrained strength  objection cyclic  The  by  framework f o r the s t a b i l i t y of  sloping seafloor static  evaluated  the  stress s t a b i l i t y  under wave l o a d i n g . The  of Sarma's (1973) method of s l i c e s  to  wave p r e s s u r e s generated by the waves. The method  an a c t i n g  of g r a v i t y loads,  f o r c e system on the s l i d i n g mass c o n s i s t i n g  wave pressure on s e a f l o o r , and  instantaneous  15  and of the  r e s i d u a l porewater  p r e s s u r e s a c t i n g on the f a i l u r e  surface  the s l i d i n g mass. The main a t t r a c t i o n of t h i s method l i e s on f a c t that i t r e c o g n i s e s the true c y c l i c nature of the  l o a d i n g and take i n t o account of porewater  wave  pressures associated  with the wave l o a d i n g .  2.5 Review Of A n a l y t i c a l Methods 2.5.1 Seed And Rahman Method Seed  and  Rahman  (1977) were the f i r s t  a n a l y t i c a l procedure f o r e v a l u a t i o n of porewater  wave  to propose an  induced  residual  p r e s s u r e that takes i n t o account both g e n e r a t i o n and  d i s s i p a t i o n e f f e c t s . The procedure i s q u i t e  similar  developed  potential  for  earthquake  evaluating  loading  liquefaction  the  first  phase,  the  shear  stresses  different  shear  of  stresses.  the wave induced shear s t r e s s e s  computer  program  using  wave  the  components  STR1. theory  are  computed  The program e v a l u a t e s the of  elasticity,  constituting  storm. The shear s t r e s s e s computed  at  for  the  the s p e c i f i e d design  the  top  of  the  soil  f o r each wave component are then used to e s t a b l i s h the  e q u i v a l e n t uniform storm using procedures proposed by al  under  method of a n a l y s i s c o n t a i n s two separate phases. In  using  deposit  that  (Seed, et a l 1971) except f o r the manner  determining the induced c y c l i c Their  to  (1975).  represented consisting  This by of  Seed  et  enables the complex wave storm l o a d i n g to be an  an  equivalent equivalent  s p e c i f i e d shear s t r e s s  ratio.  uniform number  wave of  storm  loading  uniform c y c l e s of a  16  In  the second phase, the wave induced  pressures  are  computed  program OCEAN 1.  The  through  cyclic  the  shear  residual  porewater  f i n i t e element  stresses  computer  induced  by  the  e s t a b l i s h e d e q u i v a l e n t wave l o a d i n g are used i n t h i s program to estimate  the r e s i d u a l porewater  p r e s s u r e s . Some aspects of the  theory i n v o l v e d , p a r t i c u l a r l y the ones which are common to both the Seed-Rahman method of a n a l y s i s and the method to  be developed The  problem, chosen  element  of c y c l i c  shear s t r e s s e s i s accomplished  a n a l y s i s of an  requiring  two  idealized  elastic  constants,  the porewater  moduli.  degradation  This,  in  i n the turn,  degradation  affects  of  shear and bulk moduli  shear s t r e s s e s and thereby to o b t a i n the r a t e of porewater Although  the  Seed-Rahman  the  shear  computed  important  to  i n computation reasonable  method  and shear  include  of c y c l i c  estimates  of  of a n a l y s i s takes i n t o  of the shear and bulk moduli  d e p o s i t , the maximum c y c l i c  by wave l o a d i n g i s independent  to the  p r e s s u r e , i t never c o n s i d e r s the i n the computation of  shear s t r e s s e s . I t i s a known f a c t that uniform  of  effective  i n volume c o m p r e s s i b i l i t y due  e f f e c t of i n c r e a s i n g porewater degradation  and  pressure g e n e r a t i o n .  account of the v a r i a t i o n  deep  f o r convenience,  e f f e c t i v e s t r e s s e s and  stresses. Therefore, in general, i t i s  cyclic  dimensional  pressure i n c r e a s e s , the mean normal  s t r e s s decreases, r e s u l t i n g bulk  two  to be the shear modulus and bulk modulus. The shear  bulk moduli are f u n c t i o n s of mean normal as  analysis  i n t h i s t h e s i s are presented i n Chapter 3.  computation  by a f i n i t e  of  of  the  i n the  shear s t r e s s  elastic  case  of  induced  constants.  In  17  these  cases,  the  degradation of moduli  shear s t r e s s e s are not finite  and  necessary.  non-uniform  i n the computation  However,  in  the  of  case  of  d e p o s i t s , c o n s i d e r e d to be the general  case, the shear s t r e s s e s depend on the e l a s t i c c o n s t a n t s and i t i s e s s e n t i a l to modify  the s o i l p r o p e r t i e s f o r  increasing  pressure.  porewater  general case of non-uniform considers  the  variation  of  of  it  was  first  proposed  i s outlined b r i e f l y  2.5.2  Siddharthan  soil  is  (1979, 1982)  Rahman  needed.  by Siddharthan  in the next  of  the most  for Such  along  with  the  effect  of  a  method  of  and Finn (1979) and  section.  and Finn Method  The method of a n a l y s i s Finn  to handle  properties  compressibility  i n c r e a s i n g porewater pressure analysis  order  effect  d e p o s i t s a method of a n a l y s i s which  degradation volume  In  the  proposed  by  Siddharthan  and  i s b a s i c a l l y a g e n e r a l i z a t i o n of the Seed and  method. In t h i s method of a n a l y s i s , the s t r e s s  analysis  phase i s combined with the r e s i d u a l porewater pressure  analysis  phase i n t o a s i n g l e f i n i t e element computer program t h i s way, to  be  i t i s p o s s i b l e to modify  In  e l a s t i c constants repeatedly  comparable with the c u r r e n t value of porewater pressure  and to r e - e v a l u a t e c y c l i c of  STABW.  shear  s t r e s s e s and thereby  porewater pressure g e n e r a t i o n . The  carrying  out  analysis  with  or  the  rate  program has the o p t i o n of without  soil  property  m o d i f i c a t i o n s f o r the e f f e c t of i n c r e a s i n g porewater p r e s s u r e . Apart this  from t h i s improvement, the other main d i f f e r e n c e  approach  from  in  the Seed-Rahman approach i s the manner by  18  which the e q u i v a l e n t uniform storm i s e s t a b l i s h e d . the  procedure  adopted  weighting curve to procedure  Instead  of  by Seed and Rahman which uses a simple  determine  equivalence,  the  more  proposed by Lee and Chan (1972) i s used. The  of the procedure are presented i n S e c t i o n  3.7.  general details  19  CHAPTER 3 GENERAL THEORY  3.1 Assumptions and I d e a l i z a t i o n s Most methods of under  consideration  analysis  be  require  idealized  in  that  some  way  convenient model may be formulated. The wave porewater  pressure  no exception  the  problem  so  that  induced  residual  a n a l y s i s to be developed i n t h i s t h e s i s i s  to t h i s . The assumptions and i d e a l i z a t i o n s implied  in d e f i n i n g storm c h a r a c t e r i s t i c s , ocean and s o i l p r o f i l e s described  in  this  s e c t i o n . The assumptions i n v o l v e d  elements of the a n a l y s i s , f o r example, i n governing  a  equations  shear s t r e s s e s ,  and  are  in  the  presented  the  are  i n other  development  of  computation of wave induced  in  sections  where  they  are  developed.  3.1.1 Storm Waves The  offshore  wave  environment  dependent on wind speed, water depth, and  various  other  factors.  i s a random process  mudline  However,  in  characteristics practice,  customary to d e f i n e the sea s t a t e at any time by two variables,  namely,  wave  heights  and p e r i o d s  i t is  important  e x i s t i n g at that  time. The common parameters that c h a r a c t e r i z e s the sea s t a t e i n the the  statistical  sense are the s i g n i f i c a n t wave  height  H  s  and  s i g n i f i c a n t wave p e r i o d T§. The s i g n i f i c a n t wave height i s  a n a l y t i c a l l y d e f i n e d as the average height  of the highest  of the waves and the s i g n i f i c a n t wave p e r i o d  third  i s the mean p e r i o d  20  of the waves chosen f o r the determination  of  wave  and s i g n i f i c a n t wave  height.  The s i g n i f i c a n t wave height  p e r i o d can be estimated  by wave  application  of  the  hindcasting wind  significant  techniques  involve  the  directly  i n terms of wind speed U, f e t c h F and d u r a t i o n  which  data. These a r e determined t  over  which the wind a c t s . More  direct  determined obtained  information  from from  a  on  continuous  a  wave  wave c h a r a c t e r i s t i c s can be  record  recorder.  of  The  surface  important  elevation parameters  r e q u i r e d to d e f i n e the o v e r a l l wave c h a r a c t e r i s t i c s a r e : ( i ) the z e r o - c r o s s i n g p e r i o d , T ,  d e f i n e d as the average  z  between s u c e s s i v e  zero  period  up-crossing,  ( i i ) the c r e s t p e r i o d , T  c  , d e f i n e d as the average p e r i o d between  sucessive crests-, (iii)  the  vertical  distance  from  the  lowest trough to the  highest c r e s t . In t h i s t h e s i s , the storm waves are d e s c r i b e d s i g n i f i c a n t wave height The loading  the  s p e c t r a l method of method  of  discrete  used f o r a n a l y s i s i n v o l v i n g wave  wave  analysis.  In  method this  that the process  Rayleigh  a n a l y s i s and the  thesis,  the  as a random e x c i t a t i o n  can be s p l i t  discrete  i n a wave storm  density  but  assumes  i n t o d i s c r e t e waves each of which  a s p e c i f i e d p e r i o d a s s o c i a t e d with  wave h e i g h t s  of  a n a l y s i s i s used. T h i s approach makes no attempt to  model wave l o a d i n g process  has  of  and s i g n i f i c a n t wave p e r i o d .  two approaches widely are  i n terms  i t . The d i s t r i b u t i o n of  i s assumed  to  be  f u n c t i o n and i t i s o f t e n s p e c i f i e d  given  by  a  i n terms of  21  s i g n i f i c a n t wave height p(H)  i n the form,  = 1 - exp{-2(H/H ) }  (3-1)  2  s  where, H = wave height Hg= p(H)  s i g n i f i c a n t wave height  = probability For  a  density  given  function  s i g n i f i c a n t wave h e i g h t , the p r o b a b i l i t y of  occurence of a wave of height H, o c c u r r i n g between H,  and  H , 2  where H,< H < H , i s given by, 2  P{H) = p(H,) - p ( H )  (3-2)  2  The  probability  of occurence P(H) given by equation (3-2)  i s assumed to be a s s o c i a t e d with a wave of height The  maximum wave height  using f o l l o w i n g equation  2  i n the wave height  i s assumed to be the breaking height a s s o c i a t e d water depth d and f o r shallow  (H, + H ) / 2 .  water cases,  suggested  distribution  with  a  still  i t can be c a l c u l a t e d  by McCowan  (Sarpakaya et a l ,  1981), H  For  m  = 0.78 d  (3-3)  a n a l y s i s , waves of height g r e a t e r than H  to be waves of height of H^,. In other words, the of  waves  of  height  greater  m  are assumed  total  than H,^ i n the d i s t r i b u t i o n are  added to the number a s s o c i a t e d with the wave of height The  Rayleigh  represented  by  characteristics. characteristics  distribution many It  in  is  waves, assumed  accordance  number  enables each that  of  the them these  H .  storm  w  to  be  differing  in  waves  have  with l i n e a r wave theory, which  d e s c r i b e s the wave by i t s p e r i o d , wave height and water  depth.  22  Some aspects of the l i n e a r wave theory are presented 3.8.  The  assumed  to  t r a v e l predominantly  d i r e c t i o n , that i s , the e f f e c t  of  directional  assumed  waves  are  in Section i n one  randomness  is  to be n e g l i g i b l e . A l s o , the s h o a l i n g e f f e c t s , the wave  s c o u r i n g e f f e c t s and the d i f f r a c t i o n e f f e c t s responses  are not taken  into  in  modifying  the  account.  3.1.2 S o i l P r o f i l e and Ocean F l o o r The horizontally lateral  entire  soil  layered  profile  soils,  each  i s assumed to comprise of of  them  are  of  infinite  e x t e n t . The p r o p e r t i e s of s o i l d e p o s i t s are assumed to  vary only i n the v e r t i c a l d i r e c t i o n and each d e p o s i t i s d i v i d e d i n t o l a y e r s each with uniform p r o p e r t i e s . The assumed to be p a r a l l e l to s t i l l  3.2 D e r i v a t i o n Of Governing  should  the  is  Equation  porewater pressure response incorporate  floor  water l e v e l .  As d i s c u s s e d p r e v i o u s l y the governing induced  ocean  effect  of  equation of wave  i n an o f f s h o r e environment both  dissipation  and  g e n e r a t i o n . In developing the governing equation, i t i s assumed that  Darcy's  flow  is valid.  Hence from the one dimensional  c o n t i n u i t y equation i n z d i r e c t i o n , 5/6z  { k / ? f • 5u/5z } z  w  =  5e/6t  (3-4)  where, u = excess porewater pressure  kz=  c o e f f i c i e n t of p e r m e a b i l i t y i n z ( v e r t i c a l )  T =  u n i t weight of water  w  direction  23  e = volumetric s t r a i n ,  r e d u c t i o n c o n s i d e r e d t o be p o s i t i v e .  Consider an element of s o i l with excess porewater u. Suppose i t undergoes a change  of  Au  i n excess  pressure porewater  pressure  during  an i n t e r v a l of time  interval,  i t will  be s u b j e c t e d to a c e r t a i n number of c y c l e s of  cyclic  shear  porewater  s t r e s s , which i n t u r n , w i l l  cause an  3  g  i s n e g l e c t e d then  change be of the element i n that i n t e r v a l of time =  i s the  generation.  the change i n bulk s t r e s s  Ae  time  increase i n  p r e s s u r e given by ( 6 u / 6 t ) . A t , where ( 6 u / 6 t )  r a t e of porewater pressure If  At, then d u r i n g that  m ( AU - 6ug/6t v  the volume  i s given by,  .At)  (3-5)  where, my = c o e f f i c i e n t  of volume c o m p r e s s i b i l i t y .  Now as A t — * 0 , =  be/bt  From equations b/bz  m  v  ( 5u/6t - 6u /5t  )  g  (3-6)  (3-4) and (3-6), {  ^Aui  • bu/bz  }  m  y  ( 5u/5t - 5u /6t ) g  (3-7) Equation  (3-7)  response  t o storm waves. I t has been used p r e v i o u s l y by Finn et  al  (1976)  i s the governing  equation  f o r porewater pressure  f o r the a n a l y s i s of s e i s m i c a l l y  induced  porewater  pressures.  3.3  E s t i m a t i o n Of Rate Of Porewater Pressure The  equation  Generation  r a t e of porewater pressure generation r e q u i r e d i n  (3-7) can be determined  Seed and Rahman (1977). The  basic  by the procedure steps  involved  proposed by a r e given  24  herein. The  r a t e of porewater pressure i n c r e a s e can be w r i t t e n i n  the form, 5u /6t  =  9  5u /6N  . 5N/6t  g  (3-8)  where N i s the number of s t r e s s c y c l e s d u r i n g the storm. The tests.  L  required for i n i t i a l u /o ' s  where, a^  Q  8  v  =  0  purposes,  the  undrained  relationship  i n terms of number of  liquefaction  cycles  i n the f o l l o w i n g form,  2/TT a r c S i n ( N/N  = initial  from  vertical effective  u  )'  / 2 0  (3-9)  stress  = an e m p i r i c a l constant  The for  for practical  and N can be expressed  g  obtained  g  However,  between u N  values of 5u /6N can be  r e l a t i o n s h i p i n equation  (3-9) i s given i n F i g u r e 3.1  d i f f e r e n t v a l u e s of 6. The value of 8 = 0.7 i s t y p i c a l  c l e a n medium  for  sands.  Differentiation simplification  of  equation  (3-9) with respect to N and  yields,  6u /6N  a ' /(  =  3  07rN,_ )  y 0  .  l/f(r )  (3-10)  u  where, f(r )  = S i n ^ " ' ) (0.57rr ) . Cos(0.5jrr ) 9  u  u  r  u  u  = porewater pressure r a t i o , u/o^  Also, 5N/6t where  Nq e  =  N  e q  /T  = e q u i v a l e n t number  corresponding  (3-11)  p  of  uniform  stress  cycles  to the e s t a b l i s h e d e q u i v a l e n t uniform  storm with d u r a t i o n Tp. T h e r e f o r e , from equations  (3-8), (3-10) and (3-11)  Figure 3 . 1 ;  Rate of Porewater Pressure Generation  26  6u /6t  =  g  The  o^/(07rTp) . (N q/N ) . 1/f ( r ) e  u  (3-12)  u  r a t e of porewater pressure generation 5ug/5t, at any  can  be  calculated  from  equation  time,  (3-12) knowing the value of  porewater p r e s s u r e at that time.  3.4  Solution  Technique  With the r a t e of given  by equation  (3-7)  porewater  (3-12), i t i s now  f o r the domain and boundary  formulation in d e t a i l  of  the proposed  in Section  pressure  p o s s i b l e to solve equation  shown  finite  generation  in  Figure  3.2.  The  element method i s o u t l i n e d  4.2.  To compute the r a t e of porewater pressure generation equation  (3-12)  at  any  location,  number of c y c l e s to cause i n i t i a l  from  one needs to know N ,  the  L  wave induced l i q u e f a c t i o n . Nj_  can be c o n v e n i e n t l y computed from a l i q u e f a c t i o n s t r e n g t h curve such as the one  shown i n F i g u r e 3.3.  The  shear  stress  ratio  induced by the e q u i v a l e n t storm at the l o c a t i o n of i n t e r e s t be  used to e s t a b l i s h the a p p r o p r i a t e N  liquefaction cyclic  simple  performed In  shear  t e s t or the c y c l i c  the case of t e s t s performed  the  two  v a l u e s . To e s t a b l i s h a  L  loading tests, usually  on r e p r e s e n t a t i v e undisturbed  a correction for  s t r e n g t h curve, c y c l i c  triaxial  t e s t , can  the be  samples.  i n the t r i a x i a l  apparatus,  f a c t o r has to be a p p l i e d to the r e s u l t s to account dimensional plane s t r a i n c o n d i t i o n of ocean wave  loading. A correction  f a c t o r between 0.60  to 0.70  i s considered  reasonable. However, i n the case of t e s t s conducted shear  can  apparatus,  the c o r r e c t i o n f a c t o r  in  simple  i s not necessary, as i t  3.2;  Basic Equation and S o l u t i o n Domai  Figure  3 . 3 ; L i q u e f a c t i o n Strength  Curve  ( A f t e r Seed and Rahman, 1977)  oo  29  p r o v i d e s the c l o s e s t r e p r e s e n t a t i o n  of f i e l d c o n d i t i o n s  (Seed,  1979).  3.5 V a r i a t i o n In Volume The increase be  volume  Compressibility  compressibility  i n porewater p r e s s u r e .  computed  using  the  of  soil  increases  with  The volume c o m p r e s s i b i l i t y  can  f o l l o w i n g equation proposed by  Martin  (1 976) . m /m v  =  vo  (3-13)  e * /( 1 + y + 0.5y ) 2  where, B  y = A.r  a  A = 5(1.5 - D ) r  -2T>t-  B = 3 x 2 D(- = r e l a t i v e r=  porewater pressure  m=  volume c o m p r e s s i b i l i t y  u  v  u/a;  density ratio at  porewater  pressure  ratio,  0  m = vo  pressure  initial  compressibility  at  zero  porewater  ratio  Results Figure  volume  from equation  (3-13)  for D  in  Section  r  = 50% i s given  in  3.3.  3 . 6 S o i l Moduli V a r i a t i o n As  discussed  earlier  2.5.1, the e l a s t i c  constants used i n the c y c l i c shear s t r e s s a n a l y s i s have modified  f o r the e f f e c t  of porewater p r e s s s u r e .  to  be  In the present  30  31  wave induecd r e s i d u a l porewater moduli  3.6.1  pressure  analysis,  the  soil  are m o d i f i e d i n the manner d e s c r i b e d below.  M o d i f i c a t i o n Of Bulk Modulus A  comprehensive  study by Duncan et a l (1978) r e v e a l s  that bulk modulus depends on minor p r i n c i p a l and  the  variation  can  be approximated  effective  stress  by an equation of the  form, Bm  =  K P b  q  ( a' /P 3  0  )"*  (3-14)  where B = bulk modulus m  Kfc,= bulk modulus constant m = bulk modulus exponent P = atmospheric Q  a'  3  p r e s s u r e , expressed  i n the same u n i t s  as  and B^ . a'  = average  3  e f f e c t i v e minor p r i n c i p a l  s t r e s s , assumed  to be Kj, o^  0  With porewater pressure u, the minor p r i n c i p a l e f f e c t i v e  stress  i s given by a'  =  3  ( K o o  T h e r e f o r e , from equations  - u )  V 0  (3-1.4)  (3-15) and  (3-15),  the  compatible  bulk modulus B^j. f o r the c u r r e n t l e v e l of porewater pressure i s given by Bmk/ mo B  where  B  m o  is  pressure and K Equation  0  =  the  < (*o°vo initial  " u)/  bulk  i s the c o e f f i c i e n t (3-16)  represents  (K a 0  modulus  V Q  at  )}"»  (3-16)  zero porewater  of e a r t h pressure at the  modification  of  rest. bulk  32  modulus  f o r the e f f e c t of porewater pressure adopted i n t h i s  t h e s i s.  3.6.2 M o d i f i c a t i o n Of Shear Modulus Seed and I d r i s s the  determination  of  (1970) developed maximum  shear  a  relationship for  modulus  G o m  (at shear  X  s t r a i n s l e s s than 10~^%) i n the form Gmax  =  1  ooo k  2 m f l x  (o'n  j'  (3-17)  Z  where, = mean normal e f f e c t i v e s t r e s s i n p s f k2jyioix  parameter which depends on s o i l  =  type  and  relative  d e n s i t y Dr It as  i s a l s o suggested that k max  r  o  r  2  sands (Byrne,1981) i s  follows; k max = (15 + 0.6.D ) 2  For  g r a v e l s and s i l t s , k 2»viax  k  (3-18)  r  =  (  1  5  +  °-  i s given as  2  6 5D  r)  (3-19)  F  The parameter F depends on s o i l  type and t y p i c a l values  of  F are,  The  F = 2.0  for gravels  F = 0.6  for s i l t s  e m p i r i c a l equation f o r the d e t e r m i n a t i o n of values of  maximum shear modulus, proposed by Hardin and  Drnevich  (1972)  i s of the form G * = 320.8 {(2.973 - e)*/(1 m c  +  e)}  (OCR)* (o' /P m  a  f  z  (3-20) where,  33  e = void  ratio  OCR = o v e r c o n s o l i d a t i o n r a t i o fe =  parameter that depends on the p l a s t i c i t y  index of the  soil. The equations  and i s p r o p o r t i o n a l to io'^  a^, of  (3-17) and (3-20) imply that Grnax depends on )'^. T h i s a l l o w s a m o d i f i c a t i o n  shear modulus f o r the e f f e c t of porewater  pressure  i n the  form,  mfc  -  G  G  m  >"  l°'m/°m  0  <3-2D  2  where, G {.  =  m  compatible  shear  modulus f o r the c u r r e n t l e v e l of  porewater pressure u, G^Q = initial  value of  shear  modulus  at  zero  porewater  pressure, 'mt  a  mean  =  normal  effective  s t r e s s at c u r r e n t . l e v e l of  porewater pressure u, a'  = mean  mo  normal  effective  stress  at  zero  porewater  pressure. and  o' ^  can  m  be  calculated  using  the f o l l o w i n g  equations;  where a In  y 0  °*0  =  (1  a'  =  (1 + 2 K ) / 3  w t  +  2 K )/3 0  a  = initial  a'  (3-22)  Vo  ( a;  o  vertical effective  - u )  (3-23)  stress.  t h i s t h e s i s , the m o d i f i c a t i o n of shear modulus f o r the  e f f e c t of porewater p r e s s u r e , i s taken given by equation  (3-21).  i n t o account  i n the form  34  3.7 E s t a b l i s h i n g E q u i v a l e n t Uniform Storm As  Section  2.5.2,  e q u i v a l e n t storm i s e s t a b l i s h e d u s i n g the  method  proposed  Lee  step  and  pointed  Chan  out  (1972).  earlier  The  very  in  first  distribution  by  i s to s e l e c t a  r e f e r e n c e wave i n the wave height d i s t r i b u t i o n Rayleigh  the  resulting  from  (see S e c t i o n 3.1.1). The maximum wave or  a wave of height c l o s e t o the  maximum  wave  height  is  often  chosen as the r e f e r e n c e wave. Now, deposit  the  shear  ( i e , z—»-0)  components  in  wave. Using  these  involved, (N ) L  the  the  is  r/a^  0  from  /°^0  ratio  t  T  calculated  storm  number  i s computed  curve,  stress  a  the top of the  t  f o r each  of  the  wave  and a l s o f o r the s e l e c t e d r e f e r e n c e  values at z=0, f o r each of of c y c l e s to cause i n i t i a l an  appropriate  the  waves  liquefaction  liquefaction  strength  such as the one shown i n the F i g u r e 3.3.  The  equivalent  number  of  c y c l e s , N^q, f o r the s e l e c t e d  r e f e r e n c e wave can be c a l c u l a t e d from the equation,  Nl  (3-24)  where, ^Leq = number of c y c l e s r e q u i r e d liquefaction  obtained  vo  M^ L  =  number  liquefaction curve,  at  cause  from a p p r o p r i a t e  s t r e n g t h curve, corresponding r a t i o T/O\  to  to  the  initial  liquefaction shear  stress  z=0 f o r the s e l e c t e d r e f e r e n c e wave. of  c y c l e s r e q u i r e d to cause  obtained  corresponding  from to  liquefaction  the  shear  initial strength  stress  ratio  35  r/o^  at z = 0 f o r the i  0  wave component.  N£ = number of waves of the i*** wave component i n the wave storm. Hvo = t o t a l number of  wave  components  representing  the wave storm.  3.8 L i n e a r Wave Theory Linear  wave  theory  has been used i n t h i s t h e s i s f o r  the purposes l i s t e d below: (1) To d e s c r i b e each of the wave components  i n the  storm. (2)  To  compute  seafloor  the  required  pressure  f o r the  wave l o a d i n g on the  calculation  of  shear  s t r e s s e s due to each of the wave components. The  theory  assumes  impermeable. According  that  the  seafloor  to be r i g i d and  to the theory, the equation of the  wave  p r o f i l e of a wave of height H and p e r i o d T i s given by: Y and  the  implicit  =  s  wave  H/2  Cos { 2TT (x/L - t/T) }  length  L  can  be  (3-25)  obtained from the f o l l o w i n g  equation: L  =  (p.5gT A) tanh 2  (27rd/L)  (3-26)  where, d = still  water depth  g = a c c e l e r a t i o n due to g r a v i t y x = space c o o r d i n a t e i n h o r i z o n t a l d i r e c t i o n t = time The  coordinate  pressure wave l o a d i n g  Ap, imparted  on the s e a f l o o r by  36  the wave i s given by: Ap  =  p  o  Cos { 2TT ( X / L - t/T) }  (3-27)  where, P  o  = 0.5tffcH / { Cosh  (2ird/L) }  tfft = d e n s i t y of sea water. The d e f i n i t i o n  of terms and other elements  wave theory are shown i n F i g u r e 3 . 5 .  of  linear  37  Ocean F l o o r  Figure  3 . 5 ; Wave Pressure and D e f i n i t i o n s Terms - L i n e a r Wave Theory.  of  38  .  CHAPTER 4  FINITE ELEMENT FORMULATION OF THE  4 .1  PROPOSED METHOD  Introduct ion The  method  of  a n a l y s i s developed  in t h i s thesis for  the e v a l u a t i o n of wave induced r e s i d u a l porewater pressures an extended  v e r s i o n of Siddharthan-Finn method with an  difference  in  interpolation element  degree  f o r the  computer  polynomial field,  the  of  the  porewater program  pressure  STABW3  i n t e r p o l a t i o n function for  whereas STABW uses a l i n e a r  motivation  for  interpolation It  polynomial  has  using  a  higher  i s for the reason been  observed  uses the  a  in  The  porewater  the  finite  complete  interpolation degree,  apparent  used  field.  is  cubic  pressure  function.  polynomial  in  The the  s t a t e d below.  that when a f i n i t e  s o i l deposit i s  analysed f o r the wave induced r e s i d u a l porewater p r e s s u r e s , a l l e x i s t i n g a n a l y t i c a l methods, which were b r i e f l y  reviewed  previous chapter, i n d i c a t e higher r e s i d u a l porewater at  lower  elevations  for  cases  with  soil  pressures  having  higher  p e r m e a b i l i t i e s than f o r cases with lower p e r m e a b i l i t i e s , all  other  associated  coefficient order  to  with  to the i n c r e a s e d downward  cases  where  the  soil  has  flow  examine  and  This  cannot  verify time  the  history  above of  be achieved through  phenomenon, flow  of  a higher  of c o n s o l i d a t i o n , that i s , higher p e r m e a b i l i t y .  neccessary to know the points.  while  p o t e n t i a l v a r i a b l e s remain the same. I t i s b e l i e v e d  that t h i s phenomenon i s due water  i n the  through  In  i t is nodal  the e x i s t i n g methods  39  reviewed linear One  i n Chapter  2 because of  the  fact  form k (du/dz)} as- a nodal z  A  complete  STABW3 f i n i t e variables  use a  cubic i n t e r p o l a t i o n  element  per  node  through  t o i n c l u d e flow  formulation.  This  requires  u  at  the node z  determination  of  pressure response through  variables. the time  The  and  of  interface  at  pressure flow  are s e l e c t e d as  formulation  history  nodal  the  allows  residual  the  porewater  at any depth w i t h i n the domain and  the  degree p o l y R o m i a l  two  t o uniquely d e f i n e the porewater  nodal  {in the  f u n c t i o n i s chosen i n the  the nodal point i n the form k ( d u / d z ) ,  required  field.  variable.  f i e l d . The porewater pressure  flow  they  i n t e r p o l a t i o n f u n c t i o n f o r the porewater p r e s s u r e  r e q u i r e s a higher degree polynomial  the  that  a l s o the  nodal p o i n t s . Since a higher  i s used i n the i n t e r p o l a t i o n ,  i tis  apparent  that higher accuracy and f a s t e r convergence may be achieved f o r the  solution. Though  most of the important  a s p e c t s are common f o r STABW  and STABW3, the n o t i c e a b l e d i f f e r e n c e occurs i n the f o r m u l a t i o n of  the f i n i t e element equations as a r e s u l t of  interpolation finite in for  function.  The  main d i f f e r e n c e i n STABW3  element f o r m u l a t i o n comes from the f a c t that  f u n c t i o n a l J {see equations in a  formulation. in the next development Chapter  other  differences in  3.  different  manner  the  terms  (4-12) to (4-15)} a r e accounted than  i n STABW  finite  element  The f i n i t e element f o r m u l a t i o n of STABW3 i s given s e c t i o n and the important  aspects i n v o l v e d  i n the  of t h i s method of a n a l y s i s are a l r e a d y o u t l i n e d i n  40  4 . 2 Formulation Of F i n i t e The  basic  r e s i d u a l porewater  equation  ,9u  f  may  be  =  m  -  3  the  is,  U  s  (4-i)  )  equation (4-1)  to be a f u n c t i o n of z o n l y .  Hence equation  to, 3u.  . >. Q(z>  =  w  The f u n c t i o n a l equation  s e c t i o n 3.2) governing  of time, the r i g h t hand s i d e of  (-37)  z  ^ g  v "3T — 5 T (  considered  (4-1) reduces  (see  pressure response  3 ^z 3u. 3z V 1? w  At any i n s t a n t  Element Equations  ( -2) 4  J for a d i f f e r e n t i a l  equation of the form, as  in  (4-2) i s ,  0  Expanding the above, D J  . z ,3u,. ,D H 0 "  =  )  (  U  0  with boundary  (|^)  Y  ]  + 2 Q(z)u]dz  2  dZ  w  conditions,  u = 0 at z = 0 and  iH.  =  0 at  z = D,  3z  the boundary  term in the f u n c t i o n a l  vanishes.  Hence,  D J  -  - j 17* I I (  0  Suppose the s o i l deposit finite  is  number of elements,  J  t  °  (4-3)  ) 2 + 2 Q ( 2 ) U ] D Z  w  t  a  l  =  considered  as  an  assemblage  then  elements  J  e  l  e  m  e  n  t  (4-4)  of  41  4.2.1  I n t e r p o l a t i o n Function In  function  order to e v a l u a t e the f u n c t i o n a l , an  for  u  interpolation satisfy  must  be  selected.  Let  us  interpolation  choose  a  cubic  f u n c t i o n f o r u. T h i s would be more than enough to  the completeness  criterion.  Now, 2 a  + a n  3  «=  n  = l o c a l c o o r d i n a t e system,  1  + a n  (4-5)  u  2  + a^n  3  where,  a  l  t o  a  A  =  and  c o e f f i c i e n t s which need to be  Each  elememt  has  two  evaluated.  nodes ,  therefore,  1  v a r i a b l e s per node i s r e q u i r e d to uniquely choose u and q as two q M  =  k z  From equation  define  two u.  nodal  Let  us  nodal v a r i a b l e s , where  (—)  (4-5)  |H  =  a  q  =  k  2  + 2a n + 3 a n 3  2  A  Then,  Now,  consider  z  (a  2  + 2a n + 3  the  i t h  (4-6)  3a^p ) 2  element  with  nodes  i  and  i+1  t h i c k n e s s dj .  •  r  At  n -  0,  At  n -  d ,  u -  u.  and  q -  q ; ±  n ±  u •= u  1  +  1  and  q -  q ±+1  and  42  Using  these  i  u  u  "  "  +  Solving  a  (4-7)  l  +  k  i+l for a  1  substituting  (4-8)  2 i d  a  +  a  3 i d  2  +  a  A i d  0  t o a^ f r o m into  equations  equation  e  =  I J-l  >  N.u. J  and  using  <  i+l  x = /d. n  (1 - 3 X (d./k i  (3A  N,  A  4.2.2  =  Element  2 Z  z  2  + 2X ) 3  )(1 -  -  Matrix  + X )  2X  2  +  X )  3  3 2X ) J  (d./k ) ( - X i z  2  (4-7)  3  Equation  to  (4-10)  and  back  yield,  (4-11 )  J  "i+1 q  (4-10)  (4-5) w i l l  where  —i  (4-9)  3  ( a +2a.d, + 3a.d/) 2 3 i 4 I  z  N u. — — l  u.  to get,  z 2  i l  4  and (4-6)  l  a  i  M  (4-5)  i n equations  Consider J  e  l  e  m  e  n  from equation  t  - J element  I- -  (|V  5  0  w  (4-3),  + 2 Q(n)u]dn  d.  k [  h  -  „  .  2 , OUv Z  r  7~ W w  e +  I  e  2  . +  -  X  g. , .  -  2  3  3u  , dU  -dT  ) u ] d T 1  e  (4-12)  where  z /du 2 ,  — Y  0  w  N  (-rr) 9n  dn  and  d  i .  2 m  •V  2 n V  3u u(—&)dr o l  uC-l^dn • dt  Now c o n s i d e r I , z  0 1  kd, —  Y  From e q u a t i o n  (4-11),  k d. z 1 Yw  3u,  W  dn  & .  , d  A  oA  u = N.u., j = 1,4, 1  31,  ,  ,011*2  — (—) Y dn w  , substituting  1=1,4 and j = l,4  N'.u. N'u. dX, " " k  k  2— • d Y„  J  i  N'.N.' U , dX J  k  j  this,  44  (4-13)  [S ] '{uJ} e  where  [S ] - 4 x 4  symmetric  g  matrix  with  the general term  given by, k  2 —  • o\  N'N:  dX  w  or 12  z  5  '11 =  '12  S  Yd. w 1  21  '13  '31  '14  '41  n r  '22  15 "  '24 '33  Now c o n s i d e r  S  32  =  S  =  S  =  i„ 2  -S  11  '12  e  kzY w =  "  S  S  21 1 15  42  i k Y z w  d  11  -S  '34 '44  w  4 . 1  S r% r\  '23  _1_ 5 'r 1  12  22 , a,  2 m V  u(-|7)dn dt  0 1 2 m d., N,u. N.U dX v i k k j 31, 3u,  2 m d, N, N. U dX v i kj  2 m d. u(|H)d.X v  45  where given  [D ] - 4 x 4  H> ]  <V  E  symmetric  g  (4-14)  matrix  with  the  general  by, 2 m d. v i  N, N. dX k j  or  '11  35  D  D21  12  D  '13  v i  31  11 105  k  D  D  14  =  D  Now  =  D  32  "11  D,„  44  "43  =  D  =  -D 12  22  v i k  " 14  =  consider  '33  70mv7^  m d. v i  2 105  '22  '23  13 210  41  "42  '34  Vi  35  =  i  v  '24  D  i  3  du  1  2 m  V  u (-?-*) dn Qt  0 Let  us assume a s i m p l e 3u 3t  (1-X)  linear 3u  ( f ) J  i  +  variation 3u  (-^) 3t  f o r (3u / 3 t ) g  as,  term  46  To  accomadate  (3u /3t)  this  into  the f i n i t e element f o r m u l a t i o n , l e t  as  g  3u 3u =  (  M  M l  J  M .M )  2  3  A  3u ^3t  i+l  ;  where  Using  this  M  1  =  (1-X)  M  2  =  M  M  3  =  X  =  A  0  technique,  3u 2 m d, N,u, M. {T-*}dX v i k k j 3t  3u 2 m d. N.M.{-r-*}dX v i k j 3t  31. 3u,  3u [R ] U ^ ) e  where  [R ] = 4 x 4  e  symmetric  )  (4-15  matrix  with  the  general  1  6  given by,  2 m d. N,M, dX V I  K  j  or R  31  =  Vi  10 1  -R„=  R  41  "15  m d/  11  -  4*~  R  21  10  v l  , 1  m d. v i  10  k  term  47  All  other  terms a r e zero.  4.2.3 G l o b a l M a t r i x  Equations  Now, 3J , ' element  3I. 1  _  d{u ]  3{  e ±  From e q u a t i o n s  (4-13),  6 Ui  31* 2  C +  }  3{  e Ui  31* 3  }  3{  e u  )  (4-14) a n d (4-15)  3J , e l e m  3u e  -  n t  3{u. } l Using  variational 3J 3{u}  [s ]{u. } + e  e  [D ]{u ] e  e  +  [R ]{(a^) > e  e  principles,  =  0  That i s ,  I  "element  elements  up w o u l d  {0}  3{u. } I  3u [S ]{u. } + lD ]{U ) + [R ]{(—£)  I elements Summing  =  e  e  e  yield  global  matrices  compressibility ratio.  m  v  matrix  differential  =  }  equation  =  {0}  {  and  \R]  are  and, hence,  vary  with  porewater  [s]  equation  equation  i sconstant  {0}  as  [D]  The g l o b a l m a t r i x  The  £  the global matrix  a 3u [S](u> + [ D ] { f } + [ R ] ^ } The  e  4  _  1  functions  f o r a given  6  )  of  pressure problem.  ( 4 - 1 6 ) c a n be t r e a t e d a s an o r d i n a r y  a n d be i n t e g r a t e d o v e r  t h e time  interval  48  t,  t + At  t o get 9u  tS]6{u  t + A t  } + a{u )]At + [ D ] U u t  t + A t  } - {u }] - [R]{-^*)At  = {0}  t  ( 4 - 1 7 )  where  a+B = 1  at  t and t + A t  time  constructed and  t+At.  and s u b s c r i p t s t and t+At respectively.  using  average  Rvalues  different  approximations.  Matrices  values  g r e a t e r than  correspond [5]  of variables  or equal  However,  t o values  and  \R] a r e  between  time  t o 0.5 c o r r e s p o n d s  i nthis  t to  program a value of  £ = 0.5 i s u s e d . Equation  [AQKu  ( 4 - 1 7 )  t + A t  )  -  c a n be g r o u p e d  together  t o form,  {BQ1}+(BQ2}  u  _  i  e  )  where [AQ]  =  [S]6At = [D]  {BQ1}  =  (-[S]cxAt + [5]){u )  {BQ2}  =.  3u [R]{(^r ))  With  specification  and  rows  [AQ*].  vectors  of  t  £  • At  of boundary  conditions, appropriate  [AQ] a r e s t r u c k o u t t o form  a net global  matrix  r o w s o f { B Q 1 } a n d { B Q 2 } t o f o r m net  So a r e c o r r e s p o n d i n g {BQ1*} and  columns  {BQ2*}.  Hence,  [ A Q  The varying  or  *  ] { u  t+At  }  =  { B Q 1  *  }  +  { B Q 2  *  }  =  {B  Q*  }  (4-19)  program has t h e o p t i o n of c o m p r e s s i b i l i t y , remains  constant.  In  the  event  of  either constant  49  compressibility, time  step.  equation (4-19)  However,,  equation (4-19)  is  matrices  [D]  and  estimate  of  repeated  until  number of  iterations  nodal a  i s solved i n s t a n t l y  in the event of v a r y i n g  solved £R ]  are  iteratively.  The  iterative  accuracy  every  compressibility, time  c a l c u l a t e d using the best  variables. specified  Each  for  variable current  procedure  is  or a s p e c i f i e d maximum  i s o b t a i n e d , whichever  occurs  first.  50  CHAPTER 5 ISLAND GEOMETRIES AND  5.1  Island  induced  STABW3  were  water depths 12m, the  residual  conducted  21m  and  i s l a n d s are presented The  for  analyses  only v e r t i c a l slope  31m  of  analysis  except  However,  the  liquefied  soil  for  the  play  extent The  and  vertical  detail  of  selected 5.3.  Since  analyses,  affect  the  the method of  in  water  in  the s t r u c t u r a l  containing  an  depth.  the  flow  i s l a n d f o r wave induced  sections and  considered  of  to GG  has  porewater to  moreover the top p r o f i l e has  water s u r f a c e . But of i s l a n d  depend on the shape and  in r e a l i t y , the  1, are not of  infinite  to s t i l l  water  be  of  to  be  sections, lateral surface.  the top p r o f i l e of those s e c t i o n s  slope of  the  berm.  In  the  analyses  t h i s t h e s i s , a l l such s e c t i o n s are assumed to be  of i n f i n i t e l a t e r a l extent to the s t i l l  the  role  a l s o they are not p a r a l l e l  in  to F i g u r e  in  major  also in  a c t u a l l a t e r a l length and  conducted  other  i n cases of l i q u e f a c t i o n .  to s t i l l  for example AA  i s l a n d s at  sections  variations  a  i s l a n d s and  i n f i n i t e l a t e r a l extent parallel  5.1  directly  defining  To be able to analyse pressure,  the v e r t i c a l  not  analyses  5.1.  considered  does  slopes  s t a b i l i t y of the  three d i f f e r e n t  are shown in F i g u r e  berm  pressure  r e s p e c t i v e l y . The  in Table  s e c t i o n s are  the  porewater for  berm c o n f i g u r a t i o n and  the  WAVE ANALYSES  Configuration  Wave using  SOIL PROPERTIES FOR  water  surface.  and  the top p r o f i l e  to  be  parallel  Island  Bern,  S t i l l Water  Set down  No.  height(m)  depth(m)  depth(m)  1  6.0  12.0  6.0  2  15.0  21.0  6.0  3  25.0  31.0  6.0  Table S'i  ; D e t a i l s Of  Islands  52  !  30 m *  *  Sand  F Figure  5-1;  D  E  Sections Porewater  of  Island  Pressure  c  8  A  1 f o r Wave I n d u c e d Analysis.  Residual  53  S W L  SI ope 1 :5  p  8-^^  Sa nd Bei•m Seafloor •  6m  ism 9tn  '  II w  -—'  50 m  Seafloor  Sand  "77—J T i ' r  V  u  F i g u r e 5>2; S e c t i o n s of Porewater  T  5  R  Q  p "  I s l a n d 2 for Wave Induced R e s i d u a l  Pressure  Analysis.  —  ¥  Slope 1:5  Sanr,J Berm Seafloor  1  -—  «  J  srn  L |  13 rr)  k  'L————  15 m  I7rrj  il  M —  6rrj 25rrj  21 m  50 m S e a f l o o r Sand  N  M  F i g u r e 5 - 3 ; S e c t i o n s of  L.  K  3T  1  H  I s l a n d 3 for Wave Induced R e s i d u a l  Porewater Pressure  Analysis.  55  The  above assumption i s j u s t i f i a b l e  of very g e n t l e  slopes.  believed  that  the above assumption would l e a d to  estimates  of wave induced  of  For  the e f f e c t of s t a t i c  and  of  sharp  shear s t r e s s e s . The the  rate  of  be.  drainage The berms  it  because  presence of  The  conservative faster  taken  i s a l s o due  static  pressure response  it  actually  to f a c t  that  in a slope than in h o r i z o n t a l ground.  e f f e c t s of s t a t i c be  nature  than as  is  conservative  hence the r e s u l t i n g porewater pressure  would be  can  slopes,  porewater  with the above assumptions would be higher would  of berms  r e s i d u a l porewater pressures  shear s t r e s s e s i s to r e t a r d generation  berms  in the cases  shear  into  stresses  and  the  slope  account by v a r i o u s ways as  of  briefly  d e s c r i b e d below. 1. By using a porewater pressure into  account  generation  of the i n f l u e n c e of s t a t i c  development of porewater pressure  during  model  that  takes  shear s t r e s s e s i n the cyclic  loading.  An  example would be the model proposed by Finn et a l (1978). 2. By using a modified  e q u i v a l e n t p e r m e a b i l i t y to c a t e r for the  i n c r e a s e in the drainage 3.  By using a modified  resulting  from s l o p i n g ground.  s t r e n g t h curve  to c a t e r f o r  preshearing  and p r e c o n s o l i d a t i o n . However, these because  of  gathered  from an o f f s h o r e  5.2  the  types of refinements  uncertainity  are  rarely  a s s o c i a t e d with the  required  information  site.  S p e c i f i e d Storm Waves Storm waves are d e s c r i b e d by  three  parameters.  They  56  are  the  significant  wave h e i g h t , the s i g n i f i c a n t wave p e r i o d  and the d u r a t i o n . Each location  of  of  these  parameters  depends  on the  the s i t e and s e v e r a l other f a c t o r s r e l a t e d to the  s i t e . For the purpose of the a n a l y s e s , storms are s p e c i f i e d f o r each of the i s l a n d and the d e t a i l s are given i n Table 5.2. The number  of c y c l e s i n each case, i s given by (6 x 3600)/8, which  i s equal to 2700.  5. 3 S o i l P r o p e r t i e s 5.3.1  Basic S o i l P r o p e r t i e s The  density,  b a s i c s o i l p r o p e r t i e s such as d e n s i t i e s ,  void r a t i o , specific  relative  g r a v i t y of s o l i d e t c used  i n the  analyses a r e shown i n Table 5.3.  5.3.2  Derived S o i l P r o p e r t i e s  Initial  Shear Modulus  For sands and g r a v e l s ; The  initial  value of shear modulus f o r sand and g r a v e l  were computed using the equations  (4-17),  For sand of D t - = 50%, from equation K  2  max  Max  =  9  of D = 50%, from equation  (4-19),  •  5  required equation  (4-18),  4 5.  =  For g r a v e l and r o c k f i l l k2  (4-18) and (4-19).  f o r shear  modulus  G  m < J X  calculation  in  (4-17) was c a l c u l a t e d using the f o l l o w i n g equation, =  (1 + 2K )/3 . o 0  v o  (5-1)  Island No.  (m)  (sec)  (hrs)  8.0  6.0  4:01  1  1  •  6.0.  2  9.0  8.0  6.0  3  12.0  8.0  6.0  Table 5-2 ; Spec i f i e d Storms O f the  Islands  58  Soil  Property  Total Unit Sub. Unit Specific  Weight(kN/m ) 3  Weight(kN/m ) 3,  Gravity  Void R a t i o Relative Density Angle of  (%)  Internal Friction  I n i t i a l Compressibility Vertical Empirical  permeability Constant  (deg)  (m /kN) c  (cm/sec)  Type  Sand  Gravel  Clay  19.0  19.5  18.0  9.0  9.4  8.0  2.65  2.67  2.67  0.85  0.65  0.90  50.0  50.  -  33.  37.  22.  3x 1 0 '  1 o" -1 0 ~ 3  1 .9x10"*  £  4  10.0  10^ 10"'  0.70  0.10  0.10  Bulk Modulus exponent  0.50  0.50  0.0  Poisson R a t i o  0.35  0.25  0.45  Table 5 - 3 ;  S o i l P r o p e r t i e s S e l e c t e d For Wave Analyses  59  K  0  was c a l c u l a t e d using the equation, K  (5-2)  = 1 - s i n <j>'  0  where </>' = angle of i n t e r n a l  friction.  For c l a y s ; The  initial  shear modulus G  m Q x  f o r c l a y s was computed  from the f o l l o w i n g equation, G where S  u  = 1000 S  m v l x  = undrained  (5-3)  u  s t r e n g t h of c l a y .  I n i t i a l Bulk Modulus The bulk modulus, B, f o r sand, g r a v e l computed using the e l a s t i c B/G  =  and  Poisson  were  relationship,  2(l+v)/3(1-2*)  where v = i n i t i a l  clay  (5-4)  ratio,  G = shear modulus.  5.3.3 S e l e c t i o n Of I n i t i a l Volume C o m p r e s s i b i l i t y A  c l o s e examination  of the governing equation f o r the  wave induced porewater pressure in- S e c t i o n 3.2 r e v e a l s that the parameter that p l a y s the most c r u c i a l levels  of  porewater  the c o e f f i c i e n t reason,  both  determined  pressure that may develop  k  z  and  m  v  are e q u a l l y important  experimental  data  on  compressibility  this  and should be  e x p e r i m e n t a l l y i n order t o o b t a i n the most pressures.  the  i n the berm i s  of c o n s o l i d a t i o n d e f i n e d as k^/my*^ . For  estimates of wave induced porewater no  r o l e i n determining  realistic  Unfortunately,  are a v a i l a b l e  on  60  p o t e n t i a l sand f i l l .  A brief  data on sand i s presented The  herein.  and  sand i s c o n f i n e d  vertical  e f f e c t i v e s t r e s s are is  selected compressibility  c o m p r e s s i b i l i t y of sand i s u s u a l l y  oedometer t e s t . The ring  review on  shown  in  The  recorded.  Figure  p l o t t e d against  settlements  determined  in a s t i f f under  in  an  stainless steel  increasing  vertical  A t y p i c a l oedometer t e s t  5 . 4 , where the v o l u m e t r i c  result  strain,  e %,  is  m^  defined  v  v e r t i c a l e f f e c t i v e s t r e s s , Oy  coefficient  of volume c o m p r e s s i b i l i t y  is  as, m  =  v  where  de  =  v  (5-5)  de /do^ v  change  in  volumetric  small change in e f f e c t i v e v e r t i c a l Therefore, the  form  s t r a i n corresponding  s t r e s s , do^  .  the slope of the experimental curve  shown  in  5.4,  Figure  to a  plotted  in  i s the c o e f f i c i e n t of volume  compressibi1ity. Two Figure  d i f f e r e n t phases 5.4.  The  first  the e f f e c t i v e s t r e s s corresponds  to  one  is  curve)  always  and  the c o m p r e s s i b i l i t y being  is  also  from  the  where  the  During  wave  identified  in  l o a d i n g where  The  other  effective  phase  stress  is  (slope  of  l o a d i n g phases are q u i t e d i f f e r e n t higher  Figure  the l e v e l of loading,  be  compressibi1ies  under v i r g i n  5 . 4 that d u r i n g  rebound c o m p r e s s i b i l i t y i n c r e a s e s and i n c r e a s e depends on  can  increased.  that the  under these two  seen  loading  corresponds to v i r g i n  rebounding  reduced. It i s n o t i c e a b l e the  of  further  loading. unloading  the  amount  It the of  unloading.  residual  porewater  pressures  are  61  I  \ 8 1  s NL  \  s  s. —  0  Figure 5 . A ;  10 20 30 Vtrttul Urns, t. Of/cm')  40  Oedometer Test R e s u l t s For a Libyan Sand ( A f t e r Lambe and Whitman, 1969)  62  generated. As a r e s u l t of t h i s , the e f f e c t i v e s t r e s s regime changed.  That  reduced by new  the  current  constant. cyclic  is,  Therefore,  The  data  remain  sand i s rebounding  during  e f f e c t the  portions  of  values  have  m  0  values  be  experimental c u r v e s .  The  to  be  on c o m p r e s s i b i l i t y major  data  also  by  of sand due  contribution Lee  compressibility  constant t o t a l The  and  in  (1976)  Albaisa  as  the  compressibility values  at low  the  of  s o i l s can conducted  ratios.  be determined  from  i n t h i s t h e s i s , the  of sand f i l l  (D  which  from the F i g u r e  r  = 50%)  is  3.0  ratio,  compressibility  have a marked  The  of  study of Seed et a l  compressibility  current  their  densities.  excess porewater pressure, i s  r e l a t i v e density  compressibility  2  ratio  of  the  variations  relative  emerged from the  variation  is  porewater pressure at  of porewater pressure r a t i o upto 60%,  s i z e nor  ft /lb),  the  area  (1974). Based on  with i n c r e a s i n g  conclusion  regarding  expressed  adjusted  to rebounding i s  this  s t r e s s for sands at v a r i o u s  important  have  a  to  v  comprehensive study, Seed et a l (1976) proposed rebound  in  l e v e l of r e s i d u a l porewater p r e s s u r e s .  very l i m i t e d . The experimental  , is  0  itself  v o  which means a p p r o p r i a t e  the  a^  ( o - u ) while ay  in  rebound  stress,  result  compressibility  depending on  effective  in porewater pressure to  e f f e c t i v e s t r e s s of  from  rebound  initial  increase  loading  obtained  the  is  neither influence  to  that the on  the for  grain the  rebound c o m p r e s s i b i l i t y  of  Figure  analysis  5.5.  selected x  10~  For  rebound 5  m /kN 2  the  sandy  compressibility (0.15  x  10"  5  agrees q u i t e w e l l with the corresponding value 5.5.  0  20  40 60 80 Relative Density, D - % r  F i g u r e 5 - 5 ; E f f e c t Of D e n s i t y On C o m p r e s s i b i l i t y At Low Excess Porewater P r e s s u r e . ( A f t e r M a r t i n and Seed, 1978)  100  64  Rebound c o m p r e s s i b i l i t y rebound  modulus,  compressibility Based  E,. ,  of sand can a l s o be computed  given  by  da^ /de .  i s thus the r e c i p r o c a l of the rebound  terms of i n i t i a l E  at any c u r r e n t  effective vertical  =  U' )'" /mk (a m  v  2  effective  stress  stress  , as  modulus.  thereby rebound c o m p r e s s i b i l i t y Rebound  compressibility  ) ~™  (5-6) f o r the sand, E and  2  can be computed. can a l s o be determined from the  compressibility  under v i r g i n l o a d i n g .  compressibility  value f o r v i r g i n  The f a c t o r by  loading  compressibility  be d i v i d e d  obtain  rebound  atleast  2. Table 5.4 presents the c o m p r e s s i b i l i t y  Lambe  range, about  i s often  and Whitman (1979) f o r v i r g i n  s o i l s under two d i f f e r e n t  , in  r)  vo  With a p p r o p r i a t e values of m, n and k  stress  which  In  the  i n order t o  recommended  t o be  data  loading  ranges.  the rebound c o m p r e s s i b i l i t y  quoted  for different  the low  stress  computed from above data i s  1.0 x 10~ m /kN f o r dense sand and 3.6 x 10~ m /kN f o r 5  loose  sand.  compressibility  2  5  Therefore,  f o r medium  dense  5  2  2  compressibility  of  3  x  2  sand,  i n the range 1.0 x 10~ m /kN and  m /kN may be expected. I t i s observed that  fill  rebound  on the experimental study, M a r t i n et a l (1976) developed  an e x p r e s s i o n f o r Er  by  The  v  from  rebound  3.6  the s e l e c t e d  x 10~  5  rebound  10" m /kN f o r the medium dense sand 5  2  i n the a n a l y s e s r e p o r t e d i n t h i s t h e s i s f a l l s w i t h i n  this  range. The  oedometer  measurements  of c o m p r e s s i b i l i t y  found t o be u n r e l i a b l e because of the e r r o r s standard oedometer  involved  are often i n the  equipment. The primary sources of e r r o r s a r e  V i r g i n Compressibility m  y  Soil  Relative Density  For  -S  For  6 2 - 1 0 3 kN/m  2  200 - 510 kN/m  2  Uniform Gravel  0  3.30  1 .67  1 mm< D < 5 mm  100  0.85  0.56  Well Graded Sand  0  7.24  3.92  0.02mm< D < 1 mm  100  1 .93  0.82  6.81  2.84  1 .96  0.83  Uniform Fine Sand 0.07mm< D <0.3mm  Uniform S i l t 0.02mm< D <0.07mm  0 100  0  35.71  100  2.64  5.81 1 .32  Table S-4-i C o m p r e s s i b i l i t i e s of Cohesionless Material in Given Stress Range For Relative  Densities  0% and 100%. (After Lambe and Whitman, 1979)  Note; For Rebound C o m p r e s s i b i l i t i e s , the above values have to be divided by a t l e a s t 2.  2  (10 ) m /kN  66  due t o ; 1. C o m p r e s s i b i l i t y of the oedometer system. T h i s comparable  with  that  of  sand  and  thus  i s found to be  very  d i f f i c u l t to  correct, 2. Side  friction,  3. High v o i d spaces at the contact 4. Improper c o n t a c t s 5. Inaccurate small  with the top and bottom porous  r e l a t i v e d e n s i t y measurements  specimen Because  of the c o n s o l i d a t i o n r i n g ,  resulting  from  size. of  these  e r r o r s , the c o m p r e s s i b i l i t y of sand i s  o f t e n overestimated. For t h i s reason, C o r n f o r t h the  stones,  compressibility  of  sand  in  t e s t s were conducted on Brasted  (1974)  studied  the t r i a x i a l apparatus. The  sand under  K  conditions.  0  He  observed that the c o n s o l i d a t i o n curves were p a r a b o l i c and there is  a  linear  relation  between  volumetric  strain  and  root  v e r t i c a l e f f e c t i v e s t r e s s as, =  x U  v  )  V  (5-7)  z  X i s dependent on the dry r e l a t i v e d e n s i t y , RDD, of The  r e s u l t s from h i s study are presented i n F i g u r e  the  sand.  5.6.  For Dr = 50%, X = 0.026 From equation m  v  Therefore,  (5-7), =  de /da^  = 0.005 X (o' )  v  for D  mV  =  r  (5-8)  v  = 50%, f'/2  (5-9)  0.0001 3 u \ , )  For mean e f f e c t i v e v e r t i c a l s t r e s s of 10 kN/m , 2  m  v  =  4 x IO"  5  m /kN 2  6?  Root V e r t i c a l E f f e c t i v e S t r e s s ; J«T • k^/ni*  20  10  30  40  50  60  3 a 2 "  u  -U  to  Condition -t->  e  (1)  e £  4  A  coefficient of Linearity x  70 /  Dense  50/.  Med. Dense  0-026  30/  Loose  0*040  Very LooAt  o. o^l  • 10/  o-oi9  F i g u r e 5 - 6 ; Volumetric S t r a i n Vs Root V e r t i c a l E f f e c t i v e (After Cornforth,  1974)  Stress  68  Since t h i s value i s f o r v i r g i n  l o a d i n g , i t should be d i v i d e d by  a f a c t o r of 2. Therefore, the rebound c o m p r e s s i b i l i t y i s , m Hence,  =  v  2.0 x 10~  5  m AN 2  f o r the s t r e s s range of i n t e r e s t , the s e l e c t e d value of  rebound c o m p r e s s i b i l i t y compares w e l l with the value  calculated  above.  5.4 L i q u e f a c t i o n Strength Curve The l i q u e f a c t i o n used  in  the  analyses  s t r e n g t h curve is  Figure  factor  f o r sand of D f = 54%  3.3, by reducing the c y c l i c  50/54.  =  given i n F i g u r e 5.7. The curve  deduced from the s t r e n g t h curve in  f o r sand of  shear  50% was  presented  s t r e s s r a t i o by a  Number Of C y c l e s To L i q u e f a c t i o n , 5-7;  L i q u e f a c t i o n Strength Curve  N  L  of  70  CHAPTER 6  WAVE INDUCED RESIDUAL POREWATER PRESSURE ANALYSIS  6.1  General The  reported  wave induced  herein  r e s i d u a l porewater pressure  were conducted using computer program STABW3.  In a l l cases, m o d i f i c a t i o n s of s o i l p r o p e r t i e s for of  porewater  analyses  pressure  was  taken  the  i n t o account i n the manner  discussed  i n S e c t i o n 3.6. The importance of i n c o r p o r a t i n g  property  modification  pressure  porewater  analyses  pressure  are a l l free  porewater  pressure  structures  were  soil  f o r the e f f e c t of i n c r e a s i n g porewater  has been d i s c u s s e d a l r e a d y  The  effect  responses  field  response  responses i n the v i c i n i t y  established  responses. due  not c o n s i d e r e d  c o n s i d e r a b l e c a u t i o n should  i n S e c t i o n 2.5.  to  The  in  d i s t o r t i o n of  the presence  of  i n the a n a l y s e s .  be e x e r c i s e d  the  any  Hence,  i n i n t e r p r e t i n g the  of any s t r u c t u r e s placed on the berm.  6.2 Response of I s l a n d s on Sand Foundation The sitting  of  for different  analyses  on i s l a n d s 1, 2 and 3  susceptible to  drainage  liquefaction  s e r i e s of analyses  properties  were  c h a r a c t e r i s t i c s of the sand  The i n i t i a l c o m p r e s s i b i l i t y of the sand  particular other  series  on a sand foundation  conducted fill.  first  fill  for this  i s taken as 3.0 x 10~ m /kN. The  of the sand f i l l  5  2  and s e a f l o o r sand are  given  71  in Table 5.3. The  effect  of  dissipation  on  the  porewater  i s c o n t r o l l e d by the value k /m Tf^  response  z  pressure  . Having  v  selected  the same c o m p r e s s i b i l i t y value f o r a l l the a n a l y s e s , i t i s now possible that  to  compare  i s , the  pressure  the  effect  of  e f f e c t of drainage  variation  in  k  characteristics,  on  z  the  porewater  response.  6.3 Wave Induced Porewater Pressure Response Of I s l a n d 1 to 6m, 6 hour Storm Figure  6.1  to  6.7  show  the  residual  p r e s s u r e s induced at the end of a 6 hour storm with  porewater significant  wave height of 6m at s e l e c t e d s e c t i o n s AA to GG of i s l a n d  1  the d i f f e r e n t p e r m e a b i l i t y values of k  k  10""  = 10" cm/s 3  z  =  3  that  there i s no l i q u e f a c t i o n at any of the s e c t i o n s  c o n s i d e r e d i n the analyses i n c o n s t r a s t to r e s u l t s cm/s,  where  sections. This c l e a r l y  on  the  with k  z  with  k  z  l i q u e f a c t i o n occurs to s u b s t a n t i a l depth at  all  in  z  cm/s. For the p e r m e a b i l i t y value of 10" cm/s, the r e s u l t s  indicate  10""  and  for  shows the s i g n i f i c a n c e  of  drainage  wave induced porewater pressure response. For the case = 10"  3  cm/s, the i n i t i a l drainage  the case with k  pressures developed interesting undrained  z  i s much g r e a t e r  than  = 10"" cm/s, and as a r e s u l t the porewater i n the former  case are much  lower.  It i s  t o note, at t h i s p o i n t , that the analyses assuming conditions  would  have  predicted  liquefaction  to  depths as much as 9 to 10 m i n a l l the s e c t i o n s of the i s l a n d .  72  Porewater  pressure  ratio,  26 h  32 r  36 UJ  1  Figure 6 . 1 ; Section-AA;  I  I  I  R e s i d u a l Porewater  At the end of  6m 6 hour Storm.  I Pressure Response  F i g u r e 6 . 2 ; S e c t i o n - B B ; R e s i d u a l Porewater At the end of  6m 6 hour Storm.  Pressure Respon  74  36'  '  Figure 6 . 3 ; Section-CC;  '  '  '  R e s i d u a l Porewater  At the end of  6m 6 hour Storm.  1  Pressure Response  75  6.4; S e c t i o n - D D ; R e s i d u a l Porewater At the end of 6m 6 hour Storm.  Pressure Response  76  Porewater  pressure  ratio, /^ u  S2h  361  1  F i g u r e 6.5; S e c t i o n - E E ;  1  1—  1  R e s i d u a l Porewater  At the end of  6m 6 hour Storm.  1  Pressure Response  77  2&Y  Sfcl Figure  1  6 . 6 ; Section-FF;  1  1  —-rJ  R e s i d u a l Porewater  At the end of  6m 6 hour Storm.  Pressure  Response  78  Porewater  32  pressure  ratio, /*vo u  h  561  1  1  1  1  F i g u r e 6 . 7 ; S e c t i o n - G G ; R e s i d u a l Porewater At the end of  6m 6 hour  Storm.  -I  Pressure Response  79  The presented maximum  residual  i n F i g u r e s 6.1  porewater to  6.7  pressure  show  porewater pressure r a t i o , u/a^  the 0  zone  of  trend;  increases.  In the  = 10" cm/s, the decay s t a r t s to occur beneath the  liquefaction.  This  decaying trend i s s i m i l a r to the  F i g u r e 6.8. T h i s i s as expected  such as the one  because as the shear  r a t i o decreases, the number of c y c l e s r e q u i r e d to cause liquefaction, N , increases. L  porewater  the  4  z  t y p i c a l shear s t r e s s r a t i o d i s t r i b u t i o n , in  same  , occurs very near the  top and decays r a t h e r s t e a d i l y as the depth case with k  distributions  Now  from  equation  shown stress initial  (3-12),  the  pressure generation i s i n v e r s e l y p r o p o r t i o n a l to N . L  Hence, the porewater pressure generated  would be higher at the  top and decrease as the depth i n c r e a s e s . -It  i s a l s o seen that as the depth of water i n c r e a s e s ,  example,,6 m at s e c t i o n AA to 12 m at secton GG, the pressure and  response  both  values  of  k . z  For  analyses  with  maximum porewater p r e s s u r e r a t i o developed  CC  and  decreases  hand, f o r analyses with k liquefaction  z  location  i s apparent k  for  = 10" cm/s, the 3  z  at s e c t i o n s AA to GG  are such that i t i n c r e a s e s from 47% at s e c t i o n section  porewater  i n c r e a s e s up to a c e r t a i n c r i t i c a l  then s t a r t s to decrease. The above trend  for  AA  to  66% at  to 22% at s e c t i o n GG. On the other = 10"" cm/s, the  maximum  depth  of  i n c r e a s e s from 6.5m at s e c t i o n AA to 9m at s e c t i o n  CC and then decreases  to 6m at s e c t i o n GG.  Table 6.1 shows the maximum porewater pressure response i n terms of porewater pressure r a t i o , u / a =  vo  , f o r the case with kj.  10" cm/s and i n terms of depth of l i q u e f a c t i o n 3  f o r the case  80  Shear s t r e s s  361—1  1  _i_  ratio.'Vo^  ,  ,  I  igure 6.8; Section-AA; Shear S t r e s s R a t i o D i s t r i b u t i o n At  the s t a r t  of the Storm.  81  Maximum pwp Response  Section  Water  (d/H ) s  depth(m)  pwp R a t i o  Liquefaction depth(m)  (%) k = 1 0"* cm/s 5  k = 1 0~*cm/s  47  6.5  • 62  8.0  1 .33  67  9.0  9  1 .50  65  8.5  EE  10  1 .67  43  7.0  FF  1 1  1 .83  29  6.5  GG  12  2.00  22  6.0  AA  6  1 .00  BB  7  1.17  CC  8  DD  Table 6 - 1 ; Maximum Porewater  Pressure Response At  of I s l a n d 1 At the End of the 6m 6 hour  Sections Storm  82  with kz The  = 10~" cm/s at the s e l e c t e d s e c t i o n s of the  above  results  are  r e s p e c t i v e l y . From these  presented  in  Figure  of  this c r i t i c a l  i s given approximately  a  particular  permeability  location,  there  would  prevent  critical  value  a  any  then  l e v e l of porewater pressure liquefaction  critical  pressure  r a t i o induced  to  prevent  be  any  critical  or the extent  of  value.  were  closest  conducted  at  to the  section  CC,  value of p e r m e a b i l i t y that would  or i n other words, that would l i m i t  would  greater  of the 6m, 6 hour storm i s  r a t i o t o w i t h i n 95 to 100%.  permeability  not  that  at t h i s p a r t i c u l a r s e c t i o n .  that s e c t i o n CC i s the  analyses  determine the c r i t i c a l liquefaction  is  i s l e s s than t h i s  l o c a t i o n , where the e f f e c t  severely,  would  at  of  zone depends on by how much the p e r m e a b i l i t y  Having recognised  felt  value  liquefaction  there  i s greater or l e s s e r than the c r i t i c a l  critical  the  values.  2  exists  value then l i q u e f a c t i o n would occur  the  that  by 1.4 to 1.5 times the s i g n i f i c a n t wave  l i q u e f a c t i o n and i f the p e r m e a b i l i t y  The  6.10  from F i g u r e s 6.1 t o 6.7 a l s o i n d i c a t e that f o r  that  this  and  s e c t i o n and the  l o c a t i o n d u r i n g storm a c t i v i t y . I f the p e r m e a b i l i t y than  1.  s e c t i o n i n terms of i t s water depth  height of the storm, r e g a r d l e s s of the k  Results  6.9  f i g u r e s , i t can be concluded  e f f e c t of the storm i s severe at one p a r t i c u l a r location  island  This  within  s p e c i f i e d 6m, 6 hour storm.  the  critical  entire  prevent  the porewater  serve as the minimum p e r m e a b i l i t y  liquefaction  to  island  value  of  required f o r the  F i g u r e 6 . 9 ; Maximum Porewater At the end of  Pressure Response of  6m 6 hour  Storm.  Island 1  84  Maximum Depth of  liquefaction  (m) cn  •rt  <D >  ro  cn -rt cn  a  cu  T3  -P  ro »  -2o  O  o ro  F i g u r e 6.10; Maximum Porewater At the end of  Pressure Response of  6m 6 hour Storm.  Island 1  85  Figure  6.11  shows  d i s t r i b u t i o n at s e c t i o n CC between  10"  the  residual  for  the  different  and 10"" cm/s with the i n i t i a l  3  each of these cases kept as 3.0 x 10" the  figure  porewater  that  the  critical  5  of  the  initial  values  of  k  z  compressibility in  m /kN. I t i s 2  seen  from  value of p e r m e a b i l i t y that i s  r e q u i r e d to l i m i t porewater p r e s s u r e development 100%  pressure  below  95  to  e f f e c t i v e s t r e s s f o r the s p e c i f i e d 6m, 6  hour storm i s around 8.0 x 10"" cm/s. I t i s i n t e r e s t i n g to note that the p e r m e a b i l i t y  required  to  limit  porewater  pressure  r a t i o to 65% or l e s s w i t h i n the e n t i r e i s l a n d f o r the s p e c i f i e d storm  is  10"  3  cm/s. I t i s o f t e n convenient to i n t e r p r e t these  r e s u l t s i n terms of c o e f f i c i e n t of c o n s o l i d a t i o n . coefficient  of  The  initial  c o n s o l i d a t i o n , Cy , r e q u i r e d t o meet the above 0  mentioned c r i t e r i a are 2.7 x 10"  2  m /s  and  2  3.4  x  10"  m /s  2  2  respectively.  6.3.1 Wave Induced Porewater Pressure Response of I s l a n d 4m, 6 hour  Storm  Figures  6.12  to  6.14  show  the  residual  porewater  pressure induced at the end of the 4m, 6 hour storm at AA, 10"  CC tt  and DD of i s l a n d  cm/s. I t i s evident  pressure as the  response earlier  difference  being  1 for different  k  1 to  section  v a l u e s of 10" and 3  z  from these f i g u r e s that the  porewater  show the same kind of steady decaying trend  response  with  the  6m  storm.  The  apparent  that the porewater pressure response shows a  steady decrease as the water depth i n c r e a s e s from 6m at s e c t i o n  86  F i g u r e 6.11; Porewater  Pressure Response At the end of  6m 6 hour Storm for D i f f e r e n t  Permeabilities.  87  Porewater  pressure  ratio,M/*v«  32r  36U  1  Figure 6 . 1 2 ; Section-AA; At the end of  1  1  .  R e s i d u a l Porewater 4m 6 hour Storm.  I Pressure Response  88  24H  28  H  32  36l Figure  6.13;  1  1  i  ,  S e c t i o n - C C ; R e s i d u a l Porewater At the end of 4m 6 hour Storm.  I Pressure Response  89  24  28  3 2  3$L  1  1  .  .  F i g u r e 6 . 1 4 ; S e c t i o n - D D ; R e s i d u a l Porewater At the end of 4m 6 hour Storm.  |  Pressure Response  90  AA to 9m at s e c t i o n  DD.  For analyses with k pressure r a t i o developed is  10%.  = 10"  z  cm/s,  3  the  at s e c t i o n AA  F u r t h e r , f o r the case with k  maximum  porewater  i s 19% and at s e c t i o n = 10"" cm/s  z  the  i n d i c a t e that the depth of l i q u e f a c t i o n at s e c t i o n AA and  i t reduces The  of  k  2  to 2m at s e c t i o n  plotted  in  Figures  6.15  i n Table 6.2 and  6.16.  maximum porewater pressure occurs water depth  i s 1.5  Section  AA  is  and  f o r the two the  6.5m  cases  results  are  Both f i g u r e s show that the  at  section  AA,  where  the  times s i g n i f i c a n t wave h e i g h t . could for  not the  be 4m  guaranteed  location  critical  l o c a t i o n at water depths l e s s than 6m.  as  island  i s concerned,  storm  directly  critical  the  results  DD.  maximum porewater pressure response  values are presented  since  there  as  can  the be  l o c a t i o n f o r the 4m  Figure  6.16  the minimum water depth  to i s l a n d  k  z  a l s o i n d i c a t e s that during the 4m  value of 10""  cm/s  the  storm.  depth of water beyound which l i q u e f a c t i o n would not the  a  However, as f a r  s u r f a c e i s 6m and a c c o r d i n g l y s e c t i o n AA can be t r e a t e d as critical  DD  i s approximately  storm,  the  occur  for  given by 2.42  times  the s i g n i f i c a n t wave h e i g h t . A d d i t i o n a l analyses were critical  section  for  the  conducted 4m,  p e r m e a b i l i t y values between 10" c r i t i c a l p e r m e a b i l i t y value  3  that  6  hour  and  at  storm  10"" cm/s  would  section  to determine  prevent  these  analyses are presented  i n F i g u r e 6.17.  the  for different the  liquefaction  w i t h i n the e n t i r e i s l a n d d u r i n g the storm a c t i v i t y . The of  AA,  results  I t i s evident  91  Maximum pwp Response  Section  Water  (d/Hf)  depth(m)  pwp R a t i o  Liquefaction depth(m)  (%)  k = 1 0" cm/s S  k = 1 6"*cm/s  AA  6  1 .50  19  6.5  CC  8  2.00  13  5.0  DD  9  2.25  10  2.0  Table 6 - 2 ;  Maximum Porewater of  Pressure Response At  I s l a n d 1 At the End of the 4m 6 hour  Sections Storm  92  Maximum Porewater  Figure  6 . 1 5 ; Maximum Porewater At the end of  pressure  Pressure  ratio,M/^  Response of  4m 6 hour Storm.  Island 1  93  F i g u r e 6 . 1 6 ; Maximum Porewater At the end of  Pressure Response of  4m 6 hour  Storm.  Island 1  94  Porewater O.l  pressure  ratio,^/GJO  o«6  0.4  o-8  ««0  5-  k*= 2 . 5x 1 0~* cm/s  6-  k= r  10"^ cm/s  32  3 6  s e c t i o n AA *  F i g u r e 6 . 1 7 ; Porewater Pressure Response At the end of 4m 6 hour Storm for D i f f e r e n t  Permeabilities.  95  that  the  porewater  critical  value  of  permeability  that  limits  pressure  ratio  to  w i t h i n 95 to 100% i s 2.5 x 10""  cm/s while a value' of 3.5 x'10"" cm/s i s s u f f i c i e n t porewater  pressure  ratio  to  values of i n i t i a l c o e f f i c i e n t m /s and 1.19 x 10" m /s 2  2  2  65%  effect  of  pressure  6.3  storm  results clearly the  storm,  to the Two D i f f e r e n t the  opportunity  characteristics  10"  3  on  the  Storms  to compare the  induced  porewater  at the s e l e c t e d s e c t i o n s AA, CC and DD. The  i n d i c a t e that the more severe the i n t e n s i t y  the higher the maximum porewater  w i l l be. For example, developed  x  respectively.  provides  response  limit  or l e s s . The corresponding  of c o n s o l i d a t i o n are 8.5  6.3.2 Comparison of Performance Table  to  the  f o r the  the maximum case k  of  pressure response  porewater  pressure  ratio  = 10" cm/s i s 19% (at s e c t i o n AA) 3  z  due to 4m storm, while i t i s 67% (at s e c t i o n  CC)  due  to  6m  storm. The  effect  of storm i n t e n s i t y  p e r m e a b i l i t y requirement The  f o r the  i s also c l e a r l y  criteria  discussed  p e r m e a b i l i t y r e q u i r e d to l i m i t porewater  4m  and  requirement  6m  storm  respectively.  i s more s t r i n g e n t  same trend i s apparent  earlier.  pressure r a t i o to  w i t h i n 95 to 100% i s 2.5 x 10"" cm/s and 8.0 x the  seen i n the  10""  cm/s f o r  T h i s i n d i c a t e s that the  i n the case of severe storms. The  i n the requirement  to  limit  porewater  pressure r a t i o to 65% or l e s s . To  understand  the  effect  of  the  storm i n t e n s i t y more  96  Water Section  depth  pwp r a t i o  (%)  Liquefaction  k = 1 0 cm/s z  depth(m)  k = 1 0""cm/s  3  z  (m)  H =4m  AA  6  19  47  6.5  6.5  CC  8  13  67  5.0  9.0  DD  9  10  65  2.0  8.5  s  H,=6m  H = 4m • a  T a b l e 6-3; Comparison of Maximum Porewater to Two D i f f e r e n t  Storms  * Hs = 6m'  Pressure Response  97  clearly, the a  i t is. perhaps important to compare the time h i s t o r y of  porewater response during the storms. Such a comparison particular  at  depth 3m below the i s l a n d top s u r f a c e at s e c t i o n  CC i s h i g h l i g h t e d i n F i g u r e 6.18. As can be seen from the pressure  builds  up  figure,  steadily  the  residual  i n the case with k  u n t i l the end of the storm and d i s s i p a t e s f a i r l y  z  porewater = 10~  cm/s  3  rapidly  after  the  storm a c t i v i t y . In c o n t r a s t to t h i s , the porewater pressure  in  the  case  with  k  attains liquefaction the  storm.  z  =  10"" cm/s b u i l d s up f a i r l y  l e v e l and d i s s i p a t e s rather  rapidly,  slowly  after  The c o n s t r a s t i n g behavior can be a t t r i b u t e d to the  d i f f e r e n c e s i n drainage c h a r a c r t e r i s t i c s . For  both values of k ,  pressure  z  build  up  is  the  rate  of  residual  porewater  found to be higher during the 6m storm  than the 4m storm. I t i s a l s o n o t i c e a b l e that f o r the case with k  z  = 10"" cm/s, l i q u e f a c t i o n  level  is  attained  within  first  h a l f an hour of the 6m storm, whereas f o r the 4m storm, 3 hours i s r e q u i r e d to a t t a i n the  liquefaction  l e v e l . The d i s s i p a t i o n  after  end of storms i s f a s t e r f o r 4m storm than the 6m storm. The  d i f f e r e n c e i n the r a t e of r e s i d u a l porewater pressure  b u i l d up can be equivalent  attributed  number  of  to  the  difference  in  N j, c<  the  c y c l e s of the r e f e r e n c e wave, s i n c e a l l  other p o t e n t i a l v a r i a b l e s remain the same i n i t i a l l y f o r the two storms. The major c o n t r i b u t i n g  f a c t o r to the r e s i d u a l  porewater  pressure i s the porewater p r e s s u r e generated due t o the of  cyclic  that ug i s  action  shear s t r e s s e s . I t can be seen from equation (3-12) directly  proportional  to  (Necj/N ) L  for a  given  T  —  1  »  i  1  ! — i  1  End of  Time  r  storm  (hours)  Figure € . 1 8 ; Time H i s t o r y Of Porewater  Pressure At 3m  Below Island Surface At S e c t i o n CC.  CO  99  porewater  pressure  ratio.  Since  the d i f f e r e n c e  in N  is  marginal at the s t a r t of the storms,  the  becomes  f o r the 4m and 6m storm at  N <j.  The  e  values  of  Ngq  dominating  u  s e c t i o n CC are 100 and 559 r e s p e c t i v e l y . net  porewater  pressure  response  Thus,  parameter  the  resulting  d u r i n g the storm a c t i v i t y i s  higher f o r the 6m storm than the 4m storm.  6.4 Wave Induced Porewater Pressure Response of I s l a n d 2 The porewater pressure response PP  to  W  of  island  2  at  at  selected  the end of the 6 hour storm  s i g n i f i c a n t wave height of 9m f o r the two d i f f e r e n t of  10"  and  3  the case with  It  f 10" cm/s.  to  at  depths  = 10"  ft  the  that the zone of l i q u e f a c t i o n  - 10"" cm/s i s deeper than with k  However, analyses with k  z  sections for  3  z  case with kx  with k  values  z  10"" cm/s and at a l l s e c t i o n s , except PP, f o r the  i s a l s o apparent  pressures  k  with  10"" cm/s are shown i n F i g u r e s 6.19 to 6.25. The  r e s u l t s i n d i c a t e that l i q u e f a c t i o n occurs at a l l  case with k  sections  =  10"  cm/s.  3  = 10" cm/s i n d i c a t e higher porewater 3  2  w e l l below the zone of l i q u e f a c t i o n  cm/s. T h i s kind of behaviour  dominant  z  i n the  influence  of  can  be  the d i f f u s i o n  of  than  attributed porewater  pressure w i t h i n the p r o f i l e . To i l l u s t r a t e the above argument, nodal  p o i n t , i n the form k . ( d u / d z ) , z  the  storm,  the  section  i n F i g u r e 6.26 f o r end  of the  the e f f e c t of the top drainage boundary i s f e l t  only up  z  v a l u e . I t appears  through  at the p a r t i c u l a r  QQ p r e d i c t e d by STABW3 a n a l y s i s i s presented the two cases of k  flow  that a t the  Porewater  o  0-2.  pressure o-4  o-6  ratio,"/^  o-S  10  40 •  SO  60  Figure 6 . 1 9 ; Section-PP; Residual  Porewater  Pressure Response At the end of 9m 6 hour  Storm.  Porewater pressure ratio,U/<*vo  io V  TOY  4-1  40  5 0 I-  60r  F i g u r e 6 . 2 0 ; Section-QQ; R e s i d u a l Porewater Pressure Response At the end of 9m 6 hour Storm.  k = 1 Cf cm/s 2  3  10  k = 1 0" cm/s r  4  20  £,  3 0  a D  AO  no  60 Figure 6 . 2 1 ; Section-RR;  Residual  Porewater  Pressure Response At the end of 9m 6 hour Storm.  Porewater  pressure  ratio, /0vo u  6oh Figure 6 . 2 2 ; Section-SS;  Residual  Porewater  Pressure Response At the end of 9m 6 hour  Storm.  104  Porewater pressure °  0-3  Q.4  0-6  Figure € . 2 3 ; Section-TT;  ratio,u/j^, 0-6  1-0  R e s i d u a l Porewater  Pressure Response At the end of 9m 6 hour Storm.  105  Porewater O  0-2  pressure ratio,M/fer^, O.J. 0.6 o-8 ».0  Figure 6.24; Section-UU;  Residual  Porewater  Pressure Response At the end of 9m 6 hour Storm.  Porewater O  Q-2  pressure Q>A  Figure 6 . 2 5 ; S e c t i o n - W ;  ratio,ty<rj  O-fc  «-8  Residual  0  M?  Porewater  Pressure Response At the end of 9m 6 hour Storm.  F i g u r e 6 . 2 6 ; S e c t i o n - Q Q ; Flow Through  Interface  At the end of 9m 6 hour Storm.  108  to a c e r t a i n depth, substantial with k  z  10 to 11 m and beyound t h i s depth there  downward  = 10"  3  flow.  It  is  i s a l s o seen that i n the case  cm/s, the flow through  the top drainage  boundary  i s much h i g h e r , as much as 10 times, than  i n the case with k,. =  10""  liquefaction  cm/s.  However,  presumably  because  in of  both  the  cases,  occurs  higher r a t e of porewater pressure  generation i n the top few metres. The depth of l i q u e f a c t i o n shallower  in  the  drainage through At  lower  porewater  case  with k  = 10"  z  elevations,  pressure  of  the  generation  difference for L  the  the  porewater  circumstance  diffusion  6.26  z  10""  the  same  as  that  pressure the  response,  e f f e c t of the top drainage  indicates  that  the  is  the  downward  cm/s.  This  is  because  z  = 10"  of  the  pressures  at  difference  flow 3  at  lower  cm/s than higher C  v  with value  The maximum porewater pressure 2  at  the  in  z  z  = 10"  response  end of the s p e c i f i e d  Table 6.4 f o r the two values of k plotted  high  the top few metres make the porewater  pressure higher at lower e l e v a t i o n s with k  island  a  especially  a s s o c i a t e d with i t . T h i s i n c r e a s e d downward d i f f u s i o n and porewater  of  of porewater pressure w i t h i n the p r o f i l e . F i g u r e  clearly  =  rate z  remains  e l e v a t i o n s i s higher i n the case with k k  the  two values of k are  boundary i s not f e l t e f f e c t i v e l y at depths, in  in  very low r / a ^ v a l u e s . Hence, the only f a c t o r that  could i n f l u e n c e the under  cm/s because of higher  the top boundary.  marginal because of the f a c t that N result  3  is  storm  at  3  cm/s. sections  of  i s summarized i n  c o n s i d e r e d . The r e s u l t s  F i g u r e 6.27. The porewater pressure response  are shows  109  Water  Sect ion  depth  Maximum pwp Response  (d/H )  Liquefaction  s  (m)  depth (m)  k = 1 0~ cm/s  k = 1 0 " cm/s  3  z  +  z  PP  6  0.67  0.0  7.0'  QQ  8  0.89  6.0  9.0  RR  10  1.11  8.0  11.5  SS  12  1 .33  10.5  12.5  TT  14  1 .55  11.0  1 3 .5  UU  16  1 .78  9.0  12.0  W  18  2.00  2.0  8.5  Table 6 » 4 ; Maximum Porewater of  Pressure Response At S e c t i o n s  I s l a n d 2 At the End of the 9m 6 hour Storm  1 10  F i g u r e 6.27;  Maximum Porewater At the end of  Pressure Response of  9m 6 hour Storm.  Island 2  111  the same kind of trend as b e f o r e ; that  i s , the  response  both cases i n c r e a s e s with depth of water u n t i l a c r i t i c a l i s reached and then decreases beyound that depth. The location  in  this  case  i s around  water depth i n terms of the  s e c t i o n TT and the c r i t i c a l  significant  wave  height  of the  s  the  limits  depth  crticical  storm i s approximately given by 1.50 H . I t i s a l s o found within  for  of data, the l o c a t i o n  that,  i s unique and i s not  dependent on the drainage c h a r a c t e r i s t i c s of the berm m a t e r i a l . T h i s agrees very well with the r e s u l t s obtained i n the analyses involving  i s l a n d 1.  It can be i n f e r r e d from F i g u r e water  beyound  which  6.27  liquefaction  that  would  not  the  depth  occur  of  f o r the  s p e c i f i e d storm, depends on the drainage c h a r a c t e r i s t i c s of the berm mate-rial. For the case with k terms that  of  significant  liquefaction  3  cm/s, the  10"'  high  as  cm/s, to  2.55  i s p o s s i b l e even at the  this  depth  the c l o s e s t storm, porewater 10"  3  analyses  appear  H . T h i s would mean that s  bottom  most  section  that  the  of  .  conducted at s e c t i o n TT of i s l a n d 2,  s e c t i o n to c r i t i c a l  reveal  in  i s increased  i s l a n d 2, as the maximum depth of i s l a n d 2 i s 2.34 Additional  depth  s  z  as  = 10"  wave height i s 2.10 H . I t would  i n the case of k =  considerably,  z  location  f o r the  permeabilities  9m,  required  6 to  hour limit  p r e s s u r e r a t i o to 95 to 100% and 65% or l e s s , are 2 x  cm/s and 3 x 10"  3  cm/s r e s p e c t i v e l y .  1 12  6.5 Wave Induced Porewater Pressure Response of I s l a n d 3 The porewater pressure response HH  to  storm  NN  cm/s are presented  the  case  with k with  k  predicted for k However,  k  z  values of  10"  12m, 6 hour  cm/s  3  that l i q u e f a c t i o n  and  = 10" cm/s and only at s e c t i o n s II to MM i n =  2  10"  cm/s.  3  The  zone  of  = 10" cm/s i s deeper than f o r k  liquefaction = 10" cm/s. 3  e  i s l a n d 2, higher  porewater p r e s s u r e s are p r e d i c t e d at depths below the  10""  cm/s.  presented The  f o r the case The  explanation  in section maximum  with k  z  zone  of  = 10" cm/s than f o r k 3  z  for this  behaviour  has  r  =  been  6.4.  porewater  pressure  i s l a n d 3 at the end of the s p e c i f i e d k  4  4  z  as i n the case of analyses i n v o l v i n g  liquefaction  10"  occurs at a l l s e c t i o n s i n  3  z  sections  i n F i g u r e 6.28 to 6.34.  i s observed  the case  selected  of i s l a n d 3 at the end of the s p e c i f i e d  f o r the two d i f f e r e n t  It  at  response  storm  a t s e c t i o n s of  f o r both  values  are given i n Table 6.5 and the r e s u l t s are p l o t t e d  of  in Figure  6.35. From storm  this  is felt  depth  figure,  i t i s apparent  severely at a c r i t i c a l  that the e f f e c t of the  location,  where the  water  i n terms of the s i g n i f i c a n t wave height i s approximately  given by 1.50 H , r e g a r d l e s s of the s  agree  with  islands  the  similar  results  k  z  value.  obtained  These  from  results  a n a l y s e s of  1 and 2.  Figure 6.35 suggests that the depth of water beyound which liquefaction 10"  4  would not occur  cm/s are 2.20 H  s  f o r the k  and 2.50 H  9  values of 10" cm/s and 3  z  respectively.  Porewater  pressure  ratio,U/crjo  so •  60Figure 6 . 2 8 ; Section-HH;  Residual  Porewater  Pressure Response At the end of 12m 6 hour Storm.  Porewater pressure r a t i o , U / o ^ 0;4 0-6 Q.A  Figure 6 . 2 9 ; S e c t i o n - I l ;  I  O  R e s i d u a l Porewater  Pressure Response At the end of 12m 6 hour Storm.  Porewater pressure  '  02  ratio,U/cr^J  o-6  0.4 •  •  o-a  1.1  1  10  k= z  I0" cm/s 4  20  k= x  I0" cm/s 5  30  4j  a  Q  4r0  SO  60 Figure 6.30; S e c t i o n - J J ;  R e s i d u a l Porewater  Pressure Response At the end of 12m 6 hour Storm.  O I  Porewater 0-2 1  pressure ratio,u/o^ ' 04 O-t O-fi i-O 0  1  1  1  r  •Oh  Figure 6 . 3 1 ; Section-KK; Residual  Porewater  Pressure Response At the end of 12m 6 hour Storm.  Porewater  °  kz=  °:  pressure  ratio,U/CJ^'  °-6  2  o-fl 10  10"^ cm/s  k= 2  10" cm/s  Figure 6.32; S e c t i o n - L L ;  a  Residual  Porewater  Pressure Response At the end of 12m 6 hour Storm.  o  Porewater 02  pressure ratio,M/Ov© 0-4 0.6 o-a 1.0  F i g u r e 6 . 3 3 ; Section-MM; R e s i d u a l  Porewater  Pressure Response At the end of 12m 6 hour Storm.  Porewater O  0-2  k= z  pressure 0-4  r a t i o , U/a^' o-S IO 0  0-6  10~ cm/s 3  k = 1u~ cm/s r  F i g u r e 6.34;  4  Section-NN; Residual  Porewater  Pressure Response At the end of 12m 6 hour Storm.  120  Water  Section  depth  Maximum pwp Response  (d/H )  L i q u e f a c t i o n depth (m)  s  (m)  k = 1 0" cm/s 3  x  k = 1 0" cm/s 4  z  HH  6  0.50  0.0  5.0  II  10  0.83  6.0  9.0  JJ  14  1.17  9.0  13.0  KK  16  1 .33  12.5  15.0  LL  18  1 .50  13.0  16.0  MM  22  1.83  9.0  12.0  NN  26  2.17  0.0  6.5  Table 6 - 5 ;  Maximum Porewater of  Pressure Response At S e c t i o n s  I s l a n d 3 At the End of the 12m 6 hour Storm  121  Maximum Depth of 4.  S  l i q u e f a c t i o n (m) 12 16  F i g u r e 6 . 3 5 ; Maximum Porewater At the end of  20  Pressure Response of I s l a n d 3  12m 6 hour Storm.  1 22  Additional establish  the  analyses value  were  of  k  conducted  at  section  LL  to  r e q u i r e d to prevent l i q u e f a c t i o n  2  w i t h i n the i s l a n d and a l s o to l i m i t porewater p r e s s u r e r a t i o to 65% or l e s s . The r e s p e c t i v e k 10"  6.6  cm/s  3  and 4.0  x 10"  2  v a l u e s are found  to  be  2.5  x  cm/s.  3  Summary and Comparison  of R e s u l t s of Analyses  On Sand Foundation Based  on  i s l a n d s on sand  the r e s u l t s of the a n a l y s e s i n v o l v i n g three  foundations,  the  following  conclusions  and  comments are made. The porewater pressure response during and a f t e r the storm s t r o n g l y depends on the storm c h a r a c t e r i s t i c s , the drainage and compressibility still  characteristics  water depth  particular  at  section,  of  sections the  the berm m a t e r i a l and the  of  interest.  Further,  at  a  pressure  response  at  a  porewater  l o c a t i o n depends on the depth of that island  location  the  top  s u r f a c e . As the depth i n c r e a s e s , the porewater p r e s s u r e  r a t i o developed at any i n s t a n t of time similar ratio,  from  to r/a  the  v o  distribution  of  shows  wave  a  steady  decay  induced c y c l i c  stress  .  The e f f e c t of a storm i s f e l t most s t r o n g l y at a location,  r e g a r d l e s s of the drainage and c o m p r e s s i b i l i t y  water depth to significant  specific  this  wave  location  height.  data i n v e s t i g a t e d , t h i s  is  given  by  1.50  . The  times  the  T h i s shows that w i t h i n the range of  critical  location  is  unique  s p e c i f i e d storm and f o r a severe storm the c r i t i c a l  for  a  location i s  123  deeper  than f o r a m i l d storm. For a given storm, the porewater  pressure response i n c r e a s e s with depth u n t i l the c r i t i c a l depth and decreases beyound the c r i t i c a l  water  The p e r m e a b i l i t i e s f o r a given i n i t i a l the  initial  limit  co-efficient  the  specified  maximum level  pressure  on  corrresponding  initial  the  to  limit  maximum  values  of  to  a  certain  porewater  permeabilities  the  and  co-efficient  storms  of  of  duration  6  pressure r a t i o w i t h i n the  i s l a n d s analysed to j u s t l i q u e f a c t i o n It  or  s i g n i f i c a n t wave height and  consolidation, required for d i f f e r e n t hours  compressibility  ratio  d u r a t i o n of the storm. Table 6.6 shows the the  depth.  c o n s o l i d a t i o n , Cyo , r e q u i r e d to  of  porewater  depends  water  (95 - 100%) and  to 65%.  i s e v i d e n t from these r e s u l t s that the requirements become  tougher as the storm becomes more severe. As s t a t e d e a r l i e r , dissipation k /m z  vo  as  initial  k /m  z  Vo  values  same  in  each  p r e s s u r e response  to  a  remains  m  porewater identical  co-efficient  in  of  the  rate  of  p r e s s u r e response i s consolidation,  C  v o  ,  Thus, i f a n a l y s e s were to be c a r r i e d out  Vo  with combinations of k k / vo  governs  and thereby the net porewater  o r , the  defined  the f a c t o r that  the  each  z  and m  such  that  the  ratio  case, then the r e s u l t i n g  specified  storm  would  be  case. T h i s p r i n c i p l e can be a p p l i e d to a l l  analyses presented so f a r . The p r e d i c t e d maximum depth of l i q u e f a c t i o n , that depth for  of  l i q u e f a c t i o n at the c r i t i c a l  the s p e c i f i e d storms of  values of k  z  duration  i s , the  l o c a t i o n of each 6  hours,  island  f o r the two  are presented i n Table 6.7, along with an estimate  124  I sland  Storm  95-100% (u/<r y L i m i t  No.  H (m)  k (cm/s)  1  4  2.5x1 0"  1  6  2  9  3  12  s  65% (U/<r^,)  v  k (cm/s)  C (m*/s)  t  C (m /s)  z  ve  Limit  V0  2  0.85x1 0~  z  3.5x1 0~  1 .20x1 0 T  8.0x1 0~  2.70x1 0"-  2  1.0x1 0"  ?  3.40X10"  2.0x10"*  6.80x1 0 "  2  3.0X10"  3  2.5X10"  8.50x1 0 "  2  4.0x10"''  4  4  3  Table 6 * 6 ; Drainage C h a r a c t e r i s t i c s  4  z  1 .02x10"' 1 .36x10"'  Requirement To L i m i t  Porewater  Pressure R a t i o To S p e c i f i e d L e v e l s For  Different  Strorms of D u r a t i o n  6 Hours.  £  125  Maximum Depth of L i q u e f a c t i o n  i I  Island  Storm  No.  H (m) s  STAB-W3  3  z  'Undrained'  Analysi s  K = 10" cm/s  (m)  1^ = 1 0' cm/s 4  Analysi s  1  4  0.0  6.5  7.5  1  6  0.0  9.0  10.0  2  9  11.0  13.5  13.5  2  13.5  16.0  i  3  Table 6-7;  1  P r e d i c t e d Maximum Depth of L i q u e f a c t i o n At Locations Different  6.0  Critical  Storms and P e r m e a b i l i t i e s  For I s l a n d s On Sand Foundations.  126  of  depth  of  liquefaction  from  analyses  assuming undrained  c o n d i t i o n s . I t i s i n t e r e s t i n g to note that f o r m i l d higher  k  values,  z  the e r r o r  storm  and  i n v o l v e d i n e s t i m a t i n g maximum  depth of l i q u e f a c t i o n assuming undrained c o n d i t i o n s i s h i g h . I t is quite possible  i n some i n s t a n c e s that  'undrained'  may p r e d i c t depth of l i q u e f a c t i o n t o be s e v e r a l metres, analyses  incorporating  analyses whereas  d i s s i p a t i o n e f f e c t s , such as STABW and  STABW3 a n a l y s e s , would p r e d i c t no l i q u e f a c t i o n at a l l . The c l a s s i c example i n v o l v i n g 4m, 6 hour in at  Table 6.7, that critical  f o r such  i s the  analysis  seen from the r e s u l t s  'undrained' a n a l y s i s p r e d i c t e d  liquefaction  s e c t i o n t o be as much as t o 7m, but STABW3 analyses  liquefaction  f o r the case  clearly  dissipation  case  storm. I t i s c l e a r l y  p r e d i c t e d only 6m f o r the case with  example  a  shows  effects  with  the  k k  2  z  = =  significance  10"" cm/s  and no  10" cm/s. The above 3  of  incorporating  to a v o i d unduly c o n s e r v a t i v e estimates of  depth of l i q u e f a c t i o n during wave l o a d i n g . The and  r e s u l t s a l s o suggest that  lower  k  z  v a l u e s , such as k  z  i n cases  of  severe  storms  < 10"" cm/s, the i s l a n d s are  p r a c t i c a l l y undrained i n the analyses and the estimates on  'undrained'  analyses  and  STABW3  analyses  However, f o r l o c a t i o n s other than the c r i t i c a l for  low  involved,  permeabilities,  there  may  i f the depth of l i q u e f a c t i o n  be  based  are the same. location,  significant  i s predicted  even errors  assuming  undrained c o n d i t i o n s . If  the wave p a t t e r n and the drainage c h a r a c t e r i s t i c s are  such that l i q u e f a c t i o n occurs at the c r i t i c a l  location,  then  127  the  depth of water beyound which l i q u e f a c t i o n would not occur,  i s dependent on pattern  the  itself.  drainage  characteristics  The r e s u l t s with k  the best estimate of the above depth terms  of  the  significant  estimate of the above depth  wave  = 10"  z  4  and  the  cm/s i n d i c a t e that  f o r the 6 hour  height  storm,  in  i s 2.50 H . The best s  f o r the case with k  2.20 H$. However, these estimates a r e based  wave  = 10" cm/s i s 3  z  on such  a  limited  number of analyses that they should be viewed with c a u t i o n . Finally, sand  the  foundations,  porewater  r e s u l t s of a n a l y s e s conducted indicate  pressures  liquefaction  important would  of  practically  to r e s o r t t o some  bring  down  high  are p o s s i b l e f o r drainage  of sand g e n e r a l l y encountered conditions  or  the  wave  on i s l a n d s on levels  characteristics  i n p r a c t i c e during moderate feasible  duration.  kind  remedial  of  induced  Thus,  porewater  suppressing  to  relatively  is  i t is that  p r e s s u r e s to  efficient  potential  wave  measures  a c c e p t a b l e l e v e l s . One of the popular and liquefaction  of  provide  means  of  coarse,  f r e e d r a i n i n g m a t e r i a l on top of the i s l a n d s u r f a c e ,  where the i s l a n d i s s u s c e p t i b l e to l i q u e f a c t i o n . The e f f e c t such measures i s examined i n the next  chapter.  of  1 28  CHAPTER 7  EFFECT OF ROCKFILL COVER ON WAVE INDUCED POREWATER PRESSURES  7. 1 I n t r o d u c t i o n One  of  the p r a c t i c a l  the wave induced porewater  remedial measures to b r i n g down  pressure to a c c e p t a b l e l e v e l s i s to  provide coarse cover on top of the i s l a n d s u r f a c e . T h i s chapter examines  the  effect  of r o c k f i l l  porewater  p r e s s u r e s . The choose of r o c k f i l l  has the advantages that porewater  i n reducing the wave induced as a s u i t a b l e cover  i t not only reduces  the  p r e s s u r e s s i g n i f i c a n t l y but a l s o s t a y s i n t a c t  being eroded For  analyses  respectively.  involving  Within  cover,  H  s  cover are taken as  the  liquefaction,  beyond 2.50 H  10  l i m i t e d range of data  7.2 E f f e c t of Cover  the  1m  investigated,  that i n cases  of  to water  = 10"" cm/s and  2.20  = 10" cm/s. 3  z  on Porewater  7.1  to  Pressure Response of  7.7 show the e f f e c t of 1m cover of a  coarse m a t e r i a l on the poreawter AA  z  and  1 To 6m, 6 hour Storm  Figures  from  cm/s  cover has to be extended  i n the case with k  s  i n the case with k  Island  without  the p e r m e a b i l i t y and the  the r e s u l t s from the p r e v i o u s chapter suggest possible  induced  heavily.  t h i c k n e s s of the r o c k f i l l  depths  wave  to  GG of i s l a n d  the two d i f f e r e n t  pressure response at  sections  1 at the end of 6m, 6 hour storm f o r  permeabilities  of  the  sand  fill.  It i s  129  Porewater p r e s s u r e 9  Figure  q-2.  Q-4*  ratio,4^vo  Q-6  o-B  i.o  7 - 1 ; S e c t i o n - A A ; E f f e c t of Cover on Porewater Pressure Response At the end of 6m 6 hour Storm.  130  Porewater p r e s s u r e  36l  "  '  ratio,iVo*vo  L  F i g u r e 7>2 ; S e c t i o n - B B ; E f f e c t of Cover on Porewater Response At the end of 6m 6 hour Storm.  Pressure  131  Porewater pressure  o  36I  02  o-4-  0^6  1  I  i  ratio, /**» u  o_-8  LP  1  1  F i g u r e 7 - 5 ; S e c t i o n - C C ; E f f e c t of Cover on Porewater Pressure Response At the end of 6m 6 hour Storm.  1 32  Porewater p r e s s u r e r a t i o , /0vo u  0-2.  Figure  ?>A;  0-4  Ob  O-fl  IO  S e c t i o n - D D ; E f f e c t of Cover on Porewater Pressure Response At the end of 6m 6 hour Storm.  1 33  o  36' F i g u r e 7- 5 ;  Porewater p r e s s u r e o-z o-i 0 6  I  1  1  ratio^/^o o-8  up  L  S e c t i o n - E E ; E f f e c t of Cover on Porewater Pressure Response At the end of 6m 6 hour Storm.  134  F i g u r e 7-. 6 ; S e c t i o n - F F ; E f f e c t of Cover on Porewater Pressure Response At the end of 6m 6 hour Storm.  135  Porewater p r e s s u r e r a t i o , / ^ o u  O  O-Z  0 « 4  1- no 2- 1m 3 - no 4 - 1m  32  0*6  O'A  i<0  coverl . , . - 3 , cover) * = / cover . . coverJ *= / k  10  k  1  c  0  m  c  m  s  s  36*  Figure  7>7 ; S e c t i o n - G G ; E f f e c t of Cover on Porewater Pressure Response At the end of 6m 6 hour Storm.  1 36  evident  from these f i g u r e s that the e f f e c t of the coarse cover  is  to reduce the porewater  in  some cases to n e g l i g i b l e Unlike  the porewater  the response pressure  with  ratio  occurs  decay.  significantly  and  levels. p r e s s u r e response without  cover  shows  that  the  the cover,  maximum  porewater  not at the top, but at some depth  the top of the o r i g i n a l steady  pressure response  i s l a n d s u r f a c e and t h e r e a f t e r  The r e d u c t i o n i n porewater  few metres i s a p p a r e n t l y due  to  the  from  shows  a  p r e s s u r e s at the top  influence  of  the  free  d r a i n i n g n o n - l i q u e f i a b l e cover a t t o p . It  i s also  seen that the porewater  i s much higher f o r the case with kz  the end of the storm cm/s than with k the k  r  = 10"  z  3  same depth of cover = 10"  3  p r e s s u r e response at  = 10"*  cm/s. T h i s i s as expected because  for  , the porewater  with'  cm/s has to be l e s s  pressure response  because  of  the  more  pervious  nature of the s o i l . T h i s a l s o makes i t c l e a r that the r e s u l t i n g response  for  the same depth of cover, depends on the drainage  c h a r a c t e r i s t i c s of the sand f i l l ; of  sand  fill,  the  smaller  the greater the p e r m e a b i l i t y  the  maximum  porewater  pressure  = 10"* cm/s,  analysis  shows  that with 1m coarse cover the maximum porewater  pressure  ratio  developed  response w i l l be. At s e c t i o n AA, f o r the case with k  contrast,analysis  at  the  shows  end that  of  z  the  without  would be l i q u e f a c t i o n up t o a depth 6.5m. 10"  3  storm 1m  porewater  pressure  51%.  In  coarse cover there  In the case with kz =  cm/s, a n a l y s e s with and without the cover  maximum  is  show  that  the  r a t i o developed at the end of the  1 37  storm are 11% and 47% r e s p e c t i v e l y . S e c t i o n CC i s of i n t e r e s t , because i t i s c l o s e s t critical  section  a n a l y s i s with indicate  up  f o r the  liquefaction  between the depth liquefy  f o r the 6m, 6 hour storm. The r e s u l t s of the  1m cover  that  case  and  with  k  2m and 3m, while without  10"'  cover,  t o a depth of 9m. In the case with k  without  =  2  cm/s  i s l i m i t e d to a zone of 1m extent  the maximum porewater pressure r a t i o with  to the  predicted  soil  = 10" cm/s, 3  z  from  analyses  cover are 14% and 67% r e s p e c t i v e l y .  r e d u c t i o n s i n porewater pressure response  would  are apparent  Similar at a l l  other s e c t i o n s of i s l a n d 1. The  quantitative  pressure response analyses  with  values of k  x  liquefaction, figures  in  comparison  at the end of  and without  the  the  6m,  6  maximum hour  porewater storm  from  the 1m top coarse cover f o r the two  are summarized i n that  of  Table  7.1.  In  the  event  of  i s , porewater pressure r a t i o of 100%, the  brackets  indicate  the  predicted  depth  of  liquefaction. Results  in  Table  7.1  porewater pressure response range  of  sufficient levels. cm/s,  permeability  show  that the suppression i n the  i s very  above  significant  10"  3  cm/s,  and  1m coarse cover i s  to b r i n g down the porewater pressures to  In  direct  the 1m top  contrast  coarse  cover  to  this,  is  f o r the  negligible  i n the case of ^=10"'  insufficient  to  suppress  l i q u e f a c t i o n at s e c t i o n BB to EE. In these cases, the t h i c k n e s s of  the cover has to be i n c r e a s e d s u f f i c i e n t l y  wave  induced  porewater  pressure  to  to b r i n g down the  l e v e l s c o n s i d e r e d to be  138  Maximum Porewater  Section  Pressure R a t i o , U/^c ,  k = I0~ cm/s  Ic^ = 1 CP* cm/s  3  z  No Cover  (%)  1m Cover  No Cover  1m Cover  AA  47  11  100(6.5)  51  BB  62  12  100(8.0)  100(1.0)  CC  67  14  100(9.0)  100(2.0)  DD  65 *  14  100(8.5)  100(2.0)  EE  43  13  10-0(7.0)  100(1.5)  FF  29  9  100(6.5)  50  GG  22  8  100(6.0)  40  Table  Effect  •  Of Cover On Maximum Porewater  Pressure  Response At S e c t i o n s Of I s l a n d 1 At the End Of 6m 6 hour Storm.  Note;  Figures  in b r a c k e t s  liquefaction  indicate  in metres.  the extent of the zone of  1 39  saf e. The case  of  r e d u c t i o n i n porewater  analyses  following  pressure  i n the  with coarse cover, may be a t t r i b u t e d to the  reasons;  Firstly,  the  presence  of  pervious  and  cover reduces the b u i l d up of the porewater the  response  easy  non-1iquefiable  p r e s s u r e because of  drainage at the t o p . Secondly, the cover reduces the  water depth and consequently the wave composition of the  storm  changes due to the breaking of higher waves. The changes i n the wave  composition  alters  the  depth and i n t u r n , the i n i t i a l e s t i m a t i o n of porewater 12),  increase.  shear  stress d i s t r i b u t i o n  v a l u e s of N  required  u  with  f o r the  pressure g e n e r a t i o n , as i n equation (3-  T h i s i n c r e a s e would r e s u l t  porewater  pressure g e n e r a t i o n . The reduced  pressure  generation  coupled  with  e f f e c t s give r i s e to the reduced  the  i n a slower rate of rate  of  porewater  increased d i s s i p a t i o n  residual  porewater  pressure  responses. Figure  7.8 c l e a r l y  i l l u s t r a t e s the e f f e c t of coarse cover  on the rate of r e s i d u a l porewater 6m,  6  hour  of k the  z  CC.  below  the  orinigal  top  I t can be seen from F i g u r e 7.8 that  v a l u e s , the r a t e of porewater storm  the  storm as compared to the rate of b u i l d up without  the cover at a depth 3m section  p r e s s u r e b u i l d up d u r i n g  activity  pressure  surface  at  i n both cases  build  up  during  i s reduced c o n s i d e r a b l y i n the cases with  the coarse cover on t o p . The r e d u c t i o n i s much more apparent i n the case with k  z  = 10"  3  cm/s than with k  z  = 10"" cm/s.  O  I  2  S  4  -  5  6  7  6  S  Time (hours) Figure 7 - « 3 ;  E f f e c t of Cover on Time H i s t o r y Of Pore Pressure At 3m Below O r i g i n a l  I s l a n d Surface At S e c t i o n CC.  o  141  7.2.1 E f f e c t Of P e r m e a b i l i t y Of Cover M a t e r i a l F i g u r e 7.9 shows the i n f l u e n c e of the p e r m e a b i l i t y the  cover  m a t e r i a l on the induced  at s e c t i o n AA of i s l a n d It  porewater pressure  1 at the end of the 6m, 6  i s c l e a r l y seen that there  the  materials  as  seem  reductions  i n the porewater pressure  way to reduce porewater  not  pressures  r e s o r t to the use of cover  storm.  i s i n c r e a s e d from 10 cm/s to  100 cm/s. Hence i t appears that does  response  i s no d i f f e r e n c e i n the response  when the p e r m e a b i l i t y of the cover  cover  hour  of  use to  of  highly  produce  pervious  any f u r t h e r  response and the e f f i c i e n t to  desired  with an i n c r e a s e d  levels  thickness.  i s to  142  Porewater pressure r a t i o , / ^ e o.Z C4. 0<6 0'<9 T u  O  t>o  k = 10" cm/s r  5  k = 10 to 100 cm/s 2 - / k = 10"* cm/s L l £ = 10 to 100 cm/s c  z  Figure  "7-.9 ; S e c t i o n - A A ; E f f e c t Porewater  of Cover P e r m e a b i l i t y on  Pressure Response At the End of  the 6m 6 hour Storm.  143  7.3 E f f e c t of Cover on Porewater Pressure Response of Island  1 t o 4m, 6 hour Storm  Figures  7.10 to 7.12 show the e f f e c t of 1m top coarse  cover on the porewater pressure response DD of i s l a n d  1 a t the end of 4m, 6 hour storm. The r e s u l t s show  that the p r e d i c t e d r e d u c t i o n s i n with  1m  coarse  cover  s e c t i o n AA, the c r i t i c a l k  z  =  10""  at s e c t i o n s AA, CC and  are  porewater  pressure  very s i g n i f i c a n t . For example, at  s e c t i o n f o r the 4m, 6 hour storm,  of  the  storm  developed  at  i s 36%, while a n a l y s i s without cover  that there would be l i q u e f a c t i o n to a depth of At the other s e c t i o n s , the response  for  cm/s, the r e s u l t s from the a n a l y s i s with the cover  shows that maximum porewater pressure r a t i o end  response  resulting  the shows  6.5m.  porewater  pressure  with the '1m cover are n e g l i g i b l e f o r both the cases of  permeability. Table 7.2 compares maximum porewater pressure with and without  response  the 1m of coarse cover at the end of the 4m, 6  hour storm at s e c t i o n s AA, CC and DD of i s l a n d 1. The  results  sufficient  suggest  that  the  1m  of  coarse  cover i s  to b r i n g down porewater p r e s s u r e s to safe l e v e l s f o r  the range of p e r m e a b i l i t y g r e a t e r than  10"* cm/s d u r i n g the 4m,  6 hour storm.  cm/s, the need  coarse  cover  In the case of kj, = 10" protection  s i n c e the developed  presence  of  are  f o r the  to reduce porewater p r e s s u r e s i s not  necessary  cover  3  porewater  unlikely  pressure  to exceed  without  the  20% d u r i n g the 4m  storm. But i f the p e r m e a b i l i t y of the sand f i l l  i s around  10"*  cm/s, i t i s e s s e n t i a l to have a top coarse cover p r o t e c t i o n and  1 44  Porewater p r e s s u r e  Figure  ratio,u/ovo  7 . i 0 ; S e c t i o n - A A ; E f f e c t of Cover on Porewater Pressure Response At the End of the 4m 6 hour Storm.  145  Porewater p r e s s u r e r a t i o , U / a ^  O  o>2  o«4  0-6  0-8  J-O  F i g u r e 7 • U; S e c t i o n - C C ; E f f e c t of Cover on Porewater Pressure Response At the End of the 4m 6 hour Storm.  146  Figure  S e c t i o n - D D ; E f f e c t of Cover on Porewater Pressure Response At the End of the 4m 6 hour Storm.  147  Maximum Porewater  Section  k= z  Pressure R a t i o , o/o-^ t  10" cm/s  = IO  S  No Cover  1m Cover  -4  (%)  cm/s  No Cover  1m Cover  AA  19  10  100(6.5)  35  CC  13  5  100(5.0)  24  DD  10  4  100(2.0)  18  Table 7>2 ; E f f e c t Of Cover On Maximum Porewater  Pressure  Response At S e c t i o n s Of I s l a n d 1 At the End Of 4m 6 hour Storm.  Note; F i g u r e s  in b r a c k e t s i n d i c a t e the extent of the zone of  liquefaction  i n metres.  1 48  a  cover  of  thickness  1m  is  s u f f i c i e n t to reduce porewater  p r e s s u r e s to a c c e p t a b l e l i m i t s . As mentioned e a r l i e r , the cover has to be extended beyond water depth 1Om times  H)  the  storm.  given  by  to e l i m i n a t e the p o s s i b i l i t y of l i q u e f a c t i o n  s  4m  (as  2.50 during  7.4. E f f e c t of Cover on Porewater Pressure Response of I s l a n d 2 The e f f e c t  of  the  1m  thick  coarse  cover  porewater pressure response at s e c t i o n s PP to W the  end  of  the  on  the  of i s l a n d 2 at  s p e c i f i e d storm are shown i n F i g u r e s 7.13  to  7.19. These  figures  indicate  that  there  is  considerable  r e d u c t i o n i n the porewater p r e s s u r e response as a r e s u l t of the top  coarse  cover  and a l s o  the response has the same trend as  seen before i n the a n a l y s e s of i s l a n d 10~  3  to  cm/s,  the r e s u l t s  reduce  the  liquefaction negligible 10"" the  indicate  porewater  levels  at  cm/s,  the  =  pressure sections  response  RR,  SS  to  just  below  and TT and to very z  =  e f f e c t of cover i s to reduce the t h i c k n e s s of  zone of l i q u e f a c t i o n  significantly.  In  these  cases,  the  i s l i m i t e d to a l o c a l i z e d zone of a few metres i n  e x t e n t . For example, at s e c t i o n liquefaction  TT, the t h i c k n e s s of  i s reduced from 13.5m  zone of l i q u e f a c t i o n original  z  that the e f f e c t of 1m cover i s  l e v e l s at other s e c t i o n s . But i n the case with k  liquefaction  of  1. In the case with k  the  zone  to 7m and the l o c a l i z e d  extends from depth 2m to depth 9m from the  sand berm top s u r f a c e .  149  Porewater p r e s s u r e ratio,u/^7c' o oa. 0.4e-6 o>8 uo  *  •  •  Figure 7 - i 3 ; Section-PP; Effect  of Cover on  Porewater Pressure Response At the end of  9m 6 hour Storm.  150  Porewater p r e s s u r e r a t i o ,  u  /«^o'  F i g u r e 7«14- ; S e c t i o n - Q Q ; E f f e c t of Cover on Porewater Pressure Response At the end of 9m 6 hour Storm.  151  Porewater p r e s s u r e r a t i o , 0_ o-2 o«4 c-6 o-8  i-O  F i g u r e 7<15; S e c t i o n - R R ; E f f e c t of Cover on Porewater Pressure Response At the end of 9m 6 hour Storm.  Porewater pressure r a t i o , / ° v c O Q'2 0.4. o-6 ©•* \-o u  *  '  t  *  F i g u r e 7 - 1 6 ; S e c t i o n - S S ; E f f e c t of  Cover  Porewater Pressure Response the end of 9m 6 hour Storm.  153  Porewater pressure r a t i o , A ^ » U  Figure  Section-TT;  E f f e c t of Cover on  Porewater Pressure Response At the end of  9m 6 hour Storm.  154  Porewater p r e s s u r e r a t i o , / « w O o-2 o-4 o«6 o>8 i.o u  60  1 -no 2- lm 3 - no 4- 1m  coverl y-^ coverj coverl ^ coverj  1 0~* cm/s  z  1  OP  4-  cm/s  z  F i g u r e 7-*l<8; S e c t i o n - U U ; E f f e c t of Cover on Porewater Pressure Response At the end of 9m 6 hour Storm.  Porewater pressure 0  0-3  •  Figure  Q-4  •  Q-6  ratio,U/o^ o-fi  1-0  •  S e c t i o n - W ; E f f e c t of  Cover  Porewater Pressure Response the end of 9m 6 hour Storm.  156  The comparison  of maximum porewater  pressure response  and without  the 1m t h i c k coarse at s e c t i o n s PP to W  2  end  at  the  of  the storm  maximum  occurs around of the  porewater  pressure  1m t h i c k n e s s i s not s u f f i c i e n t is  10""  cover i s r e q u i r e d  to  prevent  However, i n the case of k is  sufficient  activity.  without  cover,  r a t i o i n the case with cover cover  to suppress l i q u e f a c t i o n when  cm/s.  An i n c r e a s e i n t h i c k n e s s of  liquefaction  in  these  cases.  = 10~ cm/s, a cover t h i c k n e s s of 1m 3  z  only beyond water depth of 14m and an i n c r e a s e d  cover would be necessary up to water depth porewater  case  s e c t i o n TT. R e s u l t s a l s o i n d i c a t e that the  permeability  island  i s presented i n Table 7.3. I t i s  evident from the r e s u l t s t h a t , as i n the the  of  with  14m  to  bring  down  p r e s s u r e s to s a f e r l e v e l s d u r i n g the s p e c i f i e d  storm  157  Maximum Porewater  Section  Pressure R a t i o ,  k = 10" cm/s  k,=  3  x  No Cover  1m Cover  U/^ ,  (%)  I0" cm/s 4  No Cover  1m Cover  PP  70  11  100(7.0)  100(2.0)  QQ  100(6.0)  41  100(9.0)  100(2.5)  RR  100(8.0)  90  100(11.5)  100(4.5)  SS  100(10.5)  92  100(12.5)  100(6.0)  TT  100(11.0)  95  100(13.5)  100(7.0) "  UU  100(9.0)  27  100(12.0)  100(4.5)  W  100(2.0)  16  100(8.5)  100(3.0)  Table  7*3 ; E f f e c t  Of Cover On Maximum Porewater  Pressure  Response At S e c t i o n s Of I s l a n d 2 At the End Of 9m 6 hour Storm.  Note;  Figures  in b r a c k e t s  liquefaction  indicate  in metres.  the extent of the zone of  1 58  7.5 E f f e c t of Cover  on Porewater  Pressure  Response of I s l a n d 3 F i g u r e s 7.20 to 7.26 show cover  on  the porewater  the  the  permeabilities.  porewater  indicate  pressure  specified  Even  MM  for  the  is  2  = 10"  storm  of  the  two  the  results  case  when  k  z  =  10""  cm/s.  pressure are i n d i c a t e d  cm/s at s e c t i o n s J J t o LL.  3  pressure response at  i s l a n d 3 at the end of the storm with and without  1m of coarse cover. I t appears sufficient  coarse  occurs to c o n s i d e r a b l e depths  Table 7.4 shows the maximum porewater sections  1m  for  apparent,  L i q u e f a c t i o n or h i g h l e v e l s of porewater for the case with k  of  though s i g n i f i c a n t changes i n  response  that l i q u e f a c t i o n s t i l l  at s e c t i o n s II to  effect  pressure response at s e c t i o n s HH t o NN  of i s l a n d 3 at the end of different  the  that  1m of coarse cover  i s not  to suppress l i q u e f a c t i o n d u r i n g the s p e c i f i e d  storm  for both p e r m e a b i l i t i e s c o n s i d e r e d . However, i n the case of 10~  3  cm/s,  1m  cover  is sufficient  ( s e c t i o n LL) although i n c r e a s e d cover depths  above  sufficient  18m.  In the case of k  only beyond water  depth  beyond water depth  is z  22  required  for  k  z  18m  water  = 10"" cm/s, 1m cover i s m  and  for  depths the t h i c k n e s s of cover has t o be i n c r e a s e d .  shallower  Porewater pressure  o  o.a.  e-4  ratio, /0vc u  o-6  o-s  Figure 7 - 2 0 ; Section-HH; Effect  i.o  of Cover on  Porewater Pressure Response At the end of  12m 6 hour Storm.  160  o  Porewater p r e s s u r e r a t i o , u/tf*.' p-2 04. Q-6 6-8 10  Figure 7 . 2 i ; S e c t i o n - I I ;  E f f e c t of Cover on  Porewater Pressure Response At the end of  12m 6 hour Storm.  Porewater pressure r a t i o , Wo^'  c  O  O-Z  F i g u r e 7-22',  O-A-  0'6  Section-JJ;  o*fi  l-O  E f f e c t of  Cover  Porewater Pressure Response the end of  12m 6 hour Storm.  Porewater p r e s s u r e r a t i o , / ° v c u  O  o-2  F i g u r e 1.23;  0-4-  0-6  O-S  l-O  S e c t i o n - K K ; E f f e c t of Cover on Porewater Pressure Response At the end of  12m 6 hour Storm.  1 . 0  Porewater pressure r a t i o , u/tr l o-2 O'd0'6 v  O  F i g u r e 1'2A;  S e c t i o n - L L ; E f f e c t of Cover on Porewater Pressure Response At the end of  12m 6 hour Storm.  Porewater pressure O A  60  1- no 2- 1m 3 - no 4- lm *  ratio,u/^  O b  cover? coverj cover? coverJ * • •  1 0  -3  c m / s  z  k  1  0  -4  c  m  /  s  .  *  F i g u r e 7-25; Section-MM; E f f e c t of Cover on Porewater Pressure Response At the end of  12m 6 hour Storm.  Porewater pressure r a t i o , O o-2 OA0 6 o-8  F i g u r e 7-2^;  «o  S e c t i o n - N N ; E f f e c t of Cover on Porewater Pressure Response At the end of  12m 6 hour Storm.  166  Maximum Porewater  Sect ion  Pressure  k = 1 Cf cm/s  No Cover  Q  k=  a  z  Ratio,^/a^ ,  x  1m Cover  (%)  10" cm/s 4  No Cover  1m Cover  HH  80  12  100(5.0)  100(1.0)  II  100(6.0)  90  100(9.0)  100(4.0)  JJ  100(9.0)  98  100(13.0)  100(6.0)  KK  100(12.5)  100(1.0)  100(15.0)  100(7.0)  LL  100(13.0)  100(2.5)  100(16.0)  100(7.5)  MM  100(9.0)  22  100(12.0)  100(5.0)  NN  18 .  Table  100(6.5)  5  7-4-j E f f e c t  Of Cover On Maximum Porewater  Response At S e c t i o n s Of  18  Pressure  I s l a n d 3 At the End Of  12m 6 hour Storm.  Note;  Figures  in brackets  liquefaction  indicate  in metres.  the extent of the zone of  167  CHAPTER 8 EFFECT OF FOUNDATION CONDITIONS ON POREWATER PRESSURES  8.1 Response of I s l a n d 1 The 6 hour clay of  porewater  pressure response at the end of the 6m,  storm at s e c t i o n s AA and CC of i s l a n d  1  sitting  on  a  foundation i s presented i n F i g u r e 8.1 and 8.2 f o r the case k  =  z  10"  cm/s.  3  p r e s s u r e response  These  figures  i s very much dependent on the undrained shear  s t r e n g t h Sg of c l a y  immediately  apparent  harder  that  show that the porewater  the  the  limiting  the  porewater  porewater  p r e s s u r e s i s the one corresponding to the r i g i d at  The  greater  response  instance,  be.  clay,  It i s also  pressure  For  will  below the sand f i l l .  s e c t i o n - AA,  the  magnitude  maximum  of the base.  porewater  p r e s s u r e r a t i o developed at the end of the storm i s 66% and 42% for  S  hand,  values of 50 kPa and 30 kPa r e s p e c t i v e l y . On the other  u  at  section  porewater  CC,  pressure  the  ratios  corresponding are  l i m i t i n g wave induced porewater are  maximum  45% and 24% r e s p e c t i v e l y . The  p r e s s u r e s at s e c t i o n AA and  CC  95% and 50% r e s p e c t i v e l y . The  reason  f o r the  porewater  pressure  response being  d i r e c t l y dependent on the undrained shear s t r e n g t h the f a c t that is  induced  related  basis  (Seed  strength  of  i s due  to  i n c u r r e n t e n g i n e e r i n g p r a c t i c e the shear modulus to  the  et  al,l970).  the  undrained shear s t r e n g t h on a one-to -one  clay  Any  increase  increases  in  undrained  shear  the shear modulus and hence  a l t e r s the shear s t r e s s d i s t r i b u t i o n with  depth  in  the  sand  168  Porewater  7L Figure  pressure  ratio, /<*7o u  1 1 1 1  <3 * I ; S e c t i o n - A A ;  R e s i d u a l Porewater  At the end of 6m 6 hour Storm.  I Pressure Response  169  Porewater  51 Figure  1  8-2. ; S e c t i o n - C C ;  pressure  1  ratio,u/a^>  1  1  R e s i d u a l Porewater  At the end of 6m 6 hour  Storm.  1 Pressure Response  170  fill. Figure  8.3 c l e a r l y demonstrates the r e s u l t i n g  the shear s t r e s s r a t i o d i s t r i b u t i o n  i n the sand f i l l  AA at the s t a r t of the storm, as a r e s u l t of undrained of  the  the  at s e c t i o n  increase  in  shear s t r e n g t h from 30 kPa to 50 kPa. The consequence increase  i n shear s t r e s s d i s t r i b u t i o n as i n the above  case, w i l l be r e f l e c t e d not only on the i n i t i a l but  increase i n  also  in  the  calculation  of  values  of  N  u  the number of waves of the  e q u i v a l e n t storm Ncq i n such a manner  that  N  values  L  become  smaller and N<j value becomes l a r g e r . e  For the f i r s t kPa -  and  example, at s e c t i o n AA, the N l a y e r of the sand 50  kPa  is  fill 10.77  corresponding values of Neej are Now,  value corresponding to  L  f o r the cases of S and  10.0  1076  and  under these c o n d i t i o n s , the f a c t o r  increases  porewater  with  pressure  increasing  generation  S  u  (see  being  respectively. 1086  30 The  respectively.  (Ne*j/N ) which governs L  the r a t e of porewater pressure generation time,  u  at  any  instant  of  and so does the rate of equation  3 12). -  This  i n c r e a s e d r a t e of porewater pressure generation at the s t a r t of the  storm  results  the case of higher S  i n g r e a t e r porewater pressure response f o r u  value.  171  Shear s t r e s s  0>08  71 Figure  Q.IO  ratio^e/^v*  Q.I2  o-l-i O.lfc  i  c?'3; S e c t i o n - A A ;  t  i  i  Shear S t r e s s R a t i o  At the s t a r t of  Q.l8  Distribution  6m 6 hour Storm.  1 72  CHAPTER 9  SUMMARY AND  CONCLUSIONS  A simple method of a n a l y s i s f o r the wave  induced  porewater  pressures  is  determination  presented.  c o n s i d e r s both d i s s i p a t i o n and g e n e r a t i o n e f f e c t s loading.  It  pressures modulus  soil  wave  properties,  namely  shear  modulus,  element computer program STABW3. The interpolation  function  for  bulk  incorporated program uses  the  porewater  field.  The  computer  artificial depths  during  and volume c o m p r e s s i b i 1 i y . The method was  a cubic polynomial pressure  The method  a l s o c o n s i d e r s the e f f e c t of i n c r e a s i n g porewater  on  into a f i n i t e  program was  islands b u i l t  12m,  21m  and  used to analyse three  different  up to a set down depth of 6m 31m  respectively.  The  in  water  islands  were  subjected to d i f f e r e n t p a t t e r n s of storm waves each of 6 duration.  The  porewater  pressures  induced  in  each  i s l a n d s by the storm waves were computed f o r d i f f e r e n t characteristics incorporating  of a  non  the  berm  material.  liquefiable  coarse  The  examined. A b r i e f examination  hours of the  drainage  effect  of  cover on top of the  i s l a n d s u r f a c e on the induced porewater pressure also  of  response  of the e f f e c t of  c o n d i t i o n s on the induced porewater pressure response  was  foundation was  also  reported. In  this  study, the r e l a t i v e d e n s i t y of the berm m a t e r i a l  has been assumed to be 50%.  T h i s means  that  the  sand  has  a  1 73  relatively dramatise practices to  70%.  low the  resistance effect  tend At  liquefaction  wave  action.  which  Current  tends  higher  will  be  relative  greatly  same kind of behavoir w i l l  be  densities,  reduced obtained.  to  construction  to give r e l a t i v e d e n s i t y of the range from  the  liquefaction  of  to  the  50%  zone  of  and phenomenically  the  Hence,  the  numerial  values cannot be c o n s i d e r e d to be g e n e r a l l y a p p l i c a b l e .  The  following  general  c o n c l u s i o n s can be drawn from  the r e s u l t s of the a n a l y s e s . These were based on such a l i m i t e d number of analyses and  therefore  they  have  to  viewed  with  caut i o n .  1. For homogeneous i s l a n d berms on sand • foundations, the e f f e c t of  the  waves  l o c a t i o n . The primarily storm and  is  felt  s t r o n g l y and  water depth,  D,  to  c  this  s e v e r e l y at a p a r t i c u l a r critical  location  dependent on the s i g n i f i c a n t wave h e i g h t , H , s  i s given approximately  by D  c  = 1.50  H  s  is  of the  regardless  of  the drainage c h a r a c t e r i s t i c s of the berm m a t e r i a l .  2.  For  islands  on  sand foundations, the water depth beyound  which l i q u e f a c t i o n would not occur d u r i n g a storm on wave parameters and material.  For  a  of  H, s  storm  beyound  dependent  the drainage c h a r a c t e r i s t i c s of the berm of  6  volume c o m p r e s s i b i l i t y of 3 x 10" terms  is  hours d u r a t i o n and 5  m /kN, the water 2  for i n i t i a l depth,  in  which l i q u e f a c t i o n would not occur, i s  174  given approximately 10"  3  by 2.20 H  and 2.50 H  s  for  s  k  values  2  of  cm/s and 10"" cm/s r e s p e c t i v e l y .  3.  For  islands  on  sand  c h a r a c t e r i s t i c s of the berm porewater  pressure  foundations,  material  response  required  below  the to  drainage limit  liquefaction  the  levels,  dependent on the wave c h a r a c t e r i s t i c s ; the requirements  is  becomes  more s t r i n g e n t the more severe the storms.  4. The e f f e c t  of  coarse  material  reduce  cover  non  liquefiable placed  relatively  in  permeability  porewater of  the  pressure  berm  draining  on top of the berm slope i s to  the porewater pressure response  reduction  free  d u r i n g wave l o a d i n g . The  response  for  a  given  m a t e r i a l i s dependent on the cover  t h i c k n e s s p r o v i d e d . Moreover, the i n c r e a s e i n the p e r m e a b i l i t y of  the  cover  significant Hence,  material  reduction  the  in  not  the  seem  to  porewater  produce  pressure  further response.  i n order to suppress porewater pressure response  desired levels, of  does  i t i s more e f f e c t i v e to i n c r e a s e the  coarse  cover r a t h e r than to r e s o r t  to the  thickness  to the use of much  more p e r v i o u s m a t e r i a l as cover.  5.  The  suitable  thickness  l i q u e f a c t i o n at a p a r t i c u l a r depends  on  and the  wave  completely  the  of  cover  required  to  suppress  s e c t i o n of i n t e r e s t during a storm  drainage c h a r a c t e r i s t i c s of the berm m a t e r i a l  parameters. suppress  The  cover  liquefaction  thickness for  required  given  to  drainage  175  characteristics storm  than  given for  6.  f o r a milder storm  storm,  i t i s higher  more p e r v i o u s  For islands  response shear  on  response rigid  o f t h e same d u r a t i o n ;  for less  clay  will base.  a  severe  Again  for a  p e r v i o u s berm m a t e r i a l  foundations,  d u r i n g t h e wave l o a d i n g  the clay  i s greater f o r  than  material.  strength of the clay  harder  a  o f t h e berm m a t e r i a l ,  the  porewater  i s dependent  immediately  below  foundation, the higher the  be, up t o t h e l i m i t i n g  pressure  on t h e u n d r a i n e d  the sand porewater  berm.  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