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Modulus reduction dynamic analysis Purssell, Tanis Jane 1985

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MODULUS REDUCTION  DYNAMIC  ANALYSIS  by. TANIS JANE  PURSSELL  A . S c . , U n i v e r s i t y Of B r i t i s h  THESIS SUBMITTED  Columbia,  IN PARTIAL FULFILMENT OF  THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE Civil  We  accept to  this  STUDIES  Engineering  thesis  the r e q u i r e d  as conforming standard  THE UNIVERSITY OF BRITISH COLUMBIA July  ©  Tanis  1982  Jane  1985  Purssell,  1985  In  presenting  requirements  this f o r an  Columbia,  I  available  for  permission p u r p o s e s may or  her  of  Department  of  reference  and  study.  I  by  this thesis my  written  Civil  7 October  1985  copying the  of  Head of  It for  is  further  financial  Engineering Columbia  gain  the  of  British  it  freely  agree for  Department  understood  permission.  make  this thesis my  of  University  shall  The U n i v e r s i t y of B r i t i s h 2075 Wesbrook P l a c e V a n c o u v e r , Canada V6T 1W5  Date:  the  Library  granted  allowed without  fulfilment  the  representatives.  publication  partial  that  extensive  be  in  advanced degree at  agree  for  thesis  that  that  scholarly  or  by  copying  shall  not  his or be  ABSTRACT A s e m i - a n a l y t i c a l method o f predicting  both the  deformations, reduction  the  i s presented.  induced  in s o i l s  inertia  induced  m a g n i t u d e and The  of  The  the  to  deformations modulus  induced  reduction  cyclic  included  the during is  modulus w e r e . i n v e s t i g a t e d  The  of of  the  occurring  tailings  in a laboratory  These  San  studies  capable that  F e r n a n d o Dam  of  during  reductions  i n the  the  the  but  only  The  of  the  appropriate tests  the  cyclic  from c y c l i c  on  strain loading  conditions, to  was  provide  used  dynamic  shaking the  modulus  of  up  to  loading  table  test  earthquake  dynamically  modulus  stress-strain  yields realistic  deformations.  during  showed t h a t  reproducing  the  computing a s u i t a b l e  stress  analysis  deformations  Upper  on  appropriate  laboratory  magnitude  induced  modulus r e d u c t i o n  slope  the  effects  loading an  loading.  i s determined  field  sufficient  earthquake  modulus  pattern  T h r e e methods of  modulus  duplicate  reductions estimates  the  a  The  dynamic  from  post-cyclic  that  loading.  and  earthquake  determined  samples.  i n which  induced  simulate  in a static  magnitude  soil  tests  i s b a s e d on  through  is utilized  undisturbed  approach,  earthquake  of  modulus.  modulus  predict  of  capable  r e d u c e d modulus t o  during  also  reduced  reduced  analysis  pattern  forces developed during  deformations are  selection  analysis,  analysis  approach which uses a  softening of  dynamic  of and  a  the model  of  of F e b r u a r y ,  reduction induced to  predict  1000  the 1971.  analysis  is  deformations  and  times  may  be  required. and  Unfortunately,  inadequacies  appropriate through were  in  the  necessary  the  analyses.  to  provide  and f i e l d  Although full  verification  method  assessing loading.  data  equipment  required  that  n o t be d e t e r m i n e d Some  the  entirely  assumptions  t h e r e d u c e d modulus v a l u e s u s e d i n  these case  the r e l i a b i l i t y  of the t e s t i n g  investigations.  in selecting  demonstrate  earthquake  available  modulus r e d u c t i o n s c o u l d  laboratory  of  limitations  studies  were,  of the proposed  and s i m p l i c i t y  the performance  hence,  unable  method, t h e y do  o f t h e a n a l y s i s as  of s o i l  a  structures during  iv  TABLE OF CONTENTS  Page ABSTRACT  i i  L I S T OF TABLES  vi  L I S T OF FIGURES  v i i  ACKNOWLEDGEMENTS  ix  Chapter  1  INTRODUCTION  Chapter  2  EFFECTS OF CYCLIC LOADING ON  2.1  Liquefaction  2.2  Cyclic  Chapter  3  1 SOIL  4 6  Mobility  12  CURRENT METHODS FOR PERFORMANCE AND  EVALUATING  ESTIMATING  EARTHQUAKE  EARTHQUAKE  INDUCED DEFORMATIONS  16  3.1  P s e u d o - s t a t i c Method  16  3.2  Newmark A n a l y s i s  19  3.3  S e e d ' s Dynamic  3.4  Effective  Chapter  Path Approach  S t r e s s Dynamic  Analysis  21 24  PROPOSED MODULUS REDUCTION DYNAMIC ANALYSIS  26  4.1  Methods  27  4.2  Deformation  Chapter 5.1  4  Stress  5  f o r C a l c u l a t i n g Modulus R e d u c t i o n Analysis  Procedure  29  VERIFICATION OF MODULUS REDUCTION ANALYSIS  38  Tailings  38  Model T e s t s  5.1.1  Laboratory Tests  42  5.1.2  D e t e r m i n a t i o n of R e d u c e d M o d u l i  51  5.1.3  R e s u l t s of D e f o r m a t i o n  58  Predictions  V  5.2  Analysis 5.2.1  Chapter  6  REFERENCES  o f t h e Upper Description  San F e r n a n d o Dam  o f Dam and  70  Earthquake  Deformations  71  5.2.2  Previous Investigations  74  5.2.3  Modulus R e d u c t i o n  79  SUMMARY AND CONCLUSIONS  Analysis  89 93  vi  L I S T OF  TABLES  Page Table  5-1  Summary of H y p e r b o l i c P a r a m e t e r s o f Ottawa  Table  5-2  Soil  Parameters  f o r San F e r n a n d o  Dam  Soils  Sand  50 78  vii  L I S T OF  FIGURES  Page Figure  2-1  L i q u e f a c t i o n Due  t o Monotonic or C y c l i c  Loading  Figure  2-2  T y p i c a l S t r e s s Path Followed  During  Liquefaction  Figure  2-3  T y p i c a l S t r e s s Path Followed  During  Cyclic  7 9  Mobility  13  Figure  4-1  P o s t - C y c l i c Modulus A p p r o a c h  28  Figure  4-2  Cyclic  Strain  Approach  30  Figure  4-3  Pore Pressure  Approach  31  Figure  5-1  Model C o n t a i n e r  Figure  5-2  Grain  Figure  5-3  Observed D i s p l a c e m e n t s of Model  Figure  5-4  Soil  Response D u r i n g  Fine  Ottawa  Soil  Response D u r i n g  Fine  Ottawa  Soil  Response D u r i n g  Figure  Figure  5-5  5-6  Size Distribution  F i n e Ottawa Figure  Figure  5-7  5-8  5-9  Ottawa  Soil  Response  F i n e Ottawa Figure  5-10  Soil  Before  F i n e Ottawa  Before  Pressure  Pressure  Pressure  Pressure  and A f t e r C y c l i c Pressure  and A f t e r C y c l i c  Sand - C o n f i n i n g  Response  43  Pressure  and A f t e r C y c l i c  Sand - C o n f i n i n g  Pressure  Tests  = 50 kPa  =  45  Tests 100  kPa  46  Tests  = 150  Monotonic T r i a x i a l  Sand - C o n f i n i n g  Response  Slope  Monotonic T r i a x i a l  Sand - C o n f i n i n g Before  . 41  Monotonic T r i a x i a l  Sand - C o n f i n i n g  Fine  Sand  Monotonic T r i a x i a l  Sand - C o n f i n i n g  Response D u r i n g  Soil  of T e s t  Sand - C o n f i n i n g  Soil  F i n e Ottawa Figure  40  kPa  47  Tests  = 200  kPa  48  Loading = 50 kPa  52  Loading = 100  kPa  53  Loading = 150  kPa  54  viii  Figure  5-11  Finite in  Figure  5-12  Element  G r i d of T a i l i n g s Model  used  Static-Stress Analysis  Deformations  59  P r e d i c t e d by P o s t - C y c l i c M o d u l u s  Approach  61  Figure  5-13  Deformations  P r e d i c t e d by C y c l i c  Figure  5-14  Deformations  P r e d i c t e d by  Figure  5-15  Deformations  P r e d i c t e d by C y c l i c  Pore  S t r a i n Approach  62  P r e s s u r e Approach  63  Strain  Approach  w i t h Volume Change C o r r e c t i o n  64 67  Figure  5-16  A c c e l e r o g r a m of N i i g a t a E a r t h q u a k e  Figure  5-17  Deformations  o f Upper  San  Fernando  Dam  during  Earthquake Figure  5-18  Major  Figure  5-19  Typical and  Soil  72 Types  i n Upper San  Fernando  R e s p o n s e of H y d r a u l i c  Undrained T r i a x i a l  Figure  5-20  Liquefied  Figure  5-21  Shear  Figure  5-22  Finite  Fill  Dam  in Drained  Tests  77  A r e a s o f Dam  80  Strain Potentials Element  Analysis Figure  5-23  Predicted  Figure  5-24  Required  Figure  5-25  Predicted  Grid  82  used  of Upper San  in Static-Stress  Fernando  Dam  Deformations  Potentials  84 85  Strain Potentials Deformations  75  using  87 Required S t r a i n 88  ix  ACKNOWLEDGEMENTS I would in  initiating  towards require  The  t o thank D r . P e t e r  this  study  i t s completion. thanks  laboratory  soil  M. B y r n e  for his  Vaid  direction  and  and h e l p  Edwin  Chung  also  i n performing the  tests. assistance provided  by a N a t u r a l  R e s e a r c h C o u n c i l o f Canada p o s t g r a d u a t e  gratefully  guidance  and f o r making c r i t i c a l c o n t r i b u t i o n s  Dr. Yogi  for their  financial  Engineering is  like  appreciated.  S c i e n c e s and scholarship  1  CHAPTER 1 INTRODUCTION The of  v a r i e t y o f methods u s e d t o a s s e s s  soil  structures  substantially  in  accurately  dynamic be  a  that  tried The  simple  "equivalent"  which  induced  recognized  the  initially  accounted  models  of  soil  d e v e l o p m e n t and cyclic  loading  behavior  behavior. effective  use may a  need  earthquake  and i s c a p a b l e  of  the  correct approach  The  recognized  have  of  increasingly  soil  behavior.  i n Newmark's  analysis  earthquake  induced  of  other  behavior  finite  of  soil  and d e a l t  pseudo-static  of s o i l s  element  similar  importance on  the  pseudo-  force  stress  stresses  the  in  dependent  or  in  used  nature  strain  hyperbolic  analyses models  force  for in total  was t h e n  assessing  beginnings  by a t e m p o r a r y  The n o n - l i n e a r  incorporating  their  under  a s s u c h a method.  more r e a l i s t i c  transient  t h e y do  behavior  deformations  response  permanent  was r e p l a c e d  for soil  rudimentary  loadings.  by  soil  current  that  The p r o p o s e d modulus r e d u c t i o n  dynamic  to incorporate  increased  T h e r e a p p e a r s t o be  method  i s presented  rather  analysis,  analysis  predict  i s b a s e d on a c t u a l  t o dynamic a n a l y s i s  static  s i m p l i f y i n g assumptions  structures.  and p a t t e r n .  From t h e i r  has  o r a r e so complex and c o s t l y t h a t  p r e d i c t i n g earthquake  magnitude  loading  response  However, many o f t h e s e  realistically  relatively  performance  years.  so many  l i m i t e d to c r i t i c a l  for  of  or  loading  earthquake  recent  methods e i t h e r make not  to  t h e dynamic  analyses  stress-strain pore  response  with,  was  first  pressure during by Seed  2  in  h i s dynamic  various These  s t r e s s path  rigorous recent  generally  are  commonly  modulus  presented  as  earthquake  used  a  simple  induced  loading. the  Because  the  progressive  represented suited  f o r the  develop  the  created  method  may  limited The analysis  be  used of  the  basic  analysis  the  are  of  the  of  are  cyclic  of  expected  from  which  to  is  may  dynamic  inertia  forces  included  to  cyclic  cyclic  especially  soils  modulus,  the  loading  is  the also  the  by  an  proposed  resulting  experience  from only  shear.  proposed  in conjunction  during  results  deformations  earthquake  soil  response  to Seed's s t r e s s p a t h  predict  that  is  modulus  effects  method  reduced  changes d u r i n g  is utilized to  loading  that  approach  is similar  effects  to p r e d i c t the  soils  pore p r e s s u r e  r e d u c e d modulus strain  since  use.  predicting  develop during  in  and  analysis  reduced  t o medium dense  pressures  of  the  during  this  pore  their  for  f o r the  degradation  loose  cyclic  model  that  analyses.  practice,  s o f t e n i n g of a  i n pore pressure  selection  loading  deformations  a n a l y s i s of  during  appropriate  the  in  often requiring  dynamic  Although  r e d u c e d modulus,  However,  of  a l s o account  stiffness  rise  significant  excitation.  cyclic  by  the  dynamic  to j u s t i f y  realistic  deformations.  on  many o t h e r s  geotechnical  method  to simulate  by  complex,  verification  and  dynamic e x c i t a t i o n , i t can forces  in  later  stress  extremely  reduction  p r i m a r i l y intended  inertia  effective  lacking sufficient  The  is  non-linear  methods  parameters not  a p p r o a c h and  modulus  reduction  method e x c e p t with  a static  induced  that  a  stress-  deformations.  3  This  thesis explains  modulus  reduction  basis  two  of  intended earthquake  the  theory  method  and  case h i s t o r i e s :  to  behind  determines  a laboratory  model  the  response  loading,  and  the  experienced  substantial  earthquake of  February,  the  of  Upper  downstream 1971.  development its validity shaking  saturated San  Fernando  movements  of  the  on  table  study  tailings Dam during  the  to  which the  4  CHAPTER 2 EFFECTS OF An  earthquake  cyclically has  and  cause  Although  two  the  The  of t h e  extent  pressure  generation. loading  rise  loading  and  on  When u n d r a i n e d  of t h e t e n d e n c y shear.  As  strains  will  only  occur  i f the pore  onset  of e i t h e r  of  two  of the the  damage has  pore  resulted  changes i n pore  the magnitude of of  prevail  pore  to c o n t r a c t  pore  when  cyclic increase  subjected  pressures increase,  develop.  the  pressure  during  water p r e s s u r e s w i l l  soil  induced  rise.  from  mechanism  conditions  forces  pressures.  earthquake  pressure  d e p e n d s on  structure  inertia  pore  cause  creating  soil  transient  resulting  the  a  excess  w i t h pore  of d e f o r m a t i o n s  s o f t e n s and  the  However, s i g n i f i c a n t  soil  strains  p r e s s u r e s i n c r e a s e enough t o t r i g g e r distinct  phenomena:  liquefaction  and  mobility",  the or  mobility.  The  two  extensively to  of  loading  in  severe earthquake  of a s a t u r a t e d s o i l ,  cyclic  cyclic  i t generates  associated  pressures during c y c l i c  because  stresses  development  SOIL  dynamic  b o t h of t h e s e c o n d i t i o n s w i l l  from d e f o r m a t i o n s  to  other  shear  effects:  d e f o r m a t i o n s , most  pore  any  reversing  basically may  or  CYCLIC LOADING ON  terms,  i n the  describe  "liquefaction"  literature  a variety  Confusion  particularly  Although  the  condition  of  term  has  and  "cyclic  u n f o r t u n a t e l y have  o f phenomena by d i f f e r e n t arises  over  the  traditionally  zero e f f e c t i v e  stress within  term referred a  soil  been  occur used  investigators. "liquefaction". to  either  or  to  a  slope  5  failures being  which  used  to  resemble  the flow  describe  several  i t i s now  phenomena  observed  during  cyclic  the  " l i q u e f a c t i o n " f o r t h e d e v e l o p m e n t o f 5 o r 10  strain  in a cyclic  described  by  test  pore  when  confining  sand  flows  stresses  during  resembling  and  the  cyclic  as  a  equal  to  liquid  (1983), flow  that  until  likewise,  failure.  resistance the  For the purpose  of  will  be  r e s u l t from a l o s s  reserved in  "cyclic  mobility"  was  first  introduced  by  accumulate  in  cyclic  He  described  the  stiffness  however,  load  tests  progressive  soil  when  the  become  as  on  sand.  reduction  subjected  strains  progressively  1iquefact ion.  to  strength  undrained  develop  shear to  that  liquefaction,  shear  referred  i n 1965 t o r e f e r t o t h e s t r a i n s  saturated  a  loading.  term  as a  the  wherein  Casagrande  mobility  load  ( 1 9 7 5 ) , on t h e o t h e r phenomenon  "liquefaction"  failures  been  mass a r e a s low a s t h e r e d u c e d  Chern  term  a  percent  in a cyclic  become  Poulos  t o use  has  percentage of i t s shear  as a c o n t r a c t i v e  the flow  The  and  liquefaction  on t h e s o i l  Vaid  thesis,  describe  liquefaction"  momentarily  Castro  manner  acting  liquefaction  "Initial  loses a large  in a  resistance.  this  presssures  defined  saturated  test.  I t h a s become c u s t o m a r y  Seed and L e e (1966) a s t h e s t a g e  stresses.  hand, have  and  load  tests.  fluid,  laboratory term  loading  of a v i s c o u s  in  to  cyclic  associated  during  each  significant  as  loading.  with  cyclic  loading  cycle.  those  cyclic of  a  Unlike mobility They  resulting  may, from  6  The  distinction  necessary in  each  the  and  the  is entirely  two  state  because  between  the  soil,  static  induced  as  shear  response during  mechanism o f  different.  phenomena a r e  of  In  defined  stress.  cyclic  the  ratio,  realistically to  the  two  the  confining  the  must  associated  with  initial  the  soil  dynamically  mechanisms  phenomena  of  pressure  simulate  predict  different  by  is  involved  development  differently  To  and  mobility  development  void  the in  cyclic  by  loading  involved  strain  addition,  affected quite  deformations,  development  l i q u e f a c t i o n and  of  strain  be  fully  understood.  2. 1  L i q u e f a c t ion Liquefaction  or  strain  driving soil's or  softening  shear shear  shock  conversion  strength loading.  of  the  than  the  the  undrained support fails applied  the  soil  conditions  the  soil  strain  stresses  i n the  2-1  initiate  flows  contractive presence  proportion  of  undrained monotonic, strength  of  results drained  shear.  may  be  For  softening the  soil  from  a  condition  contractive  during  i s able  conditions,  cyclic  loading  schematically  liquefaction failures.  i n a manner  the  cyclic  occurs mass  under d r a i n e d  illustrates  of  s u b s t a n t i a l l y lower  t r i g g e r i n g s t r e s s or  Figure to  strength  although  a sufficient  liquefaction,  in  condition  and  shear  required  during  loss  shear  Thus,  undrained.  occur  mass from a p r a c t i c a l l y  strength  in-situ  only  i f a substantial  is lost  undrained  shear.  when  and  failure I t can  The  undrained  drained  flow  soils.  stresses  to a p r a c t i c a l l y soils,  is a  resembling  a  to it is the  During viscous  7  fluid  until  the  strength.  Because  unidirectional Poulos,  the  liquefaction  This  mass  constant  flow  are  as  strength  is  i t h a s been  continuously  velocity.  effective  stress,  L I Q U E F A C T I O N  UJ  OC yv> K  <  M O N O T O N I C  /  A  hi X V)  \  D U E  ( C a s t r o and  at  strength  steady-state exists a  shear  failure  shear  when  constant  strength  s t r e s s e s reached during  large  the reduced  constant  The s t e a d y - s t a t e  V) v>  suggested  that  deforming  as the reduced involve  i s the undrained  i s the strength  normal e f f e c t i v e  low  deformations  displacements,  during  strength.  constant  stresses  1975, and P o u l o s e t a l , 1985) t h a t  reached  soil  shear  the  volume,  stress  and  i s a f u n c t i o n of  and i s n o t z e r o .  T O  L O A D I N G  \ \  \  LIOUEFACTION OCCURS WHEN S T R E N G T H DROPS BELOW DRIVING S H E A R STRESS  D R I V I N G S H E A R S T R E S S  ^ L I Q U E F A C T I O N C Y C L I C  D U E  T O  L O A D I N Q  STRAIN  Figure Liquefaction  In with  Due t o M o n o t o n i c  laboratory cyclic  a rapid  development  increase of  axial  2-1  or C y c l i c Loading (Schematic) ( f r o m P o u l o s e t a l , 1985)  load tests,  liquefaction  i n pore pressures strains.  accompanied  During  cyclic  i s associated by a  sudden  loading,  the  8  progressive stress  state  envelope. the of  i n c r e a s e i n pore of the s o i l  stress  the e f f e c t i v e  envelope  or  typical  stress  of  are  had  straining.  exceeded.  strained  liquefaction.  referred The  to this  initiation  of f a i l u r e ,  strain  develops d u r i n g such  on  that  the  soil.  initial Additional  liquefaction, straining  Significant applied  shear  stress  path  the  the  behavior  strains  stop a t the onset flow  loading,  on  by  dilation  loading  and  as  limited limited  rapidly  phase  of s t r a i n  s t r e s s and c a u s e  stress  of  upon  of d i l a t i o n .  the  of t h e  arrest  reduction each  of  further in  stress  were o n l y o b s e r v e d  The  depends  1983) t o c a u s e a  found  further  failures  after  the  triaxial  during  develop  the  testing  however,  dilation  i s not reached  limited  flow, the  when  t o cause  s t r e s s was o f s u f f i c i e n t  pore  cycle.  when  the  magnitude t o exceed the  reversals  followed during these a d d i t i o n a l  shown on F i g u r e 2-2.  of  (1983),  ( V a i d and C h e r n ,  accumulations  cyclic  static  is  was f o u n d  during  failure  o f t h e sample and t h e p r o p e r t i e s  cyclic  accompanied  pressures  they  state  limits  type of  and a l t h o u g h  value  If  during  arrested  steady-state  failures  reached  V a i d and C h e r n  sufficiently  the  liquefaction.  the  were o f t e n  to  when  F i g u r e 2-2 i l l u s t r a t e s a  during  until  failure  i s triggered  prior  line.  is  the  reaches a c r i t i c a l  0 ^ / 0 3 ' ,  deformation continue  They  liquefaction  ratio,  followed  flow deformations  samples  of the s o i l  the e f f e c t i v e  towards  liquefaction  steady-state  path  d e f o r m a t i o n s may equipment  soils,  state  stress  the  steady-state  that  t o move s t e a d i l y  For contractive  effective  water p r e s s u r e c a u s e s  to  occur.  cycles  The  of l o a d i n g  FIGURE 2 - 2  Effective Stress Path of Cyclic Loading Test on Anisotropically Consolidated Loose Sand  10  The cyclic  m a g n i t u d e and r a t e  of  pore  pressure  l o a d i n g depends on t h e m a g n i t u d e o f t h e c y c l i c  number o f c y c l e s a p p l i e d , t h e e f f e c t i v e the  level  the  cyclic  of  static  deviator  significant. cyclic do  stress,  pore  stress of  excess  i n the s o i l .  Chern  pressure  = o  3 c  is  consolidated  become e q u a l  always  cyclic  less  loading w i l l  the r e s i d u a l  soon a s l i q u e f a c t i o n the  pore p r e s s u r e  loading  also  than t h e  cyclic  loading  occur,  they  generation  and  reached  during a  magnitude  of the  depends of  on  static  the r e s i d u a l during  the shear value  liquefaction  i s g i v e n by  ' (1 - (Kc ~ 1 ) ( 1 - s i n 4>' )  value  shear than  stresses,  the e f f e c t i v e of  the  pore  will  the  confining the  periodically  cyclic  residual  pore  confining  pressure.  pressure  generated  during  cyclic  and w i l l  l o a d i n g as  Thus, t h e maximum  loading w i l l  residual pressure.  f l u c t u a t e about a mean v a l u e  has o c c u r r e d .  during  samples  t o the e f f e c t i v e  However, t h e t r a n s i e n t v a l u e  exceed  liquefaction  Ur, developed  of c y c l i c  the presence of s t a t i c  during  The  (1981) showed t h a t  pore pressures,  in isotropically  pressure  during  magnitudes of  do  pore p r e s s u r e s  and  stress are  reversals  c o n f i n i n g s t r e s s e s and on t h e l e v e l  the termination  pore In  the  reached  Ur Only  stress  load, the  stress i s greater  number o f c y c l e s o f l o a d i n g .  the excess  after  shear  shear  stress reversals during  When  of  pressures  effective  The r e l a t i v e  i n c r e a s e the r a t e of pore p r e s s u r e  magnitude  specified  stress.  the s t a t i c  occur.  significantly  shear  during  confining pressures  s t r e s s and t h e s t a t i c  When  deviator  not  the  buildup  be h i g h e r  value  of  than t h e  11  residual  value given  The  susceptibility  density o ',  consolidation  high  The  required  low  levels  of  loading,  of  defined  be  This  liquefaction. at  high  Chern, sample that  static  static the  increase  only  susceptibilities  density,  a  soil  r e a d i l y at higher  not  will  confining  to liquefaction  be  pressure  The shear  reduction stress  so c l o s e  susceptible  static  at  shear.  At  the  resistance  to  cyclic  shear  i n a f i x e d number as  the  static  related to  caused  reductions  of shear the  For higher  in  i n the r e s i s t a n c e  deviator  stress  i n the  stress  may  resistance  to  to liquefaction ( V a i d and  state  effective stress  s t r e s s or only  stress  of  l e v e l s has been a t t r i b u t e d the i n i t i a l  cycles  levels  shear  the  stress  reduced  by a r e d u c t i o n  i n the s t a t i c  to the c r i t i c a l  cyclic  of  reversals.  increases  by s u b s t a n t i a l  a small  level  generation  stress  of  shear,  i s apparently  1983) t o t h e f a c t t h a t is  to greater  level  increases  s h e a r , however,  accompanied  stress,  on t h e l i q u e f a c t i o n p o t e n t i a l  the  flow deformation  magnitude of the shear static  by  generally  pore  relative  Higher e f f e c t i v e  s  be s u s c e p t i b l e  shear  with  t o cause  increases.  of s t a t i c  varies  liquefaction,  more may  given  r .  stress will  sand  relatively  rate  that  a  stresses.  influence  loose  stress,  relative  behavior  l e v e l s of c o n f i n i n g  at  by t h e c o n s o l i d a t i o n  correspond  Thus, a s o i l  lower c o n f i n i n g  of  soil  shear  For a f i x e d  contractive  pressures.  of  static  pressures  liquefaction.  exhibit  at  of a given  to l i q u e f a c t i o n i s affected  and t h e i n i t i a l  3 c  to  by C h e r n .  of  the  ratio  line  a few c y c l e s o f  12  loading  are  required  liquefaction  2.2  to  for  during  refers  to  undrained  cyclic  it  is  pore not  during  required  mobility  which  exhibit  also  develop  when  effective  stress  ratio  line  occurs  strains  No  and  of  cyclic  Unlike  development  increase  loss  in  arrest  developed  the  behavior, of  is  Although  i n medium dense t o d e n s e  the  of of  in strength  mobility.  than c o n t r a c t i v e  have  strains  accumulation  sudden A  large  sand.  a gradual  occurs.  sands a f t e r  state  stress for  dense  followed  of  cyclic  Vaid  and  Chern  the  sands it  may  liquefaction  to cause d i l a t i o n  initiated  reaches a c r i t i c a l  critical is  value  of  higher  the  than  (1983) showed t h a t  on  of  flow  shows  a  typical  mobility.  effective stress  effective  that  the  stress  stress soil  of  effective  f a i l u r e s in loose  When t h e  ratio line  value  for  mobility  arrest  2-3  the  effective  significant cyclic  Figure  when  the  of  the  critical  is  onset  and  cyclic  The  soil  mobility  sands  during  mobility  the  ratio.  ratios defining  coincide.  the  loose  by  of  on  progressive  onset  d i l a t i v e rather  in  formation  loading.  the  generally  liquefaction.  in  of  a  liquefaction, cyclic  effective  stress  r e a c h the  straining.  Like  stress  by  axial strains  initiate  sufficient  further  the  or  to  cyclic  to  tests  characterized  each c y c l e  pressures  the  loading  pore p r e s s u r e s accompanied strains  state  .  mobility  liquefaction,  stress  occur.  Cyclic Mobility Cyclic  the  state  sands path passes  experiences  a  <H-  0.4  08  1.0  1.2  (cT,'+cr3)/2  FIGURE 2 - 3  24  1.4  (kg/cm ) 2  (from Chern,  1981)  Effective Stress Path of Cyclic Loading Test on 00  Anisotropically Consolidated Dense Sand  14  significant loading  increase  cycle.  substantially go  to zero.  by  Chern.  This  static  shear  that  stress  mobility  and or  each  may  momentarily  when the  become  continues,  of  occurs.  additional  reduction  of  strains  of  pore  additional associated  cyclic  cyclic  pore p r e s s u r e  i s determined  value defined  by  of  (Vaid  mobility  the  whether and  level  by of  i t results  Chern,  1983).  pore p r e s s u r e s t r a n s i e n t l y exceed load  equal  the  during  cycle. to  the  deviator  soil  The  transient  confining  stress  is  pore  pressures  zero.  When  tends  to  dilate  and  the  pore  soil  to  cyclic  mobility  is  reduce.  The  susceptibility  influenced  by  static  deviator  develop  liquefaction  r e s i d u a l value during  mobility,  rise  momentarily  each c a u s i n g  i s independent  the  generally  the  loads,  residual  mobility,  pressures  to  development  and  single  pressures  axial strain  accumulation  residual pressure  cyclic  loading  i n the  i n the  cyclic  large  the  pressures  of  of  pore  a  mobility.  around  from c y c l i c  change  dilation  pore pressures  fluctuate  developed during  minor e f f e c t i v e s t r e s s  results  r e s u l t s i n the  The  strain  unloading,  the  Repetition  with c y c l i c  the  causing  reloading  pressures.  During  Upon  accompanied  strains,  the  However, l i t t l e  Subsequent strains  in  the  the  a  effective confining  shear.  increase  of  the  cyclic  stress divided  Although cyclic  by  increased  load  mobility twice  p r e s s u r e s and  confining  necessary ratio,  the  by  to  defined  effective  the  level  pressures  cause  cyclic  as  cyclic  minor  the  principal  15  stress  at  increasing mobility This  the  start  confining  generally  same  trend  of c y c l i c  stress.  loading,  Thus,  decreases with with  usually  the  resistance  increasing  confining  decreases to  confining  pressure  was  with  cyclic  pressure.  observed  for  liquefaction. Like soil the  to c y c l i c soil  static its  the resistance  of  varies  of s t a t i c  the l e v e l  b u t n o t i n t h e same manner.  Whereas  resistance  level  resistance  with  stress  mobility  to l i q u e f a c t i o n , the  can  reduce a s o i l ' s  to c y c l i c  static  mobility  shear.  This  o c c u r r e n c e and magnitude of shear Poulos  (1977)  strains  that  found  constitute  that  tends  to  behavior stress  without  cyclic  resistance  bias i n  levels  increase is  a  of  to l i q u e f a c t i o n , with  related  reversals.  stress  mobility  high  of  to  Castro  the the and  r e v e r s a l , the l a r g e r  do n o t o c c u r .  16  CHAPTER 3 CURRENT METHODS FOR EVALUATING EARTHQUAKE PERFORMANCE  AND  ESTIMATING EARTHQUAKE INDUCED DEFORMATIONS  3.1  Pseudo-static The  pseudo-static  analysis during  used  over of  excitation.  against  consider  evaluating  the  from  soils  strength  In  that  a  selected  of the on  interest.  permanent of  not  the  analysis  of e a r t h only  a  loading  that  may  dams  against  capabilities,  factor  sliding  For method during  however, came i n t o  method  weight,  the e f f e c t  of t h e earthquake i s  o f t h e assumed  termed  the  appreciable  loading.  horizontal static  of the weight  Today  calculations  t o s u f f e r from  cyclic  of  and does n o t result.  to preliminary design  loss during  of  structures  method was t h e s t a n d a r d  expected  by an e q u i v a l e n t  fraction  method  t o p r e d i c t s e v e r a l dam f a i l u r e s .  the p s e u d o - s t a t i c  fraction  of  seismic  of  limited  are  or s t i f f n e s s  represented as  during  safety  i t s inability  original  The method y i e l d s  Its predictive  use i s g e n e r a l l y  for  the  the performance  years the pseudo-static  earthquakes.  its  failure  was  the magnitude of d e f o r m a t i o n s  40  doubt  method  f o r assessing  seismic  safety  Method  force failure  seismic  calculated mass.  coefficient,  The is  the b a s i s of the l e v e l  or s e i s m i c i t y i n the region  The e q u i v a l e n t  force  static  a n d t o a c t i n one d i r e c t i o n assumed  failure  i s then performed  mass.  only,  is  to  be  through the c e n t r o i d  A conventional  to determine  asssumed  the  slope  factor  stability of  safety  17  against is  failure.  generally The  method  A factor  believed  initial  of s a f e t y  t o be a d e q u a t e  widespread  f o r seismic  design  (Seed,  acceptance  resulted  s i m p l e and e f f e c t i v e d e s i g n  variation  i n the choice  the  each  computed  safety  factor  may  the fact  failed, lack  that  of s t r o n g  under Dam and  In  few dams  question  design  although  factor the  method seemed t o be under  adequacy c o u l d  be a t t r i b u t e d  i t s use  of  computed v a l u e clear.  had  t o the  than t o the p r e d i c t i v e  to predict  method  into  these  the  came  t h e 1925 S h e f f i e l d  t a i l i n g s dams d u r i n g  Investigations  A major problem w i t h  indicated  method.  for its inability  method t o p r e d i c t  of  design  i t s guidelines  c a p a b i l i t y of the p s e u d o - s t a t i c  fundamental problems with  indicates  addition,  designed  the f a i l u r e s of s e v e r a l  not  available.  t h e f a i l u r e o f t h e Lower San F e r n a n d o Dam  pseudo-static  is  is  range f o r the  of the p s e u d o - s t a t i c  E a r t h q u a k e o f 1978.  is  details  earthquake motions rather  predictive  failure,  t o be an  However, a wide  a broad  of the p s e u d o - s t a t i c  t h i s apparent  The  pseudo-static  i t appeared  approach.  analytical  of s a f e t y ,  exist.  capabilities  the  o f t h e s e c h o i c e s c a n have a s i g n i f i c a n t e f f e c t on  effectiveness by  of  1979).  of  because  extremely  Because  i n t h e range o f 1.0 t o 1.2  in  1971  t h e I z u Oshima  inability  of  f a i l u r e s revealed  the  several  s u c h a method o f a n a l y s i s . the p s e u d o - s t a t i c  the f a c t o r  of s a f e t y .  f o r the factor  of safety  Although  factor  a  f a i l u r e i n a standard  static  method  of  analysis  The s i g n i f i c a n c e in evaluating of  safety  stability  less  of the  stability t h a n one  analysis,  for  18  the  pseudo-static  plastic the  deformations  transient  force w i l l small  only  accumulated whether  act  A  this  of  during  not  in  of  seismic  during  which these  determining  t o be  used  pseudo-static  in  t h a n one  the  use  of  pore  fail  for i t s  method a  to  serious  the  may  soil  by  a  pressure  fail  Slopes slope  cannot  permanent  be  horizontal  method  should  materials  development  true  stiffness  behavior  forming  a  i f the  and/or  pseudo-static slope  to give  analyses.  strength  Such  manner  a n a l y s i s of to  t h a n one to  loading.  rational  may  pseudo-static  is susceptible  The  susceptible  peak  such d e f o r m a t i o n s r e p r e s e n t s  safety greater  i n any  to  the  of  Because  m a g n i t u d e of  continue  of  onset  method of a n a l y s i s .  cyclic  force.  time  significant  may  inability  stability  material  confined  The  safety greater  forming  be  structure  m a g n i t u d e of  f a c t o r s of  static  of  be  The  the  f o r c e , the  instants  can  f a c t o r of  represented  earthquake  deformations  having  loss  the  occur.  of  indication  indicate only  may  purpose.  limitation  may  than complete c o l l a p s e .  for brief  soil  the  of  it  movements  the  predict  rather  nature  plastic  design  analysis  thus  that  during  are  cyclic  loading. The  variability  difficulty the  in assessing  pseudo-static  deviations determine  of  from the  the  computed  f a c t o r of  i t s significance limit  method.  realistic  reliability  Clearly,  conditions of  the  in  result.  safety the  there such  the  usefulness are  an  and  too  analysis  of  many to  19  3.2  Newmark The  Analysis  Newmark  method  performance of a s o i l computing factor  of s a f e t y .  structure  block  I t was f i r s t  that  the  the  slide  plane.  mass  exceed  only  brief  instants  earthquake and w i l l deformations.  result  This  periods  and  has  the  resulting  from  seismic  calculated  excess yield  of  safety and  the  as  the  equilibrium against  to eliminate  charts  yield  and  is  equations  will  occur  the  that  representing a  of small  the  failure  the f a i l u r e  pseudo-static  benefit  as a  a c t i n g on  during  given plastic loading  method  of  deformations  the  induced d e f o r m a t i o n s can  earthquake  acceleration  acceleration  over  the p e r i o d  exceeded.  The  yield  analysis  o f 1.0. required that  acceleration  which y i e l d s a such  integration,  Newmark  is  pseudo-  factor  To f a c i l i t a t e  related  in  i n which the  c o e f f i c i e n t , k, i n a s t a n d a r d  stability  the  exceedance,  the earthquake  seismic  failure  in h i s  the  forces along  a  a c t i v i t y , c a n be computed.  integrating  acceleration  defined static  by  than  by  i s b a s e d on  of the e f f e c t s of s e i s m i c  added  Newmark showed t h a t be  resistance  i n the accumulation  a p p e a r s t o be more l o g i c a l  Newmark  The method  the i n e r t i a  of  time,  treatment  analysis  by N.M.  loading  by e v a l u a t i n g  Movements a l o n g  the y i e l d  of  than  the  mass c a n be r e p r e s e n t e d  whenever  Typically, several  rather  1965).  failure  evaluates  earthquake  proposed  on an i n c l i n e d p l a n e .  p l a n e a r e assumed t o o c c u r  analysis  during  o f 1965 (Newmark,  assumption  rigid  seismic  the expected deformations  Rankine L e c t u r e the  of  of  calculations provided  t h e maximum d i s p l a c e m e n t o f  20  the  slide  values  mass t o  of  c a u s e d by of  the the  the  yield  surface  acceleration  earthquake.  providing  a  acceleration  and  and  to  the  the  maximum  surface  velocity  T h u s , Newmark's a n a l y s i s  rapid  estimate  of  is  capable  earthquake  induced  deformations. The  Newmark a n a l y s i s  induced during  acceleration an  for  earthquake,  embankment  the  decreases  (1966) and  t o Newmark's a n a l y s i s  variation mass  may  Makdisi  be and  A  major  assumption during the  seismic  inertia  from  seismic  soils  that  embankment  from c u r v e s  within  Seed and  and  slide  a  s u c h as  an  Martin  refinements  variations  on  show t h e  loading. and  or  whose b e h a v i o r  the  generation  behaves  in  the  mass.  The  potential  slide  those presented  variation  in  For not  during of  fail  to  a  rigid  i t considers  the  loose  cyclic  by  peak  provide  the that  in i t s manner  effects  of  may  result  to pore pressure  changes  t o medium d e n s e a well  loading  excess  lies  plastic  only  displacements  l o s s due  exhibit  large  Newmark a n a l y s i s in  i g n o r e s any  strength  do  the  Hence,  loading.  and  of  soil  often  will  for  However,  depth.  forces  during  analysis  the  (1978) w h i c h  the  softening  depth.  allow  earthquake  mass.  (1967) have s u g g e s t e d  which w i l l  limitation  that  increasing  Sarma  estimated  with  the  failure  effective acceleration  Seed  acceleration  entire  of  e f f e c t i v e peak a c c e l e r a t i o n  throughout  i n the  single value  the  with  Ambraseys and  acceleration  uses a  pore  defined may  be  cohesionless yield  complicated  pressures,  realistic  strength by  Newmark's  estimates  of  21  deformations. soils  For  where p o r e  earthquake, assumption  that  t h e p a t t e r n of failure  entire  computed  movement either  horizontal of t h e  useful  it  expected  3.3  not  Seed  The  direction  sliding  the  stress  provide failure  procedure  1973),  and  t o r e p r e s e n t a t i v e samples  or pore  be  are  viewed the  developed  slip  entirely  of  by H.B. (Seed  is a semi-analytical that  are  reduction  t o e s t i m a t e t h e dynamic  then  as  deformations  i n the  pressures developed  i n the  by  et  al,  method of  during  equivalent to  be  Earthquake  observing  samples.  to  cyclic  stresses  laboratory.  determined  Seed  susceptible  involves performing a simple  analysis  computed  pattern  of C a l i f o r n i a  stiffness  applied  strains  can  realistic  path approach,  dynamic  deformations  the  f o r the  mass.  for analyzing s o i l s  strength  of  unit  The  Approach  linear  induced  determined.  movements a l o n g  a  a t the U n i v e r s i t y al,  plastic  F o r a s e i s m i c model t o be  S t r e s s Path  et  a n a l y s i s designed  loading.  be  o n l y g i v e the magnitude of also  throughout  significant  cannot  Such d e f o r m a t i o n s  should  dynamic  and  rigid  b l o c k method of a n a l y s i s i s  not c l e a r .  mass.  d u r i n g an  valid.  The  movements or  h i s co-workers  1969,  the  distance.  Seed's Dynamic The  where  rigid  deformations  should  deformations  reserved for  change s i g n i f i c a n t l y  i s reasonably  w i t h the  failure  but  not  s h o u l d be  mass i s assumed t o move a s a s i n g l e  i s also  surface  i t s use  situations  behavior  problem  entire  and  i s , for  soil  Another  reason  p r e s s u r e s do  that of  this  the  22  The be  steps  involved  summarized a s  i n t h i s dynamic  s t r e s s path a n a l y s i s  may  follows:  1.  select  a design earthquake  2.  determine  the  initial  motion  static  stresses  i n the  soil  structure 3.  determine  4.  perform  a dynamic  analysis  to determine  history  of c y c l i c  stresses  and  5.  t h e dynamic p r o p e r t i e s  a p p l y t h e combined representative strains  6.  The  the  stresses  isolated  strain  Seed  static  test  to  strains  to above are  the a x i a l  or  samples when s u b j e c t e d  strains  to  the  these  whose they may  to  deformations  be  the  converted  expected  be  and  proposed  Since  are  represent p o t e n t i a l  must  stress-strain  subsequently  u s i n g the observed  field.  the  strains  corresponding  soil  accumulated  in  that  (1979)  the  as a c c u r a t e l y  potentials  compatible  the  stresses  which r e p r o d u c e  soils,  strains  observe  time  within  stresses  samples  surrounding  cyclic  the  pressures  referred  in t r i a x i a l  dynamic  the  pore  strains  soils  pressures  strains  and  and  samples a n d  estimate deformations pore  develop  and  static  of the  to occur  manipulated  deformations a  method  to  within  in  which  strain  potential  curve.  These  as  strains not  possible in  restricted  by  rather field.  than These  produce  a  the  structure.  the  soil  shear  set  shear  i s determined  to e q u i v a l e n t nodal  static  occur  strains i n the  that  stress from  stresses  f o r c e s and  of  a  the are  static  23  finite  element  deformations. by  using  These  soil  and a l l o w  and  Janzen  pressures  used  to  i t t o deform  t h e d e f o r m a t i o n s may be computed observed  under  suggested  in a static  resorted  in  of the f a i l u r e  method  o f dynamic  that  analysis  permanent d e f o r m a t i o n s .  is  used o n l y  be  expected  Byrne  to predict  the  on s o i l  b e h a v i o r and because  to determine i n the f i e l d .  response,  which  a l (1978) f o u n d t h a t  overestimate  dynamic  about  percent  30  Additional  a total  shear s t r e s s e s ,  overprediction  the  development  characteristic fundamental  of  period  the fundamental due  to  field  the  by a t o t a l stress  of  a  of the s o i l ,  may  because  would  may Finn  tend  to  p r e s s u r e s exceeded  overburden may  analyses.  of the earthquake motion  pseudo-resonance  that  approach.  pseudo-resonance  equivalent-linear  period  level  however, may n o t  stress  response  to  analysis  stresses  analysis  effective  o f dynamic  of pore  by e f f e c t i v e s t r e s s e s ,  r e s p o n s e when p o r e water of  elastic  of i t s i n a b i l i t y  shear s t r e s s  i s controlled  be r e a s o n a b l y a p p r o x i m a t e d  equivalent  The e q u i v a l e n t - l i n e a r  the c y c l i c Such  path technique  f o r the i n f l u e n c e  be an a c c u r a t e r e f l e c t i o n o f t h e a c t u a l  response  stresses.  stress  stress  t o account  predict  to  loading  the observed pore p r e s s u r e s  of t h e t o t a l  rise  from  cyclic  stress-strain analysis  pressure  et  the  the i n - s i t u  t o the s e m i - a n a l y t i c a l  because  not  post-cyclic  induced deformations.  Seed  soil  determine  e x c e s s p o r e p r e s s u r e s r e d u c e t h e s t i f f n e s s of t h e  (1981)  be u s e d  earthquake  is  Alternatively,  the pore  tests.  could  program  pressure.  also  result  response, When  the  corresponds c l o s e l y  the a m p l i f i c a t i o n  of  the  may be a s much a s 50 p e r c e n t  24  (Finn  e t a l , 1978).  overestimated they  are  laboratory expected  by a t o t a l applied  they w i l l  The  potential/nodal  justification  as  3•4  of force  the  properties  of the s o i l  during  analyses and  has  in  the  1978)  been  theoretical validated  to  so t h o r o u g h l y  a f f e c t the  as a major  saturated  safety  dam.  to  be  are available for  cohesionless relatively  w h i c h t h e s t r e s s - s t r a i n and  s o i l s to rigorous strength  are modified  t o account  f o r pore  pressure  loading.  Siddhartan  (1984)  recently  effective stress analysis  stress-strain approach.  and  no  the  Analysis  of  two-dimensional  elastic  Although  i n 1979 n o t n e a r l y  A l l tend  such as those used  Finn,  on  with the s t r a i n  is  structure  Dynamic  cyclic  non-linear  incremental  there  The method  stated  response  procedures  a  i n the  hence,  known.  e f f e c t i v e s t r e s s dynamic a n a l y s e s  analytical  the  not  is  f o r a procedure which c o u l d  loading.  presented  is,  conversion  b u t a s Seed  earthquake  changes  be  i n e x c e s s o f what may be  associated  plausible,  E f f e c t i v e Stress  calculating  to  samples  approximation  of such a c r i t i c a l  Several  soil  The r e s u l t i n g e r r o r  f o r i t s use.  one m i g h t w i s h  evaluation  representative  cause deformations  appears  extent  tend  side.  degree  approach  stresses  s t r e s s e q u i v a l e n t - l i n e a r a n a l y s i s , when  to  i n the f i e l d .  conservative  some  B e c a u s e t h e dynamic  behavior Less  is  modelled  complex,  i n which by  an  one-dimensional  i n t h e computer p r o g r a m s DESRA  (Lee  CHARSOIL ( S t r e e t e r e t a l , 1974) a r e a l s o  25  available. Finn  A comparison  et a l The  various effective assumptions  relations  development procedures All  of  models  methods  is  given  s t r e s s analyses tend to d i f f e r  made, t h e  the  are  pressures  capable  i n the  rise  are  stresses,  strains  need t o r e s o r t  is  taken  structure. in  by  by  the  of  reliable  the and  dynamic  the  and  the  motion.  time h i s t o r y  analysis,  semi-analytical  stress-  i n t o account  equations a  i n the  which  S i n c e the e f f e c t s  displacements are t o the  method  providing  included  and  the  t h e dynamic  of  soil  r e p r e s e n t a t i o n of the  soils,  to integrate  pressure  no  of pore  used  displacements  is  latter  (1978).  simplifying strain  of these  of  of  the pore  resulting  hence t h e r e stress  path  approach.  To effective  realistically stress  dependent  have become i n c r e a s i n g l y commonly  used  verification. fundamental complexity, generally  model soil  nonlinear,  Many r e q u i r e  in geotechnical practice  than  the  associated their  such other high  use.  hysteretic  b e h a v i o r , t h e s e dynamic  complex.  Although  limit  the  and  methods forms  cost,  of and  most  analyses  parameters lack  are  clearly  of  not  sufficient  dynamic a n a l y s e s lack  and  more their  verification  26  CHAPTER 4 PROPOSED METHODS FOR COMPUTING The  p r o p o s e d modulus r e d u c t i o n  was d e v e l o p e d actual  as a simple  physical  Primarily cyclic  loading,  a p p r o a c h t o dynamic a n a l y s i s  means o f a n a l y s i s i n t e n d e d  changes  intended  MODULUS REDUCTION  i n the s o i l  forsoils  prone  i t i s very  under e a r t h q u a k e  t o pore p r e s s u r e  similar  to  a p p r o a c h b u t i s p h y s i c a l l y more r e a l i s t i c need  to  r e s o r t t o an a r b i t r a r y  potentials  to  "equivalent" The pore  compatible  nodal  rise  Seed's  during  stress  path  as i t e l i m i n a t e s  the  procedure  deformations  loading.  for converting through  the  strain  use  of  forces.  p r o p o s e d method  pressures  to simulate  as the  deforms u n t i l  t h e geometry o f t h e s t r u c t u r e r e f l e c t s  the a l t e r e d  stress-strain  r e l a t i o n s h i p of the s o i l .  a  static  used  failures to  should  cyclic  undrained state  required soils  they  occur.  For the d i l a t i v e  t h e development  to mobilize not  i s used  i n strength  i s greater  the f u l l be  relied  in  a  than  behavior  upon  in  conservative  be  f o r t h e modulus i n  from  liquefaction  soils  susceptible  i s used  strain the  since the  and t h e s t e a d y -  drained  of the negative  undrained  can  s t r e n g t h may a l s o be  resulting  does n o t d e c r e a s e w i t h  strength  because  should  strength  A reduced  m o b i l i t y , no r e d u c t i o n  undrained  However,  analysis.  the loss i n strength  strength  This  t h e use o f a r e d u c e d v a l u e  stress-strain  to r e f l e c t  cyclic  that  s o f t e n s and  through  during  on t h e o b s e r v a t i o n loading, the s o i l  simulated  rise  i s based  pore  pressure  of  dilative  strength the f i e l d , analysis.  strength.  the drained Significant  27  strains  may  be r e q u i r e d  the d e c r e a s e d  stiffness  The m a g n i t u d e o f realistic  mobilize this  of d e t e r m i n i n g  onset  of  method  for calculating  this  modulus  reduction  study.  give a r e a l i s t i c  required  This  thesis  t h e modulus  to  provide  induced deformations  s u c h a r e d u c t i o n were  deformations  s t r e n g t h due t o  of the s o i l .  e s t i m a t e s of s e i s m i c a l l y  method  provide  to f u l l y  not  attempts  clear  and t h e at  to determine  reduction that  will  not  o f an a p p r o p r i a t e m a g n i t u d e b u t w i l l  p a t t e r n of  deformations  the  throughout  the  the only also soil  structure.  4.1  Methods  for Calculating  Three  alternative  determining referred  to  calculated  as  theories  the p o s t - c y c l i c the earthquake  from  the d i f f e r e n c e  stress-strain  depicts  Reduction were  a s u i t a b l e modulus r e d u c t i o n .  the t h e o r y t h a t  cyclic  Modulus  the  The  between  the p r e - c y c l i c a  soil.  induced deformations  t h e p r e - and p o s t - c y c l i c  stress-strain  stress  level  field.  calculated  directly  The s e c o n d reduction,  or  development resulting  of  soil  in  from  the  was  deformations  of  the p o s t - c y c l i c  for-  approach,  induced  between  existing  first  modulus a p p r o a c h ,  relationships  earthquake  investigated  based could  on be  and p o s t -  Figure  4-1  as the d i f f e r e n c e curves  The r e d u c e d stress-strain  at  the  modulus i s curve.  t h e o r y f o r d e t e r m i n i n g t h e e x t e n t o f t h e modulus cyclic pore behavior  strain pressures  approach, during  is directly  recognizes cyclic  influenced  that  loading  by t h e  the  and t h e  level  of  CO to  Pre-Cyclic Stress-Strain  Curve  Post-Cyclic Stress-Strain Curve  Post-Cyclic Modulus Earthquake Induced Deformations  FIGURE 4-1  Shear  Strain  P o s t - c y c l i c modulus reduction a p p r o a c h for determining e a r t h q u a k e induced d e f o r m a t i o n s  M CO  29  static  shear  earthquake. as  shown  the  field  in  the  F i g u r e 4-2,  static as  stress  soil  the  from  state  possible.  of t h e i n - s i t u  during  in  and c y c l i c  The  shear  from  a  modulus. both  static  the e f f e c t s  and c y c l i c  analysis  development  as  softening  alternative,  or  of the  determined,  which d u p l i c a t e  loading  the  conditions  i s g i v e n by t h e strain The  produced earthquake  difference  between  the  in-situ  lies  i n i t s i n c l u s i o n of  and i n e r t i a  pre-cyclic  forces  on  drained 4-3,  and  substituting  strength parameters.  causes  modulus.  a  reduction  The e a r t h q u a k e  be t h e d i f f e r e n c e pore  pressures  loading  tests  accurately  4.2  the  pore  as  to  be  into a static  This procedure,  i n s t r e n g t h as w e l l  pressure  approach,  analysis shown  cyclic  utilizing in  Figure  as a r e d u c t i o n i n  induced deformations a r e again taken t o  between t h e  that  used  duplicate  two  stress-strain  should the  curves.  be d e t e r m i n e d  field  stress  from  The cyclic  conditions  as  possible.  Deformation The  them  the  strains.  i n v o l v e s d e t e r m i n i n g the pore p r e s s u r e s generated during loading  as  r e d u c e d modulus and t h o s e  using  of d y n a m i c a l l y induced  third  tests  loading.  of t h i s method  of s t r a i n  be  r e d u c e d modulus  computed u s i n g t h i s  The a d v a n t a g e  . The  duration  s t r e s s and t h e s h e a r  combined s t a t i c  deformations  found  the  laboratory  induced deformations are c a l c u l a t e d the  and  Hence, t h e a p p r o p r i a t e modulus may  accurately ratio  stress  Analysis  analysis  Procedure  procedure  used  in  the  modulus  reduction  FIGURE 4 - 2  Cyclic strain modulus reduction approach for determining earthquake induced deformations  CO  o  Pre-Cyclic Stress-Strain C u r v e —  to to a> v_ 00  i_  D  OJ JZ  GO  Shear Stress Level Existing in Field  ^  \  "  Initial Modulus  ^X  \  N  Post-Cyclic — S t r e s s Strain Curve  Post-Cyclic Modulus ^  Earthquake Induced Deformations  FIGURE 4 - 3  ^  Shear Strain  Pore Pressure approach for determining earthquake induced deformations  oo  32  approach  t o dynamic  analysis  consists  of  the  following  basic  steps. 1.  select of  2.  3.  a design earthquake  the s o i l  structure  by a s t a t i c  determine  t h e t i m e h i s t o r y of c y c l i c  initial  the s o i l  representative soil  static  samples  initial  the earthquake  static  analysis  steps  outlined  and  above  stresses  of  reduced  modulus.  initial  f i n i t e element a  and  to observe  The  stresses  Janzen,  and  the  fundamental  are  the  static  the l a b o r a t o r y  i s used  soil  to determine  structure  and  deformations  This  i n which  elastic  i s through  a  plane  skeleton  The  of  program  program uses a  continuum.  the  method  computer  the s o i l  the  to evaluate  convenient  such a s t h e  1981).  formulation  non-linear  that  approach  most and  a  modulus  induced deformations through  stability analysis  ( B y r n e and  as  stresses  reduction  illustrate  i n the s o i l  use  modelled  equivalent-linear  induced deformations using  s t a b i l i t y analysis  magnitude of the earthquake  SOILSTRESS  modulus  the r e d u c e d  the  element  stresses  cyclic  t h e dynamic a n a l y s i s  static  the  by an  and  o f t h e modulus r e d u c t i o n  effective  evaluating  soil  response  analysis,  a  i n the  i n the l a b o r a t o r y  determine  The  stresses  analysis  structure  6.  tests.  strain  stress  c a l c u l a t e the a p p r o p r i a t e  stability  finite  effective  5.  requirements  cross-section  analysis  a p p l y t h e combined  the  a  structure  the  dynamic  The  and  determine  throughout  4.  motion  is  non-linear  33  stress-strain linear stress its  or  behavior  secant  Janzen,  represented  by  equivalent-  with the l e v e l  A complete d e s c r i p t i o n  of  the  of  induced  program  and  f o r m u l a t i o n i s g i v e n by B y r n e and  (1981).  s t u d i e s have shown t h a t  a t any s t r a i n  shear  is  compatible  stress-strain  Experimental soil  moduli  and s t r a i n .  hyperbolic  of s o i l s  modulus  level  and  the  relationship  i s assumed  strain,  the shear  then  i s mainly  a  t h e s h e a r modulus of a  function  of  s t r e n g t h of the s o i l . to exist  between s h e a r  modulus, G,  the  initial  If a hyperbolic s t r e s s and  shear  i s g i v e n by  G = G i ^1 - r__Rf where Gj = i n i t i a l  R  shear  T = shear  stress  s = shear  strength of  f  = ratio  by initial  confining  shear  stress,  modulus,  a ', m  and may Gi  where  soil  s t r e n g t h t o the  shear  stress  predicted  the h y p e r b o l i c r e l a t i o n s h i p Gi,  is  a  function  be e x p r e s s e d  = kg P a f a ' \ [Paj  of t h e mean  as  n  m  Pa = a t m o s p h e r i c kg  developed  of s o i l  ultimate  The  modulus  pressure  = s h e a r modulus  factor  n = s h e a r modulus e x p o n e n t kg  and n a r e e m p i r i c a l  with  loading  conventional  parameters that  condition.  They  d r a i n e d or undrained  vary with may  triaxial  be  soil  type  determined  tests  or  and from  estimated  34  from  published  not  parameters  fundamental  coefficients  whose  under  a  limited  from  laboratory  accurately  soil  as p o s s i b l e .  influence  of dynamic  dynamic  approach  for  required likely  value  induced  in  t o many  soil  known  total with  both  desire  for  determining  the  soil  accuracy rigorous  appropriate  dynamic  analysis  to  function  of the square  modulus  and  shear  the  dynamic  reflect  the  is  Idriss  The  root  curves  approximate  i s consistent data  are  dependent  showing  and  complexity  generation  o f t h e mean  may  s e l e c t i o n of a  analysis  showed  and  analysis i s  parameters  reasonably  strain  (1970)  earthquake.  rigorous  properties  that  is difficult  the a d d i t i o n a l  pressure  using  reduction  stresses  the s o i l  to  reduction i s  design  earthquake  dynamic  material  Seed  presented  as  deformations  of the a v a i l a b l e  pore  values.  and  evaluated  modulus  analyses.  in avoiding  damping be a  by  In a d d i t i o n ,  of accuracy  simplicity  dynamic  soil  conditions  to  induced  the use of a  equivalent-linear  an  of the  reduction  the  of c y c l i c  of the design  i n t h e more  Non-linear into  the  uncertainties,  the level  empirical  be  field  reduced  in  earthquake  justified.  stress  be  utilized  to sufficient  behavior  should  modulus  will  the level  subject  be  the  analysis  the evaluation  not  they  During  predicting  not  the behavior  duplicate  kg  rather  they a r e  loading.  Because  generally  represent  Because  are  which  of  to determine  t o be  soils.  but  of c o n d i t i o n s ,  tests  the  The  properties,  values  range  analysis  for similar  of  model.  incorporated modulus  the shear confining the  the  and  modulus stress  decrease  in  35  modulus  with  determine the  strain  the  r e l e v a n t shear  relationships  m o d u l i and  dynamic a n a l y s i s i s p e r f o r m e d  i n which the  initial  values  assumed  are  element.  New  shear  these  values and  on  values  of m o d u l u s and  developed Such  a  damping  stresses  are  ratios  used  to  during  stress  be  stress  by  be  the  converted  modulus  values  compatible  damping  strains are  i n each  calculated  with  Lee  and  The  provides soil  Chan  a  until  the  time  structure. equivalent  the  strains  weighting  equivalent  appropriate  history  These series  (1972) p r e s e n t e d of  the  cyclic  modulus  reductions  of  dynamic  of  uniform  a method  of  o r d i n a t e s of  the  stress  a p p l i e d t o r e p r e s e n t a t i v e samples  determine  approach  and  a n a l y s i s i s repeated  t o an  appropriate  time h i s t o r y .  then  analysis  within  applications.  conversion  iterative  compute t h e  damping the  an  element.  strains  may  and  by  shear  to  damping a r e  response  s t r e s s e s and  used  strains  i n each  f o r the  m o d u l i and  based  to  Such  dynamic a n a l y s i s . The  can  level.  applications  i n the  laboratory  for  computing  deformations. In t e s t s are  addition  cyclic  r e q u i r e d to evaluate  undrained  loading  parameters. most  to  Standard  convenient  availability  and  of  tests, soil  behavior  to determine  triaxial  because equipment.  of  and their  standard  the  monotonic  during  drained  appropriate  cyclic relative  triaxial  loading and  hyperbolic tests  simplicity  and  are wide  36  Evaluation post-cyclic  it  is  the  modulus  stress-strain loading.  of  in  approach  curves  Although, fact  earthquake  for  induced displacements  requires  the  soils  difficult  stress-strain  relationship exactly  which  the  shows  determine  such a curve  permanent  axial  prevented  by  isotropic samples  consolidating  generally any  fail  during  monotonic  expected  compression  in  side,  of  permanent a x i a l  strains will  liquefaction may  exceed  can  be  occurs,  the  large axial  the  limits  s t r a i n s do  performed, must be  sample  then  may  stress-strain  be  the  at  loaded  curve determined.  some  be  under  consolidated  p h a s e of  cyclic during  the • s o i l  failure  on  have t o be  that  depend  cyclic  tested on  the  conditions  loading.  s t r a i n s that  If  develop that  p o s t - c y c l i c monotonic  tests  of  axial  strains  strain and  reduction  the  To  the  ensure  monotonically  comparing  would have t o  such a n i s o t r o p i c  small  The  of  reflect  t e s t i n g equipment. and  accumulation  sample  ensure  values  development  halted  i s d e t e r m i n e d by  To  not  large axial  occur  To  compression  develop during  very  not  the  liquefaction  factor  of  would  4-1  strain.  isotropically  in  Under  in Figure  the  extensional  w i t h Kc  soil.  the  loading  samples g e n e r a l l y  under a n i s o t r o p i c c o n d i t i o n s  the p o s t - c y c l i c  axial  t e s t s , the  the  field.  charateristics  zero  loading  testing  triaxial  simple,  at  reloading  the  approach appears  represented  However, s i n c e  subsequent  post-cyclic  and  cyclic  as  cyclic  of  after  determine  triaxial  s t r a i n s during  and  to  beginning  from  conditions.  loading,  behavior  curve  the  determination  before  theoretically, this  very  the  by  initial  during  level.  The  the p o s t - c y c l i c in  part  the of  modulus the  post-  37  cyclic  stress-strain  strain  curve.  To cyclic  determine strain  loading  effective  laboratory strains  effective loading  in  shear  shear  determined  to  from  The  pore  factor  the  is  i s not reduced.  during c y c l i c  p r e s s u r e s cause decrease  two p r e c e d i n g strength also  to  to  the  in  stresses.  the The  compute  loading.  strain  approach,  the  This  cyclic  pre-cyclic  value  loading  a decrease  from  However,  in  the  shear  modulus  the  excess  pore  in  the  static  analysis.  i n t h e mean c o n f i n i n g  modulus this  method.  of  i n the e f f e c t i v e of  requires the  t h e v a l u e o f t h e modulus  reduction  inclusion  methods results  stresses  samples  used  the  the i n i t i a l  These  soil  samples.  and an a p p r o p r i a t e r e d u c t i o n  cyclic  The  generated  a  cyclic  analysis  strain  from  hence,  are  compared  as the  results  pore  cyclic  i s determined.  tests  the  and  t o compute  structure.  tests  during  the s t a t i c  cyclic  stress-  determine  p r e s s u r e method o f dynamic a n a l y s i s  same l a b o r a t o r y unlike  used  to  with appropriate c y c l i c  modulus  t h e modulus f a c t o r  tests  required  representative  these  modulus  from  are  the s o i l  i n combination  resulting  pre-cyclic  on r e p r e s e n t a t i v e s o i l  parameters  within  applied  the  standard t r i a x i a l  tests  stress-strain stresses  of  m a g n i t u d e o f modulus r e d u c t i o n from t h e  be p e r f o r m e d  triaxial  then  to that  method, b o t h  The s t a n d a r d  are  the  t e s t s must  hyperbolic  curve  shear modulus. reduction,  approach.  a  pressures The  s t r e s s and U n l i k e the  decrease  in  38  CHAPTER 5 VERIFICATION OF  The  validity  methods f o r evaluated  by  of  the  comparing  histories.  been s u b j e c t e d  and  applicability  computing  deformation  have,  and  post-cyclic  Unfortunately,  data  earthquake  l a c k of  f o r use  a suitable field  few  results  of  B r i t i s h .Columbia on  sloped the  of  shaking  saturated  case  table tests  deposit.  magnitude  observed most  i n the  accurate  deformations the  earthquake  5.1  Tailings The  tailings  model.  pattern The  that occurred  was  Model of  few  that soil  Because  three  proposed  the  to represent  reliability by  University  of  a  each  of  comparing  the  deformations  to  those  a n a l y s i s t h a t y i e l d e d the used  to  predict  F e r n a n d o Dam  the during  1971.  Tests shaking  appropriate  loading.  the  intended  then  table  tests  s l o p e s were u s e d t o d e t e r m i n e the  field  accurate  at  i n t h e Upper San  of F e b r u a r y ,  f o r the  evaluated  of  be  were i n v e s t i g a t e d u s i n g  performed  method of  deformations  results  evaluating cyclic  and  only  analysis.  history,  The  can  provide  a model t h a t was  tailings  proposed  to a c t u a l  and  i n s u c h an  p r o p o s e d methods of a n a l y s i s was  predicted  three  e a r t h s t r u c t u r e s have  shaking  methods f o r c o m p u t i n g modulus r e d u c t i o n s the  the modulus  i s a v a i l a b l e to  earthquake parameters the  of  p r e d i c t e d deformations  to severe  insufficient  PROPOSED METHOD  The  the  on  saturated  model  c o r r e c t procedure  m a g n i t u d e of modulus r e d u c t i o n due  tests  were  part  of  a  study  on  for to the  39  prediction viscous  of  flow  University  of  research.  d e f o r m a t i o n s of theory.  The  long  and  tested,  results  model  plexiglass  cm  only  slopes  The hopper with  slopes  i n t o the deaired  evenly the  across  desired  adjacent  having  of  the  a  the  Stuckert  testing  5-1.  The  slopes  degree  equipment,  in  the  were 81  cm  c o n f i g u r a t i o n s were  depth  of  8  degree  dry  sand t o  a  the  (1982).  slope  with  by  at  master's  constructed  fixed  rising  The  allowing  h o p p e r was  slope.  angle.  displacements  of  deposits  14 cm  at  the  slope  are  thesis.  water.  the  his  were  plexiglass container  the  of  B.  Stuckert,  in Figure  were formed by  to  determine  by  slopes  and  for this  part  Although various  downstream b o u n d a r y considered  i s given  shown  wide.  as  description  tailings  container  20  Columbia  complete  p r o c e d u r e , and  tailings  They were p e r f o r m e d by  British  A  liquefied  A  During  scraper  these  that  was  used  to d i s t r i b u t e  then  deposition  plexiglass  wall  smoothed silica  in  a  pattern  of  the  from a  partially  the  filled the  grid  sand  slope  beads were  to  placed  pattern.  b e a d s were m o n i t o r e d d u r i n g  m a g n i t u d e and  fall  the  dynamically  The  test  to  induced  deformat i o n s . The sand and  sand  used  i s a clean a  specific  distribution  silica  f o r the  used  .86 for  study  sand h a v i n g  g r a v i t y of  were d e t e r m i n e d as deposition  i n the  2.57.  sand. and  forming  a  f i n e Ottawa  5-2  maximum and  shows the  model  slopes  The  This grains  grain  minimum v o i d  respectively. the  sand.  rounded to subrounded  Figure  The .56  was  size  ratios  method  of  resulted in void  40  Hoppar  ELEVATION  81cm  t-Jr O v e r f l o w 0 « t l « t =tq  4- I n l e t  PLAN  VIEW  (from Byrne, Void and Stuckert, 1981)  FIGURE 5-1  Model Container  41  Ottawa  0.02  0.1  Particle  Sand  0.5 Diameter  1.0  in m m  (from Byrne, Void and Stuckert,198l)  FIGURE 5 - 2  Grain Size Distribution of Test Sand  42  ratios  of  approximately  .77  or  about  30  percent  relative  density. The The  tests  were p e r f o r m e d  t a b l e m o t i o n s were c o n t r o l l e d  console Hz.  This  frequency  was  applied.  Maximum a c c e l e r a t i o n s  During  shaking  resulted  existed  less  in  than  illustrated resulted  by  surface  in  of  greatest  are  the at  the  near  a shear  large  The  final  the  tailings  decrease  level  sets  of  the s l o p e . 30  t o 40  tests  slope  in  angles pattern  deformations from  merely  shows  a  the  s l o p e model d u r i n g a was  .08g.  o c c u r r i n g when a  to l i q u e f y .  movements  For  5-3  acceleration  of t h o s e  5  shaking  displacement  The  The  significant  displacements  with depth  Maximum movements of a p p r o x i m a t e l y  Laboratory Three  used.  Figure  i n the  s u r f a c e and  the c e n t e r of  strain  .05g,  of  practically  were  movements r a t h e r t h a n  maximum  typical  that  slope f l a t t e n i n g .  material.  the  frequency  of  .1g  table.  Simulator  cycles  beads r e v e a l e d t h a t  slope appeared  the model b a s e . occur  of  20 to  shaking  Earthquake  slopes experienced  degree.  which o c c u r r e d  displacements portion  a  deep-seated  which  .03  e x c e e d e d about  half  transport  deformations test  2.7m  to ensure the  of  substantial  the s i l i c a  from  for  t h e model  which the a c c e l e r a t i o n s were  by  by an MTS  selected  conditions  which  1.2m  which p r o v i d e d s i n u s o i d a l motions at a  undrained  5.1.1  on a  to zero 6  Such d i s p l a c e m e n t s  to  are  along 7  cm  indicate  percent.  Tests of  laboratory t r i a x i a l  tests  were p e r f o r m e d  to  FIGURE 5-3  Observed Dynamically Induced Deformations for Model Test for 8 degree Slope and .08g Maximum Acceleration  44  p r o v i d e  the  s o i l  p a r a m e t e r s  r e d u c t i o n  a n a l y s e s .  t e s t s  were  p e r f o r m e d  and  u n d r a i n e d  u n d r a i n e d s o i l  F o r 30  p e r c e n t  was  of  was  of  the  s t r e s s  r a n g e .  between  50  M o n o t o n i c The  to  200  f o r  the  and  lower  m o n o t o n i c  l o a d i n g  and  f o r  the  were  an to  s t r a i n  t r i a x i a l  d u r i n g  t e s t s  d e n s i t y  d r a i n e d  f o l l o w e d to  of  c o n d i t i o n s  by  e v a l u a t e  i n  t e s t s at  r e s u l t s l e v e l s  the the  o v e r  the  m o d e l .  m o d e l , the  c o n f i n i n g  were  i n  a p p r o x i m a t e l y  i n  e x i s t i n g  p e r f o r m e d  b o t h  The  d i l a t e .  by  a  c u r v e s  u n d r a i n e d  samples  f o r c u r v e s  shown  d r a i n e d  i s  t y p i c a l of  volume  r e d u c t i o n  Ottawa  by at  i n  i t  model  p r e s s u r e s  assumed  to  be  d r a i n e d  and  5-5,  5-6  m o d e l .  of  s a n d  50,  and  of  the h i g h e r  150  and  u n d r a i n e d and  then  most  s t r a i n  l e v e l s . a r e  the  d r a i n e d  s a m p l e s  r i s e  s t e e p l y  i n i t i a l l y ,  kPa,  t e s t s ,  the  a x i a l l y  g r a n u l a r  s o i l s .  d r a i n e d  samples  i s  r i s e  200  l o a d e d  the  b e h a v i o r  i n i t i a l  5-4,  100,  c o m p r e s s i o n , change  to  F i g u r e s  i s o t r o p i c a l l y  p e r i o d T h i s  i s  the  b e h a v i o r  i n i t i a l  f i n e  p r e s s u r e s  c o n s o l i d a t e d  u n d r a i n e d  f o l l o w e d  The  F o r  f a i l u r e .  began  m o n o t o n i c  p e r f o r m e d  t r i a x i a l  the  the  c o n f i n i n g  r e s p e c t i v e l y .  A f t e r  modulus  T e s t s  u n d r a i n e d  to  were  l e v e l s  s t r e s s  of  samples  l o a d i n g  t h e .  were  r e s p o n s e  5-7  v a r i o u s  r e s p o n s e  r e l a t i v e  s t r e s s  t e s t s  kPa  the  a  s i m u l a t e  low  the  l o a d i n g .  p e r f o r m A l l  and  a p p r o p r i a t e  v e r y  s o i l  t e s t s  t e s t s ,  to  f o r  u n d r a i n e d  C y c l i c  c y c l i c  the  and  d e t e r m i n e  l o a d i n g  u s e d  i m p o s s i b l e  to  l o a d i n g .  a f t e r  a l l  Because  D r a i n e d  m o n o t o n i c  b e h a v i o r  n e c e s s a r y  i n  r e f l e c t e d p o r e  p r e s s u r e  The  s t r e s s -  n e a r l y l e v e l  i n  o f f  h y p e r b o l i c . or  r e d u c e  45 1-  200  /  P  /  /  D  / /  /  c<  / / /  Drairied Test—^  CO CO  <D  /  ^  / /  00  /*  s  15 *>  s  O  ^ U n d r a i m 3d Test  CD Q i  4 —  —i  0  2  4  6  8  10  Axial Strain - Percent 0.4 c u  CD Q_  0.2 -  C 'D  0.0  CO  o \_ -t—  -0.2  E O >  -0.4 — 2  4  6  8  Axial Strain - Percent FIGURE 5 - 4  Soil Response During Monotonic Triaxial Loading Tests - Fine Ottawa Sand Confining Pressure = 5 0 kPa  46  FIGURE 5 - 5  Soil R e s p o n s e During Monotonic Triaxial Loading Tests - Fine Ottawa S a n d Confining P r e s s u r e = 100 kPa  47  500 o o  400  CL.  Drained Test—  -A  &  ft  ^Jllf  #  / /  to  /  (/> 300  0  • •  d> v_  00  ...J.  u 200 _o |  100  J2>"^—Undr<3 i n e d Test  ®  T 0  . >o-'  5  10  Axial Strain -  15  Percent 200  c  Undrained Test  <D  o a.  100  I  c 'o CO  _o -100 Q) E  o >  Drained Test -1- = 0  -200 5  10  15  Axial Strain — P e r c e n t  FIGURE 5 - 6  Soil Response During Monotonic Triaxial Loading Tests - Fine Ottawa Sand Confining Pressure = 150 kPa  48 600  O CL  oo oo CD l_  400-  00  _o ~o ">  200-  CD Q  O^r  5  Axial Strain -  Q-0OG--O  CD O i_ Q_  Percent 200  c  0>  15  10  0.5-  I  •0~  Undrained Test  O- -100  -Q . ~0  'o  0  Drained Test  00  -0.5  - -100  CD  E  O >  5  Axial Strain FIGURE 5 - 7  10  15  -200  Percent  Soil R e s p o n s e During Monoionic Triaxial Loading Tests - Fine Ottawa S a n d Confining P r e s s u r e = 2 0 0 kPa  49  slightly, strain of  and t h e n  harden.  to r i s e  the i n i t i a l  tests  at  distinct  slopes.  tests  The  a true liquefaction peak  loss  failure  a  Figure  occurs the  s m a l l but 5-4  t o be more in  to  pressure  Although  show  existing  for  a  indicative the  model  in strength i s anticipated  large displacements of c y c l i c  curve.  in  level  begins  softening  did  illustrated  at the s t r e s s  thus a r e s u l t  the  strain  pressures  no s i g n i f i c a n t  the model.  of  sand  at a c o n f i n i n g  of 50 kPa i s b e l i e v e d  response  Hence,  test  the  i n the s t r e s s - s t r a i n  confining  pressure  were  after  amount  peak, t h e b e h a v i o r  the s o i l  within  peak  higher  confining  a g a i n as  For the undrained  50 kPa, no s i g n i f i c a n t  after  of  start  observed  mobility  i n t h e model  behavior  which r e q u i r e s a  loss  in  the undrained  stress-strain  hyperbolic  stress-strain  parameters  rather in  curve  than  strength has been  reached. The following are  the  summarized  parameters undrained  are tests,  stresses.  For  be assumed that  on  5-1.  Table  based  on  For  the  effective  e t a l (1980),  drained  stresses,  from  tests,  while  initial  the undrained  t h e b u l k modulus f a c t o r  under u n d r a i n e d  and the  f o r the  of  tests  the  evaluated  they are a f u n c t i o n  effective may  of volume change  conditions for fully  The b u l k modulus p a r a m e t e r s  determined  Cyclic  d e s c r i b e d by Duncan  t o be v e r y h i g h t o s i m u l a t e t h e l a c k  would o c c u r  samples.  procedure  were  saturated  f o r the d r a i n e d t e s t s  were  t h e volume change m e a s u r e m e n t s .  Tests  During  the c y c l i c  loading tests  t h e samples were  initially  50  Table  5-1  Summary of H y p e r b o l i c P a r a m e t e r s F i n e Ottawa Sand  shear  modulus f a c t o r  shear  modulus exponent modulus f a c t o r  bulk  modulus exponent  angle  consolidated that  in f r i c t i o n  d u r i n g the  was  selected  than  10 c y c l e s .  the c y c l i c may  be  large  as  tests  m  .35.  had  as  .71  33.5  32.0  2. 1  with  a Kc  to l i q u e f y table that  value  tests,  The  prevented  by  at  were  to  .15.  few  entire  cycles  stress  in  in less model,  table  tests  r a t i o used  i n the  development  tests  after  of  initial  l e v e l of a p p r o x i m a t e l y  curves. generated.  loaded During  to  these  Instead  of  ratio  the  shaking  The  s t o p p i n g the  ensure  the  liquefaction  stress  monotonically  stress-strain  first  i s assumed  cyclic  1.2  the c y c l i c  d u r i n g the  occurred at a s t r a i n then  the  would cause  lower  of  Because  within  body m o t i o n  .16.  pressures  4.0  compression.  slightly  Samples were  pore  .95  L\<t>  ratio occurring  was  post-liquefaction additional  1 57  in  If r i g i d  s t r a i n s was  percent.  .68  b  angle  the v a l u e  stress  liquefaction  k  shaking  evaluated  laboratory  .62  n  anisotropically  s l o p e s appeared  loading  320  r a t i o Rf  f a i l u r e would o c c u r  model  1 35  f r i c t i o n <t>  of  change  undrained loading  kg  bulk  reduction  drained loading  2.5  provide tests the  no  pore  51  pressures  began  increasing  rate  reduced  pore  5-9  and  i n the  large from  5-10  post-cyclic  show  Determination reduced  each  was  and  the o r i g i n  was  during the  initial  yielded  an  The not  cyclic  in  undisturbed  be  the  stresses,  the  similar tests.  between  an  to  those  Figures  the  pre-  5-8, and  pressures  Moduli for  from  t h e 2.5  The  the  peak  secant  reduction from  modulus  exist  strains.  However,  in  the  laboratory  factor  laboratory would  be  the  field  and  tests  of  developed  two  strain  the  50  times,  approach  by  very  was the  subjecting  cyclic  o b s e r v i n g the at  of  moduli  Ideally,  determined and  the  6.  tests.  static  For  i n the c a l c u l a t i o n  f o r the c y c l i c  s a m p l e s t o t h e combined  to  curve. that  of  for  connecting  modulus r e d u c t i o n o f a p p r o x i m a t e l y  directly  believed  strain  comparison  t o a h y p e r b o l i c modulus  response  s h e a r modulus  to the curve  included  modulus  in soil  i n the p r e - c y c l i c  was A  post-cyclic  initial  percent a x i a l  liquefaction  the  the  the d i f f e r e n c e  loading.  initial  modulus  determined  to  at  Because  at v a r i o u s c o n f i n i n g  factor  e v a l u a t e d as  apparent  reduction  of Reduced  shear modulus.  corresponding  then  the t e s t s .  undrained  o f t h e sand  modulus  curve,  initial  and  loading.  to the  post-cyclic  tended  similarity  determined  after  curve  initially  stages of  pre-cyclic the  response  5.1.2  before  later  the  undrained  approach  slowly  strains  during  The  drop,  pressures l e d to increased c o n f i n i n g  strengths at determined  to  stresses accumulated  low  stress  52  FIGURE 5 - 8  S t r e s s - S t r a i n Behavior Before and After Cyclic Loading - Fine Ottawa Sand Confining Pressure = 50 kPa  53  400  O  •  El  oo oo CD  Pre-cyclic —^  Jul  /  s  rf  •  O  ,0-'  _o  >  "—Post-cyclic  100-  CD  Q  n  0  5  15  10  Axial Strain — P e r c e n t  o  Q_  /—Post-cyclic  I 00 00 CD  D_  !  P r e - c y c l i c — ^ «J  X  j j  111  CD i_  O  CL  0  5 Axial Strain -  FIGURE 5 - 9  10  15  Percent  S t r e s s - S t r a i n Behavior Before a n d After Cyclic Loading - Fine Ottawa S a n d Confining Pressure = 1 0 0 kPa  FIGURE 5-10  S t r e s s - S t r a i n Behavior Before and After Cyclic Loading - Fine Ottawa Sand Confining Pressure = 150 kPa  55  levels  existing  Hence, stress  any  with  cyclic  levels  Because  i n t h e model a r e e x t r e m e l y  significantly  the  confining  t h e mechanism o f  at  The  monotonic  the a p p r o p r i a t e  tendency  sample  test  began  the  confining  had  confining  slope  exhibiting conditions  of  no  strain  from  cyclic  The  deformations  accumulation  phase of each o c c u r r e d can  of  loading  that  prevail  during  used  shaking.  and  absence the  -  of  times  monotonic sand  rather  observed the  i n the  strains The to  to ensure  model  occurring  speed the that  the  2  percent. confining  less  strain  than  in the  triaxial  test  a t t h e model  stress  than  contractive. would  have  liquefaction.  slopes  represent  d u r i n g the  at which the  high  kPa,  pressure  from  than  50  a t the h i g h e r  mobility  rather  the  the  confining 50  sand  For  this  tests  the  increasing  loading  attributed  was  at  sand  - the  an  p r e s s u r e of  the the  the t e s t  strains during c y c l i c  stress cycle. be  on  in  pressures.  1  dilative  model.  occur  indicated  of between  the  softening  w o u l d have been of  for  to  performed  kPa  the  reproduce  during  1  in  at  t e s t s would not  Because the average about  performed  increases  confining  by  perform.  to l i q u e f a c t i o n  confining  occurred  resulted  the  tests  lower  those  thought  density  lowest  used  Thus t h e d e v e l o p m e n t  large  loading  at s t r a i n s  was  pressure  such  development  behavior  pressures.  model  stress,  also characterized  that  than  of a s o i l  at the  to d i l a t e  p r e s s u r e was  the  at  stress-strain  softening  higher  relative  for dilation  triaxial  The  strain  to  t e s t s w o u l d have t o be  susceptibility  increasing  model.  loading  difficult  frequency  loading  deformations of  cyclic  u n d r a i n e d c o n d i t i o n s would  56  A l t h o u g h the performed,  the  deformations strains  during  cyclic  from  A cyclic  loading  that  would produce  in  model  slope  also  determined.  confining  The  sample  would  cyclic  mobility  to be  part  applying  a cyclic  but  resulting variation cycle  i n the  indicated cyclic  to  were n e c e s s a r y also  initial  the  for  The  stress cyclic  would  was  the  developed initial  conditions.  r a t i o of  were  The  loading  determined The  only  .10,  by test  when  deviator  about  then  strains  each  strain.  by  limited  observed.  Hence s t r e s s of  the  induced  stress amplitude.  strains  develop  axial  during  ratio  the  During  stresses  were  generated  stress  conditions  The  cycle  was  consolidated  s t r a i n s were  cyclic  s i g n i f i c a n t development  a cyclic  applied  failure.  the  observed  overall effective  these  amplitude.  exceeded  anisotropic  an  stress  strains  l i q u e f a c t i o n was  .15,  loading  cyclic  the  was  appreciable  sample  flow  of  determine  cyclic  l i q u e f a c t i o n and  percent.  each  a At  in which  significant  showed t h a t  to  reduced  amplitude  on  1.2.  r a t i o of  increasing  create  kPa  The  shaking  performed at  axial strains  the  that  stress  test  2.5 a  to produce  v a l u e of  stress  with  required  of  large  application  performed to  cycles  be  development  stress  m a g n i t u d e of  not  undergo  progressive  application.  100  a f t e r an  the  during  progressively  used  of  with  a Kc  to  t e s t was  20  susceptible  approximately  reapplied  the  of  only  initial  the  t e s t was  pressure  anisotropically  to  during  load  tests could  soil  of  amplitude  each c y c l i c  loading  the  the  cycle  ratio the  of  each  stress  strains during  cyclic  potential  resulting  investigated. the  appropriate  the  stress reversals  The  test  rather  than  57  .16  as was  required  characteristic  to  generate  the  observed  in  applied.  However, s i n c e  much  the  lower bias  stress  level  comparable loading  model  confining  static  than  the  test  of  same  cumulative  tests  for  t h e model pressure  laboratory  w o u l d be  level  of t h e model t a i l i n g s  required  strain.  cannot  be  the  strains  20  a somewhat h i g h e r l e v e l  of  sample, a h i g h e r tests  the r e s u l t s  quantitatively  to  to  confirm that  strains of  will  strains  The  occurring  shear  the c y c l i c to  40  strain  shaking  as  a  times,  resulting  is  load  from  be  in  the  g  those observed slightly  lower  model  in the  slopes  from  the  resulting  during  cyclic  pressures  d u r i n g dynamic  .05  magnitude  of  loading.  The  loading  the  accumulation  to  .20  of  than  those  the  during  assumed 1000  static  strain  to  2000  range. pressure  the pore  both  approach  pressure  development  d e p e n d s on  30  i n t h e model  reduced  The  r e d u c t i o n i n t h e modulus f o r t h e p o r e  determined  the  substantial  t e s t s because  of s l o p e f l a t t e n i n g .  values  to  approximately  r e d u c t i o n s i n t h e modulus f a c t o r in k  cyclic  t h e modulus r e d u c t i o n f o r  were assumed t o be to  the  due  a  cycle.  appropriate laboratory  result  caused  loading  t o compute  may  existing  levels  The  approach  strains  from  stresses  used  corresponding  These  determined  d u r i n g each  strains  percent,  slopes.  shear  develop during c y c l i c  cause  predict  differing  t h e y do  cyclic  of t h i s  slope t e s t s  conditions,  loading  subjected  modulus r e d u c t i o n i n t h e model t a i l i n g s stress  those  a  i n t h e model  used  of  be  to  triaxial  Although  would as  cycles  s l o p e s were and  tests,  the  of  rise pore  properties  58  of  the  The  soil  magnitude  either  the  characteristics  of  the  liquefaction  effective of  and  residual  or c y c l i c  bias.  prevailed.  F o r much  Thus  the  suggested  pressures  of a p p r o x i m a t e l y  pressure.  by  to determine  is  a  excitation.  developed  of  the  model  function  Chern 75  a  (1981) would percent are  Kc  for  of  of the  value  the  the level  of  1.8  residual  pore  excess  pore  predict the  during  effective confining  utilized  in a s t a t i c  t h e modulus r e d u c t i o n and  the  stress  earthquake  deformations. reduced  determined  modulus  f o r e a c h of  substituted  analysis Figure  to  calculate  5-11  shows t h e  computer  the  analyses,  the  the  undrained  behavior  in  the  was  during  the  5.1.3  Results The  factors  three finite  the  or  modulus element  static  dynamically  finite  element  bulk  the  modulus f a c t o r  grid  of  t h e model s a n d .  s l o p e on  included  was  by  the  pressures approaches  stress  induced  stability  deformations.  used c o n j u n c t i o n the a n a l y s e s . kept  high  The  the d r i v i n g  modifying  pore  reduction  p r o g r a m SOILSTRESS t o p e r f o r m  g e o m e t r y of  deformation  the  into a  the  each of  mobility  These pore p r e s s u r e s  The  were  dynamic  pore p r e s s u r e s  relationship  pressures  induced  the  c o n f i n i n g s t r e s s e s d u r i n g c o n s o l i d a t i o n and  static  analysis  of  to  effect  shear  the  with  During simulate  of  changes  forces during  element  geometry  analysis.  of D e f o r m a t i o n  deformations the  of  Predictions  the model t a i l i n g s  t h r e e modulus r e d u c t i o n  slope p r e d i c t e d  approaches  for  the  by  model  FIGURE 5-11  Finite Element Grid of Tailings Model used in Static-Stress Analysis  60  test  with  shown  an  in  Figures  determined pressure model  8 degree  by  approaches observed  been  to  arrive  at  that  slope  half  of  kg  The  and  value  comparable  assuming initially  the  was  The  slopes,  no  volume  to that  b e a d s showed a d e c r e a s e  Figure  5-15  6  percent.  only  about  sand shows  in the  model.  in  the  300  of  times, All  deformations  similar  slope  are  the  the  deformations  but  in  only  the  about  agreement did  not  some volume c h a n g e s  the  was This  assumption  of  of  sand  the  model  upward movements i n pattern i n the  Hence an  depicted upper  increase  predicted  when  the  by  the  slope  of  model, the  must a l s o have  to  performed  volume  upper p a r t  entire  slope  model  well  l a c k of  occurred.  i n volume  lower  t o the  settlements  analysis  displacement  1 percent.  the  approach  agree very  This  allowing  in  For  strain  conditions apparently  undergoing  silica  of  However, t h e  lower  because  movements  slope.  volume  pattern  involving  changes  reasonable  comparable  was  pore  deformations.  very  reduction  lower  reduction  and  cyclic  are  i n the  i n the  modulus  downward  approximately  .10  undrained  model  appeared  undergoing  rise  observed  that  of  the  movements  because t o t a l l y  place.  the  the  observed  30  h o r i z o n t a l displacements  vertical  those  within  those  are  deformations  a p p r o a c h and  multiplied  approximately  flattening  upper  The  .08g  model.  average  slope  slope  have  5-14.  modulus  d e f o r m a t i o n s p r e d i c t e d by  deformations.  take  and  post-cyclic  reproduce  an  exist  a peak a c c e l e r a t i o n of  5-13  and  i n the  The  results  and  a p p r o a c h a r e much s m a l l e r  respectively,  the  5-12,  the  slope  using  slope  volume in  the  occurred. the  bulk  predicted initial  deformations  multiplied  30  times  slope  FIGURE 5-12  Deformations Predicted by Post-Cyclic Modulus Approach  FIGURE 5-13  Deformations Predicted by Cyclic Strain Approach  predicted  FIGURE 5-14  deformations m u l t i p l i e d  Deformations Predicted by Pore Pressure Approach  300  times  FIGURE 5-15  Deformations Predicted by Cyclic Strain Approach with Volume Change Correction  CTi  65  modulus for  was  permitted  the observed  the  lower  made  to  simulate  simulate cannot from  changes  s l o p e was  deformations the  using this  slope f l a t t e n i n g  displacements, both  and  the  result of  from  to their  the earthquake The  failure  deformations method  and  that  the  strains  during a single  r e d u c t i o n i n the  loading  i s not  Although cyclic  soil  triaxial  of  The  sufficient  tests,  monotonic  pore they  strain  the  failures  when  approach  predictions  of  the  movements  of t h e  deformation  other  predictions  f o r fundamental  results  earthquake  strains.  Implicit  relationship caused  by  strain  of t h e  aspects  pressures  had  such  the  i n the use  of  assumption  static  developed  shear  However,  from  observed  cyclic  strains. during  immediately  initial  a  d u r a t i o n on  resulting  the  predict  because  i s the the  began t o d e c r e a s e Thus t h e  to  development.  soil  reproduce  loading.  Apart  changes  modulus a p p r o a c h  of  phase of  to  but  behavior.  are  stiffness  significant  post-cyclic  good  slope  slope.  volume  the c y c l i c  realistic  stress-strain  observed  lower  i n t h e m a g n i t u d e of  influence  accumulation  post-cyclic  the  i n the  very  of the p o s t - c y c l i c  the  the  stresses  change  of t h e a p p r o p r i a t e m a g n i t u d e  ignores  generation  or  was  f o r volume  i n a b i l i t y to account  loading  no a t t e m p t  correction  predicting  providing  provide  in  The  p a t t e r n of d e f o r m a t i o n .  approaches  but  used  expansion.  undrained c o n d i t i o n s e x i s t ,  observed  two  modulus  account  volume  of sand  of  capable  slope to  movements i n t h e upper  rise  problem  of  bulk  p e r m i t t e d to reduce  appears  in  The  observed  predicted  minor  partially  not  the  i n t h e upper  i n volume.  the  duplicate  this  to reduce  the  during  modulus f o r t h e  66  post-cyclic strain test  test  levels,  were v e r y  monotonic  test  reduce  the  pore  pressures existing  to  a n d enough s t r a i n  from  intended to r e f l e c t  cease  when  induced  the  reduce  deformations  would,  stresses  strength  (1976) f o u n d Niigata  and  and/or  hardening  used  would  result  stiffness  of  that  that  caused from the  soil.  o f an  amplitude  prior  transmit  shear  the  dilates, the  soil  indicates  shears  in  deformations  induced  result  from  by t h e s t a t i c  the  shear  accelerogram,  amplitude the of  the  liquefaction,  of  the  acceleration the  soil  to  a regain in strength during  of a r e d u c t i o n i n pore  shear  of  a n d hence  after  This a b i l i t y  response  i n the  However, F i n n e t a l  to  the reduced  r e g a i n s s t r e n g t h and i s a g a i n c a p a b l e  earthquake  would  observed  reduction  approaches  indicates  as a r e s u l t  soil  The  The N i i g a t a  that  liquefaction  stresses  shear, presumably As  frequency.  to liquefaction.  tests  accelerogram  at  after  the  soil.  the  although  acceleration  differ  the t r a n s m i s s i o n of  entirely  c o n t i n u e t o be t r a n s m i t t e d , even  5-16,  not  triaxial  through  stresses,  shown i n F i g u r e  did  dynamic a c c e l e r a t i o n s ,  a much l o w e r  pre-cyclic  had o c c u r r e d t h a t t h e  of the  an e x a m i n a t i o n  Earthquake  the  has i n c r e a s e d s u f f i c i e n t l y t o  the s t i f f n e s s  through  in  i n the c y c l i c  stresses  be  moderate  relationship.  pressures  hence,  By  i n the p o s t - c y c l i c  relationship  the assumption  shear  pore  substantially  shear  existing  the p r e - c y c l i c  s e q u e n c e of l o a d i n g  the earthquake  significantly.  those  stress-strain  significantly  was  not  similar  post-cyclic  The  did  stresses.  the accumulation  of  Thus  pressures. modulus, i t transmitting  the  of s t r a i n s  observed  that  occur  67  during  several  alternatively loading stress  cycles  rise  cycle levels.  of  loading  and f a l l .  will  i n which the pore  The s t r a i n s  occurring during  depend on b o t h t h e s t a t i c  and c y c l i c  The magnitude o f t h e c u m u l a t i v e  on  t h e number o f c y c l e s o f l o a d i n g  the  duration  which  pressures  strain  is directly  each shear  depends  related to  of t h e earthquake.  8seconds  .J  L 1*7.1*  1  Figure Earthquake Accelerogram  The  post-cyclic  accumulation The of  extent  from  and  i s limited a  the  stress  generation  that  only that by  reduction  when t h e p o r e p r e s s u r e s cyclic  by u s i n g  of the deformations  dilation  of N i i g a t a Earthquake ( f r o m F i n n e t a l , 1976)  modulus a p p r o a c h a t t e m p t s  of s t r a i n s  l o a d i n g , however,  5-16  rise  the s o i l  to reproduce  a s i n g l e phase of l o a d i n g . occur  during  strain  a s i n g l e phase  hardening  i n pore p r e s s u r e s .  again will  of a d d i t i o n a l s t r a i n s  the  during soften during  resulting I t i s only  unloading  sufficiently  of  the  to allow  r e a p p l i c a t i o n of the  68  cyclic  stress.  loading, of  an  strains  cyclic  To r e p r o d u c e a n a l y s i s must  resulting  modulus  development stress  from  history  i t  fails  does  and h e n c e  Realistic  achieved  when  considered  i n the a n a l y s i s .  An  additional  approach  arises  forces.  Although  entire  because  conditions result  generally  to  develop,  modulus  inability  The  pore  to predict  response  t o the changes  stiffness  post-cyclic  failure  than the  the  pressures rise condition.  inertia  enough t o  When  approach  these  1000  does  also  not  i n the c o n f i n i n g pore  times  thus,  fails  post-  of the i n e r t i a contribute  to  to  p r e d i c t the  error  involved  reduce  substantially in  pressures  pressures. are  may  deformations.  The s i g n i f i c a n t  modulus  of  the e f f e c t s will,  is  modulus  significant  The f a i l u r e  of s t r a i n s  be  f o r the i n e r t i a  degradation,  when p o r e  to include  of the e x c e s s of  earthquake  t o account  the observed  pressure  the  t h e modulus  the  the  only  the  because  in  in  of  can  deformations.  deformations.  inclusion  cyclic  stress  observed  the  post-  any s m a l l i n c r e a s e i n t h e s h e a r  approach  shear  The  entire  deformations  fails  near  f o r c e s on t h e d e v e l o p m e n t its  the  considered less  from  a  in significant  cyclic  of  duration  it  become i m p o r t a n t soil  consider  source of e r r o r  forces  the  cyclic  t o model t h i s p r o g r e s s i v e s t r a i n  estimates  resulting  bring  c y c l e s of l o a d i n g .  not  deformations may  during  i g n o r e s the s u c c e s s i v e development of  strains.  the  behavior  be a b l e t o s i m u l a t e t h e a c c u m u l a t i o n  several  approach  because  the s t r a i n  required  occurs  created  by  Whereas r e d u c t i o n s to  predict  the  69  observed  deformations  approach  predicts  the reduced  strength that stresses,  less  those  approach, lie  in  strains of  the  the  stable,  substantial the  inertia large  related  strains  inclusion f o r c e s on  of  s u c c e s s i v e development  of  s t r e n g t h used  both  become  Repeated soil  is  levels,  the  pore  behavior  is indicative  cycles  strains  and  observed  to  of the c y c l i c  strain  cycles  effects  loading  during  lead during  approach include  to  of  of  soil  approach  loading  soil  model  influence loading  appears  and  softening  dynamically  response  cyclic  to  the  the  to  gradual accumulation  t e s t s are performed  of the  cause  deformations.  t o model t h e  pressure  can  s u c c e s s i v e p e r i o d s of  i n the p r e d i c t e d  of the  of  would  pressure  development  the  stresses  reached  the pore  successive  laboratory  effects  just  the development  Because the  to  p r e s s u r e i s enough t o make the s o i l  f o r c e s d u r i n g the  by  modulus  If  to i t s a b i l i t y  caused  times  significant.  of  effectiveness  post-cyclic  i n i t s n e g l e c t o f the  forces  significant  error  a r e 300  pore  inertia  progressive strain  r e d u c t i o n i n the  appear  small i n c r e a s e i n shear  the  with  in the  s t r e n g t h of t h e  the  the  pressure  Even  p r e s s u r e approach  the reduced  deformations.  The  The be  At  the  any  failure  causes  for  and  the  deformations  pore  loading.  the  model  the pore  5 times.  from  in  of  of  As  loading,  the  accumulation  this  to  forces.  approach,  increase  which  results  predicted  observed.  failure  inertia  barely  the  during c y c l i c  pressure  also  the problems with the pore its  model,  r e d u c t i o n s of o n l y a b o u t  effective than  of t h e t a i l i n g s  and  response  and  induced  at the the  by  its  inertia strains.  in-situ  stress  resulting  expected  of  in  soil the  70  field.  In  a d d i t i o n , the  i n f l u e n c e of  the  inertia  earthquake d u r a t i o n  are  included  i n the  equivalent  number  of  uniform  stress cycles  s a m p l e s and  using  reduction.  The  aspects  of  realistic  5.2  the  observed  approach,  soil  The  of  the  analysis  ability  of.  the  deformations  of  excitation. it  the  However, s u c h an involved  throughout  slope  experienced soil  was  only the  model  portion  excitation.  The  predict  earthquake  comprising and  the  San  hi story.  ability  of  The  response  the  induced  to  movements of  Fernando Earthquake of  indicated to  soils  modulus  rise  simple  reduction  types with  provide  varying  an  the a  dynamic  approach  earth  Fernando  entire and  the  excitation  San  were  retained  during  d e f o r m a t i o n s of  Upper  earthquake  the  which  the  predict  relatively  addition  stiffness  1971  deformations.  pressure  earthquake the  provides  whose p r o p e r t i e s  In  pore  soil  and  model  was  soil  by  modulus  significant  approach  slope.  their  several different  differing  examined.  of  f o r the  r e s u l t i n g during  of  constrained  significant  the  type  substantial not  slope  analysis  one  laboratory  the  field  the  Dam  reduction  structures  to the  induced  Fernando  tailings  modulus earth  i n the  the  applying  compute  accounts  earthquake  Upper San of  uniform  softened  thereby,  the  a n a l y s i s by  s t r a i n s to  response expected  p r e d i c t i o n s of  Analysis  since  the  f o r c e s and  to  structures properties should Dam  appropriate  be  during field  71  5.2.1  Description The Upper  in  the  San  constructed deposits  of Dam  San  F e r n a n d o Dam  Fernando between  of s t i f f  with  an dam  wide  dam  of h y d r a u l i c  During Fernando Richter  8.5  region of 6.6.  miles  d e p t h of 8 m i l e s . Fernando  Dam  involving  upstream  feet  laterally  deformations  part  of  made  from  100  6,  which  extent  of t h e movements w h i c h  failure  foot  topped  20  foot  long  berm  the  of  San  earthquake  The  and had a  of  the  the  San  part  c r e s t of t h e dam  i n d i c a t e d that  focal  movements  visible  of  moved 5  Measurements  monuments and  was  Upper  downstream  and  shows two c r o s s - s e c t i o n s  s u b s t a n t i a l downstream  a  1971,  of t h e  p a r t i c i p a t e d i n t h e downstream  5-17,  feet  toe.  settled 3 feet.  a t t h e b a s e of t h e dam  The  A  of t h e dam  slope  surface  i s 58  by an e a r t h q u a k e h a v i n g a  substantial  and  was  alluvial  material  slope,  February  epicenter  were o b s e r v e d .  of  It  forms a s u b s t a n t i a l p a r t  t o the n o r t h e a s t  downstream  located  completed s e c t i o n of  slope.  A l t h o u g h no major  slope  top  fill The  shaken  The  dam  The dam  t h e downstream  was  occurred,  o f t h e dam  fill.  material  t h e e n t i r e downstream  the  conduit  fill  on  gravels.  downstream  the e a r l y morning  magnitude  directly  paved upstream  t h e c r e s t and  Valley  located  concrete  fill  southern C a l i f o r n i a .  f e e t of h y d r a u l i c  and a 2.5:1  between  1925  c a p of r o l l e d  has a 2.5:1  comprised the  foot  crest  of  c l a y s and c l a y e y  c o n s i s t i n g o f 40  the  i s an h y d r a u l i c  Valley  1915 and  high,  18  and E a r t h q u a k e D e f o r m a t i o n s  of  from t h e o u t l e t  the  entire  movement.  o f t h e dam,  upper Figure  i n d i c a t e s the  occurred.  movements  of  the  dam  created  124 Or| o o tn  I2Z0|-  \  II  Soillvoy E L I 2 ' 2 S \ ' ~ > I Z  3 2  Crott-ltction btfori «orlKQuo»« Croii-ttction ofttr •orlhguokt  100  . El. I20O'  IZOOr-  2  • 100 •  •8 * c  1160 •  I  1140 •  u  1120 • 1100-  Sink Holt yyi ii  Stmi-hydrouiic n i l  ".  Foundation  Cutoff Trtnch  -777^7777777^7;  .— Btdrock -y/f-j/xv//-  - iikziie*urvn  iilsxiis.UL.'.  y/tw/WJi-oi*  1080 -  ( f r o m Seed e t a l , (a)  Cross-section  showing d i s p l a c e d  Tension Crocks  profile  1973)  o f dam  Tension Crocks  Compression  [displacements In feet]  (b)  D i s p l a c e m e n t s measured a f t e r  earthquake —1  FIGURE 5-17  Deformations of Upper San Fernando Dam during Earthquake  73  several that  vertical  slope  of  the  extensional  the  crack  upper  displacements  was  rolled  features within  the  tended  e n t i r e length  of  upstream  the  dam.  o b s e r v e d midway down t h e  fill  s e c t i o n of  resulting  the  the  downstream  to decrease  pressure  the  from t h e  berm r e l a t i v e  movements.  and  A  inch cracks  the  surface.  also  of  dam.  to the  slope  Another downstream  These  greater  account Some  crest  of  east  of  f o r the  dam  cracks  downstream  crest region  spreading  less  Piezometer  crack by  The  of  of  readings  slope.  less  the  result  outlet  toe  than  of  of  conduit  the  dam.  h a l f to  three  i n the  those  central  of  the  i n the  conduit,  edge of  the  dam  was  major  although  conduit  could  i n d i c a t e d by  roadway  concrete  transverse the  across  however,  a  the  spillway wall  displacements,  after  the  on  displacements.  paved  the  observed  i n d i c a t e that  above the  relative  taken  a  high  Measurements o f movements a t  outside  than  of  A 2 foot  as  were o b s e r v e d  fill  lateral  deformations  s e v e r a l one  damage t o t h e  significant  berm,  the  appears to  the  observed  and  abutment.  considerably  near  dam.  the  along  the  interior  conduit the  within  compression the  the  reduction  fill  lateral  transverse  of  of  the  downstream t o e  consisting  i n the  This  the  the  were c o n s i d e r a b l y  movements o c c u r r e d slippage  toe  failures  upstream p o r t i o n s level  at  survey  features  conduit  beyond  towards the  compressional  Extensional quarter  slope  ridge developed  indicated  the  the  i n the  dam. On  the  l o n g i t u d i n a l cracks  extended over almost  large  are  large v e r t i c a l  at  were  displacements.  earthquake  indicated  74  maximum p o r e p r e s s u r e However, the  the f i r s t  earthquake,  pressures. pressure tops  i n c r e a s e s o f 8.5  readings  allowing  In  reached  during  higher  than  very  silty  5.2.2  feet  until  dissipation the  casings.  the  earthquake  those  recorded.  h i g h pore p r e s s u r e s  sand  several  in  17  center  fill  sand  of  after  the  excess  o f t h e dam, t h e p o r e spilled  Thus t h e maximum p o r e could  have  In t h e a r e a apparently  located i n that area,  water.  24 h o u r s  of  i n c r e a s e s were s o l a r g e t h a t t h e water  of the piezometer  toe,  were n o t t a k e n some  addition,  to  been  over t h e pressures  significantly  below t h e downstream  occurred causing  in  the  loose  the formation of  boils.  Previous Investigations After  the earthquake,  an e x t e n s i v e  study  of both  the  Upper  and  Lower San F e r n a n d o Dams was made by Seed e t a l ( 1 9 7 3 ) .  In-  situ  and l a b o r a t o r y s o i l  the  characteristics foundations. by  cyclic  to  induced  Soil  triaxial  identify  cyclic  of  tests  the  soils  response tests.  forming  t o dynamic A dynamic  p o s s i b l e areas  m o b i l i t y would  were p e r f o r m e d  dams  l o a d i n g was  and  their  investigated  a n a l y s i s was t h e n  performed  w i t h i n t h e dam where l i q u e f a c t i o n o r  occur  and  to  estimate  5-18 p r e s e n t s  an i d e a l i z e d  F e r n a n d o Dam d e l i n e a t i n g t h e f o u r m a j o r  the  the  determine  the  earthquake  deformations.  Figure  dam.  to  Because  s e c t i o n o f t h e Upper San zones  of  soil  the a l l u v i u m and the h y d r a u l i c f i l l  major p a r t of the  dam  and  because  their  soils  i n the formed  characteristics  lower a l l u v i u m  FIGURE 5-18  Major Soils Types in Upper San Fernando Dam -J  76  would  tend  testing  to  the  primarily  of  hydraulic fine  common  i n both  fairly  clean  layers  of  clay.  fill  coarsest,  homogeneous fill  was l o o s e  the  to  fill  clayey  with  less  embankment  silt  from  percent.  N values  The  field  and  laboratory  were v e r y  alluvium fill  relative  density  hydraulic  fill.  as a very  clay  tended  and  distinct  was  to  o f 67 p e r c e n t , Shelby  to  towards the The  compaction  tests  and c l a y e y but  be  fairly  hydraulic  relative  were  slightly  density of  54  c o r e of somewhat  graded. some  coarser It  had  10 p e r c e n t  ranging  from  than an  higher  t u b e samples o f t h e a l l u v i u m  heterogenous s o i l  the c e n t r a l  of the s h e l l .  be  better  i n the outer  tended  core.  fill,  occasional  near  materials  low i n t h e s i l t  s a n d s and g r a v e l s  hydraulic  with  an a v e r a g e  c e n t r a l p o r t i o n of the h y d r a u l i c i n outer  sands  of the inner  t o medium-dense w i t h  determined  higher  c o n s i s t e d of l a y e r s of  the g r a i n s i z e d e c r e a s i n g  sandy  consisted  c l a y l a y e r s were  The l a y e r i n g was most p r o n o u n c e d becoming  the s o i l  alluvium  sand, a l t h o u g h  The h y d r a u l i c  The o u t e r  fine  o f t h e dam,  soils.  and  coarse  o f t h e embankment,  the  deformations  to these  s a n d s and s i l t y  o f t h e dam.  it  to  soils.  part  the  the  p r o g r a m was c o n f i n e d  Both  parts  control  the  average than the  identified  l a y e r s or p o c k e t s of  t o l a y e r s or p o c k e t s of sands and g r a v e l s . Static  samples  of  loading both  triaxial the  5-19  shows a t y p i c a l  and  undrained  t e s t s were p e r f o r m e d on  hydraulic  fill  and t h e a l l u v i u m .  response of the h y d r a u l i c  loading.  undisturbed  A f t e r an i n i t i a l  fill  to  Figure drained  p e r i o d of compression  77  8 E o cr t_  <u  a  o»  <  i  3  i  1  —  »—-•  0  Undrclined  6  4  / / 1  Dra ned -o-- «  .  cn o o >  2  1/ \l IJ  Q  IC-U Te st - Fine S»ilty Sand °3c  8 E u  sr  I  a I  3  -r-L  I.O  12 16 Axial Strain -percent  ^<  3  V  O  - -i.o  o  i  I  20  24  c a> o  \u, Undrained Test  v.  c  2.0 kg per ;>q. cm.  I  cl  ct  8  •  ;r  y  Drained TE-st,  Av/v-*-  i  >  s  <1  o  1  •  I CO o _ a> E  s  -10  <u  3  o  c  5  cl  1.0  0  8 12 16 Axial Strain-percent  20  24  >  ( f r o m S e e d e t a l , 1973)  FIGURE 5-19  Typical Response of Hydraulic Fill in Drained and Undrained Triaxial Tests  78  the  fill  tended  significant tests. the  Water  5-2  data  loss  presents  o b t a i n e d by  Resources.  triaxial  dilate  strength  Table  test  to  tests  on  The  near  and  after the  the  after  failure  soil  was  parameters  failure. indicated  by  determined  S t a t e of C a l i f o r n i a ,  the from  Department  p a r a m e t e r s were d e t e r m i n e d  undisturbed  No  from  of  drained  s a m p l e s of t h e h y d r a u l i c f i l l  and  alluvium. Table Soil  Parameters  5-2  f o r Upper San  F e r n a n d o Dam  alluvium  fill shear  modulus f a c t o r  shear  modulus e x p o n e n t  reduction angle  Cyclic  to  occur  loading  program  hydraulic rapid  fill fill  .71  38.0  40.0  rise  2.0  a l s o performed the observed and than  cyclic  loading.  None of  strains.  occurred.  the  was  a  more  testing of  s a m p l e s of  failure  Instead,  soils.  appeared  fill  response  a true l i q u e f a c t i o n  condition resulting  both  the a l l u v i u m , t h e the  large  on  movements  because the  determining  experienced  large strains  .73  on  d e v e l o p m e n t of  liquefaction of  to  .64  1 .4  were  pressure  concentrated  hydraulic  a  tests  the m a j o r i t y of  to pore  .85  a n g l e A<p  w i t h i n the h y d r a u l i c f i l l  susceptible  120  Rf  in f r i c t i o n  However, b e c a u s e  105 n  f r i c t i o n <j>  of  change  ratio  kg  Soils  the the  involving transient  i n the p r o g r e s s i v e development  This behavior  is  characteristic  of  79  cyclic in  mobility  strength. shear  within  the s o i l  static  bias.  concluded expected  the  samples.  5.2.3  i f samples  large  where  as  strain  t h e dam a n d would  Figure  to  used  be 5-20  within  by  Seed  in triaxial  test  have  developed  density  a n d was  Based on t h e r e s u l t s o f  subjected stress  and  initial  t o have l i q u e f i e d  the s t r a i n s that  were  of  levels  pressure  strains  considered  analysis.  levels  strain  would o c c u r w i t h i n  "liquefaction"  the f i e l d  Modulus R e d u c t i o n  would o c c u r  to  cyclic  i n the triaxial  conditions.  Analysis  a n a l y s i s o f t h e movements o f t h e Upper San F e r n a n d o Dam  made  reduction. were  areas  of  a loss  t e s t s and a dynamic  because of i t s h i g h e r  Seed's  the  o f t h e embankment.  not  pore pressures  reproduced  triaxial  of 5 percent  was  on  confining  Seed c o n s i d e r e d  the development  fill  that  The was  part  The t e r m  in  of  several  strain  t e s t s , Seed d e t e r m i n e d  hydraulic tests  that  fill.  considered  these  levels  the c y c l i c  i n the outer  data  involves  t o cause s p e c i f i c  development  The a l l u v i u m  significant not  the  areas  hydraulic to  of  and 5 percent  even  extensive  identified  that  the  refers  is  basis  l i q u e f a c t i o n which  required  f o r various  Seed  liquefaction  shows  stresses  the  analysis,  than  Seed p r e s e n t e d  cyclic  On  rather  by  the  proposed  Although extensive  cyclic  strain  investigations  method and  made by Seed e t a l (1973) a f t e r t h e e a r t h q u a k e ,  not i n t h e a p p r o p r i a t e  form  f o r s u c h an a n a l y s i s .  o f modulus soil  tests  their Since  data no  Zona* of fodtfft dw« to liquefoclioA indicotod bj onofy*<i after 6 seconds of shot ma.  f///y\ V///A  FIGURE 5-20  Zone* of fdilw* due to hquefoction mdicotod by onoiym r3 seconds of ehosmg  Liquefied Areas of Dam  81  further strain  testing potentials  reduction  by  To cyclic from  the  cyclic  static  assumed  laboratory  isotropic  and  the  strains  cyclic  loading  tests.  criteria  were not strain  that  modulus r e d u c t i o n s  hence,  not  result  of  alluvium indicated hydraulic  on  In in of  the  that fill  500  he  the  to  dam  are  region  of  was  not  70  percent  the  dam.  not  modulus  existing  at  in  Seed  Figure  5-21.  potentials  dam,  use  resulted  i n the  confined was  in  and, as  used  outlet  of  outer  saturated  was  alluvium  the  that  reduction  i n the  movement was The  To  Elements were  of  dam.  range  modulus r e d u c t i o n  the  the  strain the  under  magnitudes  shown on  of  in  primarily  duplicated  these  part  slope  of  were  conditions.  potentials  deformations observed  majority  the  strain  t e s t s , both  conditions  3000 t i m e s .  No  shear  throughout  strain  t o e x p e r i e n c e any  the  the  50  the  by  determined  stress  would have t o be  central  to  softening.  because  the  modulus  potentials  loading  in selecting  the  by  d i s t r i b u t i o n and  The  the  stresses  field  stress  downstream  expected soil  the  dam  Seed u s e d  potentials  embankment  the  conditions,  throughout  specified.  the  on  s t r a i n s w h i c h would o c c u r  many c y c l i c  the  i n the  occur  relied  reduction  strain  would p o t e n t i a l l y o c c u r  locations  The  estimate  These  at  determining  specific  to  to  shear  shear  anisotropic  such  determined  analysis  were d i v i d e d  Seedi  performed  s t r a i n s that  the  modulus  in-situ  performed  with  determine  Seed  stress analysis  tests Seed  concerned  the  represent  Although  by  appropriate  recommended by  to  performed,  s t r a i n approach.  the  s t r a i n approach a  be  presented  determine  potentials  the  could  in  a the  conduit to  also  the 25  to  FIGURE 5-21  Shear Strain Potentials  83  30  percent  stronger  loading.  Hence,  alluvium  w o u l d be  than  the  hydraulic  much  less  significant  some r e d u c t i o n c o u l d o c c u r .  t h e upper  rolled  this  perform  fill  finite  and t h u s  element  program  the s t a t i c - s t r e s s  analysis  induced  grid  computed stress  used  f o r each by  the  element  fill,  assumed  recommended  from  elements  throughout  due  to slope  results  and s e t t l e of  where an a r e a  5.0 f e e t  shear  were u s e d  i n the  was assumed  to  The  geometry  the a n a l y s i s  stresses  that  of  t o account might  occur  flattening.  The c r e s t  movements  factors,  static  shear  value.  any s m a l l r e d u c t i o n i n t h e d r i v i n g  downstream  the  t h e b u l k modulus was n o t p e r m i t t e d  for  The  modulus  potential,  pre-cyclic  corrected  computing  the i n - s i t u  Because u n d r a i n e d  its initial was  The r e d u c e d  strain  d u r i n g the earthquake,  reduce  analysis.  for  F i g u r e 5-22 shows t h e f i n i t e  by d i v i d i n g  occur  feet  the  No d a t a was a v a i l a b l e f o r  required  i n the a n a l y s i s .  stress  feet  in  SOILSTRESS was a g a i n u s e d t o  deformations.  static  5-23.  than  no modulus r e d u c t i o n was  element  earthquake  the  cyclic  area.  The  to  under  t h e m a g n i t u d e o f any modulus r e d u c t i o n i n t h e  although  in  fill  of t h e d e f o r m a t i o n  a n a l y s i s a r e shown on F i g u r e  o f t h e dam was p r e d i c t e d  t o move downstream  2.5 f e e t .  Horizontal  displacements  the  t o 4.3 f e e t  at the s t a r t  of  further  crest  extension down  the predicted  was  indicated  t h e berm.  horizontal  After  by  2.5  increased o f t h e berm  still  greater  r e a c h i n g a maximum o f  displacements decreased  a t t h e edge o f t h e berm and c o n t i n u e d t o  decrease  t o 3.9 to  2.3  FIGURE 5-22  Finite Element Grid of Upper San Fernando Dam used in Static Stress Analysis  2.5 (4.9) •2.7 (4.9)  2.5 (2.5)  1.8 (1.9)  I  ^ - 3 (6.4) 4  3.9 (7.2) i n i t i a l dam p r o f i l e 3.7 (5.8) predicted post-earthquake dam p r o f i l e  2.3 (3.6)  predicted deformations m u l t i p l i e d 3 times  observed displacements i n brackets displacements i n feet  co  FIGURE 5-23  Predicted Deformations of Upper San Fernando Dam  86  feet  a t the t o e .  those observed, the  dam.  An  Although  these deformations  t h e p a t t e r n of d e f o r m a t i o n  a r e a of c o m p r e s s i o n  the berm and  elements with  in  were  dam  Figure well  The  justified  within  the  The  the magnitude of  and  upper  parts  the  strain  few  of  higher  static  slope  of  displacements  agree  i n the c r e s t  used  in  strain  elements  located  potentials pore  were  in  pressure  shear the  stresses  berm.  are  of t h e dam  with those  a r e a , may  tests  shown  beyond t h e downstream t o e of  t h e d i s p l a c e m e n t s and  t o be  increases  agree  at the c r e s t .  observed,  in their  for calculating  in very  Apart  analysis both  pattern.  have been a c h i e v e d performed  The  shown  t h e modulus r e d u c t i o n dynamic  that  the Only  were c h a n g e d a r e  of h i g h e r s t r a i n  just  in  i n F i g u r e 5-24.  displacements except  laboratory  strains  the  reduction  the h i g h l e v e l  the  predicted  deformations  shown  The  downstream  from m i n o r d i s c r e p a n c i e s ,  actual  a t the toe of  u s i n g t h e s e minor c h a n g e s  with the observed  appropriate  necessary  f o r a very  use  by  of  predicted  a g r e e m e n t , even  of  i n t h e dam,  potentials  to occur  because  5-25.  predicts  the  required  observed  deformations  observed  values;  t h e dam.  be  and  occurring  assumed only  the toe of  development  of  that  i n the c e n t r a l  have been m o d i f i e d as  new  t h i s a r e a may  the  to determine  which the s t r a i n  their  potential near  the d e f o r m a t i o n s  used  modulus f a c t o r  half  dam.  To p r e d i c t potentials  duplicates  is indicated  berm w h i l e e x t e n s i o n i s i n d i c a t e d of  a r e about  in  Better i f the  to determine  the  t h e modulus r e d u c t i o n .  15 20 20  FIGURE 5-24  Required Shear Strain Potentials  10  10  oo  2.9 (4.9) 4.0 (2.5)  5.1 (4.9) 6.6 (6.4)  2.6 (1.9)  i n i t i a l dam p r o f i l e -  .4 (.2)  •6.1 (7.2) 5.9 (5.8)  predicted post-earthquake  3.7 (3.6)  dam profile  observed displacements in brackets displacements in feet  FIGURE 5-25  Predicted Deformations using Required Shear Strain Potentials  89  CHAPTER 6  SUMMARY AND The  modulus  analytical  method  earthquake pattern. as  a  reduction  The e f f e c t s  analysis  is  experience  in  used  effectively changes  The  to  the s t i f f n e s s intended  for  softening  saturated  of the  during cyclic  times as  a  for soils result  pore  of c o m p u t i n g  a reduced  was  of p r e d i c t i n g  i s determined  and  after  develop  their  pressure  forces  loading.  to predict  be a s  large  l i q u e f a c t i o n or  strain  and the pore  approach  loading,  fails  Both  approach  magnitude.  in  the  pressure  to  methods  r e d u c t i o n s o f such a m a g n i t u d e .  approach,  are  i t c a n be  Of t h e t h r e e p r o p o s e d  by c o m p a r i n g  cyclic  which  susceptibility  modulus, o n l y the c y c l i c  modulus  The  to experience only  l o a d i n g may  reductions of s u f f i c i e n t  post-cyclic  reduction  of pore  are required  that  of  pressure r i s e .  modulus a p p r o a c h  to predict  The  soils  inertia  which are expected  and  are represented  the modulus r e d u c t i o n a n a l y s i s ,  observed  3000  the p o s t - c y c l i c  magnitude  of the s o i l .  as a r e s u l t  the e f f e c t s  substantial  before  properties  semi-  of p r e d i c t i n g  i n pore water p r e s s u r e d u r i n g c y c l i c  mobility  capable  capable  on a s o i l  r e d u c t i o n s i n the modulus t h a t  1000  failed  of  effective  o f an e a r t h q u a k e  for soils  the d e f o r m a t i o n s  cyclic  analysis  an  realistic  significant  incorporated into  is  a  primarily  also  as  dynamic  However, b e c a u s e  limited  analysis  induced deformations  reduction  rise.  of  CONCLUSIONS  which  t h e modulus  stress-strain  to predict  curves  deformations  90  of  sufficient  the  magnitude.  inability  development  of  This  such  of s t r a i n s  a  failure method  during  r e l a t i o n s h i p that  account  the  during The  for  the unloading  strains  limited  that  periods  in  of  hardening,  strain  alternatively significant  Only  development and  fall  accumulation  in will  successive post-cyclic  that  stress  develops  application.  a single load cycle w i l l  resulting  pressures.  rise  The  to  f o r t h i s a n a l y s i s cannot  cyclic  during  related  the  loading.  i s used  phase of each  pore  model  i n p o r e water p r e s s u r e  develop  by s t r a i n  reduction  the  increase  to  cyclic  stress-strain  i s presumably  from  dilation  by c o n s i d e r i n g  which  the  and  pore  observed  a  successive pressures  an a n a l y s i s be a b l e  of s t r a i n s  be  t o model  during  cyclic  loading. The  pore p r e s s u r e  displacements  approach a l s o  of t h e t a i l i n g s  of  the excess pore p r e s s u r e s  the  model, t h e r e d u c t i o n  lower The  than  that  failure  inertia  though the  created  near  failure  because  approach  i t ignores  When o n l y  in  pore  a minor  inertia  water p r e s s u r e  increase  forces they  generally  substantially  unless  a r e very  sensitive.  However, t h e i n e r t i a  large  when  during  water not or  forces w i l l  i n p o r e water p r e s s u r e  deformations. realistic  the s i g n i f i c a n c e of the  occur  do  inclusion  predict  strains  i n the pore  deformations  when t h e i n c r e a s e  of  to  realistic  conditions in  t o p r e d i c t the observed  f o r c e s on t h e d e v e l o p m e n t  increases  the  Even  i n t h e s h e a r modulus was  required  results  to predict  model.  of the pore p r e s s u r e  deformations  fails  cyclic  loading.  pressure  occurs,  cause the  substantial  soil  become  brings  substantial  is  very  significant  the s o i l  so n e a r  91  the  failure  condition  forces  causes  effects  of  loading to  effects inclusion  on  of  both  the  be  cyclic  strain  lies  forces  inertia  approach  in i t s  the  periods  of  approach  hence,  to  on  soil  i n the  softening  analysis.  number of and  the  entire equivalent  reproduce  the  effects  of  the  magnitude  in i t s strains  stress cycles,  depend  of  the  the  cyclic  and  to  loading  earthquake  observed  softening  the  stress  loading,  the  and  The  response expected  from  of  in-situ  of  cyclic  soil  sufficient  duration  soil  computed  shear  effects  in predicting a  incorporation  equivalent magnitude  of  and,  t e s t s performed at  an  include  pore pressure  laboratory  modulus r e d u c t i o n  include will  the  Because the  will  the  driving  deformations.  the  by  the  successive  reductions  duration  the  represented  The  of  modulus  in  F a i l u r e to  during  earthquake  the  applied.  behavior  observed  i n the  with  increase  i n a b i l i t y of  modulus r e d u c t i o n  of  observed  i n the  success  sufficient  small  forces  sufficient  the  The  levels  inertia  results  reproduce  any  s u b s t a n t i a l deformations.  the  predict  that  the  are  observed  i n the  field.  strains  inertia  will  forces  predict  and  realistic  deformations.  The  a d v a n t a g e of  uses r e l a t i v e l y predict  earthquake  geotechnical triaxial analytical  simple  and  the  modulus r e d u c t i o n  dynamic  and  induced  parameters  that  cyclic  triaxial  analysis  static-stress  deformations. may  t e c h n i q u e p e r m i t s the  be  tests  inclusion  analyses Only  determined are  the  it to  common  from  required. of  i s that  The  simple semi-  effects  of  92  pore  pressure  rise  on s o i l  behavior  a r i g o r o u s and complex e f f e c t i v e method, method  thus,  appears  for predicting  earthquake  loading.  without  stress  analysis.  t o be an e f f e c t i v e  the deformations  having  to resort The  and r e l a t i v e l y  of s o i l  to  proposed simple  structures during  93  REFERENCES Ambraseys, N.N. a n d Sarma, S.K. "The Response o f E a r t h Dams S t r o n g E a r t h q u a k e s , " G e o t e c h n i q u e 17, No. 3, p p . 181-213.  to  Annaki, M. a n d L e e , K.L. 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" C o n s i d e r a t i o n s i n t h e E a r t h q u a k e - R e s i s t a n t Design of E a r t h a n d R o c k f i l l Dams," G e o t e c h n i q u e 29, No. 3, 1979, pp. 215263. Seed, H.B. " S o i l L i q u e f a c t i o n and C y c l i c Ground during Earthquakes," Journal E n g i n e e r i n g D i v i s i o n , ASCE, V o l . 105, No. pp. 201-255.  Mobility f o r Level of t h e G e o t e c h n i c a l GT2, F e b r u a r y 1979,  96  Seed, Design 63.  H.B. " E a r t h q u a k e - R e s i s t a n t D e s i g n o f E a r t h Dams," S e i s m i c o f Embankments and C a v e r n s , ASCE Symposium, 1983, p p . 41-  Seed, H.B. and I d r i s s , I.M. " I n f l u e n c e of S o i l Conditions on Ground Motions during Earthquakes," Journal of t h e S o i l Mechanics and Foundation E n g i n e e r i n g D i v i s i o n , ASCE, V o l . 95, No. SM1, P r o c . P a p e r 6347, J a n u a r y 1969, pp. 99-137. Seed, H.B. and I d r i s s , I.M. " S o i l M o d u l i and Damping F a c t o r s f o r Dynamic R e s p o n s e A n a l y s e s , " R e p o r t No. EERC 70-10, U n i v e r s i t y o f California, Earthquake Engineering Research Center, Berkeley, C a l i f o r n i a , December 1970. Seed, H.B. a n d I d r i s s , I.M. " S i m p l i f i e d P r o c e d u r e f o r E v a l u a t i n g S o i l L i q u e f a c t i o n P o t e n t i a l , " J o u r n a l of the S o i l Mechanics and Foundation Engineering D i v i s i o n , ASCE, V o l . 97, No. SM9, P r o c . P a p e r 8371, September 1971, pp. 1249-1273. Seed, H.B., I d r i s s , I.M., L e e , R.L. a n d M a k d i s i , F . I . "Dynamic Analysis of t h e S l i d e i n t h e Lower San F e r n a n d o Dam d u r i n g t h e Earthquake of February, 1971," Journal of the G e o t e c h n i c a l Engineering Division, ASCE, V o l . 101, No. GT9, P r o c . P a p e r 11541, September 1975, pp. 889-911. Seed, H.B. a n d L e e , K.L. " L i q u e f a c t i o n o f S a t u r a t e d Sands D u r i n g C y c l i c Loading," J o u r n a l of the S o i l Mechanics and Foundation E n g i n e e r i n g D i v i s i o n , ASCE, V o l . 92, No. SM6, November 1966, p p . 105-134. Seed, H.B., L e e , K.L. and I d r i s s , I.M. " Analysis of the S h e f f i e l d Dam Failure," Journal of the S o i l Mechanics and Foundation Engineering Division, ASCE, V o l . 95, No. SM6, November 1969, pp. 1453-1490. Seed, H.B., L e e , K.L., I d r i s s , I.M. a n d M a k d i s i , F. " A n a l y s i s o f t h e S l i d e s i n t h e San F e r n a n d o Dams during the Earthquake of Feb. 9, 1971," Earthquake Engineering Research Center, Report No. EERC 73-2, June 1973. Seed, H.B., M a k d i s i , F . I . and D e A l b a , P. " P e r f o r m a n c e of Earth Dams during Earthquakes," Journal of the Geotechnical E n g i n e e r i n g D i v i s i o n , ASCE, V o l . 104, No. GT7, P r o c . Paper 13870, J u l y 1978, pp. 967-994. 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" S o i l Motion Computations by Characteristics Method," Journal of the Geotechnical Engineering Division, ASCE, Vol. 100, No. GT3, P r o c . P a p e r 10410, M a r c h 1974, pp. 247-263. S t u c k e r t , B. "Model S t u d y of S l o p e d T a i l i n g s D e p o s i t s , " M.A.Sc. T h e s i s , U n i v e r s i t y of B r i t i s h C o l u m b i a , V a n c o u v e r , Canada, 1982. Vaid, Y.P. and Finn, W.D.L. "Static Shear and L i q u e f a c t i o n P o t e n t i a l , " J o u r n a l of t h e Geotechnical Engineering Division, ASCE, Vol. 105, No. GT10, P r o c . P a p e r 14909, O c t o b e r 1979, pp. 1233-1246. V a i d , Y.P. and C h e r n , J . C . " E f f e c t of S t a t i c S h e a r on R e s i s t a n c e t o L i q u e f a c t i o n , " S o i l s and Foundations, Japanese Society of S o i l M e c h a n i c s and F o u n d a t i o n E n g i n e e r i n g , V o l . 23, No. 1, M a r c h 1 983. Vaid, Y.P. and Chern, J.C. "Mechanism of D e f o r m a t i o n during C y c l i c U n d r a i n e d L o a d i n g of S a t u r a t e d S a n d s , " S o i l Dynamics and E a r t h q u a k e E n g i n e e r i n g , V o l . 2, No. 3, 1983, pp. 171-177. Wong, K.S. and Duncan, J.M. "Hyperbolic S t r e s s - S t r a i n Parameters f o r N o n - L i n e a r F i n i t e E l e m e n t A n a l y s e s of S t r e s s e s and Movements in Soil M a s s e s , " R e p o r t No. TE-74-3, U n i v e r s i t y of C a l i f o r n i a , Berkeley, 1974. W i l s o n , E.L. and C l o u g h , R.W. "Dynamic R e s p o n s e by Step-by-Step Matrix A n a l y s i s , " P r o c e e d i n g s Symposium on t h e Use of Computers in C i v i l E n g i n e e r i n g , Lisbon, P o r t u g a l , October, 1962.  

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