UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Numerical studies of some aspects with pressuremeter tests and laterally loaded piles Yan, Li 1986

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1986_A7 Y36.pdf [ 10.9MB ]
Metadata
JSON: 831-1.0062673.json
JSON-LD: 831-1.0062673-ld.json
RDF/XML (Pretty): 831-1.0062673-rdf.xml
RDF/JSON: 831-1.0062673-rdf.json
Turtle: 831-1.0062673-turtle.txt
N-Triples: 831-1.0062673-rdf-ntriples.txt
Original Record: 831-1.0062673-source.json
Full Text
831-1.0062673-fulltext.txt
Citation
831-1.0062673.ris

Full Text

NUMERICAL STUDIES OF SOME ASPECTS WITH PRESSUREMETER TESTS AND LATERALLY LOADED P I L E S  by LI B.Sc,  YAN  Dalian I n s t i t u t e  A THESIS SUBMITTED  of Technology,  I N PARTIAL FULFILMENT OF  THE REQUIREMENTS FOR THE DEGREE OF MASTER OF A P P L I E D SCIENCE  in THE FACULTY OF GRADUATE STUDIES Department o f C i v i l E n g i n e e r i n g  We a c c e p t t h i s  t h e s i s as conforming  to the r e q u i r e d standard  THE UNIVERSITY OF B R I T I S H COLUMBIA October, ©  1982  1986  L i Y a n , 1986  In p r e s e n t i n g  this thesis  i n partial  f u l f i l m e n t of the  r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y of  British  Columbia,  it  freely available  I agree that f o r reference  agree that p e r m i s s i o n  the Library  shall  and study.  I  make  further  f o rextensive copying o f t h i s  thesis  f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e h e a d o f my d e p a r t m e n t o r by h i s o r h e r r e p r e s e n t a t i v e s . understood for  that  copying or p u b l i c a t i o n  f i n a n c i a l gain  C I V I L  E N C V I N E E R I N C X  The U n i v e r s i t y o f B r i t i s h 1956 Main Mall V a n c o u v e r , Canada V6T 1Y3 Date  Oci.  10  ,  thesis  s h a l l n o t be a l l o w e d w i t h o u t my  permission.  Department o f  of this  It is  i  966  Columbia  written  ABSTRACT Analyses subgrade  of  laterally  reaction  describing  the  lateral  force-deflection for  obtaining  method  or  P-Y in  In  little  addition,  installation. responses  to  which  can  obtained.  The the  P-Y  soil  disk  pressuremeter  a  and  is  curves  is  presented.  which  study.  disturbed from  linear the  a  simple  the  curve  nonlinear  the  soil  of  existing or  the  as  effects  measures  methods  suffer  parameters  of  from  input.  of  pile  lateral  a promising  lateral  and  of  pile  soil  in-situ  problem  rational  method  of  pressuremeter  curves  is  analysis. by  examining  pile  to  the  lateral  response  loads.  obtained  from a n a l y s i s  expansion  problem.  By  so  obtained  comparing  from  curves  to  The  installation  effect  on  and  P-Y  installation having  intact  is  the  obtain  evaluated  effect  different  from  and  P-Y  a  modelled  strength  a  by  a  modulus  soil.  triangular soil  is  of  analysis,  pressuremeter  curves  of  The  is  curves  soil  nonlinear  the  obtained  The  strain  of  the  the  curves  terms  curves  cavity  modifying  in  which  for  a  empirical  taken  element  of  A  is  finite  pressuremeter  properties  reliable  from  method  of  Most  either  using  rationality  offers  expansion  P-Y  zone  the  expansion,  surrounding  cylindrical  parametric  are  curves  curve  the  pressuremeter  curves.  Herein,  P-Y  using  P-Y  piles  reaction  account  cavity  from  examined  P-Y  on  The p r e s s u r e m e t e r , a  constructing  soil  obtaining  method be  rely  curves  difficulties  loaded  is  finite  modelled  i i  as  element an  program,  incremental  in  elastic material with hyperbolic stress strain employed t h r o u g h o u t . A t h i n  relation, is  i n t e r f a c e e l e m e n t and a s i m p l e  t e n s i o n c u t - o f f model s i m u l a t i n g t h e s o i l - p i l e  interface  b e h a v i o r has been i n c o r p o r a t e d i n t h e p r o g r a m . R e s u l t s o f t h e p r o g r a m and t h e i n t e r f a c e s i m u l a t i o n a r e i n good agreement w i t h c l o s e d form From c o m p a r i s o n  solutions.  of t h e r e s p o n s e s of p r e s s u r e m e t e r  l a t e r a l p i l e c o n d i t i o n s , the pressuremeter a d j u s t e d t o r e p r e s e n t t h e P-Y  c u r v e s can  c u r v e s . H o w e v e r , due  and be  to  f e a t u r e s o f t h e l o a d i n g m e c h a n i s m , t h e i n s t a l l a t i o n has d i f f e r e n t e f f e c t on p r e s s u r e m e t e r  c u r v e s t h a n on P-Y  For pressuremeter c u r v e s , the i n i t i a l  stiffness  a  curves.  i s much  a f f e c t e d by t h e s o i l  d i s t u r b a n c e s , but the u l t i m a t e p r e s s u r e  i s not s i g n i f i c a n t l y  a f f e c t e d . The  observed effects  f o r P-Y  c u r v e s . The  i n d e v e l o p i n g P-Y  opposite effects  practical  c u r v e s from  expansion curves i s d i s c u s s e d .  iii  are  s i g n i f i c a n c e of pressuremeter  these  Table of Contents ABSTRACT  i i  L I S T OF TABLES  viii  L I S T OF FIGURES  x  ACKNOWLEDGEMENTS  xv  DEDICATION 1.  2.  xvi  INTRODUCTION  1  1.1 I n t r o d u c t i o n  1  1.2 Scope o f T h e s i s  3  1.3 O r g a n i z a t i o n  4  of Thesis  REVIEWS OF PREVIOUS WORK  6  2.1 I n t r o d u c t i o n  6  2.2 M e t h o d s o f A n a l y s e s  6  2.3 S p e c i f i c a t i o n o f P-Y C u r v e s 2.3.1 S e m i - e m p i r i c a l  Methods  14  2.3.2 I n - s i t u T e s t i n g M e t h o d s  28  2.3.3 C e n t r i f u g e  30  Testings  2.3.4 F i n i t e E l e m e n t M e t h o d s 3.  13  ....32  F I N I T E ELEMENT PROGRAM  37  3.1 I n t r o d u c t i o n  37  3.2 F i n i t e E l e m e n t F o r m u l a t i o n  37  3.3 U n i f i e d A p p r o a c h - An E f f e c t i v e S t r e s s M e t h o d  4.  ..42  3.3.1 U n d r a i n e d A n a l y s i s  42  3.3.2 D r a i n e d  47  Analysis  3.4 S t r u c t u r e o f t h e P r o g r a m  48  3.5 S t r e s s - R e d i s t r i b u t i o n  49  CONSTITUTIVE RELATIONS  52  4.1 I n t r o d u c t i o n  52 iv  4.2 I n c r e m e n t a l N o n l i n e a r E l a s t i c 4.3 B i l i n e a r  5.  S o i l Model  E l a s t i c - p l a s t i c Model  ....58  4.4 I n c o r p o r a t i o n o f T e n s i o n F a i l u r e  60  CYLINDRICAL CAVITY EXPANSION THEORY  62  5.1 I n t r o d u c t i o n  62  5.2 E l a s t o - p l a s t i c  C l o s e d Form S o l u t i o n s  5.2.1 P r o b l e m s  63 .....63  5.2.2 C l o s e d Form S o l u t i o n s 5.3 F i n i t e E l e m e n t S i m u l a t i o n  65 70  5.3.1 F i n i t e e l e m e n t mesh domain  70  5.3.2 O u t e r b o u n d a r y e f f e c t s  72  5.4 F i n i t e E l e m e n t P r e d i c t i o n s  6.  53  74  5.4.1 M a t e r i a l M o d e l s a n d A n a l y s e s  74  5.4.2 M a t e r i a l P r o p e r t i e s  75  5.4.3 R e s u l t s a n d C o m p a r i s o n  77  F I N I T E ELEMENT STUDIES OF PRESSUREMETER TESTS  101  6.1 I n t r o d u c t i o n  101  6.2 F i n i t e E l e m e n t Mesh a n d B o u n d a r y C o n d i t i o n s  ... 107  6.3 A n a l y s e s a n d S o i l P a r a m e t e r s  109  6.4 I n f l u e n c e s o f P r e s s u r e m e t e r L/D R a t i o s  114  6.4.1  Cohesive S o i l s  115  6.4.2 C o h e s i o n l e s s S o i l s  128  6.4.3 Summary  1 40  6.5 C o m p a r i s o n s o f C y l i n d r i c a l C a v i t y E x p a n s i o n A n a l y s e s and F i e l d P r e s s u r e m e t e r T e s t D a t a ....142  7.  6.5.1 C o h e s i v e S o i l s  142  6.5.2 C o h e s i o n l e s s S o i l s  161  S O I L - P I L E INTERFACE ELEMENTS  175  v  7.1  Introduction  175  7.2 D e f o r m a t i o n Modes a t I n t e r f a c e  178  7.3 R e v i e w on I n t e r f a c e E l e m e n t s  180  7.3.1 J o i n t E l e m e n t s w i t h  180  Zero T h i c k n e s s  7.3.2 T h i n L a y e r I n t e r f a c e E l e m e n t 7.4 The P r o p o s e d M o d e l f o r S o i l - p i l e  Interface  7.4.1 F o r m u l a t i o n o f S t i f f n e s s M a t r i x C o n s t i t u t i v e Laws 7.4.2 D e f o r m a t i o n a n d S t r e n g t h 7.4.3 I n c o r p o r a t i o n  185 ....189  -  190  C h a r a c t e r i s t i c s 192  o f D e f o r m a t i o n Modes  7.4.4 I n t e r f a c e E l e m e n t - Mesh L a y o u t a n d I t s Thickness  199  7.4.5 P r e l i m i n a r y A s s e s s m e n t s - D i r e c t Condition  202  Shear  F I N I T E ELEMENT STUDIES ON LATERALLY LOADED P I L E S 8.1  194  ..216  Introduction  216  8.2 P l a n e S t r a i n . M o d e l  220  8.3 C l o s e d  222  Form S o l u t i o n  8.4 F i n i t e E l e m e n t S i m u l a t i o n  230  8.4.1 F i n i t e E l e m e n t Mesh L a y o u t  230  8.4.2 O u t e r B o u n d a r y C o n s i d e r a t i o n  233  8.4.3 I n t e r f a c e E l e m e n t  236  8.5 C o h e s i v e S o i l s 8.5.1  242  Soil Properties  8.5.2 R e s u l t s 8.6 C o h e s i o n l e s s  and D i s c u s s i o n s Soils  243 246 260  INSTALLATION EFFECTS ON PRESSUREMETER CURVES AND P-Y CURVES FOR LATERALLY LOADED P I L E S IN COHESIVE SOILS  268  9.1  268  Introduction vi  9.2 E x p e r i m e n t a l a n d A n a l y t i c a l E v i d e n c e s on Extent of S o i l D i s t u r b a n c e A f t e r P i l e Installation  270  9.3 F i n i t e  274  Element A n a l y s i s  9.3.1 D i s t u r b a n c e 9.3.2 F i n i t e  Simulation  E l e m e n t Mesh  281  9.4 R e s u l t s a n d D i s c u s s i o n  284  9.4.1 P r e s s u r e m e t e r  284  Curves  9.4.2 P-Y C u r v e s  10.  276  289  9.5 Summary  298  SUMMARY AND CONCLUSIONS  300  REFERENCES  306  APPENDIX A  313  APPENDIX B  315  vii  L I S T OF  TABLES  T a b l e 5.1 S o i l P a r a m e t e r s of C o h e s i v e C a v i t y Expansion S i m u l a t i o n  Soils for Cylindrical 76  T a b l e 5.2 S o i l P a r a m e t e r s of C o h e s i o n l e s s S o i l s f o r C y l i n d r i c a l C a v i t y Expansion S i m u l a t i o n T a b l e 5.3  R e l a t i o n between S h e a r  76  Modulus Reduction F a c t o r  and F a i l u r e P o i s s o n ' s R a t i o  93  T a b l e 6.1  S o i l Parameters  for Axisymmetric Analyses  T a b l e 6.2  S o i l Parameters  f o r C a v i t y Expansion  T a b l e 6.3 L/D Soils T a b l e 6.4 L/D Strength  R a t i o E f f e c t s on I n i t i a l  ....  Analyses..113  Slopes i n Cohesive 119  R a t i o E f f e c t s on D e r i v e d U n d r a i n e d  Shear 125  T a b l e 6.5 L/D R a t i o E f f e c t s on D e r i v e d U n d r a i n e d S t r e n g t h ( B o r s e t t o e t a l , 1980) T a b l e 6.6 L/D R a t i o E f f e c t s on I n i t i a l Cohesionless S o i l s  Shear 127  Slopes i n 132  T a b l e 6.7 L/D R a t i o E f f e c t s on t h e D e r i v e d F r i c t i o n in Cohesionless S o i l s  Angles 137  T a b l e 6.8 P r e s s u r e m e t e r T e s t R e s u l t s a t H a m i l t o n T e s t San F r a n c i s c o T a b l e 6.9  113  S o i l Parameters  f o r San  F r a n c i s c o Bay Mud  Site, 153  ....  155  T a b l e 6.10  S o i l Parameters  f o r M c D o n a l d Farm S i t e  165  T a b l e 6.11  Soil  from Byrne  166  Parameters  and Cheung  T a b l e 7.1 P r o p o s e d C o e f f i c i e n t s o f S k i n F r i c t i o n S o i l s and C o n s t r u c t i o n M a t e r i a l s T a b l e 7.2  between 195  S o i l P r o p e r t i e s f o r I n t e r f a c e Elements  T a b l e 7.3 S h e a r S t r e s s D i s t r i b u t i o n w i t h i n I n t e r f a c e at I n t e g r a t i o n P o i n t s ( f o r C o h e s i v e S o i l s )  205 Element 206  T a b l e 7.4 A p p l i e d S h e a r S t r e s s v s R e l a t i v e D i s p l a c e m e n t I n t e r f a c e E l e m e n t under V a r i o u s A s p e c t R a t i o s T a b l e 7.5 S h e a r S t r e s s D i s t r i b u t i o n w i t h i n I n t e r f a c e at I n t e g r a t i o n P o i n t s ( f o r C o h e s i o n l e s s S o i l s ) T a b l e 8.1 P l a s t i c i t y Lateral Circular  of 208  Element 212  S o l u t i o n o f U l t i m a t e S o i l R e s i s t a n c e on P i l e i n Cohesive S o i l s 238 viii  T a b l e 8.2 P a r a m e t e r s o f E l a s t o - p l a s t i c S o i l , P i l e I n t e r f a c e E l e m e n t s f o r FE A n a l y s i s S l o p e s o f P r e d i c t e d P-Y  and  T a b l e 8.3  Initial  T a b l e 8.4  U l t i m a t e S o i l R e s i s t a n c e o f P r e d i c t e d P-Y  245  Curves  248 Curves 251  T a b l e 8.5 N o n l i n e a r S o i l P a r a m e t e r s f o r FE A n a l y s e s o f Curves  ix  P-Y 258  L I S T OF  FIGURES  Fig  2.1 W i n k l e r  Spring Approach  Fig  2.2 A T y p i c a l Shape of P-Y  Fig  2.3 C o n s t r u c t i o n  Fig  2.4  Coefficient  of P-Y  ...9 Curve  11  Curves f o r S o f t Clay  A for Stiff  anf F i s s u r e d C l a y  F i g 2.5 C o n s t r u c t i o n  of P-Y  Curve f o r S t i f f  Fig  of P-Y  C u r v e f o r Sand  2.6 C o n s t r u c t i o n  17 19  Clay  19 21  F i g 2 . 7 ( 1 ) , ( I I ) Assumed S o i l F a i l u r e M e c h a n i s m s a r o u n d P i l e 23 Fig  2.8 N o n d i m e n s i o n a l C o e f f i c i e n t  Fig  2.9  Fig  2.10  Fig  3.1  Element Types employed  Fig  3.2  S t r e s s S t a t e a s s o c i a t e d w i t h Load Shedding  Fig  4.1  Hyperbolic :  Fig  4.2 S t r e s s S t r a i n C u r v e s f o r D r a i n e d Sand  Fig  4.3  B i l i n e a r E l a s t i c P l a s t i c Model  Fig  5.1  Problem of C y l i n d r i c a l C a v i t y E x p a n s i o n i n S o i l  B i l i n e a r P-Y  A and B  ....25  C u r v e f o r Sand p r o p o s e d by S c o t t  FE Domain e m p l o y e d  ....26  by Y e g i a n and W r i g h t  33  by CONOIL  Representation  40 50  of A S t r e s s - s t r a i n  Curve  T r i a x i a l Tests  on  55 57 59  Masses  64  Fig  5 . 2 ( a ) S o i l Domain u s e d f o r FE A n a l y s i s  71  Fig  5.2(b) FE Mesh f o r C a v i t y E x p a n s i o n S i m u l a t i o n  71  Fig  5.3 I n f l u e n c e s o f O u t e r B o u n d a r y R a d i u s i n C a v i t y Expansion Simulation F i g 5.4 C o m p a r i s o n o f O r i g i n a l P r o g r a m and C l o s e d Form Solution Fig Fig Fig  73 78  5.5 D i s p l a c e m e n t D i s t r i b u t i o n u n d e r U n d r a i n e d Strain Condition  Plane  5.6 C o m p a r i s o n o f M o d i f i e d P r o g r a m and C l o s e d Solution  Form  5.7  Stress Distribution  80  i n Comparison w i t h Closed x  82 Form  Solution  84  Fig  5.8 P r e s s u r e E x p a n s i o n C u r v e O r i g i n a l Program  Fig  5.9  Fig  5.10 P r e s s u r e E x p a n s i o n C u r v e a f t e r D i s c a r d i n g Memory  F i g 5.11  for Cohesionless Soils  from 86  S o i l S t r e s s Path i n C a v i t y Expansion Problem  88  Stress 90  P r e s s u r e Expansion Curve w i t h S m a l l e r R e d u c t i o n  F a c t o r of Shear Modulus  94  F i g 5.12  Load Shedding E f f e c t  on P r e s s u r e E x p a n s i o n C u r v e  F i g 5.13  P l a s t i c Volume C o r r e c t i o n  F i g 5.14  Pressure Expansion Curves a f t e r  f o r FE A n a l y s i s 'Plastic'  95 97  Volume  Correction  99  F i g 6.1  L/D  R a t i o E f f e c t on D i s p l a c e m e n t P a t t e r n  103  Fig  6.2  L/D  R a t i o E f f e c t on E l a s t i c M o d u l u s  105  Fig  6.3  FE Mesh f o r A x i s y m m e t r i c A n a l y s i s  108  Fig Fig  6.4 FE Mesh f o r C a v i t y E x p a n s i o n A n a l y s i s 110 6.5 L/D R a t i o E f f e c t on P r e s s u r e m e t e r C u r v e s i n C o h e s i v e Soils 116 F i g 6.6(a) G i b s o n and A n d e r s o n M e t h o d f o r d e r i v i n g U n d r a i n e d Shear S t r e n g t h 122 Fig  6.6(b) P r e s s u r e m e t e r C u r v e s  Fig  6.7  i n Semi-log Scale  N o n l i n e a r S o i l Response under  D i f f e r e n t L/D  123 Ratio 129  Fig  6.8  L/D  R a t i o E f f e c t on P r e s s u r e m e t e r C u r v e s i n  Cohesionless Soils  130  F i g 6.9(a) P r e s s u r e m e t e r C u r v e s  in Cohesionless S o i l s . . .  Fig  i n Log-Log S c a l e  6.9(b) P r e s s u r e m e t e r C u r v e s (Cohesionless Soils)  136  138  Fig  6.10  Pressuremeter Curve Measured a t H a m i l t o n S i t e  Fig  6.11  L o g of B o r e h o l e a t H a m i l t o n S i t e  Fig  6.12  Engineering Soil  Fig  6.13  Undrained S t r e n g t h w i t h Depth  ..144 145  Properties at Hamilton Site....147  xi  148  Fig  6 . 1 4 C o e f f i c i e n t of E a r t h Pressure  151  Fig  6 . 1 5 Comparison w i t h F i e l d Measurements ( 1 )  156  Fig  6 . 1 6 Comparison w i t h F i e l d Measurements ( 2 )  157  Fig  6 . 1 7 S o i l F a i l u r e Mode a s s o c i a t e d w i t h Tests  Pressuremeter 160  i n Cohesive S o i l s  Fig  6 . 1 8 S o i l P r o f i l e a t M c D o n a l d Farm  Fig Fig  6 . 1 9 Pressuremeter Curve measured a t McDonald Farm...164 6 . 2 0 C o m p a r i s o n o f FE P r e d i c t i o n w i t h F i e l d D a t a (SBPMT & CPT d a t a ) 1 69  Fig  6 . 2 1 C o m p a r i s o n o f FE P r e d i c t i o n w i t h F i e l d D a t a & Cheung d a t a )  Fig  6 . 2 2 E f f e c t o f t h e Assumed P o i s s o n ' s FE R e s u l t s  Fig  7 . 1 S o i l Movement a t S h a l l o w  Fig  7 . 2 S o i l Flows around P i l e a t Depth  177  Fig  7 . 3 S c h e m a t i c o f D e f o r m a t i o n Modes a t I n t e r f a c e  179  Fig  7 . 4 J o i n t Element w i t h Zero T h i c k n e s s . .  181  Fig  7.5 Cylindrical  184  Fig  7 . 6 Thin Layer I n t e r f a c e Element  Fig  7 . 7 Stress Conditions Modes  Fig  7 . 8 Mesh L a y o u t f o r T r i a n g u l a r I n t e r f a c e E l e m e n t  Fig  7.9  Fig  7 . 1 0 R e l a t i v e D i s p l a c e m e n t v s I n t e r f a c e R e s i s t a n c e under Various L / t Ratio for Cohesive S o i l s . . . . . 2 0 9  Fig  7.11 R e l a t i v e Displacement vs I n t e r f a c e Resistance Various L/t Ratio for Cohesionless S o i l s  Fig  8 . 1 Concept of.P-Y C u r v e s  218  Fig  8 . 2 ' D i s k ' A n a l y s i s f o r P-Y C u r v e s  221  Fig  8 . 3 Outer Boundary and P o i s s o n ' s Stiffness Ratio n  226  Fig  162  (Byrne 170  R a t i o V a l u e on t h e 172 176  Depth  I n t e r f a c e Element  186-  with Various  Interface Deformation 196  S i m u l a t i o n of D i r e c t Shear T e s t i n g  . . . . . 2 0 3  under 213  R a t i o E f f e c t s on  8 . 4 B o u n d a r y E f f e c t on t h e E x t r e m e V a l u e s o f M xi i  201  227  F i g 8.5  FE Mesh f o r L a t e r a l l y L o a d e d P i l e  232  F i g 8.6(a) E f f e c t s of I n t e r f a c e Element L / t R a t i o  239  Fig  8.6(b) E f f e c t s o f I n t e r f a c e E l e m e n t L / t R a t i o  241  Fig  8.7  247  F i g 8.8  FE P r e d i c t i o n o f P-Y  Curves u s i n g Model  I n f l u e n c e of I n t e r f a c e B e h a v i o r  F i g 8.9 P-Y C u r v e s f r o m FE P r e d i c t i o n Tension Cut-off Model) F i g 8.10  (1)  250  ( I s o t r o p i c Model  vs 253  S o i l Stress D i s t r i b u t i o n  F i g 8.11 P-Y Soil  Curves f o r E l a s t i c  256  Plastic  F i g 8.12 H y p e r b o l i c C u r v e F i t t i n g Soils  S o i l and  f o r P-Y  F i g 8.13 O u t e r B o u n d a r y E f f e c t on t h e P-Y Cohesionless S o i l F i g 8.14 Soil  Interface Effect  F i g 8.15  Curve F i t t i n g  on The P-Y  f o r P-Y  Nonlinear 259  Curves i n Cohesive 261 Curve i n 263  Curve i n C o h e s i o n l e s s 265  Curves i n C o h e s i o n l e s s S o i l s 267  Fig  9.1  F i e l d Data of E x c e s s Pore P r e s s u r e from P i l e  Fig  9.2  Typical Stress Distribution after P i l e Driving  Fig  9.3  T y p i c a l V a r i a t i o n of C  Fig  9.4  S i m u l a t i o n of I n s t a l l a t i o n  Fig  9.5  Assumed M o d u l u s  u  Driving 272  a t end o f C o n s o l i d a t i o n for Pile  and S t r e n g t h V a r i a t i o n  9.6  .275 277.  within  D i s t u r b e d Zone Fig  ..273  278  S i m u l a t i o n of I n s t a l l a t i o n  f o r P r e s s u r e m e t e r ....280  Fig  9.7 FE Mesh f o r S t u d y i n g I n s t a l l a t i o n E f f e c t on Pressuremeter Curves F i g 9.8 FE mesh f o r S t u d y i n g I n s t a l l a t i o n E f f e c t on Curves  282 P-Y 283  Fig  9.9  P r e s s u r e m e t e r C u r v e s under V a r i o u s S o i l D i s t u r b a n c e s 285  Fig  9.10 R e l a t i v e I n i t i a l S l o p e o f P r e s s u r e m e t e r C u r v e v s S i z e o f D i s t u r b e d Zone 287 xi i i  Fig  9.11 R e l a t i v e I n i t i a l S l o p e o f P r e s s u r e m e t e r C u r v e v s Extent of D i s t u r b a n c e 288  Fig  9.12 P-Y caly)  C u r v e s Under V a r i o u s S o i l D i s t u r b a n c e s  (stiff 290  Fig  9.13 P-Y caly)  C u r v e s Under V a r i o u s S o i l D i s t u r b a n c e s  (soft  Fig Fig  291  9.14 R e l a t i v e I n i t i a l D i s t u r b e d Zone  S l o p e of P-Y  9.15 R e l a t i v e I n i t i a l Disturbance  S l o p e o f P-Y  C u r v e v s S i z e of 293 Curve vs E x t e n t of 294  Fig  9.16 R e l a t i v e U l t i m a t e R e s i s t a n c e o f P-Y of D i s t u r b a n c e  Curve vs  Fig  9.17 R e l a t i v e U l t i m a t e R e s i s t a n c e o f P-Y of D i s t u r b a n c e  Curve vs Extent 297  xiv  Size 296  ACKNOWLEDGEMENTS I wish Professor  t o express  my g r e a t  g r a t i t u d e t o my a d v i s o r ,  P e t e r M. B y r n e f o r h i s s u p p o r t ,  i n v a l u a b l e guidance d u r i n g a l l t h e stages am a l s o d e e p l y careful  reviews  indebted  p a t i e n t and of t h i s t h e s i s . I  t o P r o f e s s o r W.D.Liam F i n n  and c o n s t r u c t i v e  forh i s  suggestions.  I a l s o want t o t h a n k P r o f e s s o r s R.G. C a m p a n e l l a a n d Y.P.  V a i d , a n d D r . P.K. R o b e r t s o n f o r t h e i r h e l p s a n d u s e f u l  d i s c u s s i o n s d u r i n g my s t a y a t UBC. The p r e s s u r e m e t e r r e s u l t s a t M c D o n a l d Farm were g e n e r o u s l y P.K.  by D r .  Robertson. The  Civil  provided  test  r e s e a r c h a s s i s t a n t s h i p a w a r d e d by t h e D e p t . o f  Engineering  gratefully  during  t h e p e r i o d o f 1985-1986 i s  acknowledged.  T h a n k s a r e a l s o e x t e n d e d t o my c o l l e a g u e s ,  Upul  A t u k o r a l a , F r a n c i s c o Salgado, John A l a n Howei, and B l a i r G o h l who s h a r e common i n t e r e s t s i n S o i l  Mechanics.  S p e c i a l t h a n k s go t o my w i f e , Chunyan f o r h e r s u p p o r t , t y p i n g and e d i t t i n g  the f i r s t  F i n a l l y , but not l e a s t ,  draft. I wish  t o thank  Professor  Shou-I T s i e n , I n s t i t u t e o f M e c h a n i c s , C h i n e s e Academy o f Sciences,  f o r i n t r o d u c i n g me t o t h i s  the M i n i s t r y of E d u c a t i o n  f a s c i n a t i n g f i e l d , and  of P e o p l e ' s R e p u b l i c  a w a r d i n g me a f e l l o w s h i p f o r s t u d y i n g  xv  of China f o r  i n Canada.  DEDICATION  TO MY PARENTS  xvi  1.  1.1  INTRODUCTION  INTRODUCTION P i l e s h a v e been u s e d a s p a r t o f s t r u c t u r a l  foundations  f o r many c e n t u r i e s . They m i g h t h a v e been known a s  one  o l d e s t type of f o u n d a t i o n  the  system t o mankind. With  d e v e l o p e m e n t s i n human c i v i l i z a t i o n ,  of  the  t h e need t o c o n s t r u c t  v a r i o u s t y p e s of m a s s i v e s t r u c t u r e s , such as h i g h r i s e complex b u i l d i n g , more and piled  p o r t and  more u n f a v o r e d  s i t e s has  f o u n d a t i o n . In order  cost-effective  piled  research e f f o r t  has  harbour,  offshore p l a t f o r m , at  i n c r e a s e d the usages of  to design a safe  and  f o u n d a t i o n s y s t e m , a l a r g e amount o f been p a i d i n t h i s a s p e c t  knowledge of p i l e b e h a v i o r  under d i f f e r e n t  t o improve  our  governing  factors. General  f o r c e s a c t i n g on a p i l e d  c o n s i s t of a x i a l  l o a d s , l a t e r a l l o a d s , and  F o r many y e a r s , v e r t i c a l p i l e s resist axis.  the a x i a l  foundation u s u a l l y bending  are considered only able  l o a d s t h a t were a p p l i e d i n l i n e w i t h  Therefore, p i l e s  that are r e q u i r e d to support  l o a d s , were i n s t a l l e d a t a b a t t e r . H o w e v e r , i t i s realized  t h a t the  moments. to  pile  lateral now  l a t e r a l r e s i s t a n c e of a v e r t i c a l p i l e i s  considerable. Although  i n recent years  l a r g e numbers o f a n a l y s i s  m e t h o d s h a v e been p r o p o s e d , p e o p l e design  are s t i l l  not a b l e  the l a t e r a l l y loaded p i l e w i t h c o n f i d e n c e  e f f e c t i v e n e s s . People  continue 1  t o seek f o r t h e  to  and  simple  and  2  rational At P-Y  method. present,  curve  is  analysing accuracy  laterally  have  been  around  a  method,  the  however,  curves.  proposed  These  Their  to  loaded curves  of  most  field  of  different  the  such  behavior  as  for  those  sand,  universal  rational  of  soils  recommended  obtained  in  of  The  curves  tests  adoptability  piles. the  generally  load  method  on  model  are  nonlinear  depends  P-Y  pile,  loaded  with  by  from  stiff  clay  and  usages  thus  is  questionable. New  procedures  proposed. finite  The  analysis  rigorous  and  incorporate  the  curves  for  the  from  further  is  P-Y  now  curves  curves  from  generally method.  nonlinear  purposes,  P-Y  soil soil  factors  soil-pile  have  been  2-dimensional  considered  This  method  behavior  such  as  interface  be  can  and  properties.  to  develop  However,  pile  simulation  deserve  considerations.  expansion  test  method  similarity  provoked  of  fundamental  effects,  Development  laterally  developing  rational  the  the  practical  installation  for  development  element  most  easily  This  P-Y  laterally  backcalculation  the  versatile  of  shapes  still  the  responses  of  clay.  method  be  development  soft  reaction  to  this  API'(1976).  subgrade  considered  the of  the  is  of  is  simple  loaded  curves  another  between  the  P-Y  piles.  effort  of  method  and  the  from  Its  that  rational,  loading  the  in  pattern  practical  theoretical  pressuremeter  has  appeared  the of  light  recently.  of  the  pressuremeter  attraction  studies,  which  and  has include  3 the examination of the basic  assumption  in interpreting  d a t a , a n d t h e p o s s i b i l i t y o f d e v e l o p i n g P-Y c u r v e s pressuremeter  test  from  curves.  1.2 SCOPE OF THESIS Main 1.  of t h i s t h e s i s  are threefold  :  t o examine a n a l y t i c a l l y t h e v a l i d i t y o f a x i s y m m e t r i c plane s t r a i n assumption  f o r the pressuremeter  study the pressuremeter  membrane l e n g t h t o d i a m e t e r  ratio 2.  purposes  (L/D) e f f e c t  on t h e p r e s s u r e m e t e r  t o examine a n a l y t i c a l l y t h e f a c t o r s  test  t e s t s , and  results,  a f f e c t i n g the  d e v e l o p m e n t o f P-Y c u r v e s f r o m 2D p l a n e s t r a i n such as t h e s o i l - p i l e 3.  interface  behavior.  t o examine a n a l y t i c a l l y t h e p o s s i b l e installation  effects  different  on t h e p r e s s u r e m e t e r  curves and t h e l a t e r a l l o a d - p i l e P-Y  analysis,  expansion  deflection  curves ( i . e .  curves).  Thus, t h e t h e s i s cylindrical  cavity  mainly consists  expansion  responses, and l a t e r a l l y p r o g r a m CONOIL ( V a z i r i ,  theory,  of t h r e e  parts:  pressuremeter  loaded p i l e .  The f i n i t e  1986) was u s e d  element  throughout the  thesis. The  p r o g r a m was f i r s t v e r i f i e d by e x a m i n i n g t h e  cylindrical  cavity  elasto-perfectly  expansion problem.  f o r both  p l a s t i c c l a y and e l a s t o - p l a s t i c  sand were compared w i t h c l o s e d reliability  Results  form s o l u t i o n s .  o f t h e p r o g r a m was e n s u r e d .  frictional  Thus, t h e  4 In  t h e second  s t r a i n assumption theoretically  part, the v a l i d i t y f o r pressuremeter  of axisymmetric-plane  t e s t s was e x a m i n e d  by m o d e l l i n g p r e s s u r e m e t e r  response  i n a 3D  a x i s y m m e t r i c a l d o m a i n u n d e r d i f f e r e n t L/D r a t i o a n d a 2D axisymmetri-plane  s t r a i n domain r e s p e c t i v e l y .  Pressuremeter  t e s t s a t two s i t e s ( c l a y s a n d s a n d s ) were a l s o using plane  s t r a i n f i n i t e element s i m u l a t i o n of c a v i t y  e x p a n s i o n . The r e s u l t s were c o m p a r e d w i t h f i e l d In curves  the f i n a l from  performed The  finite  importance  element plane  s t r a i n f o r m u l a t i o n was  with available  c l o s e d form  of p r o p e r l y s i m u l a t i n g s o i l - p i l e  i s illustrated  Furthermore,  data.  p a r t o f t h e t h e s i s , d e v e l o p m e n t o f P-Y  and v a l i d a t e d  properties  analysed  from  the i n s t a l l a t i o n  the f i n i t e  solution.  interface  element  results.  e f f e c t s of pressuremeter  p i l e on t h e i r p r e s s u r e - e x p a n s i o n a n d P-Y c u r v e s  and  were  e v a l u a t e d by p e r f o r m i n g a p a r a m e t r i c s t u d y , a n d t h e installation P-Y c u r v e s  e f f e c t s were d i s c u s s e d f o r t h e d e v e l o p m e n t o f  from p r e s s u r e - e x p a n s i o n  curves.  1.3 ORGANIZATION OF THESIS The  thesis consists  of t e n c h a p t e r s p r e s e n t i n g t h r e e  main t o p i c s : c y l i n d r i c a l c a v i t y e x p a n s i o n pressuremeter Chapter analysis  t e s t , and l a t e r a l l y 2 briefly  of l a t e r a l l y  examination introduction  theory,  loaded s i n g l e  pile.  r e v i e w s t h e p r e v i o u s work on t h e loaded p i l e s .  of t h e i r advantages  E m p h a s i s i s g i v e n on t h e  and shortcomings.  o f t h e p r o g r a m CONOIL  A brief  i s given i n Chapter  3.  5 Chapter in  4 presents the s t r e s s - s t r a i n  the t h e s i s . Chapter  relation  of s o i l  5 e x a m i n e s CONOIL i n c a v i t y  used  expansion  c o n d i t i o n a n d some n u m e r i c a l f e a t u r e s w h i c h were m o d i f i e d and added i n t h e program. Comparison closed  form s o l u t i o n s  illustrates  of the r e s u l t s with  t h e c a p a b i l i t y of the  m o d i f i e d program i n s o l v i n g these problems. p r e s e n t s the s t u d i e s of pressuremeter the t e s t field  r e s u l t s , and t h e f i n i t e  test  6  L/D r a t i o e f f e c t on  element  p r e d i c t i o n s of  data.  Chapter modelling  Chapter  7 d i s c u s s e s the i n t e r f a c e element  soil-pile  i n t e r f a c e b e h a v i o r . Chapter  t h e d e v e l o p m e n t o f P-Y c u r v e s f r o m p l a n e s t r a i n E m p h a s i s i s on t h e p r o p e r behavior. Chapter pressuremeter  used i n 8 studies model.  simulation of s o i l - p i l e  9 examines t h e i n f l u e n c e of p i l e  interface and/or  i n s t a l l a t i o n s on t h e P-Y c u r v e s a n d  p r e s s u r e - e x p a n s i o n curves r e s p e c t i v e l y , and i t s s i g n i f i c a n c e in  c o n v e r t i n g the pressuremeter A g e n e r a l summary o f t h i s  c u r v e s t o t h e P-Y c u r v e s . r e s e a r c h and major  c o n c l u s i o n s a r e presented i n Chapter researches are a l s o suggested  in this  10. P o s s i b l e chapter.  future  2. REVIEWS OF PREVIOUS WORK  2.1  INTRODUCTION A complete a n a l y s i s of l a t e r a l l y  difficult  and c o m p l i c a t e d ,  nonlinear  stress-strain  practical application, a l w a y s made i n an In review  loaded p i l e s  r e q u i r i n g a 3D a n a l y s i s w i t h t h e  relation  of the s o i l .  For the  s i m p l i f i c a t i o n s of s o i l  behaviour  are  analysis.  t h i s Chapter,  e f f o r t s a r e made t o g i v e a g e n e r a l  o f t h e p r e v i o u s work i n t h e a n a l y s e s  loaded p i l e s .  i s very  Concentration  of  laterally  i s on t h e e x a m i n a t i o n  of  a d v a n t a g e s a n d l i m i t a t i o n s w i t h e a c h a p p r o a c h . R e v i e w s on t h e d i f f e r e n t methods o f a n a l y s i n g t h e p r o b l e m a r e g i v e n i n Section  2.2 w i t h e m p h a s i s on t h e n o n l i n e a r s u b g r a d e r e a c t i o n  a p p r o a c h , and t h e c u r r e n t methods o f s p e c i f y i n g t h e nonlinear in  soil  r e a c t i o n ( o r P-Y c u r v e s )  curves  are  reviewed  S e c t i o n 2.3.  2.2 METHODS OF ANALYSES A l a r g e number lateral  o f methods f o r t h e c a l c u l a t i o n of t h e  d e f l e c t i o n s and of the d i s t r i b u t i o n  moments a t w o r k i n g  l o a d s and of t h e u l t i m a t e  r e s i s t a n c e of s i n g l e p i l e s and p i l e p r o p o s e d . To d a t e into  four groups  the s o i l  lateral  t h e s e m e t h o d s c a n be b r o a d l y (Banerjee  responses,  bending  g r o u p s have been  and D r i s c o l l ,  B y r n e , 1984) d e p e n d i n g on t h e s i m p l i c i t y for  of  classified  1976, A t u k o r a l a a n d of models adopted  i . e . the modulus of subgrade 6  7  reaction element  method,  formulation,  The (1971) soils  elastic  in  a  form  the  (Mindlin,  the of  based  interior  on of  1936).  applicable  to  experiences  interaction  case a  nonlinearity  of  overestimate  the  shown  developed  behavior  by  solution  for  elastic  and  that  of  piles,  analysis  of  pile  soil-piles  since  it  interaction  point  the  between  soil  made  use  load  behaves and  method  can  and  not  is  as  the  foundation.  ignores  interaction,  a  soil  the  group  that  and  is  material  Consequently  small  piles  continuum the  homogeneous  finite  Poulos  between  Mindlin's  assumes  the  approach.  which  nonlinear  have  element  factor  holds. of  approach,  interaction  isotropic  the  approach  The method  superposition in  boundary  the  semi-infinite,  law  used  and  the  elastic  be  continuum  the  linear of  elastic  continuum  evaluates  calculated in  the  only  Past  the method  and  tends  to  piles  (Novak,  finite  element  1979). Many method  in  attempts the  foundation 1976, and  analysis  (Baguelin  Kuhlemeyer,  Byrne,  have  1984).  been of  et  1979, In  al,  1977,  Yegian  the  finite  the  complex  stress-strain-strength  and  the  complicated  simulated.  Although  computers  geotechnical  and  discreted  geometry recent their  engineering  1980,  into  of  pile  and  1973,  Abel, Atukorala the  elements  in  which  characteristics  of  soils  the  problem  successful to  a  formulation,  finite  development  enable  of  Desai  Wright,  element  soil  the  resistance  and  surrounding  large  is  lateral  to  of  can  the  a  properly  ability  application  perform  be  of  in  non-linear  8  analysis  of  the  way  only  whole of  to  The method.  has  interaction of  Mindlin's  element  analysis. required  by  choosing  soils  is  less  the  routine an  nonhomogeneous  is  The one  of  handling  oldest  beam a n d uncoupled as  shown  problem,  discretes Winkler in  Fig.  the  subgrade  reaction  used  treats  the  springs.  pile  Those  represent  the  boundary element  to  for  as  soils  so  research  method,  soil  in  laterally  finite  soil,  the  a  that  that remain  the  into  the  tool.  which  may  be  soil-structure  linearly  uncoupled  the  the  also  difficulties  analyse  surrounding  of  but  not  nonlinear  another  to  used  1976)  solution  the  as  the  2.1  the  regarded  methods  been  that  (e.g.  the  compared  soil  of  al,  appropriate  medium  vast  force  of  has  boundary  an  the  point  type  soil-pile  the  than  approximate  relation  some  over  shown  and  modulus  interaction  was  remains  in  to  1978)  work,  generally  the  et  al,  this  numerical  soil  method  et  for  enormous.  the  design  and  the  soils)  expensive  cost  stress-strain-strength method  it  of  integrates  (Banerjee  cases  interaction  another  for  The  (Banerjee  be  discretizes  homogeneous  element.  to  applied  and  solution  for  most  However  is  seems  required  s t i l l  method  interface  soils  analysis  is  which  the  work  The method  force  homogeneous  In  and  successfully  surface  piles.  simulate  cost  element  solution  problems,  problem  problems.  nonhomogeneous  in  real  been  point  discretized  loaded  a  soil-pile  elementary  in  system,  boundary It  surface  on  dimensional  rigorously  soil-pile  analyses  only  three  a  bed  Winkler  elastic of springs  load-deflection  M  H  independent springs  pile segments -OHM-  Fig.  2.1 W i n k l e r S p r i n g  Approach  10  properties equation on  the  for  this  d'y T-t dx  = axial  pile  at  per  unit  length;  soil  The  governing  system  solution  The  for  a  reaction  governing  is  derived  based  beam-column  is  taken  equation  is  as in  on  a  line  the  d y — f - p = 0 ; dx  an  form:  2  load  point  loadings.  soil-pile  where  + Px  q  the  of  Hetenyi's  1946).  EI  Px  lateral  type  foundation,  (Hetenyi,  where:  the  classical  elastic load  under  on  piles;  x along and  (2.2.1)  2  EI  the  is  y  =  pile  the  lateral  length;  flexural  deflection  p  = soil  rigidity  of  reaction  of  the  pile. In  the  above  representing more  reasonably  curves  at  typical  shape in  length  and  reaction secant  and  Y  as  is a  P  is  the  the  the  is  can  Winkler's be  usually  shown  in  reaction  pile  of  the  length  lateral  of  modulus  pile  soil  pile  p,  springs  curve  function  subgrade  Fig. in  force  Es,  and  as  1981).  2.2.  deflection,  soil,  linear  specified  (Scott,  deflection  the  either  springs  The per  in  which  deflection,  P-Y A  unit  expresses depth  (Reese,  or  P-Y  soil  via  1962),  = -P/y  indicated Es,  along P-Y  model,  reaction,  nonlinear  of  which  Es  soils,  soil  points  curve,  as  the  analytical  the i.e.  (2.2.2)  Fig.  2.2.  The  can  vary  in  is  not  a  secant  subgrade  modulus  of  an  arbitrary  manner  with  depth  unique  parameter  of  soil  but  the  a  PILE DEFLECTION, y  .  2.2  A Typical  S h a p e o f P-Y  curve  1 2 computation  device  incorporates soil.  the n o n l i n e a r i t y  Then a c o m p l e t e  distribution, along set  to f a c i l i t a t e  length  of d i f f e r e n t i a l  solution  including  b e n d i n g mement  c a n be r e a d i l y o b t a i n e d  equat ions  i n computer  properties  along  stresses  by s o l v i n g a  o f E q . (2.2.1) w i t h t h e along  boundary c o n d i t i o n s .  incorporated soil  and nonhomogeneity of the  P-Y c u r v e s a t p o i n t s  appropriate  that  d e f l e c t i o n d i s t r i b u t i o n and s h e a r  the p i l e  specified  the s o l u t i o n  the p i l e  This  program  length  procedure  so t h a t  and the  h a s been  the v a r i a t i o n of  t h e d e p t h c a n be e a s i l y a c o u n t e d f o r  i n an a n a l y s i s . In  s u c h an a p p r o a c h ,  adjacent at  springs  above  assumption the  i s i g n o r e d , which  a p a r t i c u l a r point  either  i s not c o r r e c t  readily  applicable  In stress  soils.  order  (1971) compared elastic  implies  i t . Strictly since  soil  speaking,  elements  this  of p i l e  group  action.  the s i g n i f i c a n c e of i g n o r i n g the  the s o l u t i o n s with  method,  Poulos  f o r the s i n g l e p i l e s from t h e those  from t h e subgrade  reaction  t h e o r y . The c o m p a r i s o n  showed t h a t  subgrade  reaction  satisfactory results  regards  does not g i v e  t o the magnitudes of displacement,  b e n d i n g moments, b e c a u s e as  compared w i t h  element  t h e method may n o t be  to the a n a l y s i s  theory  that  by t h e s o i l  i n the subgrade r e a c t i o n  continuum  between t h e  i t ignores the c o n t i n u i t y of  Therefore,  to evaluate  transfer  transfer  i s not a f f e c t e d  i t o r below  surrounding  the stress  i t overestimates  the e l a s t i c  continuum  t h e method o f with  r o t a t i o n s and these  theory,  quantities especially  1 3  for  relative  flexible  Another method  piles.  limitation  ignores  the  used  i n the  properties  with  the  Special  this  continuity  parameters  1983).  with  of  analysis  half-space  parameters  method the  are  have  soil, not  soil  i s that the  the  the  soil  fundamental  continuum  t o be  as  devised  soil  (Horvath, for  this  approach. However, Winkler design  in spite  spring of  approach  laterally  simplicity  i n the  the  soil  adjusting  Es,  or  Winkler  spring  The  i n terms  concept  McClelland  and  development area  owing  reaction to  (Atukorala a)  of to  the and  of  OF of  P-Y the  P-Y  often  due  in  the  to i t s  and i t s  nonlinear  subgrade  used  behaviour  modulus  important  of  factor  of  soils,  in  accurate description  of  soil  CURVES c u r v e s was  successful  c u r v e s may  first  Since then  c u r v e s has  semi-empirical  of  nonlinear  curves.  (1958).  Byrne,  mainly  t h e most  P-Y  most  formulation  secant  in practice.  P-Y  method  i s the  P~Y  Focht  method  obtain  the  approach  SPECIFICATION  limitations,  incorporation  c u r v e s . Thus,  parameters  2.3  i s the  mathematical  i n the  P-Y  above  loaded p i l e s ,  versatility by  of  become  an  proposed the  To  date,  be  generally  method;  rational  intensive  application  1984):  by  the  of  the  research  subgrade  different grouped  as  methods follows  14 b)  in-situ  testing  c) c e n t r i f u g e d)  2.3.1  finite  method;  test;  element  and  method.  SEMI-EMPIRICAL METHODS In  the group  proposed  by M a t l o c k  construct adopted  of s e m i - e m p i r i c a l methods, the  t h e P-Y  by  (1970) and  Petroleum  methods a r e b a s e d  upon back  loaded p i l e  and  laboratory according soft  from tests  two  unit  stiff  clay,  based  and  where: Pu  t h e P-Y  soft  Pu,  with  (1976). field  Their  laterally  curves are provided  of s o i l  conditions, i.e.  by M a t l o c k  sites  and  lateral from  soil  load  expression to resistance  per  depth:  (2.3.1)  soil  ultimate  = undrained s o i l  tests  some model  method e m p l o y s an  of the u l t i m a t e  was  Cu D  = ultimate  nondimensional  have been  sand.  clay  The  and  c u r v e s o b t a i n e d from  on a n a l y s i s o f d a t a f r o m  the v a r i a t i o n  length,  of  t h e method p r o p o s e d  ( M a t l o c k , 1970).  Pu = Np  Cu  test,  clay,  particular  describe  calculation  the s t r e s s - s t r a i n  compression  soft  developed  Institute  to a general d e s c r i p t i o n  clay, For  tests  Reese e t a l (1974) t o  c u r v e s a r e most w i d e l y u s e d  the American  procedures  resistance  lateral  soil  per u n i t  length,  resistance  s h e a r s t r e n g t h , and D = p i l e  Np  = a  coefficient, diameter.  15  The Np,  is  value  a  reaches  of  soil  to  forward  depending plate  with  square (Reese, (1970)  for  prescribed  for  Np  Np  =  3 +  X  >  Xcr  failure.  to  to  be  wedge,  the  pile  failed  by  the  range  of  2 to  4  is  considered  as  a  resistance  or  whether  is  a  shearing  3 was pile.  along  recommended Thus,  such  the  by  a  it  sides  Matlock  variation  is:  a /Cu  + J  x/D  <  9  (2.3.2)  (2.3.3)  constant clays  head,  segment  soil  of  of  the  flow  = 9  surface,  failure  assumed  It  which  plastic  near  form  pile  soil  with  a = effective  offshore ground  for  in  depth,  While  reduces  the  cylindrical  Xcr  empirical  Np  A value  <  Np  of  is  coefficient,  surface.  horizontal  pile.  upward  ground  large  of  pile  resistance  the  9 at  the  frontal  X  for  where:  a  and  section  1958).  of  the  whether  only  cross  of  soil  below  assumption  value  upon  depth  around  front  corresponding  ultimate  value  the  soils  in  shearing  of  limiting  corresponds  the  the  function a  failure  of  and and  transforms  overburden  with  an  0.25  for  Xcr to  stress  approximate stiffer  = critical  confined  at  depth  value  clays, depth  plastic  X  at  plane  of  X,  J  0.5  = depth which strain  =  an  for  soft  below  surface flow  1 6  Matlock  found  experimental as  shown  in  p  where:  Pu  and  =  y  c  e  using  2.3  Pu  of  the  similar  =  basis  best a  able  to  cubic  match  the  parabolic  function,  :  (Y/Yc)  °'  soil  pile,  in  3  (2.3.4)  3  resistance,  y  ,  of  is  the  y  = pile  pile.  determined  And  defection, the  from  reference  laboratory  In  be  a  the is  to  e  c  the that  is  strain  UU t r i a x i a l above the  the  assumption  the  value of  not  absence  P-Y  values  of  of  c  of  «  the  e  c  the  plays  c  for  in  test  proposed  by  the  P-Y  curves curves  an  are of  important  clay.  triaxial  represent  maximum  test.  stress-strain  curves  triaxial e  half  that  f r o m UU  truely of  one  employment  determined  may  at  compression  laboratory  construction  tests,  conditions data,  this in  Matlock  Skempton  (1970)  (1951)  used.  However, more  principal  for  strain  suggested  (2.3.5)  Therefore,  Because  ground.  D  c  in  shape  the  of  e  function  soils. in  2.5  stress  parabolic  that  by  = major  c  The  could  curves  reference deflection  deviator  value  was  via:  where:  part  he  = ultimate  y„ c  the  Fig.  = 0.5  deflection tests  P-Y  that  Jiamiolkowski  precise  tests  are  and  Garassino  required  to  (1977)  obtain  e  commented .  They  F i g . 2.3  C o n s t r u c t i o n of P-Y (after  curves  Matlock,  for Soft Clay  1970)  18  suggested most  to  use  For suggested based  on  by a  for  formula  same  used  mathematical  soil  and  for  [2  measurements  is  in  The (1975) same a s of  in  fourth In  the  Reese  et  a + 2.83  soil  al  Cu  P-Y  <  equation  very  poor.  An  is  consisting  method  Matlock's  and  method in  the  the  curves.  calculation  x]  (1975)  site  The  method  differences  of  (1975)  of  maximum  is:  11  Cu D  with  empirical  (2.3.6).  a  resistance  above  Eq.  the  notable  the  into  at  clay.  in  the  ,  the  (2.3.6)  field  coefficent,  Variation  of  A  A with  is depth  2.4.  the  function P-Y  curve  Matlock's  method  used for for  by  Reese  and  Welch almost  stiff  clay  is  soft  clay  but  the  a  parabola  may  raise  order. the as  above  CK U: tests.  consolidated,  0  as  for  practice,  K  logic  employed  problems  0  jointed  several  numerical 1  the  during  and Welch  tests  shape  of  define  with  construction  Reese  load  maximum  mathematical  to  (1975),  the  the  Cu D +  Fig.  tests  followed  for  by  introduced  shown  with the  was  be  clay,  lateral  function  Agreement  then  of  al  general  formula  =  et  but  resistance  Pu  fissured  Reese  clay  The  to  overconsolidated,  the  soft  path  compression  shearing.  series  heavily  follows  stress  and  stiff  triaxial  1  0  appropriate  consolidation  of  CK U  the  parabolic  initial  undrained  P-Y  modulus triaxial  curves of  the  parabolic  compression  0  Fig.  2.4  Stiff (after  Coefficient  and F i s s u r e d Reese  et  al,  A  for  Clay 1975)  Fig.  Ay  c  y  2.5  6Ay  e  c  DEFLECTION, > . in.  Construction for  (after  Stiff  Reese  et  of  !8Ay  c  P-Y  curve  Clay al,  1975)  20  curve  tends  (1975) using  to  infinity.  construct a  composite  parabolic straight  .  E  =  s  to  curve  this for  composed  The  defined  = k  si  P-Y  curve  segments. line  E  where:  the  Due  initial  of  subgrade  modulus,  the  initial  subgrade  modulus  with  for  clay  usually  related  to  The shown  figure, may  Fig. the  fissured  of  2.5  for  the  clays.  relation  above,  the  problem  value,  e„ c  can to  (1974)  to  fit  data  for  straight  and is  the  The  and  k  =  g  gradient  values  of  shear  of k  g  strength  the  occurs  this  the  clay  As  indicated  in  the  with  reliable  in  an  problem  are in  the  curves,  phenomenon  approach  a  stiff  which  the  stiff,  initial  mentioned  estimate  of  exists,  cohesionless  Island,  for  softening  obtain  in  three  clay  curve  = depth,  undrained  loadings.  overcome  semi-empirical  constructed  x  depth.  the  degredation  curves  Mustang  lines  the  describing  curves  static  Although  P-Y  s t i l l  P-Y  strain  linear  The  reaction  the  extreme  represent  fissured  1975).  shapes  in  al  (2.3.7)  subgrade  al,  of  et  by:  of  et  and  straight  portion  coefficient  (Reese  stiff  Reese  -x  initial  are  reason,  procedures soils  from a  Texas each lines  et  desired a  al,  construction  developed  particular  (Cox  and  were  for  lateral  1974).  depth.  parabola,  by  Each as  P-Y  shown  Reese  load  et  al at  are  consists in  P-Y  test  curves  curve  of  Fig.  of 2.6.  Fig.  2.6  Construction  (after  o f P-Y  Reese e t a l , 1974)  curve  f o r Sand  22  The  initial  "elastic" portion the  portion  is  a  behaviour  of  the  is  sand.  parabola  horizontal, These  and  a  two  straight  straight  sloping  the  experimental  from  the  bending  ' The  slope  the  initial  Eq.  (2.3.7).  moment  of  soil  line  the  P-Y  are  initial  The  in  straight  modulus,  E  .,  as  here  values  in  straight behaviour  parabola  were  of  a  and  empirically  which  measurements  the  connected with  selected  curves  final  "plastic"  line.  were  representing  the  the  lines  straight  straight  of  and  represents  intermediate shape  sand,  line  the  to  fit  determined  field. line  the  is  same  defined form  by  as  in  si  relative  density  The  et At  a  the  as  of  2.7(1),  follows  Pu  at the soil  (II).  E  . are  related  si  to  the  sand. resistance for  two  Pu  for  cases.  static  loading  (Reese,  1962,  was  and  the  depth  soil the  pile  in  failure The  is  assumed  soil a  is  the  formulae  fail  assumed  horizontal  by  to  to  plane.  researchers  derived  by  upwards  fail The is  Reese  in  by assumed  shown  in  et  are  al  :  Above  =  soil  surface,  around  1).  the  of  1974).  while  mechanisms Fig.  the  theoretically  al,  wedge,  flowing  of  ultimate  calculated Reese  But  a  the  critical  {D  (Kp  -  Kz  (tan$)  Ka) -  + x  depth  tan/3  tana]}  (X  [Kp  <  Xcr),  tana  + (2.3.8)  -fDirection ol Pile Movement  Load  Mudhne-  7H Pile of  Ft  (b)  <c) Fig.  2.7(1)  Assumed P a s s i v e Failure  Near  Wedge-Type  .  2.7(11)  Surface  (a)  G e n e r a l Shape  (b)  F o r c e s on Wedge  (c)  F o r c e s on  Pile  of  A s s u m e d Mode  Failure Wedge  Section  (b)  Elevation Reese  Soil  by L a t e r a l F l o w  (a)  (after  of  through of et  the al,  the  Pile  Pile 1974)  24  2).  Below  Pu  = 7 D z 2  where:  the  critical  (Kp  Kz  depth  + 2 Kz  3  tanc?  -  Kp  2  (X  >  tan^  +  Xcr),  Ka)  (2.3.9)  Pu  = ultimate  soil  effective  overburden  stress  effective  unit  diameter,  Kp  =  tan  + ^>),  Ka  = coefficient  of  active  =  tan (45  -  Kz  = coefficient  of  lateral  (45  2  2  regarding the 0  =  45  ^),  horizontal  + ~$/2  Fig.  the  of  the  field  P-Y  x,  up  depth  to  was  curves.  x,  =  a =  pile  pressure pressure  earth  pressure  generally  taken  vV3  K , 0  < a  as  ^ ?  curves  Scott  from  for  (1980)  piles.  different  poor.  ultimate  Reese  B to  et  obtain  of  cohesionless  based  The method  others.  One  cohesionless  curves Reese  as et  shown al  semi-empirical  al the  A and  soil proposed P  m  B are  and  P  shown  is  approach  the  to  method  proposed  the  centrifuge  has  two  significant  features  different  features  that  P-Y  these  sands Fig.  procedures  is  simply  2.9. for  By  is  test  develop  on  of  in  soil  ;  depth.  computed  The v a l u e s  D  earth  at-rest,  A and  length,  average  earth  critical  above  data  7 =  stresses,  pressure  = the  unit  depth  passive  effective  Xcr  per  2.8. Another  for  of  coefficients,  r  in  at  soils  earth  and  with  empirical  values  P-Y  ,  of  comparison  resistances  of  = coefficient  coefficient  The  the  weight  resistance  results  the  represented compared  constructing  by  with P-Y  on  model  curves  bilinear  the  curves  by  for  u in  Fig.  2.8  Nondimensional C o e f f i c i e n t  (after  Reese e t a l , 1974)  A and  B  p  F i g . 2.9  Bilinear  P-Y  ( a f t e r Murchinson  c u r v e f o r Sand p r o p o s e d by and O ' N e i l l ,  Scott  1984)  to  27 sands, can  Scott  serve  method the  of  just  the  of  k x/4.  as  slope  Young's  segment  concluded well of  As  P-Y  the  to  the  modulus, the  that  E  such  give  curve  second  soil, is  simple  bilinear  satisfactory  initial of  a  is  i.e.  ^ E.  empirically  segment  results.  segment Es  has  a  P-Y  defined The  defined  curve  In  his  close  to  second by  a  constant-non  slope  zero  5  slope,  the  linearly  method  with  resistance therefore As curves load  not  Matlock  extent  at  soil  lateral  displacement  The  the on  in  data  measured  at  be  the  above,  these  a or  The  no  ultimate  resistance  concept  semi-empirical  set  of  particular  particular  good  as  model  agreement as  is  the  curves  universal  P-Y lateral  tests  between  reported  The methods  their  with  increases  the  responses  sites.  site-oriented,  soil  all  from  expected,  resistance  method.  sites  conditions.  to  soil  ultimate  specific  and  is  tests  in  based  tests  that  applied  shown  predicted  the  value.  are  similar  the  implies  by  were  on  the  Reese  and  developed  developed validity  are  to  from some  is  questionable. Both  for  assessments other  load  predicting poor  cohesive  on  the  test  1984).  Those  fundamental warranted.  cohesionless  validity  cases  have  deflections  (Murchinson  and  and  studies  and  of  shown  is  1984;  suggested of  that  moments  O'Neil,  mechanisms  applying  above  the  limited methods  confidence  unfortunately  Gazioglu  that  lateral  soils,  further  pile-soil  and  to in  rather  O'Neil,  research  into  interaction  is  28  2.3.2  IN-SITU TESTING As  soil  loading tests  elements  pattern  may  be  deformation laterally  loaded  loaded  piles  1.  use  in to  test  use  of  predict  the  P-Y  the  pressuremeter  measurements  second  the  test  whole  of  soil  related  make  use  design  of  results  to  of  to  the  the  laterally  soil  obtain  a  reaction.  pressure-expansion  based  Menard  on  and  Es,  from  the  as  directly  a  the  curve  of  pressuremeter  the  P-Y  function  At  from  proposed  modulus  constructed  curves.  results  Gambin  pressuremeter  choice,  reaction  pressure-expansion  to  subgrade  obtain  from Menard  are  similar  1982):  to  obtained  deflection  tests,  direction  ways  for  al,  choice,  reaction,  soil  the  undergo  to  curves.  subgrade  lateral  et  tests,  formulae  the  in  two  horizontal  first  pressuremeter  pile  in-situ  pressuremeter  make  the  are  results  to  In  provide  (Briaud  the  of  pressuremeter  there  of  empirical  front  piles.  modulus  In  in  characteristics  pressuremeter  2.  as  able  Generally,  to  METHODS  a  Menard  set  horizontal  modulus,  Em,  curves  (Gambin,  curves  describing  of  pile  from  present,  the  there  of  1979). the  lateral shapes are  two  of general  ways: (a). shapes  of  (Robertson  The  P-Y  the  entire  et  al,  curves  are  constructed  pressure-expansion  1983,  Atukorala  and  by with  Byrne,  scaling certain 1984),  the factors  29  (b). the  Alternatively,  lateral  movement  components: frictional 1982,  the  pressuremeter f-y  curves.  from  the So  f-y  and  far,  promising above  Then,  it  and  methods  the q-y  has  of  but  entire  been  piles.  different  pressuremeter  disturbances  due  pressuremeter extent.  This  for  the  the  curves  the  must  and  the  et  al,  (Briaud  from  the  used  to  can  be  to  two  curves)  sides  be  curve  resistance  into  q-y  obtained  that  taken  effects  both  obtain  the  constructed  approaches  However  account  none  the  are  of  the  factor  of  between  the  pressuremeter  mechanisms  are  associated  laterally  loaded  installation  and  different  pressuremeter curves  and  curves  the  interest.  loading  to  on  P-Y  shown  properly  installation  the  soil  curves.  different As  (called  theory  practical  have  are  of  separated  curves)  curves  curves,  is  reaction  (f-y  The q - y  mechanism  piles  frontal  reaction  1983).  of  the  the  P-Y  effect  may  curves  may  be  pile,  affect to  a  simply  converted  laterally  loaded  pile  by  to  some  with  soil the  different  important  are  and  when  the  obtain  the  P-Y  mutiplying  factors. But  the  methods  consideration, installation same the  assuming  of  the  consequential P-Y  aspect  curves as  yet  incorporate  mentioned  for to  the  soil  above  disturbances  pressuremeter effects piles.  evaluate different  on No  implicitly  the work  such  an  effect  and/or  neglect  induced the  such  by have  the  pressuremeter  curves  and  has  on  been  done  assumption in  the  pile  and  this  to  converting  factors,  30 if  necessary.  2.3.3  CENTRIFUGE TESTINGS Due  t o the complex nature  understanding laterally  curves  field  mechanisms a s s o c i a t e d w i t h  o b s e r v a t i o n . The  lateral  possibility  is particular  prohibit  experimental  This request  has  c e n t r i f u g a l modelling techniques  limited  s t u d i e s of the  where  the  parametric  s t u d i e s on  prompted the e v o l u t i o n of r e c e n t l y . The  been shown t o be a c o n v e n i e n t  making parametric  response  and  centrifugal v i a b l e way  of p i l e s  l o a d i n g t o e n r i c h our c u r r e n t l i m i t e d d a t a  However, the g e o t e c h n i c a l c e n t r i f u g e s a r e not present  the  for offshore p i l i n g ,  expenses almost  of c o n d u c t i n g  size piles.  t e s t i n g has  b a s e d on  of  l o a d t e s t d a t a a s m e n t i o n e d i n S e c t i o n 2.3.1.  t h e d i f f i c u l t i e s and  lateral  the  s e m i - e m p i r i c a l development  so f a r , h o w e v e r , a r e m a i n l y  Such a s i t u a t i o n  full  the  loaded p i l e s u s u a l l y r e q u i r e s h i g h - q u a l i t y  experimental P-Y  of d e f o r m a t i o n  of the problem,  to base.  popular  b e c a u s e o f t h e h i g h l y s o p h i s t i c a t e d and  of  at  expensive  equipments. As curves bending  i n the  field  the development of the  P-Y  from the c e n t r i f u g a l t e s t s c o n s i s t s of measuring  the  moments, M,  load tests,  a l o n g the model p i l e . Then, the  c u r v e s a t v a r i o u s depths of s o i l s are generated v a l u e s o f P and lateral  Y at each depth  l o a d i n g . The  by  P-Y plotting  for increasing levels  v a l u e s o f P and  Y are d e r i v e d  by:  of  31  Y  = //  ( M/EI  )  dx  (2.3.10)  d M 2  As an  in  (2.3.11)  deriving  instrumented  P-Y  pile,  difficulties  in  the  Eq.  in  which  (2.3.11)  fitting  the  the  shape  be  magnified  of  from  and  centrifugal  P-Y  Mustang  et  the  constitutive  Reese  the  et  al,  the  and  but  shape  Comparisons  with  Matlock  resemblence  in  et  al the  very  in  P,  from  used  for  sensitive  test  data  would  developed  question.  sands  The  P-Y Reese  and  to  those  by  those  directly  representative with  seems  Reese to  curves et  It  al  criteria  qualitatively  near  by  the  pile  overestimates  with  showed  curves  al  method  also  distribution  et  suggested  resistance  depth.  of  experimental  recommended  (1980),  P-Y  series  similar  1974).  data  soil  its  is  on  from  curve  curves  in  using  the  at  the  performed a  al  that  it  between  reaction,  P-Y  those  et  of  and  soil  errors  al,  test  ultimate  stiffness  suffers  Comparisons  indicated  the  et  analysis  that  tests  also  data  the  piles  sand.  showed  of  with  load  differentiation.  (1983)  (Cox  overestimates  initial  little  al  Matlock  for  general  underestimates head,  site  the  field  of  sometimes  model  element  recommendation  and  are  compared  law  moment  double  et  on  (1974),  finite  support  tests  tests  al  curve, the  of  derivative  bending  Finn  were  the  the  procedure  accuracies  island  curves  Reese by  the  centrifugal Barton  at  the  during  Consequently,  this  from  determination  measured  to  curves  from  depth. that the  there two  is  32  methods,  the  stiffness, the  pile  about  head  computing  P-Y  method  to  laterally to  powerful in  cost  tedious  routine  a  for  problems and  development  design  of  a  that  under  a  interaction,  as  their  was  shown  in  recent 2D  short  attention  curves  more  proved  to  but  high  3D a n a l y s i s application  may  be  interaction  formulation  method  being in  has  become  a  direct  piles.  they  was  a  2.10,  to  the  static  loads  in  of  domain  quarter  boundary to  attributed  analysed  term  analyses,  employed  for  more  level,  prohibit  regard  where  Fig.  and  fundamental  this  element  soil-structure  s t i l l  symmetrical  conditions  of  curves  been  loaded  the  P-Y  has  element  (1973),  of  finite  method  using  in  the  P-Y  curves  attempt  In  than  parameters.  the  its  laterally  clay.  soil  develop  However,  finite  pile  basic  near  element  feasibility  of  the  and  data  the  contained  boundary  detail  that  single  to  element  input  Wright  greater  finite  r e c e i v e d more  need  P-Y  and  saturated  has  the  first  from  analysing  means.  for  the  initial  resistance  depths  the  development  of  tool  The Yegian  more  design  indicated  piles  finite  tool  at  with  application  numerical  The  it  soil  the  METHODS  continuous  rigorously.  ultimate  confirm  directly  years,  loaded  the  did  ELEMENT  the  the  Comparisons  curves  recent  overestimating  overestimating  however,  FINITE  ' In  a  and  4 diameters.  2.3.4  curves  underestimating  prediction,  due  Matlock's  and  an  response  2D  antisymmetrical  simulate  the  in  plane  which  soft  soil-pile strain  33  Direction of Ditploctmtnt  Fig.  2.10  Finite  Yegian  Element  and  Pil«  Domain  Wright  employed  (1973)  by  34 condition  was  assumed  condition  for  places  the  finite  element  cylindrically deformation radius  of  section, about was  on  a  They  pile  plane  boundary  on  which  has  found  lateral  element  strain  formulations  soil-pile  occur of  when  of  analyses did  that  is  little  not  interface  which,  tensile  cracking  center of  to  be  plane  in  is  the  fixed solution,  significant  for  addition,  their  In  the  and  the  reality,  occurs  the  strain  stress  for  pile  Matlock's  of  plane  the  conclusion  from  the  effect  the  soil  influence  their  of  fixed  varying of  pile  and  1979).  allow  By  resistances  element  both  there  However  size  (Bardet, in  be  the  theoretically  boundary  to  analyses  finite  outer  stress  considered  zone  soil  the  The  plane  in  plane  separation  would soils  the  at  probably at  the  back  piles. In  and  the  from the  and  boundary.  diameters.  stiffness  finite  the  that  study  the  was  this  away  stress  not  outer  pile  beyond  depth  surface.  used  comparison  did  been  the  at  assumption  boundary  the  element  method.  the  concluded  8 times  finite  near  occurring  they  places  domain  under  outer  based  for  their  Chang,  stress  1970)  strain  cylindrical strain  were  slip  a  of  for  soils  to  the  Although was  that  as  taken  they  will  relationship  describe  soil  appropriate  stages,  condition  hyperbolic  employed  elements.  mainly  elastic  boundary  was  behavior  behaviour  results linear  analysis,  for  elements the  the  exist  nonlinear and  nonlinear  into  employed  not  the  account, pile the  for  (Duncan  the stress their  responses  at  antisymmetrical the  nonlinear  35  soil  responses. From  Matlock  the  (1970),  reasonably finite  comparison  the  the  ultimate  attributed soil-pile that  the  to  the  with  overpredict underpredict  Matlock's  From a  29%  Wright  resistances  are  much  great  of  change  the  as  difference  between  criteria. P-Y  This  curves  much  in  as  37  the  result  (1973)  dependent  percent  from  which  found  ultimate  pile  ultimate  and  plane  stress  since,  as  conditions  conditions  interface  properties  found  that  on  out  the  is  soil  soil-pile  interface  ultimate  itself  that  element  may  soil  bigger  analyses  suggests  finite  was  properties  element  therefore  it  the  resistance.  the  predicted  finite  predicted  for  interface  consider  an  strain  stress  which  assumed  variation  resistance  of  in  difference  significant  ultimate  and  the  a  the  the  was  mainly  depth,  strain  plane  the  criteria  not  yield  very  a  from  This  be  did  between  plane  Yegian  elements,  may  at  by  conditions,  method.  areas  are  depths,  Matlock's  they  plane  study  characteristics  yield  by  results,  interface  stress  that  to  of  parametric  varied,  predicted  by M a t l o c k  31% w h i l e  about  be  however,  differences  about  can  midway  corresponding The  shallow  the  proposed  recommended  at  element  limitation  approximately  predictions. compared  finite  curves  that  resistance  For  P-Y  plane  resistances,  criteria  resistances  lateral  the  the  curve  using  separation.  resistance  were  method  by  shown  P-Y  ultimate  overestimated in  was  accurate  element  although  it  with  than  and the  method  the  Matlock's accuracy depends  36  on  the  accurate  interface  under an  and  laterally  element  Finn  the  (1983)  loaded  method.  The  plane  piles  soil  also in  finite  strain  elastic-plastic  computed  of  predicted  dense  element  conditions.  material  curves  were  then  experimental  curves  from  centrifuge  close  to  pile  close  agreement  the  depths  greater  curves  were  with than  less  difference  head,  the  the  and  soil-pile  stiffer  finite  The  was  modelled  soil of  tension.  with  tests. P-Y  In  the  curves  the  as  The  areas  were  computed  depths  in  however,  experimental  severe  as  their  curves,  5 diameters,  more  using  curves  conducted  computed  the  P-Y  was  compared  than  the  analysis  experimental  about  became  sand  incapable  P-Y  the  behaviour  properties.  Barton for  description  a at  P-Y  curves,  and  increased  to  10  diameters. In great  general,  potential  loaded  piles  factors soil  behavior,  to  be  loaded  the  soil  the  in  with the  piles.  the  P-Y  studies,  tensile These  Therefore to  the  development  soil such  factors if  of  element  curves  failure,  analysis  regard  finite  fundamental  further  considered.  necessary methods  in  the  predict  simulation.  complicated is  to  from  deserve  interface  although  the  the  and  the  will pile  be  offers  laterally  properties,  several  description  further  research  curves  of for  of  soil-pile  installation  application P-Y  for  as  further  method  work  finite the  effect is  element laterally  a  3.  3.1  following  expansion new  Vaziri  tests  high  geotechnical program In  at  and  is  finite  and  order  (1986)  undrained,  the  UBC.  PROGRAM  contained  verifications  of  this  to  current  modification comparison  of  the  with  Herein,  a  formulation,  brief  the  is  program  to  any  practical  understand  the  adopted  3.2  ELEMENT  In  the  replaced smaller  finite  with  an  continua  connected  at  a  In  perform  based  for  large  Doctoral present  were  accuracy  problems. will  be  by  varieties of  of  the  Dissertation. studies,  made, and  on  drained,  documentation  some  modifications  efficiencies The  in  verification  given  in  Chapter  and 5  in  solution.  presentation  procedures  FINITE  given.  analyses  for  form  methods  are  can  program  closed  piles  program  program  interested  pressuremeter  CONOIL d e v e l o p e d  Vaziri's  the  of  program  CONOIL  improve  loaded  A complete  in  use  solving  This  problems.  analyses  laterally  consolidation  to  made  element  element  order  were  ELEMENT  INTRODUCTION The  the  FINITE  of  of  the  analyses,  the  and  application  problem,  program,  it  and  finite the  of  is  element  numerical  finite  essential  ensure  its  element to  accuracy.  FORMULATION element  analyses,  equivalent called  finite  finite  finite  number  of  37  the  soil  assemblage  elements. nodes.  Those  continuum of  discrete  elements  Therefore  is  spacial  are  38 variation  of s o i l  r e p r e s e n t e d by in  each  p r o p e r t i e s can  the average  be  approximately  (or weighted  average) p r o p e r t i e s  element.  The  finite  element method assumes a d i s t r i b u t i o n  for  t h e unknown q u a n t i t y o v e r  the domain of each  The  unknown q u a n t i t y u s e d c a n  be t h e d i s p l a c e m e n t ,  b o t h . When t h e unknown i s d i s p l a c e m e n t , formulation  i s usually  element.  These d i s t r i b u t i o n  f i e l d s are u s u a l l y  specified  sometimes would g i v e u n r e a l i s t i c pressure, especially  condition and De  (Nagtegaal  order  solutions  answers i n the  e t a l , 1974,  S l o a n and  prediction undrained  Randolph,  It i s for this  p o l y n o m i a l , the approximating  reason  field  of o r d e r of  continuous conforming.  of the a p p r o x i m a t i n g  field.  For  f o r m u l a t i o n , the displacement  a c r o s s the edges of e l e m e n t s . The  displacement  field  and  within  Such a c o n d i t i o n i s g e n e r a l l y r e g a r d e d  displacement  that  the  must be c o n t i n u o u s  a l s o must h a v e c o n t i n u o u s d e r i v a t i v e s a t l e a s t  admissibility  1982,  a r e e m p l o y e d i n CONOIL.  a d d i t i o n t o the requirement  elements.  Past  elements  in axisymmetrical  B o r s t and V e r m e e r , 1 9 8 4 ) .  higher order elements In  using  t o the r e a l answer. Elements w i t h h i g h e r  e x p e r i e n c e s h a v e shown t h a t t h e l o w e r  limit  the  method,  order polynomials are c a l l e d higher order elements.  of  or  respectively.  polynomials. Generally, high order polynomial give that are c l o s e r  stress  s t r e s s or both,  r e f e r r e d t o as d i s p l a c e m e n t  s t r e s s method or h y b r i d method  field  as  the  the  must  be  Such elements  s h o u l d a l s o be a b l e  are to  39 represent both r i g i d  body m o t i o n a n d t h e c o n s t a n t s t r a i n  s t a t e of t h e e l e m e n t . These referred  refined.  usually  t o a s c o m p l e t e n e s s o f t h e e l e m e n t s . The  c o n d i t i o n s are required element  two c o n d i t i o n s a r e  solution  f o r the convergence of the  t o t h e c o r r e c t answer  B a s e d on t h e f i n i t e  element  are  theory, displacement  elements t h a t a r e complete but  than the conforming elements  upperbound  nonconforming  a l s o w i d e l y u s e d . I n some c a s e s , t h e y may  results  finite  a s t h e mesh i s  f o r m u l a t i o n w i t h conforming elements would g i v e s o l u t i o n . The  above  give  better  ( s u c h as the  n o n c o n f o r m i n g p l a t e e l e m e n t ) . However, t h o s e n o n c o n f o r m i n g e l e m e n t s can not g i v e t h e bounded s o l u t i o n , whether For  the r e s u l t  i s an u p p e r b o u n d  CONOIL, t h e f o r m u l a t i o n  d i s p l a c e m e n t method. The or  cubic  i t i s not  o r l o w e r bound  i s b a s e d on  linear  s t r a i n t r i a n g u l a r , a s shown i n F i g . 3.1.  strain  The  i s a d m i s s i b l e , c o m p l e t e and  elements are conforming. Therefore i n theory, the from the program  solution.  the  e l e m e n t c a n be e i t h e r  assumed d i s p l a c e m e n t f i e l d  clear  s h o u l d be t h e u p p e r b o u n d  of the  the  results real  answer. B a s e d on t h e a s s u m e d d i s p l a c e m e n t f i e l d , relating  t h e e l e m e n t n o d a l f o r c e s and d i s p l a c e m e n t s c a n  derived using variational p r i n c i p l e , virtual The  the e q u a t i o n s  or the p r i n c i p l e  be  of  work. e q u a t i o n c a n be w r i t t e n  {Q}  = [K]  {q}  i n the form :  (3.2.1)  a) L i n e a r  strain  (b)  Fig.  3.1  Element  Types  Cubic  strain  41 where: [K]  i s the element s t i f f n e s s  {Q}  i s the nodal force  matrix  vector  {q} i s t h e unknown d i s p l a c e m e n t v e c t o r Then t h e e q u a t i o n  f o r each element  i s combined  i n the  s t a n d a r d manner t o o b t a i n t h e g l o b a l e q u a t i o n f o r e n t i r e finite  e l e m e n t mesh.  The method a d o p t e d f o r t h e a b o v e major the  factor  entire  i n f l u e n c i n g t h e e f f i c i e n c y and computer  f i n i t e e l e m e n t a n a l y s i s . As t h e h i g h  elements a r e employed the  equation s o l u t i o n  i n the program, a d r a s t i c  is a  c o s t of  order increase i n  b a n d w i d t h o f s t i f f n e s s m a t r i x e x i s t s . T h e r e f o r e a method  other than t r a d i t i o n a l In  bandwidth s o l v e r s  CONOIL, t h e f r o n t a l  i s employed  for solving  solution  the above  i s adopted.  technique (Irons,  1970)  simultaneous e q u a t i o n s . In  t h i s p r o c e d u r e , a s s e m b l y and e l i m i n a t i o n o f t h e e q u a t i o n a r e combined, of  t h e n t h e c o r e s t o r a g e r e q u i r e m e n t and t h e number  a r i t h m e t i c a l operations are s i g n i f i c a n t l y  result,  the g l o b a l  s t i f f n e s s matrix  formed. B e s i d e s , w i t h the f r o n t a l the  explicitly  s o l u t i o n the numbering  e l e m e n t n o d e s becomes i m m a t e r i a l . U s e r s c a n o r d e r  nodes not  i s never  r e d u c e d . As a  i n t h e way  the  t h e y w i s h , t h e r e f i n e m e n t o f t h e mesh d o e s  r e q u i r e r e n u m b e r i n g t h e e n t i r e mesh. Under  given d i s p l a c e m e n t f i e l d , the f o r m u l a t i o n of  stiffness matrix, depends soils,  of  [ K ] , of each element  upon t h e s t r e s s - s t r a i n the s t r e s s - s t r a i n  (see Eq.  (3.2.1))  laws of the m a t e r i a l .  In  r e l a t i o n s a r e o f t e n g o v e r n e d by  42 effective  s t r e s s e s rather than t o t a l  effective  stress  finite  element  stresses.  Therefore,  a p p r o a c h a p p e a r s more r a t i o n a l  i n the  f o r m u l a t i o n w h i c h would widen t h e scope o f  analysis.  3.3  U N I F I E D APPROACH - AN E F F E C T I V E STRESS METHOD The  concept  p r i n c i p l e of e f f e c t i v e  stress  i n geotechnical analysis.  i s an i m p o r t a n t  Analytical  methods  based  on t h i s c o n c e p t h a v e been p r o p o s e d by many r e s e a r c h e r s . An e l e g a n t a p p r o a c h p r o p o s e d by N a y l o r (1973) w i l l h e r e i n . A s shown l a t e r ,  t h i s approach provides a u n i f i e d  procedure w i t h which t h e undrained a n a l y s i s either  total  analysis  stress  be p r e s e n t e d  or e f f e c t i v e  stress,  i n terms of  and t h e d r a i n e d  c a n be p e r f o r m e d b a s e d on t h e same m a t h e m a t i c a l  formulation.  3.3.1  UNDRAINED ANALYSIS According t o Terzaghi's theory, thep r i n c i p l e of  effective  stress  c a n be e x p r e s s e d by :  {ACT}  {ACT'} +  {m}  {ACT}  v e c t o r of t o t a l  (3.3.1)  Au  where  {ACT'}  stress  vector of e f f e c t i v e  changes  stress  changes  Au - p o r e p r e s s u r e c h a n g e s {m}  = either  upon w h e t h e r  {1,1,0}  T  o r {1,1,1,0,0,0} , T  i t i s p l a n e s t r a i n o r 3D  depending analysis  43 Other effective  r e l a t i o n s h a v e a l s o been p r o p o s e d stress  that  take account of the  c o n t a c t a r e a (Skempton, problems  f o r the  intergranular  1 9 6 0 ) , b u t f o r most e n g i n e e r i n g  a t low p r e s s u r e s , T e r z a g h i ' s d i f i n i t i o n  is  sufficiently accurate. The  total  changes,  s t r e s s changes  c a n be r e l a t e d t o t h e s t r a i n  { A e } , by a c o n s t i t u t i v e m a t r i x [D] f o r u n d r a i n e d  conditions, i . e .  {Aa}  = [D] {Ae}  (3.3.2)  B a s e d on t h e p r i n c i p l e o f e f f e c t i v e s t r e s s , b e h a v i o r of s o i l [D']  skeleton  i s governed  the  by c o n s t i t u t i v e m a t r i x  i n t e r m s o f e f f e c t i v e s t r e s s p a r a m e t e r s . Then t h e  effective  s t r e s s changes  {Aa'}  = [D']  a r e r e l a t e d t o s t r a i n changes  {Ae}  Suppose t h e pore f l u i d  Au = B  where B^  f  :  (3.3.3)  element  undergoes  s t r a i n change Ae^ as the pore p r e s s u r e changes undrained conditions,  by  a  volumetric by Au i n  then  Ae^  i s the apparent pore  (3.3.4)  fluid  b u l k modulus.  r e l a t e d t o the b u l k modulus of the pore f l u i d ,  B ,  s o l i d p a r t i c l e s t i f f n e s s , B , by t h e p o r o s i t y ,  n,  w  B^ i s and by  the  44  (Naylor  e t a l , 1981)  1/B  It there  is  = n/B  f  assumed  will  +  w  (1-n)/B  that  f o r the f u l l y  be no movement  of  skeleton,  and consequently  undergoes  t h e same  the  undrained  and  therefore  Au  L  v  = Ae / n v  Eq.  = B,  {m}  T  principle  effective  is  related  apparent  It  can  =  [D']  bulk  +  represent  linear  and the pore  fluid  i . e . the c o m p a t i b i l i t y  Ae/n  1  of  (3.3.6)  (3.3.7)  (3.3.3)  in  and (3.3.7)  equation  terms  of  (3.3.1),  total  constitutive  modulus  by  then  stress model  into  :  (3.3.8)  f  in Eq.  on t h e forms elastic  the  and the  T  that  the  parameters  {m}{m} B /n  be n o t e d  imposed  to the  becomes:  to the e f f e c t i v e  should  restriction  {m}  stress  [D]  fluid  relative  that  (3.3.2),  matrix  pore  [D]  Eq.  fluid  condition  Ae/n  of  constitutive  =  undrained  the skeleton  So  (3.3.4)  substitution of  pore  deformation,  condition.  Ae  (3.3.5)  s  of  (3.3.8), [D],  properties,  [D']  there  is  a n d B^.  or any form  no They of  45 nonlinear, can  be  applied  For linear  elastic  the  or  elastic  p l a s t i c r e l a t i o n . The  t o any  elastic  the  following  invovle  b u l k modulus B  t h e n Eq.  only (or  (3.3.8) would  model t o the  Eq.  ( 3 . 3 . 9 ) and  a  effective  i s o t r o p i c undrained  analysis.  effective stress analysis  same u n d r a i n e d  undrained analysis  extend the  above  of u n s a t u r a t e d o i l s a n d  'Homogenized C o m p r e s s i b l e P h a s e ' . D e t a i l s  as  saturated  ( 1 9 8 6 ) , and  cohesive s o i l s are  will  Total Stress  shown b e f o r e , t h e  assumed  flexibility  Analysis  above e f f e c t i v e s t r e s s and  ease f o r t o t a l  method  stress  with of  not  studies.  E f f e c t i v e S t r e s s and  to  condition.  a d o p t e d N a y l o r ' s a p p r o a c h and  presented herein  p r o v i d e s the  (3.3.10) p r o v i d e  b e t w e e n t o t a l and  t h i s c o n c e p t were c o v e r e d i n V a z i r i  present  give  (3.3.10)  f  of c o n v e r t i n g  c o n c e p t of  B'),  condition  + B /n  f o r e i t h e r t o t a l or  Vaziri  two  (3.3.9)  performed f o r the  As  [D']  (either  :  r e l a t i o n s of  They a l l o w  the  and  p a i r of  s t r e s s parameters for e l a s t i c  the  materials.  = G'  c o n v e n i e n t way  be  [D]  r e l a t i o n s for plane s t r a i n  B = B'  The  the  (or G'),  e t a l , 1981)  G  formulation  i s o t r o p i c c o n s t i t u t i v e law  parameters. For  shear modulus, G  (Naylor  c o n s t i t u t i v e laws of  incremental l i n e a r ) ,  and  same  and  in  46  effective based  on In  the  same  compatibility accomplished  not  by  pore  B^  range  the  undrained in  the  condition proposed evaluated Skempton  frequently 1984).  generally In total is  effective  bulk long  100  fact,  stress  because  B'.  It  can  to  500 v  [D'],  be is  and  a  Choice  much  of  larger shown  of  can  be  which  B^,  form  in  than  that  range  pore  non-zero  equivalent  the  stress  finite in  stress  a  changes  is  pressure  approach is  which  This  researchers  approach  analysis  element  parameters.  iteration  is  in  (1968),  pore  change  there  is  B'  parameters  B^.  B^  the  many  this  the  as  total  requires  matrix  effective  pressure  of  The  fact,  the  a  value  of  to  using  an  0.495  to  0.499  analysis.  on  by  stress  modulus  ratio,  of  the  However,  condition.  for  effective  analysis  Christian  determination  undrained  and  The  of  used  pressure  strain.  modulus  from  pore  allows  volumetric  based  pore  the  method  undrained  as  way  is by  the  stress  Another  of  the  the  Poisson's  total  condition  through  fluid  bulk  loading  obtained  the  critical  undrained  analysis,  constitutive  effective in  in  is  of  effective  apparent is  stress  components change  of  formulation.  determination  pressure  the  analysis  effective  explicit stress  stress  the  pore  based  pressure  on  the  approach  has  (e.g.  the  undrained  formulation  relative  from  for  Byrne  and  is  been Janzen,  inefficient,  total  stress  change  pressure  from  method.  This  procedure.  of  linked relation  obtaining to  the  pore  Naylor's  between  the  apparent  pore  47 fluid  bulk  (Byrne,  modulus  1985)  most  cases,  that  interest  pressure. that  it  effective analysis  is  as  separation  undrained  equivalent  to  shown  method, matrix  the [D']  modulus,  Bj.  condition drained  in  drainage  total  shear  Poisson's  case  obtained  rather  using  than  C^. a  close  of  is  pore  and  than  drained  the  tests  effective then  bulk  to  and  rather  from  And  high  there  a  indicated  procedure  pressure,  such  and  has  total  loading  in  stress  (1983)  the  stress  place  place,  with  pore  are  ratio  as  skem  :  undrained  take  Byrne  strength by  for  effective  work  zero  effective  takes  of  to  which  with  of  above  often  conditions,  simulated  DRAINED As  no  parameters  terms  is  loadings  desirable  soil  in  condition  3.3.2  in  adopted  appropriate  such  or  often  derivation)  complicated  little  those  the  B  (3.3.11)  the  The  the  for  parameter,  skem  however,  stresses,  evaluated  /(1-B  Skempton's  A  soils.  For  is  skem'  unnecessarily  cohesive  manner no  is  B'B  the  Appendix  =  approach in  (see  B /n f  In  and  the  stresses, undrained  modulus  which  is  0.5.  ANALYSIS in  Eq.  total are  (3.3.8),  stress  related  Therefore  where  analysis  there can  matrix by  for is  be  in  no  the  the [D]  effective and  the  equivalent  simulation change  implemented  in  of  effective  pore the  pore  simply  stress  fluid  drained  pressure, by  setting  stress bulk loading a  48  f = 0. I n t h i s c a s e ,  as f a r as t h e stress, changes a r e  c o n c e r n e d , t h e r e becomes no d i s t i n c t i o n and  total  s t r e s s a n a l y s i s , and t h e a p p r o p r i a t e  parameter and  between  effective soil  (such as 0 ' , C ,  from d r a i n e d t e s t s a r e used  E',  u') i n t h e a n a l y s i s .  3.4 STRUCTURE OF THE PROGRAM CONOIL c o n s i s t s o f two s e p a r a t e  subprograms : Geometry  program and M a i n program. Geometry program i n t e r p r e t s t h e finite  e l e m e n t mesh d a t a , a n d p r o v i d e s  information  f o r t h e M a i n p r o g r a m . The i n f o r m a t i o n i s  connected through pitfalls  the geometry  a link  file.  T h i s procedure can reduce the  u s u a l l y involved i n the set-up  of f i n i t e  element  mesh. CONOIL i s an i n c r e m e n t a l  l i n e a r program u s i n g  tangent  s t i f f n e s s m e t h o d . T h i s method d i v i d e s t h e a p p l i e d l o a d several small  increments,  and assumes t h a t s o i l s  linear-elastic  i n each l o a d increment.  load  i s analysed  increment  modulus v a l u e s the b e g i n n i n g modulus v a l u e s increment. and  f o r the s o i l  increment.  behave  In t h e program, each  twice, the f i r s t  time  using  e l e m e n t b a s e d on t h e s t r e s s e s a t  of the increment,  and t h e second time  using  b a s e d on t h e a v e r a g e s t r e s s e s d u r i n g t h e  The c h a n g e s i n s t r e s s a n d s t r a i n  the changes i n nodal  increment  into  point displacement  in soil during  a r e added t o the v a l u e s a t t h e b e g i n n i n g For the a n a l y s i s without  stress redistribution  shear  elements each of the  volume c o u p l i n g o r  u s u a l l y o n l y two i t e r a t i o n s a r e  49  performed. out  for  For a  the average  displacements, end  of  load  the  increment,  stress  strains  temperature  effects,  several shear  analyses.  redistribution  is  the  are  increment,  are printed  printed  while  out  for  the  other  volume  Among  frequently  abilities  coupling,  them,  used  only  in  the  of  and  performing stress  stress thesis.  STRESS-REDISTRIBUTION  when  For  an  incremental  the  stress  Mohr-coulumb state, zero,  path  would,  for a  of  adjacent stress  set  to  the shear  a  stress  increment  the strength  of  that  in  the s o i l s  the strength state 3.2.  would  will  methods  exist  in  The method b a s e d  the  the  is  in  so  back  that to  close element  this  to will  increment  if  the  stress  laterally  loaded  horizontal,  failure  shedding  stress  The  Moreover,  envelope  be u s e d  that  arise  (i.e.  a  loading.  behind  violate  be b r o u g h t  in  would  value  the normal  A method of  should  such  envelope  such  as  envelope  small  is  elements  overstresses.  is  problems  For  loading  Fig.  Several  the s o i l .  element.  stress  state  failure  that  unless  in  the  in  pile,  shown  program,  stay  such  then  of  further  decreases,  predicted  that  offending  however,  increment  reach  modulus  w h i c h means  change  linear  criterion)  the shear  overstress  as  of  and s t r e s s e s  redistribution  not  level  properties  increment.  CONOIL p o s s e s s e s  3.5  soil  the  criterion,  the overstress  to  the overpredicted  the  failure  the c o r r e c t i o n on c o n s t a n t  envelope.  of  mean  normal  50  (a) S t r e s s  (b) S t r e s s  Path around  Correction Normal  Fig.  3.2  Stress  State  Lateral.Pile  b a s e d on C o n s t a n t Mean Stress  associated  Shedding  with  Load  51 stress  i s e m p l o y e d i n t h e t h e s i s . T h i s m e t h o d seems more  consistent  with  t h e common a s s u m p t i o n t h a t  undergoes f a i l u r e w i t h  the s o i l  element  no v o l u m e b u t d i s t o r t i o n c h a n g e .  H o w e v e r , t h i s a p p r o a c h may meet p r o b l e m s i n b o u n d a r y e l e m e n t s when m a j o r o r m i n o r p r i n c i p a l s t r e s s elements i s the s p e c i f i e d s t r e s s c o n d i t i o n  i n those  at boundaries.  B a s e d on F i g . 3 . 2 ( b ) , t h e c o r r e c t i o n o f t h e o v e r s t r e s s w i l l be: Aa  X  Aa  X  Aa  y  Ar  = Aa  y  =  a„ X  a' X  =  a, y  a' y  =  -  T  -  T  1  xy xy xy a = tan" (2AT / ( a - a )) xy x y 1  Aa AT The applying principle  y  xy  3  = [(a -a )/2 1  3  ( ( a, +a  3  (( a , + a  ) sin0+c*cos<£) ] c o s 0 3  ) s i n 0 + c * c o s 0 ) ] sin<£  removal of these o v e r s t r e s s e s a s e t of nodal forces of v i r t u a l  stress level the  = [(a,-a )/2 -  c a n be a c h i e v e d by  w h i c h i s o b t a i n e d by t h e  w o r k . Due t o t h e g e n e r a l n a t u r e o f  dependency of t h e f a i l u r e  strength  c o m p u t e d s t r e s s s t a t e may v i o l a t e t h e f a i l u r e  again a f t e r the a p p l i c a t i o n of the nodal forces. i t e r a t i o n s may be r e q u i r e d assigned  to bring  Therefore  the stress state  of s t r e s s  shedding) technique, the s o i l  approximately as nonlinear mater i a l .  envelope  to the  tolerance.  With the incorporation load  envelope,  elastic  r e d i s t r i b u t i o n (or  c a n be m o d e l l e d perfectly  plastic  4.  4.1  loaded very  predicting soil  Only  the  finite  technique.  idealizing  not  deformation  masses,  powerful  behavior.  the  soil  Therefore,  the  the  accuracy  procedures,  but  also  conditions  and  stress-strain The  behavior  being  dependent.  represent  elastic  plastic soil  the  can  model,  be  and  represent  the  some  modelling  to  models  it  are  dependent  and  numerical  the  subsoil  simulating  real  have  These  by  the  models  range  constitutive  very  proposed  from  simple  elastic that  unique can  are  level  been  appears a  soil  stress  sophisticated  represented  particular  of  and  generally  proposed  steps  stress-strain  idealize  models  soil.  highly  However,  the  of  its  a  soil.  inelastic  stress-strain  several  discretization to  in  provides  predictions  ability  real  behavior  of  requires  mathematical  of  accurately each  the  distribution  method  characteristics  models  models.  and  of  nonlinear,  Various  stress  element  accurate  formulate  stress-strain  complex,  linear  on  and  The method  mass  on  to  RELATIONS  INTRODUCTION In  of  CONSTITUTIVE  no  real  stress-strain  only  at  best  features  of  real  soils. In  many  geotechnical  nonlinearity, three  stress  important  behavior  of  requirement  level  engineering dependency,  characteristics  soils.  Modelling  in  soil  the  of  these  the  and  the  inelasticity  are  stress-strain  aspects  stress-strain  52  applications,  becomes  relationship.  a  primary Among  53 s e v e r a l methods o f m o d e l l i n g n o n l i n e a r s o i l fitting and  methods  behavior,  curve  involving hyperbolic functions are simple,  h a v e been w i d e l y u s e d w i t h some  successes.  4.2 INCREMENTAL NONLINEAR E L A S T I C SOIL MODEL CONOIL e m p l o y s t h e i n c r e m e n t a l n o n - l i n e a r isotropic (1970).  elastic,  s t r e s s - s t r a i n m o d e l p r o p o s e d by Duncan a n d Chang  I n t h i s m o d e l , t h e two e l a s t i c  parameters a r e  r e q u i r e d t o c h a r a c t e r i z e t h e n o n l i n e a r s t r e s s - s t r a i n and v o l u m e c h a n g e b e h a v i o r . The i n d e p e n d e n t e l a s t i c  parameters  commonly u s e d a r e t h e Y o u n g ' s m o d u l u s , E, a n d P o i s s o n ' s ratio,  u. The b u l k m o d u l u s , B, a n d t h e s h e a r  m o d u l u s , G, a r e  p e r h a p s more f u n d a m e n t a l p a r a m e t e r s a s t h e y r e p r e s e n t t h e volume and d i s t o r t i o n components o f s o i l  responses,  and  w o u l d be t h e most d e s i r a b l e o n e s t o u s e . H o w e v e r , d e t e r m i n a t i o n of t h e shear modulus from l a b o r a t o r y t e s t i n g s is d i f f i c u l t ,  requiring  m o d u l u s , G, b o t h can  be d e t e r m i n e d  special  equipments. U n l i k e  b u l k m o d u l u s , B, a n d Young's m o d u l u s , E, from t h e c o n v e n t i o n a l t r i a x i a l  Young's m o d u l u s i s v e r y s i m i l a r  response. For  r e a s o n , M o d u l u s , E, a n d B a r e u s e d i n t h i s In  t e s t . The  i n c h a r a c t e r t o t h e shear  modulus as b o t h a r e a measure o f d i s t o r t i o n a l this  shear  the incremental nonlinear s o i l  thesis.  response, the  a p p r o p r i a t e v a l u e s o f E a n d B d e p e n d upon t h e l e v e l o f s t r e s s , and they tests. express  are u s u a l l y determined  In the i n t e r p r e t a t i o n of these the d i s t o r t i o n a l  response  from l a b o r a t o r y tests,  i t i s common t o  i n terms of m o d i f i e d  54 hyperbolas  and t h e v o l u m e t r i c  B a s e d on K o n d e r ' s s t r e s s - s t r a i n curves  f o r a number o f s o i l s c a n be a c c u r a t e l y by a h y p e r b o l a ,  Chang ( 1 9 7 0 ) p r o p o s e d a m o d i f i e d  s t r e s s - s t r a i n curve  = —  (0,-0-3)  — E.  +  (a,-a ) 3  (4.1.1) f  hyperbola  i s shown i n  t h e above h y p e r b o l i c  stress-strain  t h e t a n g e n t Young's modulus i s e x p r e s s e d a s :  E.  ,  = E.  t  The  hyperbolic  j-pj  4.1. D i f f e r e n t i a t i n g  curve,  Duncan  as :  A t y p i c a l shape o f t h e m o d i f i e d Fig.  form.  (1963) f i n d i n g s t h a t t h e  approximated reasonably and  response i n e x p o n e n t i a l  R f ( a , - a ) .,  (1 - —  1  shear s t r e n g t h  3  3  —f- 1  (0^-03)^  (a, - a  3  )  (4.1.2)  2  —  ) i s g o v e r n e d by M o h r - C o u l u m b f  criterion: / (  \ a  i  _  a  3 >  f  2 C cos</> + 2 a (i-sintf)  =  3  sin0  (4.1.3)  and  0=0,-  The  variation  confining stress, formula:  A</>log(a /P )  (4.1.4)  3  of the i n i t i a l a  3  i s expressed  Young's m o d u l u s E^ w i t h u s i n g Janbu's  (1961)  r° W "  —  3  «v° > 3  f  1  /  Stress Diiiference  (0  ^  ^  AE. l\  .  3.  / /  R  Axial  Fig.  4.1  Strain,  f  ( 0  r°3>uit  c  Hyperbolic Representation  A Stress-strain  of  Curves  cn cn  56  n  E. l  For  (4.1.5)  Pa  the  exponential  nonlinear  volumetric  expression  is  behavior,  commonly  used  the  following  :  m  A shown  typical in  Fig.  behavior  of  parameters the  type  and  are  example 4.2.  the E  of  f c  soil  of  is  B^.  These  and  the  K  Young's  n K  is D  the the  is  terms  Young's  the  bulk  behavior  complete by  two  of  of  modulus modulus  modulus  sand  soil  turn  depend  within  soil  is  stress-strain  in  stress  seven  for  elastic  parameters  level  in  is  the  defined  specified E  nonlinear  Therefore  soil  and  (4.1.6)  the  upon  soil,  constants  :  sand  confining  number exponent  number  a m is  the  bulk  Rf  is  the  failure  0,  is  the  peak  stress L\<P i s  the  of  ratio  1  angle  in  increase  failure in  the  cohesion  intercept  0  is  the  slope  the  tests  Byrne  et  are al  for  of  of  strength  evaluating  described (1983)  angle  confining  is  procedures  of  at  a  atm  C  laboratory (1980).  exponent  friction  decrease  tenfold  The  modulus  also  in  sand  for  a  stress  the  strength  envelope  envelope  these detail  present  of  parameters by  Duncan  particular  from et  al  values  57  16 _  Strttt  D i f f t r i n c t v« A i i o l  Stroin  (a)  O Oj • 4) kg /cm* & 0* • 3kg/cm* * cr • I kg/cm* e  c  2  3 4 Axiol Stroin,  5  6  %  (b)  O  10  20  Volumetric Stroin,  Fig.  4.2 S t r e s s tests  strain on s a n d  c -% ¥  Curves f o r d r a i n e d ( a f t e r Byrne  triaxial  & Cheung, 1984)  58  for  cohesive Using  the  soil  the  while  above  incorporation  nonlinear  Byrne  and  hyperbolic  of  Eldridge  (1983)  stress-strain  load  shedding  iteration  elastic-plastic  behavior  of  soils  for  sands.  relation  with  technique, can  be  simulated.  4.3  BILINEAR In  stress the  ELASTIC-PLASTIC  some  cases,  strain  curve,  undrained  model  case,  by  the  level, zero.  elastic  The  reaches the  the  failure,  the  Fig.  4.3)  load  shedding  bilinear  is  close  to  by  iteration  This  model  finite  element  is  also  program.  C^.  small  model  can  useful  in  of  This  In  the  =  2  in  shear  this  stress  both  is  a^-o  (i.e.  set  to  stress  equivalent 2C )  in  u  the  plastic BC  line  modulus a  obtained  the  be  (4.1.1).  Therefore be  the  deviatoric  are  deformation  4.3,  can  n are  the  (i.e.  procedure.  elastic-plastic  soils.  when  be  stress-strain Fig.  Eq.  m and  elements  using  in  also  segment) in  strength  soil  cart  independent  occurs  plastic  simulated  zero  criterion  When  4.3)  AB  under  bilinear  shown  exponents  shear  failure  large  As  are  a  clays  hyperbolic  (i.e.  failure  plasticity.  Fig.  curve  modulus  undrained  Tresca's  classic  Rf  Such  general  parameters  plastic  the  in  modification.  elastic  elastic-plastic  overconsolidated  shown  above  putting  thus,  as  bilinear  conditions.  (as  the  slight  linear  obtained  to  using  with  initial  curve  appear  such  loading  stress-strain simulated  soils  MODEL  in and  the  simple for  examination  cohesive of  the  Fig.  4.3  Bilinear  Elastic  Plastic  model  60 4.4 INCORPORATION OF TENSION FAILURE In g e n e r a l , stress.  s o i l s a r e very  I t i s , therefore, often  strength of s o i l s In order  i n the earth  to simulate  weak i n s u s t a i n i n g to neglect  structure analysis.  a tension  i n t h e above s o i l  failure  should  be i n c o r p o r a t e d  simple  t e n s i o n c u t - o f f model i s p r e s e n t e d . element  plastic  model. Herein,  hyperbolic/or  to a tensile  s t r e s s becomes n e g a t i v e , (for cohesive  s t r e s s , i . e . minor  or l e s s than t h e s o i l  soil,  i.e. soil  of the  subsequent s t r e s s . At t h i s  time,  soil  principal  tensile  cohesion), the  element i s assumed t o l o s e e n t i r e c a p a b i l i t y any  a  bilinear  s t r e s s - s t r a i n c u r v e s w h e r e a s , when a  element i s s u b j e c t  strength  criterion  i s i n c o m p r e s s i o n , t h e element i s  assumed t o f o l l o w t h e above n o n l i n e a r elastic  the t e n s i l e  the t e n s i l e cracking or c a v i t y i n  s o i l s behind the l a t e r a l p i l e s ,  When a s o i l  tension  of s u s t a i n i n g  shear and bulk  the element a r e both d e f a u l t e d t o s m a l l v a l u e s , element undergoes l a r g e shear d i s t o r t i o n  change i n t h e f o l l o w i n g l o a d i n g p r o c e s s .  Load  moduli so t h a t  and v o l u m e t r i c shedding  i t e r a t i o n procedure i s employed t o r e d i s t r i b u t e excess stresses t o the adjacent The  foregoing  minor p r i n c i p a l  simple  elements. t e n s i o n c u t - o f f m o d e l b a s e d on t h e  stress state, strictly  adequate f o r the responses of r e a l  speaking,  soils.  In r e a l i t y ,  i s a n i s o t r o p i c m a t e r i a l , i t may l o s e i t s s t r e n g t h d i r e c t i o n due t o t h e t e n s i l e c r a c k i n g still  possess c e r t a i n strength  may n o t be soil  i n one  i n that d i r e c t i o n , but  to resist  the s t r e s s i n other  61 directions. of  natural  To c o p e w i t h soils,  an a n i s o t r o p i c  cross-anisotropic simple tension  c u t - o f f model i s c o n s i s t e n t  w o u l d be t h e f i r s t hyperbolic  step  isotropic to simulate  stress-strain  response  s t r e s s - s t r a i n model such as  m o d e l s h o u l d be u s e d . H o w e v e r ,  framework of i n c r e m e n t a l  using  t h i s kind of a n i s o t r o p i c  with  elasticity  the  approach,  the tension  relations.  the above  failure  and  5. CYLINDRICAL CAVITY EXPANSION THEORY  5.1  INTRODUCTION In g e o t e c h n i c a l e n g i n e e r i n g , t h e r e a r e v a r i o u s  p r a c t i c a l problems the  expansion of a c a v i t y  interpretation Anderson, the  w h i c h c o n c e r n an a n a l y t i c a l p r o b l e m  and  mass, such as  of the pressuremeter t e s t  1961, Hughes e t a l , 1977,  effect  1979)  in a soil  of  the  ( G i b s o n and  B a g u e l i n et a l , 1978),  o f p i l e i n s t a l l a t i o n ( R a n d o l p h , C a r t e r and the b e a r i n g c a p a c i t y of deep f o u n d a t i o n  Wroth,  (Vesic,  1972). I n g e n e r a l t h e r e a r e two  types of problems  i n the  e x p a n s i o n of a c a v i t y  in a soil  mass, i . e . c y l i n d r i c a l  cavity  spherical  cavity  e x p a n s i o n , and  former case the c a v i t y cylindrically  under  expansion. In the  i s a s s u m e d t o be  expanded  c o n d i t i o n s of axisymmetry  s t r a i n w h i l e i n the l a t t e r case the c a v i t y expanded under either  c o n d i t i o n of s p h e r i c a l  case the problem  problem  i s s i m p l i f i e d , and  i n the c l o s e d  Due cavity  similar  the  r a d i a l . Therefore  i n some c a s e s , u n d e r  b e h a v i o r , the problem can  certain be  form.  to i t s a v a i l a b i l i t y  in closed  form s o l u t i o n s ,  expansion t h e o r y i s a l s o o f t e n used  a c c u r a c y of f i n i t e  i s assumed t o be  i s o n l y o n e - d i m e n s i o n a l because  i d e a l i z a t i o n s of the s o i l solved  plane  symmetry. However, i n  d i s p l a c e m e n t s i n t h e medium a r e e v e r y w h e r e the  and  element  the  to evaluate the  program i n t h e a n a l y s e s of  b u t more c o m p l e x p r o b l e m s . 62  For present  interests,  63 only c y l i n d r i c a l exclusively to  cavity  expansion  problem w i l l  be d i s c u s s e d  i n t h i s c h a p t e r . The p u r p o s e o f t h i s c h a p t e r i s  examine t h e a c c u r a c y  o f CONOIL. B a s e d on t h e e x a m i n a t i o n ,  some f e a t u r e s o f t h e o r i g i n a l  p r o g r a m were m o d i f i e d s o t h a t  the program can a c c u r a t e l y and e f f i c i e n t l y  simulate  those  problems.  5.2 ELASTO-PLASTIC CLOSED FORM SOLUTIONS  5.2.1  PROBLEMS For  the c y l i n d r i c a l c a v i t y expansion  mass s u b j e c t e d t o a c y l i n d r i c a l cavity will plane  move r a d i a l l y  p r e s s u r e , P, a t t h e w a l l o f  outwards under t h e axisymmetry and  strain conditions. Therefore,  t h i c k n e s s w i t h an i n i t i a l the s o i l  problem, the s o i l  cavity,  an i n f i n i t e d i s k o f u n i t  r, 0  c a n be t a k e n  across  mass f o r t h e a n a l y s i s . S u c h an a n a l y t i c a l m o d e l i s  shown i n F i g . 5.1. Initially, soil  the c a v i t y has a r a d i u s r ,  and t h e e n t i r e  0  mass i s s u b j e c t e d t o an i n - s i t u  isotropic  P . As t h e p r e s s u r e , P, i n c r e a s e s , t h e c a v i t y  i s expanded  0  radially  outwards. At the beginning,  the e n t i r e  d i s p l a c e d e l a s t i c a l l y . ' L a t e r , a t some s t a g e s deformation plastic  soil  mass i s  the p l a s t i c  i s i n i t i a t e d a t t h e w a l l of c a v i t y , and the  r e g i o n s p e c i f i e d by t h e e l a s t o - p l a s t i c  interboundary, pressure  stress state,  continues  displacement  i n F i g . 5.1 w i l l  enlarge as the a p p l i e d  t o i n c r e a s e . The p r e s s u r e  or the c i r c u m f e r e n t i a l  strain  vs the r a d i a l  forms t h e so  64  Elastic  Fig.  5.1  P r o b l e m of  Cylindrical  E x p a n s i o n i n S o i l Mass  Cavity  65 c a l l e d pressure expansion  curve.  5.2.2 CLOSED FORM SOLUTIONS a) C o h e s i v e  Soils  Many c l o s e d f o r m cohesive  soils  s o l u t i o n s h a v e been p r o p o s e d f o r  (Gibson and Anderson,  B a g u e l i n e t a l , 1978). elasto-plastic  For present  1961 a n d  i n t e r e s t s , only the  s o l u t i o n by B a g u e l i n e t a l ( 1 9 7 8 ) i s  presented herein: It  i s assumed t h a t t h e c o h e s i v e  accordance  - a  r  = 2 C  r  the e l a s t i c  Aa  soils  r  start  (5.2.1)  u  r e g i o n , t h e s t r e s s changes i n s o i l s  follow the e l a s t i c i t y  and  fails in  with the Tresca's c r i t e r i o n , i . e .  o  In  soil  theory  (Timoshenko and G o o d i e r ,  = - Ao-0  1951):  (5.2.2)  f a i l u r e when  reaches  a particular  value  P ,i . e . f  P  which  exists  condition propagates  f  = P  0  + C  (5.2.3)  u  i n the elasto-plastic  is first  reached  into the s o i l  interface,  r ^ . This  a t t h e w a l l of c a v i t y and then  medium a s t h e a p p l i e d p r e s s u r e P  66 continues  to  increase.  Stress Fields When s o i l the  elastic  r  a  o  region  =  P  °  +  = P  9  starting  i s i n the e l a s t o - p l a s t i c  -  0  from the  Stresses f o l l o w the  a  As  P  f  (P  "  (5.2.4)  2  f  - P )(r /r)  f  in  equations:  oHr /r)  p  0  (5.2.5)  2  f  boundary of  i n the annular  elasto-plastic plastic  following equations  region,  r^.  r e g i o n , however, would  f o r the  small s t r a i n  theory:  = P  f  + 2 C  u  ln(r /r)  (5.2.6)  CTg = P  f  - 2 C  u  ln(r /r)  (5.2.7)  r  the  i s of  10%  f  i n p r a c t i c e , the  e r r o r of  small  strain  small s i g n i f i c a n c e .  From t h e Eq.  (5.2.6),  the a p p l i e d pressure  AP  f  s t r a i n of p r e s s u r e m e t e r e x p a n s i o n t e s t s i s  seldom beyond theory  (  f o l l o w the  range, s t r e s s e s  = C  u  + 2 C  AP  u  P = a  r  when r = r . 0  Therefore,  is  ln(r /r ) f  0  (5.2.8)  67 Since i n undrained  (r /r ) f  Therefore  AP  for  for  0  + 2 C  u  elasto-plastic Therefore  curve  i s 2G,  P  (5.2.9)  u  0  u  ln(2Ge /C ) 0  (5.2.11)  u  s l o p e of the p r e s s u r e  the l i m i t pressure P  + C„[1  follows The  w o u l d be  :  (5.2.12)  U  Soils c l o s e d form  ( G i b s o n and A n d e r s o n ,  Hughes e t a l , 1 9 7 7 ) .  selected  L  expansion  + ln(G/C„)]  U  cohesionless soils  1972,  of  and  Many r e s e a r c h e r s h a v e d e v e l o p e d for  i s i n form  response.  Li  b) C o h e s i o n l e s s  curve  (5.2.10)  the i n i t i a l  and  = P  T  0  0  response,  = C  e /C  the pressure expansion  = 2 G U /r  elastic  AP  = 2 G  2  0  (no v o l u m e c h a n g e ) c o n d i t i o n s :  solutions  1961,  Vesic,  H e r e i n Hughes e t a l s o l u t i o n  f o r the comparison,  which  i s presented  briefly  is as  : soil  frictional  c o n t i n u u m i s a s s u m e d a s an  plastic  and  isotropic  elastic,  shear-volume c o u p l i n g m a t e r i a l i n  Hughes e t a l f o r m a u l a t i o n . The  soil  behaves e l a s t i c a l l y  and  68  obeys Hooke's law u n t i l t h e o n s e t o f p l a s t i c is  yielding,  which  g o v e r n e d by M o h r - C o u l u m b c r i t e r i o n , i . e .  a  = N o  (5.2.13)  e  r  where N  1 + Sin0 ;—* , a n d 1 - Sin0  =  <f> i s t h e f r i c t i o n a l a n g l e ,  For the  simplicity,  equilibrium equation da  a + —  V  dr  Stress  elastic  of  i s a d o p t e d , and  i s then :  a  ft  - = 0  (5.2.14)  the e l a s t i c  region, the stresses  equations as f o r cohesive s o i l s  follow  t h e same  ( e . g . Eq. (5.2.6)  (5.2.7)). In  Eq.  -  required  theory  field  In  and  the small strain  the p l a s t i c  r e g i o n , however,  combining the  (5.2.12) and (5.2.14) w i t h t h e o u t e r boundary the p l a s t i c  solution  zone, i . e . a t r = r ^ ,  = o^,  conditions  the s t r e s s  is:  In(a /a ) r  f  =  (1-N)In(r /r) f  (5.2.15)  69  Furthermore, occurring  in  simplicity. change  the  in  the  the  failure  Therefore,  the  plastic  r ,  e =  e  f  r  = r ,  e =  e  0  f  0  for  e  e  f  the  r  f  = P (1  e  f  = P  Thus  the  where  AP  P  the  0  is  + P  pressure  is  0  the  insitu  and  the  of  boundary  =  within  0  volume  conditions  :  the  annular  plastic  zone  is:  (5.2.17)  measured  at  the  wall  of  cavity,  / e  applied  and  (5.2.18) (5.2.19)  expansion  plastic  ( e  materials for  no  Sin0/2G  elasto-frictional  AP  assumption  + Sin0)  0  0  herein  .  f  strain  a  ignored  granular  2/(1-N)  « U /a )  0  is  0  V  of  (5.2.16)  strains  , 38  is  the  region,  =  effect  stage  using  r  solution  where  dilatancy  f  )  curve  cohesionless  (  1  N  )  /  incompressible  soils  is:  (5.2.20)  2  pressure  isotropic  for  at  pressure.  the  wall  of  cavity,  and  70 5.3  F I N I T E ELEMENT SIMULATION  5.3.1  F I N I T E ELEMENT MESH DOMAIN As d i s c u s s e d b e f o r e , t h e c y l i n d r i c a l  i s an a x i s y m m e t r i c a l and p l a n e s t r a i n and  strain  cross section  finite  element  s i m u l a t i o n of the problem,  stress  radial  a large  soil  t h e c e n t r a l a x i s , an  elememt mesh was  i n F i g . 5 . 2 ( b ) . The  condition  imposing the displacement c o n s t r a i n t s For t h i s  purpose,  nodes of b o t h upper  problem  axisymmetric  employed i n the a n a l y s e s , as  plane s t r a i n  and  but  i s taken f o r the  i s shown i n F i g . 5 . 2 ( a ) . S i n c e t h e  i s a x i s y m m e t r i c about  at  the  i n f i n i t e d i s k of u n i t t h i c k n e s s of the  d i s k of the s o i l c r o s s s e c t i o n  direction.  expansion  i s then taken f o r t h e a n a l y s i s . However, f o r  analyses, which  finite  problem,  f i e l d s a r e o n l y d e p e n d e n t upon t h e  d i s p l a c e m e n t . An  the f i n i t e  cavity  shown  i s o b t a i n e d by  i n the  vertical  a s e r i e s o f r o l l e r s were p l a c e d  bottom  b o u n d a r i e s o f t h e mesh  d o m a i n . H o w e v e r , f o r t h e i n n e r and  outer boundaries  stress  b o u n d a r y c o n d i t i o n s were a s s u m e d . At the i n n e r boundary,  t h e p r e s s u r e P i s a p p l i e d on  c a v i t y , w h i l e a t the o u t e r boundary the s t r e s s e s a c t i n g are  equal t o the i n s i t u s t r e s s s t a t e , assuming  changes i n t h e s o i l s beyond t h i s  boundary.  b o u n d a r i e s a r e f r e e t o move r a d i a l l y p r e s s u r e P. The  t h e a p p l i e d p r e s s u r e and circumferential  strain  Hence,  outwards  pressure expansion curve  no  both  under  the from  the r e s u l t i n g d i s p l a c e m e n t , or The  on  stress  i s obtained  at the w a l l of c a v i t y .  the  the  Fig.  5.2(a) S o i l Domain u s e d f o r F i n i t e  Element  Analysis  Fig.  5.2(b) F i n i t e E l e m e n t Mesh f o r C a v i t y Simulation  Expansion  72 circumferential small strain initial  strain  i s c a l c u l a t e d as A U / r 0  0  b a s e d on t h e  t h e o r y . I n a l l t h e f o l l o w i n g a n a l y s e s , an  cavity  radius, r  = 50 mm.  0  i s assumed.  5.3.2 OUTER BOUNDARY EFFECTS The  i n f l u e n c e s o f t h e o u t e r b o u n d a r y R o f t h e mesh  d o m a i n on t h e f i n i t e cohesive  soils  e l e m e n t p r e d i c t i o n was e x a m i n e d f o r  under u n d r a i n e d  analyses with outer  c o n d i t i o n . Two f i n i t e  radia of 50r  o  and l 0 0 r  element  were p e r f o r m e d  o  u s i n g t h e d e s c r i b e d mesh d o m a i n a n d b o u n d a r y c o n d i t i o n s . The r e s u l t s a r e shown i n F i g . 5.3. As e x p e c t e d , larger  outer  expansion 50r . o  soil  o  gives a softer  As  pressure  than t h a t w i t h t h e s m a l l e r outer r a d i u s , r a d i u s i s l a r g e r , more  r e g i o n i s s t r e s s e d , and c o n s e q u e n t l y  a softer  more  i s c a l c u l a t e d a t the w a l l of c a v i t y ,  shown i n t h e f i g u r e , response  leading to  t h e two mesh m o d e l s g i v e  i n the very  medium i s c o m p l e t e l y  o f s o i l medium b e g i n  small strain  i n the e l a s t i c  to yield,  s t a g e . When p a r t s  t h e d i f f e r e n c e between t h e  the larger  t h e mesh d o m a i n i s , t h e f i n i t e  the outer  i fthe outer  7%.  radius R of  element r e s u l t s a r e c l o s e r t o  t h e r e a l a n s w e r , t h e e r r o r due t o t h e f i n i t e be s i g n i f i c a n t  almost  l e v e l where t h e  m o d e l s becomes l a r g e r , b u t g e n e r a l l y l e s s t h a n Therefore, although  not  soil  response.  identical  two  element p r e d i c t i o n w i t h t h e  i s b e c a u s e when t h e o u t e r  deformation  soil  radius, 100r ,  curve  This  the f i n i t e  mesh d o m a i n may  radius i s s u f f i c i e n t l y  APPLIED PRESSURES P - KPfl 0.0  CD  40.0  80.0  120.0  160,0  200  74  large. the  The  soil  difference  medium  interests, following  an  is  outer  analysis.  element  analyses  results  in  5.4  good  FINITE  5.4.1  in  would the  radius  were  soils.  using  such  a  agreement  later  to  can  the  closed  form  analyses on  both  using  cohesive  compare  the 5.2,  elasto-frictional  employed  for  cohesive  however,  were  For assumed  volume  the  arbitrarily of  0.499.  pressure plastic  Total was  shear  strength  C^.  shear  strength  C  plastic  strain  herein  for  soils,  undrained  which  modulus  of  was  soils For  the  the  soil  form  soil  and  behavior,  simplicity. loading  to  by a  loading  specified  were  soils  adopted,  the  plastic  softening,  obtained  was  during is  one  real  equivalent  analysis  cohesionless closed  cohesionless  effect  evaluated  ,  and  the  and  element  elasto-perfectly  considered  stress  yielding  soils  the  bulk  not  finite  solution.  foregoing  of  analysis,  high  the  hardening,  coupling  cohesive in  soils  strain  not  the  provide  elasto-plastic  model  and  Sec.  the  material  shear  the  ANALYSES  in  the  when  present  for  comparisons,  domain  with  only  For  selected  mesh  presented  The  picture stage.  was  o  solution  respectively.  the  PREDICTIONS  element  order  l00r  in  performed  In  of  seen  M A T E R I A L MODELS AND  mesh  into  elasto-plastic  As  ELEMENT  Finite  come  by  the  condition using  an  Poisson i.e.  was  the  ratio pore  process.  The  undrained  shear  stress  below  the  undrained  will  behave  elastically  while  75  for  the  shear  perfectly For was  plastic  which  strength  in  is  the  not  soil  stress-strain 5.2  for  The  initial  soils  stress which  stress  modulus  assigned For angle closed  to  function analysis,  the  practical  sands.  by  soil  the  assumed  basically  The  behaves  as  material.  required are  and  of  Rf  is  soil  elastic  in  the  presented  cohesionless  a  assumed to  flag  of  in  the  soil  and  medium  form  program  Unless  5.1  respectively.  soil  closed  the  the  Table  soils  in  the  in  behavior.  moduli  hyperbolic  to  was  solution. indicate  for  nonlinear  are  not  dependent therefore  the  elasto-plastic  model,  numbers  in  the  elasto-plastic  model  soil  were  zero.  the  large the  soil,  stress  solution,  and  is  Mohr-Coulomb  in  at of  a  condition  ratio  level  <t> w i t h  materials  loading  Poisson's  equivalent  cohesionless  form  as  The  governed  condition  is  elasto-plastic  the  value  the  behaves  drained  cohesionless  relationship  the  the  are  parameters  small  on  for  plastic  The  behavior,  soil  PROPERTIES  cohesive  isotropic,  the  the  analysis.  the  elasto-frictional  The  ,  soils,  unusual  Hence,  MATERIAL  C  material.  characteristics  criterion.  5.4.2  above  cohesionless  employed  0.2,  stress  the  level  nor  strain  program was  the  the  variation is  the  to  effect  dilation  therefore,  assigned  the  considered  dilatancy  level,  was,  not  of  not  zero  in  of  friction in  the  granular  iteration  used the  in  the  Table  5.1  S o i l Parameters of C o h e s i v e S o i l s f o r C y l i n d r i c a l Cavity Expansion Simulation Soil Parameters C  u  Elasto-Plastic Model  (Kpa) K  E  B  V  n m Rf K  0  cr ( K p a ) 0  Table  Model  7.5 59.21 9869 0.499 0.0 0.0 0.9 1 .0 80.0  7.5 59.21 9869 0.499 0.0 0.0 0.0 1 .0 80.0  K  Nonlinear  5.2  S o i l Parameters of Cohesionless S o i l s f o r C y l i n d r i c a l Cavity Expansion Simulation Soil Parameters  Elasto-Plastic Model 50 36° 600 360 0.2 0.0 0.0 0.0 1 .0 50.0  ( % ) 0  K  E  K  B  n m Rf K  0  (KN/m ) 1.  v  Q  2  i s the i n i t i a l  elasto-plastic  model.  Nonlinear 50 36° 600 360 0.2 0.5 0.25 0.9 1 .0 50.0  p o i s s o n ' s r a t i o of sands  Model  77 5.4.3 RESULTS AND In  COMPARISON  the f o l l o w i n g  p r o g r a m were f i r s t Based  on t h i s  good agreement The  studies,  results  Original  the o r i g i n a l  compared w i t h t h e c l o s e d  comparison,  form  solution.  t h e p r o g r a m was t h e n m o d i f i e d , a n d  with the c l o s e d  form  modifications are presented  A.COHESIVE  from  solution  in detail  was  obtained.  herein.  SOILS  Program  The  predicted  pressure expansion  curve  from t h e  original  program u s i n g the e l a s t o - p e r f e c t l y  plastic  behavior  i s shown  with the closed  form  solution,  i n F i g . 5.4  It i s clearly  elastic,  early  pressure  expansion  form.  small s t r a i n  starts  near  error  the c a v i t y .  prediction  soil  a s more  i s found shear  the program  predicts  of the p r e d i c t e d  curve  o f 0.8mm, i . e . 1.8%  deformation  medium  has  between t h e c u r v e s  r e g i o n becomes p l a s t i c .  prediction  appeared  The  i n the  35%, w h i c h o c c u r s a t t h e end o f  and t h e c o r r e s p o n d i n g e r r o r i s about  i n the  agreeable to the c l o s e d  level  soil  that  the program g i v e s t h e  The d i f f e r e n c e  i n displacement  i s more t h a n  analysis,  elastic  i n the f i g u r e  d i s p l a c e m e n t . The d e v i a t i o n  seems t o a c c u m u l a t e  It  strain  where t h e p l a s t i c  occurred  figure  level  t o grow a t t h e d i s p l a c e m e n t  strain,  largest  shown  curve c l o s e l y  However, a t l a r g e  much l e s s  i n comparison  soil  i n the pressure  10%.  out that  i n the o r i g i n a l  and b u l k m o d u l i  program the  are defaulted  by a f a c t o r o f  Fig.  5.4  Comparison  of  Original  Program  and  Closed  Form  Solution  CD  79  1000  and  10  failure. the  respectively  The  large  small  plastic  increments.  defaulted  element  has  to  be  simulation  of  undrained  using of  a  softer In  the  the  can  inner  undrained  and  (or  relationship  was  Fig. the  real  would if  found  5.4,  The  change)  and  is  relax  to  the  bulk  the soils.  is  simulated  Poisson's modulus  changes,  for leading  calculated  to  and  As  shown  outer  displacements  in  Fig.  will  boundary  5.5,  result  the  in  a  displacements:  (5.4.1)  0  expansion  not  response from  element  fully  curve  stiffer was  ratio  condition  condition  not  result  basis,  cohesive  volume  boundaries.  was  even  the  condition  of  load for  will  for  the  (5.4.1)  modulus  to  from  finite  been  simulate  modulus  undrained  the  stiffer  considered  the  for  pressure  bulk  some  to  curve.  of  inner  = R-6/r  0  it  reduction  checked  volume  that  Eq.  have  the  no  bulk  physical  as  is  reaches  subsequent  equivalent  expansion  outer  the  undrained  produce  between  U  It  the  quality  be  the  of  element  modulus  conditions  modulus  will  pressure fact  lack  the  Therefore,  simulation at  bulk  elements  in  inappropriate  analysis,  high  0.499.  failed a  our  soil  shear  defaulting  considered  In  the  deformation  However,  shear-failed  when  than  satisfied.  predicted what  defaulted  predicted the  high  results  by  is by  the  stress  the in  factor program ratio  in  Therefore,  from  shown a  shown  program  Fig. of  5.4  10. is  attracted  in  Fig.  5.5  Displacement  Distribution  Plane S t r a i n  under  Condition  Undrained  81  failure extra  elements.  stresses  failure the  pressure excess  such  a  are  expansion  the  load  procedure  failure  a  effective  Program  of  respect  to  the  above  of  can  be  the  form  is  by  modified using  i n F i g . 5.6  predicted  and  pressure  in excellent  the  to  in  the  spread  the  adjacent  technique. orginal  However,  program  for  program the  an  initial  nearly  invisible.  was  the  ability  for cohesive  the  modulus  bulk  load  shedding  that  a  then  employed  same d a t a  original  expansion  slope In  improve  original  analysis  the  i n comparison the  to  i n the  general  for  and  soils. failure  iteration c,  <t> m a t e r i a l  program.  agreement  having  condition  defaulting  i n c o r p o r a t e d so  handled  solution  i n the  d i s c a r d e d , and  was  same p r o b l e m shown  program  f e a t u r e of was  The  remain  in  the  limitations  accuracy  technique  to  analysis,  some  will  method  i n c l u d e d i n the  m o d i f i c a t i o n s w e r e made  elements  in  response  iteration  program,  The  they  elements  shedding  the  envelope  stiffer  failure  not  incremental  inevitable,  An  was  of  soils.  Modifications With  nature  giving  curve.  from  i s the  cohesive  the  almost  elements,  stress  elements  to  o f f e n d i n g the  elements  failure  Due  about  this  before.  The  with  those  from  curve  from  the  It  closed  the  i s accurately simulated  as  the  form The  Eq.  the are  closed that  modified  undrained the  results  i s seen  the  1.0226(2G^).  case,  analyse  as  program.  with  to  program  solution error  is  loading (5.4.1)  the  is  :  cro n  _  H ^ x  o'-^  I  0.0  —  CLOSED FORM SOLUTION h ORIGINAL PROGRAM MODIFIED PROGRAM x NONLINEAR SOILS  0  I  4.0  I  I  I  Fig.  I  12.0  8.0  I  I  16.0  I  I  I  20.0  I  24.0  CIRCUMFERENTIAL STRAIN  5.6  Comparison of M o d i f i e d  I  1  I  28.0  [%)  Program a n d C l o s e d  Form  I  I  32.0  Solution  I  36.0  I  40  83 satisfied  w i t h an  error  In a d d i t i o n , b e h a v i o r was  the  also  compared w i t h the an  plastic  solution.  the  of  end  result  closed  initial  the  1%.  nonlinear, stress  i t gives a softer  exhibit  than  employed i n the  m o d i f i e d program, the expected,  less  dependent  analysis  i s also  using  the  shown i n F i g .  5.6.  pressure expansion curve  form s o l u t i o n .  The  linear e l a s t i c portion T h e r e f o r e , the  f i r s t load  soil  initial  increment  As  as  c u r v e does  as  not  in e l a s t i c  slope calculated  is less  t h a n 2G.  in  at the  I  nonlinear, In the  stress  the  meantime, the  stress  m o d i f i e d program i n the  compared w i t h the Sec. As  l e v e l dependent  5.2.2. The  figures,  and  the  form s o l u t i o n  the  presented  shown i n F i g .  pattern  predicted  i n good agreement w i t h the B.  d i s t r i b u t i o n predicted  from  e l a s t o - p l a s t i c s o i l mass i s  comparisons are  shown i n t h e  distribution  closed  analysis.  of  s i z e of  closed  form  the  in  5.7(a),  (b).  stress  p l a s t i c zone are a l l solution.  COHESIONLESS SOILS It  solution  s h o u l d be of  the  noted f i r s t that  f o r the  c o h e n s i o n l e s s s o i l s has previous researchers  u n d e r s t a n d the  elasto-plastic  p r e s s u r e e x p a n s i o n c u r v e from the  element a n a l y s i s  difficulties.  the  An  not  (She,  by  expansion  been e x a m i n e d so 1986)  a t t e m p t was  different  element a n a l y s i s  c y l i n d r i c a l cavity  to  f a r by  in the  i t s inherent  made i n t h i s t h e s i s  factors  means of  due  finite  which a f f e c t  comparing the  the  finite  to finite element  84  -  CLOSED  1  +  FINITE  4.0  8.0  FORM  SOLUTION  (a)  ELEMENT  CC"  c/v_:-  or  -  c r  CD " d o  0.0  CC  CLOSED +  +  16.0  12.0  RADIAL  FORM  20.0 DISTANCE  24.0  28.0  (R/RO)  i—  36.0  32.0  SOLUTION  (b)  F I N I T E ELEMENT  a  40.0  Q  cn. 1-  ,_U5  cn CCo  or  or  0.0  4.0  8.0  12.0  16.0  RAOIHL  Fig.  5.7  20.0 DISTANCE  24.0  28.0  32.0  36.0  with  Closed  (R/RO)  S t r e s s D i s t r i b u t i o n i n Comparison Form S o l u t i o n  40.0  85 prediction with i t s counterpart, closed  form s o l u t i o n .  The  o r i g i n a l p r o g r a m was t h e n m o d i f i e d t o o b t a i n an a g r e e m e n t b e t w e e n t h e s e two s o l u t i o n s .  Original  Program  The p r e d i c t e d p r e s s u r e e x p a n s i o n c u r v e s f r o m t h e o r i g i n a l program u s i n g e l a s t o - p l a s t i c  frictional  m o d e l i s p r e s e n t e d i n F i g . 5.8. F o r t h e s a k e o f the e l a s t o - p l a s t i c finite  element  The c l o s e d et  al  closed  comparisons,  form s o l u t i o n and t h e n o n l i n e a r  p r e d i c t i o n a r e a l s o shown i n t h e F i g . 5.8.  form s o l u t i o n  i s of the form proposed  by Hughes  ( 1 9 7 7 ) , w h i c h h a s b e e n p r e s e n t e d i n S e c . 5.2. The  initial which  P o i s s o n r a t i o used  remains  varies  i n a l l t h e a n a l y s e s was  constant f o r the e l a s t o - p l a s t i c  0.2,  a n a l y s e s but  f o r the nonlinear a n a l y s i s .  As  shown i n F i g . 5.8, t h e e l a s t o - p l a s t i c  analysis gives results agreeable with closed only  material  i n the small s t r a i n  elastic  s o i l medium  Beyond t h a t the f i n i t e  level, element  level,  form  element  solution  i . e . up t o 0.1%, where t h e  i s i n the e l a s t i c the p l a s t i c  finite  deformation stage.  deformation of s o i l s  a n a l y s i s t h e n p r e d i c t s much  occurs,  softer  p r e s s u r e e x p a n s i o n c u r v e . The d e v i a t i o n o f t h e s e two c u r v e s seems t o a c c u m u l a t e deformation  a s more s o i l  stage.  C o m p a r i n g t h e two f i n i t e elasto-plastic until  region i s i n the p l a s t i c  solution  the s t r a i n  level  element  is stiffer reaches  p r e d i c t i o n s , the  t h a n t h e n o n l i n e a r one  2.4%, w h i c h  i s usually  o  cr Q_  •+— o  (NI  0.0  Closed Form Solution r- FEU: E l a s t i c P l a s t i c e> FEtl: Nonlinear S o i l s  0.4  0.8  1.2  i  i  1.6  i  i  2.0  i  i  i  2.4  CIRCUMFERENTIAL STRAIN Fig.  5.8  Pressure Soils  Expansion Curve from  Original  for  i  2.8  r  3.2  3.6  4.0  IX)  Cohesionless  Program oo cn  87 expected.  However,  elasto-plastic for  incorrect  trend  original  shown  solution  nonlinear  the  as  the  the  even  level  beyond  FE p r e d i c t i o n s  program  in  figure,  becomes  strain  of  in  the  the  softer  than  the  2.4%,  Such  an  questions  the  elastic-plastic  accuracy  of  analysis.  Modifications of the Program 1) Permanent failure stress record ' As  stated  expansion This of  was  curve found  failed  original records  the  will  be  to  state  the  of  is  be  process,  e.g.  Point  modified  in  the  is  a  in a  independent  for  Fig.  soils of  current  Mohr-Coulomb  memory  state  This  all  the  implies  will the  of  treatment the  which Once  the  on  the  the  following  a  element  element  that  stay  soft.  In  elements.  therefore  is  stress  failure  loading  5.9.  treatment  is  where  the  frictional  the  and  too  program.  state  stress  is  numerical  failed  element  point  such  of  failure  soil  A  improper original  ratio  pressure  analysis  stress  forever.  cohesive  upon  to  memorized,  same  cohesionless  dependent the  is  the  failed  reality,  strength  due  failed,  the  undrained  element  stress  failure  at  elasto-plastic  finite  there  shear  envelope  the  elements  permantly  regarded  For  be  program,  element  the  from to  soil  soil  In  earlier,  only  the  current  soils, state  diagram  appropriate  undrained normal  however,  of in  stresses, Fig.  5.9.  shear  stress  the as  for  state.  strength shown  is in  00 00  89  As  shown  elastic  region  constant, line the  the  point  A,  a  However,  A  is  improper  stress The  expansion moving  curve  oscillation  is  Byrne, have  not  the  been  the  the  in  in  form  in  envelope  at  occurs.  increase  as  the  load  the  element  instead  program.  of  will staying  Therefore,  stress  state  program,  the  it  record  the  the  result  ,  the  predicted  than  the  previous  one,  solution.  However,  high  indicates  that  curve,  occurred  1986).  When  soils.  stiffer  in  of  in  straight  failure  will  failure  expected  the  the  is  remains  envelope.  following  the  medium  therefore  envelope  error  As  stress  failure  increment  permanent  closed  fully  in  soil  deformation  element  assumed  reported She,  reach  failure  becomes  instability  1984,  path  5.10.  appears  frequently  the  is  the  plastic  frictional  Fig.  towards  numerical  a  correcting  in  of  of  stress  have  on  element  inclined  to  A  the  normal  increment  increase  as  initially mean  Point  an  strength  cohesionless  shown  to  forever  After is  up  the  path  amount  the  point  for  stress  large  normal  at  which  of  the  along  figure,  state  increments. move  the  in  vertically stress  mean  in  which  in  the  analysis.  previous  However  the  work  reason  pressure  This  problem  (Atukorala and  and  treatments  explored.  2) R e d u c t i o n f a c t o r f o r s h e a r m o d u l u s Fluctuation is  considered  modulus  for  to  the  of  the  predicted pressure  be  due  to  failure  the  too  elements.  much In  the  expansion  reduction original  of  curve shear  program,  cr o_  ^ -1 (\J co  0.0  —  C l o s e d Form S o l u t i o n  -+  FEM: w i t h s t r e s s memory  -O  FEM: w i t h o u t  0.4  0.8 Fig.  s t r e s s memory  |— | | | | 1.2 1.6 2.0 CIRCUMFERENTIAL  5.10 P r e s s u r e E x p a n s i o n  |  | | | 2.4 2.8 STRAIN it)  3.2  3.6  4.0  C u r v e a f t e r D i s c a r d i n g S t r e s s Memory  o  91 the of  shear  modulus  1000, w h i c h  for  is  cohesionless  mean  normal  a  small  path  incrementally line,  for  by  from  numerical  adopted  be  for  path  increments  more  gradually  rather  than  In  a  for  which  failure  envelope,  is  a  the  horizontal  large  value  stress failure  path  the  inclined  if  a  from a  a  be  a  factor  Therefore,  increases  with  the  an  abrupt  large  number  that  the  stress  suddenly  nearly  failure  and  horizontal  envelope.  incurred,  condition  smaller  As  a  especially  and  the  with  to  For  so  an  that  material  would  change  to  an  inclined  stress  slope  reduction  then  in  is  nearly  in  as  well.  undrained  factor  used the  the  path  cohesionless be  case,  optimal  the  0 = 0 ,  move  is  this  f r i c t i o n a l angle  of  reduction  factor  line.  loading  envelope  In  line  the  would,  reduction  soils.  that  upon  should  envelope,  will  soils.  changes  to  by  undergo  saying  line  horizontal  increment  value  to  stability  seems  line  envelope.  reduction failure  of  modulus  vertical  depends  failure  strength  elasto-plastic  nearly it  cohesive  elements  cohesionless  exists,  soils,  the  from a  theory,  value  material.  improved  the  small  elements  amounts  instability  inspection,  therefore,  the  shear  the  a  for  vertical  along  elasto-plastic By  in  failed  a  to  failure  This  the  as  where  the  change  zigzagging  result,  same  soils  number.  followed  defaulted  the  stress,  back-and-forth to  is  view  of  path  the  For  cohesive strength  analysis to  allow  horizontally  soils,  stress  0 of  shear  the  used  factor  the  along  instead, the  a  a  smaller  inclined  increment  the  can  92 approach  the f a i l u r e  Such a concept analysis  i s consistent with past experiences i n the  f o r sands.  numerical  e n v e l o p e more c l o s e l y a n d g r a d u a l l y .  I n t h e dense sand,  i n s t a b i l i t y problem  i n t h e l o o s e sand  i t was f o u n d t h a t t h e  i s more l i k e l y t o o c c u r  i f t h e same r e d u c t i o n a s f o r c l a y  than  i s used.  T h i s i s because  i n t h e d e n s e s a n d , t h e f r i c t i o n a n g l e <t> i s  high, a smaller  reduction  factor  i s therefore expected  than  in the l o o s e sand. For the n o n l i n e a r a n a l y s i s , as the s t r e s s path' i n c r e m e n t  i s curved, gradually approaching the f a i l u r e  e n v e l o p e , t h e r e f o r e t h e n u m e r i c a l p r o b l e m may n o t be e n c o u n t e r e d even a l a r g e v a l u e o f r e d u c t i o n However, such an o p t i m a l r e d u c t i o n  factor  factor  i s used.  i s d i f f i c u l t to  d e t e r m i n e a p r i o r i f o r an a n a l y s i s . Since i n the hyperbolic elastic ratio,  stress strain  r e l a t i o n , the  moduli a r e r e l a t e d t o each o t h e r v i a P o i s s o n ' s t h e r e i s a r e l a t i o n s h i p between t h e r e d u c t i o n  and t h e P o i s s o n ' s r a t i o  i f t h e b u l k modulus  unchanged. Such a r e l a t i o n s h i p  u  f  f  =  1 .5B - G zrz — 3B + G  remains  i s shown a s :  f  f o r the  s h e a r m o d u l u s . T a b l e 5.3 i l l u s t r a t e s t h e  between t h e r e d u c t i o n the  (5.4.2)  f  where G^ = G/Rd, a n d Rd i s t h e r e d u c t i o n f a c t o r failure  factor  relation  f a c t o r and t h e P o i s s o n ' s r a t i o  f a i l u r e e l e m e n t s . A s shown i n t h e t a b l e , a  reduction  f a c t o r o f 1000 i s c o r r e s p o n d e n t t o a P o i s s o n ' s r a t i o o f 0.49965.  for  93 Table  5.3  R e l a t i o n s h i p Between S h e a r M o d u l u s R e d u c t i o n F a c t o r and F a i l u r e P o i s s o n R a t i o «d 1000 350 70 35 25 20  In  0.49965 0.499 0.495 0.490 0.485 0.480  view of t h i s , a f a i l u r e  P o i s s o n ' s r a t i o o f 0.48  c o r r e s p o n d i n g t o a r e d u c t i o n f a c t o r of about T a b l e 5.3, was u s e d  20 i n  i n t h e a n a l y s i s . The r e s u l t s a r e shown  i n F i g . 5.11. A s e x p e c t e d , t h e p r e d i c t e d p r e s s u r e curve  i s clearly  reduction  3) L o a d  s m o o t h e d up w i t h t h e s m a l l e r v a l u e o f  f a c t o r , which proves the f o r e g o i n g a n a l y s i s .  shedding  effect  Due t o t h e i n c r e m e n t a l n a t u r e o f t h e f i n i t e analysis,  the s t r e s s path increment  f a i l u r e envelope of  element  zigzags along with the  when t h e s o i l e l e m e n t  i s failed.  Accuracy  t h e a n a l y s i s t h e r e f o r e i n p a r t d e p e n d s on t h e s i z e o f  each  load  increment. Since the optimal s i z e of load  increment  isdifficult  iteration  technique i s c o n s i d e r e d as n e c e s s i t y  t o determine  analysis to redistribute in  expansion  failure  elements  the excess  a priori,  load  shedding  i n the  shear s t r e s s  attracted  t o t h e a d j a c e n t u n f a i l e d e l e m e n t s . The  i n f l u e n c e of the s t r e s s r e d i s t r i b u t i o n pressure expansion curve  on t h e p r e d i c t e d  i s shown i n F i g . 5.12. A f t e r  stress  cr  4-  CNJ  ro  Closed Form  Solution  -+ FEN: l a r g e r e d u c t i o n •o FEM: s m a l l r e d u c t i o n  i 0.0  0.4  0.8  1  1.2  1  1.6  1  1 2.0  1  i  i  2.4  CIRCUMFERENTIAL STRAIN  Fig.  5.11  Pressure Expansion Curve Reduction  Factor  r  {%)  2.8  with Smaller  f o r Shear  Modulus  3.2  3.6  4.0  96  redistribution, failure  the high  elements a r e load-shedded t o the adjacent  therefore producing  4) P l a s t i c - v o l u m e As  correction  smaller  iteration  elements,  a s o f t e r response.  shown i n F i g . 5.12, t h e p r e d i c t e d p r e s s u r e  curve with  that  shear s t r e s s r a t i o s a t t r a c t e d i n  reduction  f a c t o r and l o a d  i s much s o f t e r t h a n t h e c l o s e d  formulation  of the c l o s e d  expansion  shedding  f o r m . I t i s aware  f o r m s o l u t i o n shown i n S e c .  5.2 e m p l o y s t h e no v o l u m e c h a n g e a s s u m p t i o n t h r o u g h o u t t h e entire elasto-plastic analysis, according  soil  region. For the f i n i t e  to the e l a s t i c i t y  c h a n g e w i l l be i n h e r e n t l y t r u e  in elastic  mean n o r m a l s t r e s s r e m a i n s c o n s t a n t . plastic  region  "plastic" bulk  t h e no v o l u m e  r e g i o n where t h e  However, i n t h e a n n u l a r  t h e program w i l l a u t o m a t i c a l l y c a l c u l a t e t h e  volume change i n c r e m e n t a l l y  modulus as i n t h a t r e g i o n  increase with  theory,  element  the load  through the e l a s t i c  t h e mean n o r m a l s t r e s s w i l l  increments.  Therefore,  i f the f i n i t e  e l e m e n t p r e d i c t i o n i s t o be r e a l l y c o m p a r e d w i t h t h e c l o s e d form s o l u t i o n , the " p l a s t i c " corrected As  from the f i n i t e  volume change s h o u l d  element  results.  shown i n F i g . 5.13, t h e e x t r a d i s p l a c e m e n t a t t h e  c a v i t y due t o t h e v o l u m e c h a n g e i n t h e a n n u l a r region  be  of f i n i t e  AU  f f  1 = r  plastic  e l e m e n t a n a l y s i s c a n be c a l c u l a t e d a s :  n  E  (e . r . A r . ) V  o  i  =  1  1  1  1  (5.4.3)  97  A P  2ir r  AU  0  f f  Fig.  5.13  = I "i.i  Plastic  Finite  (2w  e . r - Ar. ) vi 1 i  Volume C o r r e c t i o n  Element  Analysis  for  9 8  w h e r e : AU^ i s t h e r a d i a l d i s p l a c e m e n t a t t h e w a l l o f c a v i t y due  t o t h e volume change i n a n n u l a r p l a s t i c  volumetric Ar.  1  v  r  zone,  r. i s the r a d i u s of  '  to the central a x i s ,  e ^ i s the  i n the annular p l a s t i c  i s the w i d t h of the element,  elements the  s t r a i n of elements  zone,  1  i s the i n i t i a l  0  r a d i u s of  cavity. S u c h an e x t r a d i s p l a c e m e n t  i s then s u b t r a c t e d from t h e  p r e d i c t e d d i s p l a c e m e n t a t t h e w a l l o f c a v i t y . The p r e s s u r e expansion curve a f t e r  the p l a s t i c  i n F i g . 5.14 i n c o m p a r i s o n shown i n t h e f i g u r e ,  volume c o r r e c t i o n  with the closed  the response  form s o l u t i o n .  is stiffer  i s r e m a r k a b l e . The i n i t i a l  e q u a l t o 2G^. The n o n l i n e a r e l a s t i c from m o d i f i e d program i s a l s o expected, initial  i t i s softer  As  than the  p r e v i o u s one, and i t s agreement w i t h t h e c l o s e d solution  i s shown  form  slope i s approximately pressure expansion  included  than the e l a s t i c  curve  i n F i g . 5.14. As plastic  curve, i t s  s l o p e i s l e s s t h a n 2G^. T h e r e f o r e t h e a c c u r a c y o f  the m o d i f i e d program i s a s s u r e d . In  summary, t h e m o d i f i e d p r o g r a m i s c a p a b l e o f  p r o v i d i n g the r e s u l t s that a r e i n remarkable the c l o s e d soils.  form s o l u t i o n s  Different  be r e q u i r e d especially  failure  agreement w i t h  f o r b o t h c o h e s i v e and c o h e s i o n l e s s shear modulus r e d u c t i o n f a c t o r s  f o r c o h e s i v e s o i l s and c o h e n s i o n l e s s f o r dense sand  soils,  i n w h i c h a s m a l l e r v a l u e may  n e c e s s a r y . I t i s a l s o shown i n t h e f o r e g o i n g a n a l y s i s the load shedding facilitate  iteration  may  be that  technique i s a powerful tool to  the program t o s i m u l a t e the s o i l  failure  o  —~]  CE w  l  C l o s e d Form  "  ~ ro 1-  I  —  _  Solution  H  h  FEM: b e f o r e volume  O  O  FEM: a f t e r volume  X  X  FEM: n o n l i n e a r  correction correction  solution  4.0  Volume  Correction  c o n d i t i o n s u s i n g the relat ion.  simple  hyperbolic  stress-strain  6. F I N I T E ELEMENT STUDIES OF PRESSUREMETER TESTS  6.1  INTRODUCTION In  the f i e l d  of s o i l  m e c h a n i c s , t h e r e h a s l o n g b e e n an  e m p h a s i s on l a b o r a t o r y t e s t i n g  fordefinition  of the design  p a r a m e t e r s f o r e a r t h s t r u c t u r e s . However, b e c a u s e o f t h e r e c o g n i t i o n o f b a s i c p r o b l e m s c r e a t e d by d i s t u r b a n c e s a n d stress-relief process,  i n the sampling  and sample p r e p a r a t i o n  w h i c h a r e more common i n t h e c a s e o f c o h e s i o n l e s s  sands, i n - s i t u  t e s t i n g p r o c e d u r e s have g a i n e d  increasing  a t t e n t i o n . One o f t h e common a n d a t t r a c t i v e d e v i c e s f o r in-situ the  t e s t i n g of s o i l s  results  from a pressuremeter  determine the i n - s i t u stress-strain The simple, finite  i s the pressuremeter.  lateral  In theory,  t e s t c a n be u s e d t o  s t r e s s i n t h e s o i l , and t h e  response and shear  strength of the s o i l .  basic idea of the pressuremeter  test  i t involves expanding a c y l i n d r i c a l ,  i s relatively flexible,  membrane a g a i n s t t h e s i d e s o f a h o l e w i t h i n t h e  infinite  soil  medium. H o w e v e r , f r o m p a s t  been r e c o g n i z e d  t h a t t h e t e s t c o u l d be c o m p l i c a t e d  s u c h a s t h e amount o f s o i l probe i n s e r t i o n p r i o r deformation  experiences,  by i s s u e s  d i s t u r b a n c e b e f o r e and d u r i n g t h e  to testing  , the kind of s o i l  p a t t e r n around the f i n i t e  under g i v e n p r e s s u r e m e t e r  i t has  L/D r a t i o ,  determine the basic engineering data.  101  pressuremeter  membrane  and t h e method t o  parameters from t h e t e s t  102 At  present,  the  pressuremeter  test  properties  the  of  data soil  expansion  theory,  under  conditions  and  the  Anderson,  Palmer,  established membrane test  length  infinite should  soil  be  The the  to  (1971)  was  of of  a  such  et a  and  al,  test  ratio  finite the  the  length  plane  can  with  (Gibson  Ladanyi,  as  effect  expanded  1963  and  be  sufficient  membrane  end  is  strain  only  a  (L/D)  cavity  cavity  1972,  theory  in  pressuremeter  (1946)  borehole,  he  the  pressuremeter  within of  the  in  test  based  conclusions  using  sands.  6.1  broad  an  equation  pressuremeter  on  shows  the membrane  of  results  probe  shown  in  Livneh  based  the by  work,  a  had  Using in  a effect  Schmertmann  confirmed on  Livneh's  cohesionless  L/D  Poisson's  6.1  patterns  little  from Hartman's  Fig.  al  finite  results and  on  the  pressure  and  analyses  et  on  displacement  length  L/D  pressuremeter  borehole.  Hartman  element  of  of  radial  Tranter's  range  ratio  the  analysis,  infinite  results.  the  from  material  for  that  finite  diameter  researchers.  theory,  elastic  concluded  also  many  elastic  ideal  to  parameters  by  membrane  Tranter's  Fig.  soil  mathematical  an  Hartman's  engineering  cylindrical  axisymmetry  a  the  cylindrical  and  examined  generated  a  the  interpreting  considered.  linear  using  a  Baguelin,  medium,  conducted  (1975),  which  expanding  conventional  on  involve  of  of  determine  diameter  influence  data  methods  pressuremeter  determination  test  to  However,  for  involves  in  1961,  1972).  common  ratio  suggested  that  analyses values. under  Fig.  6.1  Influence  (after  of  L/D  Laier  Ratio  et  al,  on  Displacement  1975)  Patten  1 04  normal over  testing  the  central  remained  computed greater  4,  over than  the 94%  infinitely  long  modulus,  E  or  response  of  cavity  that  is  the  consistent modulus  et  membrane limit  al  that  influence  Fig.  (1975)  resulted  the  radial  with  the  6.2,  that  for  from  based  on  minor  chamber Laier  et  the  Livneh  ratio  membrane  is  computed the  initial  error  for  an  deformation  infinite  test al  L/D  elastic  cylindrical  in  values.  results  (1975)  for  sands,  concluded  the  L/D  ratio  on  the  pressuremeter  influence  confirmed  the  The  displacement  finite  that  membrane  effects.  displacement  pressuremeter,  by  end  radial  the  only  deflection  pressuremeter  suggested  triaxial  under  length  Therefore,  theory  This  controlled were  does  pressures.  length  of  range,  had  no  afore-mentioned et  al  (1971),  Hartman  and  (1975).  However, Laier  by  evaluated  predictions  Schmertmann  1/3  significant  values.  the  showed  pressuremeter  in  elastic  elastic  This  be  Menard  or  theoretical  the  their  shown  for  center  G can  on  curves  probe.  the  of  average  of  expansion  Based which  the  the  unaltered  displacement  than  in  two-thirds  essentially  predicted greater  conditions  The in  Laier's  have  elasto-plastic  test  a  to  the  find  marked  increase  of  reduction  experimental  pressuremeter the  able  density  that  effect  the of  the  results  ratio  would  results  after  the  and  tested  sands,  pressuremeter on  the  measured  pressuremeter  L/D  range,  of  limit seem  pressure. to  indicate  significantly  soil  consequently  membrane  the  medium  is  in  the  axisymmetrical  105  Fig.  6.2  Influence  Values  (after  of  L/D  Laier  Ratio et a l ,  on E l a s t i c 1975)  Modulus  106  plane  strain  sufficient  cavity  L/D  to  characteristics In  expansion  determine  from  addition,  of  the  pressuremeter  the  development  of  P-Y  curves  piles,  loading  assumption, converted  to  (Atukorala plane the of  strain  More  P-Y  work  study  is In  L/D  L/D  and  data  with  the  Then  using  significance The  is  of  soil  two.  in  a  an  are  the  cylindrical  the  analyses test  are  disturbance,  be  simply  factors  axisymmetrical  influence  of  parametric  a  is is  Such  a  studies. element  broad  with  cavity to  curves.  viewpoint.  finite  for  development  expansion  range  the  of  finite  expansion  repredict  some  expansion  discussed  which  can  the  with  are  the  and  cavity  herein  in  data  compared  made  loading  assumption  the  strain  depth,  key  axisymmetrical  are  at  the  element  plane  attempts  the  the  this  scaling  pressure  performed  lateral  curves  theoretical  finite  that  Under  Therefore,  examine  for  similarity  certain  the  results  pressuremeter no  to  first  axisymmetrical  simulation. test  for  the  is  data.  assumed  expansion  pattern  on  test  pile  pressuremeter  ratio  chapter,  study  element  of  the  the  by  1984).  warranted  parametric ratio,  between  based  suitable this  and  curves  Byrne,  curves is  usually  therefore  displacement  pressuremeter  out  P-Y  interpretation the  is  pressuremeter  the  and  and  exists  the  it  expansion  strain,  pattern  strength  application  loaded  plane  with  the  laterally  in  used  in for  all  shear  be  pressuremeter  curves  pressuremeter  the  should  the  expansion  the  theory  in  assumed  field  model.  The  details. to  equivalent  be to  carried the  107  test  with  reality,  a  "ideal"  some  soil  pressuremeter have be  an  influence  on  the  exclusively  ELEMENT  finite  Shown  in to  be  the  is  m,  and  assumed  to  sufficiently  field.  The  bottom  end.  elements  pressure In  the  is  kept  which  of  the  varied, ratio  and  for For  zero while  the  stress for  assumed.  change  This  depth  where  soils  from  producing  in  D,  of  in  the  left  is  the  in  figure,  adjacent the  different  at  the  the  pressured  membrane  to  far  boundary of  the  is  comparing  soil  mesh  test  the  depth  diameter while  analyses  pressuremeter  shown  the  pressuremeter  will  length  values  length is  of  L/D  analyses. upper  the  the  effect  Therefore  sparse on  constant,  therefore  the  applied  an  consequently  9.  test  As  used  and  analyses,  is  half  are  m.  the  deep.  membrane,  the  0.1  and  axisymmetric  diameter, be  In  CONDITIONS  the of  device.  self-boring  Such  Chapter  diameter,  fine  pressuremeter is  to  relatively  pressuremeter  in  for  the  a  introduced  results.  depth  be  for  BOUNDARY  mesh  The  pressuremeter  considered  the  MESH AND  6.3.  5.0  test later  element  Fig.  pressuremeter with  even  inevitablly  FINITE  assumed  disturbances be  The is  pressuremeter  may  examined  6.2  self-boring  and  the being  boundaries,  conditions  bottom is  outer  high  and  employed  respectively,  no  vertical  displacement  for  overburden  displaced  stress  are  boundary,  reasonable  zero  the  pressuremeter  pressure  vertically.  of  The  test  is at  soils  prevents  bottom  boundary  109  is  selected  and  the  Except  outer for  condition As  is  the  the  far  radius,  plane  and  the  on  of  the  same  on  above  linear  fine to  The  inner  strain  stress  the  left  hand  which  is  mesh  is  a  boundary.  condition this  Fig. in  high  the as  case  bottom  strain  same  for  a  is  6.4. the  mesh  soil  is  used  outer  the  series  boundaries  pressure  finite  stress  sparse  has  axis.  change  in  the  whereas  in  central  employed  represent  membrane,  cylindrical  shown  boundary  and  finite  zero  simulation  boundary  the  the  of  outer  upper  the  the  However,  both  from  plane  probe,  condition.  incrementally the  The  case.  strain  In  for  the  Q  axisymmetrical  pressuremeter  field.  placed  an  pressuremeter  away  r  for  condition,  around  the  area,  sufficiently  axisymmetric are  5,  of  100  employed  used  expansion a  is  pressured  is  distribution in  boundary  also  mesh  to  midpoint  chapter  Similarly, next  the  the  in  element cavity  at  to  of  rollers  ensure  the  applied  boundary.  element  triangular  mesh type  the  elements  with  7  are  all  intergration  points.  6.3  ANALYSES A  AND  nonlinear,  relationship  of  cohesive  soils,  assumed.  The  undrained modulus  SOIL  PARAMETERS  stress  soils  dependent  is  adopted  undrained  analysis  condition  equivalent  is  is to  for  the  pressuremeter based  on  simulated a  hyperbolic  Poisson's  total by  a  analyses. test  of  For  condition  stresses,  large  ratio  stress-strain  value 0.499.  and of For  is the  bulk  Fig.  6.4  Finite  Element  Mesh  for Cavity  Expansion  Analysis  111.  cohesionless soils, sufficiently  slow  the pressuremeter  test  i s assumed  that the drained loading condition i s  prevailing. In soil  the axisymmetric  a n a l y s e s , the nonhomogeneity of t h e  parameters w i t h depth  stress  i s c o n s i d e r e d , and the i n - s i t u  i s assumed i s o t r o p i c  and i s p r o p o r t i o n a l l y v a r i e d  from zero a t t h e s u r f a c e t o c e r t a i n v a l u e s a t 5 m while i n the axisymmetrical plane homogeneous, i s o t r o p i c case,  the s o i l  correspond  Cohesive In soils,  soil  s t r a i n analyses the  medium i s a s s u m e d . I n t h e l a t t e r  parameters and t h e i n i t i a l  t o the depth  depth,  stress state  of 5 m i n the a x i s y m m e t r i c a l  case.  Soils the case  of axisymmetric  the Normally  analyses  Consolidated clay  parameters such as undrained  shear  f o r cohesive  i s a s s u m e d . The  strength, C  modulus, E a r e p r o p o r t i o n a l t o t h e e f f e c t i v e pressure  a t the depth  C  u  y  and  soil  initial  overburden  of i n t e r e s t , i . e .  = 0.25 a' v  (6.3.1) (6.3.2)  E = M^C U  where M i s t h e m o d u l u s m u l t i p l i e r .  I t usually varies in  r a n g e o f 2 0 0 - 1 2 0 0 , d e p e n d i n g on t h e m e t h o d s c h o s e n t o determine sampling  i t . Laboratory  t e s t s where some d i s t u r b a n c e s i n  and p r e p a r i n g samples a r e i n v o l v e d , u s u a l l y g i v e  smaller values while i n - s i t u  t e s t s and computer back  112 analyses  u s u a l l y show h i g h e r  1977). H e r e i n For deposit  the  values  (Clough  and  Denby,  a r e p r e s e n t a t i v e v a l u e o f M = 800 simplicity  in calculation,  i s divided into  parameters. In the  the  i s selected.  5 m N.C  4 l a y e r s i n the c a l c u l a t i o n  l a y e r s except  t h e b o t t o m one,  clay of  the  soil  soil  parameters are c a l c u l a t e d at r e p r e s e n t a t i v e depths which at  the midpoint  however, the  of t h e  soil  l a y e r s . For  the bottom  layer,  parameters are c a l c u l a t e d at the depth  5 m,'  i . e . a t t h e b o t t o m b o u n d a r y . The  this  l a y e r a r e a l s o employed f o r the a x i s y m m e t r i c a l  strain  behavior  behavior  soils,  both  are considered.  i s obtained  with very  in Table  small value  6.1  Cohesionless  soils, initial  and  The  and  elasto-plastic  nonlinear soil  using hyperbolic stress-strain o f Rf  ( s e e C h a p t e r 3 ) . The for cohesive  the nonhomogeneity of s o i l s t r e s s d e p e n d e n t , and  soil  s o i l s are  shown  initial  analyses  for cohesionless  parameters with depth i s  i t w o u l d be a u t o m a t i c a l l y s t r e s s s t a t e assumed f o r  i s v a r i e d w i t h depth.  isotropic  In the a n a l y s e s ,  s t r e s s s t a t e i s assumed t o  and  the  the  be  p r o p o r t i o n a l l y v a r i e d f r o m z e r o a t s u r f a c e t o 50 Kpa d e p t h o f 5 m,  relation  Soils  the case of a x i s y m m e t r i c a l  deposit  initial  plane  6.2.  accounted f o r i f the soil  parameters for  elasto-plastic  parameters used i n the a n a l y s e s  In  soil  of  analyses.  For cohesive soil  are  a dense sand of r e l a t i v e d e n s i t y D  at =  75%  1 13 T a b l e 6.1 Soil Soil Parameters 7 (KN/m ) C (Kpa) 3  u  <t> (°) 4>cv ( o ) L\<$> K  E  K  B  n m Rf K  0  a (Kpa) G.W.T (m) v  Parameters  f o r Axisymmetric  Cohesive Elastio-Plastic  Soils Nonlinear  Cohesionless Soil Nonlinear  16 1 .5 H  20  16 1 .5 H  •  11.84 H 1973.79 H 0.0 0.0 0.0 1 .0 6 H 0.0 Table  Soil  Analyses  Parameters  11.84 H 1973.79 H 0.0 0.0 0.9 1 .0 6 H 0.0  42° 33° 4° 1500 900 0.5 0.25 0.7 1 .0 10 H 0.0  6.2  f o r C a v i t y Expansion  Analyses  Soil Parameters  Cohesive Elastio-Plastic  Soils Nonlinear  Cohesionless Soil Nonlinear  7 (KN/m ) C (Kpa)  16 7.5  16 7.5  20  3  u  <j> (°)  <t>cv ( o ) L\<f> K  E  K  B  n m Rf K  0  a (Kpa) G.W.T (m) D e p t h (m) v  1. 2.  59.21 9868.95 0.0 0.0 0.0 1 .0 30 0.0 5  H - D e p t h o f i n t e r e s t (m) , G.W.T - G r o u n d w a t e r t a b l e .  59.21 9868.95 0.0 0.0 0.9 1 .0 30 0.0 5  42° 33° 4° 1 500 900 0.5 0.25 0.7 1 .0 50 0.0 5  11 4  is  simulated.  stress 6.2. and  strain  These Cheung For  soil  The  parameters  the  are  also  included  referred  axisymmetrical are  used.  assigned  soils,  isotropic  are  required  to  by  in  in  hyperbolic  Table  values  6.1  from  and Byrne  (1984) .  state  cohesive  parameters  relation  parameters  stress  soil  and  the  for  to  the  strain  The  difference  the  elements.  initial  homogeneous  correspondent  plane  stress  of  lies As  state  throughout  depth  analyses,  5 m in  in  is  the  in  the  the  the  same  initial  case  of  assumed  mesh  domain,  and  is  axisymmetrical  analyses.  6.4  INFLUENCES Based  with  on  strain  influence  of  pressuremeter consequently  i.e.  analysis the  the  the  L/D  = 1 , 4 ,  the  design  of  of  using  results  the  test  can  be  used  the  practical  the  soil  ratio  plane  common  parameters, on  the  pressuremeter  and assumption  of  L/D  analyses.  range  the  for  theoretically.  3 values  the  analyses  axisymmetrical  strain  validated  in  element  evaluated,  discussion,  12 w e r e cover  be  and  same L/D  can  RATIOS  finite  ratio  axisymmetrical  following  to  L/D  pressuremeter  test  For  believed  axisymmetrical  values  pressuremeter  are  PRESSUREMETER L/D  the  different  plane  the  OF  of  the  ratio,  These L/D  membrane.  values  ratio  in  1 15 6.4.1 COHESIVE SOILS 1) P r e s s u r e e x p a n s i o n  curves  For t h e sake of comparisons,  the pressure  expansion  c u r v e s from t h e a x i s y m m e t r i c a l p l a n e s t r a i n a n a l y s i s and t h e a x i s y m m e t r i c a n a l y s i s w i t h L/D r a t i o o f 1, 4, 12 a r e a l l shown i n F i g 6.5. The p r e s s u r e e x p a n s i o n c u r v e s a r e p l o t t e d in  terms of t h e a p p l i e d p r e s s u r e and the r e s u l t e d  displacement at the f i r s t  node.  For the i d e a l c o n d i t i o n , strain condition, It  result  especially  i.e.the axisymmetrical plane  the pressure expansion curve  i s shown i n t h e f i g u r e t h a t  ratios  in stiffer  1.  i s curve  i n g e n e r a l , s m a l l e r L/D  pressure expansion  curves,  i n t h e c a s e o f L/D = 1; t h e p r e d i c t e d  expansion curve  radial  pressure  i s much h i g h e r t h a n t h e o t h e r c u r v e s .  H o w e v e r , t h e c u r v e s w i t h L/D r a t i o o f 4 a n d 12 a r e p r a c t i c a l l y close to the ideal curve  (i.e.  Curve  7).  The a b o v e r e s u l t s a r e r e a s o n a b l e . When t h e p r e s s u r e m e t e r membrane i s s m a l l , t h e a p p l i e d p r e s s u r e basically  spread out as i n the case of s p h e r i c a l  expansion w i t h i n  soil  cavity  medium, t h e n h i g h e r p r e s s u r e s a r e  r e q u i r e d t o overcome t h e s u r r o u n d i n g s o i l three dimension,  will  so c a l l e d  'end e f f e c t s '  1978). I n t h i s c a s e , t h e p r e s s u r e m e t e r  resistance i n (Baguelin et a l ,  tests are closer to  the s p h e r i c a l c a v i t y expansion c o n d i t i o n  rather  than the  e x p e c t e d c y l i n d r i c a l c o n d i t i o n . As t h e p r e s s u r e m e t e r membrane l e n g t h i s i n c r e a s e d , t h e a d d i t i o n a l  test  a p p l i e d p r e s s u r e ) t o o v e r c o m e t h e 'end e f f e c t s '  energy (or  becomes a  -+  4-  FEM:CV.EXP.E-P  -o FEMrPNT FEM:PMT  X-  L/D=12  E~P  L/D=4  E-P  -a FEM:PMT L/D=1  E-P Pi = 6.6 C  u  Elastic  0.0  1  1.0  I  I  2.0  RADIAL  I  I  3.0  I  r~ 4.0  DISPLACEMENT Fig.  ~i  1  5.0 (MM)  r  D=0  6.0 1CM  6.5 T h e i n f l u e n c e o f L/D r a t i o Curves i nCohesive  Soils  7.0 TEST  AT  on P r e s s u r e  Plastic  8.0 5M  DEPTH  Expansion  Soils  9.0  10  11 7  progressively pressures  smaller  spread  out  fraction under  of  the  the  total,  and  axisymmetrical  more  plane  strain  conditions. Therefore, cylindrical is  is  predicted or  and  result  in  than the  Therefore,  as  cohesive  development  would  the  the  validity  theory  for  of  ratio.  L/D  However,  based  curves  on  be  approximate  increase  of  L/D  improvement  the  common  L/D  ratio  far  as  P  -  close  the  that  the  the  equal  to  theoretical  4 to  12 w i l l  only  pressuremeters  as  commonly  the  the the  ratio  usually  experimental  under  has  accuracy.  4,  such  tests  the  study,  the  expansion  concerned,  and  to  from  than  pressure  Y curve,  to  in  which  L/D  self-boring  greater  the is  large,  ratio  the  Ideally,  this  with  4 would  of  pressuremeter  pressuremeter  expansion  soils  of  sufficiently curve  for  a marginal  with  that  values  ratio.  practice,  designed  soft  the  pressure  curve,  clear  expansion  valid  L/D  greater  In  upon  only  infinitive  is  cavity  dependent  theory  it  around  curves  for used  are 8.  for  the  the L/D  pressure  ratio  are  expansion  t h e o r e t i c a l plane  strain  condition.  2) I n i t i a l Under the  the  initial  equal of  slopes of the pressuremeter  to  the  used  to  2G^  ideal  slopes (see  of  the  Chapter  experimental determine  cylindrical  pressure  the  cavity  pressure 5).  initial  curves expansion  expansion  Therefore, expansion elastic  the  condition,  curves  are  initial  slopes  curves  are  usually  modulus  for  the  tested  118  soil  medium.  modulus  is  Another  to  utilise  elasto-plastic The curves initial first  load  level  of  soil  finite or  the  this to  strain  level,  is  in in  elastic  with  be  For  As  3) L i m i t  6.3,  value  of  shear  derived The  the  error  the  L/D  ratio  greatly  in  Table length  with  pressures  the  L/D  of  the  in  a  entire  slopes  with  great  are  less  results  ratio  show  L/D  pressuremeter  the  accuracy,  marginally than  affected the  L/D  4, by  reduced however,  the  initial  ratio  ratio  =  = 4.  value slopes  1 is  where  that  on  data  as  4  in to  from  from the  6.2% derived  L/D  obtained  about  to  the  from  of  the  equal  test  ratio  to  7%,  ratio  influences  equal  close  than  improve  L/D  The  end  the  L/D  less  of  the  the  6.3,  expansion  6.3.  of  only  is  membrane that  is  The  the  increase to  same.  generally  the  errors  length  have  from  for  initial  modulus.  not  at  From  range.  2G^ w i t h  membrane  4 does  calculated  except  predicted  justified  shown  than  a  elastic  Table  stage.  modulus  the  larger  the  other  than  study,  ratio.  such  the  Table  small  In  modulus  1.5%.  in  is  initial  not  tabulated  elastic  loop.  pressure  strain  elastic  12 may  predicted  the  pressuremeter  elastic  are  are  where  the  greater  the  methods  increment,  shown  the  two  initial  unload-reload  is  theoretical is  of  the  curve  0.08%.  unity,  the  of  of  6.5  determine  slope  these  slopes Fig.  to  each  medium As  to  in  slope  the  theory,  initial  shown  method  30%  119 Table  6.3  I n f l u e n c e s o f L/D R a t i o on I n i t i a l S l o p e s o f Pressuremeter Curves i n Cohesive S o i l s  L/D  ratio  Slopes 1 .289(2Gi) 1 .062(2Gi) 1 .0!5(2Gi)  4 12 - Initial  Shear Modulus  E x t r a p o l a t i n g the p r e d i c t e d pressure expansion  curves  shown i n F i g . 6.5, i t i s shown t h a t , u n l i k e t h e i n i t i a l s l o p e s where s o i l s a r e i n t h e e l a s t i c has g r e a t e r e f f e c t s S m a l l e r L/D r a t i o  on t h e p r e d i c t e d  results  s t a g e , t h e L/D  ratio  l i m i t pressures.  i n higher predicted  limit  pressure. As shown i n F i g . 6.5, f o r L/D r a t i o  e q u a l t o 1, t h e  limit  p r e s s u r e i s p r e d i c t e d much h i g h e r t h a n t h e o t h e r s ,  while  f o r t h e L/D r a t i o s  predicted  e q u a l t o o r g r e a t e r t h a n 4, t h e  l i m i t p r e s s u r e s a r e c l o s e , a n d seem t o a p p r o a c h  the t h e o r e t i c a l  l i m i t pressure, P  L  = 6.6 C^ w h i c h i s  o b t a i n e d from Eq. (5.2.12). The e f f e c t s and  their  o f L/D r a t i o  l i m i t pressures w i l l  on t h e p r e s s u r e m e t e r i n turn affect  shear s t r e n g t h , shear s t r e s s - s t r a i n strain  plastic  the undrained  c u r v e , and t h e f a i l u r e  o b t a i n e d from t h e p r e s s u r e m e t e r  i n d i c a t e t h a t t h e L/D r a t i o  curves  test.  These t e n d t o  becomes i m p o r t a n t when t h e  deformation occurs i n the s o i l  medium.  1 20 4)  Undrained  shear s t r e n g t h  Using the pressuremeter  test data i n cohesive  the u n d r a i n e d shear s t r e n g t h and t h e shear  soils,  stress-strain  c u r v e s c a n be e v a l u a t e d t h r o u g h d i f f e r e n t a v a i l a b l e ( G i b s o n and Anderson, 1972,  Palmer,  1978). soil  1 9 6 1 , L a d a n y i , 1963, B a g u e l i n e t a l ,  1972, P r e v o s t a n d H o e g ,  1975, a n d Denby,  I n G i b s o n and A n d e r s o n method, t h e e l a s t o - p l a s t i c  b e h a v i o r i s assumed f o r t h e a n a l y s e s , w h i l e i n t h e  o t h e r m e t h o d s , no p r e a s s u m p t i o n  on s o i l  r e q u i r e d , but v a r i o u s curve f i t t i n g for  methods  behavior i s  t e c h n i q u e s a r e employed  the analyses. At p r e s e n t , t h e a c c u r a c y  i n d e r i v i n g undrained  s t r e n g t h from t h e p r e s s u r e m e t e r  tests  shear  i s s t i l l questionable,  and  i t d e p e n d s on s e v e r a l  1.  the i n t e r p r e t a t i o n  2.  t h e r a t i o o f membrane l e n g t h t o d i a m e t e r , a s a l l t h e methods a r e based  f a c t o r s . Among them t h e r e  include:  method,  on p l a n e s t r a i n  conditions.  The i n f l u e n c e o f t h e v a r i o u s i n t e r p r e t a t i o n m e t h o d s on t h e o b t a i n e d u n d r a i n e d s h e a r s t r e n g t h h a v e been e x a m i n e d by Denby  ( 1 9 7 8 ) . I t was f o u n d t h a t t h e d i f f e r e n c e  i s usually  within  10%. T h u s , t h e m e t h o d i t s e l f  may n o t be a l a r g e  factor  i n the d e t e r m i n a t i o n . In t h e f o l l o w i n g analyses of  t h e i n f l u e n c e o f L/D r a t i o on t h e u n d r a i n e d s h e a r t h e method p r o p o s e d  by G i b s o n a n d A n d e r s o n ( 1 9 6 1 ) i s  employed, as i n present s t u d i e s t h e e l a s t o - p l a s t i c soil  i s assumed.  strength,  cohesive  121  In (1961) test  the for  in  a  that,  Gibson  interpretation  of  an  it  shear  is  resulted  in  natural  the  pressuremeter  L/D  =  above The  P,  is  6.5  predicted 4,  as  volumetric  failures.  is  line  1 -  =  2  the  except  Except  for  be  Fig. the  and to  result the  logarithm  is  the  probe,  AV  is  to  an  clay,  the  cavity.  a  a  V  equal  current the  Moreover, of  C .  of  the  if  line  (or  This  u  6.6(a). pressure  finite  strain,  expansion  curves  element  analysis  in  6.6(b),  Fig.  pressure,  (1+e^)"  the  gradient  calculated  circumferential  =  the  0.5  to  as  characterized  leads  where  the  replotted  applied  strain  expected,  straight  the  been  the  AV/V  As  in  from  of  will  of  method  pressuremeter  behaves  in  related  AV/V,  used  interests,  12 h a v e  manner  predicted  are  illustrated  present  ratio  pressuremeter  curves)  For  1,  strain  Anderson  material  initiated  volume  logarithms  clay  analysis  linearly  or  the  The  been  is  the  Poisson's  and  undrained  plastic  C^.  has  cavity  the  Fig.  a  strength  change  procedure  G,  volumetric  the  that  perfectly  pressure,  of  assumed  failure  resulted  volume  of  modulus,  after  applied  analysis  elastic,  shear  undrained  the  the  clay,  perfectly by  original  P,  against  according  e^,  by  the  in  with in  the  ln(AV/V).  to  the  relationship  :  2  (6.4.1)  e  Q  points  lie  for  those  the  line  remarkably  prior with  to  L/D  the ratio  close  to  a  initiation of  1,  the  of other  kN/m* 2000  1900  1800  1700  1600  1500  /  'D -i  7  Fig.  6.6  (a)  Gibson of  1  8  1—I—u_i  9 10 11 12  and A n d e r s o n  U n d r a i n e d Shear  I l I • • • •  H  16  18 20 A V . ,  Procedure Strength  for  (after  Determination Wroth,  1982)  in  CD .  (0  a 0) u 3  M cn <u  CD .  o + o x •  <D Closed Form Solution + Cav.Exp.Solution(FErl) o L/D = 1 (FEU) x L/D = 4 (FEM) • L/D =12 (FEM)  <!>  <I>  co  a a <  xa  xm+  XCHXG4XDf O >0O  O  X3f XLD-1-  O  O  o  o  O  o  xa+o XD-KD  u cu x>  <!>  . <!> O  o  •  >• 83  o  (M  O  o  CD  o  CD .  0  e< "  10-'  I  7  i  i  10°  Volumetric Strain Fig.  ' I ' M  I  6.6  10'  7  AV/V  (%) i n l o g  (b) P r e s s u r e Expansion  i n Semi-log S c a l e ( E l a s t i c  _ 1 0  scale  Curves Plastic  Clays)  1  I 7  1  1  IO  2  124  lines  with  L/D  ratio  expansion  condition.  which  the  are  summarized For determine the  the  cavity  according  for  in  the  As  to  Eq.  in  shown  shear  closed  (5.2.11), The  in  form  and  closed  second  which  is  element  analyses  L/D  fraction  of  one  estimated derived shown  C  in  with  value  the of  should  ratio the  as  for  Table  is  lines,  are  procedure  also In  first  to  applied this  to  case,  the  calculated  transformed  to  the  shear  solution  are  Kpa.  is  form  strength  also  50%,  noted  table,  higher  The  ratio  by  u  be  of  1,  4,  26% a n d  that  the  to  the  method  from  the  the  error  expansion  derived  C  the  higher  may  method  involved  from  finite  respectively.  itself  closed  the  from  errors  due  the  12 a r e  20%  evalution  all  than  results  the  cavity  6.4,  L/D  the  as  errors  the  C  7.5  of  well  approximately y  above  is  column  input  the  strengths,  the  form  initial  from  those  6.4. the  it  for  then  strengths  However,  gradients  curve  shear  input  cavity  solution.  undrained  the  the  strength  derived  than  to  repredicted undrained  expansion  Table  close  shear  comparisons,  expansion  6.6.  cavity  selected  undrained  undrained  Fig.  included  of  cavity  12 a r e  6.4.  expansion  theoretical  Shown  Table sake  4 or  The  derived  in  the  =  form  may in  come  used. be the  solution.  closed  The  As  form  u solution  is  about  7.7%  higher,  the  error  involved  in  the  the  range  reported  by  Denby  which  method  may  itself.  (1978).  roughly This  indicate  error  lies  in  125 Table  6.4  I n f l u e n c e o f L/D R a t i o on D e t e r m i n e d U n d r a i n e d Shear S t r e n g t h  L/D  ratio  D e r i v e d Cu (Kpa)  Error (1)(%)  Error (2)(%)  8.078 8.333 11.249 9.476 8.972  7.7 1 1 50 26 20  3 39 17 1 1  C l o s e d Form Cav.Exp.(FE) 4 12  Error (3)(%)  35 14 8  1. The i n p u t u n d r a i n e d s h e a r s t r e n g t h C = 7.5 Kpa 2. C l o s e d f o r m s o l u t i o n i s o b t a i n e d t h r o u g h E q . ( 5 . 2 . 1 0 ) & Eq. (5.2.11) f o r c y l i n d r i c a l c a v i t y e x p a n s i o n 3. C a v . E x p . ( F E ) i s t h e f i n i t e e l e m e n t s o l u t i o n o f t h e c y l i n d r i c a l c a v i t y expansion 4. D r i v e d C i s o b t a i n e d using Gibson and Anderson method 5. E r r o r ( 1 ) i s t h e c o m p a r i s o n o f d e r i v e d C w i t h C = 7.5 Kpa 6. E r r o r ( 2 ) i s t h e c o m p a r i s o n o f d e r i v e d C w i t h C = 8.078 Kpa 7. E r r o r ( 3 ) i s t h e c o m p a r i s o n o f d e r i v e d C w i t h C = 8.333 Kpa u  u  In order  u  u  u  u  u  u  t o e l i m i n a t e t h e method e r r o r m e n t i o n e d  the d e r i v e d undrained  shear s t r e n g t h s a r e compared w i t h  from t h e c l o s e d form s o l u t i o n , and t h e f i n i t e  It  are s t i l l  higher  o f L/D r a t i o  gives higher  o f L/D r a t i o .  Smaller  derived undrained  s t r e n g t h . As compared w i t h t h e d e t e r m i n a t i o n m o d u l u s , t h e L/D r a t i o  shear  t h a n t h e i n p u t v a l u e . The e r r o r  p e r c e n t a g e d e p e n d s upon t h e v a l u e value  two  6.4.  i s shown t h a t a l l t h e d e r i v e d u n d r a i n e d  strengths  that  element c a v i t y  e x p a n s i o n s o l u t i o n . The r e s u l t s a r e shown i n t h e l a s t columns of Table  above,  shear  of e l a s t i c  g e n e r a l l y has a g r e a t e r  i n f l u e n c e on  126  the  undrained  shear  pressuremeters undrained theory  membrane  where  shear  may  be  Borsetto  et  analysis,  al  the  by  et  al  of  et  also  that  is  al  are the  of  the  (1980)  L/D  2 led  undrained  carried  present L/D  ratio  the  behavior soils the  are  soil  was  nonlinear,  different  L/D  nonlinear  soil in  the  cavity to  of  derived expansion  the  finite  the  researchers.  finite  in of  ratio a  test  silty  L/D  Table the  element 6.5.  It  is  influence  foregoing  the  was  also  program  clay.  reported  results  in  the  =  field  in  the  by  Porto  conducted  Therefore  predict  test  the  35% h i g h e r  4 probe. did  investigated  Tests  strengths  analyses  discussions, However, stress  response  ratio, model.  Table  many  with  than the  influence  of  data.  behavior  assumed.  soil  to  shear  an  from  previous  nonlinear  included  with  element  observed  5) N o n l i n e a r In  out  finite  6,  10% d u e  by  order  in  consolidated  to  about  shown  L/D  normally  those  cylindrical  designs  6.4.  Tolle =  about  performed a  similar  Table  influence  Jamiolkowski  present  is  reported  results  note  The  ratio  using  were  (1983)  to  column  the  effects.  interesting  third  L/D  strength  results  and  Borsetto  the  For  o v e r p r e d i c t e d by  length  Similar  strength.  6.1  in  the  reality,  dependent. of  similar  the  In  most order  pressuremeter  analyses  The  nonlinear  and  6.2  for  elasto-plastic  were  soil  the  soil  cohesive to  evaluate  tests  performed  parameters  axisymmetrical  under with  are  also  1 27  Table 6 . 5  Influence of Length to Diameter Ratio on Derived Undrained Shear Strength ( a f t e r Borsetto et a l . , 1983)  LENGTH TO DIAMETER RATIO  UNDRAINED SHEAR STRENGTH OVERPREDICTION (%)  2  36  4  26  6  22  128 a n a l y s e s and  the a x i s y m m e t r i c a l plane s t r a i n  analyses  respect i v e l y . The  nonlinear analysis results  As c o m p a r e d w i t h t h e r e s u l t s shown i n F i g . 6.5,  a r e shown i n F i g .  for elasto-plastic  soil  similar  elasto-plastic  behavior. Therefore, the previous  soil  t o those o b t a i n e d from  c o n c l u s i o n s drawn f r o m t h e e l a s t o - p l a s t i c  In  model  I t i s shown t h a t t h e n o n l i n e a r s o i l  g i v e s the responses  be v a l i d  6.7.  f o r the n o n l i n e a r s o i l summary, b a s e d  model  the  a n a l y s e s seem t o  b e h a v i o r as  well.  on t h e f o r e g o i n g a n a l y s e s , t h e  i n f l u e n c e of the pressuremeter  L/D  ratio  on  the  d e t e r m i n a t i o n of shear s t r e n g t h c h a r a c t e r i s t i c s  i s more  pronounced than  modulus.  far  i n the d e t e r m i n a t i o n of e l a s t i c  as t h e p r e s s u r e m e t e r  modulus a r e c o n c e r n e d , sufficient  e x p a n s i o n c u r v e s and  t h e L/D  ratio  elastic  e q u a l t o 4 would  to p r o v i d e the pressuremeter  practically  the  test  c l o s e t o the c y l i n d r i c a l c a v i t y  As  data that  be are  expansion  c o n d i t i o n s a t d e p t h . However, t h e u n d r a i n e d s h e a r s t r e n g t h prediction will  be a b o u t  the c y l i n d r i c a l c a v i t y  6.4.2  15% h i g h e r t h a n t h a t o b t a i n e d  expansion  solution.  COHESIONLESS SOILS 1) P r e s s u r e e x p a n s i o n  curves  For the c o h e s i o n l e s s s o i l s , the axisymmetry  plane s t r a i n  a n a l y s e s w i t h L/D Fig.  from  6.8.  The  ratio  of  the p r e d i c t e d curves  a n a l y s i s and  1, 4,  the  from  axisymmetric  12 a r e a l l shown i n  a n a l y s e s f o r the c o h e s i o n l e s s s o i l  were  x-  FEM -+ FEM -x FEM -Q FEM  CAV.EX PAN SI ON 3DPMT L/D=1 3DPMT L/D=4 3DPMT L/D=12  4.0  6.0  C I R C U M .  Fig.  6.7  S T R A I N  Nonlinear  8.0  (X)  Soil  i 10.0  1  12.0  =7.5KPA N - L  Response  r  T  T  .14.0 C L A Y  under D i f f e r e n t  16.0  D=0.IM  L/D R a t i o  18.0  20  o-  •« +  i^il/  •+ FEM -  3DPMT  L / D - 1  3DPMT  L / D = 4  3DPMT  L/D=12  FEM  CYLIN.CAV.EXP.  Nonlinear  .8 CIRCUM 1  Fig.  2.4 STRAIN  3.0 [%) N- L  3.6 4.2 SAND ( D = 75.v) r  6.8 I n f l u e n c e o f L/D R a t i o o n P r e s s u r e Curves i n Cohesionless  4.8  Soils  Expansion  Soils  5.4  131  performed  using  expansion  curves  pressure of  and  probe.  boundary In for is  was  is  Unlike  for  of  0  it  at  0  node  of  to  those  with  L/D  curve  is  resistances.  With  cohesive  from  the  seems for  the  to the  to of  for  soils,  ratio  accumulate L/D  with  L/D  the  ratio  predicted  4 to  plane  12,  strain  with  the  increase  12,  the  best  =  the  cavity  about  3.0%.  ratio  is  soft  softer,  expansion  the  from  axisymmetrical  strain the  L/D  higher  progressively  for for  = 1  almost  case  was  wall  obtained ratio  cylindrical cavity  up  the  bottom  the  influence than  applied  from  curves  only  The  become  predicted curve  the  the  similar  soil  of  At  much  cohesive  expansion large more  soils.  slopes of the curves  initial  tabulated  strain  the  pressure  (AU /r )  first  curves.  Even  the  The  are  level.  significant  end  other  curve  observed  2) I n i t i a l  the  predicted curves  the  of  The p r e d i c t e d c u r v e  The d e v i a t i o n  strains,  the  results  significantly  agreement  curves  soils.  expansion  strain  terms  The  calculation.  much h i g h e r  pressure  one  the  the  showing  condition.  deviate  for  at  than  approaching  of  used  the  in  model.  circumferential strain  stiffer  ratio,  curve.  the  soil  plotted  The d i s p l a c e m e n t  cohesive much  nonlinear are  general,  linear, L/D  a  slopes  different in  Table  the  level  less  L/D  6.6.  first  of  predicted pressure  ratios The  load  than  the  shown  initial  In  Fig.  slope  increment,  0.05%.  in  this  which  is is  strain  6.8  expansion are  calculated  at  generally  in  level,  the  a  1 32 Table L/D  6.6  R a t i o E f f e c t s on I n i t i a l S l o p e s in Cohesionless S o i l s  L/D  ratio  1 4 12 Cav.Exp.(FE)  Initial Slopes 1.075(2Gi) 0.844(2Gi) 0.843(2Gj) 0.844  1. G i - I n i t i a l s h e a r m o d u l u s o f t h e s o i l , 2. C a v . E x p . ( F E ) - The f i n i t e e l e m e n t s o l u t i o n c y l i n d r i c a l c a v i t y expansion c o n d i t i o n entire soil As except  medium i s i n t h e e l a s t i c  ratio  elastic,  initial  elastic  Although the i n i t i a l model a r e g e n e r a l l y t h e i n f l u e n c e o f L/D  c a n be  ratio  to the n o n l i n e a r  L/D seen  larger  expansion  portion.  l e s s than the l i n e a r e l a s t i c  solution,  r a t i o c a n be e x a m i n e d by c o m p a r i n g  ratios. f r o m T a b l e 6.6  t h a t the s l o p e s of  than 4 a r e v e r y c l o s e t o t h a t of s l o p e o f t h e L/D  r a t i o equal to or l a r g e r  than 4 has  the  cavity ratio  27% h i g h e r t h a n t h e e x p e c t e d . T h i s seems t o  t h a t t h e L/D  the  expansion case w i t h the o t h e r s  e x p a n s i o n c a s e , but the i n i t i a l about  the  s l o p e s from the n o n l i n e a r e l a s t i c  s l o p e from the c a v i t y  from d i f f e r e n t  is  l e s s than  t h e r e f o r e the p r e d i c t d pressure  c u r v e s l a c k an  It  T h i s i s due  slopes,  s t r e s s d e p e n d e n t m o d e l o f s o i l s assumed i n t h e  a n a l y s i s , and  initial  initial  = 1, a r e g e n e r a l l y  t h e o r e t i c a l v a l u e o f 2G^.  L/D  range.  shown i n t h e t a b l e , t h e p r e d i c t e d f o r t h e L/D  of  no  = 1  suggest  1 33 significant  i n f l u e n c e on t h e i n i t i a l  pressuremeter  elastic  p o r t i o n of t h e  c u r v e , and c o n s e q u e n t l y , t h e i n i t i a l  modulus determined  will  elastic  be l e s s a f f e c t e d . T h i s seems t o  c o n f i r m the previous a n a l y t i c a l  and e x p e r i m e n t a l  results  o b t a i n e d by L i v n e h e t a l ( 1 9 7 1 ) , H a r t m a n a n d Schmertmann ( 1 9 7 5 ) , and L a i e r e t a l (1975) f o r t h e Menard  pressuremeter.  3) L i m i t p r e s s u r e s As  shown i n F i g . 6.5, f o r a l l t h e L/D r a t i o  h e r e i n , the d e v i a t i o n of the p r e d i c t e d pressure  studied expansion  c u r v e s from t h e c y l i n d r i c a l c a v i t y e x p a n s i o n c u r v e significant  i n the l a r g e r  strain  becomes  level. Extrapolating  these  c u r v e s , t h e p r e d i c t e d l i m i t p r e s s u r e s seem n o t t o a p p r o a c h the c y l i n d r i c a l c a v i t y ratio  e x p a n s i o n c a s e , e v e n f o r t h e L/D  = 12. The r e a s o n  for this  i s the fact that a  presuremeter  w i t h f i n i t e membrane l e n g t h was b e i n g e x p a n d e d . As t h e s o i l medium g e t s i n t o t h e p l a s t i c plastic  soil  forms around  s u c h an e l a s t i c  plastic  applied pressures later soil  f a i l u r e s , a zone o f s o f t  the pressuremeter  composite  system,  membrane. I n  most o f t h e  a r e t a k e n by t h e s t i f f e r  region surrounding the p l a s t i c  s o f t zone.  elastic  In the three  dimensional a x i s y m m e t r i c a l c o n d i t i o n , the s t i f f e r  elastic  soil  in this  region out of the l o a d i n g plane p a r t i c i p a t e s  a c t i o n , as a r e s u l t , of  plane s o i l  than  more s o i l  r e s i s t a n c e comes f r o m t h e o u t  r e g i o n , l e a d i n g t o much h i g h e r l i m i t p r e s s u r e  i n the plane s t r a i n  c a s e . I n o t h e r words, t h e above  1 34  higher  predictions  membrane  length  dimensional The  (Laier  were  et  results, to  give  limit  value.  pressuremeter  the  optimal  L/D  cohesionless  4)  found  the  from  limit  soil the  in  many et  al,  L/D for  regarding  1980).  shear  strengths by  pressuremeter  test  method  such  In drained sand  to  the  data  et  Hughes et  al  The  has  L/D  the  Jewell  6.2  the  was  than  the  that  was  correct  et  =4  theoretical  =  limit  results  ratio  the  al found  measured  value  used.  when  Therefore,  tests  limit  on  pressure  is  of  been  angle  frictional al  test  are  <j>. U s i n g  the  soils,  angle  usually  it  based  is on  the  (1977). for in  the  sand,  before  in  to  interpretation it  is  failure,  stresses  leads  initiated  soils  cohesionless  effective  analysis  characteristics  cohesionless  method  elastically  ratio  dilation.  in  as  pressuremeter  constant  In  pressuremeter  frictional  the  behaves  failure  the  of  determine  Hughes  on  conclusive.  characterized  possible  three  18% h i g h e r  Determination of shear s t r e n g t h The  finite  redistribution.  reported  ratio the  of  ratio  with  they to  the  experimental  pressure  close  ratio  stress L/D  test  However,  for  mechanism  of  Jewell  with  soils  pressures  plastic  became  the  far  to  pressuremeter  pressure  still  due  1975,  measured  theoretical  limit  influence also  al, the  a  are  elastic  large  pressure  of  the  the  and  assumed and a  result  sand,  the  of that  fails  constant that,  a  at  the a  rate  of  after  logarithm  of  the  1  effective of  the  slope  radial  strain of  the  the of  angle Rowe  the of  of In  Hughes  (1  i  For  n  *  al  to  of  effective  in  expression:  frictional the  stress  frictional  obtained  angle  angle,  and  dilatancy <t> a n d  the  a  value  and  for  expansion  angles 6.7.  of  of  of  in  in the  the  c  <j> a n d of  4  -  3  frictional  v  with  must the  the  33° is  be  values  granular assumed.  (1984),  practical  curves  <j> ^ i s  general,  Cheung  most  -  volume.  value  composition  Byrne  Table  In  6  )  . (6.4.4)  constant  assumed.  is  theory  (  c  a  v  via:  sin<£ ^),  (1977),  ,  l b . 4 . 2 ;  Employing  at  The  .  determine angles  frictional  summarized  6.9(a).  R  studies,  pressure  following  logarithm  sinv)  +  be  upon m i n e r a l  representative  Fig.  the  [2KS-(K-1 ) ] = -—^ +^ )  or  be  in  to  [(K-l)S+2]  method  referred to  related  + sin0  material  order  present  derived  "  the  (1  the  v can  is  the  1  by  c  experimentally depends  given  + sin0 ^,)/(1 -  the  et  is  1971),  Sinv  angle  illustrated  dilation.  S  K =  is  angle  angle  where  which  = sin0  (1961,  dilation  linearly  line  B  <t> i s  is  e^,  s  where  stress  35  and  sands.  log-log  is The  scale  foregoing  obtained of  material. This  value  believed slopes and  manner  the are  to of  p  kN/m'  SOO  ISO  too  350  300  250  Fig.  6.9  (a)  -i S  1 6  i 7  1 8  ».  Pressure Expansion in Cohesionless ( a f t e r Wroth,  t  V.  Curves  Soils 1982)  co CTi  1 37  Table L/D  L/D  Ratio Effects Pressuremter  Ratio  Slopes  on t h e Curves  (S)  Derived F r i c t i o n Angle in Cohesionless Soils  0.7086 0.5786 0.5492 0.5339  1. 2. 3. 4.  0  57.4° 50.0° 46.7° 45.7°  40 22 14 11  Error (2) %  % % % %  26 % 10 % 2 %  C a v . E x p . - the f i n i t e element s o l u t i o n of c y l i n d r i c a l 'cavity expansion c o n d i t i o n ; the input m a t e r i a l f r i c t i o n angle 0 = 4 1 ° ; E r r o r (1) - t h e c o m p a r i s o n o f p r e d i c t e d 0 w i t h 0 = 4 1 ° which i s the input v a l u e ; E r r o r (2) - t h e c o m p a r i s o n o f p r e d i c t e d 0 w i t h 0 = 4 5 . 7 ° which i s o b t a i n e d from c y l i n d r i c a l c a v i t y expansion solution.  As curves  shown from  Therefore, the  is  the  are  input from  slopes  are  that  practically  expansion, value the  stress  shapes  of  tests these  angle  illustrated the  slopes  that  especially  in  small  0 =  Fig.  of  in  studies, dependent  element  analyses.  effects  of  the it  curves  soil  be  granular  material  in  of  was  the was  expansion  the  L/D  log-log  affected 6.9(b)  with  values  noted  behavior  Moreover,  upon  L/D  by  the  ratio  of  0 are  that  L/D et  12  The  with  the  ratios. al  in  shear-volume ignored.  4 or  predicted  method  nonlinear  employed  6.7.  cavity  compared  Hughes  =  and L/D  Table  As  smaller  ratio.  scale  and  cylindrical  with  application should  pressure  strains.  4 1 ° , much h i g h e r  pressuremeter  also  lines  to  the  curves  in  of  of  depend  are  close  However, current  the  frictional  These seen  before,  pressuremeter  derived  ratio. It  from  Error (1) %  Predicted  0 4 12 Cav.Exp.  6.7  the  to  elastic, finite  coupling shear-volume  Applied Pressure  1U  3 I  1  1  I  5 I  (Kpa)  in  log  7 IO  _ 1 0  scale  3 I  2  »  I  II  I  I  I  5 I  7 I  I  X  O  +  G  X  O  +  G  o  +  OJ  <  II  —»• IV) „ ^  m  +  II  —•  m  X TJ  CO  o  lutio FEM) (FEM)  +  II  m  + + +  10  3  I  I  1 39  coupling strain  effects  level  than  4%  and  high  initial  however,  encountered the  test  stress  Nevertheless, may  not  be  results.  The  reflected shown  the  not  the  state  using  fourth  analyses  current  the  this  column  of  frictional  angle  of  <f> = 4 1 ° w o u l d  possible and  to  error  predicted compared  with  The  Table  6.7.  that  results After  pressuremeter  and  2%  other  are  respectively based the  ratio  to  equal  the  cavity  L/D  the due  on  material  generally  less  relatively  the  the it  ratio  the  the  greater  L/D  is  of  1,  frictional  angle  by  the  ratios  are  that  strain)  of the  would 26%,  effects.  plane  membrane  10% In  strain  length  produce  good  with  an  error  found  in  the  of  L/D  results  less  than  10%. Similar chamber  evidences  calibaration  were  test.  also Jewell  et  al  (1980)  the  only,  <t> a b o u t  length  about  itself  plane  12  is  theoretical  column  4,  it  eliminate  L/D  shown  angle  4 may  which  ratio  (i.e.  axisymmetrical  than  partly  procedure  last  finite  with  in  to  different  in  be  the  order  evaluation  frictional to  may  method  element  overpredicted  In  of  finite  6.7,  expansion  pressuremeter or  be  correction,  with  the  analytical  procedure,  <t> f o r  included  this  Table  case.  the  angles  overpredict  words,  in  al  influence  for  tests  assumption,  for  the  frictional  case.  probably  expansion  involved  illustrate  et  al  procedure  Hughes  cavity  since  where  to  on  the  depth  et  based  for  at  was  Hughes  that  11%  significant  existed.  theory,  in  be  simulated  applicable  error  in  in  was  in  exactly  may  triaxial conducted  1 40  'cast  insitu'  ratios ratio of the by  in  the  and  L/D  derived  6.4.3  triaxial  insitu  ratio  about  self-boring  6.2  frictional  shown  different  under  the  same  It  was  4 resulted  angle  earlier,  length  is  an  the  i n t e r p r e t a t i o n of  the  axisymmetrical  foregoing effects  on  the  For  from  found  in  an  44.5°  L/D  initial  that  void  reduction  overprediction  to  50.6°  of  (increasing  curve,  pressuremeter  L/D  and  undrained higher  curve the  expansion  pressuremeter to  be  ratio for  considered  test  assumption. seems  to  cohesive  shear that  effects  is is  results Based  have  soils  close  in  using  on  the  different and  to  the by  predicted from  cohesive  shape  of  the  than  4,  that  for  soils,  When  the  the  general  plane is  derived  undrained  for  L/D L/D  also  ratio. =  close  be  cavity  to  shear  The  4 will  cylindrical  shape  strain^  modulus  the  the  pressuremeter  determination.  elastic  affected  soft  the  greater  However,  obtained  in  on  modulus  strength  solutions.  tests  derived  much more  than  factor  strain L/D  ratio  theoretical value. is  of  pressuremeter  results  elastic  pressuremeter  strength  the  the  limited  the  conditions,  ratio  important  pressuremeter  has  and  test  L/D  soils.  the  ratio  the  plane  analyses,  cohesionless  the  to  two  14%).  membrane  of  state.  with  SUMMARY As  L/D  chamber  stress  from  tests  15%  141 For c o h e s i o n l e s s s o i l s ,  the e f f e c t  o f L/D r a t i o  i s more  p r o n o u n c e d . The p r e s s u r e e x p a n s i o n c u r v e s p r o v i d e d by t h e conventional pressuremeter  o f L/D r a t i o  the plane s t r a i n c o n d i t i o n  i n the r e l a t i v e l y  level a  ( s a y l e s s t h a n 4 % ) . The l i m i t  f i n i t e membrane  length w i l l  = 8 will  be c l o s e t o  small  strain  pressures predicted with  be s i g n i f i c a n t l y  higher than  the plane s t r a i n v a l u e s . I t was a l s o  found t h a t a l t h o u g h l a r g e  between t h e l i m i t pressuremeter  pressures i n the f i n i t e  test  i s caused  modulus and t h e f r i c t i o n a l  difference length  by 'end e f f e c t s ' ,  the e l a s t i c  a n g l e s d e r i v e d from t h e e a r l i e r  part of the curve  ( l e s s than a s t r a i n  o f 4% i n t h i s s t u d i e s )  are l e s s a f f e c t e d  ( s e e F i g . 6 . 9 ( b ) a n d T a b l e 6 . 7 ) . T h i s may  t h e r e f o r e suggest  that the i n t e r p r e t a t i o n  t e s t d a t a t o o b t a i n <j> s h o u l d more c o u n t of t e s t  i f the plane s t r a i n c o n d i t i o n  of pressuremeter on t h e e a r l i e r  part  i s g o i n g t o be u s e d .  However, i n p r a c t i c e  i t i s known t h a t t h i s e a r l i e r  of t h e p r e s s u r e m e t e r  c u r v e i s most v u l n e r a b l e t o t h e s m a l l  s o i l d i s t u r b a n c e s . In f a c t , soils,  the small  induced d u r i n g t h e i n s e r t i o n of the probe i s  i n e v i t a b l e . T h e r e f o r e , how t o o b t a i n a  frictional deserve  i n cohesionless  due t o t h e g r a i n s i z e o f s a n d p a r t i c l e s ,  disturbance almost  f o r the tests  portion  a n g l e from t h e p r e s s u r e m e t e r  further  investigation.  reliable  t e s t may  still  1 42  6.5  COMPARISONS OF C Y L I N D R I C A L FIELD To  PRESSUREMETER  assess  the  expansion  model  expansion  curves  cylindrical those were '  made  for  were  Fig.  6.4.  certain  pressuremeter hyperbolic  based  on  so  that  stress  test,  condition  soils  and  test  purpose. the  were  each  as  to  case,  give  used  strain  the  in  from  mesh  actual  relationship  different  was  analyses shown  scaled  radius  tests.  soils.  two  mesh was  with  Comparisons  element  element  the  compared  cohesionless  data  the  pressure  under  tests.  Finite  finite  cavity  the  analyses  pressuremeter  in  was  cylindrical  element  pressuremeter this  COHESIVE  of  in by  the  Nonlinear employed  in  all  SOILS  Self-boring Denby  (1978)  Hamilton  Air  in  of  soil  laboratory performed  a  San  Francisco Base  at  the  site  for  was  selected  because  available In  comprehensive  test  particularly  Mud  obtained  employed  information  to  results  were  location  method  test Bay  investigations.  interpretation are  pressuremeter  Force  particular  amount  that  finite  field  AND  analyses.  6.5.1  This  the  pressuremeter  for  factors  of  cohesive  However,  EXPANSION ANALYSES  DATA  expansion  from  used  performed  the  from  both  were  the  for  Self-boring  sites  validity  cavity  obtained  TEST  CAVITY  program,  useful  for  a  set the  of  of  Denby  and  the  comparison. the  from p r e v i o u s  particular,  obtain  the  of  by  large  field  (1978)  developed  soil  an  parameters  hyperbolic  finite  and  143  element  analyses.  The consists and  self-boring  pressuremeter  of  cylinder  7.5mm  flexible ratio  a  in  diameter,  rubber  to  for  measured  at  this  parameters selected  the  based  field  PROPERTIES  1)  Soil  Information  and  of  Treasher  interest where grey  geology  number  drilled  to  silty  Basic  in  covered  probe  the  at  depth  pressure  shown  data  in  Fig.  finite base  depth  is  has  of  length by  a  the  L/D  6.8m  was  expansion  curve  6.10.  soil  element  from  both  The  analyses  were  laboratory  tests  Soil  of  Fig.  about  the  6.11 27.4  3 m below  Properties  the  BASE  at  ground  a  a  been  and log  the  and  water  has  Trask  m at  lies  ground  site  shows  homogeneous,  The  FORCE  data  including  analysis  more  clay.  test  condition  authors,  this  2 to  from  testing.  -  data  AT HAMILTON AIR  (1961).  a  to  soil  between  testing  120mm  partially  flexible  the  tests.  SOIL  a  is  The  is  for  the  A.  by  test  depth  on  approximate  The  analysis.  required  in  6.  pressuremeter  selected  The  which  membrane.  approximate The  and  bronze  used  of  of  mainly  was  Rolston  site.  depth  found  level  investigated  a  borehole  The  soil  around  consists to  during  (1951)  of  6.8 of  m, soft  fluctuate the  field  200-  150Pressu-emeter C u r v e d . •  IZ  100-  5U-  Stress-Strain Curv* TEST NO HPH19 DEPlm 6-8 n. BAY HUO HOMOGENEOUS  RflOIRL STRAIN 7. F i g . 6.10 P r e s s u r e E x p a n s i o n C u r v e M e a s u r e d a t 6.8 m D e p t h , H a m i l t o n A i r F o r c e Base S i t e  ( a f t e r Denby, 1978)  1 45  On  45l Oxidation Zone Roofs extremely abundant. Lf. grey stiff silty clay  55-  -5  DEI  0_  CO k. CU  uu < u.  Me  X  r-  20- -6  25-  30-  35-  40-  8 9  Oork greenish cn: grey clay §o Shells common"  17  ii  his  60'  Soft,grey, silty clay  9  Organics, shells Open fissures, organics  65" -20  X rCL LU -21 Q  Soft grey silty day Silt lens, mica, organics  Light olive brown to light yellowish brown clay  70  -22  Soft grey silty clay 75  -23  10  Completely remolded Highly fissile  II  Numerous silt Lenses  -24 80-25  12  Organics, shells Silt lens  85-  ,3 45  la) 5°l  CO"  Sample dropped out of tube 15-  UJ  16  Oxidised Discoloration Fissures, organics, shells  10-  Silt lens Shells, organics uj  50-  26  Dark greenish grey clay Organics common  r-27 90-  F i g . 6.11 Log of Borehole at Hamilton Air Force Base ( a f t e r Denby,  1978)  1 46 Fig.  6.12 g i v e s some o f t h e e n g i n e e r i n g  d e r i v e d f o r Bay Mud a t t h e s i t e soil  samples as r e p o r t e d  soil  profile  properties  f r o m t e s t s on  by C l o u g h a n d Denby  ( 1 9 8 0 ) . The  c o n s i s t s of a d e s i c c a t e d c r u s t of grey c l a y  that gradually transforms t o a soft normally clay deposit  a t a depth about  to a depth of approximate overconsolidated  about  this  3  Bay Mud l a y e r i s e n c o u n t e r e d .  d e p t h . The p l a s t i c  6 0 % a b o v e 2.1 m a n d  and l i q u i d  limits are  u n i t weight i s  t o a d e p t h o f 2.1 m a n d 14.8 kN/m  Sensitivities  extends  15m, a t which a moderately  45 a n d 90 r e s p e c t i v e l y . The t o t a l  1.5.7 kN/m  consolidated  5.5 m. The s o f t c l a y  The n a t u r a l w a t e r c o n t e n t i s a b o u t 90% b e l o w  undisturbed  of the s o i l  Consolidation  below  2.1 m r a n g e  t e s t s (Duncan,  showed t h a t t h e s o i l  3  thereafter.  f r o m 6 t o 8.  1965 a n d Denby, 1978)  f r o m a 5.5m t o w a r d s t h e s u r f a c e i s  increasingly overconsolidated,  presumably  due t o t h e  d e s i c c a t i o n c r u s t . B e l o w 5.5m, t h e r e s u l t s s u g g e s t e d t h e Bay Mud t o a d e p t h o f a b o u t overconsolidated  that  15m i s s l i g h t l y  w i t h OCR = 1.1 t o 1.3.  - Undrained Shear  Strength  The u n d r a i n e d s h e a r s t r e n g t h v a l u e s pressuremeter t e s t s reported  derived  from t h e  by Denby ( 1 9 7 8 ) a r e p l o t t e d  v e r s u s d e p t h i n F i g . 6.13. A l s o shown a r e t h e s h e a r  strength  f r o m t h e UU t e s t s by Duncan ( 1 9 6 5 ) , a n d t h e l a b o r a t o r y v a n e and CU t r i a x i a l  t e s t s by Denby  (1978).  D E P T H - Meters 1  1  1  1  1  1  1  1  1  (\\\\\\\\\\\W\\\\ i  Li  l  •  Soft (New  i  Grey Cloy Boy Mud)  i  — r  1  i  r—  Dessicotion Zone - 1  1  |  1 48  UNDRAINED SHEAR STRENGTH- kN / m  0  Fig.  10  20  30  40  6.13 U n d r a i n e d S t r e n g t h s w i t h (after  C l o u g h and  Denby,  2  Depth  1980)  1 49 Both r e s u l t s triaxial  i n F i g . 6.12  c o m p r e s s i o n and  and  F i g . 6.13  l a b vane t e s t s  r a p i d d e c r e a s e of u n d r a i n e d  from the  indicate  shear s t r e n g t h w i t h  that  t o a d e p t h of  f o l l o w i n g by a r e g i o n where t h e  r a t i o of the u n d r a i n e d  to the  r  a  depth  t h r o u g h t h e d e s i c c a t e d c r u s t up  s t r e n g t h , C^  UU  5.5m,  e f f e c t i v e overburden pressure,  shear  P,  i s of  0.32. CU b a s e d on  triaxial  test  r e s u l t s p e r f o r m e d by Denby  SHANSEP ( t h e S t r e s s H i s t o r y And  Engineering  f o l l o w s C /P  =  u  Mud  b e t w e e n 5.5  Denby ( 1 9 8 0 ) p o i n t e d and  w i t h OCR  15 m i s  values  of  C^/P  r a t i o of the  i n - s i t u s o i l may  that  i n d i c a t e d by  the  s a m p l e s t h a t may  b a s e d on  the  t e s t data  reported  C^/P  z o n e c o u l d be values  t h e OCR  values  ratio  i n d i c a t e d by =  1.2  increase  was  t o 0.45 the  1.3,  that  the  as  =1)  disturbed.  from  Foott  be  are  1.0  (1974),  t o 1.3.  by Thus,  dessiccated  estimated 6.13.  Therefore,  increased  r a t h e r than the  t e s t s . The  than  or l a b vane  below the  shown i n F i g  actual  samples t h a t  by L a d d and  Mud  out  s l i g h t l y higher  r a t i o should  f o r Bay  a r o u n d 0.4  t h e c a s e o f OCR  to  (OCR  slightly  reported u  the  0.37  be  s u g g e s t e d t h a t t h e C /P as  1.1  t e s t s p e r f o r m e d on  t e s t s on  t o 20%  = 1  slightly  be  reconsolidated to v i r g i n conditions  10%  1974)  0.35.  overconsolidated  they  Foott,  Soil  i n c r e a s e o f s h e a r s t r e n g t h w i t h OCR  H o w e v e r , C l o u g h and t h e Bay  Nonlinear  P r o p e r t i e s ) method ( L a d d and  i n d i c a t e that the  (1978)  0.32 C /P u  to for  150 In view of the f o r e g o i n g a n a l y s i s , s t r e n g t h v a l u e s were c h o s e n One  was  d i r e c t l y adopted  two  f o r the f i n i t e  selected  element  i s 24.1  different  Kpa.  of E a r t h P r e s s u r e a t Rest  coefficient  of e a r t h p r e s s u r e a t r e s t , K ,  s t r e s s . F i e l d measurements of K  0  to  with  effective depth  r e p o r t e d by Denby (1978) a r e shown i n F i g . 6.14. Denby's s e l f - b o r i n g p r e s s u r e m e t e r t e s t d a t a , K f o u n d t o d e c r e a s e f r o m 0.8 0.5  - 0.6  Glotzl 0.8  f o r d e p t h s o f 3.5  load c e l l  tests  z o n e a t 7.0  between t h e K determined K water  0  0  m.  t o 9.1m.  show t h a t K  0  However, d a t a  h a s v a l u e s o f 1.0 f o r the  v a l u e s a r e much d e p e n d e n t  upon t h e  the u n i t weight of s o i l s ,  measurement o f i n - s i t u h o r i z o n t a l 0  horizontal  i . e . K = 0 . 5 , 1.0,  total  and  slightly  o  stress  exists The  ground and  the  p r e s s u r e on t h e p r e s s u r e m e t e r  In c o n s i d e r a t i o n of the u n c e r t a i n t y  v a l u e s of K ,  to  from  v a l u e s f r o m t h e s e two t y p e s o f t e s t s .  measurements of l i f t - o f f  on  v a l u e s were  Therefore, significant difference  table position,  curves.  0  Based  i n t h e d e s i c c a t e d z o n e a t 2.9m  f o r t h e d e s s i c c a t e d zone a n d o f 0.7  O.C.  is  0  d e f i n e d as the r a t i o of e f f e c t i v e h o r i z o n t a l vertical  Kpa.  from  t e s t s r e p o r t e d by Denby ( 1 9 7 8 ) , w h i c h i s 22.5  The  from  from the average v a l u e s of t h e  undrained shear s t r e n g t h r e s u l t s a v a i l a b l e  - Coefficient  analysis.  from the v a l u e d e t e r m i n e d  SBPMT u s i n g D e n b y ' s method ( 1 9 7 8 ) , w h i c h A n o t h e r was  undrained shear  stress  i n the  (or K  0  field  values),  were u s e d t o c a l c u l a t e  i n t h e a n a l y s i s . The  horizontal  two  the  Total Horizontal  Fig.  6.14  Stress  KN/m  C o e f f i c i e n t of  2  Earth  ( a f t e r Denby,  Pressure  1978)  K  1 52  total  stress  stress  with  ground  water  was the  calculated assumed  table  a  0  ri  where  ov, i s  in-situ  Shear  at  initial  determined  slope initial  the  table  are  modulus  depth  of  using  U  stress, is  0  a' v  the  shown  in  (22.2ft) values  As  gave were  from  the  C  =  u  assumed  is  the  hydrostatic  M =  990,  average  obtained  were  values  of  obtained  curve.  Table.  in  shear  used  6.8.  shear  shown a  Kpa.  be  from Denby's  in  24.1  are  2  22.5  modulus  M.  can  expansion  to  KN/m ,  multiplier  are  modulus  interpretation  7425  Soil  and  Denby's  G =  2)  total  derived undrained  These  correspondent  =  the  is  stress,  pressure  multiplier,  6.8m  and M =780.  u  and  (6.5.1)  shear  shear  the  C  soil  effective  interest.  of  tests  derived  That  of  horizontal  tangent  pressuremeter  at  weight  vertical  0  effective  d e p t h of  initial  shear  U  the  Modulus  The the  - a ' + v  in-situ  vertical  pressure  -  the  ri  unit  position.  = K  u  from  shear  by  Denby,  and  are  for  Finite  Element  Also  in  and  table, of  the  KN/m  and  of  the  analysis,  are  they  modulus  correspondent  to  2  are  values,  and  Analyses  test  They  set  modulus  in the  6250  1978),  Kpa.  Parameters  shown  analysis.  (Denby,  Another  chosen  self-boring  modulus the  The  strength the  from  Table at  6.8 P r e s s u r e m e t e r  Hamilton  DEPTH  Test  Site  (after  TEST NO.  FT.  Test  Results  Denby,  M  V kN/m  kN/m  2  2  9.5  14  28.2  5250  560  12.4  15  25.5  5400  640  15.0  16  22.1  5250  710  17.3  17  23.1  6800  880  20.0  18  21.8  5000  690  22.2  19  24.1  6250  780  24.9  20 *  22.7  4100  540  27.5  21  24.1  10000  1200  31.1  22  24.1  8400  1040  36.0  23  26.8  9500  1060  40.9  24  31.4  12800  1220  45.8  25  33.3  11600  1040  49.1  26  37.2  19100  1500  E = 2(1 + e ) G *  1978)  Effects  of d i s t u r b a n c e  evident  1 54  Based  on  the  information  at  assumed  the  for  above  the  sets  They  are  shown  in  case  (1),  the  soil  self-boring Denby soil  of  pressuremeter  In  the  isotropic before, The  using  be  The  initial  isotropic  in-situ  and  vertical  in two  the  sensitivity the  analysis  study.  be  of  from  developed  a  set  average  of  interpretation  the  by  general  values  medium  were  of  procedures  assumed  Consolidated  based  a  of  on was  total  to  be  clay.  As  stress  assumed,  and  analyses  was  of  approach. simulated  0.499.  used  in  the  and  which  the  each  discussed  of  equal  values  set were  of  K .  The  soil  assumed  neglecting  later.  the  0  was  K  0  to  the  from  of  deposit  assumed  to  calculated  soil  values  effects  was  given  real for  it  was  with  stress  The  interpreted  (2),  the  analyses.  analyses  procedure  be  analyses.  the  Normally  Therefore,  initial  will  soil  stress of  in  computer  case  condition  stress  used  can  data.  homogeneous,  effect  analyses.  different  were  stress  overburden  consolidation  the  ratio  horizontal  the  different lab  parameters  those  from  testing  Poisson's  are  using  homogeneous  a  the  selected  the  analyses  undrained  In  soil  expansion  were  of  with  and  soil  analyses  analyses,  and  the  were  available  cavity  parameters 6.9.  the  the  parameters  the  on  element  Table  data  1978),  site,  results  In  parameters  (Denby,  soil  test  (1978).  test  finite  Two  review  K  0  neglected parameters, for  condition  in  155 T a b l e 6.9 Soil  P a r a m e t e r s a d o p t e d f o r San F r a n c i s c o Bay Mud i n F i n i t e E l e m e n t A n a l y s e s  Soil Parameters  Cohesive (1)  C (Kpa) Gi (Kpa) M  24. 1 6250 780 0.499 75 o r 110 0.5 o r 1.0 16 0.87 2 6.8  u  a  v  H  Soils (2)  (Kpa)  K 7 (KN/m ) Rf G.W.T. (m) D e p t h (m) 0  3  22.5 7425 990 0.499 75 o r 110 0.5 o r 1.0 16 0.9 2 6.8  M - Modulus M u l t i p l i e r ; G.W.T. - G r o u n d W a t e r T a b l e . B. RESULTS AND DISCUSSION The  results  from p l a n e s t r a i n c a v i t y  finite  element  a n a l y s e s a r e shown i n F i g . 6.15 a n d F i g . 6.16 r e s p e c t i v e l y for  t h e f i r s t and t h e second  i n T a b l e 6.9. The f i e l d the  sets of s o i l  expansion curve i s a l s o  shown  included i n  f i g u r e s f o r comparison. Generally, the r e s u l t s of the f i n i t e  are  parameters  i n good agreement w i t h t h e f i e l d  uncertainty  i n the s o i l  parameters.  element  analyses  data, considering the In a l l the analyses, the  p r e d i c t e d p r e s s u r e e x p a n s i o n c u r v e s b a s e d on t h e c a v i t y expansion conditions  f i tthe f i e l d  p e r f e c t l y , w i t h o n l y minor Comparing the r e s u l t s from t h e average  soil  expansion curve  almost  deviation. f r o m SBPMT p a r a m e t e r s  parameters,  and those  i t was f o u n d t h a t t h e  99  I  o o . CM  ©  0  1  i  F I E L D MEASUREMENTS FEM(AVERAGE DATA) K =1.0  i  1  o  0  <$  FEM(AVERAGE DATA) K =0.5 o  LJ  -r\j _  ~r  1.0  i  i 2.0  CIRCUM.  1  1 3.0  i  STRAIN{%)  Fig.  1 4.0  SAN  1  1 5.0  1  FRANSICO  1 6.0  BAY  6.16 C o m p a r i s o n w i t h F i e l d  1  1 7.0  1  1 8.0  1  MUD(C =22.5KPA) u  Measurements  1 9.0  r  10.0  158 analyses  with  response  at  at  strains.  large  soil  the  However,  shear the  parameters  was  is  found  smaller  the  that  in  of  field  seem  data  cohesive than of  all  hyperbolic good San  fits  stress with  Francisco The  finite  reasons  element  expansion sufficient active  role:  did  some  finite  the  the  is  higher, the  stiffer  response  in  data  later  second but  first  different  different  set  of  the  one.  showed  set  of  that  soil  not of  the  minor  the  cavity  strain  test  analyses  tend  relation  data  in  soft  results  with that  suggest be  able  are  cohesive  soils,  in  ratio close  to  In  that to  with  that  L/D  condition.  to  may  the  conclusion  results  expansion  also  curves.  deviations,  test  in  significant  predicted  previous  stresses,  resulted  generate  element  the  initial  stress  pressuremeter  results  the  provide such  as  in  Mud. for  the  analysis  condition, L/D  a  as  field  initial  shape  produce  field Bay  but  confirm  soils,  the  with  higher  exist  cylindrical  addition,  softer  than  with the  predict  invisible.  the  to  lower  from  general  all  4 may  is  results  there  a  modulus  compared  the  the  comparison  those  strength  and  reasonable  initial  nearly  Although  larger  is  displacements,  difference  soft  the  parameters  stage,  resulted  Comparing it  This  results  difference  soil  earlier  parameters,  undrained  the  general  ratio,  may  consistent under be  that  the  results  cylindrical  postulated, the  p r e d i c t e d by  following  in  the  cavity  addition  factors  to  play  the an  1 59  1.  2.  The  soil  parameters  laboratory  tests  The  strain  stress  appear  more  strength are  low  by  Ladd  Bay  anisotropy. isotropic  K  consolidation testing,  occur  in  the  modes  shown  K  that  undrained be  in  Fig.  of  the  is  a\) K  <  0  the  on  the  may  that  the  tests  data  (1976),  degree  San  of  linear  elastic,  appropriate  to  this  to  type  in  of  pressuremeter,  These  on  and  soils  three  prinicipal  failure  their  Wroth  true (1977)  or  where  vertical  principal  the  greater  than  readjustment occurs  started,  6.17.  very  horizontal  the  relative  rapidly  after  the  failure  by  the  difference  is  The  of  slightly  and  governed and  the  in  the  initial  may  depending  possible  Based  Wood  of  the  normally  alone,  Fig.  modes  In  initially  1),  be  important.  failure  6.17.  much  has  be  magnitudes  stresses  stresses  shown  the  data,  clay,  considered  as  mild  Mud  compression  Based  not  condition.  0  shearing  horizontal plane  or 0  magnitudes  and  Bay  reported  Prevost  more  may  around  for  (K CT',  stresses  be  relative  overconsolidated z  (1965)  a  possible  experimental  (o'  Francisco  incremental  may  soil  i.e.  concluded  San  soils.  only  effect  in-situ  are  of  (1977),  of  three  stresses,  can  al  and  others.  field  stress  et  analysis than  triaxial  other  SBPMT  quality.  Duncan  to  is  both  extension  Therefore,  soils  the  in  from  high  relation  Mud  of  upon  of  hyperbolic.  relative  Francisco  0  are  difference  reported  3.  derived  mode  of  of  vertical  the soils  of  rid stress  160  Fig.  6.17  Soil  Failure  Pressuremeter  Modes a s s o c i a t e d w i t h  Tests i n Cohesive  ( a f t e r Wood a n d W r o t h ,  1977)  Soils  161 q u i c k l y becomes i n t e r m e d i a t e p r i n c i p a l little  e f f e c t on t h e w h o l e  test  s t r e s s , and  results.  In l i g h t  these experimental evidences, the i n i t i a l  stress w i l l  of  isotropic  s t r e s s s t a t e a s s u m e d i n t h e a n a l y s i s , w h i c h was from the i n - s i t u h o r i z o n t a l  has  soil  obtained  not generate  r e s u l t s that are s i g n i f i c a n t l y d i f f e r e n t  from the  field  response.  6.5.2  COHESIONLESS SOILS Self-boring pressuremeter test  by Hughes a n d R o b e r t s o n research s i t e Vancouver  (SBPMT) r e s u l t s  (1984) a t M c D o n a l d  l o c a t e d on an a b a n d o n e d f a r m n e a r  I n t e r n a t i o n a l A i r p o r t , were e m p l o y e d  comparison  in cohesionless  A summary o f t h e s o i l  6.18.  The  upper  profile  2 m of s o i l  c o m p r e s s i b l e c l a y s and s i l t s , 13 m. of the  The  ground  ground water  c o n s i s t s of  i s shown i n soft,  f o l l o w e d by a s a n d l a y e r up t o  i s generally  size with 1 to 2 m  t e s t d a t a o b t a i n e d a t d e p t h o f 7 m was  l a y e r s of f i n e  t e s t i n g was L/D  (CPT)  layers below  hydrostatic.  c o m p a r i s o n , where s o i l few t h i n  f o r the  s u r f a c e , and t h e ground water p r e s s u r e s a r e  approximately The  the  b a s e d on s a m p l i n g ,  s a n d h a s a medium t o c o a r s e g r a i n  f i n e s a n d . The  UBC  soils.  l a b o r a t o r y and cone p e n e t r a t i o n t e s t i n g Fig.  Farm, a  obtained  a 76 mm  r a t i o = 6. The  chosen f o r  m a i n l y c o n s i s t s of c o a r s e sand w i t h a s a n d . The  pressuremeter used f o r the  i n d i a m e t e r w i t h a f l e x i b l e membrane o f p r e s s u r e e x p a n s i o n measured  at the depth  PORE PRESSURE FRICTION RESISTANCE U (BAR) „ fC (BAR) 0  BEARING RESISTANCE QT (BAR) 2 00  SOIL PROFILE  DIFFERENTIAL P.P. RATIO AU/QT„ 0 . Bo  FRICTION RATIO RF = FC/QT 1%) 0 2  0  Soft CLAY S SILT  Coarse SAN 0 Loose to Dense with layers ot line Sand 10  I 0-  Fine SAND, some si 11  0, = 6 0 %  (Boldi el ol ,1982)  Soft, normally consolidated clayey SILT Sand = 1 0 % Sill = 7 0 % Cloy •• 2 0 % L.L. 38% P.I. • 1 5 % w •• 3 5 %  20  n  k=s8X|0" cmA«c 7  Ce = 0.3 30  "Equilibrium pore pressure  -I  r  i  i  1  i  I BAR = lOOkPa - l k g f / c m  Fig.  6.18  2  = I Ton/ft.  2  S o i l P r o f i l e f o r Research S i t e a t McDonald Farm, Sea I s l a n d  163 is  shown i n F i g . 6.19.  A. SOIL PARAMETERS Comprehensive at  soil  t e s t i n g p r o g r a m s h a v e been c o n d u c t e d  t h e McDonald Farm, g e n e r a t i n g l a r g e amounts o f s o i l  information,  from which c o r r e l a t i o n s  p a r a m e t e r s h a v e been e s t a b l i s h e d  f o r basic  soil  (Robertson and Campanella,  1 984) From t h e c o n e b e a r i n g p r o f i l e ,  the r e l a t i v e  density,  D , a n d f r i c t i o n a n g l e , <t>, o f t h e s a n d d e p o s i t c a n be determined  (Robertson and Campanella,  density of D  r  1984). A  relative  = 6 0 % a n d a f r i c t i o n a n g l e o f <f> = 42° were  obtained a t the depth of 7 m f o r the a n a l y s i s . The  i n i t i a l elastic  m o d u l u s G o r E u s e d was d e t e r m i n e d  from t h e s e l f - b o r i n g p r e s s u r e m e t e r t e s t d e p t h o f 7 m, t h e i n i t i a l e l a s t i c  shear modulus,  f o u n d t o be 42 Mpa. Then t h e e l a s t i c obtained  (SBPMT) d a t a . A t G, was  Young's modulus,  through  E = 2G (1 + u)  (6.5.1)  w i t h an a s s u m p t i o n t h a t t h e d r a i n e d P o i s s o n ' s r a t i o , sand  u,  for  i s e q u a l t o 0.2. Two s e t s o f s o i l  The  E, was  first  p a r a m e t e r s were u s e d  s e t o f p a r a m e t e r s was s e l e c t e d  d a t a . They a r e shown i n t h e f i r s t c o l u m n Another  f o r the analyses.  f r o m CPT a n d SBPMT o f T a b l e 6.10.  s e t was f r o m t h e d a t a r e p o r t e d by B y r n e a n d Cheung  164  I lOOr-  ~  o  IOOO  -  900  -  800  -  O.  0  1.0  2.0  3.0  4.0  5.0  6.0  R o d i o l Dtsplocement  7.0  8.0  9.0  (%) R  Fig.  6.19  Pressure  Expansion  Depth,  McDonald's  (after  Hudges  Curve measured  Farm  and R o b e r t s o n ,  1984)  at 7 m  100  165 T a b l e 6.10 S o i l Paramters adopted f o r C o h e s i o n l e s s S o i l s a t M c D o n a l d Farm S i t e i n F i n i t e E l e m e n t A n a l y s e s Soil  Parameters D  SBPMT & CPT (1)  (%) <t> (°) (°) 0 (°) G i (Mpa) K K n m Rf  60 % 42° 2° 33° 42 995 587 0.5 0.25 0.8 0.2 20.0 90 90 o r 65 1.0 o r 0.9 2 7.0  r  C V  E  B  v  7 (KN/m ) a (Kpa) aii ( K p a ) K G.W.T. (m) D e p t h (m) 3  v  0  1.  B y r n e & Cheung (2) 60 % 38° 2° 33° 40.5 960 576 0.5 0.25 0.8 0.2 20.0 90 90 o r 65 1.0 o r 0.9 2 7.0  G.W.T. - G r o u n d W a t e r T a b l e .  ( 1 9 8 4 ) . T h e i r d a t a a r e shown i n T a b l e 6.11, w h i c h were d e t e r m i n e d from t h e f i n i t e field  element  back a n a n l y s i s o f t h e  s e t t l e m e n t o b s e r v a t i o n s , a n d from a comprehensive  r e v i e w o f t h e d a t a base tests.  The s o i l  from t h e l a b o r a t o r y and t h e f i e l d  properties are r e l a t e d t o the r e l a t i v e  d e n s i t y o f sand, and t h e r e l a t i v e  density D  r  i s determined  f r o m t h e SPT b l o w c o u n t s . Herein, the r e l a t i v e  d e n s i t y o f t h e sand a t t h e t e s t  d e p t h o f 7 m c a n be e v a l u a t e d d i r e c t l y profile. at  from t h e cone b e a r i n g  As s t a t e d e a r l i e r , t h e e s t i m a t e d r e l a t i v e  t h i s depth i s about  60%. T h e r e f o r e , a complete  density set of  T a b l e 6.11 S o i l  D  r  25 50 75 100  N  l  5 10 25 > 50  P a r a m e t e r s p r o p o s e d by B y r n e a n d Cheung  k  E  300 600 1500 3000  n  .5 .5 .5 .5  k  B  180 360 900 1500  m  .25 .25 .25 .25  (1984)  •l  A<t>  4>  R  33 36 41 50  0 2 4 9  33 33 33 33  0.9 0.8 0.7 0.6  cv  F  167  soil  parameters  analysis  was  parameters As  obtained  is  in  also  the  the  soil  and  correspond  Based  '  the  can  based  on  ground As of  in  table  in  the  analyses,  stress  B.  with  RESULTS  Fig  soil  K  0  AND  Finite of  two  unit  soils, is  which  = 0.9  and  each  in  curve  of  K  0  of  in  homogeneous, stress.  effective  pressure.  obtained  pressure  stress  effective  lift-off  at  depth  of  of  170  Kpa  = 0.9  was  estimated  soil  sensitive  values  and  the  was  assumed  of  that to  the  the  initial  to  the  measurements  soil state  in-situ  were  used  horizontal  1.0.  Table  set  of  are  elastic  moduli  (i.e,  E  assumed  initial  horizontal  considering  analysis  state  0.2.  the  isotropic,  corresponds  stress  of  6.10.  weight  very  initial  ratio  of  COMPARISONS  element  For  the  value  different  parameters  6.21.  soil  This  position.  pressure  disturbance,  set  in-situ  lift-off a  6.11.  horizontal  6.19),  therefore  element  be  expansion  a  finite  soils,  pressure  cohesive  lift-off  in-situ  estimated  water  to  from  and the  cohesive  estimated  be  hyperbolic  Table  the  Fig.  obtained,  in  assumed  the  the  Table  SBPMT d a t a ,  From t h e  7 m (see  from  of  was to  for  shown  case  medium  on  stress  required  In  Poisson's  order ratio  results 6.10  are  with shown  parameters, compared.  and to of  B)  are  In  on  the  different  set  in  Fig.  6.20,  results  from  different  Table  estimated  investigate sand  two  the  6.10, with  the Poisson's  influence  analysis  of  the  results,  168 another  finite  element  elastic  modulus c a l c u l a t e d  P o i s s o n ' s r a t i o o f 0.3 shown i n F i g 6.22 set  of s o i l  in  F i g 6.20.  f r o m SBPMT a n d CPT  (see Eq.  ( 6 . 5 . 1 ) ) . The  i n Table  from the f i r s t The  performed with  the  data  using  results  w i t h comparison of those from the  parameters  Results  a n a l y s i s was  finite  first  6.10.  s e t of s o i l  element  are  p a r a m e t e r s a r e shown  analysis with  cavity  expansion c o n d i t i o n p r e d i c t s pressure expansion curves similar  to the f i e l d  interesting  measurements i n shape.  to note that the curve p r e d i c t e d w i t h K  which i s the v a l u e measured i n f i e l d agreement w i t h t h e f i e l d the  It is  stress  0.9  portion,  but  strains.  L o o k i n g a t t h e c u r v e f r o m t h e same s e t o f parameters higher i n i t i a l  =  g i v e s a v e r y good  curve i n the i n i t i a l  c u r v e becomes s o f t e r a t l a r g e  0  (K  0  soil  =1.0), i t i s o b s e r v e d  t h a t t h e c u r v e i s s h i f t e d u p w a r d s due  to the h i g h e r  initial  s t r e s s s t a t e . S u c h a r e s u l t c a n a l s o be o b s e r v e d i n F i g w i t h the second  s e t of s o i l  parameters. T h e r e f o r e , the above  r e s u l t s seem t o s u g g e s t t h a t t h e f i e l d initial  shear modulus,  6.21  measurements of  and t h e h o r i z o n t a l e f f e c t i v e  stress  from the s e l f - b o r i n g p r e s s u r e m e t e r t e s t a t t h i s depth a r e probably reasonable. It  i s shown i n F i g 6.21  parameters  that the a n a l y s e s w i t h the  f r o m B y r n e a n d Cheung (1984) a l s o p r e d i c t  same t r e n d a s t h o s e w i t h t h e p a r a m e t e r s d i r e c t l y In  small s t r a i n  K  = 0.9  0  the  f r o m SBPMT.  r a n g e up t o 1%, t h e c u r v e p r e d i c t e d  i s a l s o very c l o s e to the f i e l d  soil  with  measurement, but  Fig.  6.20  Comparison Field  of F i n i t e  Measurements  Element  (SBPMT a n d  Prediction CPT  with  data)  vo  o  o .  X  _  ©  ©— —©f I  1  a  -o. •oo  <3>—  1 1  F I E L D MEASUREMENTS F E M ( B y r n e & Cheung  d a t a ) K =t.O  FEM(Byrne  d a t a ) K =0.9  4> 0  0  & Cheung  o  CD  0.0  I  I  I  I  I  1.2 2.4 3.6 CIRCUM. STRAIN {%) Fig.  I  I  I  1  6.21 C o m p a r i s o n o f F i n i t e Field  I  I  1  I  4.8 6.0 7.2 8.4 MCDONALD FARM SAND(DR=60X)  Measurements  Element P r e d i c t i o n  ( B y r n e a n d Cheung  I  1  1  9.6 10.8 DEPTH=7M  12.0  with  data)  o  171 becomes s o f t e r results,  in larger  strains.  Similar  the curve p r e d i c t e d w i t h K  o v e r p r e d i c t s the f i e l d  to the  = 1.0  0  curve i n the s t r a i n  is stiffer, i t l e s s than  b u t u n d e r p r e d i c t s t h e r e a f t e r . Compared w i t h t h e predicted  from the f i r s t s e t of parameters,  B y r n e a n d Cheung p a r a m e t e r s j u s t i f i a b l e as the i n i t i a l are  slightly As  less  is slightly m o d u l u s and  r a t i o would influence  the curve w i t h  the f r i c t i o n a l  i s generally  For the r e s u l t s from  angle  6.10).  assumed  initial  shows t h a t t h e h i g h e r P o i s s o n ' s  give a s l i g h t l y  curves predicted  curve  than the f i r s t ones (see T a b l e  F i g . 6.22  2.4%,  softer. This i s  f o r the i n f l u e n c e of the d i f f e r e n t  Poisson's r a t i o ,  earlier  stiffer  c u r v e . However, the  insignificant.  shown a b o v e , t h e p r e s s u r e finite  element  expansion c o n d i t i o n are generally  expansion  a n a l y s e s under  cavity  i n good agreement w i t h t h e  f i e l d d a t a i n s m a l l s t r a i n s , b u t t h e y a l l become s o f t e r the f i e l d data at l a r g e s t r a i n s , obtained using higher i n i t i a l  e x c e p t one  that  than  was  s t r e s s and h i g h e r P o i s s o n ' s  ratio. The  deviation  be a t t r i b u t e d interesting  from the f i e l d data at l a r g e s t r a i n s  t o many f a c t o r s . F i r s t  of a l l , i t would  t o n o t e t h a t t h e t r e n d shown i n F i g 6.20,  where f i e l d m e a s u r e m e n t s a r e c o m p a r e d w i t h c a v i t y prediction  is similar  w i t h the c a v i t y observation  s i m u l a t i o n was  that the s t i f f e r  6.21,  where  compared  expansion plane s t r a i n a n a l y s i s .  seems t o s u g g e s t  be  expansion  t o t h e t r e n d shown i n F i g 6.8  the a x i s y m m e t r i c a l pressuremeter  may  This  field  Fig.  6.22  Influence  of P o i s s o n ' s  Element  R a t i o on  the  Finite  Prediction to  173 pressuremeter cylindrical L/D  curve at large s t r a i n ,  deviating  c a v i t y e x p a n s i o n c o n d i t i o n , may  r a t i o e f f e c t , as the p r e s s u r e m e t e r  t e s t i n g was  a probe  o f L/D  =  l a r g e s t r a i n s may  element  a l s o be due  in  effect will  the f i e l d  the f i n i t e  incorporated  stiffen  data at  the s o i l  the  response. Therefore, o f t h e s a n d may  have  pressuremeter not accounted  for  was  i n the a n a l y s e s , the p r e d i c t e d c u r v e would  a b o v e r e s u l t s , i t may  have  c u r v e a t l a r g e s t r a i n s . From t h e  be c o n c l u d e d t h a t  the  r a t i o of 6 can p r o v i d e t h e f i e l d  curve that  field  analyses. I f this effect  become c l o s e r t o t h e f i e l d  w i t h L/D  field  r a t i o e f f e c t , the  s t r a i n s . S u c h an e f f e c t was element  i n the  ( 1 9 8 3 ) showed t h a t  then s t i f f e n e d the measured  curve at large  t o the  t o the d i l a t a n c y e f f e c t of  measurements, the d i l a t i o n  o c c u r r e d , and  in  L/D  p r e d i c t i o n from  s o i l s at large s t r a i n s . Eldridge dilatancy  be due  6.  In a d d i t i o n t o the pressuremeter d e v i a t i o n of f i n i t e  used  the  pressuremeter  pressure  i s c l o s e t o the a x i s y m m e t r i c a l plane  expansion  strain  condition. The  i n c o r p o r a t i o n of d i l a t a n t s o i l  nonlinear  hyperbolic  o b t a i n e d by B y r n e neglect  6.20,  strain  element  and E l d r i d g e  of the d i l a t a n t s o i l  the v a r i a b i l i t y Fig  finite  6.21  behavior i n the  a n a l y s i s has  (1984). A l l o w i n g  f o r the  behavior i n the a n a l y s e s  of n a t u r a l s o i l s , tend to suggest  and  t h e r e s u l t s shown i n  that a n a l y s i s with  r e l a t i o n can p r o v i d e r e a s o n a b l e f i t s  measurements of p r e s s u r e m e t e r  been  t e s t . However,  with  hyperbolic field  futher  investigation  i s necessary to confirm t h i s  statement.  7. S O I L - P I L E INTERFACE ELEMENTS  7.1 INTRODUCTION The the  a n a l y s i s of the l a t e r a l l y  l o a d e d p i l e s i s one o f  s o i l - s t r u c t u r e i n t e r a c t i o n problems r e q u i r i n g the  consideration has  of the s o i l - s t r u c t u r e i n t e r f a c e behaviour. I t  been r e c o g n i z e d  influence  the p i l e  especially Wright,  that  the interface c h a r a c t e r i s t i c s  lateral  on t h e u l t i m a t e  resistance soil  significantly,  resistance  (Yegian and  1973).  In  reality,  loadings,  as a v e r t i c a l  mean n o r m a l s t r e s s e s  pile  i s subjected  i n the s o i l  to lateral  will  increase i n  f r o n t o f t h e p i l e , and decrease behind t h e p i l e . Displacements i n the s o i l the  pile  behind will the  will  t e n d t o be r a d i a l l y  i n f r o n t of t h e p i l e , and r a d i a l l y  i t . A t some s t a g e s ,  away f r o m  towards the p i l e  near the ground s u r f a c e ,  a gap  p r o b a b l y open up a t t h e i n t e r f a c e b e t w e e n t h e p i l e a n d soil  behind i t , with  soil  i n front of p i l e  failing in a  wedge t y p e o f m e c h a n i s m , a s shown i n F i g . 7.1. F u r t h e r the  pile  shaft, soil  will  eventually  h o r i z o n t a l l y around the p i l e . between p i l e cylindrical Fig.  and s o i l slippage  7.2. T h e r e f o r e ,  resistances  In t h i s  fail  by  down  flowing  case, the interface  e x p e r i e n c e s no g a p p i n g b u t r e l a t i v e around the p i l e  s h a f t , a s shown i n  i n order t o p r e d i c t  accurately  it  i s desirable  in  t h e program so t h a t  using  the p i l e  the f i n i t e element  t o have an e f f i c i e n t  lateral  procedure,  b u t s i m p l e model  built  t h e i n t e r f a c e c h a r a c t e r i s t i c s between 1 75  176  Fig.  7.1  Soil  (after  Movement  Broms,  1964)  a t Shallow  Depth  fan zone  7  \  /  f I  Fig  /  /  ( 1  V  -  ,  t  pile  7.2 S o i l F l o w s a r o u n d L a t e r a l  'sliding concentric cylindrical shells  Pile  ( a f t e r R a n d o l p h & H o u l s b y , 1984)  a t Depth  1 78 soil  a n d p i l e c a n be a p p r o x i m a t e l y a c c o u n t e d  f o r i n the  analysis. In t h i s c h a p t e r , t h e p o s s i b l e modes w i l l  be d e s c r i b e d f i r s t ,  review of d i f f e r e n t  interface  and then  interface  deformation  f o l l o w e d by a b r i e f  element models a v a i l a b l e a t  present time. F i n a l l y , a simple but r a t i o n a l element model i s p r e s e n t e d . T h i s model w i l l finite of  element a n a l y s i s  laterally  interface be u s e d  t o simulate the interface  i nthe  behaviour  loaded p i l e s approximately.  7.2 DEFORMATION MODES AT INTERFACE Under s t a t i c  loading  conditions,  the s o i l - p i l e  i n t e r f a c e may u n d e r g o v a r i o u s t y p e s o f r e l a t i v e movements. T h e s e r e l a t i v e d e f o r m a t i o n c h a r a c t e r i s t i c s c a n be classified  i n t o t h r e e modes a s i l l u s t r a t e d  t h e two d i m e n s i o n a l  remains  i n F i g . 7.3 f o r  condition:  a) S t i c k o r no s l i p - when n o r m a l compressive  generally  and shear  T  stress  l e s s than t h e shear  s  stress  developed  strength,  a  n  is  on t h e i n t e r f a c e  e . g . d e f i n e d by  Mohr-Coloumb c r i t e r i o n . I n t h i s c a s e , i . e .  T  where C , a interface,  s  < C  a  + a  n  tantf.  a r e t h e a d h e s i o n , and f r i c t i o n a l  angle a t  I  respectively;  b) S l i p - when t h e s h e a r interface  (7.3.1)  I  stress  i s g r e a t e r than t h e shear  r  s  developed  on t h e  s t r e n g t h but normal  A = Total  W-  ///^  -Jifi-  A  (a)  (b)  Fig.  7.3  Schematic  a) S t i c k  o r no  b)  Slip  c)  Gapping  (after  of Modes a t slip  Desai et a l ,  1984)  Interface  Area  180 stress  a  remains  n  compressive;  c ) G a p p i n g - when n o r m a l  stress  a  n  becomes t e n s i l e .  In g e n e r a l , t h e above d e f o r m a t i o n c h a r a c t e r i s t i c s a r e d e p e n d e n t upon t h e m e c h a n i c a l interface  7.3  as w e l l  as the s t a t e  and g e o m e t r i c a l p r o p e r t i e s of stresses  at interface.  REVIEW ON INTERFACE ELEMENTS A variety  proposed  of i n t e r f a c e  e l e m e n t m o d e l s h a v e been  by many r e s e a r c h e r s t o a c c o u n t  the s p e c i a l  deformation behaviour  interfaces,  particularly for static  have i n c l u d e d  characterization  approximately f o r  at soil-structure loadings.  of behaviour  These models of j o i n t s i n  r o c k s and i n t e r f a c e s  of s o i l - s t r u c t u r e i n t e r a c t i o n  The  among t h o s e m o d e l s l i e s  major d i f f e r e n c e  different  treatments of the c o n s t i t u t i v e  interface  elements.  of  of  A comprehensive  j o i n t or interface  been g i v e n by D e s a i loadings. which  p i l e s are presented  in their  laws  f o r the  r e v i e w on t h e s u b j e c t s  b e h a v i o u r and t h e i r m o d e l l i n g s has  (1981) b o t h f o r s t a t i c  H e r e i n , o n l y some o f i n t e r f a c e  h a v e been u s e d  systems.  i n the analysis  and dynamic  element models  of l a t e r a l l y  f o r t h e sake of completeness  loaded and l o g i c  development.  7.3.1  JOINT ELEMENTS WITH ZERO THICKNESS Joint  e l e m e n t m o d e l was f i r s t  T a y l o r and Brekke  proposed  (1968). A schematic  by Goodman,  o f t h i s m o d e l i s shown  i n F i g . 7.4. I n t h i s m o d e l , t h e e l e m e n t s t i f f n e s s i s  \ \ \  Solid  Element  /  -fc s o  Fig.  Joint  7.4  Solid  Element  element  Joint  Element  with  Zero  Thickness  co  182 f o r m u l a t e d b a s e d on t h e r e l a t i v e n o d a l d i s p l a c e m e n t s s o l i d elements surrounding  the i n t e r f a c e  element w h i c h has  z e r o t h i c k n e s s . The e l e m e n t s t i f f n e s s m a t r i x  [K] = ;  where [ B ' ]  [ B ' ] [ C ] . [ B ' ] dx  r e l a t i v e displacements  of the i n t e r f a c e  of t h e a d j a c e n t  of t h e i n t e r f a c e  matrix  i s expressed  k  n  0  0  analysis,  k  = shear  normal and shear  the c o n s t i t u t i v e  r (7.3.3)  V  S  r  s  r = shear  s t i f f n e s s and u  displacements  system t o the g l o b a l  r  and v  k„ = n o r m a l n are r e l a t i v e  r  Then t h e  from the l o c a l c o o r d i n a t e  c o o r d i n a t e s y s t e m , and t h e s t i f f n e s s  f o r the i n t e r f a c e  system i s f i n a l l y  stress,  respectively.  element s t i f f n e s s i s transformed  matrix  the length  \  u  where a„ = n o r m a l s t r e s s , n s  i s over  •  S  k  [C]^i s  as:  • =  stiffness,  element t o the nodal  s o l i d elements,  f  T  r e l a t i n g the  element.  t h e two d i m e n s i o n a l  n  as  (7.3.2)  c o n s t i t u t i v e m a t r i x and t h e i n t e g r a t i o n  For  i s written  T  L  i s the transformation matrix  displacements  of the  element i n t h e g l o b a l  assembled i n t o the e n t i r e  coordinate  structure  s t i f f n e s s m a t r i x by s t a n d a r d manner a c c o r d i n g t o t h e interface  nodal connection  with the adjacent  solid  elements.  183 S u c h a m o d e l has nonlinear Clough  been i n c o r p o r a t e d i n t o  linear  i n t e r a c t i o n a n a l y s i s by a number o f  and Duncan  (1971) used  investigators.  i t with a great success for  the p l a n e s t r a i n a n a l y s i s of r e t a i n i n g w a l l s , determined t e s t s and  the shear expressed  B a s e d on  stiffness,  similar  e l e m e n t a s shown i n F i g . 7.5  a cylindrical  and  pile  a finite  in their  loaded  p e r i m e t e r . The  deformations around  the p i l e  e x p r e s s e d by a b i l i n e a r  cylindrical  radial  (or  shear)  s h a f t were a l l o w e d f o r and  e q u a t i o n . However, s i n c e t h e  i n t e r f a c e d e f o r m a t i o n s were r e s t r i c t e d the s o i l - p i l e  for in their  piles.  l e n g t h encompassing a  segment o f t h e p i l e  Inconveniences  cylindrical  i s of z e r o t h i c k n e s s i n t h e  d i r e c t i o n but p o s s e s s e s  accounted  box  interface  section,  curves f o r the l a t e r a l l y  i n t e r f a c e element  normal) d i r e c t i o n ,  shear  they  t o t h a t by Goodman e t a l ,  to s i m u l a t e the  r e l a t i v e movement b e t w e e n s o i l  The  k , from d i r e c t s  (1973) d e v e l o p e d  p r e d i c t i o n s o f P-Y  i n which  i t i n terms of h y p e r b o l i c r e l a t i o n s h i p .  the concept  Y e g i a n and W r i g h t  and  i n the r a d i a l  s e p a r a t i o n was  i n t e r f a c e element  (or  not  model.  w i t h the above z e r o - t h i c k n e s s j o i n t  element models are the l a c k of a p h y s i c a l b a s i s f o r a d o p t i n g a r b i t r a r y v a l u e s of k  n  and  k  g  and  the need t o f o r m u l a t e a  s p e c i a l element s t i f f n e s s m a t r i x based displacements.  on t h e  relative  -Interface  (a ) •  Elements  - Interface element at soll-plle boundary.  Fig.  7.5  x  Cylindrical  (after  Yegian  &  Interface Wright,  (K)  '  " Displacement pattern for Interface elements.  Element  1973) co  185 7.3.2 THIN LAYER INTERFACE ELEMENT Essentially, member i n v o l v e s layer  the interface  a thin layer  of zero thickness.  interface  layer  between s o i l  and s t r u c t u r a l  of s o l i d m a t e r i a l  rather  The b e h a v i o u r o f t h i s  may be d i f f e r e n t  than a  thin  from t h e b e h a v i o u r o f t h e  s u r r o u n d i n g s t r u c t u r a l and s o i l m a t e r i a l s ,  due t o d i f f e r e n t  d e f o r m a t i o n c h a r a c t e r i s t i c s between t h e s o i l  and  B a s e d on t h e s e i d e a s ,  e l e m e n t was  a thin  layer  interface  p r o p o s e d by D e s a i  (1981) t o s i m u l a t e t h e s p e c i f i c  of  a s shown i n F i g .  the interface,  for the thin  layer  interface  special  element  i s formulated  features of the t h i n l a y e r  treatment of i t s c o n s t i t u t i v e  thickness,  and t h e i n c o r p o r a t i o n  behaviour  7.6. The s t i f f n e s s m a t r i x  same way a s f o r t h e o t h e r s u r r o u n d i n g s o l i d distinguishing  structure.  i n the  e l e m e n t s . The  element a r e the  law, choice of i t s  of i n t e r f a c e  deformation  modes. Unlike the joint thin  layer  element  element, the c o n s t i t u t i v e  i s s i m i l a r t o that  law f o r t h e  f o r t h e normal  solid  element, e x p r e s s e d i n terms of t h e i n c r e m e n t a l s t r e s s and strain, i.e.  [Aa]  = [ C ] [Ae]  The i n c r e m e n t a l s t r e s s direction  (7.3.4)  i  and s t r a i n a r e s p e c i f i e d i n  o f normal and t a n g e n t i a l  respectively, i . e .  to the interface,  Interface  (a)  Two-dimensional  8 • (average) c o n t a c t dimension  Fig.  7.6 T h i n L a y e r (after  Interface  Element  D e s a i e t a l , 1984)  co CTi  187  ns [C]  (7.3.5)  where [ C ] , [ C ] a r e t h e n o r m a l n  stiffness [C  s t i f f n e s s and  g  s u b m a t r i c e s of the t h i n  shear  l a y e r element,  a n d [C  ] r e p r e s e n t the c o u p l i n g e f f e c t s of the normal  and  b e h a v i o u r , which a r e not c o n s i d e r e d a t p r e s e n t time they are d i f f i c u l t The n o r m a l are  shear  since  t o e v a l u a t e from t h e e x p e r i m e n t a l d a t a .  stiffness  [C ] o f t h e t h i n n  interface  element  o f t e n assumed t o be t h e same a s t h o s e o f t h e s u r r o u n d i n g  soil  elements  ( D e s a i , 1981 a n d D e s a i e t a l , 1 9 8 4 ) , w h i l e t h e  shear s t i f f n e s s  [ C ] of the t h i n g  u s u a l l y o b t a i n e d from d i r e c t composed o f a s h e a r modulus m o d u l u s G^ c a n be i n t e r p r e t e d r e s u l t s , and e x p r e s s e d 9r G  i  for  " 9u  layer  displacement, a  n  f o r t h e i n t e r f a c e . The from d i r e c t  For the l i n e a r component  the given normal  constitutive interface  test  stress a  and u  r  =  (7.3.6)  n  relative  s t r e s s a c t i n g on t h e s h e a r  s t r e s s a c t i n g on t h e s h e a r b o x .  elastic,  i s uncoupled  shear  shear  i n form o f :  = the normal  and r = t h e shear  i n t e r f a c e element i s  s h e a r t e s t s , a n d p r e s u m e d t o be  where t = t h i c k n e s s o f t h e e l e m e n t ,  box,  ],  isotropic  from the normal  behaviour, the shear component  i n the  l a w s , and t h e c o n s t i t u t i v e m a t r i x f o r t h e  i s g i v e n based  on t h e g e n e r a l i z e d H o o k e ' s  Law,  188 i.e.  f o r t h e two d i m e n s i o n a l c o n d i t i o n  C [C].  c  -  0 0  c  2  0  (7.3.7)  0  where: E  (1 - u)  (1+u)  0-2u)  E v (1+y)(1-2U)  where E i s t h e e l a s t i c ratio, the  and  direct  exactly If  Young's modulus, u i s P o i s s o n ' s  i s the shear modulus which s h e a r t e s t . The  v a l u e s o f C, a n d C  t h e same a s f o r t h e s u r r o u n d i n g s o i l the behaviour of the t h i n  a s s u m e d t o be n o n l i n e a r e l a s t i c elastic  m o d u l i , E,  u a n d G. •  are  s t r e s s dependent,  hyperbolic  and  elements.  isotropic,  then  I  and c a n be e x p r e s s e d i n t e r m s  function are determined  and d i r e c t  shear  r e q u i r e d f o r the from a p p r o p r i a t e t r i a x i a l  tests.  i n t h e a n a l y s i s , D e s a i e t a l (1984)  0.1  - 0.01  the  average  of  4. H o w e v e r , i n  f o r the a p p r o p r i a t e t h i c k n e s s of the t h i n  quadrilateral  the  l  f u n c t i o n , as d i s c u s s e d i n Chapter  the  is  i n the c o n s t i t u t i v e m a t r i x [C].  hyperbolic  element  from  however, a r e  2  i n t e r f a c e element  t h i s case, the i n t e r f a c e parameters  As  i s determined  i n t e r f a c e element  suggested  that  w i t h t h i c k n e s s of  L would p r o v i d e s a t i s f a c t o r y l e n g t h of a d j o i n i n g  interface  r e s u l t s , where L i s  elements.  189 The  concept  of  using  the  thin  layer  than  zero  thickness  interface  element  rather  attempted  by  researchers  (1970)  and  many  Desai  studied  and  element  analysis  associates  applied  usage  not  yet  thin  in  layer  researches  THE  to  employed  a  The  It  is  believed  the  in  out  is  thesis  loaded  the  layer  of  soil  deformation surrounding  to  the  relative  be  thin  to  that  mainly  the  The However,  piles  has  concept  useful of  for  of the  the  which  used  displacement,  a  the similar  interface  element  interface  behaviour  the  soil-pile  of  layer  interface  attributed  characteristics soil.  the  a  b).  INTERFACE  basis  thin  the  some  The  than  his  loaded  and  al  finite  interest.  approach  layer  study  et  thesis.  Wright  rather of  this  the  1984a,  that  and  SOIL-PILE  piles.  concept  characteristics  considered  on  piles,  in  al,  simple  been  systematically  and  laterally  and  foregoing  the  is  of  practical  the  loaded  Yegian  et  has  been  Desai  of  element  carried  based  laterally  thin  of  the  element  element  and  analysis  has  by  promising  PROPOSED MODEL FOR  concept  the  problems  as  Zienkiewcz  implementation  Desai  explored.  are  concept  and  laterally  Unlike joint  the  many  interface  of  The  1981,  the  been  analysis  7.4  is  in  to  (Desai,  application its  (1981).  including  element  to  associated  the  the  zero  layer  the  involves  thickness. are  differences  with  of  proposed  interface of  is  pile  in  the  and  the  190 In  reality,  undergoes  the  concrete  negligible  pile  deformation,  lateral  deflection  and  usually  treated  rigid-plastic  Therefore, normal  it  soil  as  may  be  elements  elements  emcompassing  relative  deformation  interface the  can  proposed  discussed  7.4.1  in  to  with  stress  the  formulation  interface soil  the of  elements  elements.  it  in  the  form  CONOIL a n d  in  the  Desai's  used  in  modulus,  constitutive CONOIL E,  to  distortion, modulus,  above  other  Poisson's if  thin  the  four  soil-pile  Some  features  of  are  same  as  material  for  that  proposed  the  there  laws  adjacent exists  employed  a  in  generalized  Hooke's  modulus,  and  bulk  volume  modulus,  Desai  et  al  moduli  and is  the  element,  the  elastic u,  for  LAWS  element.  elastic  by  CONSTITUTIVE  interface  Young's  ratio,  the  layer  i.e.  the  proposed  of  interface  that  interface  constitutive  law,  than  -  matrix  noticed  express  the  independent  is  elastic  However, by  of  as  modifications  layer  the  employs  rather , as  thin  exactly  However,  the  MATRIX  stiffness  difference  The  and  ring  sections.  Desai's  is  the  is  analysis.  thin  so  simulated.  STIFFNESS  the  at  pile  the  a  its  the  boundary  perimeter,  element  following  in  propose  characteristics  F O R M U L A T I O N OF to  pile  with  Thus  material  given  essentially  compared  deformation.  approximately  the  as  reasonable  interface  Similar the  be  soil  section  only  elastic  B,  change E,  and  (see are  two and  Young's  and  elastic  shear  Eq.  (7.3.7)).  related of  law  them  to are  isotropic  each  191 (Timoshenko and G o o d i e r , that,  in principle,  1951).  t h e form  Therefore,  i t i s believed  of c o n s t i t u t i v e m a t r i x used i n  CONOIL i s e q u i v a l e n t , a n d i n t e r c h a n g e a b l e t o t h e f o r m in the Desai's  thin  In p r a c t i c e ,  layer  interface  used  element.  i f the i n t e r f a c e p r o p e r t i e s i n terms of  b u l k m o d u l u s , a n d Y o u n g ' s m o d u l u s c a n be p r o p e r l y e v a l u a t e d for  t h e i n t e r f a c e e l e m e n t by c e r t a i n  tests,  then  i t i s possible to utilize  matrix d i r e c t l y  types of experimental t h e same c o n s t i t u t i v e  f o r t h e i n t e r f a c e element w i t h o u t any  modification. In t h i s c a s e ,  t h e normal and shear  i n t e r f a c e element a r e e x p r e s s e d  behaviour  of the  i n terms of e l a s t i c  m o d u l u s , B, Y o u n g ' s m o d u l u s , E, a n d t h e P o i s s o n ' s  bulk  ratio,  u.  F o r t h e two d i m e n s i o n a l c o n d i t i o n , E q . ( 7 . 3 . 7 ) t h e r e f o r e becomes :  0 0 0  (7.3.7)'  0  where 3B + E 2(1+I>)  3B - E 2(1+o) E 2(1+y)  The  v a l u e s o f B a n d E c a n be e i t h e r c o n s t a n t s f o r l i n e a r  1 92 elastic  behaviour  nonlinear e l a s t i c  or f u n c t i o n s of s t r e s s l e v e l behaviour  f o r the  a s d e f i n e d by u s i n g h y p e r b o l i c  function. For t h e subsequent a n a l y s e s of l a t e r a l l y CONOIL h a s  b e e n m o d i f i e d so t h a t t h e p r o p o s e d  element can be e a s i l y  be  i n c o r p o r a t e d and  the  corresponding  piles,  interface  i n t e r f a c e behaviour  s p e c i f i e d as e i t h e r b i l i n e a r  or n o n l i n e a r e l a s t o - p l a s t i c  input  loaded  elasto-plastic  can  model  m o d e l by a s s i g n i n g a  n e g a t i v e v a l u e o f Rf  (-1  < Rf < 0)  i n the  data.  7.4.2  DEFORMATION AND  STRENGTH CHARACTERISTICS  Since the proposed  i n t e r f a c e elements  t h i n as compared t o t h e o t h e r s o i l failure criterion regarded  of the  a s g o v e r n e d by  are  elements,  the s t r e n g t h or  i n t e r f a c e element can the adhesion  r e s i s t a n c e at the s o i l - p i l e  and  relatively  be  basically  frictional  interface. Therefore,  i t can  g e n e r a l l y proposed  t h a t d u r i n g the l o a d i n g process  i n t e r f a c e elements  h a v e t h e same d e f o r m a t i o n  as the a d j o i n i n g s o i l i n t e r f a c e adhesion  and  elements,  frictional  m o b i l i z e d . Such a treatment  may  p r e s e n t a n a l y s i s of l a t e r a l l y i n t e r f a c e between s o i l  and  linear  shear  strain  the  pile  the  characteristics  soil-pile  r e s i s t a n c e are  fully  be a c c u r a t e e n o u g h f o r t h e  l o a d e d p i l e s where  monotonic r e l a t i v e d i s p l a c e m e n t s loading. Furthermore,  until  be  the  only involves simple under the s h o r t term  as the element i s r e l a t i v e l y  a c r o s s the element can  and static  thin,  be a g o o d  the  1 93 representation slip)  of t h e r e l a t i v e displacement  between t h e r i g i d p i l e  elements  (or r e l a t i v e  and t h e a d j o i n i n g  soil  elements. The usually  strength related  c h a r a c t e r i s t i c s of i n t e r f a c e elements a r e  to the strength  surrounding s o i l For the p i l e condition  resistance  by c e r t a i n c o e f f i c i e n t s ( P o t y o n d y ,  installed  i s usually  term s t a t i c  c h a r a c t e r i s t i c s of the  loading.  i n the saturated  clay,  a s s u m e d i n an a n a l y s i s  the undrained  under t h e s h o r t  I n t h i s c a s e , t h e maximum  at the s o i l - p i l e  interface  i s often  a f r a c t i o n of the u n d r a i n e d shear s t r e n g t h  1961).  shear expressed as  of the c l a y  deposit, i . e .  C  where C  a  soil-pile  = a.C  i s t h e maximum i n t e r f a c e  shear r e s i s t a n c e ,  a d h e s i o n , a i s an a d h e s i o n  undrained shear  strength  c a s e s where t h e p i l e the f r i c t i o n a l often  (7.4.1)  related  of the saturated  i s surrounded  resistance  clay.  u  at the s o i l - p i l e  i s the  In other  by c o h e s i o n l e s s  to the internal f r i c t i o n  cohesionless s o i l  soils,  interface i s  angle of the  , such as :  4> = 0-0  (7.4.2)  i  where  f a c t o r , and C  or the  i s the f r i c t i o n a l  interface, ^ i s a friction  resistance  angle at s o i l - p i l e  a n g l e f a c t o r , a n d <j> i s t h e  194 internal  friction  In p r a c t i c e ,  angle of the c o h e s i o n l e s s s o i l . t h e above a d h e s i o n  f a c t o r and t h e f r i c t i o n  a n g l e f a c t o r a r e b o t h d e p e n d e n t i n v a l u e upon t h e p i l e construction material, pile  s u r f a c e roughness  l o a d i n g c o n d i t i o n as w e l l . A comprehensive the adhesion  f a c t o r and t h e f r i c t i o n  and t h e  c o m p i l a t i o n of  angle factor f o r  v a r i o u s c o n s t r u c t i o n m a t e r i a l s was r e p o r t e d by  Potyondy  ( 1 9 6 1 ) , a n d i s shown i n T a b l e 7.1. Some o f t h e v a l u e s proposed  7.4.3  by P o t y o n d y  will  be u s e d  in this  thesis.  INCORPORATION OF DEFORMATION MODES M o d i f i c a t i o n h a s been made i n CONOIL s o t h a t t h e a b o v e  d e f o r m a t i o n and s t r e n g t h b e h a v i o u r of t h e i n t e r f a c e c a n be i m p l e m e n t e d  i n the f i n i t e  element  procedure.  element Various  d e f o r m a t i o n modes a t t h e i n t e r f a c e c a n be i n c o r p o r a t e d i n t h e a n a l y s i s by e x a m i n g t h e s t r e s s s t a t e s a t t h e i n t e r f a c e element  a n d by a s s i g n i n g d i f f e r e n t d e f a u l t v a l u e s t o t h e  interface elastic As  moduli  when t h o s e d e f o r m a t i o n modes o c c u r .  shown i n t h e Mohr s t r e s s d i a g r a m ,  when a l l t h e p r i n c i p a l  stresses  i n t h e i n t e r f a c e element a r e  c o m p r e s s i v e , and t h e shear s t r e s s , element  remains  interface,  r , developed  l e s s than the f r i c t i o n a l  and the s o i l  isstill  i nthe  r e s i s t a n c e of the  then t h e d e f o r m a t i o n of the element  mode o f ' s t i c k ' surface.  i . e . F i g . 7.7(a),  i s i n the  b o n d e d on t h e p i l e  I n t h i s c a s e , no d e f a u l t v a l u e s a r e a s s i g n e d t o  shear or bulk m o d u l i .  T a b l e 7.1 P r o p o s e d coefficients of s k i n f r i c t i o n between s o i l s a n d c o n s t r u c t i o n  y^/ -^-f " =~^-: Ccs  c  Construction material  UlX  without factor of safety]  Sand 0 0 6 <D< 2-0 m m  Surface finish of construction material  Dry  Sat. Dense  f*  J*  materials  Cohesionless silt  Cohesive granular soil  0-002 < £ > < 0 - 0 6  5 0 % Clay + 5 0 % Sand Consist. I. = 1-0-0-5  Sat.  Dry Dense  Loose  Dense  J*  f*  ft  f*  fc  Clay  £><006  Consist. Index: 10-0-73  f*  fc  0-50  0-25  0-50  Smooth  Polished  0-54  0-64  0-79  0-40  0-68  0-40  Rough  Rusted  0-76  0-80  0-95  0-48  0-75  065  0-35  0-50  0-50  0-80  0-76  0-85  0-92  0-55  0-87  0-80  0-20  0-60  0-4  0-85  0-88  0-89  0-98  0-63  0-95  0-90  0-40  0-70  0-50  0-85  —  Steel  Parallel to grain Wood  | A t right angles to grain <•  Concrete-  mm  Smooth  Made i n iron form  0-76  0-80  0-92  0-50  0-87  0-84  0-42  068  0-40  100  Grained  Made i n wood form  0-88  0-88  0-98  0-62  0-96  0-90  0-58  0-80  0-50  100  Rough  Made on adjusted ground  0-98  0-90  1-00  0-79  1-00  0-95  0-80  095  0-60  100  Oj  a,  "i  03  a  b)  Fig.  7.7  Slip  Stress Conditions  Deformation  c)  with Various  Gapping  Interface  Modes  CTi  1 97 T , reaches  When t h e s h e a r s t r e s s d e v e l o p e d , frictional remain  r e s i s t a n c e but the p r i n c i p a l  compressive,  interface w i l l  r  S  > C  o c c u r . That  + oa.  the r e l a t i v e  n  tan0.  and  a  technique  a c t i o n , and  1000  > 0  (7.4.3) i s r e a c h e d  t o s h e a r i n g and  the e x t r a s t r e s s i n  to the a d j a c e n t elements.  the r e l a t i v e  theory, cohesionless soils  i n c a p a b l e of t e n s i l e  are  iteration  i m p l i e s t h a t the i n t e r f a c e element  resistance  slip  s t r e s s reaches the t e n s i l e  , and  are u s u a l l y completely  stress until  may  the  s t r e n g t h . H e r e i n , the  the s o i l - p i l e  o c c u r r e d when t h e m i n o r  stress  i s g r e a t e r than the s o i l - p i l e  adhesion  i.e.  :  < 0  tensile  tensile interface  s e p a r a t i o n i s assumed t o h a v e  principal  the s e p e r a t i o n c r i t e r i o n  further  i s occurring.  i s a s s i g n e d t o be e q u a l t o t h e s o i l - p i l e  adhesion C  Such a  h a s no  stress, while cohesive s o i l s  s u s t a i n a s m a l l amount o f t e n s i l e  3  i n some  to a small value to simulate  i s t r i g g e r e d to r e d i s t r i b u t e  procedure  a  (7.4.3)  the load shedding  i n t e r f a c e elements  strength  1 f 2  then the shear moduli of those elements  the p l a s t i c  In  soil-pile  1  d e f a u l t e d by a f a c t o r o f  failed  s l i p at the  still  i s , a s shown i n F i g . 7 . 7 ( b ) ,  Thus, i f t h e c o n d i t i o n of Eq. elements,  stresses  the  for  i s i n t e n s i o n and  in absolute value,  cohesionless soils,  or (7.4.4)  198 o  3  < 0 a n d I<r I > C  This condition Strickly criterion stress  3  i s shown i n F i g . 7 . 7 ( c ) . speaking, such a s o i l - p i l e s e p a r a t i o n  o n l y a p p r o x i m a t e l y r e p r e s e n t s r e a l s i t u a t i o n . The  e x a m i n e d s h o u l d be t h e s t r e s s  interface, o .  for cohesive s o i l s  3  i . e . a , rather n  than t h e minor  to the s o i l - p i l e  principal  stress,  However, i n t h e case of l a t e r a l l y l o a d e d p i l e s t h e  critical  a r e a s where t h e g a p p i n g  right behind the p i l e section. the minor  principal stress  perpendicular the minor normal Eq.  normal  stress,  (7.4.4)  i.e. a  i sclose  to the direction  interface,  i s approximate  o r i n other words, i n value to the  a^. T h e r e f o r e , t h e c r i t e r i o n o f  3  may be a g o o d a p p r o x i m a t i o n . On t h e o t h e r h a n d ,  since the stress, interface  probably occur a r e  I n those a r e a s , d i r e c t i o n of  to the s o i l - p i l e  principal stress  would  a, n  perpendicular to the s o i l - p i l e  i s normally larger  than t h e minor  stress,  the application  of t h e minor  gapping  c r i t e r i o n would  provide the results  pile deflection. principal stress,  stress,  principal  principal stress t h a t have  In view of these c o n s i d e r a t i o n s , a , i s used, 3  rather  a , to identify the s o i l - p i l e n  as the larger  t h e minor  than t h e normal separation f o r the  sake of s i m p l i c i t y . When E q . ( 7 . 4 . 4 )  i s s a t i s f i e d i n a element,  shear moduli and bulk moduli a factor  i n t h e element  then  both  a r e d e f a u l t e d by  o f 1000 t o s m a l l v a l u e s . The l o w e r v a l u e s o f s h e a r  modulus w i l l  prohibit  the stress  changes i n t h e element i n  199 the  subsequent  bulk  modulus  simulates  loading  will  the  process,  provide  formation  while  large  of  the  volume  cavity  or  lower  values  changes,  gapping  of  which  behind  the  pile. The of  above  interface  rational the  for  short  procedure  to  incorporate  deformation  is  simple  the  term  procedure  can  presented  in  analysis  static be  sections  INTERFACE  7.4.4  The  element finite  ELEMENT  significant  interface  model  thickness, two  bodies.  element  can  be  and  appropriate shedding various distinct element  it  is  stress  By  in to  layout  and  that  a  at  under  the  above  results  ITS  a  THICKNESS soil-pile  proposed  element thin  of  layer  interface small  of  feature,  same  way  as  programme  and  implement.  the  and  is  possible  soil-pile  choice  of  of to  are  element  solid With  load handle  interface.  discussion  interface  other  incorporation  it  the  material  this  deserve the  the  solid  of  techniques, modes  element  proposed  represents  easy  which  the  fact  virtue  but  piles of  modes  follow.  of  represents  bouundary  deformation features  finite  MESH L A Y O U T AND  the  it  loaded  Justification  which  -  formulated  iteration  mesh  in  and  between  the  feature  lies  essentially  elements,  from  different  programming  laterally  loadings.  seen  the  of  in  the  the  Its  other  finite  thickness.  200  Mesh l a y o u t Unlike Desai's q u a d r i l a t e r a l  thin  e l e m e n t , CONOIL employs t r i a n g u l a r Chapter be  3. T h e r e f o r e a t l e a s t  used t o represent  the  in Fig.  triangular usually that at  the uniform  of the i n t e r f a c e  interface  results strain  since  Additional  stress  gradient  element' and ' d i a g o n a l  interface  mesh l a y o u t  i n an a n a l y s i s .  be s l i g h t l y  to give  better linear  represent  element.  showed t h a t  there  This  of t r i a n g u l a r  may  element f o r  d e t a i l s of the t r i a n g u l a r  may n o t be o f i m p o r t a n c e .  i s no  from t h e ' c r o s s  e l e m e n t ' mesh l a y o u t .  simulation  higher  i . e . the four  the r e s u l t s  i n the a p p l i c a t i o n  As  a c r o s s the i n t e r f a c e  interface  between  e l e m e n t so  e l e m e n t . However, s u c h a  numerical analyses  difference  that  may  four  c a n be m a i n t a i n e d  e l e m e n t s , c a n more a c c u r a t e l y  t h a n one q u a d r i l a t e r a l  indicate  layer  i t s composite elements,  triangular  significant  interface  e l e m e n t ' c a n be e x p e c t e d  extremely high  layer  interface  such as  the areas which a r e  involved  the computing c o s t  than the q u a d r i l a t e r a l  the  to replace  t h e e x p e n s e o f more e l e m e n t s  'cross  layer,  should  7.8(a) or the ' d i a g o n a l  by one q u a d r i l a t e r a l  the uniformity  a consequence,  the  interface  elements  7.8(b). F o r the c r o s s element,  elements a r e used  covered  interface  elements as d i s c u s s e d i n  two t r i a n g u l a r  ' c r o s s e l e m e n t ' shown i n F i g .  element'  layer  element  Aspect  Ratio = L/t  (a) ' C r o s s E l e m e n t '  Fig.  7.8  Mesh L a y o u t f o r T r i a n g u l a r  (b) ' D i a g o n a l E l e m e n t '  Interface  Element  202 Element  thickness  With regard thickness,  to the c h o i c e  an a s p e c t  ratio  of i n t e r f a c e element  i s d e f i n e d as the r a t i o  average  l e n g t h , L, o f t h e i n t e r f a c e e l e m e n t  height,  t , a s shown i n F i g . 7.8. S i m i l a r t o D e s a i ' s  layer the  i n t e r f a c e element,  i n t e r f a c e behaviour  the q u a l i t y using  of the  to i t s thin  of the s i m u l a t i o n of  t h e p r o p o s e d model d e p e n d s  upon t h e t h i c k n e s s o f t h e i n t e r f a c e e l e m e n t . I f t h e thidkness the  i s too l a r g e i n comparison with  surrounding  elements,  behave e s s e n t i a l l y computational large  difficulties  of t h i c k n e s s  considered  will  element. I f i t i s too s m a l l ,  may a r i s e ,  especially  when a  parametric element  f a c t o r t o be  this  c a n be r e s o l v e d by  performing  s t u d i e s i n which t h e p r e d i c t i o n s from the f i n i t e  results  experimental proposed  i s , t h e r e f o r e , an i m p o r t a n t  i n the a p p l i c a t i o n of the proposed i n t e r f a c e  element. I d e a l l y ,  7.4.5  as a s o l i d  i n t e r f a c e element  number o f e l e m e n t s a r e i n v o l v e d i n an a n a l y s i s . The  choice  will  the thin  the dimension of  with  various  observations.  t h i c k n e s s a r e compared  A p r e l i m i n a r y assessment  i n t e r f a c e model a n d t h e c h o i c e  be d e s c r i b e d  i n the next  with of the  of the t h i c k n e s s  section.  PRELIMINARY ASSESSMENTS - DIRECT SHEAR CONDITION The  condition  relative  slippage  was s i m u l a t e d  element. A schematic illustrated  i n the d i r e c t  Using  shear  test  the proposed i n t e r f a c e  diagram of the d i r e c t  shear  i n F i g . 7.9(a) and the c o r r e s p o n d i n g  test i s interface  (b) F i n i t e (a) S c h e m a t i c o f D i r e c t  Fig.  Shear  7.9  Condition  Simulation  Direct  of D i r e c t  Shear  Element Shear  Mesh f o r  Condition  Testing  to o oo  204 element  mesh l a y o u t i n F i g . 7 . 9 ( b ) . The b o t t o m  the element  mesh was p i n - c o n n e c t e d , a s s u m i n g  shear d i s p l a c e m e n t s . Therefore the r e l a t i v e interface stress,  boundary of  no n o r m a l a n d slip  across the  l a y e r c a n be s i m u l a t e d by a p p l i e d a n u n i f o r m  T , on t h e u p p e r  s u r f a c e of the i n t e r f a c e  The s t u d y was p e r f o r m e d cohesionless s o i l  shear  elements.  i n b o t h c o h e s i v e s o i l and  using two-dimensional plane  c o n d i t i o n , and t h e b i l i n e a r  elastic-plastic  strain  material  b e h a v i o r was a s s u m e d f o r b o t h m a t e r i a l s . The m a t e r i a l p r o p e r t i e s e m p l o y e d i n t h e s t u d y a r e p r e s e n t e d i n T a b l e 7.2.  Cohesive  soils  Numerical  s t u d i e s were p e r f o r m e d  i n cohesive  soils  u n d e r t h e u n d r a i n e d c o n d i t i o n s . The u n d r a i n e d s h e a r s t r e n g t h of  the s o i l  i s a s s u m e d t o be 7.5 K p a . The i n i t i a l  c o n d i t i o n assumed i n t h e i n t e r f a c e e l e m e n t s w i t h a normal interface applied  stress,  stress  i s isotropic  a , o f 30 Kpa a c t i n g n o r m a l n  l a y e r , and t h e u n i f o r m shear s t r e s s ,  to the  T ,is  i n c r e m e n t a l l y on t h e t o p o f i n t e r f a c e e l e m e n t s , a s  shown i n F i g . 7 . 9 ( b ) . The a s p e c t r a t i o s  s t u d i e d a r e 1, 10,  100, 1000.  a) S h e a r  stress  distribution  T a b l e 7.3 shows t h e r e s u l t s o f c a l c u l a t e d at for  each  i n t e g r a t i o n p o i n t of four l i n e a r  the a p p l i e d shear  aspect  ratios.  stress,  shear  triangular  T , o f 4 KPa u n d e r  stress elements  different  205 Table Soil  Properties  Parameters  Cohesive  C (Kpa) 4> (°) A0 (°) 0cv (°) Kg K v n m R E (Kpa) B (Kpa) a (Kpa)  7.5  u  f  Elements  S o i l s Cohesionless  s  B o t h c o h e s i v e a n d c o h e s i o n l e s s s o i l s a r e a s s u m e d t o be elasto-plastic; N e g a t i v e Rf i s f l a g t o i n d i c a t e t h e i n t e r f a c e e l e m e n t s ; E, B a r e t h e Y o u n g ' s a n d b u l k m o d u l u s r e s p e c t i v e l y f o r the s o i l s . As shown i n t h e t a b l e , t h e t h i c k n e s s  element i n f l u e n c e s  the shear  of t h e i n t e r f a c e  stress d i s t r i b u t i o n across the  interface layer  s i g n i f i c a n t l y . When t h e a s p e c t  equal to u n i t y ,  i . e . the composite  same t h i c k n e s s stress  as i t s l e n g t h ,  i s extremely  i n t e r f a c e element has the  e r r a t i c i n each element.  i n t e r f a c e e l e m e n t becomes l a r g e r shear  ratio is  the d i s t r i b u t i o n of  i n t e r f a c e e l e m e n t becomes t h i n n e r ,  i.e.  than  shear  As t h e  the aspect  r a t i o of  10, t h e c o n d i t i o n  of  stress d i s t r i b u t i o n across the i n t e r f a c e layer i s  improved. is  Soils  38° 0.0° 0.0° 986.9 1316.0 0.375 0.0 0.0 -1 10.0x10 13.3x10" 477.0  6  n  2. 3.  for Interface  59.21 9869.0 0.499 0.0 0.0 -1 6000 10 30.0  B  1.  7.2  As an e x t r e m e c o n d i t i o n ,  1000, t h e s h e a r  in which  case  when t h e a s p e c t  stress d i s t r i b u t i o n i s extremely  the values of c a l c u l a t e d  shear  ratio uniform,  s t r e s s a t each  206 Table  7.3  Shear S t r e s s D i s t r i b u t i o n w i t h i n I n t e r f a c e Element at I n t e g r a t i o n Points ( f o r Cohesive S o i l s ) Element I n t e g . No. Points  1.  L/t=1  Aspect L/t=10  Ratios L/t=100  L/t=1000  1  1 2 3 4 5 6 7  -2.6526 -6.7057 -2.6370 -4.7919 -2.4023 -4.8011 -3.9984  -4.2994 -3.9235 -4.0450 -3.9655 -4.1871 -4.1155 -4.0893  -4.0054 -3.9982 -4.0006 -3.9990 -4.0033 -4.0019 -4.0014  -4.0001 -4.0000 -4.0000 -4.0000 -4.0000 -4.0000 -4.0000  2  1 2 3 4 5 6 7  -2.6446 -2.6446 -6.7099 -4.7986 -4.7986 -2.4018 -3.9997  -3.9043 -3.9043 -3.7551 -3.8253 -3.8253 -3.9132 -3.8546  -3.9982 -3.9982 -3.9971 -3.9976 -3.9976 -3.9982 -3.9978  -4.0000 -4.0000 -4.0000 -4.0000 -4.0000 -4.0000 -4.0000  3  1 2 3 4 5 6 7  -6.7057 -2.6526 -2.6370 -2.4023 -4.7919 -4.8011 -3.9984  -3.9235 -4.2994 -4.0450 -4.1871 -3.9655 -4.1155 -4.0893  -3.9982 -4.0054 -4.0006 -4.0033 -3.9990 -4.0019 -4.0014  -4.0000 -4.0001 -4.0000 -4.0000 -4.0000 -4.0000 -4.0000  4  1 2 3 4 5 6 7  -2.6535 -6.7033 -2.6535 -4.7993 -2.4117 -4.7993 -4.0034  -3.9585 -3.9834 -3.9585 -3.9717 -3.9570 -3.9717 -3.9668  -4.0002 -3.9977 -4.0002 -3.9989 -4.0004 -3.9989 -3.9994  -4.0000 -4.0000 -4.0000 -4.0000 -4.0000 -4.0000 -4.0000  The a p p l i e d s h e a r s t r e s s a t t h e s u r f a c e e l e m e n t i s -4.0 K p a .  integration point  of i n t e r f a c e  of four t r i a n g u l a r elements are equal,  they a l l correspond t o the exact value  of shear  stress  a p p l i e d on t h e t o p o f c o m p o s i t e i n t e r f a c e e l e m e n t . T h i s therefore,  and  suggest that the shear s t r e s s c o n d i t i o n  may,  across  207  the  interface  simulated ratio  of  by  b)  than  shear  soils,  layer  as  are  the  displacement  aspect  ratios  of  shown  in  proposed  7.4,  the  be  ultimate  shear  the  and  segment  also  initial  relatively  displacement rather  both  than  curve a  one,  is  sudden  the  shown  of  is  shear  in  showing  form  slippage  for  the  aspect  in  7.4  and  Fig.  in  the  ratio  7.10,  Fig.  stress  the  for  5  For  the  KPa,  by  vs  than  relative  occur.  7.10,  interface  relative  of  a  the  gradual  larger  ratios  displacement.  about  displacement  shear  of  thickness  slip  about  The whole a  the  strength  relative  the  7.10.  smaller the  stress  aspect  relative  resistance  However, Table  as  set  results  Fig.  7.10,  for  e x p e c t e d , has  element,  undrained  soft.  as  predicted  to  underestimating the  in  shear  each  various  predicted before  equal  for  displacements  Since,  typical  Fig.  element,  interface  would  7.4.  with  Table  and  aspect  large,  applied  d i f f e r e n c e among  shown  on  relative  Table  10 a r e  the  predicted  a  the  soils.  the  1 and  The  ratio  of  only  effect  aspect  of  associated  interface  displacement  in  that  resistance  diagram,  significant  the  functions shown  ratios,  in  results  properly  sufficiently  and  ratio  thinner  is  displacement  invisible  the  element  be  provided  cohesive  become  As  model,  can  for  aspect  relative  shear  10  interface  large  direct  interface  cohesive  and 'aspect  of  proposed  larger  Relative For  of  the  the  instance,  layer  30  %,  response  is  relative deformation layer. 10,  as  shown  displacement  208 Table  7.4  A p p l i e d Shear S t r e s s vs R e l a t i v e Displacement of I n t e r f a c e Element under V a r i o u s A s p e c t R a t i o s Shear S t r e s s (Kpa) 0.0 2.0 4.0 5.0 6.0 7.0 8.0 9.0  3.  — —  0.0 0.010540 0.021085 0.026357 0.031628 0.036899 0.073145 9.099900  0.0 0.00100 0.00200 0.00250 0.00300 0.00350 0.00400 8.79380  0.0 0.00010 0.00020 0.00024 0.00030 0.00035 0.00040 0.8748  L/t=1  Cohesionless L/t=l0  soils L/t=100  L/t=1000  0.0 0.028803 0.057605 0.537270 10.79608  0.0 0.00275 0.00550 0.00826 0.08949 30.3666  0.0 0.00028 0.00055 0.00083 0.00862 77.5750  N o r m a l s t r e s s e s on i n t e r f a c e e l e m e n t s u r f a c e a r e 30 Kpa f o r C o h e s i v e s o i l s a n d 477 Kpa f o r c o h e s i o n l e s s s o i l s respectively; R e l a t i v e displacement of i n t e r f a c e element i s i n u n i t mm; L / t i s the aspect r a t i o of the i n t e r f a c e element.  response and  L/t=1000  0.0 0.61715 1.71240 31.6680  0.0 100.0 200.0 300.0 400.0 500.0  2.  Soils L/t=100  0.0 0. 18201 0.36401 0.91234 69.1570  Shear s t r e s s (Kpa)  1.  Cohesive L/t=l0  L/t=1  exhibit  an a l m o s t  resistance relative  bilinear  horizontal  c u r v e w i t h an i n i t i a l line after  steep  line  the u l t i m a t e shear  i s reached. This i n d i c a t e s that the i n i t i a l  displacement  i s very s m a l l , then a l a r g e  s l i p p a g e o c c u r s when t h e u l t i m a t e r e s i s t a n c e  relative  is fully  mobilized. In all  t h i s case, the p r e d i c t e d u l t i m a t e r e s i s t a n c e s are  about 8 KPa, which  shear  s l i g h t l y overestimates the undrained  s t r e n g t h of the i n t e r f a c e  l a y e r . The e r r o r  i s less  o  —•©  L/t  H  — h  L / t = 10  1  0.0 J  2.0 1  = 1  -  1  4.0 1  RELATIVE  r — — — 6.0 i  1  8.0 1  DISPLACEMENT(MM)  1  1 10.0  1  .  . 12.0  o  1  . 14.0  ELASTIC-PLASTIC  .  CLAY  r  . . . 1 r6 . 0  Cu-1 5KPA  F i g . 7.10 R e l a t i v e D i s p l a c e m e n t v s I n t e r f a c e R e s i s t a n c e under V a r i o u s L / t R a t i o f o r C o h e s i v e  Soil  18.0  20  210  than  7 %.  However,  considering  the  such  results  incremental  are  nature  satisfactory of  the  when  numerical  procedure. Therefore, soil  the  relative  simulated aspect least  ratio  10  under  considered %,  condition with  was  elements. resistance  The  aspect  analyses.  for  the  tests  of  that  interface  for  the  layer  cohesive  can  be  by  the  proposed  model,  and  be  sufficiently  large,  such  direct  were  shear  of  frictional in  stress, applied  test  the as  at  condition.  be  T  =  s  ratios  performed  dense  angle  the a , n  The  <t>^ =  to  the  n  of  tan0. I  1,  =  10,  as  373  100,  cohesionless  477 on  layer  relative  Kpa. the  was  density  initial  elements  theoretical  calculated  a  of  3 8 ° . The  interface equal  in  interface  sand  incrementally  Therefore, can  also  conditions.  consist  assumed  normal  stress  should  drained to  and  concluded  soils  Numerical  80  be  slippage  used  Cohesionless  =  may  satisfactorily  being  soils  it  was  of  ultimate  stress  isotropic  Uniform  top  shear  interface shear  :  Kpa R  1000  were  used  Dr  in  the  21 1 a) S h e a r s t r e s s d i s t r i b u t i o n For the i n v e s t i g a t i o n of shear within  the  i n t e r f a c e elements,  stress distribution  a s e r i e s of n u m e r i c a l  were p e r f o r m e d under v a r i o u s a s p e c t element. T y p i c a l shear  one,  r e s u l t s are t a b u l a t e d  s t r e s s , r , e q u a l t o 200 As  r a t i o s of the  interface  i n T a b l e 7.5  for  KPa.  shown i n t h e t a b l e , f o r t h e a s p e c t  the shear  studies  r a t i o equal  to  s t r e s s d i s t r i b u t i o n i s v e r y random w i t h i n  four l i n e a r t r i a n g u l a r elements, improved as the a s p e c t  however, the c o n d i t i o n  r a t i o becomes l a r g e r t h a n  e x t r e m e c o n d i t i o n , when t h e a s p e c t t h e d i s t r i b u t i o n of shear  ratio  10. As  i s equal to  s t r e s s a c r o s s the  the is an  1000,  interface  e l e m e n t s i s v e r y u n i f o r m , v a l u e s of the shear  s t r e s s at each  i n t e g r a t i o n p o i n t of the four t r i a n g u l a r elements are identical,  and  equal to the a p p l i e d  b) R e l a t i v e d i s p l a c e m e n t As  and  f o r the c o h e s i v e s o i l ,  displacements are presented applied  shear  shear  stresses  and  shear  stress.  resistance  the p r e d i c t e d r e l a t i v e  i n Table aspect  7.4  as f u n c t i o n s  r a t i o s of  of  interface  e l e m e n t . I n a d d i t i o n , the r e s u l t s f o r the a s p e c t r a t i o s of 1,  10,  100 a r e a l s o  Similar  illustrated  r e s p o n s e . When t h e a s p e c t i n t e r f a c e model p r e d i c t s initial  7.11.  to the r e s u l t s f o r c o h e s i v e s o i l s ,  r a t i o has a g r e a t i n f l u e n c e on  large  in Fig.  ratio lower  the  aspect  the r e l a t i v e displacement i s s m a l l , the ultimate  shear  r e l a t i v e d i s p l a c e m e n t s , and  the  proposed resistance initial  and  212 Table  7.5  Shear S t r e s s D i s t r i b u t i o n w i t h i n I n t e r f a c e Element at I n t e g r a t i o n P o i n t s ( f o r Cohesionless S o i l s ) Element Integ. No. Points  Aspect L/t=10  Ratios L/t=100  L/t=1000  1 2 3 4 5 6 7  -77.881 -328.31 -48.089 -180.29 -81.045 -113.69 -114.37  -210.56 -197.62 -199.95 -198.08 -205.71 -204.34 -202.71  -200. 17 -199.95 -200.02 -199.97 -200.10 -200.06 -200.04  -200.00 -200.00 -200.00 -200.00 -200.00 -200.00 -200.00  2  1 2 3 4 5 6 7  -80.942 -171.82 -356.16 -265.61 -145.10 -195.24 -254.93  -195.69 -195.69 -195.38 -195.52 -195.52 -195.70 -195.58  -199.94 -199.94 -199.91 -199.93 -199.93 -199.95 -199.93  -200.00 -200.00 -200.00 -200.00 -200.00 -200.00 -200.00  3  1 2 3 4 5 6 7  -345.77 -205.24 -146.29 -165.62 -248.47 -283.22 -232.44  -197.62 -210.56 -199.95 -205.71 -198.08 -204.34 -202.71  -199.95 -200.17 -200.02 -200.10 -199.97 -200.06 -200.04  -200.00 -200.00 -200.00 -200.00 -200.00 -200.00 -200.00  4  1 2 3 4 5 6 7  -146.58 -321.21 -194.30 -264.40 -161.44 -236.26 -220.70  -200.21 -196.57 -200.21 -198.28 -200.42 -198.28 -199.00  -200.01 -199.93 -200.01 -199.97 -200.01 -199.97 -199.98  -200.00 -200.00 -200.00 -200.00 -200.00 -200.00 -200.00  1  t  1.  L/t=1  The a p p l i e d s h e a r s t r e s s on t h e s u r f a c e o f i n t e r f a c e e l e m e n t i s -200 K p a .  p o r t i o n of r e l a t i v e d i s p l a c e m e n t curve  is relatively  flat.  A s t h e a s p e c t r a t i o becomes l a r g e r , i . e . t h e i n t e r f a c e e l e m e n t becomes t h i n n e r ,  the p r e d i c t e d  becomes s m a l l e r , a n d t h e i n i t i a l  initial  p o r t i o n of  displacement  relative  0.0  4.0  "i  i  8.0  RELATIVE  i  i  12.0  i  i  16.0  i  DISPLACEMENT(MM) Fig.  i  20.0  i  i  :  24.0  i  i  28.0  ELASTIC-PLASTIC  7.11 R e l a t i v e D i s p l a c e m e n t  i  i  32.0  r  36.0  40 .0  SAND DR=8CU  vs I n t e r f a c e Resistance  under V a r i o u s L / t R a t i o f o r C o h e s i o n l e s s  Soil  ro  oo  214 displacement larger of and  than  bilinear  c u r v e becomes s t i f f e r .  For the aspect  100, t h e r e l a t i v e d i s p l a c e m e n t  curve  ratio  i s i n form  with n e g l i g i b l e displacements at the beginning  enormous d i s p l a c e m e n t s a f t e r  the ultimate resistance i s  predicted. For the p r e d i c t i o n  of u l t i m a t e r e s i s t a n c e , the proposed  m o d e l c a n p r e d i c t a c o n s i s t e n t v a l u e o f 400 KPa i f t h e aspect r a t i o  i s kept  The o v e r p r e d i c t i o n  larger  than  100, a s shown i n T a b l e  7.4.  i s a b o u t 7% a s c o m p a r e d w i t h t h e  t h e o r e t i c a l v a l u e . T h e r e f o r e , i n c o n s i d e r a t i o n of the shear s t r e s s and r e l a t i v e d i s p l a c e m e n t  simulation,  the appropriate  a s p e c t r a t i o may n e e d t o be a s l a r g e a s 100 f o r c o h e s i o n l e s s soils  i n the d i r e c t  shear  conditions.  Summaries In direct  summary, b a s e d shear c o n d i t i o n ,  on t h e a b o v e n u m e r i c a l s t u d i e s f o r i t i s found  that the proposed  i n t e r f a c e model can s a t i s f a c t o r i l y p r e d i c t  the ultimate  r e s i s t a n c e and t h e r e l a t i v e  s l i p of the i n t e r f a c e ,  that the appropriate aspect  ratio  i s s e l e c t e d . The a s p e c t  r a t i o of t h e i n t e r f a c e element has a s i g n i f i c a n t the s i m u l a t i o n of both shear displacement,  provided  s t r e s s and  i t s h o u l d be d e t e r m i n e d  effect  on  relative  by p e r f o r m i n g  p a r a m e t r i c s t u d i e s f o r d i f f e r e n t problems a t hand. For the d i r e c t  shear c o n d i t i o n , based  r e s u l t s , an a p p r o p r i a t e a s p e c t range  on t h e f o r e g o i n g  r a t i o may be s u g g e s t e d  o f 10 t o 100 The h i g h e r number seems t o be more  i n the  215 appropriate  f o r the cohesionless  note t h a t the range of aspect  soils.  ratio  same a s t h a t s u g g e s t e d by D e s a i  I t i s interesting to  s u g g e s t e d above i s t h e  (1984) f o r h i s t h i n  i n t e r f a c e element, i n which Desai  simulated  shear c o n d i t i o n and compared t h e r e s u l t s analyses The  w i t h those  from d i r e c t  t h e same  direct  from f i n i t e  element  s h e a r box t e s t i n g s .  above p r e l i m i n a r y assessments of t h e p r o p o s e d  i n t e r f a c e model and t h e c h o i c e b a s e d on t h e n u m e r i c a l study  layer  of element t h i c k n e s s a r e o n l y  parametric  studies. Although  such a  i s e s s e n t i a l f o r t h e v e r i f i c a t i o n and a p p l i c a t i o n o f  the proposed model, t h e u l t i m a t e proof appropriate studies  o f t h e model and t h e  s e l e c t i o n of element t h i c k n e s s would  i n which f i n i t e  experimental  require  element r e s u l t s a r e compared  observations,  such as d i r e c t  shear t e s t  with data.  S u c h c o m p a r i s o n s a r e n o t a c c o m p l i s h e d h e r e i n due t o l a c k o f the a p p r o p r i a t e  experimental  d a t a , and i t i s b e l i e v e d  they a r e beyond t h e scope of t h i s t h e s i s . T h e r e f o r e , researches  may be w a r r a n t e d  in this  P-Y c u r v e s ,  to  simulate  interface effects  t h e p r o p o s e d i n t e r f a c e m o d e l w i l l be e m p l o y e d  the s o i l - p i l e  i n t e r f a c e element aspect parametric  further  direction.  In the f o l l o w i n g s t u d i e s of s o i l - p i l e on  that  i n t e r f a c e behavior.  There t h e  r a t i o w i l l be s e l e c t e d b a s e d on t h e  s t u d i e s w i t h comparison of c l o s e d form  solution.  8.  8.1  FINITE  STUDIES  ON L A T E R A L L Y  LOADED  PILES  INTRODUCTION Almost  some  all  degrees  crucial  are  piled  where  of  of  oil  research  into  laterally  and  have  far,  a  number  researchers. available  each  the  soil  springs,  analysis.  linear of  or  the  in  Sec.  these  given  approaches However,  approach, replaced a  that by  versatile  Thus,  there  more  an and  is  springs  a  216  large  recent  and  more  of  more  active  been four  research  proposed groups  problem. 2.2. its  the  array  advantages it  and  appears in  in  that  which  uncoupled  practical continuous P-Y  review  discussed  approach of  by  of  A brief  As  balance,  (or  accurately.  are  is  to  engineering.  has  on  practice  activated  and  have  of  nonlinear  analysis  approaches  analysis  is  provides  foundation  The  abutment,  Problems  important  in  spring  domain  an  there  was  have  r e c e i v e d more  general,  defficiencies.  Winkler  design  of  and  bridge  problem.  least  require  exposed  designs  at  loadings.  Moreover,  In  approaches  2.2,  have  of  piled  pressures.  become  So  the  kind  piles  them  to  geotechnical  usually  traditional  mechanics  certain  the  this  of  lateral  in  or  platform  soil  these  Sec.  earth  kind  are  subjected  Some  the  wall  foundations  in  methods  this  retaining  loaded  attention,  of  drilling  are  loadings.  withstanding  lateral  offshore  many  in  problems  pile  foundations  lateral  earth  the  amounts  area  piled  designs  traditional  of  ELEMENT  way  for  need  curves)  to  used  routine define in  this  217  The of  Fig.  concept 8.1  installed pile  (Reese  into  section  would  be  zero.  This  of  et  the  at  experiences  lateral  load,  an  a  is a  the  be  soil  in  unbalanced  soil  it.  this  unbalanced  stress  distribution  soil  reaction,  P,  exerting  as  illustrated  in  Fig.  is  dependent The  relationship  soil  a  on  8.1(c).  or  the  of  of  would  front  This  reaction  is  the  pile  to  the be  pile  a  surface  Y,  and  the of  resultant of  the  pile,  pressure, of  describing  the  such  referred  a  of  integration  resultant  often  on  force  would  give  deflection, curve  Y due  the  been  loadings  When  the  aid  acting  reaction  state  result,  the  lateral  function of  As  with  has  state  8.1(b).  front  behind  section.  soil  stress  in  pile  lateral  deflection  increase  the  any  Fig.  decrease  upon  the  stress  resulting  shown  illustrated  After  before  lateral  stress  can  1977).  depth  with  section  stress  al,  certain  situation  with  curves  ground,  isotropic  gene'rated  P-Y  P,  pile a  to  as  P-Y  curves. In  Winkler  discreted program  COM622  (Reese,  1977).  is  usually  replaced  by  deformation  controlling  For  along  segments  are  the  the  several  nonlinear  and  approach,  into  reaction  curves  spring  generally the  flexible  piles in  of  P-Y  each  P-Y of  non-linear.  soil  encountered  a  behavior  shapes  ultimate  such  At  pile  is  its  length,  segment,  curve. soils,  The  curves  usually  Due the  the to  at  practice,  their the  of  P-Y  elements  the  initial  heads  which  large  in  the  slope,  resistance. loaded  as  soil  shapes  important are  such  lateral  are  F i g . 8.1 Concept of P-Y c u r v e s  219  deflection  of  piles,  the  in  areas  range p u  and  near  while  reactions curve.  ultimate entire the  the  in  are  pile  curve  mainly  soil  based  curves  are  tests.  This  offshore is  both  on  time  and  site-oriented. for  the It  A  is  well  spring  approach  curves  must  range  of  piles,  which  are  is  must  and  other  effects.  P-Y  curves  reaction,  P,  is  u  in  the  of  from  code,  P-Y  on the  that  finite  element  it  in  the  current given  is  in  accuracy P-Y  are these  the  design  this and  of  approach is  also  approaches Section of  to  2.3.  Winkler's These  mechanism  which  P-Y  load  nonlinearity,  analyses  slope,  approach.  curves.  desirable  its  of  lateral  of  soil  along  which  field,  deformation  incorporate  in  the  the  the  curves  However,  was  short,  spring  popular  specified  soil  Therefore,  field  the  shape  P-Y  the  of  initial  in  curves  the  of  1974).  review  the  in  soil  portion  the  method  the  consuming  of  Winkler  development  the  mobilized  and  t  head,  result,  resistance,  relatively  evaluations P ]_ >  soil  initial  fully  especially  (API  relies  they  effects.  be  semi-empirical  represent  from  may  established  pile,  these  the  general  the  a  pile  below  of  As  the  cost  development  soil  portion  depth.  far  calculated  platforms  with  ultimate  the  approach  upper  the  factors  the  back  the  resistance,  Conventionally,  the  exceeding  Therefore,  soil  in  decreases  head,  resistance  important  mainly  always  in  rigid  length.  are  or  areas  For  ultimate  are  deflection  approaching  ]_4-f  P-Y  piles  around  interface  compute  the  incorporates  220 In t h i s  Chapter, the  plane s t r a i n c u r v e , and these  8.2  conditions  will  t o examine the  be  element f o r m u l a t i o n  in  used t o compute the  different  f a c t o r s that  P-Y  influence  curves.  PLANE STRAIN MODEL In the  curves,  plane s t r a i n  are  uniformly  direction soil  and  sections  transverseed  by  piles  long,  and  they  loads  in horizontal  movement o f any  cross  s e c t i o n of  pile  i s i n d e p e n d e n t of  of h o r i z o n t a l d i s k section  P-Y  lateral  the  cross  loaded  infinitely  the  the  deformation  Beikae,  f o r the  a n a l y s i s , as  of  1984). A  i s thus t a k e n of  the  the  unit  soil  and  shown i n  8.2.  r a d i u s , a,  d i s k model, a c y l i n d r i c a l  i s embraced a t the  o u t e r r a d i u s , R. large outer radial lateral  and  by  boundary c o n d i t i o n s of the  movement w i l l ( Y e g i a n and  soil  not  section  a soil at a  is  Y.  the  of  domain  of  sufficiently  domain i s f i x e d w i t h  influence  Wright,  concentrated l a t e r a l  s e c t i o n , and  loading  center  pile  t a n g e n t i a l displacements, assuming that  pile  1 9 7 7 ) . The  The  r a d i u s , R,  far f i e l d  pile  and  that  In t h i s  the  rigid  d e v e l o p m e n t of  laterally  b e l o w o r a b o v e i t ( P y k e and  pile  Fig.  the  so  thickness the  model f o r the  i t i s assumed t h a t  embedded i n s o i l s a r e  of  finite  1973,  load,  resulted pile  the  soil  Baguelin P,  no  the region  in  et a l ,  i s applied  on  d e f l e c t i o n i n the  the axis  I  »-  y  Fig.  8.2 ' D i s k ' A n a l y s i s  f o r P-Y C u r v e s  222 S u c h a 2D p l a n e concept  s t r a i n model i s e q u i v a l e n t t o t h e  of Winkler's s p r i n g approach  supporting  each  s p r i n g a c t s i n d e p e n d e n t l y of the o t h e r s , and i s  particularly  reasonable a t depths  s t r e s s e s of overburden to  i n which  h o r i z o n t a l plane  where h i g h  s o i l s may r e s t r i c t  ( M a t l o c k , 1970),  confining  the s o i l  movement  and o u t - p l a n e  d i s p l a c e m e n t may n o t be s i g n i f i c a n t . H o w e v e r , f o r t h e a r e a s near  t h e ground  results  s u r f a c e , c o r r e c t i o n s s h o u l d be made t o t h e  from t h e p l a n e s t r a i n model t o account  confining  stress  r e d u c t i o n due t o t h e p r e s e n c e  f o rthe of f r e e  s u r f a c e a n d 3D d e f o r m a t i o n c o n d i t i o n s ( P y k e a n d B i e k a e , 1984). A s i m p l e s t c o r r e c t i o n t o t h e s o i l s u r f a c e may be s u g g e s t e d  using linear  r e a c t i o n near t h e  interpolation  from t h e  s u r f a c e where p l a n e s t r e s s c o n d i t i o n may be p r e v a i l i n g t o t h e d e p t h where p l a n e s t r a i n c o n d i t i o n  i s more a p p r o p r i a t e .  8.3 CLOSED FORM SOLUTION F o r t h e a b o v e two d i m e n s i o n a l p l a n e s t r a i n m o d e l , a theoretical elastic The  s o l u t i o n c a n be o b t a i n e d i f t h e s o i l  ( B a g u e l i n e t a l , 1977, B a r d e t , displacement  i s linear  1979).  boundary c o n d i t i o n s f o r the s o l u t i o n  are: at  the p i l e U  at  = Y c o s 0 a n d U„ = Y s i n e o  (8.3.1)  the outer boundary, r = R U  and  r  surface , r = a  r  = 0 and U = 0 fj  the p e r f e c t adhesion  fl  (8.3.2)  i s a l s o assumed a t t h e s o i l - p i l e  223 interface.  Displacement The  radial  the  above  the  Airy  closed  Solution and t a n g e n t i a l  displacement function  forms  displacements,  boundary  conditions  a n d c a n be e x p r e s s e d  in polar  coordinates  in 6)  (r,  which  satisfy  are derived the  from  following  (Baguelin  et a l ,  1 977) :  °r  r  B "  U  "  TZ T H 3 - 4 87rE 1-U ±  £  U  ) l n ( r  " r; T { ( 3 - 4 8irE 1-u ±  where  £  U  ratio  seen  the above  from  solutions  from  R.  increases, decrease.  - ? ^ [ ( ^ ) 2  ) l n ( r  5  )  of  As  both  T2  2  lateral  loading  semi-infinite  not provide  response  of  a  three  the  outer  condition,  the outer reality  medium. realistic  soil  domain.  It  plane of  strain  the  outer  R,  R tends  this  under  in a  analytical  solution  meduim.  tend  to the  displacements  displacement soil  c a n be  displacements  the i n f i n i t y  Therefore,  dimensional  and the  displacements  boundary,  to  modulus  boundary,  both  the s o i l  (8.3.4)  displacement  the distance of  (8.3.3)  y  the Young's  that  upon  do n o t e x t e n d  soil  4  - ^ ] } s i n e 3-4u  2  and t a n g e n t i a l  To the extreme  in  _  two-dimensional  the distance  However,  3  elastic  equations  when  - ^ ] } c o s ^  2  the l i n e a r  radial  2  - ^ [ ( ^ ) R +r r  the e l a s t i c  the i n f i n i t y  infinity.  can  2  r  a r e much d e p e n d e n t  boundary,  to  )  E and v a r e r e s p e c t i v e l y  Possion's  model  5  model  for the  224 Linear Winkler  Spring  When s e t t i n g lateral the  0 = 0, a n d r = a t o t h e E q . ( 8 . 3 . 3 ) , t h e  displacement,  lateral  Stiffness  Y, o f t h e p i l e  l o a d , P, i s o b t a i n e d  Y = U (a,  (Bardet,  from  1979), i . e .  0)  r  P  section resulted  1 +o  R  R —a 2  y  Therefore  2  the l a t e r a l  9  2  — — [(3-4 )ln(-) -^-^ 87rE 1-D a R +a 2  27  (-T—)] 3-4u  force dispalcement  (8.3.5)  i s related via  K as f o l l o w s :  P = K Y  (8.3.6)  where K i s t h e s t i f f n e s s o f t h e l i n e a r W i n k l e r it  c a n be s i m p l y d e t e r m i n e d  from Eq. (8.3.5),  s p r i n g , and i . e:  K = M E  where LI i s c a l l e d empirical  s t i f f n e s s c o e f f i c i e n t which r e l a t e s the  'coefficient  fundamental s o i l  (8.3.7)  o f s u b g r a d e r e a c t i o n ' , K, t o t h e  property, e l a s t i c  v a l u e o f K may be r e p r e s e n t i t i v e t h e P-Y c u r v e  a t very  Young's m o d u l u s , E. The  f o r the i n i t i a l  small strain  range.  slope of  225  Boundary and P o i s s o n ' s R a t i o E f f e c t s It the  it  readily  stiffness  strain  For of  showed  that  the  undrained  for  drained  8.3.  The  the  value  to  extreme  boundary of  undrained  cohesive  key  linear  for  Winkler's  difficulties using  two  Stress  to  (8.3.7)  that  two-dimensional  Poisson's  Bardet  on  value  the  of  ratio,  cohesive  Bardet's of  a/R  ratio  where  spring,  plane  and  v,  soils,  the  the  are  in  of of  is  maximum  minimum Poisson's  shown  in  coefficient  Fig.  8.4.  The  especially  for  ratio  is  outer  radius  is  stiffness  of  the  clearly  is  where  stiffness shown  the  results n  and  soils  Poisson's  This  studied  jn. T h e  pronounced,  analysis  K.  modeling  the  selection  model  of  results  are  is  (1979)  coefficient,  cohesionless  proper  disk  the  values  soil  dimensional  close  indicates  three-dimensional  soil  to a  the medium  idealization.  Solution  Unlike the  in  the  ratio,  ratio,  boundary  Therefore, problem  of  stiffness  of  0.25.  influence  0 . 5.  of  conditions  close  versus  ratio  conditions  is  (8.3.5)  from  M,  function  boundary  Poisson's  for  Fig.  a  Eqs.  a/R.  given  effect  ratio  is  ratio, a  from  coefficient,  analysis  boundary  seen  stress  boundary  of  1. e .  R  for  the  solution  solutions the »:  for  have  elastic  displacements  limit  soil  values  medium  when  extends  and the to  stiffness, outer infinity,  226  228  a  P r  =  r  -  =  1- v  a  a  fact, a/R  1- u  Initiation The and  stress  0.1  not  be  However,  the  plasticity  the  soils,  cohesive Tresca's  irreversible major  and  a,,  principal of  the  be  plane for  (8.3.10)  strain  infinite  reasonablly  used  a  3  by  (Baguelin  condition soil  can  medium.  approximated  et  al,  are  In  when  1977).  yield  deformation  P^.,  soil  theory  medium  plastic  is  yield  which  criterion  in  which  when  stresses  initiates  the  commonly  soil  difference  satisfies  used  undergoes in  :  (8.3.11)  u  respectively and  soil.  the  the  elastic  evaluated.  the  principal  stresses,  cohesive  be  the  of  force,  criterion,  2 C  upon  plasticity  lateral  soils,  yield  based  incorporating  can  plastic  minor  are  when  the  =  where  are  valid  of  is  can  solutions  criteria  For  sin0  of P l a s t i c i t y  initiated.  soil  solution  values  than  above  will  two-dimensional  limit  smaller  [(1-2o)(a/r)+(a/r) ] 3  4 na  limited the  (8.3.8)  (8.3.9)  P  -  cos0  r  Therefore, give  [(3-2u)(a/r)-(a/r) ] 3  4 na  C  u  Using  is  the  induced major  the  undrained  this  yield  and  shear  criterion,  minor  strength the  229 lateral  f o r c e i n i t i a t i n g the p l a s t i c  determined  P  as  ( B a r d e t , 1979)  = 2 ir a C  k  deformation,  (8.3.12)  J  r a d i u s . The  occur  i n the s o i l s adjacent  plasticity  a r i g h t angle t o the l o a d i n g a x i s  of c o h e s i v e to the p i l e  used i s t h e Mohr-Coulomb c r i t e r i o n , stress c o n d i t i o n s are s a t i s f i e d a  a 1  x  +  ~° —) + 2a 3  o  3  i s equal to sin0,  3  a  0  the p i l e  plasticity  surface at  where t h e  commonly  yielding  <f> i s t h e  i n which  ratio frictional  isotropic  i n d u c e d m a j o r and is initiated  f - ^ 3-4u  ( -7-4sin 0  +  initiates 1979)  the p l a s t i c i t y  a,,  principal adjacent  3 -  ,  4u  )]-  0  -  the l a t e r a l  i s obtained  (8.3.13)  5  load,  P^  ;  as  :  > = 2 Tr a o K in which  minor  i n the s o i l  1 0  z  U s i n g the Mohr-coulomb c r i t e r i o n ,  (Bardet,  s t r e s s , and  s u r f a c e at angle of 9 t o the a x i s of l o a d i n g :  9 = cos-U  which  criterion  when t h e s t r e s s  i s the i n - s i t u  are r e s p e c t i v e l y the  s t r e s s e s . The to  will  0  a n g l e of s o i l s , a  soil  (9 = ~ ) .  For c o h e s i o n l e s s s o i l s , the y i e l d  (—  is  :  where a i s p i l e initially  P^,  0  [ -7-7sm 0 2  +  —  — 3 -  v i s the Possion's r a t i o ,  iv  ]-°'  5  (8.3.14)  a i s the r a d i u s of  pile.  230 Although the real  s o i l behaviour i s neither  nor  purely elasto-plastic,  are  still  finite  useful  element  t h e above c l o s e d  elastic,  form  solutions  f o r b a s i c assessment of the r e s u l t s  from  program.  8.4 F I N I T E ELEMENT SIMULATION As m e n t i o n e d a b o v e , t h e r e a l elastic,  s o i l behaviour i s neither  n o r even p u r e l y e l a s t o - p l a s t i c ,  n o n l i n e a r , and s t r e s s l e v e l dependent. development o f g e n e r a l c l o s e d  but appears h i g h l y  Therefore,  form s o l u t i o n  i s usually  o b s t r u c t e d . R e c e n t l y , many r e s e a r c h e r s h a v e r e s o r t e d t o t h e finite  e l e m e n t a n a l y s i s t o d e v e l o p t h e P-Y c u r v e s d i r e c t l y  b a s e d on f u n d a m e n t a l s o i l p r o p e r t i e s a n d b e h a v i o u r . of  t h i s approach include the plane s t r a i n analyses performed  by Y e g i a n a n d W r i g h t ( 1 9 7 3 ) , B a r t o n a n d F i n n A t u k o r a l a and Byrne  s i m i l a r . However, t h e r e a r e s t i l l  of  unresolved P-Y c u r v e s ,  i n the f i n i t e  researchers are  some common p r o b l e m s a s  e l e m e n t method f o r development  such as outer boundary e f f e c t s ,  s i m u l a t i o n . Those problems d e s e r v e c a r e f u l context of the f i n i t e pile-soil  8.4.1  (1983),  ( 1 9 8 4 ) , a n d more r e c e n t l y by She ( 1 9 8 6 ) .  B a s i c c o n c e p t s e m p l o y e d by d i f f e r e n t  yet  Examples  interface  studies  i n the  element m o d e l l i n g of l a t e r a l l y  loaded  i n t e r a c t i o n problems.  F I N I T E ELEMENT MESH LAYOUT As u n d e r t h e l a t e r a l  move l a t e r a l l y  l o a d i n g , s o i l and p i l e  section  i n t h e d i r e c t i o n o f l o a d i n g . The a x i s o f  231  loading  is  therefore  movements. half  of  finite nodes  the  provided  element  there that  and  the  dependent, a  antisymmetry  of  can  be  finite  Section the  nonlinear  element  advantages used  for As  of  shown  discreted  the  symmetry P/2  is  is  used  about  not  stress  not  arrive  soil  and  further  at  1973).  employed,  quarter  in  Fig.  2.10,  reduced.  their  method.  and  imposition  Therefore,  boundary,  the  soil are  level level  soil-pile If  such  of  total  as  will on  an  circular  the  number  discussed not  the  degenerate the  8.5.  the  However,  boundary,  unjustifiably  model  assumptions  will  a  Fig.  stress  and Wright,  is  and  made  These  are  displacement  displacement  antisymmetry are  at  semi-disk in  only  into  placed  no  This  symmetry  antisymmetry  will  the  in  in  shown  soils,  present  are  load,  as  this  analysis  an  condition,  are  illustrated  strain  stress  (Yegian  elements  2.3.4,  is  soil  discreted  ensure  boundary.  above  and  is  rollers to  assumptions  boundary used  the  exists  failure  occur  of  of  boundary  8.2  characteristics.  soil  tensile  Fig.  boundary  the  modulus  the  seperation  disk  also  strain  in  analyses to  boundary  symmetry  series  to  certain  soil  A  symmetry  additional  boundary,  where  disk  domain.  the  symmetry  this  perpendicular  In  stress  of  circular  along  finite  that  view  element  induced for  In  the  exist  in for  finite  the  semi-disk  model  is  studies. Fig.  into  8.5,  linear  condition applied  at  of  both strain the  the  soil  region  triangular  displacement,  pile  center,  the  and  pile  section  elements. a  Due  concentrated resulting  to  233 displacement procedure  a t t h i s node i s u s e t o p r o d u c e P-Y c u r v e s .  w i l l be a c c u r a t e when t h e p i l e  relatively  reality,  extends  CONSIDERATION  t h e s o i l medium i s s e m i - i n f i n i t e , a n d  to the i n f i n i t y  purpose of f i n i t e  in horizontal direction.  element a n a l y s i s , a f i n i t e  always chosen t o represent t h e i n f i n i t e As  elements a r e  rigid.  8.4.2 OUTER BOUNDARY In  This  shown i n t h e f o r e g o i n g e l a s t i c  soil  For the  medium i s medium.  c l o s e d form  solution,  t h e r a d i u s o f t h e o u t e r b o u n d a r y , R, h a s a g r e a t i n f l u e n c e on  the two-dimensional  displacement,  plane-strain solution for  and consequently  on t h e c a l c u l a t e d  o f s u b g r a d e r e a c t i o n , K. T h e r e f o r e , the outer  s e l e c t i o n of  r a d i u s , R, i s a k e y p r o b l e m i n t h e a n a l y s i s u s i n g  two-dimensional  finite  e l e m e n t a n a l y s i s , a n d h a s been  e x a m i n e d by s e v e r a l r e s e a r c h e r s Scott,  the proper  coefficient  ( B a g u e l i n e t a l , 1977,  1981 a n d S h e , 1 9 8 6 ) .  B a g u e l i n e t a l (1977) i n t e r c o n n e c t e d t h e s t r a i n obtained  f r o m 2D a n d 3D a n a l y s e s . The 2D s t r a i n  n e a r t h e p i l e was o b t a i n e d b a s e d on t h e e l a s t i c s o l u t i o n , w h i l e t h e 3D s t r a i n  field  used  c l o s e d form  f i e l d a t f a r f i e l d was f r o m  t h e M i n d l i n ( 1 9 3 6 ) p o i n t f o r c e s o l u t i o n . And t h e y the outer  fields  determined  r a d i u s i n s u c h a way t h a t t h e d i s p l a c e m e n t s  c a l c u l a t e d a t t h e i n t e r s e c t i o n p o i n t o f 2D, a n d 3D s t r a i n f i e l d s a r e t h e same. From t h e c o m p a r i s o n o f W i n k l e r ' s solution with the e l a s t i c  continuum s o l u t i o n , Baguelin e t a l  234 recommended t h a t t h e o u t e r b o u n d a r y r a d i u s f o r t h e ' d i s k ' analysis  i n undrained  cohesive  soils:  a) P i l e s w i t h f r e e h e a d s s u b j e c t t o l o a d s a t t h e h e a d  R = 7 1  for flexible piles  0  R = 3 h  (h/l >7/3)  (8.4.1)  0  (h/l <7/3)  for rigid piles  (8.4.2)  0  b) P i l e s w i t h f i x e d h e a d s s u b j e c t e d t o l o a d s a t t h e h e a d  R = 12 1  0  R = 8 h  for flexible piles for rigid  piles  (h/l >1.5) (h/l <1.5)  is  stiffness  the r i g i d i t y  of s o i l For half  0  i s the 0  section, E  g  2  5  ,  (EI) p  i s the c o e f f i c i e n t  reaction.  the c o h e s i o n l e s s d r a i n e d s o i l s ,  o f t h e a b o v e v a l u e s s h o u l d be u s e d .  s e l e c t i o n of outer may  and 1  f a c t o r d e f i n e d a s [ 4 ( E I ) /E ] ' p s  of the p i l e  subgrade  (8.4.4)  0  where h i s t h e embeded l e n g t h o f p i l e s , relative  (8.4.3)  0  r a d i u s depends  they  suggested  that  Therefore,  upon s e v e r a l f a c t o r s ,  and  n e e d t o be e x a m i n e d f o r e a c h p r o b l e m . I t i s a l s o  apparent  from t h e i r  flexible  piles  r e s u l t s that the a n a l y s i s f o r fixed-head  i n undrained  cohesive  soils  requires largest  o u t e r boundary r a d i u s . For  finite  elastic  medium o f s a n d s , b a s e d on  or F i g . 8.4), Scott  (1981)  Bardet's  results  ( s e e F i g . 8.3  compared  Winkler  s p r i n g s o l u t i o n u s i n g K = E ( i . e . (i = I i n  235 Eq.  (8.3.7))  with elastic  continuum s o l u t i o n , and r e p o r t e d  t h a t t h e o u t e r b o u n d a r y o f 50 p i l e r e s u l t s that agreed  r a d i u s would  with h i s c e n t r i f u g e test data  More r e c e n t l y , She ( 1 9 8 6 ) s t u d i e d t h e o u t e r effects using f i n i t e  strain s o i l s the  on t h e  s l o p e o f t h e p r e d i c t e d P-Y c u r v e s , b u t n o t s o g r e a t  the ultimate s o i l  cohesionless s o i l s ,  r e s i s t a n c e , P ,.. W h i l e f o r ult t h e o p p o s i t e r e s u l t s were o b s e r v e d .  e f f e c t s o f mesh r a d i u s on b o t h lower  boundary  cohesive  e f f e c t s of o u t e r boundary r a d i u s a r e s i g n i f i c a n t  on  i n sands.  element a n a l y s i s . Under p l a n e  c o n d i t i o n s , She showed t h a t f o r u n d r a i n e d  initial  provide  the i n i t i a l  s l o p e and t h e  p o r t i o n s h a p e o f t h e p r e d i c t e d P-Y c u r v e s  s i g n i f i c a n t as i n c o h e s i v e resistance,  p u  i / t  was f o u n d  soils,  The  a r e not as  but the u l t i m a t e  t o be s e n s i t i v e  soil  to the v a r i a t i o n  o f mesh r a d i u s . H o w e v e r , t h e c o n c l u s i o n f o r c o h e s i o n l e s s s o i l s may n e e d f u r t h e r v e r i f i c a t i o n s . B a s e d on t h e a b o v e r e s u l t s , r a d i u s o f t h e 2D f i n i t e meaningful  prediction  selection  of the outer  e l e m e n t mesh d o m a i n i s c r u c i a l  of i n i t i a l  c l a y s , but not t h a t important  fora  s l o p e s o f t h e P-Y c u r v e s i n  f o r the o v e r a l l  shapes and t h e  u l t i m a t e values of the curves. F o r t u n a t e l y , the design of the l a t e r a l l y  loaded p i l e s  moderate s t r a i n s a t working strains. Therefore,  i n c l a y s i s mainly loads r a t h e r than  the plane  analysis  f o r P-Y c u r v e s  remaining  difficulties  g o v e r n e d by initial  s t r a i n model o f f i n i t e  is still  useful despite the  i n outer boundary  selection.  small element  236 In pile  the f o l l o w i n g  diameter  (D)  s t u d i e s , an o u t e r r a d i u s o f 50  i s s e l e c t e d f o r the f i n i t e  a n a l y s e s of p i l e s  i n undrained  the average values suggested (if  cohesive  element  soils.  This value i s  by B a g u e l i n e t a l and  K = E, R = 83 D f r o m F i g . 8.4  for cohesive  25 and  f o r the p i l e s  50 p i l e  in cohesionless s o i l s ,  diameter  8.4.3  two  radii  curves  of  boundary  for cohesionless  soils.  INTERFACE ELEMENT In  order t o s i m u l a t e the deformation  soil-pile of  i n Appendix  are used t o e v a l u a t e the  r a d i u s e f f e c t s on t h e P-Y  Bardet  soils).  D e t a i l s of c a l c u l a t i o n of t h i s v a l u e are g i v e n B. W h i l e  times  i n t e r f a c e under the l a t e r a l  mechanism a t  loadings, a thin  the ring  i n t e r f a c e elements  was  p l a c e d around the p i l e  perimeter  a s shown i n F i g . 8.5.  The  b a s i s f o r the proposed  thin  i n t e r f a c e elements procedures The  the r e l a t i v e  the s o i l - p i l e  l o a d i n g s . The  s l i p p a g e and  (see Table  i s to soil  7. represent  flow around  s e p a r a t i o n under s e v e r e  s t r e n g t h c h a r a c t e r i s t i c s of the  are r e l a t e d to those  the adhesion  numerical  i n Chapter  purpose of i n t e r f a c e elements  and  elements  the corresponding  were d i s c u s s e d i n d e t a i l  approximately pile,  and  factor,  7.1).  a, and  of the a d j a c e n t  the  frictional  the  lateral  interface soil  angle  medium  by  f a c t o r , |3  In the subsequent a n a l y s i s , v a r i o u s v a l u e s  0 i n Table  of  a, and  7.1  a r e employed t o study  of  i n t e r f a c e p r o p e r t i e s on  t h e P-Y  curves.  the i n f l u e n c e  237  In  the  application  special  attention  (Desai,  1984).  0.6m  diameter  undrained soil for  is the  pile  (Potyondy,  to  soil  The the  (L/t) the  aspect  The  ultimate  plasticity  Kpa,  is  The  8.5. 3,  which  the  are  a  the  of  the  factor  used  are  concrete  pile  assumed  Bilinear  and  Table  with  different  definition  The  resistances in  strength  with  500  elastic  assumed.  performed  2,  solution  = 0.5,  elements.  under  adhesion  elements  Fig.  soil  a  the  a  thickness  performed  soils  shear  pile  soil  is  cohesive  and  element,  element  study  the  the  of  is  the  and  element.  ratio  to  clay  were  in  in  interface  soft  behavior  shown  given  undrained  7.5  And  than  interface is  be  thin  parametric  The  the  studies  be  elements  1961).  stronger  plastic  of  to  interface  a  the  installed  condition.  correspondent  times  should  Herein  assumed  of  of  the  p r e d i c t e d P-Y  12 a r e are 8.1  shown  Fig.  with  (Randolph  and  ratio  aspect  curves  in  compared  aspect  ratio  under  8.6(a).  the  classic  Houlsby,  1984). As  shown  the  predicted  the  thin  soil  P-Y  resistences  the  equals that  Fig.  P  The  In  are  best  this  ,./C D = ult u  compared  with  very  initial  However,  sensitive  to  between  value  found  case  the  was  finite  This  theoretical  elastic  insensitive  agreement  11.556.  the  are  elements.  theoretical 3.  8.6(a),  curves  interface  thickness. and  in  the  the  when  value  is of  in  the  of  thickness  predicted  the  element  value  to  portions  of  ultimate  element predicted  the  aspect  method an  error  10.820  in  value ratio  predicted of  6.8%  Table  as  8.1.  238 Table  8.1  P l a s t i c i t y Solution of U l t i m a t e S o i l Resistance on L a t e r a l C i r c u l a r P i l e i n C o h e s i v e S o i l s a  p  ult/ u c  0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1. 2. 3.  D  9. 1 42 9.527 9.886 0.220 0.531 0.820 1 .088 1 .336 1 .563 1 .767 1 .940  a i s the s o i l - p i l e adhesion f a c t o r , a = C /C ; D i s the p i l e diameter; R e s u l t s a r e a f t e r Randolph and Houlsby ( 1 9 8 4 ) . a  Increases  i n t h i c k n e s s of the i n t e r f a c e  the aspect r a t i o of 3 t o 2 r e s u l t e d in the predicted significant  ultimate  i n the i n i t i a l  the p i l e d e f l e c t i o n  soil  of about  element  from  i n an i n c r e a s e o f 7.7%  resistance,  portion  u  but not  o f t h e P-Y c u r v e up t o  1.2% p i l e d i a m e t e r .  However,  i n c r e a s e o f t h e a s p e c t r a t i o f r o m 3 t o 12, i . e . r e d u c e t h e element  t h i c k n e s s of the f i r s t  problem  which  spoiled  i t e r a t i o n performance, at  the load  plastic starting  well  ring, resulted  the convegence of load then a b o r t i n g  below t h e u l t i m a t e  s o l u t i o n , and a l s o  resulted  from t h e d e f l e c t i o n  shedding  the e n t i r e  calculation  v a l u e g i v e n by t h e i n a soften  a t about  T h e r e f o r e , r e g a r d i n g the element contradiction  i n a numerical  P-Y  curve  0.7% p i l e d i a m e t e r . thickness,  a  e x i s t s between t h e above r e s u l t s and t h o s e  o o  ©O I.F. ASPECT RATI0=3  Q 2 : CO  1 1  1 1  0  —e>  (Pile  I °-°  6  -0  I  I  12.0  I 18.0  I  I 24.0  I  I 30.0  1  1  1  36 0  DISPLACEMENT Y - MM D=0.6M, DEPTH=5M.  1  1  42 0  COEFF  1  = 500«Soil)  1  48 0  oi = 0.5  1  54 0  1  60 .0  (a) Fig.  8.6  Effects of Interface  Element L / t r a t i o  co vo  240 shown i n C h a p t e r  7. As shown i n C h a p t e r  s h e a r c o n d i t i o n where e l e m e n t s s u b j e c t e d t o pure element  7,  f o r the simple  were o f u n i f o r m s i z e  shear s t r e s s , the proposed  and  interface  c a n go a s t h i n a s 0.1-0.01 o f i t s l e n g t h w i t h  satisfactory such a t h i n problems  s t r e s s and d i s p l a c e m e n t p r e d i c t i o n s . triangular  element  i n a l a r g e problem  e s p e c i a l l y when m i x e d  will  However,  generate numerical  w i t h complex l o a d i n g  with different  s i z e of  conditions,  elements.  S e v e r a l a t t e m p t s were made t o u s e t h e i n t e r f a c e of  higher aspect r a t i o ,  would soil of  i t was  found t h a t the a s p e c t  increase to 5 i f r e l a t i v e stiffness  i s reduced  r a t i o of p i l e  f r o m 500  both  ratio  stiffness  t o 100. And  p r e d i c t i n g the u l t i m a t e r e s i s t a n c e  element  to  the accuracy  i s marginally  i n c r e a s e d , a s shown i n F i g . 8 . 6 ( b ) . This result pile  element  i n d i c a t e s that the r e l a t i v e  s t i f f n e s s t o the s o i l  element  some i n f l u e n c e s on t h e c h o i c e o f i n t e r f a c e  r a t i o of  stiffness  stiffness will  prohibit  i n t e r f a c e e l e m e n t s , maybe due ill-condition Cook  of the g l o b a l  (1981)  has  element  t h i c k n e s s . L a r g e r d i f f e r e n c e between the s o i l element  the  and  t h e use of v e r y  pile  thin  t o t h e r o u n d - o f f e r r o r and  the  stiffness matrix.  suggested that  i n o r d e r t o have a good  s o l u t i o n of s t r e s s u s i n g t r i a n g u l a r elements, the a s p e c t r a t i o of t h e element load shedding  be e m p i r i c a l l y  iteration  b a s i s . Very t h i n  procedure  triangular  stress solution especially  i n t h e r a n g e o f 3-4.  i s based  element  may  on a  generate  i n complex problems,  stress erratic and  The  o  o-  -© L / t = 12 -+ L / t = 5  2:0 ^ 00  L/t=3 -x L / t = 2  1  V  1 6.0  LATERAL  12.0  1  1  18.0  DISPLACEMENT  1  1  24.0  -  ~~  (Pile = lOO"Soil)  1 30.0  1  1  r — 1  36 0  Y (MM) C U = 7 . 5 K P A  42 0  1  48.0  54.0  (X: = 0 . 5 D l A M =0.6M,  (b) F i g . 8.6 E f f e c t s o f I n t e r f a c e  1  Element L / t r a t i o  60 .0  242 t h e r e f o r e engender n u m e r i c a l load shedding  problems i n the convergence of  iteration.  B a s e d on t h e a b o v e p a r a m e t r i c  s t u d i e s , an a s p e c t  o f 3 was s e l e c t e d f o r t h e t h i c k n e s s o f t h e i n t e r f a c e in  a l l the f o l l o w i n g analyses. This s e l e c t i o n  agreeable ratio  t o the rule-of-thumb  of t r i a n g u l a r Although  elements suggested  ratio,  to illustrate  pile  The  factor  i s the fact that the s o i l  d e f o r m a t i o m mechanism  in  of the really  elements next t o  s m a l l so as t o r e p r e s e n t  closely.  f o r e g o i n g and f o l l o w i n g a n a l y s e s  p r o p e r t i e s c a n be a c h i e v e d  ratio  i n t h e s i m u l a t i o n . The  agreements w i t h c l o s e d form s o l u t i o n  the  the aspect  t h e above and f o l l o w i n g  e l e m e n t s s h o u l d be r e l a t i v e l y  the s o i l  i s generally  by C o o k .  that the aspect  e l e m e n t s may n o t be i m p o r t a n t important  element  t h e i n t e r f a c e elements employed a r e not very  thin' i n terms of aspect studies tend  for selecting  ratio  show t h a t good  under v a r i o u s  with satisfactory  i n t e r f a c e elements with aspect  ratio  interface  accuracy,  when  of 3 a r e employed  t h e a n a l y s e s . In g e n e r a l , t h e e r r o r i s o n l y about  7%.  8.5 COHESIVE SOILS The  a n a l y s e s a r e b a s e d on t h e u n d r a i n e d  approach, as d i s c u s s e d i n Chapter types of s o i l  total stress  3. I n t h e a n a l y s i s ,  models a r e employed f o r t h e c o h e s i v e  three  soils,  namely: 1.  Bilinear  elastic  plastic  model,  2.  Bilinear  elastic  plastic  with tension cut-off  model,  243 3.  Nonlinear The  to the  hyperbolic  w i t h t e n s i o n c u t - o f f model.  c o n s t i t u t i v e law  classic  of  elasticity  purpose of u s i n g  and  the  first  model i s  plasticity  t h i s model i s t o o b t a i n  theories. finite  s o l u t i o n s which are comparable to the c l o s e d The failure the  s e c o n d and of  soils,  t h i r d models i n c o r p o r a t e  model, the  i n f l u e n c e of  soil-pile  separation  on  evaluated  f o r the cohesive  8.5.1  soil  t h e p r e d i c t e d P-Y  element  the  tensile  results with  cracking c u r v e s can  and be  soils.  S O I L PROPERTIES Soil  Elements  In present pile  the  The  form s o l u t i o n s .  t h e r e f o r e , by c o m p a r i n g t h e  first  equivalent  installed  considered. saturated  The  analysis, a relatively in a normally normally  l o n g and  flexible  consolidated clay  was  c o n s o l i d a t e d c l a y was  w i t h a u n i t w e i g h t of  7  assumed  . = 16 KN/m , and 3  fully  an  S3. L  undrained shear s t r e n g t h which i n c r e a s e s o v e r b u r d e n s t r e s s as C  in  which  For  the  = 0.25  u  follows:  a;  (8.5.1)  i s e f f e c t i v e overburden pressure a n a l y s i s of u n d r a i n e d c o h e s i v e  deformation strength  w i t h the e f f e c t i v e  modulus are  soil,  o f t e n r e l a t e d to the  i n t e r m s o f m o d u l u s number, M,  i.e.  at the the  depth.  elastic  undrained  shear  244 E = M C  (8.5.2)  u  A g a i n , a v a l u e o f 800 was  used i n the a n a l y s i s . With the  g i v e n Y o u n g ' s m o d u l u s t h e b u l k m o d u l u s c a n be d e t e r m i n e d u n d e r c e r t a i n assumed v a l u e s o f P o i s s o n ' s r a t i o . Y o u n g ' s a n d b u l k m o d u l u s number, K program  are then b a c k - c a l c u l a t e d  E  and K  from Eq.  The  employed  g  (4.1.5)  elastic i n the  and  (4.1.6) . Under t h e u n d r a i n e d c o n d i t i o n , t h e i n i t i a l m o d u l i a r e assumed i n d e p e n d e n t o f t h e t o t a l  elastic  stress  level,  hence  t h e above modulus e x p o n e n t s , m and n a r e e q u a l t o  zero,  i . e . m = n = 0. So m o d u l u s numbers a r e d e t e r m i n e d a s  follows:  where P  K  E  K  B  E  -  /  B  P  (8.5.3)  a  (8.5.4)  / a P  i s the atmosphere  a  The  soil  presented  Pile  =  p r e s s u r e = 101.33  parameters employed  i n Table  KPa.  i n the a n a l y s i s  are  8.2.  Elements In  the a n a l y s i s ,  the p i l e  elements are  basically  t r e a t e d as s o i l  elements but p o s s e s s i n g s t i f f n e s s  s t r e n g t h o f 500  times those f o r s o i l  d e f o r m a t i o n and  failure  i n the p i l e  and  elements to l i m i t  the  e l e m e n t s . In g e n e r a l ,  245  T a b l e 8.2 Parameters of E l a s t o - p l a s t i c S o i l , P i l e and I n t e f a c e E l e m e n t s i n t h e F i n i t e E l e m e n t A n a l y s e s o f P-Y C u r v e s Soil Parameters C  u  Soil Elements  (Kpa)  7.5  <t> (°) K  9869.0  n m Rf  1. 2.  V  0  (Kpa)  59.21  500  x 59.21  9869.0  500  x  9869.0  0.0 0.0 0.0  0.0 0.0 0.0  0.0 0.0 0.0  0.499 80.0  0.499 80.0  0.499 80.0  i s regarded as e l a s t i c  a n a l y s e s . I t s parameters  Interface  elements  material  i n a l l the  a r e a l s o p r e s e n t e d i n T a b l e 8.2.  Elements  As d i s c u s s e d i n C h a p t e r  7, t h e p r o p o s e d  thin  interface  for the s o i l - p i l e interface are basically  formulated  i n t h e same way a s t h e s u r r o u n d i n g s o i l  T h e r e f o r e , they g e n e r a l l y  elements  s t r e n g t h s a r e r e a c h e d . The i n t e r f a c e the adjacent s o i l  elements.  f o l l o w t h e same s t r e s s - d e f o r m a t i o n  c h a r a c t e r i s t i c s as t h e s o i l  before t h e i r  a a n d 0 r e p o r t e d by P o t y o n d  interface  s t r e n g t h s were  s t r e n g t h i n terms  a, a n d f r i c t i o n a l a n g l e f a c t o r  (see  x 7.5  500  The p i l e e l e m e n t s a r e 5 0 0 t i m e s s t r o n g e r i n s t i f f n e s s and s t r e n g t h than s o i l e l e m e n t s ; a i s the s o i l - p i l e i n t e r f a c e adhesion f a c t o r .  the concrete p i l e  to  Pile Elements  a  7.5  59.21  E  KB  o  Interface Elements  of adhesion  related factor,  /3. The e x p e r i m e n t a l v a l u e s o f  (1961)  were u s e d  i n the analysis  T a b l e 7 . 1 ) . The i n t e r f a c e p r o p e r t i e s a r e a l s o  presented  246 in Table  8.5.2  8.2.  RESULTS AND Factors  finite  DISCUSSIONS  a f f e c t i n g t h e p r e d i c t i o n of P-Y  curves  e l e m e n t m e t h o d were e x a m i n e d s e p a r a t e l y  in  from  the  analysis. The using  p r e d i c t e d P-Y  the  values  first  of the  curves from f i n i t e  model a r e  presented  i n t e r f a c e adhesion  adhesion f a c t o r s represent pile  The various  the of  interface the 0.0  1.0.  curves curves  under  a a r e compared w i t h B a r d e t ' s e l a s t i c  closed  form  (see  Section  8.3).  element a n a l y s e s  and  i n T a b l e 8.3.  same a s  i n the  finite  t h e p r e d i c t e d P-Y 0.2%  Results closed  100  pile  slope at such a s t r a i n  elastic  where a level  plastic  form s o l u t i o n are form s o l u t i o n , the  r a d i u s was  element analyses.  curves are  (Ay/a),  o f two  In the c l o s e d  boundary r a d i u s of  l e v e l of  various  o f t h e p r e d i c t e d P-Y  tabulated outer  a =  o f t h e P-Y  i n i t i a l slopes  solution finite  slopes  f a c t o r , a. The  for  from the p e r f e c t smoothness of a =  surface, varying  Initial  i n F i g . 8.7  analyses  the d i f f e r e n t roughness of  t o the p e r f e c t roughness of  1)  element  used, which i s Initial  c a l c u l a t e d at the  i s the p i l e  slopes strain  radius.  Initial  i s correspondent to the  initial  subgrade modulus. From t h e  comparison of  m o d e l s , i t i s shown t h a t t h e  the  r e s u l t s from the  i n i t i a l slopes  first  of the  P-Y  two  o o.  © — — ©€) ADHESION COEFF.a=l.O 1 1  0 —  1 + I - ADHESION  COEFF.a=0.5  —e> • ADHESION COEFF.a=0.0  I  -€)  0.0  i  6.0  i  i  12.0  i  i  i  18.0  DISPLACEMENT Fig.  i  24.0  1  1  30.0  1—n  36.0  1  1  42.P  1  1—  48.0  Y - MM,D-0 . 6 M , C = 7 . 5 K P A , <2=C«/C U  54.0  60.0  U  8.7 F i n i t e E l e m e n t P r e d i c t i o n o f p-Y C u r v e s using  Model  (1) w i t h  Various  o  ro  248 Table  8.3  I n i t i a l S l o p e s o f P r e d i c t e d P-Y C u r v e s under V a r i o u s Adhesion F a c t o r  1.  Adhesion Factor a  Isotropic Model  0.0 0.5 0.8 1 .0  1.1615 1 .2686 1 .2686 1 .2686  Tension Cut-off Model  E E E E  1 . 1468 1.2663 1.2663 1.2663  I n i t i a l S l o p e o f P-Y c u r v e f r o m c l o s e d f o r m s o l u t i o n = 1.162 E, where E i s t h e Y o u n g ' s m o d u l u s o f s o i l medium.  curves are independent  of the t e n s i o n b e h a v i o r of  T h a t i s t o be e x p e c t e d , a s a t d e p t h t h e h i g h confining tensile  stress  in soil  piles,  mass w i l l  stress at small s t r a i n  From T a b l e 8.3, the i n i t i a l  insensitive  have not r e a c h e d t h e i r  full  in-situ  level.  s l o p e s o f t h e P-Y  to the s o i l - p i l e  f o r v e r y smooth  curves are  distinct  the i n t e r f a c e  level,  the i n t e r f a c e  s t r e n g t h s , they s t i l l  interface relative  s t r e n g t h has slip  f e a t u r e s o f s t r e n g t h and  layer w i l l  elements follow  the  soil deformation  o n l y come i n t o e f f e c t s when t h e  been f u l l y  and c a v i t y  generally  interface behavior. This i s  same s t r e n g t h c h a r a c t e r i s t i c s o f t h e s u r r o u n d i n g e l e m e n t s . The  soils.  prevent the f o r m a t i o n of  i t seems t h a t e x c e p t  because at very s m a l l s t r a i n  of  E E E E  m o b i l i z e d , and  of s o i l - p i l e  interface  the have  occurred. S i m i l a r o b s e r v a t i o n s h a v e a l s o been r e p o r t e d by and W r i g h t  ( 1 9 7 3 ) where t h e y u s e d c y l i n d r i c a l  joint  Yegian  249 i n t e r f a c e element w i t h zero t h i c k n e s s to s i m u l a t e soil-pile they  i n t e r f a c e b e h a v i o r . By v a r y i n g t h e c o e f f i c i e n t  found  t h a t the  interface properties affect  p r e d i c t e d u l t i m a t e p r e s s u r e s , b u t do s l o p e s o f P-Y  curves, except  the sake of comparison,  Fig.  In view of t h i s ,  8.8.  not a f f e c t  f o r the case  z e r o . For  their  the proposed  i n t e r f a c e elements,  difference  although  there  a,  the the  initial  of a e q u a l  to  r e s u l t s are  shown i n  i n t e r f a c e element i s  a l s o a b l e t o p r e d i c t t h e same t r e n d s a s t h e z e r o joint  the  is a  i n the c h a r a c t e r i s t i c s w i t h these  thickness  significant two  types  of  elements. As  shown i n T a b l e  8.3,  from the comparison of  model r e s u l t s w i t h c l o s e d form s o l u t i o n , was  obtained  i n the case  of a e q u a l  t h e p e r f e c t smooth p i l e . rough p i l e s ,  a l l finite  t h e o r e t i c a l v a l u e of  to zero, that i s , for  element a n a l y s e s o v e r p r e d i c t  1.162E w i t h an e r r o r a b o u t 9%.  the The  e l e m e n t method i s n o r m a l f o r  incremental nonlinear f i n i t e  as d i s c u s s e d i n Chapter  2)  agreement  F o r o t h e r v a l u e s o f a, t h a t i s , f o r  o v e r - p r e d i c t i o n of f i n i t e conforming  the best  isotropic  the  element f o r m u l a t i o n ,  3.  Ultimate s o i l resistances The  ultimate soil  r e s i s t a n c e s of a c i r c u l a r  predicted  from the f i r s t  Table  under d i f f e r e n t  8.4  corresponding included  two  models are p r e s e n t e d  i n t e r f a c e adhesion  v a l u e s from p l a s t i c i t y  i n t h e t a b l e . As  pile in  factors.  theory are  The  also  shown i n t h e t a b l e , u s i n g  the  200  y (Inches)  8.a  I n f l u e n c e s of I n t e r f a c e  ( a f t e r Y e g i a n and W r i g h t ,  Behavior  1973)  251 Table  8.4  Ultimate S o i l Resistance ( P i t / u ^ P r e d i c t e d P-Y C u r v e s c  °^  D  u  1.  Adhesion Factor a  Isotropic Model  Tension Cut-off Model  Closed Form  0.0 0.5 0.8 1.0  9.333 11.554 12.444 12.889  8.444 9.778 10.666 11.556  9.142 10.820 11.563 11.940  The c l o s e d f o r m s o l u t i o n i s a f t e r R a n d o l p h H o u l s b y ( 1 9 8 4 ) shown i n T a b l e 8.1.  first  model,  i.e. bilinear  elastic  plastic  element method p r e d i c t s t h e t h e o r e t i c a l  model,  limit  a good a c c u r a c y i n a l l c a s e s . G e n e r a l l y , t h e i s a b o u t 7%.  T h i s e r r o r may  be a t t r i b u t e d  and  the  finite  pressure  with  overprediction  to several  reasons. First  o f a l l , due t o t h e i n c r e m e n t a l n a t u r e o f t h e  nonlinear analysis,  the conforming f i n i t e  i s bound  to give s t i f f e r  solution  (Cook,  of the l i n e a r  p r e d i c t i o n of p l a s t i c  strip  reported here l i e s  form  strain  i n the  t r i a n g u l a r element i n  u l t i m a t e l o a d s . S l o a n and  (1982) r e p o r t e d a s i m i l a r using this  r e s u l t s than the c l o s e d  analysis  1981).  Secondly, the error capability  element  Randolph  r a n g e o f a c c u r a c y o b t a i n e d when  type of element t o p r e d i c t the c o l l a p s e  loads for  f o o t i n g . They s u g g e s t e d t h a t h i g h e r o r d e r e l e m e n t s be  used t o o b t a i n b e t t e r Finally,  results.  as mentioned b e f o r e , the s i z e of  e l e m e n t mesh may  also affect  finite  the accuracy, e s p e c i a l l y f o r  252  those  elements  close  to  of  the  limit  next  pile  to  the  section  pressure  would  pile are  be  elements.  refined,  expected  a  As  the  closer  (Sloan  elements prediction  and  Randolph,  1982). In  view  procedure capable As results  and  of  consistent  the  interface  pile  In  this  behavior,  the  indicate  Such  an  solution element  interface context,  for  are  that  affected  by  observation  is  (Randolph  results  elements  the  and  from  (Yegian  proposed  approximately  the  thin  simulating  previous and  interface soil-pile  behavior. the  effects  separation,  model  from (d),  joint  adequate  for  soil-pile  finite  element  here  significantly  properties. form  finite  results.  clearly is  the  employed  interface  resistance  interface  using  of  8.7  and  is  failure  Fig.  1984),  element  As  in  closed  1973).  (c),  influences  in  element  satisfactory  the  Wright,  those  considerations,  with  researchers  cut-off  above  interface  ultimate  soil-pile  As  the  the  shown  Houslby,  the  providing  for  predicted the  of  were  shown of  soil  finite  Table  model,  the  figure,  soils  and  the  reduces  resistances  under  considered  herein.  analyses  Results  as  shown  failure  are in  and  using  compared  Fig.  tension with  8.9(a),  (b),  8.4.  in  markedly  tensile  element  performed.  isotropic and  of  all As  the  incorporation  soil-pile  seperation  of  tensile  behind  the  predicted  ultimate  soil  the  interface  adhesion  factors  shown  in  Table  8.4,  the  the  differences  253  -0  Isotropic  -+  Tension Cut-off  Model Model  -O  A d h e s i o n F a c t o r a - 0.0  4.0  12.0  8.0  LATERAL  16.0  DISPLACEMENTS  €)  Isotropic  +  Tension C u t - o f f Model  20.0  Y  -  MM  24.0  28.0  32.0  (DIAMETER-0.6M.  36.0  40.0  DEPTH=5M)  Model  (b)  -O  A d h e s i o n F a c t o r a • 0.5  I  0.0  6.0  I  I  I  12 0.  I  I  18.0  DISPLACEMENT  Y  I  I  24.0 -  MM  1  30.0  D=0.6M  1  1  36.0  1  1  42 0  DEPTH-5M  F i g . 8.9 P-* C u r v e s f r o m F i n i t e Element ( I s o t r o p i c model V B T e n s i o n C u t - o f f  Prediction Model)  T  i  48.0  r -1 54.0  r  60.0  254  F i g . 8.9  P-Y C u r v e s f r o m F i n i t e E l e m e n t  (Isotropic  model v s T e n s i o n C u t - o f f  Prediction Model)  255 between than  the  10%.  two  From  difference  finite  table,  it  is  becomes  larger  as  the  smaller.  tensile  failure  becomes  more  This of  This  soils  result  likely  to  pile  than  rough  a  may  important  more  the  prediction  of  ultimate  separation)  3) S o i l  changes  is  from  in  8.10(a),  Sect.  soil-pile the  results, soil  in  piles as  resistance,  behavior  are  a  to  of  to  pile  behind  the  have  the  reasonable simulation  soil-pile  masses.  (b),  solution  The  element  perfect  will  stress  analysis  soil-pile  (c). (see  introduce  The Eqs.  stress  distribution using  adhesion  results  the  are  bilinear  model  are  compared  (8.3.8)-(8.3.10)  plotted with  in  8.3)). As  shown  predictions  is  condition.  accurate  (including  be  smooth  loading  order  a  separation  separation  same  factor  simulation  soil-pile smooth  the  adhesion  the  reasonable,  movement  finite  plastic  form  pile  soil  elastic  closed  that  that  larger  Distribution  within  Fig.  above  of  all  necessary.  lateral  predicted  the  are  noted  value  the  under  interface  Stress  The  the  pile  on  soil-pile  and  when  undergo  also  indicate  seems  Based  of  predictions  the  becomes  analysed.  element  in  are  these all  in  figures, good  solution.  This  indicates  functions  well  in  the  the  finite  agreement  that  analysis  the of  with  finite  element closed  element  laterally  form program  loaded  piles.  the  256  — c l o s e d form + f i n i t e element  —i 0.0  1 8.0  1  1 16.0  1  1 24.0  (a)  1  1 32.0  1  1 10.0  1  1 48.0  1  1 56.0  1  1 64.0  1  — C l o s e d form + F i n i t e element cr a. *  1 72.0  r80.0  (b) a„  -I  dp' in LU i — LOO  =>T  0 0  cr  I  I 8.0  1  1  I  16.0  1 24.0  1  1 32.0  1  1 40.0  1  1 48.0  1  1 56.0  1  1 64.0  C l o s e d Form + F i n i t e element  1  (c)  CLin  1 72.0  "j— . 80.0  xy  cr  COo'  in LUo_|  CU ' p—  «"> CCm (X • UJ7' X  cn  8.0  —i 16.0  Fig.  r —i  24.0  8.10  32.0  Soil  r ~i  40.0 40.0  Stress  r 48.0  56.0  Distribution  64.0  72.0  Of.)  257  4)  Nonlinear S o i l In  reality,  stress-strain plastic  stress  strain  stra'in  in  of  it  For  compute  the  P-Y  required  predicted  using  nonlinear  model  is  with  that  shown  curve  from  tension It  for  for  most  follow  shown  hyperbolic  in  Chapter  6,  stress  observations.  predict  the  laterally  stress  loaded  strain  soils.  stress for  that  hyperbolic  field  hyperbolic  elastic  analyses.  showed  as  using  with to  bilinear  element strain  curve  nonlinear  the  analyses were  soils.  hyperbolic  using performed  The  model  to  soil  are  shown  in  8.5. The  P-Y  well  nonlinear  conditions  Moreover,  finite  curve  the  (1970)  test  cohesive  reason,  appear  foregoing  expansion  the  hyperbolic  parameters Table  for  than  Chang  reasonable  using  soils  the  triaxial  agree  is  this  nonlinear  and  cavity  responses  relationship  in  relationship.  relations  Therefore,  rather  assumed  Duncan  soils  predictions  cohesive  behavior  (1963),  cohesive  pile  most  behavior  Konder  Response  the for  observed  is  in  resistance  of  Fig.  from  8.11.  bilinear  cut-off  nonlinear  that  curve  stress-strain  shown  the  P-Y  in  the  For  is  the  initial  the  P-Y  that is  are  element  analysis  tension  cut-off  of  the  comparison,  stress-strain  included  in  shape  generally  plastic  slope  curve  sake  plastic  soils  elastic  with  the  also  figure  cohesive  bilinear  curve  elastic  model  finite  soils.  and  the  not  affected  the of  P-Y  However,  by  soil the  curve  figure.  softer  ultimate  the  curve than It  is  Table Nonlinear  S o i l P a r a m e t e r s f o r FE A n a l y s e s  Parameters C  8.5  Cohesive S o i l  (Kpa)  u  Cohesionless  a  1. 2.  (°) E  K  B  59.21 9869.0 0.0 0.0 0.9 80.0  n m Rf (Kpa)  0  Soil  41° 4° 33° 1500 900 0.5 0.25 0.9 50.0  (°) K  Curves  7.5  <p ( ° )  0cv  o f P-Y  t h e p i l e e l e m e n t s a r e 500 t i m e s s t r o n g e r i n s t i f f n e s s and s t r e n g t h t h a n s o i l e l e m e n t s ; t h e s o i l - p i l e i n t e r f a c e a d h e s i o n f a c t o r a i s assumed t o be 0.5.  n o n l i n e a r i t y of the s o i l s . This result  has i t s p r a c t i c a l  t h a t t h e P-Y c u r v e s  f o r the nonlinear cohesive  constructed s a t i s f a c t o r i l y  by s i m p l y c o n n e c t i n g  s l o p e and t h e u l t i m a t e s o i l The i n i t i a l the  s l o p e c a n be e s t i m a t e d  s o i l medium a c c o r d i n g  be e s t i m a t e d  according  t o the plane  strain  the  initial  elastic  r e s i s t a n c e o f t h e P-Y  from t h e u n d r a i n e d  shear  strength,  t o the f i n i t e element a n a l y s i s u s i n g  plastic  stress strain  tension  failure  of s o i l s , such as the v a l u e s  8.4.  s o i l s c a n be  from Young's modulus o f  elastic  Table  indicating  r e s i s t a n c e u s i n g a smooth c u r v e .  theory, while the u l t i m a t e s o i l can  significance,  curve  curve  C , u  bilinear  which i n c o r p o r a t e s the shown i n  o Q CJ \  CM  © H  © ELASTO-PLASTIC K NONLINEAR  CLAY  CLAY  I to-  LU Cd O o -r\j _  0.0  2.0 NORMALIZED 1.0  3.0 LATERAL Fig.  4.0 5.0 DEFLECTION  8.11 P-Y c u r v e s and N o n l i n e a r  T  forElastic  Soil  T  T  6.0 7.0 8.0 9.0 Y/D ( C = 7 . 5 K P A . D=0.6M)(«io- ) 2  U  Plastic  Soil  10  260  The for  simplest  nonlinear  function  as  P  /  (  C  curve  cohesive  used  u  D  describing soils  -  kind  of  may b e t h e same  for the stress  >  such  strain  P-Y  curve  hyperbolic  relationship,  i.e.  JTil/U)  a  (  8  '  5  -  7  '  where a b  = C /K u  =  C  u  D  /  P  u l t  D  is  the p i l e  K  is  the i n i t i a l close  Hyperbolic nonlinear Fig.  for  soils  function  the above  connection  function  best  of  field  using  data.  in  t h e P-Y modulus  curve, of  Eq.  (8.5.7)  the f i g u r e , to  which  the s o i l  f o r the above  P-Y is  the  represent  medium.  curve  shown  is  for  in  simple t h e P-Y  curves  soils. statements  are subject  t h e above  test  of  c a n be u s e d  cohesive  However,  the  fitting  illustrated  nonlinear  proof  slope  the Young's  curve  cohesive  8 . 1 2 . As  hyperbolic  to  diameter,  results  Therefore,  and t h e  to  further  would  proposed v e r i f i c a t i o n . The  be t h e c o m p a r i s o n  further  research  with  is  warranted.  8.6  COHESIONLESS Similar  the  finite  cohesionless  soils  SOILS  soils.  are considered  criterion.  Due t o  element  analyses  The s t r e n g t h  t o be g o v e r n e d  lack  were  of  closed  also  performed  characteristics by  form  Mohr-coulomb solution  for  of  for the  F i g . 8 . 1 2 H y p e r b o l i c Curve F i t t i n g Cohesive  Soils  f o r P-Y  curves in  262 cohesionless s o i l , S t u d i e s w i l l be  only nonlinear analyses  l i m i t e d on  interface property soil  the outer  e f f e c t on  t h e P-Y  b o u n d a r y e f f e c t and curves.  p r o p e r t i e s used i n the a n a l y s e s  Table  were p e r f o r m e d .  The  the  nonlinear  are a l s o included i n  8.5.  1) Outer Boundary E f f e c t s As  f o r the outer  analyses  with outer  boundary e f f e c t s ,  finite  b o u n d a r y r a d i u s o f 25D  p e r f o r m e d , where D i s t h e p i l e d i a m e t e r . r e l a t i v e d e n s i t y o f 75% r e s u l t s are t h a t the  s i z e of o u t e r  curves  affect  and  were  Dense s a n d  with  I t i s shown i n t h e  figure  the  initial  p o r t i o n of the  for cohesionless soils.  i n the l a r g e displacement  However, the  range. Smaller  the  predicted  s i z e of  d i f f e r e n c e observed  i n the p r e d i c t i o n of d i s p l a c e m e n t  f o r t h e mesh d o m a i n v a r y i n g f r o m 25D  Similar  r e s u l t s w e r e r e p o r t e d by She  the above r e s u l t s a r e not due  2)  to the  The  finite  in a stiffer  15%  response.  likely  due  not  predicted  mesh d o m a i n r e s u l t s  about  The  b o u n d a r y o f t h e mesh d o m a i n d o e s  e l e m e n t mesh d o m a i n d o e s s i g n i f i c a n t l y a f f e c t curve  50D  assumed i n t h e a n a l y s e s .  shown i n F i g . 8.13.  significantly P-Y  was  element  the  largest  to  50D.  (1986).  to numerical  is  Therefore error  s t r e n g t h c h a r a c t e r i s t i c s of c o h e s i o n l e s s  but  soils.  Interface Property E f f e c t s As  f o r the  t h e p r e d i c t e d P-Y  interface property curves  e f f e c t s , F i g . 8.14  for cohesionless  soil  with  shows  264  interface  o f /3 u s e d  range or  f r i c t i o n angle  wood p i l e As  generally  s a t u r a t e d sands  i n F i g . 8.14,  not  affected  by  displacements  of about  20%  displacement by  the  level,  interface  has  influence  Simple As  for  Curve  noted  interface  of t h e p i l e  properties.  of c o h e s i v e  3)  the  soils,  on  the  lend  supports  curves In  8.14,  function,  P/ED  in general, interface  the this  affected unlike property  curves.  soils  can  a l s o be  t o h a v e no This result  curve  as d i s c u s s e d i n S e c .  curves ultimate tends  c o n s t r u c t i o n of  to P-Y  2.3. curves  r e p r e s e n t e d by  for a simple  power  as:  = a  (Y/D)  b  where: a =  appear  t h e above p r e d i c t e d P-Y  such  Beyond  t h e p r e d i c t e d P-Y  at large displacement.  f o r sands,  cohesionless  to  Fitting  to S c o t t ' s b i l i n e a r  fact,  are  p r o p e r t i e s up  soil-pile  nonlinear cohesionless soils resistance  7.1).  curves  are only moderately  Therefore,  The  concrete  (see T a b l e  diameter.  t h e p r e d i c t e d P-Y  i n F i g . 8.13,  soil  1.0.  t o the  t h e p r e d i c t e d P-Y  the c u r v e s  the case less  0.8,  i s generally correspondent  i n d r y and  shown  0 = 0.5,  factor,  0.3798087,  b = 0.54962493,  (8.5.8)  266 As shown  i n F i g . 8.15, t h e power f u n c t i o n Eq  can p r o v i d e a reasonable f i t w i t h the f i n i t e  (8.5.8)  element  p r e d i c t e d P-Y c u r v e s f o r t h e n o n l i n e a r c o h e s i o n l e s s s o i l s . However t h e p r o p o s e d deserves lateral  s i m p l e power f u n c t i o n  further verification load  tests.  by p r e d i c t i n g  f o r t h e P-Y the f i e l d  curve  Fig.  8.15 Soils  Curve F i t t i n g  f o r P-Y  curves  in Cohesionless  9. INSTALLATION EFFECTS ON PRESSUREMETER CURVES AND  P~Y  CURVES FOR LATERALLY LOADED P I L E S I N COHESIVE SOILS  9.1  INTRODUCTION It  i s a w e l l known f a c t t h a t t h e p i l e  d i s t u r b s the s o i l s around t h e p i l e soils soil  t h a t have d i f f e r e n t s o i l deposit. This  lateral  p r o p e r t i e s from t h e n a t u r a l s o i l s has s i g n i f i c a n t  responses, i n c l u d i n g the response t o  loadings.  At p r e s e n t , for  and c r e a t e s a zone o f  zone o f d i s t u r b e d  i n f l u e n c e on t h e p i l e  many a n a l y t i c a l m e t h o d s h a v e been p r o p o s e d  the a n a l y s i s of l a t e r a l l y  Banerjee and D r i s c o l l , a homogeneous s o i l disturbance  loaded p i l e s  deposit  around the p i l e  due t o t h e p i l e  installation  t o be t h e e a s i e s t a p p r o a c h e s installation  assume  shaft, the s o i l  i s usually  ignored.  r e a c t i o n m e t h o d seem  to incorporate  the p i l e  e f f e c t i n the a n a l y s i s .  In t h e subgrade  r e a c t i o n method, t h e i n c o r p o r a t i o n of  pile  installation  soil  r e s p o n s e , i . e . P-Y c u r v e s .  i s v i a the p r o p e r development  the p i l e  the derived  installation P-Y c u r v e s .  of nonlinear  I n t h e development  c u r v e s f r o m t h e back c a l c u l a t i o n o f f i e l d  in  ( P o u l o s , 1971,  1976). However, they g e n e r a l l y  F i n i t e element method and t h e s u b g r a d e  data,  installation  o f P-Y  lateral  load test  effects are i m p l i c i t l y  included  H o w e v e r , s u c h an a p p r o a c h i s  c o s t l y a n d s i t e - o r i e n t e d , a n d i n a d d i t i o n , how t h e d i s t u r b e d soil  zone a r o u n d t h e p i l e  shaft a f f e c t s the s o i l  responses i s not c l e a r . 268  P-Y  269  As  stated  advantages element for  a  in  earlier the  analysis.  material  in  Chapter  2,  there  development  of  One  advantages  of  analysis  such of  P-Y  are  curves  disturbance  several  from a  is  that  effects  2D  it  due  finite  allows to  pile  installation. Moreover, pressuremeter  in  is  as  a  they  process.  Thus  pressure  expansion  can  piles,  curves  for  (Robertson al,  it  represent  loaded  1980,  et  pressure  commonly  believed  kind  of  physical  model  experience becomes  curves  a  a  common  disturbance  that- they  can  loaded  1983,  be  piles  Atukorala  that  pressuremeter  used  obtain  and  pile  the  on  a  the  the  effects  by  the  installation  belief  from  from  that  for  similar  obtained  and  the and  applied is  is  loading  in  pressuremeter  the  subsequent  to  the  simple Byrne,  even  soil  tests  laterally the  scaling 1984,  P-Y factor  Briaud  et  part  examine  difference.  of  the the  to  the  In  in  the  the  former,  latter, the  mechanism  the  pile  and  of  soil  extent  purposes  laterally  pile  installation  loading  same  significant  Although  similar  the  a  tests. while  responses  under  It  in  a  is  between  axisymmetrically.  disturbance. this  mechanism  experience  different  there  direction,  difference  is  that  pressuremeter  one  applied  pressuremeter,  obvious  the  the  generate  curves  is  soil  it  in  piles  is  P-Y  it  the  al,  of  1981).  difference  load  has  laterally  However,  loaded  development  curves,  presssuremeter installation  the  of  this  the  the and  process, may  the  chapter  to  270 In s i z e and  this  c h a p t e r , some o f t h e a v a i l a b l e e v i d e n c e s on  e x t e n t of s o i l  installation analysis  are f i r s t  d i s t u r b a n c e zone a f t e r  based  on p l a n e  formulation,  i n w h i c h b o t h t h e p i l e and  installation  e f f e c t s are simulated.  9.2  EXPERIMENTAL AND  investigations after  installed  h a s b e e n g i v e n by De M e l l o i n t o a deep c l a y  Cummings e t a l ( 1 9 5 0 ) a n d F l a a t e  this  layer,  Driving a pile  reduced  due  interface.  extends  from the  the pile  p i l e d i a m e t e r . Some d i s t u r b a n c e s b e y o n d  conditions, pile  t y p e s , and  are the  procedures. will  c o h e s i v e s o i l s , Lo and  Johannessen  pile  the  zone a r e a l s o o b s e r v e d . O b v i o u s l y , the r e s u l t s  d r i v i n g methods and  a  (1972) r e p o r t e d t h a t  zone measured i n t h e f i e l d  d e p e n d e n t upon t h e s o i l  In  field  (1969).  i s usually  the severe remolding at the s o i l - p i l e  -2.0  SOIL  INSTALLATION  u n d r a i n e d shear s t r e n g t h of the c l a y  s u r f a c e t o 1.5  EXTENT OF  i n t o the e x t e n t of d i s t u r b a n c e around  installation  remolded  pressuremeter  i n c l a y , a summary o f some  If p i l e s are driven  to  element  strain  ANALYTICAL EVIDENCES ON  DISTURBANCE AFTER P I L E For p i l e s  pile  r e v i e w e d , and a f i n i t e  i s then performed  the  change the s t r e s s e s i n the Stermac  ( 1 9 6 0 ) , K o i z u m i and  (1965), Bjerrum  ground.  and  I t o ( 1 9 6 7 ) , O r r j e and  Broms  (1967) a l l r e p o r t e d t h a t h i g h pore p r e s s u r e s i n t h e range 2-4  times the t o t a l overburden  measured near  the t e s t p i l e s  of  p r e s s u r e o r h i g h e r were  (up t o 2 d i a m e t e r p i l e  from  the  271  pile the  face).  effective  driving,  and  These and  that  shown  mainly  after  pile  shear  strength.  In  its  shear  initial  Broms,  1967).  adhesion  C  that  and  low  as  Balaam  et  A  Randolph  al,  the  linear  the  be  Fig.  for  stiff  pile  after 9.2.  failure soil  as  high  end  of  linear the  pile,  dissipate of  undrained  of  in  soft  clays,  somewhat 1972,  the  1.5  (De  a  from  between  as  clays  in  measurements  increase  (Flaate,  cohesion  pile  gradients  pressures  found  correlations  of  of  the  higher  Orrje  than  and  pile-soil  soil  for  C  very  Mello,  u  ,  it  would  soft  clay,  1969,  1975).  logarithm  plastic upon  0.2  often  field  can  cavity.  state in  on  theoretical  cylindrical  shown  the  (at  high  away  the  installed  is  undrained  and Wroth  simulated  stress  Based  C_/C as  few  in  by  time  Field  vary  pore  term  piles  strength  and  a  appear  for  value  excess  reduction  substantially.  have  distance  a  the  time.  pressures  long  at  strength  accompanied the  soil  with  radial The  caused  pressures  radially  9.1.  reconsolidation), undrained  pore  with  driving,  the  shear  induced pore  Fig.  pressure  within  excess  fashion in  pore  stresses  high  the  logarithm  high  reduced the  dissipate  show  as  These  studies  Carter  (1979),  and  driving  process  Randolph pile The  Randolph as  et et  an  al  results  driving  in  Boston  excess with  pore  induced pore  conditions.  As  the  al  of Blue  pressure  radial  (1979), (1979)  are  pressure  of  short  a  term  Clay  varies  distance.  pressures pore  al  expansion  et  fashion and  by  are in  Zones  a of  dependent dissipates,  272  Uo  Bjerrum & Johannessen (1961)  (kN/m ) 2  c ~l5kN/m  ft~70kN/m  2  u  2  I201—  best fit straight line  x  field measurements  eob 40h  Uo  Is  (kN/m ) I2012  \  Koizumi & Ito (1967) c ~30kN/m 2  u  \  0,'~6OkN/m  \ \  2  \ \  x \  40h  \  Uo  \  \  Lo & Stermac (I96S) c ~ 2 0 kN/m , &i~!20 kN/m  IkN/m ) 2  2  2  u  I20h  \x  X  \  SOr \  40h  \ x  \  In lr/r ) 0  r = 2r  Fig.  0  r«5r  0  r»IOr  0  r = 30r  0  9.1 F i e l d M e a s u r e m e n t s o f E x c e s s P o r e Resulting  from p i l e d r i v i n g  W r o t h , 1979)  Pressure  ( a f t e r Randolph and  Boundary of Critical Stat« Region  OCR-8  F i g . 9.2 T y p i c a l  r e s u l t s of s t r e s s  immediately a f t e r p i l e d r i v i n g a l , 1979)  distribution ( a f t e r Randolph e t  274 the  shear s t r e n g t h of s o i l s regains  i t s value.  Randolph e t a l s o l u t i o n of undrained v a r i a t i o n with time,  shear  strength  and w i t h r a d i u s a t end of s o i l  r e c o n s o l i d a t i o n a r e shown i n F i g . 9 . 3 ( a ) ,  ( b ) . The s t r e n g t h  a t t h e end o f c o n s o l i d a t i o n i s about 60% g r e a t e r initial  i n - s i t u v a l u e , and t h i s  ultimate strength  with the logarithm of the radius u n t i l i n - s i t u value  a t about  10 p i l e  than the decreases  i t reaches the  radius.  T h e r e a p p e a r s t o be l e s s i n f o r m a t i o n a v a i l a b e piles for  i n c l a y on t h e e x t e n t  bored p i l e s  the c l a y d u r i n g 0.45 C  u  of d i s t u r b a n c e ,  f o r bored  b u t some  data  i n London c l a y s u g g e s t e d t h a t s o f t e n i n g o f installation  of p i l e s  reduces C  t o about  &  (Balaam e t a l , 1975).  T h e r e i s e v e n l e s s i n f o r m a t i o n on c h a n g e s i n t h e deformation the c y c l i c the post  p a r a m e t e r s . B y r n e e t a l ( 1 9 8 4 ) r e p o r t e d b a s e d on triaxial  cyclic  t e s t data  deformation  on p l a s t i c  clayey  silt,  that  modulus would reduce as low as  by a f a c t o r o f 10. However i n t h e a n a l y s i s , i t i s r e a s o n a b l e t o assume t h a t t h e r a t i o constant  of s o i l  f o r the undrained  (D'Appolonia  total  modulus t o c o h e s i o n i s stress analysis  e t a l , 1 9 7 1 , C l o u g h a n d Denby, 1977,  Byrne e t a l , 1984).  9.3 F I N I T E ELEMENT ANALYSIS  275  16  c [T*| u  Cgl0)  1-4 OCR - I to 32  13  12 II IO IO  IO  _s  -4  IO° » T  Fig.  IO'* IO' Kc lo)t  1  =  IO°  IO  1  u  9.3(a) T y p i c a l v a r i a t i o n w i t h time of undrained shear s t r e n g t h of s o i l a t r=1.15r  0  ( a f t e r Randolph  et a l , 1979)  OCR » I to 32  1 cfl  115  Fig.  I  2  I  I I I I  I  III  IO  r/r  I  I I I I  III  IOO  0  9.3(b) T y p i c a l v a r i a t i o n w i t h r a d i u s of undrained shear s t r e n g t h of s o i l a t end of c o n s o l i d a t i o n ( a f t e r Randolph et a l , 1979)  276 9.3.1  DISTURBANCE SIMULATION Piles On  in Clay  the b a s i s of the a v a i l a b l e e v i d e n c e s  of p i l e  on  the  i n s t a l l a t i o n d i s c u s s e d p r e v i o u s l y , i t has  assumed f o r t h e  finite  element a n a l y s e s  of p i l e s  effects  been in clay  t h a t t h e r e e x i s t s a d i s t u r b e d z o n e t o r a d i u s , r^ a r o u n d pile,  extending  to a depth  shown i n F i g . 9 . 4 ( a ) .  The  of r ^ below the p i l e  from a v a l u e of  to the value E  interface  the outer  limit  analysis,  i . e . plane  laterally  loaded p i l e s .  of t h e  o f t h e d i s t u r b e d z o n e . As  intact  s t r a i n c o n d i t i o n was  disturbed soil  t h e u n d i s t u r b e d and  0.499 t o r e p r e s e n t u n d r a i n e d  modulus to the u n d r a i n e d  assumed t o be  t h e same f o r b o t h Therefore,  s t r e n g t h of the C  , at the ud  soil  Values  i n t a c t and  r^/r  modulus r a t i o  0  of  interface to C  1, 2,  u  to cover  u  t h e e f f e c t s of  0.5,  The  disturbed  soil  soils,  the  linearly  at the outer The  same  from  limit  of  isotropic  regions.  5 h a v e been c o n s i d e r e d , and  1, 2,  the  strength  5 have been a n a l y s e d  installation  to  strength i s  i n d i s t u r b e d z o n e , E^/E^, ( o r s h e a r  r a t i o C j / C ) , o f 0.2, u c  3,  ratio  been t a k e n  i n the d i s t u r b e d zone,  s t r e s s s t a t e i s assumed f o r b o t h of  has  shear  t h e d i s t u r b e d z o n e , a s shown i n F i g . 9.5. in-situ  Poisson's  i s a l s o assumed t o v a r y  soil-pile ^  at  l o a d i n g of the p i l e .  r a t i o of s o i l  800.  soil  T h e r e f o r e , a c r o s s s e c t i o n showing  of b o t h  equals  the  performed f o r the  i n F i g . 9.4(b).  and  at  before, a 'disk'  the a n a l y s i s model i s g i v e n  be  t i p , as  Young's modulus of t h i s d i s t u r b e d  zone i s a s s u m e d t o v a r y l i n e a r l y soil-pile  the  f o r both d r i v e n  so  and  as  A  "7—7  T  - A  Section  7—T  7  (a)  (b) Fig.  9.4  Simulation  of  Installation  for  Pile  Fig.  9.5 Assumed within  modulus and s h e a r  disturbed  strength  variation  zone  ts) CO  279  bored  Full  piles.  Displacement In  this  assumed  for  chapter, the  pressuremeter installation generate  is of  is  full  study  of  usually a  similar  generally  Pressuremeters  full soil  In  disturbance  zone  illustrated  in  as  for  Fig.  9.6(a).  In  Young's  disturbed  zone  limit  values  of  of  of  r^/r  pressuremeter excess  dissipated  the 0  varied  the  of  2, and  there  is  a  simulating pressure  they  would  As  the  P-Y  can  problem the  finite  assumed  the  laterally  shear E, a to  u  Fig.  been  for  loaded  varied,  C  (or  ,) ua C  9.5).  under  the  in  at  )  and the  the  at  the  Again,  considered,  curves  the  strength)  (or  E  is  is  analyses,  are  so  that  same  examined.  with  the  laterally  the  This  element  zone  it  soil  pressuremeter.  (see  developed for  the  similar  from  be  would  pile  disturbed  5 have  the  for  interface  3,  tip,  of  model  for  zone  cone  top  Therefore  undrained  disturbed 1,  the the  the  piles.  this,  linearly  disturbance  pore as  annular  (or  curves  soil  Surely,  the  is  tests.  solid  was  the  conditions  membrane-soil  pressuremeter extent  the  modulus  pressuremeter outer  of  strain  a  As  pressuremeter  as  of  pressuremeter  effects.  with  physical  assumed  expansion  the  a  is  pressuremeter  size  mounted  consideration  plane  the  disturbance  displacement  axisymmetric,  piles,  Clay  displacement  disturbance  regarded  installation.  in  by  full  loaded  displacement piles,  installation  piles.  unless have  •4-4-  r  d  Axisymmetric  ++• Co  Plane  Strain  (a) Fig.  9.6 Test  Simulation  of I n s t a l l a t i o n  f o r Pressuremeter 00 O  281  As  in  performed desired the  practice, soon  after  depth.  The  installation  the  pressuremeter  tests  the  instrument  installed  high  may  excess  pore  have  enough  not  completely.  The  effective  then  for  piles,  be  unlike  able  to  gain  likely  to  around  the  softer  zone  element were  be  its  probe. of  In  soil  analysis.  FINITE In  time  in  undrained  with  value. a  disturbance of  E,/E d u  soils  are  during  s t i l l  strength  this  the  low,  will  not  tests  are  zone  of  soils  difference,  considered C  the  dissipate  disturbed  (or  at  induced  Therefore,  of  is  to  shear  softer  consideration  the  ELEMENT  ,/C ) ud u  in  the  of  0.2, '  a  finite 0.5, '  1  effects,  condition  assumed  the  MESH  following  installation is  finite the for  axisymmetrical  discussed  in  radius  the  of  elements  Chapter  6  element  the  plane is  soils.  to The  the  are  different  from  For  the  laterally  loaded  mesh  discussed  in  analyses 30  cm.  (see An  Fig.  9.8).  annular  zone  strain  element  of  (see  Fig.  assumed  cavity  and  the  finite  is  0  strength  expansion  expansion  r ,  wall  cavity  of  pressuremeter  employed  elements  element  analyses  cylindrical  pressuremeter,  adjacent  disturbed  be  pressures  usually  analysed.  9.3.2  and  the  Values  1  stresses  original  performed  is  are  other  piles,  Chapter  8  be  present  stiffness  mesh  9.7). to  in  tests,  The 5 cm.  the  The  zone  of  those  elements. the  is  plane  strain  employed  The  pile  radius,  of  soil  elements  r , 0  is  next  for  finite  the  assumed to  the  to  pile  r,4~  Disturbed Zone  Fig. Studying  9.7  F i n i t e Element Mesh f o r  Installation  Effects  on P r e s s u r e m e t e r C u r v e s  ro co  Fig.  9.8  F i n i t e Element Mesh f o r  Studying I n s t a l l a t i o n  Effects  on P - Y C u r v e s to co  CO  284 s h a f t s i m u l a t e s t h e d i s t u r b e d z o n e . The deformation from the  modulus a s s i g n e d  i n those  i n C h a p t e r 8,  a thin  are employed around the p i l e  9.4  soil-pile  RESULTS AND B a s e d on  finite  adhesion  the  foregoing disturbance  loaded  piles,  t e n s i o n c u t - o f f m o d e l was  bilinear  e m p l o y e d i n C h a p t e r 6, the  9.4.1  bilinear  C h a p t e r 8.  s t u d i e s were soil  tests, while  elasto-plastic  e m p l o y e d . The  other  soil  were t h e  same  The  the  r e s u l t s are  for  with  as discussed  PRESSUREMETER CURVES pressuremeter  e x t e n t s of s o f t e r  soil  is  following sections.  The  for  s i m u l a t i o n and  elasto-plastic  parameters r e q u i r e d f o r the analyses  in  the  f a c t o r o f 0.5  element parametric  employed f o r the pressuremeter  laterally  i n t e r f a c e elements  DISCUSSION  performed. In the a n a l y s e s ,  the  An  soil  i n t e r f a c e elements.  e l e m e n t mesh, f i n i t e  model was  r i n g of  different  intact  surface to simulate  interface behavior.  assumed a t t h e  and  elements are  r e s t of elements r e p r e s e n t i n g the  medium. As  soil-pile  strength  curves  soil  zone are  d i s t u r b e d zone of 2 r , 0  disturbance  c u r v e s . The  has  disturbance  (loss  0  the  i n the  under  different  shown i n F i g .  3r , 5r  significant  degree of the  o f d i s t u r b a n c e , and  obtained  0  9.9(a),(b),(c)  r e s p e c t i v e l y . As  effect  on  the  pressuremeter  i n f l u e n c e d e p e n d s upon t h e  s i z e of the d i s t u r b e d zone. s t r e n g t h and  noted,  m o d u l u s ) and  extent Severe  large  285  F i g . 9.9  T y p i c a l pressuremeter  s o i l disturbance  curves under d i f f e r e n t  286  disturbed seems  also  region.  to  exist to  predicted  less  affected  The  greatly  soften  the  to  extent  in  where  initial  from  by  the  the  amount  can  disturbed  be  observed slopes  of  disturbed  zone,  r^/r ,  the  disturbed  zone.  It  figures extent the  of  the  change  the  of  with the  disturbed  of  is  E^/E^  of  of  the  =0.2  disturbed  finite  disturbed  of  about  goes  results  strain)  less  0  zone  to  to  the  the  tests  initial  (which  obtained  is from  the  are  the if  practically  by  vary  to  the  slopes the  level than  Fig.  one.  off twice  9.11, slope Surely,  will  be  if 5.  full right  after  measured  defined  pressure  of  linearly  However,  factor the  the  initial  performed and  the  disturbed  undisturbed  that  modulus  from  larger in  the  plotted  the  to  seems  shown  9.10,  influence  The 2.  becomes  slope  the  the  seem  zone  infinity,  indicate  to  than  As  to  the  to  affected  zone.  3 between  pressuremeter  pressure  slopes  disturbed  compared  installation,  ultimate  of  more  disturbed r^/r  and  appears  compared  The  Fig.  are  u  0  are  pressuremeter.  zone  above  as  in  for  size  factor  displacement  slopes  zone.  ratio  the  radius  a  (slope)^/(slope)  disturbance,  modulus  radius  The  the  initial  significantly  the  there  the  the  influence once  u  that  size  with  in  E  of  relative  size  j /  limit  seems  slopes  from  against (  analysis  initial  i.e.  E  strain  disturbance.  one,  ratio,  influence  theoretical  element  the  the  large  the  soil  initial =  the  undisturbed the  SR  of  on  also  curves,  slope,  finite  effects  curves  the  some  the  disturbance  pressuremeter 9.11,  both  Compared  pressure be  zone  at  expansion  certain curve  Fig.  9.10 curves  Relative vs  size  initial of  slopes  disturbed  of  zone  pressuremeter  o in  o o H  0.0  I  I  0.5  I  I  I  I  1.0  E /E d  Fig.  1  1.5 u  9.11 curves  I  I  I  2.0 -  Modulus  Relative vs  Ratio  initial  extent  I  2.5  of  I  ~~1  3.0  in Disturbed  slopes  soil  of  I  3.5  1  I  4.0  I  I  4.5  1  5.0  Zone  pressuremeter  disturbance  to oo co  289  will  be  significantly  reduced  by  the  installation  soil  disturbance.  9.4.2  P-Y As  curves  CURVES  for  the  under  plotted  in  different  Fig  for  laterally  the  pile  curves soft  in  with  clay.  9.12  E^/E  >  As  as  in  much  curve,  size  softer  initial  much more  of  reaction. ratio  of  may  on  is  the  found  large  zone  P-Y  clay).  in at  also The  Fig.  9.14  end  initial  and  9.15.  of  the  first  called  the  initial  relative  initial  slopes  modulus of  the  of  to  the  is  of  modulus  P-Y  of  in  soils  the  the  curves  upon  soil  and  initial and P-Y  of  the  resistance  the  of  results  comparison  the  initial  in  pile  depending  is slope.  the  size  curves  slopes  increment.  shown  the  disturbance  slopes  load  P-Y  influence  disturbance  The  the  stiffer  ultimate  extent  simulate  P-Y  a  From  than  curves  in  that  the  may  zone  resistance  the the  to  ultimate  of on  shows  P-Y  range,  soil  curves,  are  the  which  P-Y  displacement  seems  of  influence zone  1,  9.13  results  zone  shows  disturbed  in  zone  <  predicted  correspond  softer  stiff  u  Fig.  disturbance  calculated are  it  or  9.12  ^ / E  E  by  shown  they  a  stiffer  soft  disturbance  soil  affected  disturbed  are  which  larger  effects  slope,  The  /or  of  while  disturbed  the  the  Fig.  especially  of  (i.e.  disturbance  1,  curves,  with  disturbed  well,  condition  u  expected,  stiffer  curves  pile  clays,  while  The  9.13.  stiff  the  curve.  extent  and  loaded  softens a  pressuremeter  are  Therefore  subgrade figures  with  soil  is  the  290  -O  0.5  OUturbwS I . / I ,  0.2  0.0  -1 1 12.0  6.0  1 1 18.0  1 1 24.0  1 r 30.0  36.0^  LATERAL DISPLACEMENT Y - MM (DI5  n  O  Undliturbcd B / e  O  6  Diiturtxd I / E  ^  d  d  u  Disturb** « / t  1-  d  0  12.0  T"  i  42_._p_ _ 4.80. _ 54.0  r—1  1,0.0  ?0NE=2'R0 E-P CLAY)  - 1.0  u  • 0.S  u  . 0.2  18.0  24.0  30.0  36 0  02 0  48 0  LATERAL DISPLACEMENT Y - MM (DIST.Z0NE=3R0  54.0  60..0  E-P CLAY)  1.0 «  — 0  Disturbed « /B„ • 0.S d  0.2  .0  12.0  18 0  24.0  Fig.  9.12 T y p i c a l P-Y  30.0  36 0  42 0  under  various  1  48.0  1  disturbance  (stiff  curves clay)  soil  1  54 o  LATERAL DISPLACEMENT Y - MM (DIST Z0NE=5R0 E-P CLAY)  r  60.0  291  o— — o 4  d i s t u r b e d Ed/Eu=2  (a)  —f> d i s t u r b e d Ed/Eu=5  i <  1 1 1 1 1 1 1 1 1 1 1 1 1 1 r 8.0 12.0 16.0 20.0 24.0 28.0 32.0 L A T E R A L D I S P L A C E M E N T Y - MM (rd=2T, S O F T C L A Y )  —i 4.0  o —o XL  40.0  (b)  d i s t u r b e d Ed/Eu=2 d i s t u r b e d Ed/Eu=5  0 —e>  2=S  36.0  Io  0.0  4.0  8.0  12.0  i  i i 16.0  i i 20.0  i i 24.0  L A T E R A L D I S P L A C E M E N T Y - MM (r =3 T. d  i 28.0  i — i — i — i — 32.0 36.0  SOFT CLAY)  d i s t u r b e d Ed/Eu=2 d i s t u r b e d Ed/Eu=5  0.0  Fig.  -1 4.0  i  i 8.0  i  i i 12.0  i i 16.0  i 20.0  r  L A T E R A L D I S P L A C E M E N T Y - MM  9.13  Typical  disturbance  P-Y  (soft  curves clay)  1  i 24.0 U=5T.  1 1 1 1 32.0 SOFT CLAY)  28.0  under  1  36.0  various  r  40.0  soil  292 d i s t u r b a n c e t o t h a t w i t h no As the  shown i n F i g . 9.14  s i z e of s o i l  initial  soil and  be  9.15,  both the e x t e n t s  d i s t u r b a n c e have c e r t a i n  subgrade modulus, however, the  l e s s as compared t o the c a s e Fig.  disturbance.  9.10  and  9.11  reasonable  w i t h the  two  curves  the case  applied  i n one  the p i l e  has  of l a t e r a l l y  direction,  less  the pressuremeter  r e s u l t s seem t o  different  loading  t e s t s and  loaded p i l e s ,  the  i n f l u e n c e s on case,  t h e P-Y  the p r e s s u r e  the case  expansion  of the pressuremeter  soil  disturbance  curves.  In c o n t r a s t  expansion  c o n d i t i o n , the  s i z e o f d i s t u r b a n c e zone seems t o h a v e c o n t i n u o u s initial  s u b g r a d e r e a c t i o n ( s e e F i g . 9.10  the s i z e of t h e d i s t u r b e d zone c o n t i n u e a p p e a r s f r o m F i g . 9.15 i s a b o u t 75%  o f 5, a n d  piles  at s o i l - p i l e  c e n t e r . T h i s r e s u l t may  installed  in stiff  s o f t c l a y s , w h i c h may soil-pile  interface  the d i s t u r b e d zone extends  from the p i l e  influence  and  9.14)  if  to increase. I t  t h a t the d i s t u r b e d subgrade modulus  o f t h e u n d i s t u r b e d one,  disturbed soil  behind  the p r e s s u r e s are a p p l i e d  zone w i l l  affect  region  are  c u r v e s . However, f o r  so t h a t t h e w h o l e a n n u l a r  the  laterally  the loads  the d i s t u r b e d s o i l  axisymmetrically  on  (see  piles.  In  to  the  i n f l u e n c e i s much  same s c a l e ) . The  mechanisms between the p r e s s u r e m e t e r loaded  i n f l u e n c e s on  of pressuremeter  as t h e r e e x i s t s  and  be  i n t e r f a c e , the  c l a y s . While represented initial  when t h e s t i f f n e s s i s reduced t o 2.5  pile  represent for pile by E ^ / E  by a  u  of  factor  diameter the case  of  installed  in  = 5.0  subgrade modulus  at will  o o  o  — 0  3  •O  E  —h  H  0.2  V u V u •  0.5  E  0  0  V u -  2.0  x—  X  E  d u "  5.0  E  /E  O  o • _ 2 CD CI >  10  o o n  1.0  i  i  1.5  i  i  2.0  i  i  2.5  i r-/r  Fig.  9.14 of  i  3.0  - Size  0  Relative  disturbed  i  i  3.5  i  i  of D i s t u r b e d  initial  slope  i  4.0  o f P-Y  i  4.5  i  i  5.0  i  i  5.5  i  6.0  Zone  curves  vs  size  zone  (D  co  Fig.  9.15 "extent  Relative of  soil  initial  slope  disturbance  of  P-Y  curves  vs  295 increase  by a b o u t 36% f o r r / r d  The r e l a t i v e the  strength  reduction  0  = 5.  of u l t i m a t e  and modulus l o s s e s  r e s i s t a n c e due t o  i n disturbed  shown i n F i g . 9.16 a n d 9.17. The r e l a t i v e resistance  i s defined  from t h e d i s t u r b e d P-Y c u r v e . on  soil  ultimate  as the r a t i o of u l t i m a t e  P-Y c u r v e s t o t h a t  region are  from t h e  resistance undisturbed  As shown i n F i g . 9.16, c o m p a r e d t o t h e i n f l u e n c e  the subgrade modulus, the s i z e of the d i s t u r b e d  zone has  a more p r o n o u n c e d b u t l i m i t e d e f f e c t on t h e u l t i m a t e r e s i s t a n c e . The i n f l u e n c e seems t o l e v e l larger  the extents  of s o i l  i n f l u e n c e on t h e u l t i m a t e  subgrade modulus. For r ^ A o and  shear s t r e n g t h  the  soil-pile  the p r e d i c t e d  disturbance  resistances  = 5, r e d u c t i o n  interface results ultimate  (b),  is  than the  of t h e modulus  values  (c)).  s o i l at  i n about a 73% r e d u c t i o n i n  i n s o f t c l a y s h o w e v e r , due t o t h e  t h e P-Y c u r v e s w o u l d be s t i f f e r ,  of ultimate  this  installed in  of u n d r a i n e d shear s t r e n g t h a t t h e end of  reconsolidation, higher  0  have  r e s i s t a n c e s . In the p r a c t i c e ,  c l a y s . For the p i l e s  increase  also  by f a c t o r o f 5 i n t h e d i s t u r b e d  might correspond, t o t h e c o n d i t i o n of p i l e s stiff  r^/r  t h a n 2.  Similarly, larger  o f f when  resistances  (see F i g .  soil and have  9.13(a),  o 4) U  c  10  o  o Ed/Eu = 0.2  H  1- Ed/Eu = 0.5  Ul a  4)  4J  (0  E  LO  C  o 4-1  o  3 •O ro " 01 K 0) >  « 1 .0  ~i 1.5  1  1  1  2.0  1  1  1  2.5 r  Fig.  9.16 size  1  3.0 d/ o r  Relative  -  1  1  3.5  S i z e of the Disturbed  ultimate  of disturbed  r  1  4.5  4.0  resistance  5.0  5.5  5.0  Zone  o f P-Y  curves  vs  zone  CT\  < cn  298 9.5  SUMMARY As  pile it  stated before, s o i l  installation  s h o u l d be  disturbance effect  i s important to the p i l e  included  i n t h e P-Y  due  lateral  c u r v e s . The  i s necessary  f o r t h e d e v e l o p m e n t o f P-Y  finite  element a n a l y s i s or from the p r e s s u r e m e t e r  u n d e r s t a n d i n g o f how the p r e s s u r e m e t e r  disturbance affects  to the pressuremeter  f o r t h e P-Y contrast  c u r v e s . As  t h e P-Y  curves  and  be c o n c l u d e d  that:  expansion curves, the s o i l d i s t u r b a n c e  e f f e c t s on t h e i n i t i a l 2.  from  curves.  for pressuremeter due  curves  this  e l e m e n t a n a l y s i s a l l o w s an  B a s e d on t h e a b o v e a n a l y s e s , i t may 1.  behavior,  study of  effect  shown b e f o r e , t h e f i n i t e  to the  installation  h a s much more  s l o p e s than the l i m i t p r e s s u r e s ,  c u r v e s i n the l a t e r a l l y  loaded p i l e s ,  t o the case of p r e s s u r e m e t e r  tests,  in  the  u l t i m a t e r e s i s t a n c e s o f t h e c u r v e s a r e much more a f f e c t e d by t h e s o i l installation subgrade 3.  d i s t u r b a n c e due  than i s the i n i t i a l  to the  pile  modulus of the  reaction,  Compared t h e e f f e c t s of s o i l pressuremeter  c u r v e s and  d i s t u r b a n c e on  t h e P-Y  the  c u r v e s , i t i s found  t h a t u n d e r t h e same e x t e n t o f s o i l  d i s t u r b a n c e , the  e f f e c t s a r e more p r o n o u n c e d i n p r e s s u r e m e t e r in In  t h e P-Y  curves  than  curves.  practice,  the pressuremeter  a p h y s i c a l model f o r p i l e pressuremeter  soil  is generally  installation.  The  regarded  self-boring  s i m u l a t e s the bored p i l e , w h i l e the  full  as  299  displacement pressuremeter  s i m u l a t e s the d r i v e n  However, t h e r e i s a problem u s i n g p r e s s u r e m e t e r , as loaded long a f t e r  in simulating  i n the f i e l d  the p i l e d r i v i n g ,  t h e p o r e p r e s s u r e due the pressuremeter the i n s t a l l a t i o n  the pore  P-Y  test  has  b a s e d on p r e s e n t s t u d i e s ,  after  dissipated,  t o the d i f f e r e n t  curves  p r a c t i c e , a s t h e z o n e and  the l a t e r a l l y  incorporation w i l l the e x t e n t of s o i l  are very d i f f i c u l t  d e p e n d upon v a r i o u s f a c t o r s , the i n s t a l l a t i o n i s warranted.  including  and  mechanisms loaded  factor  c u r v e s from the p r e s s u r e m e t e r  c u r v e s . H o w e v e r , s u c h an  the i n s t a l l a t i o n  and  loading  i t i s desirable to consider t h i s  d e v e l o p m e n t o f P-Y  there i s a  e f f e c t on p r e s s u r e m e t e r  Therefore,  this direction  long  responses.  the pressuremeter  t y p e s , and  pressure  starts  associated  to  usually  dissipate.  to the i n s t a l l a t i o n  e f f e c t on p i l e  installation  c u r v e s , due  responses  e x p a n s i o n t e s t can not p r o p e r l y s i m u l a t e  In a d d i t i o n , different  the p i l e  the p i l e s are  generated d u r i n g the p i l e d r i v i n g would Therefore, unless the pressuremeter  pile.  i n the  expansion  be d i f f i c u l t  in  d i s t u r b a n c e due  to determine, soil  pile.  they  conditions,  pile  procedure. Further studies i n  10. SUMMARY AND CONCLUSIONS Numerical  s t u d i e s h a v e been p e r f o r m e d  aspects r e l a t e d t o the pressuremeter laterally  loaded p i l e s .  The s t u d i e s  expansion  The  a n d P-Y C u r v e s  newly developed  finite  Pressuremeter  f o r L a t e r a l l y Loaded  Piles.  e l e m e n t p r o g r a m CONOIL was  examined and m o d i f i e d f o r these  purposes.  On t h e s i m u l a t i o n o f c y l i n d r i c a l condition,  t e s t s and the  include three topics :  S o l u t i o n of C y l i n d r i c a l Cavity Expansion, Expansion Curves  t o e x a m i n e some  cavity  expansion  i t h a s been shown t h a t t h e m o d i f i e d p r o g r a m i s  c a p a b l e o f p r o v i d i n g t h e r e s u l t s t h a t a r e i n good agreement with the closed it  f o r m s o l u t i o n . B a s e d on t h e p r e s e n t  studies,  i s found that using the simple h y p e r b o l i c s t r e s s - s t r a i n  relation, different required  fordifferent  The  types of s o i l s .  reduction factor  than t h a t failure  f a i l u r e m o d u l u s r e d u c t i o n f a c t o r s may be  f o r c o h e s i o n l e s s s o i l may be l o w e r  f o r cohesive s o i l  so as t o s i m u l a t e t h e s h e a r  o f s o i l s and a v o i d t h e n u m e r i c a l i n s t a b i l i t y .  load shedding facilitate  iteration  i s f o u n d t o be a u s e f u l t o o l t o  the s i m u l a t i o n of s o i l  On t h e p r e s s u r e m e t e r  t h e L/D r a t i o  interpretation cylindrical results  test  results  pressuremeter  i s required  curves. A  i . e . L/D  results,  i s based  on t h e  ratio  sufficiently  i n o r d e r t o have a p l a n e 300  i t is  i f the  e x p a n s i o n t h e o r y . A s m a l l e r L/D  in a stiffer  l a r g e L/D r a t i o  expansion  i s an i m p o r t a n t f a c t o r  of pressuremeter  cavity  failure.  membrane l e n g t h e f f e c t s ,  r a t i o e f f e c t on t h e p r e s s u r e m e t e r found t h a t  The  strain  301 condition  i n the pressuremeter  For c o h e s i v e s o i l s ,  i f L/D  tests. ratio  i s e q u a l t o 4,  g e n e r a l shape of t h e e x p a n s i o n c u r v e and modulus a r e c l o s e expansion  w i t h L/D  4.  ratio  of  For c o h e s i o n l e s s s o i l s , condition  pressuremeter  the f r i c t i o n  t h e L/D  seems t o be l a r g e r .  ratio  as  than f o r modulus  a f f e c t e d by t h e L/D  p a r t of the c u r v e  field  i s most v u l n e r a b l e  o b t a i n the f r i c t i o n further  angle from the  to  pressuremeter  r e s e a r c h work.  B a s e d on t h e c o m p a r i s o n o f p l a n e s t r a i n t e s t d a t a , i t i s found t h a t the f i n i t e  analyses with hyperbolic stress-strain strain  curve  ratio.  a s m a l l amount o f s o i l d i s t u r b a n c e . T h e r e f o r e , how  field  and  i t i s known i n g r a n u l a r c o h e s i o n l e s s  that the i n i t i a l  test deserves  the  a n g l e d e r i v e d from the e a r l y p a r t of t h e  optimistically,  reliably  even  I t i s found t h a t  H o w e v e r , s u c h a r e s u l t c a n n o t be a p p l i e d t o t h e  to  15%  to provide plane  V a l u e s of the d e r i v e d e l a s t i c  g e n e r a l l y not s i g n i f i c a n t l y  soils  shear  o v e r - p r e d i c t e d by  e x p a n s i o n c u r v e i s more a f f e c t e d  cohesive s o i l s .  are  cavity  t h e o r y . However, the d e r i v e d u n d r a i n e d significantly  strain  the d e r i v e d e l a s t i c  t o t h o s e from the c y l i n d r i c a l  s t r e n g t h w o u l d be  the  analysis  and  element  relation  and  plane  c o n d i t i o n can p r o v i d e r e s u l t s t h a t a r e i n good  agreement w i t h the f i e l d measurements. However, f o r cohesionless s o i l s , softer  the plane s t r a i n  solution  t h a n t h e f i e l d m e a s u r e m e n t s . The  m e a s u r e d i n f i e l d may  be due  i s found to  stiffer  to the i n s u f f i c i e n t  curve L/D  ratio  be  302 of the pressuremeter  u s e d . On  o f t h e p r e d i c t e d c u r v e may  the o t h e r hand, the  a l s o i n d i c a t e the  of the h y p e r b o l i c s t r e s s - s t r a i n  relation  softness  insufficiency  in describing  g r a n u l a r c o h e s i o n l e s s s o i l s as r e g a r d t o t h e  dilation  effect. Good a g r e e m e n t w i t h t h e f i e l d m e a s u r e m e n t s i n c o h e s i v e s o i l s may i s not  a l s o tend to i n d i c a t e that K  that important  as the r e a d j u s t m e n t principal  of the r e l a t i v e m a g n i t u d e s of  s t a r t e d , and  the f a i l u r e  the d i f f e r e n c e of h o r i z o n t a l  and  has  of s o i l  three  the  undrained  i s governed  s t r e s s e s a l o n e . The  effect  on t h e w h o l e t e s t  t o complement the f o r e g o i n g  investigation interpretation  r e g a r d i n g t h e L/D of p r e s s u r e m e t e r  ratio effect  on  results.  and  S u c h e x p e r i m e n t a l d a t a may  t e s t , and  test data. Numerical  on  the  test data, stress  element around the pressuremeter  true t r i a x i a l  the t r i a x i a l  s t u d i e s of these  are  numerical  in the s o i l the t e s t  stress,  results.  However, f u r t h e r a n a l y s e s of e x p e r i m e n t a l d a t a necessary  by  initial  s t r e s s soon becomes i n t e r m e d i a t e p r i n c i p a l little  effect  f o r the n o r m a l l y c o n s o l i d a t e d c l a y s ,  s t r e s s e s occurs very r a p i d l y a f t e r  s h e a r i n g has  vertical  consolidation  0  chamber  variation i t s effect  i n c l u d e the  calibration  t e s t d a t a may  also  p r o v i d e o p p o r t u n i t i e s t o e v a l u a t e the s t r e s s - s t r a i n model of s o i l s employed i n the As  analysis.  r e g a r d t o the l a t e r a l l y  loaded p i l e s ,  i n t e r f a c e e l e m e n t m o d e l b a s e d on t h e element i s presented  a  simple  f o r m u l a t i o n of o r d i n a r y  f o r t h e s t u d y of s o i l - p i l e  interface  303 behavior.  B a s e d on  plasticity  the comparison w i t h the  s o l u t i o n , i t i s found that the proposed i n t e r f a c e  element can  provide  l o n g as  i n t e r f a c e element  the  relative  to the  s t u d i e s are parametric  test  the  soil  cohesionless soil-pile  for cohesive  present  r e s i s t a n c e o f P-Y soils,  the  results,  soils,  the  t h e d e v e l o p m e n t o f P-Y  such as d i r e c t  curves are  reduces the  cohesive the  for i n s e n s i t i v e to  curves.  cohesionless  soil  can  f u n c t i o n and validity  to incorporate P-Y  simply  curves for  represented  p r e s s u r e m e t e r c u r v e s and  finite these cohesive  by  power f u n c t i o n r e s p e c t i v e l y .  field  load test  different installation  performed i n cohesive  these f a c t o r s i n  of t h e s e f u n c t i o n r e q u i r e s  e x a m i n a t i o n by a n a l y z i n g f o r the  be  reaction.  I t i s shown t h a t t h e tool  that  soil-pile  ultimate s o i l  incorporate  I t i s a l s o found t h a t the  pore pressure  for  affect  while  t e n s i l e c r a c k i n g or  element a n a l y s i s i s a powerful  However, the  comparing  i n t e r f a c e p r o p e r t i e s . I t i s a l s o found  i t i s d e s i r a b l e to  As  t h i s m o d e l by  curves,  w h o l e P-Y  Therefore,  hyperbolic  in size  e l e m e n t s . However, f u r t h e r  s t u d i e s , i t i s found t h a t  significantly  and  as  data.  seperation  effects.  form  small  interface properties significantly  ultimate s o i l  the  p i l e and  is sufficiently  necessary to evaluate  B a s e d on soils,  agreeable r e s u l t s with closed  studies with experimental  s h e a r box  classic  P-Y  soils.  curves,  further  data.  e f f e c t s on  a parametric  study  I t i s n o t e d t h a t due  generated during  the  installation,  to a  the  was  304 pressuremeter  expansion  c e r t a i n depth  i s u s u a l l y performed  zone o f s o i l s a r o u n d  test right after  installation Based  expansion effect  with a softer  before p i l e  on p i l e  responses.  u n d e r t h e same amount o f s o i l  i t i s found that  with the pressuremeter For pressuremeter  even  d i s t u r b a n c e , i n s t a l l a t i o n has  on t h e p r e s s u r e m e t e r  c u r v e s due t o t h e d i f f e r e n t  the i n i t i a l  loading, the  t e s t can not p r o p e r l y s i m u l a t e t h e  on t h e p a r a m e t r i c s t u d i e s ,  a different effect  disturbed  t h e probe. Unless the pore p r e s s u r e has  d i s s i p a t e d as they would pressuremeter  installed at  c u r v e s a n d t h e P-Y  l o a d i n g mechanisms a s s o c i a t e d  and t h e l a t e r a l l y  loaded  piles.  expansion c u r v e s , i t i s found  that  s l o p e o f t h e c u r v e i s much a f f e c t e d by t h e s o i l  d i s t u r b a n c e , b u t n o t s o much f o r t h e u l t i m a t e p r e s s u r e . However, t h e o p p o s i t e e f f e c t s a r e o b s e r v e d curves, the ultimate s o i l  resistance  i s significantly  a f f e c t e d by t h e s i z e a n d e x t e n t o f s o i l the i n i t i a l  modulus of s o i l  subgrade  insensitive to the i n s t a l l a t i o n  disturbance while  reaction  effect.  i s relatively  In view of t h e s e , i t  is desirable to incorporate this different effect  f o r t h e P-Y  s o i l disturbance  i n t h e d e v e l o p m e n t o f P-Y c u r v e s f r o m  pressure  expansion curves. In  the present s t u d i e s of i n s t a l l a t i o n  effects,  h o w e v e r , t h e c o n d i t i o n o f s t r e s s c h a n g e s due t o t h e p i l e installation  i s not c o n s i d e r e d i n the a n a l y s i s , and t h e  study i s a l s o l i m i t e d  to the undrained cohesive  A d d i t i o n a l work i s d e s i r a b l e  soils.  f o r studying the i n s t a l l a t i o n  305 effect  on p i l e s  driven  in cohesionless s o i l s .  a c c o m p l i s h e d by s i m u l a t i n g t h e p i l e d r i v i n g  T h i s may  in cohesionless  s o i l s as a c a v i t y  expansion p r o c e s s , then l o a d i n g the  i n one  or l o a d i n g the  direction,  axisymmetrically. formulation warranted  be  pile  pressuremeter  In t h i s procedure, l a r g e  strain  i s necessary. Therefore, further research i s  in this  direction.  REFERENCES A m e r i c a n P e t r o l e u m I n s t i t u t e ( 1 9 7 6 ) , A P I Recommended P r a c t i c e f o r Planning, Designing, and C o n s t r u c t i n g F i x e d O f f s h o r e P l a t f o r m , API RP-2A, 7 t h ed., pp21-26 A t u k o r a l a , U. a n d B y r n e , P.M. ( 1 9 8 4 ) , P r e d i c t i o n o f P-Y Curves from P r e s s u r e m e t e r T e s t s a n d F i n i t e Element A n a l y s i s , Soil Mech. Series, No.66. D e p t . o f C i v i l E n g i n e e r i n g , UBC B a g u e l i n , F., F r a n k , R. a n d S a i d , Y.H. ( 1 9 7 7 ) , T h e o r e t i c a l Study o f L a t e r a l R e a c t i o n Mechanism o f P i l e s , Geotechnique, V o l . 2 7 , No.3, pp405-434 B a g u e l i n , F., F r a n k , R. ( 1 9 8 0 ) , T h e o r e t i c a l S t u d i e s o f P i l e s u s i n g t h e F i n i t e E l e m e n t M e t h o d , P r o c . Num. M e t h . O f f s h o r e P i l i n g , London, pp83-9l B a l a a m , N.P., P o u l o s , H.G, a n d B o o k e r , J . R . ( 1 9 7 5 ) , F i n i t e Element A n a l y s i s of the E f f e c t s of I n s t a l l a t i o n o f P i l e L o a d - s e t t l e m e n t B e h a v i o r , Geotechni cal Engineering, V o l . 6, 1975 B a n e r j e e , P.K. a n d D a v i e s , J . G . ( 1 9 7 8 ) , The B e h a v i o r o f A x i a l l y a n d L a t e r a l l y L o a d e d S i n g l e P i l e s Embeded i n Nonhomogeneous s o i l s , Geot echni que, V o l . 2 8 , No.3, p p 3 0 9 - 3 2 6 B a n e r j e e , P.K a n d D r i s c o l l , R.M. ( 1 9 7 6 ) , T h r e e - d i m e n s i o n a l A n a l y s i s o f R a k e d P i l e G r o u p , Proc. ICE. P a r t 2, 6 1 . Dec. pp653-671 Bardet, J.P.  ( 1 9 7 9 ) , Private  Communication  B a r t o n , Y.O., F i n n , W.D.L., P a r r y , R.H.G., T o w h a t t a , I . , (1983) L a t e r a l P i l e R e s p o n s e a n d P-Y C u r v e s f r o m C e n t r i f u g e T e s t s , Proc. 15th Annual Meeting of OTC, V o l . 1, pp503-508 B o r s e t t o , M., I m p e r a t o , L . , N o v a , R., a n d P e a n o , A. ( 1 9 8 3 ) , E f f e c t s of Pressuremeters of F i n i t e Length i nS o f t C l a y , Proc.  Symp.  IFP-LPC,  Pressuremeter  and  Its  Marine  Application,  Paris  B r i a u d , J . L . , S m i t h , T.D., a n d M e y e r , B. ( 1 9 8 2 ) , D e s i g n o f L a t e r a l l y Loaded P i l e s u s i n g Pressuremeter Test R e s u l t s , Proc.  Symp.  Pressuremeter  IFP-LPC, pp377-395,  and  Its  Marine  Application,  Paris  B r i a u d , J . L . , S m i t h , T., a n d M e y e r , B. ( 1 9 8 3 ) P r e s s u r e m e t e r G i v e s E l e m e n t a r y M o d e l f o r L a t e r a l l y L o a d e d P i l e s , Int. Symp.  on  Soil  and  Rock  Investigation  306  by  In-situ  Testing,  307 May,  Paris.  B y r n e , P.M. ( 1 9 8 3 ) , S t a t i c F i n i t e E l e m e t n A n a l y s i s o f S o i l - S t r u c t u r e S y s t e m s , Soil Mech. Series, No.71, Dept. of C i v i l E n g i n e e r i n g , UBC B y r n e , P.M. a n d E l d r i d g e , T.L. ( 1 9 8 3 ) , A T h r e e P a r a m e t e r D i l a t a n t E l a s t i c S t r e s s - s t r a i n M o d e l f o r S a n d , Soil Mech.  Series,  N o . 5 7 , May, 1983  B y r n e , P.M., V a i d , Y.P., a n d S a m a r a s e k e r a , L . ( 1 9 8 3 ) , Undrained D e f o r m a t i o n A n a l y s i s u s i n g P a t h Dependent M a t e r i a l P r o p e r t i e s , Soil Mechanics Series, No.57, D e p t . of C i v i l E n g i n e e r i n g , UBC, V a n c o u v e r , C a n a d a , May 1983 B y r n e , P.M., M o r r i s , D,V. a n d C a l d w e l l , J . ( 1 9 8 3 ) , S e i s m i c • S t a b i l i t y o f A T a i l i n g s Impoundment on S o f t C l a y e r S i l t D e p o s i t s , Soil Mech. Series, No 77, D e p t . o f C i v i l E n g i n e e r i n g , UBC, N o v . 1983 Byrne,  P.M. a n d J a n z e n , W. ( 1 9 8 4 ) , I N C O I L . , Soil Mech. No. 80, D e p t . o f C i v i l E n g i n e e r i n g , UBC  Sereis,  B y r n e , P.M. ( 1 9 8 5 ) , C.E. 573 : N u m e r i c a l M e t h o d s i n S o i l Mech. Class Notes, D e p t . o f C i v i l E n g i n e e r i n g , UBC C a r t e r , J . P . , R a n d o l p h , M.F. a n d W r o t h , C P . ( 1 9 7 9 ) S t r e s s and Pore P r e s s u r e Changes i n C l a y d u r i n g a n d a f t e r t h e E x p a n s i o n o f A C y l i n d r i c a l C a v i t y , Int. J. Num. and Anal.  Meth.  in  Geom.  V o l . 3, p p 3 0 5 - 3 2 2  C h r i s t i a n , J.T. ( 1 9 6 8 ) , U n d r a i n e d N u m e r i c a l M e t h o d s , J.S.M.F.D.,  S t r e s s D i s t r i b u t i o n by ASCE, No.Sm6, 1968  C l o u g h , G.W. a n d D e n b y , G.M. ( 1 9 7 7 ) , S t a b i l i z i n g Berm f o r T e m p o r o r y W a l l s i n C l a y , ASCE, V o l . 1 0 3 , No GT2, F e b . 1977  Design  C l o u g h , G.W. a n d D u n c a n , J.M. ( 1 9 7 1 ) , F i n i t e E l e m e n t A n a l y s i s o f R e t a i n i n g W a l l B e h a v i o r , ASCE V o l . 9 7 , No SM12, Dec. 1971 C o o k , R.D. C o n c e p t s a n d A p p l i c a t i o n s o f F i n i t e A n a l y s i s , J o n W i l e y & S o n s , 2 n d e d . 1981 Cox,  Element  W.R., R e e s e , L.C., a n d G r u b b s , B.R. ( 1 9 7 4 ) , F i e l d T e s t i n g o f L a t e r a l l y L o a d e d P i l e s i n S a n d , OTC, p a p e r No. 2 0 7 9 , May, 1974  Cummings, A.E., K e r k h o f f , G.O. a n d P e c k , R.B. ( 1 9 5 0 ) , E f f e c t of D r i v i n g P i l e s i n t o S o f t C l a y , Trans. ASCE. V o l 115, pp275-285 D ' A p p o l o n i a , D.J, P o u l o s , H.G., a n d L a d d , C C ( 1 9 7 1 ) , I n i t i a l S e t t l e m e n t o f S t r u c t u r e s on C l a y , /. Soil  Mech.  308 Found.,  Div.,  ASCE,  V o l 97, ppl359-1377  De M e l l o , V.B.F. ( 1 9 6 9 ) , F o u n d a t i o n s Proc.  7th  Int.  Conf.  Soil  S t a t e o f the A r t Volume, De  Mech.  of B i u l d i n g s i n Clay, Eng. Mexico C i t y ,  Found.  pp49-l36  B o r s t , B. a n d V e r m e e r , P.A. ( 1 9 8 4 ) , P o s s i b i l i t i e s a n d L i m i t a t i o n s o f F i n i t e Elements f o r L i m i t A n a l y s i s , Geotechnique,  34, No.2, p p l 9 9 - 2 l 0  D e s a i , C S . a n d A p p e l , G.C. ( 1 9 7 6 ) , 3D A n a l y s i s o f L a t e r a l l y Loaded  2nd  Structures,  B l a c k b u r g , ASCE, V o l  Int.  Conf.  1, pp405-418  Num. Meth.  in  D e s a i , C S . (1981), Behavior of I n t e r f a c e s between S t r u c t u r a l a n d G e o l o g i c a l M e d i a , Int. Conf. on Advances  in  Dynamics,  Geot ech.  Earthquake  Engineering  and  Geom.  Recent Soil  V o l . 1 1 , S t . L o u i s , MO. 1981  D e s a i , C.S., Zaman, M.M., L i g h t e r , J . G . a n d S i r i w a r d a n e , H.J. ( 1 9 8 4 ) , T h i n - l a y e r Element f o r I n t e r f a c e a n d Int.  Joints,  J.  Num.  Anal.  Meth.  in  Geom.  V o l . 8,  PP19-43 D u n c a n , J.M. ( 1 9 6 5 ) , Ph.D D i s s e r t a t i o n , U n i v e r s i t y B e r k l e y , 1965  of C a l i f .  D u n c a n , J.M. a n d C h a n g , C-Y. ( 1 9 7 0 ) , N o n l i n e a r A n a l y s i s o f Stress  Div.,  and S t r a i n  ASCE,  in Soils,  /. of  the  Soil  Mech.  Found.  V o l . 9 6 , No. Sm5, S e p t . 1970  D u n c a n , J.M., B y r n e , P.M., Wong, K.S., a n d M a b r y , P. ( 1 9 8 0 ) S t r e n g t h , S t r e s s - s t r a i n and Bulk Modulus Parameters f o r F i n i t e Elemen A n a l y s i s o f S t r e s s e s a n d Movements i n S o i l M a s s e s , Report No. UCB/GT/80-01, Univ. of C a l i f o r n i a , B e r k l e y , C a l i f . A n g . 1980 D u n c a n , J.M. a n d C l o u g h , G.M. ( 1 9 7 1 ) , F i n i t e E l e m e n t A n a l y s e s o f P o r t A l l e n L o c k , ASCE, V o l . 9 7 , No. SM8, Aug. 1971 F l a a t e , K. ( 1 9 7 2 ) , E f f e c t s o f P i l e Geot.  J.  9. 81  Driving  i n C l a y s , Can.  (1972)  G a m b i n , M. ( 1 9 7 9 ) , C a l c u l a t i o n o f F o u n d a t i o n s S u b j e c t e d t o H o r i z o n t a l F o r c e s u s i n g P r e s s u r e m e t e r D a t a , Sols Soils, N o . 3 0 - 3 1 , 1979 G a z i o g l n , S.M., a n d O ' N e i l l , M.W. ( 1 9 8 4 ) , E v a l u a t i o n o f P-Y R e l a t i o n s h i p s i n C o h e s i v e S o i l s , Proc. Symp. on Analysis and Design of Pile Foundations, San F r a n c i s c o , C a l i f . O c t . 1984 Goodman, R.E., T a y l o r , R.L. a n d B r e k k e , T . L . ( 1 9 6 8 ) , A M o d e l  309  f o r t h e M e c h a n i c s o f J o i n t e d R o c k , J. S. M.F. D. ASCE, VOL.94, NO.SM3, P r o c . p a p e r 5937, May, p p 6 3 7 - 6 5 9 H a r t m a n , J . P . a n d Schmertman, J . ( 1 9 7 5 ) , FEM S t u d y o f E l a s t i c P h a s e o f P r e s s u r e m e t e r T e s t , Proc. Spec. COnf. on  In-Situ  Measurement  of  Raleigh, North Carolina,  Soil  Properties,  ASCE,  pp.190-207  H e t e n y i , M. ( 1 9 4 6 ) , Beams on E l a s t i c F o u n d a t i o n , Univ. Michigan Press, Ann A r b o r , M i c h , a n d O x f o r d U n i v . London Horvath, John.S. Perspective,  of  Press,  ( 1 9 8 3 ) , M o d u l u s o f S u b g r a d e R e a c t i o n : New  Proc.  ASCE.  No.GT. D e c . 1 9 8 3 , p p 1 5 9 l - 1 5 9 6  I r o n s , B.M. ( 1 9 7 0 ) , A F r o n t a l S o l u t i o n P r o g r a m f o r F i n i t e E l e m e n t A n a l y s i s , Int. J. Num. Engng. 2, pp5-32 J a m i o l k o w s k i , M., a n d G a r a s s i n o , A. ( 1 9 7 7 ) , S o i l M o d u l u s f o r Laterally on  Piles  Loaded P i l e s ,  due  Spec. S e s s . 1977  to  Surcharge  The  or  Effect  Seismic  of  Horizontal  Loads  Effects,  Proc. 10, 9 t h I n t . C o n f . SMFE., T o k y o , J u l y , 14,  K o n d e r , R.L. ( 1 9 6 3 ) , H y p e r b o l i c S t r e s s - s t r a i n R e s p o n s e : C o h e s i v e S o i l s , J.S.M.F.D., ASCE, V o l . 8 9 , No. Sm1 , F e b , 1963, p i 15 K u h l e m e y e r , R.L. ( 1 9 7 7 ) , S t a t i c a n d D y n a m i c L a t e r a l l y L o a d e d F l o a t i n g P i l e s , Proc. ASCE. V o l . 1 0 5 , GT2, p p 2 8 9 - 3 0 4 L a d d , C.C., F o o t t , R., I s h i h a r a , K., S c h l o s s e r , F. a n d P o u l o s , H.G., S t r e s s - D e f o r m a t i o n a n d S t r e n g t h C h a r a c t e r i s t i c s , Proc. of 19th Inter. Conf. on SMFE, T o k y o , V o l . 2, 1977, pp.421-494 L a i e r , J.E., Schmertmann, J.H., Schaub, J.H. ( 1 9 7 5 ) , o f F i n i t e P r e s s u r e m e t e r L e n g t h i n D r y S a n d , Proc. Conf.  on  In-Situ  Measurement  of  Soil  Propertier,  Effect Spec. ASCE,  R a l e i g h , N.C., V o l . 1, pp.241-259 L i v n e h , M., G e l l e r t , M., U z a n , S. ( 1 9 7 1 ) , D e t e r m i n a t i o n o f t h e E l a s t i c M o d u l u s o f S o i l by t h e P r e s s u r e m e t e r T e s t , T h e o r e t i c a l B a c k g r o u n d , /. of Materials, V o l . 6, No. 2, pp.348-355 L o , K.Y. a n d S t e r m a c , during Soil  Pile  Mech.  A.G. 1965, I n d u c e d  D r i v i n g O p e r a t i o n s , Proc.  Found.  Eng.,  Pore  Sixth  Pressures Int.  M o n t r e a l 2, p p 2 8 5 - 2 8 9  Conf.  M a t l o c k , H. ( 1 9 7 0 ) , C o r r e l a t i o n s f o r D e s i g n i n g o f L a t e r a l l y L o a d e d P i l e s i n S o f t C l a y , OTC, p a p e r No. OTC 1204 M c C l e l l a n d , B. a n d F o c h t , J o h n A. J r . ( 1 9 5 8 ) , S o i l  Modulus  310 Trans.  f o r L a t e r a l l y Loaded P i l e s , No.2954, p p l 0 4 9 - 1 0 8 6  ASCE.,  Vol.123,  M i n d l i n , R.D. ( 1 9 3 6 ) , F o r c e a t A P o i n t i n t h e I n t e r i o r S e m i - i n f i n i t e S o l i d , Physics 7, p p l 9 5 ~ 2 0 2 Murchison,  J.M., a n d O ' N e i l l , M.W.  Relationships Analysis  Calif.  and  i n Cohesionless  Design  of  Pile  paper of A  ( 1 9 8 4 ) , E v a l u a t i o n o f P-Y Soils,  Foundations,  O c t . 1984  Proc.  Symp.  on  San F r a n c i s c o ,  N a g t e g a a l , J . C . , P a r k s , D.M., a n d R i c e , J . R . ( 1 9 7 4 ) , On N u m e r i c a l l y A c c u r a t e F i n i t e Element S o l u t i o n s i n t h e F u l l y P l a s t i c R a n g e , Computer Methods in Applied Mechanics  and Engineering  4 pp153-177  N a y l o r , D.J. (1973), D i s c u s s i o n , P r o c . Role  of  Plasticity  P291-294,  in  Soil  of  Mechanics,  Sept.  the Symp. on the C a m b r i d g e , 13-15,  N a y l o r , D . J . P a n d e , G.N., S i m p s o n . B , a n d T a b b , B., F i n i t e Element i n G e o t e c h n i c a l E n g i n e e r i n g , P i n e r i d g e P r e s s , S w a n s e a , U.K., 1981 N o v a k , M. ( 1 9 8 0 ) , D i s c u s s i o n , Proc. Piling,  Num.  Method  Offshore  L o n d o n , 1977  O r r j e , 0. a n d B r o m s , B. ( 1 9 6 7 ) , E f f e c t s o f P i l e Soil  P r o p e r t i e s , Proc.  ASCE.  Vol.  9 3 , No SM5, PART 1, S e p t .  D r i v i n g on  Potyondy, J.G. (1961), S k i n F r i c t i o n Between V a r i o u s S o i l s a n d C o n s t r u c t i o n M a t e r i a l s , Geotechnique, 1 1 , 4, pp339-353 P o u l o s , H.G. ( 1 9 7 1 ) The b e h a v i o r o f L a t e r a l l y L o a d e d P i l e s , I - S i n g l e P i l e , Proc. ASCE, V o l . 9 7 , SM5, p p 7 3 8 - 7 5 l P r e v o s t , J.H. (1976), Undrained of  Clays,  No.  GT12,  /. of  Geot.  D e c . 1976,  Eng.  Stress-Strain-Time Behavior  Div.,ASCE.,  Vol.  102,  pp.1245-1260  P y k e , R. a n d B e i k a e , M. ( 1 9 8 4 ) , A New S o l u t i o n f o r t h e Resistance of Single P i l e s to Lateral Loading, Laterally Loaded  SPT  Deep  835,  Foundations:  Analysis  and  Performance,  ASTM  pp3-20  R a n d o l p h , M.F., C a r t e r , J . P . a n d W r o t h , C P . ( 1 9 7 9 ) D r i v e n P i l e s i n Clay - theE f f e c t s of I n s t a l l a t i o n and S u b s e q u e n t c o n s o l i d a t i o n , Geotechnique, V o l . 2 4 , No. 4, pp36l-393 R a n d o l p h , M.F. a n d W r o t h , C P . ( 1 9 7 9 ) , An A n a l y t i c a l S o l u t i o n f o r the C o n s o l i d a t i o n around a D r i v e n P i l e ,  311 Int.  J.  Num.  Anal.  Meth.  Geom.,  V o l 3, p p 2 1 7 - 2 2 9  R a n d o l p h , M.F. a n d H o u l s b y , G.T. ( 1 9 8 4 ) , The L i m i t i n g P r e s s u r e on A C i r c u l a r P i l e L o a d e d L a t e r a l l y i n C o h e s i v e S o i l , Geotechnique 34, No. 4, pp613~623 Reese, L.C. ( 1 9 5 8 ) , D i s c u s s i o n o f " S o i l Modulus f o r L a t e r a l l y L o a d e d P i l e s " by B. M c C l e l l a n d a n d J o h n A. F o c h t , J r . , Trans. ASCE, V o l . 1 2 3 , pp1071-1074 Reese, L.C. (1962), U l t i m a t e R e s i s t a n c e a g a i n s t a R i g i d C y l i n d e r M o v i n g L a t e r a l l y i n C o h e s i o n l e s s S o i l , /. Society  of  Petroleum  Engineers,  Dec.  1962  Reese, L.C. ( 1 9 7 7 ) , L a t e r a l l y Loaded P i l e s : Program D o c u m e n t a t i o n , PROC. ASCE, No.GT4, A p r i l 1977 R e e s e , L . C , C o x , W.R., a n d Koop, F.D. ( 1 9 7 5 ) , F i e l d and A n a l y s i s o f L a t e r a l l y Loaded P i l e s i n S t i f f Proc. 7th OTC, Vol.11 pp-671-690  Testing Clay,  R e e s e , L . C , C o x , W.R., a n d Koop, F.D. ( 1 9 7 4 ) , A n a l y s i s o f L a t e r a l l y L o a d e d P i l e s i n S a n d , OTC, P a p e r NO. OTC 2080 R e e s e , L . C . O ' N e i l l , M.W., a n d S m i t h , E . ( 1 9 7 0 ) , A n a l y s i s o f P i l e F o u n d a t i o n s , Proc. ASCE, V o l 9 6 , SM1, pp235-250 R e e s e , L . C . a n d W e l c h , R.C. ( 1 9 7 5 ) , F o u n d a t i o n s i n S t i f f C l a y , Proc. pp633-649  Generalized  L a t e r a l Loading ASCE, Vol.101,  o f Deep No.GT7,  R o b e r t s o n , P.K, H u g h e s , J.M.O., C a m p a n e l l a , R.G., a n d S y , A. (1983), P r e d i c t i o n o f L a t e r a l l y Loaded P i l e s u s i n g P r e s s u r e m e t e r T e s t s , Soil Mechanics Series, No.67, D e p t . o f C i v l E n g i n e e r i n g , UBC, V a n c o u v e r , C a n a d a , May 1983 Samarasekera, L a i (1982), N o n l i n e a r E l a s t i c Undrained S t r e s s - s t r a i n Model f o r A n i s o t r o p i c C o n s o l i d a t e d C a l y , M.A.Sc T h e s i s , D e p t . o f C i v i l E n g i n e e r i n g , UBC, A p r i l S c o t t , R.F. A n a l y s i s o f C e n t r i f u g e P i l e T e s t s : S i m u l a t i o n o f P i l e D r i v i n g , Research Report, A P I OSAPR P r o j e c t 1 3 , C a l t h , P a s a d e n a , C a l i f . , J u n e 1980 S c o t t , R.F., F o u n d a t i o n A n a l y s i s , P r e n t i c e - H a l l , I n c . E n g l e w o o d C l i f f , N . J . , 1981 She, J . ( 1 9 8 6 ) , F o r t h c o m i n g M.A.Sc T h e s i s , D e p t . o f C i v i l E n g i n e e r i n g , UBC, V a n c o u v e r Skempton,  Building  B e a r i n g C a p a c i t y o f C l a y s , Proc. the L o n d o n , I C E , D i v . 1:180 A.W. ( 1 9 5 4 ) , C o e f f i c i e n t s A a n d B,  A.W. ( 1 9 5 1 ) ,  Skempton,  Geotechnique,  Research  Congress,  V o l 4, p143  312 S k e m p t o n , A.W. , ( 1 9 6 0 ) , E f f e c t i v e S t r e s s e s i n S o i l , C o n c r e t e , a n d R o c k , Conf. Pore Pressure and Suction Soils, L o n d o n , pp4-16  in  S l o a n , S.W. a n d R a n d o l p h , M.F. ( 1 9 8 2 ) , N u m e r i c a l P r e d i c t i o n of C o l l a p s e L o a d s u s i n g F i n i t e E l e m e n t M e t h o d s , Int. J. Num.  Anal.  Meth.  Geom.  vol.6,  pp47-76  T i m o s h e n k o , S. a n d G o o d i e r , J . N . ( 1 9 5 1 ) , T h e o r y o f E l a s t i c i t y , 2 n d ED. M c G r a w - H i l l , N.Y., 1951 V a z i r i , H. ( 1 9 8 6 ) , Ph.D D i s s e r t a t i o n , D e p t . o f C i v i l E n g i n e e r i n g , UBC, V a n c o u v e r V e s i c , A.S. ( 1 9 7 2 ) , E x p a n s i o n M a s s , /. Soil Mesh. Found. •SM3, p p . 2 6 5 - 2 9 0  of C a v i t i e s Divn.,  i nInfinite Soil V o l . 98,  A.S.C.E.,  Y e g i a n , M. a n d W r i g h t , S.G. ( 1 9 7 3 ) , L a t e r a l S o i l R e s i s t a n c e Displacement R e l a t i o n s h i p s f o rP i l e Foundations i n Soft C l a y , O r e , p a p e r No. 1893, D a l l a s  APPENDIX A -- R e l a t i o n parameters B  b e t w e e n B^/n a n d S k e m p t o n ' s p o r e s  k  e  pressure  :  m  From t h e c o m p a t i b i l i t y o f t h e u n d r a i n e d c o n d i t i o n  Ae  f  v  =  n  ^  From E q . ( 3 . 3 . 4 ) i n t h e t e x t , t h e r e f o r e  Au = B  c  :  :  Ae (A2)  f where A e i s t h e v o l u m e t r i c v  fluid  s t r a i n change of t h e pore  element under u n d r a i n e d c o n d i t i o n s ,  corresponding volumetric  Ae  v  i s the  s t r a i n change of t h e s o i l  skeleton.  Since  - Au m = B' A e v ACT  (A3)  From E q . ( A 2 ) , E q . ( A 3 ) becomes :  ACT  m  - Au (A4)  313  314 Therefore  =  ACT  .  /  AU  (1 +  AB  »n "  Br)  m  From t h e d e f i n i t i o n  of t h e Skempton's p a r a m e t e r  B  s  k  e  m  i  Au skem ~ m 1 1 +  B  (A5)  -n  B'  f  R e a r r a n g i n g E q . (A5) :  B  f/  n  " ' B  B  sken/  ( 1  "  B  skem  )  T h i s i s t h e Eq. (3.3.11) i n t h e Text,  APPENDIX B B a s e d on B a g u e l i n e t a l ( 1 9 7 7 ) r e s u l t s Eqs.  (8.4.1) t o ( 8 . 4 . 4 ) ) , assuming t h a t a f l e x i b l e  cohesive  soils  i s loaded  R = 7 t o 12 1  where 1  g  ]  0  2 5  , (EI)  In the f i n i t e a s s u m e d 500 t i m e s stiffness.  stiffness  conditions :  f a c t o r d e f i n e d as  i s the r i g i d i t y of s o i l  of the p i l e  subgrade  element a n a l y s i s , s t r o n g e r than  i s equal  the s o i l  (8.3.7), then  elements are  elements i n the  of s o i l  t o t h e Young's modulus  t a k i n g u = 1 i n Eq.  section,  reaction.  the p i l e  I f assuming the c o e f f i c i e n t  reaction, E  pile in  .  0  i s the c o e f f i c i e n t  (i.e.  under u n d r a i n e d  i s the r e l a t i v e  0  [4(EI)_/E E  (see  subgrade  of the  the r a t i o  soils  o f E /E = P s  500. Since I  = 7rD /64,  by t h e d e f i n i t i o n lo  Therefore, t o 37  where D i s t h e p i l e  4  of  diameter,  then  1 , 0  = [4(EI) /E ]°' P  = 3.15  2 5  sc  the o u t e r boundary  D.  r a d i u s R = 7 t o 12 1  0  = 22 D  D. B a s e d on B a r d e t ' s  coefficient  of s o i l  Young's modulus, boundary  E,  r a t i o a/R  results  shown i n F i g . 8.4,  i f the  subgrade r e a c t i o n K i s c l o s e t o the for undrained i s equal  cohesive  soils,  the outer  t o 0.006, i . e . R = 83 D, 315  while  316 for  drained cohesionless s o i l ,  = 25  a/R  i s e q u a l t o 0.02,  i.e. R  D. B a s e d on t h e a b o v e r e s u l t s , a r e p r e s e n t a t i v e v a l u e o f  = 50 D i s u s e d f o r t h e piles  i n undrained  cohesive  t h e v a l u e s s u g g e s t e d by b e l i e v e d t o be  finite  element a n a l y s e s of  soils.  This value l i e s  B a g u e l i n e t a l and  reasonable  for present  flexible between  B a r d e t , and  analysis.  is  R  

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0062673/manifest

Comment

Related Items