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Hydraulic gradient similitude method for geotechnical modelling of pile group subjected to static lateral… Panwalkar, Anant 1994

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HYDRAULIC GRADIENT SIMILITUDE METHOD FOR GEOTECHNICAL MODELLING OF PILE GROUP SUBJECTED TO STATIC LATERAL LOAD by Anant Panwalkar B.Eng. Bombay U n i v e r s i t y , Bombay, India,1990 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS OF THE DEGREE OF MASTER OF APPLIED SCIENCE i n THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF CIVIL ENGINEERING We accept t h i s t h e s i s as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA October 1994 © Anant Panwalkar,1994 In presenting this thesis in partial fulf i lment of the requirements for an advanced degree at the University of Brit ish Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. C iv i l Engineering The University of Brit ish Columbia 2324 Ma in Mal l Vancouver. Canada V 6 T 1W5 Date: A/ ove^x be r 2. l •={ <? ^ ABSTRACT The t h e s i s considers the problem of v e r t i c a l p i l e group response to l a t e r a l s t a t i c loads. There are various s o l u t i o n s a v a i l a b l e for s i n g l e p i l e response to l a t e r a l loads. These s o l u t i o n s have been v e r i f i e d against a large database obtained from f i e l d experiments and model experiments. For p i l e groups very few t h e o r i e s have been proposed and due to the comparatively smaller database a v a i l a b l e i t i s not p o s s i b l e to develop and t e s t a sound theory for p r e d i c t i n g the p i l e group response to l a t e r a l loads. This t h e s i s i s aimed at Obtaining a database for response of p i l e groups comprising of two p i l e s subjected to l a t e r a l s t a t i c loads. Tests were c a r r i e d out i n the H y d r a u l i c Gradient S i m i l i t u d e Device i n order to b r i n g the s t r e s s s t a t e i n the s o i l to the f i e l d s t r e s s l e v e l . For t e s t i n g purposes three cases were considered, s i n g l e p i l e , s i n g l e p i l e adjacent to a loaded p i l e , and a p i l e group of two p i l e s . The s i n g l e p i l e t e s t r e s u l t s showed that the t e s t r e s u l t s were repeatable and r e l i a b l e . The t e s t s on a s i n g l e p i l e adjacent to a loaded p i l e showed that the p o s i t i o n of the p i l e w i t h respect to the loaded p i l e has a strong i n f l u e n c e on the response of the p i l e . - The unloaded p i l e i n the d i r e c t i o n of the loading and i n f r o n t of the loaded p i l e i s most e f f e c t e d . At a spacing of 2 diameters bending moment developed i s up to a I l l maximum of 20 percent of bending moment developed i n s i n g l e p i l e . This percentage decreases r a p i d l y w i t h i n c r e a s i n g spacing. I f the unloaded p i l e i s located behind the loaded p i l e or i s at 90° to the loading d i r e c t i o n , i t e s s e n t i a l l y p i c k s up very l i t t l e load from the loaded p i l e . The i n s t a l l a t i o n of two p i l e s d e n s i t i e s the s o i l i n between. In case of p i l e groups, the load sharing among the p i l e s i s based on the p i l e l o c a t i o n and the i n t e r a c t i o n e f f e c t i s not r e c i p r o c a l . The lead p i l e , i . e . the p i l e i n the d i r e c t i o n of load, shares maximum load with t r a i l p i l e sharing smaller load. V TABLE OF CONTENTS ABSTRACT i i AUTHORIZATION i v TABLE OF CONTENTS V LIST OF TABLES i x LIST OF FIGURES X ACKNOWLEDGEMENT x i v CHAPTER 1 : INTRODUCTION 1 1.1 INTRODUCTION 1 1 . 2 SCOPE OF STUDY 3 1.3 ORGANIZATION OF THESIS 4 CHAPTER 2 : LITERATURE REVIEW 6 2.1 INTRODUCTION 6 2.2 REVIEW OF THE SINGLE PILE RESPONSE TO LATERAL LOADS 6 2.2.1 THEORETICAL STUDIES 6 2.2.1.1 The E l a s t i c Boundary Element Approach 8 2.2.1.2 The Modulus Of Subgrade Reaction Approach 9 2.2.1.3 FINITE ELEMENT APPROACH 16 2.2.2 FIELD TESTING 16 2.2.3 MODEL STUDIES 19 2.3 REVIEW OF THE PILE GROUP RESPONSE TO THE LATERAL LOADS 21 v i 2.3.1 FIELD TESTING 22 2.3.2 MODEL TESTING 23 2.3.3 ANALYTICAL STUDY 25 2.3.3.1 FINITE ELEMENT ANALYSIS 29 2 .4 SUMMARY 3 2 C H A P T E R 3 : H Y D R A U L I C G R A D I E N T S I M I L I T U D E P R I N C I P L E . . . 35 3.1 INTRODUCTION 35 3.2 Hy d r a u l i c Gradient S i m i l i t u d e P r i n c i p l e . . . . 36 C H A P T E R 4 : M O D E L S O I L AND P I L E P R O P E R T I E S 4 0 4 . 1 MODEL SOIL 4 0 4.2 MODEL PILE PROPERTIES 41 C H A P T E R 5 : H Y D R A U L I C G R A D I E N T S I M I L I T U D E T E S T I N G D E V I C E 47 5 . 1 INTRODUCTION 47 5.2 Hy d r a u l i c Gradient S i m i l i t u d e T e s ting Device . . 47 5.2.1 SAND CONTAINER AND AIR PRESSURE CHAMBER . 5 0 5.2.2 WATER SUPPLY AND CIRCULATION SYSTEM . . 52 5.2.3 PILE HEAD LOADING AND MEASURING SYSTEM . 52 5.2.4 DATA ACQUISITION SYSTEM 55 5.2.5 DATA REDUCTION 57 C H A P T E R 6 : T E S T P R O C E D U R E 61 6.1 Test Procedure 61 6.2 RECONSTITUTION OF SAND DEPOSIT 61 v i i 6.3 PILE INSTALLATION 6 2 6.4 SOIL LOADING AND PILE LOADING 6 3 6.5 PILE HEAD LOADING 64 C H A P T E R 7 : R E S U L T S AND D I S C U S S I O N 6 6 7.1 INTRODUCTION 6 6 7.2 Tes t i n g Series 66 7.2.1 R e p e a t a b i l i t y of the t e s t r e s u l t s . . . . 67 7.2.2 Series I (SI) Si n g l e P i l e t e s t i n g r e s u l t s 68 7.2.2.1 LOAD DISPLACEMENT RESPONSE . . . . 71 7.2.2.2 P- (y-y 0) CURVE 71 7.2.2.3 BENDING MOMENT AND SHEAR FORCE PROFILE 7 3 7.2.3 Series I I (S2) P i l e Group Of Two P i l e s ( One P i l e Loaded) . . . . 74 7.2.3.1 Load Displacement Response . . . . 74 7.2.3.2 Bending moment and shear fo r c e d i s t r i b u t i o n 79 7.2.3.3 P- (y-y 0) CURVE 91 7 .2.3.4 CASE 2 = 90°) 94 7.2.3.5 CASE 3 (cj> = 180°) 94 7.2.4 SERIES I I I (S3) 97 7.2.4.1 Load Displacement 97 7.2.4.2 P-y CURVES . . . . . 101 7.2.4.3 Bending moment P r o f i l e 103 v i i i C H A P T E R 8 : P R E D I C T I O N O F T H E P I L E G R O U P R E S P O N S E . . . . 114 8.1 INTRODUCTION 114 8.2 THE FREE FIELD CONCEPT AND ITS APPLICATION . . . 114 8.3 PREDICTION OF PILE RESPONSE 116 8.3.1 COMPARISON OF BENDING MOMENT 117 8.3.2 LOAD DISPLACEMENT RESPONSE 119 8.4 SUMMARY 122 C H A P T E R 9 : SUMMARY AND C O N C L U S I O N 125 R E F E R E N C E S 128 i x L I S T O F T A B L E S TABLE 3.1 SCALING RELATIONS FOR CENTRIFUGE AND HYDRAULIC GRADIENT TESTS 39 TABLE 4.1 HYPERBOLIC SOIL PARAMETERS FROM DRAINED COMPRESSION TRIAXIAL TESTS 42 TABLE 4.2 PHYSICAL PROPERTIES OF MODEL PILES 43 X L I S T O F F I G U R E S FIGURE 2.1 CONCEPT OF WINKLER SPRINGS 11 FIGURE 2.2 n h i VS RELATIVE DENSITY, AFTER MURCHISON AND 0'NEILL(1984) 15 FIGURE 2.3 FACTORS FOR Pu, AFTER MURCHISON AND O'NEILL (1984) 15 FIGURE 2.4 CONCEPT OF WINKLER SPRINGS FOR TWO PILES (TROCHANIS ET AL, 1991) 34 FIGURE 3.1 HYDRAULIC GRADIENT SIMILITUDE PRINCIPLE . . 39 FIGURE 4.1 GRAIN SIZE DISTRIBUTION OF THE FINE OTTAWA SAND (YAN L I , 1991) 45 FIGURE 4.2 VARIATION OF PERMEABILITY VS VOID RATIO (YAN L I , 1991) 45 FIGURE 4.3 PILE INSTRUMENTATION 46 FIGURE 5.1 HYDRAULIC GRADIENT SIMILITUDE DEVICE . . . . 49 FIGURE 5.2 CONTAINER LID - PLAN AND VIEW 53 FIGURE 5.3 WATER FLOW SYSTEM IN UBC-HGT DEVICE . . . . 54 FIGURE 5.4 LOAD CELL 56 FIGURE 5.5 PILE HEAD DEFLECTION MEASUREMENT 58 FIGURE 7.1 LOAD DISPLACEMENT BEHAVIOUR - COMPARISON . . 69 FIGURE 7.2 P- ( y -y 0 ) CURVE - COMPARISON 69 FIGURE 7.3 BENDING MOMENT PROFILE - COMPARISON . . . . 70 FIGURE 7.4 LOAD-DISPLACEMENT CURVE - SINGLE PILE . . . 72 FIGURE 7.5 P- ( y -y 0 ) CURVES - SINGLE PILE . 72 x i FIGURE 7.6 BENDING MOMENT PROFILE - SINGLE PILE . . . . 75 FIGURE 7.7 DISPLACEMENT PROFILE - SINGLE PILE . . . . 75 SERIES 2 FIGURE 7.8 LOAD-DISPLACEMENT CURVES - ADJACENT PILE . . 77 FIGURE 7.9 LOAD DISPLACEMENT CURVES - LOADED PILE . . . 77 FIGURE 7.10 LOAD-DISPLACEMENT CURVES (S/D =2) 78 FIGURE 7.11 LOAD-DISPLACEMENT CURVES (S/D =4) 78 FIGURE 7.12 LOAD-DISPLACEMENT CURVES (S/D =6) 80 FIGURE 7.13 LOAD-DISPLACEMENT CURVES (LOADED PILE ) . . 80 FIGURE 7.14 COMPARISON OF INTERACTION COEFFICIENT . . . 81 FIGURE 7.15 BENDING MOMENT PROFILE- PILE 2 (S/D = 2) . . 83 FIGURE 7.16 BENDING MOMENT PROFILE- PILE 2 (S/D = 4) . . 83 FIGURE 7.17 BENDING MOMENT PROFILE- PILE 2 (S/D = 6) . . 84 FIGURE 7.18 BENDING MOMENT PROFILE- PILE 1 (S/D = 2) . . 84' FIGURE 7.19 BENDING MOMENT PROFILE- PILE 1 (S/D = 4) . . 86 FIGURE 7.20 BENDING MOMENT PROFILE- PILE 1 (S/D = 6) . . 86 FIGURE 7.21 COMPARISON OF BENDING MOMENT PROFILES(S/D=2) 87 FIGURE 7.22 COMPARISON OF BENDING MOMENT PROFILES(S/D=4) 87 FIGURE 7.23 COMPARISON OF BENDING MOMENT PROFILES(S/D=6) 89 FIGURE 7.24 DEFLECTION PROFILE- PILE 2 (S/D = 2) 89 FIGURE 7.25 DEFLECTION PROFILE- PILE 2 (S/D = 4) 90 FIGURE 7.26 DEFLECTION PROFILE- PILE 2 (S/D=6) 90 FIGURE 7.27 DEFLECTION PROFILE- PILE 1 (S/D = 2) 92 FIGURE 7.28 DEFLECTION PROFILE- PILE 1 (S/D = 4) 92 FIGURE 7.29 DEFLECTION PROFILE- PILE 1 (S/D = 6) 93 FIGURE 7.30 P - y CURVES- PILE 1 (S/D = 2) 95 x i i FIGURE 7.31 P - y CURVES- PILE 1 (S/D = 4) 95 FIGURE 7.32 P - y CURVES- PILE 1 (S/D = 6) 96 FIGURE 7.3 3 LOAD - DEFLECTION CURVE-PILE 1 : LOADING ANGLE 90° 96 FIGURE 7.34 BENDING MOMENT PROFILE-PILE 1 : LOADING ANGLE 90° 98 FIGURE 7.35 BENDING MOMENT COMPARISON : LOADING ANGLE 180° 98 SERIES 3 FIGURE 7.36 LOAD - DISPLACEMENT CURVE (S/D = 2) 99 FIGURE 7.37 LOAD - DISPLACEMENT CURVE (S/D = 4) 99 FIGURE 7.38 P-y CURVE (S/D = 2) 102 FIGURE 7.39 P-y CURVE (S/D = 4) 102 FIGURE 7.40 BENDING MOMENT PROFILE (S/D =2) 104 FIGURE 7.41 COMPARISON OF BENDING MOMENT PROFILE . . . . 104 FIGURE 7.42 DEFLECTION PROFILE (S/D = 2) 106 FIGURE 7.43 BENDING MOMENT PROFILE (S/D =4) 106 FIGURE 7.44 COMPARISON OF BENDING MOMENT PROFILE . . . . 108 FIGURE 7.45 DEFLECTION PROFILE (S/D = 4) 109 FIGURE 7.46 COMPARISON OF BENDING MOMENT (S/D =2) . . . 109 FIGURE 7.47 COMPARISON OF BENDING MOMENT (S/D =4) . . . I l l FIGURE 8.1 COMPARISON OF BENDING MOMENT FROM EXPERIMENT AND LATPILE FOR SINGLE PILE 118 FIGURE 8.2 COMPARISON OF BENDING MOMENT FROM EXPERIMENT AND LATPILE- PILE 2 (S/D = 2) 120 FIGURE 8.3 COMPARISON OF BENDING MOMENT FROM EXPERIMENT x i i i AND LATPILE- PILE 2 (S/D = 2) 120 FIGURE 8.4 COMPARISON OF BENDING MOMENT FROM EXPERIMENT AND LATPILE- PILE 2 (S/D = 4) 121 FIGURE 8 . 5 COMPARISON OF BENDING MOMENT FROM EXPERIMENT AND LATPILE- PILE 2 (S/D = 4) 121 FIGURE 8.6 COMPARISON OF BENDING MOMENT FROM EXPERIMENT AND LATPILE- PILE 2 (S/D = 6) 123 FIGURE 8.7 COMPARISON OF BENDING MOMENT FROM EXPERIMENT AND LATPILE- TRAILING PILE (S/D = 2) . . . . 124 FIGURE 8.8 COMPARISON OF BENDING MOMENT FROM EXPERIMENT AND LATPILE- TRAILING PILE (S/D = 4) . . . . 124 xiv Acknowledgements I would l i k e to take t h i s opportunity to express my great g r a t i t u d e to my research supervisor, Professor Peter M. Byrne for h i s i n v a l u a b l e support and guidance during a l l the stages of t h i s research work. I am al s o deeply indebted to Professor Y.P. Va i d for h i s help w i t h the equipment and t e s t i n g procedures. I would l i k e to acknowledge the t e c h n i c a l support provided by A r t , Harold and Ron, tech n i c i a n s i n the C i v i l Engineering Workshop. I would a l s o l i k e to extend my thanks to L i Yan who made s p e c i a l e f f o r t to help me during the course of my research. A l s o I would l i k e to thank my colleagues Raju M., Uthaya Kumar, Debasis Roy, Hendra J i t n o , for t h e i r help and u s e f u l d i s c u s s i o n s . S p e c i a l thanks to my family and f r i e n d s who wit h t h e i r support and understanding made t h i s research work p o s s i b l e . Research grant awarded by The Department of C i v i l Engineering i s g r a t e f u l l y acknowledged. CHAPTER 1 1 CHAPTER 1 : INTRODUCTION 1.1 I N T R O D U C T I O N In foundation engineering p r a c t i c e , p i l e s are f r e q u e n t l y used to r e s i s t l a r g e h o r i z o n t a l loads from the s u p e r s t r u c t u r e . In the past, p i l e foundations were designed and constructed based on experience. In recent years, due to research conducted i n t h i s area, a better understanding of p i l e response to the loads has been achieved. This has l e d to more e f f i c i e n t , economical designs and safety. Through f i e l d and model studies of p i l e s , sound t h e o r i e s have been developed for s i n g l e p i l e s loaded v e r t i c a l l y and h o r i z o n t a l l y . In a d d i t i o n , r e l i a b l e s o l u t i o n s have a l s o been developed for v e r t i c a l l y loaded p i l e groups. However, there i s a l a c k of r e l i a b l e theory and s o l u t i o n to p r e d i c t the response of p i l e groups to l a t e r a l loads and t h i s t h e s i s i s d i r e c t e d towards t h i s problem. To develop a r e l i a b l e theory which can p r e d i c t the response of p i l e groups to l a t e r a l loads, a large data base of p i l e group response i s required. So f a r , various researchers have proposed e m p i r i c a l s o l u t i o n s based on a very l i m i t e d f i e l d database. C H A P T E R 1 2 The database can be generated by conducting e i t h e r f i e l d t e s t s or labo r a t o r y model t e s t s . F i e l d t e s t s give the a c t u a l performance of the p i l e group, but are very c o s t l y . In model t e s t s , the s i z e of the sample and the t e s t p i l e s has a considerable e f f e c t on the response of the p i l e group. The model p i l e group can give s i m i l a r response as the f i e l d t e s t only i f the sample i s at the same s t r e s s l e v e l as the f i e l d s o i l . In recent years innovative techniques to conduct small model t e s t s at f i e l d s t r e s s l e v e l have been introduced. One of the methods to increase the sample s t r e s s l e v e l i s the Ce n t r i f u g e model t e s t . In t h i s procedure the r e q u i r e d s t r e s s l e v e l i s obtained by r o t a t i n g the sample at a given c e n t r i p e t a l a c c e l e r a t i o n to achieve the f i e l d s t r e s s l e v e l i n the model. Another method used to increase the sample s t r e s s l e v e l i s the Hydraulic Gradient method. The technique was f i r s t developed by Zelikson(1969) to increase the s t r e s s l e v e l of samples before conducting Centrifuge model t e s t , but l a t e r was developed i n t o a separate t e s t i n g - method. The H y d r a u l i c Gradient S i m i l i t u d e method, as i t i s known, uses a p r i n c i p l e s i m i l a r to the Centrifuge Model t e s t , i . e . i t increases the s t r e s s l e v e l of the sample by i n c r e a s i n g the body forces on the s o i l p a r t i c l e s . The d i f f e r e n c e i s i n the method used to increase the body forces. Whereas the Centrifuge model t e s t uses a c e n t r i p e t a l a c c e l e r a t i o n to increase the body f o r c e s , the Hydr a u l i c Gradient S i m i l i t u d e Method (HGSM) uses h y d r a u l i c CHAPTER 1 3 gradient to increase the body forces. Using t h i s technique Yan and Byrne (1991a) developed a Hydraulic Gradient S i m i l i t u d e T e s t i n g Device (HGST). In t h i s t h e s i s , the HGS method i s used to study the i n t e r a c t i o n e f f e c t between the l a t e r a l l y loaded p i l e s i n a group of v e r t i c a l p i l e s . The HGS model t e s t s were conducted to study the response of a p i l e group of two p i l e s subjected to l a t e r a l loads. One of the p i l e s was instrumented to measure the bending moments along the p i l e l e n g t h . The load on the p i l e s and p i l e head d e f l e c t i o n s were measured for each p i l e d uring the t e s t . A computer software program was used to record and s t o r e the data. The measured r e s u l t s from the t e s t s are compared w i t h the p r e d i c t i o n s from analyses. 1.2 S C O P E O F S T U D Y The major concerns for the l a t e r a l l y loaded p i l e are the bending moment, shear force and d e f l e c t i o n of the p i l e . In recent years, the patterns of the bending moment and shear fo r c e developed i n the s i n g l e p i l e and the d e f l e c t i o n s of the s i n g l e p i l e have been observed by various researchers. In t h i s t h e s i s a study of a p i l e group comprised of two p i l e s subjected to l a t e r a l loads i s conducted. The scope of the study of the t h e s i s i s as f o l l o w s Study the bending moment, shear force and d e f l e c t i o n p r o f i l e s of the s i n g l e p i l e subjected to l a t e r a l load. CHAPTER 1 4 Study the e f f e c t of the presence of an adjacent unloaded p i l e on the l a t e r a l response of a p i l e . Study the bending moment, shear force and d e f l e c t i o n p r o f i l e s of p i l e s i n a p i l e group comprised of two p i l e s subjected to l a t e r a l loading. 1.3 ORGANIZATION OF THESIS The t h e s i s i s d i v i d e d i n to seven chapters as f o l l o w s CHAPTER 1 :- INTRODUCTION. In t h i s chapter, the t h e s i s o b j e c t i v e and the t e s t i n g p r i n c i p l e i s given. CHAPTER 2 :- LITERATURE REVIEW. In t h i s chapter a l i t e r a t u r e review of the s i n g l e p i l e subjected to l a t e r a l s t a t i c loads, and p i l e groups subjected to l a t e r a l and v e r t i c a l loads i s given. The current t h e o r e t i c a l methods and previous f i e l d and model t e s t s are c r i t i c a l l y reviewed for t h i s purpose. CHAPTER 3 :- HYDRAULIC GRADIENT SIMILITUDE PRINCIPLE. The h y d r a u l i c gradient s i m i l i t u d e (HGS) t e s t i n g p r i n c i p l e used i n t h i s t h e s i s i s explained i n t h i s chapter. CHAPTER 4 :- MODEL SOIL AND PILE PROPERTIES. P r o p e r t i e s of the s o i l and p i l e used i n the model are described i n t h i s chapter. These p r o p e r t i e s can be used to p r e d i c t the p i l e response based on the e x i s t i n g s o l u t i o n s , e.g. e l a s t i c s o l u t i o n by Poulos C H A P T E R 1 5 (1971) . CHAPTER 5 : - HYDRAULIC GRADIENT SIMILITUDE TESTING DEVICE. The h y d r a u l i c gradient s i m i l i t u d e t e s t i n g device based on the HGS p r i n c i p l e explained i n the chapter 3 i s described i n d e t a i l i n t h i s chapter. CHAPTER 6 : - HYDRAULIC GRADIENT SIMILITUDE TESTING PROCEDURE. The h y d r a u l i c gradient s i m i l i t u d e t e s t i n g procedure for t e s t i n g l a t e r a l l y loaded p i l e s i s described i n d e t a i l i n t h i s chapter. CHAPTER 7 :- TEST RESULTS AND DISCUSSION. The r e s u l t s of the l a t e r a l load t e s t s on the s i n g l e p i l e and p i l e group are reported i n t h i s chapter. The r e s u l t s are discussed as to the e f f e c t of various parameters on the behaviour of the p i l e group and the d i f f e r e n c e s i n the behaviour of p i l e group and s i n g l e p i l e . CHAPTER 8 : - PREDICTION OF RESULTS USING LATPILE PROGRAM. The response of s i n g l e p i l e s and p i l e groups are p r e d i c t e d using the LATPILE program. The theory used for the p i l e group a n a l y s i s i s explained before the p r e s e n t a t i o n of the r e s u l t s . CHAPTER 9 :- SUMMARY AND CONCLUSIONS. In t h i s chapter, the t e s t r e s u l t s and conclusions are summarized. C H A P T E R 2 6 C H A P T E R 2 : L I T E R A T U R E R E V I E W 2.1 INTRODUCTION P i l e supported foundations are used for a l a r g e number of s t r u c t u r e s . Although they have been used for a long time, they are g e n e r a l l y analyzed and designed using e m p i r i c a l methods. With an increase i n the use of p i l e foundations, more and more researchers are aiming t h e i r research to f i n d a more r e l i a b l e and economical design method. Although there are some em p i r i c a l s o l u t i o n s a v a i l a b l e which can be used to p r e d i c t s t a t i c response of l a t e r a l l y loaded p i l e s , i t i s very d i f f i c u l t to p r e d i c t dynamic response of the p i l e foundations due to the complexity of the problem. Furthermore, p r e d i c t i o n of p i l e group response i s more d i f f i c u l t due to va r i o u s f a c t o r s involved, l i k e s o i l - p i l e i n t e r a c t i o n , p i l e - c a p - p i l e i n t e r a c t i o n . In t h i s chapter, the methods used to analyze l a t e r a l l y loaded s i n g l e p i l e are reviewed, f o l l o w e d by a review of methods used for the a n a l y s i s of p i l e group. The review i s l i m i t e d to the response of v e r t i c a l p i l e s subjected to l a t e r a l loads. 2.2 REVIEW OF THE SINGLE PILE RESPONSE TO LATERAL LOADS 2.2.1 THEORETICAL STUDIES When a s i n g l e p i l e i s loaded l a t e r a l l y , the load i s C H A P T E R 2 7 r e s i s t e d by the s o i l surrounding the p i l e as w e l l as by the p i l e i t s e l f i n bending and shear. In the case of p i l e groups, load t r a n s f e r by p i l e - s o i l - p i l e i n t e r a c t i o n a l s o occurs. The main concerns for l a t e r a l l y loaded p i l e s are P i l e d e f l e c t i o n Maximum Bending moment Maximum Shear force These can be computed by e i t h e r a f i e l d t e s t , model t e s t or by using a v a i l a b l e s o l u t i o n s . The l a t e r a l response of the p i l e foundation can be computed using one of the f o l l o w i n g methods 1. E l a s t i c boundary element approach 2 . Winkler sp r i n g approach or modulus of subgrade r e a c t i o n approach 3. F i n i t e element approach The e l a s t i c boundary element approach uses an e l a s t i c continuous s o i l model and e l a s t i c p i l e model, whereas the subgrade r e a c t i o n approach considers that the s o i l response can be simulated by compliance springs. These springs can be modelled as l i n e a r or nonlinear to simulate nonlinear response. In the f i n i t e element approach, the s o i l and p i l e are d i v i d e d i n t o small elements ( s o i l elements and beam elements) and the behaviour of these elements can be l i n e a r or n o n l i n e a r . The only disadvantage of the f i n i t e element approach i s that i t i s time consuming and c o s t l y . These methods are discussed i n d e t a i l i n the f o l l o w i n g C H A P T E R 2 paragraphs. 8 2.2.1.1 The E l a s t i c Boundary Element Approach The s o l u t i o n based on e l a s t i c boundary element approach was developed by Poulos (1971) . The e l a s t i c boundary element approach i s based on l i n e a r e l a s t i c theory for the s o i l medium and uses M i n d l i n ' s s o l u t i o n s for the s o i l displacements due to a p o i n t load w i t h i n an e l a s t i c i s o t r o p i c homogeneous h a l f s p a c e . The p i l e i s simulated by using a v e r t i c a l column w i t h the equ i v a l e n t s t i f f n e s s , EI, of the p i l e . C o m p a t i b i l i t y of s o i l and p i l e displacements i s forced at d i s c r e t e p o i n t s along the p i l e l e n g t h . The main parameters used for t h i s a n a l y s i s are the e l a s t i c parameters for s o i l , the Young's modulus, the Poisson's r a t i o , and the s t i f f n e s s of the p i l e given by the term EI. The r e s u l t s are a v a i l a b l e i n the form of Design c h a r t s and have been widely used by researchers and p r a c t i s i n g engineers. The advantage of t h i s method i s that i t considers the s o i l as a continuum, which makes i t easy to analyze the p i l e group behaviour. But, at the same time, i t should be noted that the e l a s t i c continuum s o l u t i o n i s s t r i c t l y a p p l i c a b l e only to small s t r a i n l e v e l s . Various other f a c t o r s a f f e c t i n g the l i n e a r behaviour of the s o i l , such as s o i l y i e l d i n g , f i n i t e depth of s o i l l a y e r , non-homogeneity, etc can be taken i n t o account by i n t r o d u c i n g a c o r r e c t i o n f a c t o r to the e l a s t i c s o l u t i o n . Since, the p i l e - s o i l behaviour i s n o n - l i n e a r , i t i s CHAPTER 2 9 d i f f i c u l t to s e l e c t the appropriate Young's modulus and Poisson's r a t i o (Poulos 1980,1987; Poulos et a l 1992). 2.2.1.2 The Modulus Of Subgrade Reaction Approach In t h i s approach, the p i l e i s t r e a t e d as a l i n e a r e l a s t i c beam-column and the surrounding s o i l i s replaced by a bed of uncoupled Winkler springs. The model i s i l l u s t r a t e d i n f i g u r e 2.1 and represents l o a d - d e f l e c t i o n p r o p e r t i e s of s o i l - p i l e system under l a t e r a l loadings. The governing equation for t h i s type of model i s based on the c l a s s i c a l H e t n e y i 1 s s o l u t i o n for a beam column on an e l a s t i c foundation. The r e s u l t i n g governing equation i s given as d V d2y d z 4 d z 2 eq. (2.1) Pz = a x i a l load on the p i l e y • = l a t e r a l d e f l e c t i o n of the p i l e at depth z along the p i l e l e n g t h z = depth below the ground surface of the p o i n t under c o n s i d e r a t i o n P = s o i l r e a c t i o n per u n i t length and EI = the f l e x u r a l r i g i d i t y of the p i l e In the above model, the Winkler's springs can be e i t h e r l i n e a r or no n l i n e a r . Their force d e f l e c t i o n response i s u s u a l l y termed as P-y curves and i s s p e c i f i e d at p o i n t s along the p i l e l e n g t h . This method provides a v e r s a t i l e a n a l y t i c a l t o o l to C H A P T E R 2 10 i n c o r p o r a t e both the s o i l non-homogeneity and nonlinear response. However, t h i s approach does not take i n t o account the s o i l c o n t i n u i t y and hence can not be r e a d i l y a p p l i c a b l e to p i l e group a n a l y s i s . The s o i l r e a c t i o n , P, i n equation 2.1 i s r e l a t e d to the l a t e r a l d e f l e c t i o n , y, l i n e a r l y as f o l l o w s , P = Kh y eq. (2.2) Where Kh i s the h o r i z o n t a l subgrade r e a c t i o n modulus The c o e f f i c i e n t of h o r i z o n t a l subgrade r e a c t i o n , k h , used i n s o i l mechanics i s defined as p = k h y eq. (2.3) where p i s the s o i l pressure, k h i s r e l a t e d to the h o r i z o n t a l subgrade modulus as fo l l o w s k h = Kh / D eq. (2.4) where D i s the p i l e diameter. The c o e f f i c i e n t of h o r i z o n t a l subgrade r e a c t i o n given by Terzaghi(1955) v a r i e s l i n e a r l y w i t h depth. In p r a c t i c e , the v a r i a t i o n of k h w i t h depth can be non l i n e a r . Various c l o s e d form s o l u t i o n s for l i n e a r as w e l l as p a r a b o l i c d i s t r i b u t i o n s are a v a i l a b l e (Scott 1981; Poulos 1982; F r a n k l i n and Scott 1979;). Various f a c t o r s a f f e c t i n g the c o e f f i c i e n t of h o r i z o n t a l subgrade r e a c t i o n have been reported. These f a c t o r s a r i s e because the Winkler sp r i n g system i s uncoupled and ignores the s o i l c o n t i n u i t y and hence i s not a fundamental approach and needs c a l i b r a t i o n w i t h more fundamental a n a l y s i s and f i e l d CHAPTER 2 11 Ground Level P i l e or Winkler's Springs F i g . 2.1 Concept Of W i n k l e r ' s S p r i n g s C H A P T E R 2 12 experience. However, i t has the advantage that both non-homogeneous and nonlinear s o i l e f f e c t s can be simply incorporated. Various methods to determine the P-y curves have been proposed. The method proposed by Reese et a l ( l 9 7 4 ) i s e m p i r i c a l and has been adopted by the American Petroleum I n s t i t u t e (API) design code. This procedure was based on the back - a n a l y s i s of the f u l l s c a l e instrumented p i l e load t e s t s on Mustang I s l a n d , Texas (Cox et a l 1974) . The P-y curves are constructed at d e s i r e d depths w i t h the i n i t i a l slope of curves d e f i n e d as Khi = n h i . z eq. (2.5) where z i s the depth of P-y curve, Khi i s the subgrade r e a c t i o n modulus, and n h i i s the c o e f f i c i e n t of subgrade r e a c t i o n modulus. Reese (1974) suggested that the values of n h i to be used should be 2.5 to 4 times larger than those suggested by Terzaghi(1955). I t should be taken i n t o c o n s i d e r a t i o n that the Terzaghi values are at the working load values while the Reese et a l values are the i n i t i a l values. Jamolkowski and Garassino (1977) suggested the f o l l o w i n g expression for the c o e f f i c i e n t of subgrade r e a c t i o n modulus n h i = 19 7W . ( Dr ) ]" 1 9 eq. (2.6) where yw i s the u n i t weight of water, Dr i s the r e l a t i v e density of submerged s o i l s . Murchison and 0 ' N e i l l (19 8 3) gave the n h i values for the dry C H A P T E R 2 13 sands i n terms of r e l a t i v e density and f r i c t i o n angle (Figure 2.2). Yan and Byrne(1991a) have shown that the i n i t i a l slope of the P-y curves can be represented by the maximum Young's modulus of the s o i l , E m a x, obtained from downhole or crosshole seismic t e s t s . The u l t i m a t e s o i l r e s i s t a n c e , Pu, i n the Reese et a l P-y curve was determined from the l e s s e r of the f o l l o w i n g , Pu = yz [ D (Kp - Ka ) + z Kp tan 0 tan S ] eq. (2.7) Pu = Y D z [ K P 3 + 2 K o K P 2 tan <|> + tan <$> - Ka. ] eq. (2.8) where P u i s the u l t i m a t e s o i l r e s i s t a n c e force per u n i t depth, z i s the depth, Y i s the e f f e c t i v e u n i t weight of s o i l (submerged or t o t a l ) , Ka, Kp are the Rankine a c t i v e and passive c o e f f i c i e n t s r e s p e c t i v e l y , K0 i s the at r e s t earth pressure c o e f f i c i e n t , 0 i s the angle of i n t e r n a l f r i c t i o n , and 6 = 45° + 4>/2 . eq. (2.9) A number of s t u d i e s i n d i c a t e that Pu for cohesionless s o i l i s not w e l l d e f i n e d (Kubo, 1966; Yoshida and Yoshinaka 1972; Scott 1981; Ting et a l 1987). Despite these f i n d i n g s , the concept of Pu i s s t i l l used to define the P-y curves. Bogard and Matlock (1980) proposed the f o l l o w i n g equations for the u l t i m a t e s o i l pressures i n sand Pu = ( C, z + C2 D ) Y z eq. (2 . 10) Pu = C3 D Y z eq. (2 .11) C H A P T E R 2 14 The parameters C 1 ( C2, C3 are given i n Figure 2.3. Murchison and O'Neill(1984) gave the f o l l o w i n g equation for determining the s o i l r e s i s t a n c e P at any d e f l e c t i o n value, y, P = T ] A P u t a n r [ ( - ^ - ) y] Ar\ P eq. (2.12) i n which Pu i s taken as lesser value of eqn.s 2.10 and 2.11. The e m p i r i c a l f a c t o r A i s given as A =0.9 for c y c l i c loading and eq. (2.13) = 3 - 0 . 8 z/D > 0.9 for s t a t i c loading eq. (2.14) The 1987 API code has adopted t h i s equation to describe the P-y curves and n i s a fact o r used to describe p i l e shape e f f e c t . During t h e i r t e s t i n g , Yan and Byrne (1990) found that the p i l e head response and bending moment are s i g n i f i c a n t l y a f f e c t e d by the r e l a t i v e s o i l - p i l e s t i f f n e s s , p i l e diameter, p i l e head e c c e n t r i c i t y and p i l e head f i x i t y . I t was a l s o found that the P-y curves are not a f f e c t e d by the p i l e diameter, p i l e head e c c e n t r i c i t y and p i l e head f i x i t y but s i g n i f i c a n t l y a f f e c t e d by the r e l a t i v e s o i l - p i l e s t i f f n e s s due to the s o i l s t r e s s l e v e l s . I t was found that for the monotonic loading the s t r e s s l e v e l dependency of the P-y curves can be reasonably normalized by the Young's moduli of the s o i l s and the p i l e diameter for P-y curves at depths below l p i l e diameter, using the hy p e r b o l i c s t r e s s -s t r a i n r e l a t i o n s h i p for s o i l s . 3 0 0 2 5 0 2 0 0 c 1 5 0 1 0 0 5 0 (1) / (2), V 8 , 0 0 0 6 , 0 0 0 c B CO c 4 , 0 0 0 jg c g 'co c 2 , 0 0 0 1 2 0 4 0 6 0 8 0 Relative Density - Dr (%) (1) - SAND ABOVE THE WATER TABLE (2) - SAND BELOW THE WATER TABLE 1 0 0 g. 2 . 2 nhi vs. relative density, after Murchison and O'Neil l (1984) CM O T3 4 c co O i 3 3 -• y • C2 C3 1 0 0 8 0 6 0 4 0 2 0 3 £ c 92 ' o CD o O CO CD ca > 2 0 2 5 3 0 3 5 Angle of Internal Friction (Deg.) 4 0 Fiq. 2.3 Factors for Pu, after Murchison and O'Neill (1984) C H A P T E R 2 16 2.2.1.3 FINITE ELEMENT APPROACH Various s t u d i e s have been conducted on the behaviour of the p i l e s using the f i n i t e element methods. Due to i t s v e r s a t i l i t y t h i s method i s most s u i t a b l e for studying e f f e c t s of v a r i o u s parameters such as s o i l n o n l i n e a r i t y , s o i l nonhomogeneity, e t c . on the p i l e response. Nair et al(1969) conducted a d e t a i l study of s i n g l e p i l e s and p i l e groups using f i n i t e element methods. B u t t e r f i e l d and Banerjee(1971) used f i n i t e element method to study the e f f e c t s of various m a t e r i a l s on the p i l e foundation, i . e . concrete, s t e e l and wood. The s o i l - p i l e s e p a r a t i o n i s s t r e s s dependent and a f f e c t s the p i l e c a p a c i t y s i g n i f i c a n t l y . To model t h i s s t r e s s dependency a d e t a i l e d three dimensional f i n i t e element program i s required. 2.2.2 FIELD TESTING In the f i e l d t e s t i n g of s i n g l e p i l e s , a h y d r a u l i c actuator and a r e a c t i o n p i l e are used to apply a h o r i z o n t a l force on the p i l e . The loading connection can be made as requi r e d . Generally a f r e e head connection i s made. In t h i s type of connection the p i l e head i s allowed to ro t a t e with the a p p l i c a t i o n of load. The p i l e i s instrumented to measure and record the a p p l i e d loads and displacements. The bending moment along the p i l e l ength can a l s o be computed by a t t a c h i n g s t r a i n gauges at var i o u s depths. Also the r o t a t i o n of the p i l e at the p i l e head or ground l e v e l can be c a l c u l a t e d or observed. Reese and Cox (1986) have proposed a C H A P T E R 2 17 method to develop the P-y curves along the l e n g t h of the p i l e u s ing the p i l e head d e f l e c t i o n s and r o t a t i o n s , along w i t h the corresponding loads. In p r a c t i c e , f i e l d t e s t s are very c o s t l y . A l a r g e number of the case h i s t o r i e s reported have been performed on the p i l e s w i t h p i l e response measured only at the p i l e head. Very few t e s t s are performed on f u l l y instrumented p i l e s . R e s u l t s of the few f u l l y instrumented f u l l s c ale p i l e t e s t s are used along w i t h the other t e s t s to evaluate the p i l e - s o i l i n t e r a c t i o n behaviour along the p i l e length. F u l l y instrumented t e s t p i l e s were used by A l i z a d e h and Davisson (197 0) i n the Arkansas River P r o j e c t . In t h i s p r o j e c t , the p i l e s were s t e e l H shaped p i l e s i n medium den-se sand subjected to l a t e r a l s t a t i c and c y c l i c loads. The loads were a p p l i e d h o r i z o n t a l l y at the ground l e v e l . In the a n a l y s i s of the c y c l i c behaviour of the p i l e s , the unloading behaviour of the p i l e s i s very important. The r e s i d u a l moments l e f t i n the p i l e s are a l s o very important. Unfortunately these were not reported. The l o a d - d e f l e c t i o n behaviour of the p i l e head and the bending moments along the p i l e s at various load l e v e l s were reported. Using the Matlock and Reese (1960) method, where the observed p i l e head response i s modelled e l a s t i c a l l y , i t was found that the p i l e model parameter, n h, depends on the displacement or the load l e v e l . The p i l e head d e f l e c t i o n was found to s i g n i f i c a n t l y i n c r e a s e w i t h number of c y c l e s under one-way c y c l i c l o a d i n g . However, s o i l - p i l e i n t e r a c t i o n i n terms of P-y curves was not C H A P T E R 2 18 evaluated i n these s t u d i e s . The major breakthrough i n the a n a l y s i s of s i n g l e p i l e s subjected to l a t e r a l loads came i n 1974, when Cox et a l (1974) reported t e s t r e s u l t s of the s i n g l e f u l l y instrumented p i l e embedded i n sand subjected to l a t e r a l monotonic and c y c l i c loads. In these t e s t s , the p i l e head response was measured along w i t h the bending moments along the length of the p i l e . This a s s i s t e d i n determining the p i l e - s o i l i n t e r a c t i o n not only at the ground l e v e l but along the length of the p i l e as w e l l . Based on these r e s u l t s Reese et a l (1974)proposed P-y c o n s t r u c t i o n method for the v e r t i c a l p i l e s i n cohesionless m a t e r i a l s subjected to l a t e r a l loads. Brown et a l ( l 9 8 7 ) of the U n i v e r s i t y of Houston conducted displacement c o n t r o l l e d two-way c y c l i c loading on s i n g l e p i l e s . The p i l e s were embedded i n sand o v e r l y i n g s t i f f c l a y deposits up to about 10 p i l e diameters deep. I t was found that response of the p i l e s i n sand was not a f f e c t e d s i g n i f i c a n t l y by the number of two-way loading c y c l e s . I t was also found that the Reese et a l (1974) P-y curve procedure underestimates the f i e l d measurements. Most of the f i e l d studies were not comprehensive and hence do not a l l o w for a fundamental study. I t i s d e s i r a b l e to perform f u l l y instrumented f u l l scale l a t e r a l p i l e load t e s t s . However, such p i l e t e s t s are expensive and time consuming. C H A P T E R 2 2 . 2 . 3 M O D E L S T U D I E S 19 Model t e s t s are ofte n used due to the low cost i n v o l v e d and the convenience. Previous to the development of the Ce n t r i f u g e model t e s t i n g , a l l the model t e s t s were performed i n l g gravity-c o n d i t i o n and the p i l e responses were e x t r a p o l a t e d to f i e l d c o n d i t i o n . But due to the d i f f e r e n t s t r e s s c o n d i t i o n s , the model t e s t s had severe l i m i t a t i o n s over the f u l l s c a l e f i e l d t e s t i n g . With the development of the Centrifuge t e s t i n g method, the number of model t e s t s conducted at the f i e l d s t r e s s l e v e l s i s i n c r e a s i n g , but i s s t i l l very small due to the l a r g e costs i n v o l v e d . Kubo(1963) conducted l g model p i l e t e s t s i n sand. The p i l e s e c t i o n was e i t h e r rectangular or c i r c u l a r and the p i l e head c o n d i t i o n s used were e i t h e r f i x e d or free head r e s t r a i n t . Based on the r e s u l t s of these experiments an equation for the s o i l pressure along the p i l e length was proposed as f o l l o w s : p = k . z . y°6 eq. (2.15) where k i s the f i t t i n g parameter, z i s the depth along the p i l e , y i s the p i l e d e f l e c t i o n . Based on the a n a l y s i s of some l a t e r a l load t e s t s on sandy and clayey s o i l s using the subgrade r e a c t i o n method, Yoshida and Yoshinaka (1972) i n d i c a t e d that for a c i r c u l a r p l a t e the h o r i z o n t a l s o i l r e a c t i o n modulus i s a f u n c t i o n of the diameter of the p l a t e . These r e s u l t s c o n t r a d i c t the r e s u l t s reported by CHAPTER 2 ZU Terzaghi (1955), Reese et a l (1974). Poulos reported some model t e s t s at l g c o n d i t i o n f o r studying the s i n g l e p i l e and p i l e group responses i n c l a y (Mattes and Poulos,1971) and sand (Selby and Poulos, 1983) . Using these t e s t r e s u l t s Poulos c a l i b r a t e d the e l a s t i c boundary element s o l u t i o n f o r use i n p r a c t i c e . Scott (1976) performed a s e r i e s of model p i l e t e s t s i n the c e n t r i f u g e . The t e s t i n g program was designed to simulate the f u l l s c ale f i e l d t e s t i n g at the Mustang Is l a n d performed by Cox et a l (1974). The f u l l s c a l e t e s t i n g c o n d i t i o n was simulated i n 100 g with both dry and saturated s o i l c o n d i t i o n s . The model t e s t r e s u l t s from these t e s t s underestimated the f i e l d p i l e head response. This shows the d i f f i c u l t i e s i n the model t e s t i n g even at the f i e l d s t r e s s l e v e l s . Barton(1982) conducted a more comprehensive study of p i l e s subjected to s t a t i c and c y c l i c l a t e r a l loads i n the c e n t r i f u g e t e s t i n g machine. The comparison between the experimental P-y curves and those proposed by Reese et a l (1974) showed that Reese et a l curves underestimate the s o i l r e s i s t a n c e near the ground surface and overestimate i t at greater depth. Zelikson(1978) f i r s t employed the h y d r a u l i c gradient s i m i l i t u d e method to study model p i l e s under i n c l i n e d loads. Yan (1991) conducted a thorough study of model p i l e s subjected to s t a t i c and c y c l i c l a t e r a l loads using the same p r i n c i p l e . In h i s study, the model p i l e c o n s i s t e d of s t e e l pipe p i l e s e i t h e r f i x e d or pinned at the top. The experimental P-y curves were compared C H A P T E R 2 21 w i t h the t h e o r e t i c a l P-y curves obtained by using API method. He found that the same set of P-y curves can be used r e g a r d l e s s of p i l e head e c c e n t r i c i t y and f i x i t y . Based on t e s t r e s u l t s , he found that the API method tends to overpr e d i c t the bending moment and shear force at la r g e loads and underestimates displacement at smaller loads. A lso on the b a s i s of the f i n i t e element s t u d i e s , he found out that the h y p e r b o l i c s o i l parameters give o v e r a l l better p r e d i c t i o n i n a l l aspects of p i l e response for plane s t r a i n a n a l y s i s . 2 . 3 R E V I E W O F T H E P I L E GROUP R E S P O N S E T O T H E L A T E R A L L O A D S Although there i s a good understanding of the s i n g l e p i l e response to l a t e r a l loads, the response of the p i l e group and the l o ad t r a n s f e r and the p i l e - s o i l - p i l e i n t e r a c t i o n i s s t i l l not completely understood. Very few f i e l d p i l e group t e s t s are conducted due to la r g e costs i n v o l v e d . Because i t i s very d i f f i c u l t to o b t a i n the same s o i l s t r e s s i n the l a b o r a t o r y as i n the f i e l d the number of model t e s t s conducted are a l s o very few. The t h e o r i e s that have been proposed are based on a small database and cannot be v a l i d a t e d c o r r e c t l y due to l a c k of a l a r g e database. In the past few decades some research has been d i r e c t e d towards t h i s problem and as r e s u l t there i s some understanding of the p i l e group response to l a t e r a l loads. The f o l l o w i n g paragraphs present a d e t a i l e d review of the t e s t i n g and the t h e o r e t i c a l s o l u t i o n s developed during past few years. C H A P T E R 2 2 2 2 . 3 . 1 F I E L D T E S T I N G A l l the l a t e r a l p i l e load t e s t s were conducted by a p p l y i n g the load using a r e a c t i o n p i l e at some distance away. The loads on the p i l e s i n the p i l e group and the displacement of the p i l e s at the top i n the p i l e group were measured. The bending moment was obtained at s p e c i f i e d p o i n t s along the p i l e l e n g t h and i n t e g r a t e d n u m e r i c a l l y to obta i n the bending moment p r o f i l e . This bending moment i s then i n t e g r a t e d to get slopes and d e f l e c t i o n s , and d i f f e r e n t i a t e d to get force and s o i l pressures on the p i l e . As the i n s t a l l a t i o n of the s t r a i n gages and measuring the s t r a i n s produced i s c o s t l y , many researchers s t i l l measure only the p i l e head load and d e f l e c t i o n s . Schmidt (1981,1985) conducted an extensive f i e l d t e s t i n g program on a group of v e r t i c a l p i l e s . He subjected the p i l e group to one c y c l e of loading. C y c l i c l o a d i n g was f o l l o w e d by lo a d i n g one p i l e i n the p i l e group and measuring the displacements of the adjacent p i l e . The r e s u l t s of the experiment showed that the induced displacements have no r e l a t i o n s h i p w i t h the e f f i c i e n c y of the p i l e group. The e f f i c i e n c y of the p i l e group i s defined as, the r a t i o of the t o t a l l o ad taken by the p i l e group d i v i d e d by the product of the load taken by s i n g l e p i l e for same displacement and the number of p i l e s i n the group. I t should be noted here t h a t , during h i s t e s t i n g he f i r s t subjected the p i l e to one c y c l e of l o a d i n g and then used the same set up to study the e f f e c t of the induced CHAPTER 2 2 3 then used the same set up to study the e f f e c t of the induced displacement on the p i l e group e f f i c i e n c y . A l so, during the experiments he noticed that the depth of the maximum bending moment i n the rear p i l e s i n p i l e groups i s more than that i n the s i n g l e p i l e . S i m i l a r r e s u l t s were obtained from the t e s t s conducted by Sharnouby and Novak ( 1 9 8 5 ) . In t h e i r t e s t i n g they used a p i l e group of s i x p i l e s subjected to l a t e r a l load. A p i l e group of eight p i l e s was t e s t e d by Holloway(1981). Reese et al(1987) conducted l a t e r a l load t e s t s on p i l e group. Based on the r e s u l t s of these t e s t s , they suggested that the e f f e c t of p i l e group can best be achieved by not i n c r e a s i n g y i n the t y p i c a l P-y curves f o r the p i l e - s o i l system but by reducing P. Ochoa and O'neil (1989) conducted f u l l scale l a t e r a l l o a d p i l e group t e s t i n g i n submerged sand from medium to high r e l a t i v e density. Their r e s u l t s show that the i n t e r a c t i o n between the p i l e s i n the l a t e r a l l y loaded p i l e group i s very much dependent on the p i l e p o s i t i o n s and the load a p p l i e d . This suggests i t i s unwise to assume the r e c i p r o c i t y of the i n t e r a c t i o n f a c t o r s . 2.3.2 MODEL TESTING Although the f i e l d t e s t i n g i s very c o s t l y , not many researchers have conducted model s t u d i e s of groups of p i l e s . One of the reason f o r t h i s i s that u n t i l r e c e n t l y model studi e s i n v o l v e d only reducing the s i z e of the prototype and t e s t i n g i t under low s t r e s s c o n d i t i o n s . Since the behaviour of the s o i l i s C H A P T E R 2 24 s t r e s s dependent the response of the small s o i l sample at low s t r e s s l e v e l i s very d i f f e r e n t than the f i e l d response. A second reason was that, due to boundary e f f e c t s , there was a l i m i t to the s i z e of the model that could reasonably represent the f i e l d prototype. In 7 0's and 8 0's, w i t h the development of the c e n t r i f u g e modelling technique, model t e s t i n g was given an a l t o g e t h e r d i f f e r e n t p e r s p e c t i v e . Using t h i s technique, i t became p o s s i b l e to conduct t e s t s on small models at s t r e s s l e v e l s e q u i v a l e n t to that i n the f i e l d . But the c e n t r i f u g e model t e s t i n g i s very c o s t l y . A l s o i t requires h i g h l y s k i l l e d t e c h n i c a l s t a f f to maintain and operate the machine. Therefore, many researchers s t i l l p r e f e r to conduct the t e s t s i n normal s t r e s s c o n d i t i o n s . Meyerhof et a l (1988) reported group t e s t s on model p i l e s of v a r i o u s m a t e r i a l s . Davisson and S a l l y (1970) rep o r t the model t e s t i n g of a l a r g e group of p i l e s for the Arkansas River N a v i g a t i o n P r o j e c t . These t e s t s were conducted under a s t r e s s c o n d i t i o n of l g . Aurora (1983) reports c e n t r i f u g e t e s t i n g used for the a n a l y s i s of behaviour of group of p i l e s of l a r g e diameter. The t e s t s conducted by K u l k a r n i et a l (1985) i n c l u d e d groups of p i l e s having two or three p i l e s , and the t e s t s were conducted i n the c e n t r i f u g e machine. The p i l e s were f i x e d at the top and connected with a p i l e cap. During t h e i r t e s t s they n o t i c e d that the n o n - l i n e a r i t y of the s o i l and the p l a s t i c flow of the s o i l around the p i l e are very important i n the l a t e r a l l y loaded p i l e group a n a l y s i s . Also i t was seen that the f r o n t C H A P T E R 2 2 5 p i l e s share a much larger load and f l e x u r a l s t r e s s e s . The t e s t s conducted by Shibata et a l (1989)on l a t e r a l l y loaded p i l e group were under normal s t r e s s c o n d i t i o n s . The e f f i c i e n c y of the p i l e group from experiment was compared w i t h the t h e o r e t i c a l e f f i c i e n c y . The s o l u t i o n given by Randolph(1981) was used for t h i s purpose. A discrepancy of 30% was observed i n the r e s u l t s . 2.3.3 ANALYTICAL STUDY A n a l y t i c a l methods for p i l e groups i n c l u d e the t h e o r e t i c a l s o l u t i o n s and the s o l u t i o n s based on numerical methods. T h e o r e t i c a l s o l u t i o n s of a s i n g l e l a t e r a l l y loaded p i l e have been explained i n previous paragraphs. The e l a s t i c approach can be r e a d i l y extended to analyze the p i l e groups, while i t i s d i f f i c u l t to analyze p i l e groups by the P-y curve approach. In case of s i n g l e p i l e s the P-y curve approach i s the most widely used method of a n a l y s i s . The current p r a c t i c e for an a l y s i n g the p i l e groups i s to use softened P-y curves for the group a n a l y s i s . The modulus of subgrade r e a c t i o n approach for s i n g l e p i l e s was described above. Broms (1964) f i r s t proposed a theory to analyze the group of p i l e s loaded l a t e r a l l y . The main concept of h i s theory was that the p i l e s can be treated as beams and long p i l e s develop p l a s t i c hinges at a c e r t a i n depth below the ground l e v e l . I f t h i s depth can be determined and the p i l e response compared wi t h C H A P T E R 2 2 6 that of the beam, then the beam can be used to p r e d i c t the p i l e response. Randolph (1981) developed an expression to c a l c u l a t e the i n t e r a c t i o n f a c t o r s based on the f i n i t e element a n a l y s i s of p i l e groups. He solved the d i f f e r e n t i a l equations using the Four i e r technique i n s t e a d of the boundary element method used by Poulos (1971) . The expression for a f i x e d head p i l e given by Randolph i s as f o l l o w s , E 1/7 r, - a = 0 J 6 P c ( ^ ) — (1 + c o l l i ; ) p F c Gc S eq. (2.16) i Where a p F i s the i n t e r a c t i o n c o e f f i c i e n t for a p i l e group w i t h f i x e d head, S i s the p i l e spacing, r 0 i s the p i l e r a d i u s , \|r i s the angle between p i l e centres and the d i r e c t i o n of the load, p c f a c t o r to take i n t o account the v a r i a t i o n of s o i l s t i f f n e s s w i t h depth, 0.5 for s t i f f n e s s p r o p o r t i o n a l to the depth, 1.0 for homogeneous s o i l s , Gc the average value of G* over the a c t i v e l e n g t h of the p i l e , G* = G ( l + 3 u / 4 ) , eq. (2 .17) u Poison's r a t i o , C H A P T E R 2 G shear modulus of the s o i l , I f a p F > 0.5 then a p F = 1 - ( 4 a p P ) 27 eq. (2.18) S i m i l a r l y for f r e e headed p i l e s the i n t e r a c t i o n f a c t o r i s given by p G S eq. (2.19) c I f a p h > 0.5, then a p h = 1 - ( 4 a p h ) 1 eq. (2.20) Focht and Koch (1973) proposed a theory, c a l l e d y-modifier approach, which i s most widely used i n p r a c t i c e . They suggested use of e l a s t i c i n t e r a c t i o n f a c t o r s given by Poulos(1971) for i n t e r a c t i o n of p i l e s and use of P-y curve method for o b t a i n i n g d e f l e c t i o n of s i n g l e p i l e . According to t h e i r method the d e f l e c t i o n of a p i l e group, pk, i s given by m Where P Unit d e f l e c t i o n at the mudline, p.j Displacement of j t h p i l e , I n t e r a c t i o n e f f e c t of p i l e k on p i l e j , y t D e f l e c t i o n of the s i n g l e p i l e . The l i m i t a t i o n s of the theory come from the d i f f e r e n c e s i n the assumptions made i n the subgrade modulus theory and the C H A P T E R 2 2 8 e l a s t i c theory by Poulos. The subgrade modulus theory i s based on the assumption that the s o i l response can be modelled by w e l l d e f i n e d springs which are not connected to each other whereas the e l a s t i c model assumes the s o i l to be an e l a s t i c continuum. The y m o d i f i e r approach suggested above softens the P-y curve not only at mudline but at a l l depths. Hence the r e s u l t i n g moment and d e f l e c t i o n curve overestimate the moments and d e f l e c t i o n s . The above equation can be r e w r i t t e n as Where p k i s the d e f l e c t i o n of the k p i l e , pP Unit reference displacement of a s i n g l e p i l e under a u n i t h o r i z o n t a l load, from e l a s t i c theory, Hj L a t e r a l load on p i l e j , a j p k j C o e f f i c i e n t to get i n f l u e n c e of p i l e j on p i l e k, R R e l a t i v e s t i f f n e s s f a c t o r , where R i s the r a t i o of mudline d e f l e c t i o n of a s i n g l e p i l e from P-y method to the mudline d e f l e c t i o n from Poulos 1s method, Hk L a t e r a l load on p i l e k, m number of p i l e s Reese et a l (1984) compared the r e s u l t s from t h i s method wit h the r e s u l t s from the f i e l d t e s t s . They a l s o compared the r e s u l t s by analysing the p i l e group as a l a r g e diameter C H A P T E R 2 2 9 imaginary p i l e . They found that the y modifier approach by Focht and Koch(l973) i s very s e n s i t i v e to the R value used. Sharnouby and Novak (1986) proposed a new method based on M i n d l i n ' s displacement f i e l d i n the e l a s t i c h a l f space. The main concept i s to view the whole p i l e group w i t h the s o i l as one compressible continuum whose c o n d i t i o n s of e q u i l i b r i u m are s p e c i f i e d at a number of d i s c r e t e p o i n t s . The s t i f f n e s s of t h i s composite continuum i s obtained by combining the p i l e s t i f f n e s s w i t h the s o i l s t i f f n e s s . The p i l e s are assumed v e r t i c a l and of constant c i r c u l a r cross s e c t i o n . The s t i f f n e s s of s o i l i s d e r i v e d using M i n d l i n ' s s o l u t i o n for displacement f i e l d generated i n the i n t e r i o r of the e l a s t i c h a l f space by a h o r i z o n t a l p o i n t load. The displacements i n the v e r t i c a l d i r e c t i o n and the d i r e c t i o n perpendicular to the d i r e c t i o n of l o a d i n g are considered to be zero. To get the s t i f f n e s s of the continuum, the s t i f f n e s s of the p i l e and s o i l are added together. This theory i s b a s i c a l l y a l i n e a r theory, but the non-l i n e a r i t y i s approximated by a d j u s t i n g the s o i l s t i f f n e s s and m a t e r i a l damping to the l e v e l of s t r a i n s expected and by i n c o r p o r a t i n g a weakened zone around the p i l e . Brown et a l (1988) proposed a concept of P m u l t i p l i e r based on the a n a l y s i s of f i e l d experiments. This approach amounts to reducing the s o i l pressure for the given displacement rather than i n c r e a s i n g the displacements for given s o i l pressures. I t i s argued that the e f f e c t of the overlapping shear zones i n reducing the s o i l r e s i s t a n c e i s more dominant than the C H A P T E R 2 30 s u p e r p o s i t i o n of s t r a i n s . Thus i f P-y curves for s i n g l e p i l e are a v a i l a b l e along w i t h the P - m u l t i p l i e r f a c t o r ( f j then one can e a s i l y o b t a i n the P-y curves for the p i l e s i n the p i l e group. 2 . 3 . 3 . 1 F I N I T E E L E M E N T A N A L Y S I S One of the main advantages of the f i n i t e element a n a l y s i s i s that i t i s very easy to incorporate a s o i l model that i s more appro p r i a t e , i . e . e l a s t i c , incremental e l a s t i c , e l a s t o - p l a s t i c , e t c . Other advantage i s that i t i s easier to study the e f f e c t s of v a r i o u s f a c t o r s on the p i l e group response. A l s o the v a r i a t i o n s and r e s t r i c t i o n s of three and two dimensional analyses can be compared. The main drawback of the f i n i t e element a n a l y s i s i s that the s o l u t i o n i s vary c o s t l y compared to the s o l u t i o n s i n the form of charts and f i g u r e s . A number of researchers have c a r r i e d out f i n i t e element a n a l y s i s of p i l e groups subjected to l a t e r a l loads. Nair et a l (1969) conducted a three dimensional a n a l y s i s to study the p i l e group response. They used the concept of equivalent c a n t i l e v e r which was a m o d i f i c a t i o n of the model proposed by Broms (1964) . In t h i s method each p i l e i s replaced w i t h an e q u i v a l e n t c a n t i l e v e r which has 1. s t r u c t u r a l s e c t i o n i d e n t i c a l to the o r i g i n a l p i l e 2. equivalent a x i a l length (Lc) for r e s i s t i n g d i r e c t loads 3. e q u i v a l e n t bending length (Lb) or r e s i s t i n g l a t e r a l loads C H A P T E R 2 31 and moments. The b a s i s for determining L c and L b i s that the behaviour of the c a n t i l e v e r and the a c t u a l p i l e be equivalent under d i r e c t loads . The h y p e r b o l i c model developed by Duncan and Chang (197 0) was used by Tamura et a l (19 82) and l a t e r by Muqtadir et a l (1985) i n t h e i r f i n i t e element a n a l y s i s . In t h e i r a n a l y s i s Muqtadir et a l developed a s p e c i a l element c a l l e d t h i n l a y e r element to model i n t e r a c t i o n behaviour between the s o i l and the p i l e . In t h e i r a n a l y s i s , Kay et al(1983) compared the f i n i t e element response wi t h the P-y curve approach for s i n g l e p i l e s , w h i l e the group e f f e c t was accomplished by a p p l y i n g the f r e e f i e l d displacements to the p i l e , i n s t e a d of c a l c u l a t i n g the i n t e r a c t i o n f a c t o r s by e l a s t i c method. This approach has p r e v i o u s l y been used for p i l e s near slopes and i n o f f s h o r e p i l e s i n mud s l i d e areas. The main advantage of the method i s that, both the s i n g l e as w e l l as group p i l e behaviour can be obtained from one f i n i t e element program. Also, the error that occurs i n the Focht-Koch method due to the non c o m p a t i b i l i t y of the two methods, P-y curve approach and e l a s t i c continuum approach, used i s e l i m i n a t e d . Chow et al(1987) used a new approach by which they d i v i d e d the p i l e s o i l system i n t o two systems. One system c o n s i s t e d of the group p i l e s acted upon by an e x t e r n a l a p p l i e d loads and p i l e - s o i l i n t e r a c t i o n forces and second system c o n s i s t e d of a C H A P T E R 2 3 2 l a y e r e d s o i l continuum acted upon by a system of p i l e - s o i l i n t e r a c t i o n forces at the imaginary p o s i t i o n s of the p i l e s . N a j j a r and Zaman(1988) incorporated a p l a s t i c i t y model developed by Desai and co-workers to model the s o i l non-l i n e a r i t y i n t h e i r study while p i l e s and p i l e cap were assumed l i n e a r e l a s t i c . Trochanis et al(1991) used the method proposed by Kay et al(1983) and conducted a three dimensional a n a l y s i s . During t h e i r study they changed various v a r i a b l e s l i k e load e c c e n t r i c i t y , p i l e spacings,etc. Based on these s t u d i e s they developed a simple one dimensional f i n i t e element program and c a l i b r a t e d i t with the r e s u l t s of the three dimensional a n a l y s i s . In t h i s program the p i l e s were connected w i t h each other to take i n t o c o n s i d e r a t i o n the p i l e i n t e r a c t i o n e f f e c t and at the same time the s t i f f n e s s of the springs between p i l e s and between p i l e and s o i l was adjusted so as to o b t a i n the non-l i n e a r i t y of system. The schematic r e p r e s e n t a t i o n of the model i s shown i n Figure 2.4. 2.4 SUMMARY From the above review i t appears that the n o n - l i n e a r i t y of the s o i l , s o i l - p i l e system, and the non-homogeneity of the system i s c r i t i c a l i n the a n a l y s i s of the l a t e r a l l y loaded p i l e groups. At present there i s no c o s t - e f f e c t i v e sound t h e o r e t i c a l s o l u t i o n which can be used for analysing p i l e group behaviour C H A P T E R 2 3 3 under l a t e r a l load. Although some of the s o l u t i o n s discussed above are c u r r e n t l y used i n p r a c t i c e they are mostly based on experience. At the same time these methods do not take i n t o account a l l the f a c t o r s that s i g n i f i c a n t l y i n f l u e n c e the p i l e group response. The a n a l y t i c a l method can be developed and evaluated by comparing i t wi t h the experimental r e s u l t s . The most r e l i a b l e data can be obtained by conducting f i e l d t e s t s . Due to the high costs i n v o l v e d very few f i e l d t e s t s are done. The c e n t r i f u g e t e s t i n g machine or the h y d r a u l i c gradient s i m i l i t u d e t e s t can be e f f e c t i v e l y used to o b t a i n model t e s t r e s u l t s that are s i m i l a r to the f i e l d response. The h y d r a u l i c gradient s i m i l i t u d e t e s t as used for t h i s t h e s i s i s a cost e f f e c t i v e method of conducting a model s c a l e t e s t to represent the f i e l d prototype. CHAPTER 2 34 M M K G.L. H - M A A -P i l e K 1W P - y Springs or Winkler's Springs i R K W SW K sw K iw i s r K sw i s K 1 i s sw between the p i l e s F ig . 2.4 Concept Of Winkler 's Spr ings For Two-Pi les ( T rochan i s et a l , 199 1) C H A P T E R 3 3 5 C H A P T E R 3 : H Y D R A U L I C G R A D I E N T S I M I L I T U D E P R I N C I P L E 3.1 INTRODUCTION In t h i s chapter the t e s t i n g p r i n c i p l e and s c a l i n g laws of the h y d r a u l i c gradient s i m i l i t u d e method ( HGST) are described. This t e s t i n g p r i n c i p l e was f i r s t introduced by Z e l i k s o n i n 1969. Since then i t has been used i n model t e s t s of anchor and p i l e problems ( Z e l i k s o n 1978,1988a, Yan 1990, Dau 1991). Z e l i k s o n et a l (1982) and Z e l i k s o n and Laguay (1981) have compared HGST w i t h c e n t r i f u g e model and good r e s u l t s were observed where comparison was p o s s i b l e . This technique was o r i g i n a l l y developed to co n s o l i d a t e the s o i l sample before conducting the c e n t r i f u g e model t e s t . Later i t was modified to conduct model t e s t i n g of foundations on l e v e l surfaces. The f i r s t HGST model t e s t i n g equipment i n the North America was developed at U n i v e r s i t y of B r i t i s h Columbia by Yan and Byrne(1991a). Various t e s t s were conducted i n c l u d i n g the model study of shallow f o o t i n g s , s i n g l e p i l e response to s t a t i c and dynamic l a t e r a l load, downhole and crosshole seismic t e s t s . These t e s t s were used to study the various f a c t o r s a f f e c t i n g the t e s t r e s u l t s and the t e s t i n g device was upgraded cont i n u o u s l y . For t h i s study the equipment was modified to conduct p i l e group t e s t i n g . The p r i n c i p l e used i n HGST i s s i m i l a r to that used i n c e n t r i f u g e t e s t i n g . The body forces a c t i n g on the s o i l C H A P T E R 3 3 6 p a r t i c l e s are increased to simulate the f i e l d s t r e s s c o n d i t i o n s . But where the c e n t r i f u g e t e s t uses c e n t r i p e t a l a c c e l e r a t i o n to inc r e a s e the body forc e s , the HGST technique i n v o l v e s i n c r e a s i n g body fo r c e s by i n c r e a s i n g the seepage force through the porous m a t e r i a l . 3.2 Hydraulic Gradient Similitude P r i n c i p l e Figure 3.1 shows a sample of s o i l subjected to a c o n t r o l l e d downward h y d r a u l i c gradient, i . The downward h y d r a u l i c gradient w i l l i n c rease the body force on a u n i t volume of the sample by an amount iv,,- This i s equivalent to i n c r e a s i n g the u n i t weight of the m a t e r i a l by iv,,- The e f f e c t i v e u n i t weight of the model s o i l Ym c a n £>e given by Ym = iYw + Y' eq. (3.1) Where i i s the a p p l i e d downward h y d r a u l i c g r a d i e n t , Y „ i s the u n i t weight of the water, and Y ' i s the submerged u n i t weight of the s o i l Thus the sample s o i l or model can be considered to have a u n i t weight, ym. I f the s o i l i n the f i e l d (prototype) has an e f f e c t i v e u n i t weight, Yp» then the sc a l e f a c t o r , N , i s given by N = Ym / Y P ( i Y „ + Y ' ) / Y P I f Y P = Y 1 i then N = ( i Y w + Y ' ) / Y ' C H A P T E R 3 3 7 N ~ iYw / Y ' ( Since iy„ >> Y 1 ) and s i n c e y w ~ Y 1 / N ~ i ( approximately ) eq. (3.2) The f a c t o r N i s c a l l e d the Hydraulic gradient s c a l e f a c t o r . For a h y d r a u l i c gradient t e s t with gradient N=n, where n i s the s c a l e of the model used, the stresses due to the s e l f weight i n the model and prototype at the homologous p o i n t s w i l l be equal as shown below. Model Prototype Y M = N . Y P Y P = Prototype s o i l d e n s i t y Zm = Zp / N Zp = Depth at a point i n prototype (ov)m = Y M • Zm and (o v) p = Y p • Zp ( o v ) m = (N. Y p) • (Zp/N) = Y P • ZP where Zm and Zp are the model and prototype depths and ( o v ) m and (a v ) p are the e f f e c t i v e v e r t i c a l stresses at the homologous p o i n t s of model and prototype s o i l elements, r e s p e c t i v e l y . This shows that the scale factor for s t r e s s e s w i l l be u n i t y . Thus i f same s o i l i s tested i n the model, as i n prototype, and the same s t r e s s path i s followed then the s t r a i n s i n the model and the prototype w i l l be same at homologous p o i n t s w h i l e the displacement of the prototype w i l l be 1N 1 times that of the model. Therefore the Hydraulic gradient s i m i l i t u d e t e s t s are expected to f o l l o w the same s c a l i n g laws as the c e n t r i f u g e modelling t e s t s . CHAPTER 3 J O This s c a l i n g laws, f o r the h y d r a u l i c gradient s i m i l i t u d e t e s t i n g method, were examined by Yan (1990) and Dou (1991). A summary of these laws i s given i n t a b l e 3.1. Since i t i s d i f f i c u l t to simulate both the s p e c i f i c g e o l o g i c a l s e t t i n g s of the prototype s o i l c o n d i t i o n s and the exact s t r e s s path followed i n the prototype loading, d i r e c t comparisons between model and prototype i s not always p o s s i b l e . Therefore, another experimental technique known as modelling of models was used by Yan to v e r i f y the r e s u l t s obtained from the HGST. In t h i s method models of d i f f e r e n t scales are t e s t e d at various h y d r a u l i c gradients such t h a t they w i l l represent the same prototype. The r e s u l t s are then compared to v e r i f y the s i m i l i t u d e laws. The HGST device used i n t e s t i n g was f i t t e d with three pore water pressure transducers and the h y d r a u l i c gradient was monitored continuously throughout the t e s t . The p i l e s were t e s t e d i n the HGS device under a constant h y d r a u l i c gradient. The h y d r a u l i c gradient throughout the sample was monitored continuously to maintain the constant gradient. The major o b j e c t i v e of using the modelling t e s t s i n t h i s study was to generate a data base on P i l e group response to l a t e r a l loads from which methods of a n a l y s i s can be t e s t e d . Modelling t e s t s can be used to analyze and i n v e s t i g a t e prototype behaviour d i r e c t l y . CHAPTER 3 FIG. T o t a l Downward Pressure, PI PI > p 2 t S e e p a g e F o r c e 17* H FTTTTTTTTTI H T o t a l Upward Pressure, P 2 3.1 H y d r a u l i c G r a d i e n t S i m i l i t u d e P r i n c i p l e TABLE 3 .1 SCALING RELATIONS FOR CENTRIFUGE AND HYDRAULIC GRADIENT TESTS QUANTITY FULL SCALE MODEL AT N g ' S LINEAR DIMENSION 1 1/N AREA 1 1/NT2 VOLUME 1 1/NT3 STRESS 1 1 STRAIN 1 1 FORCE 1 1/N"2 ACCELERATION 1 N VELOCITY 1 1 T IME - IN Dynamic TERMS 1 1/N TIME - IN DIFFUSION CASES 1 1/N~2 FREQUENCY IN DYNAMIC PROBLEMS 1 N C H A P T E R 4 40 C H A P T E R 4 : MODEL S O I L AND P I L E P R O P E R T I E S 4.1 MODEL SOIL The sand used i n the t e s t s i s uniform rounded Ottawa sand. The mineral composition of t h i s sand i s p r i m a r i l y quartz. I t has a s p e c i f i c g r a v i t y of 2.67 and a constant volume f r i c t i o n angle c}>cv of 31°. The g r a i n s i z e d i s t r i b u t i o n curve for t h i s sand i s shown i n Figure 4.1. Only sand r e t a i n e d on #14 0 s i e v e was used for t e s t i n g purpose. Reference minimum and maximum v o i d r a t i o of the sand are 0.58 and 0.88 r e s p e c t i v e l y . Figure 4.2 shows the v a r i a t i o n of p e r m e a b i l i t y with v o i d r a t i o . The h y p e r b o l i c s t r e s s s t r a i n parameters of the sand for r e l a t i v e d e n s i t i e s of 30% and 75% are given i n the t a b l e 4.1. Using these p r o p e r t i e s and the hy p e r b o l i c model proposed by Duncan and Chang (1980) the P-y curves for the given p i l e - s o i l system can be developed. For f i n i t e element a n a l y s i s the f o l l o w i n g formulae were used to c a l c u l a t e the st r e s s e s i n the s o i l sample, the i n i t i a l Young's modulus, and the Young's modulus at var i o u s stages of l o a d i n g . A constant r e l a t i v e density of 75 was used for a l l the t e s t s . CHAPTER 4 4 1 A e l where £v i s the volumetric s t r a i n , ex i s the major p r i n c i p a l s t r a i n , i s the deviator s t r e s s , i s the mean normal s t r e s s , i s the tangent Young's modulus, Bt i s the tangent bulk modulus 0"m E t eq. (4.1) P _ A CT« eq. (4.2) Ac — — B. E - M I - ^ V E Q ' ( 4 " 3 ) a4f ^3 ^ „ eq. (4.4) A B =KEPA(2l)~ Cq- ( 4 ' 5 ) I E A v p A W h e r e E L i s t h e i n i t i a l Y o u n g ' s m o d u l u s , P i s t h e a t m o s p h e r i c p r e s s u r e , i s t h e u l t i m a t e d e v i a t o r s t r e s s , 4 . 2 M O D E L P I L E P R O P E R T I E S T w o p i l e s w e r e u s e d i n t h e e x p e r i m e n t . B o t h t h e p i l e s w e r e CHAPTER 4 42 TABLE 4.1 Hyperbol ic Soi l Parameters F r o m Drained Compression Tr iax ia l Tests Sands n Kb m R f *1 8<p K 0 D = 30% r 600 0 . 88 470 0.25 0.95 32 0. 0 31 0.5 D = 75% r 1600 0. 67 600 0. 05 0.70 39 4.0 31 0.4 Where K E n Kb m R f 6<f> K„ The Young's Modulus Number The Young's Modulus Exponent The bulk modulus number The bulk modulus number The f a i l u r e s t r e s s r a t i o The m o b i l i z e d f r i c t i o n angle a t a c o n f i n i n g s t r e s s of 1 atra. The decrease i n the m o b i l i z e d f r i c t i o n angle f o r a t e n f o l d i n c r e a s e i n the c o n f i n i n g s t r e s s The constant volume f r i c t i o n angle The a t - r e s t pressure c o e f f i c i e n t ( 1 - s i n <p ) CHAPTER 4 43 T A B L E 4.2 Physical Properties O f Mode l Piles Outer Diameter, inches 1/4" Thic k n e s s , i n c h e s 0.032" Length, mm. 424.0 Weight,gm. 20.3 m (gm/mm) 0.0479 EI (N.mm2) 4.03 X 10 6 NOTE : - Two i d e n t i c a l p i l e s were used f o r the t e s t s . One of the p i l e s was instrumented with e i g h t p a i r s of s t r a i n gauges while the other was uninstrumented. C H A P T E R 4 44 of diameter 6.75mm. ( 1/4 inch) and 424mm. long. The p i l e s were made of 6061-T6 aluminium tubing. One of the p i l e s was instrumented w i t h 8 p a i r s of s t r a i n gauges for measurement of the bending moment. This arrangement i n p a r t i c u l a r a l lows measurement of the bending moment v a r i a t i o n along the p i l e l e n g t h and thus gives a d e f l e c t i o n p r o f i l e along the l e n g t h of the p i l e . The connections for these s t r a i n gauges were provided on the c y l i n d e r l i d . The f l e x u r a l r i g i d i t y of the p i l e was measured by f i x i n g one end of the p i l e i n a clamp and a p p l y i n g a known load at the free end. From the d e f l e c t i o n and load measurements the p i l e f l e x u r a l r i g i d i t y value was determined. The value i s given i n TABLE 4.2. Eight p a i r s of 120 Q f o i l type s t r a i n gauges mounted on the outside of the p i l e were used. The p o s i t i o n of the s t r a i n gauges i s shown i n Figure 4.3. The advantage of using a p a i r of s t r a i n gauges mounted on opposite s i d e s i s that the e f f e c t of tension and compression, on the opposite faces of the p i l e , i s compensated. The p i l e s were i n s t a l l e d i n the sample a f t e r the p r e p a r a t i o n of the s o i l sample. For t h i s purpose various guiding blocks were designed to push the p i l e s i n t o the s o i l . The p i l e guides were made from p l e x i g l a s s and designed i n such a way as to provide the r e q u i r e d spacing i n between the p i l e s . CHAPTER 4 45 c cs F i g u r e 4 . 1 G r a i n S i z e D i s t r i b u t i o n of F i n e O t t a w a S a n d ( Y a n L i , 199 1) Void Ralio - e F i g u r e 4 . 2 V a r i a t i o n of P e r m e a b i l i t y V s V o i d R a t i o ( Y a n L i , 199 1) CHAPTER 4 90.8 20.0 15.0 20.0 20.0 30.0 40.0 60. 0 129.2 SG # 1 SG # 2 SG # 3 SG # 4 SG # 5 SG # 6 SG # 7 SG # 8 Instrumented P i l e ( O.D. 1/4 " ) igure 4.3 Pile Instrumentation A l l Dimensions i n mm. CHAPTER 5 47 C H A P T E R 5 : H Y D R A U L I C G R A D I E N T S I M I L I T U D E T E S T I N G D E V I C E 5.1 INTRODUCTION In t h i s chapter the h y d r a u l i c gradient s i m i l i t u d e t e s t i n g device developed at U n i v e r s i t y of B r i t i s h of Columbia i s described i n d e t a i l . The design and f a b r i c a t i o n of t h i s device was s t a r t e d i n December, 87. The device was designed i n such a way that the c o n s t r u c t i o n and the operation of the device i s simple and at the same time f a c i l i t a t i n g v e r s a t i l i t y i n a p p l i c a t i o n with r e l i a b i l i t y of r e s u l t s . The device has been under continuous m o d i f i c a t i o n and improvement to incorporate various a p p l i c a t i o n s . At present the device i s mainly designed to perform load c o n t r o l l e d l a t e r a l load t e s t s on v e r t i c a l p i l e s . I t can also be used to conduct displacement c o n t r o l l e d t e s t , a x i a l load t e s t on p i l e s or other types of foundations r e s t i n g on l e v e l ground with some minor m o d i f i c a t i o n s . In a d d i t i o n to the s t a t i c t e s t i n g the dynamic loads or seismic loads can a l s o be a p p l i e d to the p i l e s . 5.2 H y d r a u l i c Gradient S i m i l i t u d e T e s t i n g Device The UBC-HGST device i s shown i n f i g u r e 5.1. The device c o n s i s t s of 1. a large s o i l container and a i r pressure chamber CHAPTER 5 4 8 2 . water supply and c i r c u l a t i o n system. 3. A i r pressure system 4. Loading system 5. Data a c q u i s i t i o n and c o n t r o l system. During a t e s t , the water i s continuously s u p p l i e d by a high power c e n t r i f u g a l water pump. The h y d r a u l i c gradient across the s o i l deposit i s obtained by appl y i n g an a i r pressure i n the a i r chamber with water drainage provided at the base of the s o i l c o n t a i n e r . The water l e v e l i s maintained about one inch above the sand surface by balancing the a i r pressure and water flow f o r a given h y d r a u l i c gradient. The pore pressure development i n the s o i l sample due to the increased h y d r a u l i c gradient i s measured by three pore pressure transducers mounted on the w a l l s of the s o i l container. The average h y d r a u l i c gradient w i t h i n the sand deposit i s obtained from the pore pressure measurements and sample height as follows : When the bottom drainage valve i s c l o s e d and there i s no water flow , i . e . i=0 When the bottom drainage valve i s open and water i s flow i n g under g r a v i t y e f f e c t , i . e . i = 1. When the bottom drainage valve i s open and water i s flowing with c o n t r o l l e d a i r pressure a p p l i e d at top , i - - + /-/ 5 eq. (4.1) CHAPTER 5 4 A i r Regulator Data Acquisition A i r Pressure Chamber Water Regulator LVDT's Dispenser Model P i l e s F i l t e r ^Drainage Pore Pressure Transducers F i g u r e 5.1 H y d r a u l i c G r a d i e n t S im i l i t ude D e v i c e CHAPTER 5 ou Where Plr P 3 are water pressures at top and base of the s o i l sample, r e s p e c t i v e l y , Hs i s the sample height and Hw i s the height of water above the sample base. 5.2.1 SAND CONTAINER AND AIR PRESSURE CHAMBER The s o i l container i n which the model p i l e groups are t e s t e d i s a rectangular box with 404 x 190mm i n s i d e dimensions and a depth of 400mm. The thickness of the w a l l i s 19.05mm. The box i s made of t h i c k welded aluminium p l a t e s anodized with hard coatings to prevent water c o r r o s i o n . The rectangular shape of the box helps i n reducing the boundary e f f e c t s and at the same time reducing the box area s i z e and the flow q u a n t i t y . The maximum h y d r a u l i c gradient that can be ap p l i e d to the s o i l using the e x i s t i n g device i s 100. The corresponding maximum a i r pressure r e q u i r e d i s about 350 kPa. The s o i l i s r e t a i n e d i n the box with the help of a f i l t e r supported on a g r i d of perfor a t e d aluminium s t r i p s . The s t r i p s are about 25.4mm. or 1 i n . t h i c k . This f i l t e r helps i n two ways, i t prevents the s o i l from being washed away with the water and at the same time the space provided below the f i l t e r allows the water to flow f r e e l y before d r a i n i n g out of the s o i l container. The f i l t e r i s prepared by p u t t i n g a s e r i e s of s t a i n l e s s s t e e l sieves i n c l u d i n g #10, #140, #200 mesh sieves r e s t i n g on top of a 6.35mm. t h i c k p e r f o r a t e d aluminium p l a t e . As the sand used has been r e - s i e v e d and only the p o r t i o n r e t a i n e d on sieve #140 i s used i n the t e s t s , the s o i l w i l l be re t a i n e d on the f i l t e r with CHAPTER 5 51 very l i t t l e head l o s s across i t . The f i l t e r and i t s support s t r i p s are designed as a g r i d system under a uniform d i s t r i b u t e d load. The spacing of the c e l l u l a r support i s chosen so that the vert i c a l ' ' d e f l e c t i o n of the f i l t e r at each c e l l centre would be l e s s than 0.1mm. The s o i l container l i d i s 19.1mm. t h i c k p l a t e and i s b o l t e d on to the container with 14 Hex Head cap s t a i n l e s s s t e e l b o l t s . A rubber gasket i s used to s e a l the water pressure between the l i d and container w a l l . The side view and plan of the container l i d are shown i n Figure 5.2. The l i d has a 5"(127mm.) open hole at i t s centre to allow f o r p i l e and s o i l loading and instrumentation. An annular block 2.5"(63.5mm.) high i s permanently b o l t e d on the l i d to provide v e r t i c a l space f o r mounting loading and d e f l e c t i o n measurements u n i t s . A p l e x i g l a s s c y l i n d e r s i t t i n g on top of the annular block forms the a i r chamber. The cap on top of the c y l i n d e r i s f i t t e d with s p e c i a l pressure t i g h t e l e c t r i c a l plugs f o r instrumentation. The a i r pressure connection i s also provided i n the cap. The p l e x i g l a s s c y l i n d e r allows a v i s u a l observation during the t e s t . The connection between the annular block and l i d and those at top and bottom of the p l e x i g l a s s c y l i n d e r are sealed using O-ring. On the i n s i d e of the l i d a f i l t e r i s provided to d i s s i p a t e the flow of the incoming water so as to minimise the disturbance to the sample. The l i d i s provided with a 1" I.D. hole f o r water i n l e t . CHAPTER 5 52 5.2.2 WATER SUPPLY AND CIRCULATION SYSTEM Figure 5.3 shows the water flow chart i n UBC-HGST device. The water pump used i s a c e n t r i f u g a l type with a capacity of 24 US GPM at a t o t a l pressure head of 100 f t . manufactured by Monarch I n d u s t r i e s Ltd. The pump has a 1.5hp b u i l t i n motor and 1.4" and 1" ID suction and o u t l e t pipes, r e s p e c t i v e l y . The pump i s connected to the water tank and the container by p l a s t i c hoses. Before r a i n i n g the sand i n t o the container the whole system i s connected and saturated. The water flow i s c o n t r o l l e d by valves at top and bottom of the s o i l container. During the t e s t valve #1 and #3 are opened to create a downward gradient and an upward gradient i s created by opening valve #2 and c l o s i n g valves #1 and #3. Although there i s an air-water i n t e r f a c e above the sand surface considering the short d u r a t i o n and dynamic nature of the t e s t the e f f e c t of a i r d i f f u s i o n can be neglected. 5.2.3 PILE HEAD LOADING AND MEASURING SYSTEM The loading system included a two way p i s t o n to provide two way loads. Both chambers of the p i s t o n were connected to regulated a i r supply systems. Load was a p p l i e d by c o n t r o l l i n g the a i r pressure i n both the chambers. The load c e l l was connected between the p i s t o n and the r i g i d loading ram to measure the applied load. A low f r i c t i o n loading bushing without O-ring was used to CHAPTER 5 (a). Plan View of Soil Container Lid double acting air piston dispersive material model pile (b). Side View of Soil Container Lid Figure 5.2 Conta iner Lid — P lan and Side View CHAPTER 5 F i g u r e 5.3 W a t e r F l o w S y s t e m in U B C - H G T D e v i c e CHAPTER 5 55 t r a n s f e r the load to the p i l e head. The two way a i r p i s t o n was mounted on the s o i l container l i d . The load c e l l was c a l i b r a t e d using known weights f o r both tension as w e l l compression and was found to be l i n e a r w i t h i n the p r a c t i c a l range. For t e s t i n g the p i l e group i n which both the p i l e s were loaded simultaneously a new load c e l l was designed to measure the load a p p l i e d to each of the p i l e s . This load c e l l i s shown i n Figure 5.4. This load c e l l was used only to measure t e n s i l e f o r c e s . A f r i c t i o n l e s s a i r l e a k i n g bearing system i s used f o r the LVDT cores. These LVDT's are placed on the s o i l container l i d as shown i n Figure 5.5. The LVDT's were so s i t u a t e d that the displacements of the p i l e opposite the loading ram were measured at the loading point and at a distance above the loading point ( 20.0mm.). The displacement of the other p i l e was measured by a t t a c h i n g an LVDT to the loading ram . 5.2.4 DATA ACQUISITION SYSTEM A micro-computer based data a c q u i s i t i o n system was used i n t h i s research. This system comprised of three components: a multichannel s i g n a l a m p l i f i e r , multichannel analog to d i g i t a l converter DT2801A card, and a IBM-PC computer. A l l transducers were e x c i t e d by a common supply of 6 V o l t s . T o t a l of 16 channels were monitored during the t e s t i n g . Three channels were used f o r monitoring the pore pressures at the top, centre and bottom of the s o i l sample to c a l c u l a t e the h y d r a u l i c gradient. Eight channels were used to monitor the p i l e CHAPTER 5 56 BOLT CONNECTIONS S i d e V i e w A - A F i g u r e 5.4 L o a d C e l l C H A P T E R 5 57 s t r a i n gauges, three channels were used to monitor the LVDT's and the remaining two channels were used to monitor the two load c e l l s . The transducer s i g n a l s except 2 LVDT's were a l l a m p l i f i e d at a gain of 1000 by the a m p l i f i e r . The DT2801A A/D converter has 12 b i t s i n i t s accuracy which gives 4.88mV accuracy for a +10V b i p o l a r c o n f i g u r a t i o n . The noise l e v e l was monitored for each channel and found to be ± 5mV at the scanning frequency of 0.5Hz. This gave an accuracy of ± 0.2kPa for the pore water pressure, ± 0.02mm. for the LVDT's, and ± 0.014kg for the load c e l l . A program w r i t t e n i n Quick b a s i c was used to monitor the h y d r a u l i c gradient during the g r a v i t a t i o n a l process and LABTECH NOTEBOOK software was used to monitor channels during the t e s t . The data obtained was then processed to o b t a i n v a r i o u s r e s u l t s . 5.2.5 DATA REDUCTION In the t e s t s , the bending moment d i s t r i b u t i o n along the p i l e i s obtained from the s t r a i n gage readings. Based on the simple beam theory the bending moment can be i n t e g r a t e d or d i f f e r e n t i a t e d to obtai n the p i l e i n c l i n a t i o n ^ , d e f l e c t i o n , y, or shear f o r c e , Q, or s o i l r e s i s t a n c e , P, as f o l l o w s eq. (4.2) CHAPTER 5 5 8 Water Dispersion System LVDT Cores SIDE VIEW F i g u r e 5.5 P i l e H e o d D e f l e c t i o n M e a s u r e m e n t C H A P T E R 5 5 9 Q dM dz eq. (4.3) y= eq. (4.4) d2M P = dz2 eq. (4.5) Where EI i s the f l e x u r a l r i g i d i t y of the model p i l e , z i s the dis t a n c e along the p i l e . Since the bending moment i s only known at some d i s c r e t e l o c a t i o n s along the p i l e , a numerical curve f i t t i n g scheme i s necessary to o b t a i n the needed s o i l r e s i s t a n c e s and p i l e d e f l e c t i o n s along the p i l e length at each l o a d i n g stage. The d e s i r e d P-y curve at a given depth can be obtained by re p e a t i n g the curve f i t t i n g scheme at various l o a d i n g stages. For d e f l e c t i o n s simple numerical i n t e g r a t i o n i s s u f f i c i e n t s i n c e any s l i g h t e r r o r i n the bending moment data becomes smoothed i n the i n t e g r a t i o n process. However for s o i l r e s i s t a n c e any s l i g h t e r r o r s or d e v i a t i o n s i n the bending moment data becomes g r e a t l y magnified during double d i f f e r e n t i a t i o n . To a l l e v i a t e t h i s problem a cubic s p l i n e f i t t i n g i s used. In t h i s procedure a CHAPTER 5 60 at each p o i n t . Then the s p l i n e i s d i f f e r e n t i a t e d to give the d i s t r i b u t e d shear force and s o i l r e s i s t a n c e along the p i l e and i n t e g r a t e d to give the p i l e i n c l i n a t i o n and d e f l e c t i o n . Boundary c o n d i t i o n s used are 1. For free head s i n g l e p i l e the bending moment at the loading point i s set t o be zero. 2. For two p i l e s when only one p i l e i s loaded the bending moment above the ground f o r the adjacent p i l e i s zero. For the loaded p i l e bending moment i s zero at the loading p o i n t . 3 . For both p i l e s loaded the bending moment at the loading point i s zero. CHAPTER 6 61 C H A P T E R 6 : T E S T P R O C E D U R E 6.1 Test Procedure The t e s t procedure for the h y d r a u l i c gradient s i m i l i t u d e t e s t can be d i v i d e d i n t o three steps as 1. R e c o n s t i t u t i o n of s o i l deposit 2. P i l e i n s t a l l a t i o n 3 . S o i l l oading and subsequent p i l e l o a d i n g 6.2 RECONSTITUTION OF SAND DEPOSIT The technique used for the sample p r e p a r a t i o n i n v o l v e s upward seepage forces together w i t h sedimentation and d e n s i f i c a t i o n processes to reform s o i l d eposits f o r each t e s t as descr i b e d below. During the sample preparation, the top cap of the c e l l was removed and the drainage l i n e s from the c i r c u l a t i o n chamber ( f i g u r e 5.3) were closed. De-aired water was used to f i l l the c e l l and a l l the measurement l i n e s . A f i x e d amount of oven d r i e d sand was weighed i n f l a s k s . Water was added to each f l a s k and the sand water mixture was b o i l e d . A f t e r c o o l i n g to room temperature the b o i l e d sand was t r a n s f e r r e d to the c e l l u s i n g a water p l u v i a t i o n technique, f l a s k by f l a s k . To remove the l a y e r i n g e f f e c t a c o n t r o l l e d upward seepage gradient was ap p l i e d . The s l u r r y formed due to the upward gradient i s then C H A P T E R 6 62 s t i r r e d to o b t a i n a homogeneous s t a t e . The upward gradient was then turned o f f and the r e q u i r e d s o i l d e n s i t y was achieved by d e n s i f y i n g the s o i l by tapping the s i d e and base of the c e l l . A f t e r each t e s t was completed, the sand was loosened by an upward gradient and reformed as discussed above. 6 . 3 P I L E I N S T A L L A T I O N A f t e r p r e p a r a t i o n of the sand deposit was completed, the model p i l e s were i n s t a l l e d by pushing the p i l e s i n t o the sand de p o s i t . P i l e d r i v i n g guides for d i f f e r e n t p i l e spacings were designed so that p i l e group can be t e s t e d w i t h v a r i o u s spacing between the p i l e s . The p i l e s were a l i g n e d w i t h the l o a d i n g ram and LVDT measurement cores. A l l the model p i l e s were c l o s e d ended at the t i p and a l l were d r i v e n to the bottom of the sand deposit and r e s t e d on the base wi t h an embedment le n g t h of 310mm. Thus the model represents f u l l displacement end bearing hollow c i r c u l a r s t e e l p i l e s . A study of model p i l e i n s t a l l a t i o n i n sand at the 1 g. c o n d i t i o n was conducted by Robinsky and Morrison(1964). The sand displacement and compaction around the p i l e s were found to be dependent upon the p i l e property, s o i l s t r e s s l e v e l and s o i l d e n s i t y . I t was found that the s o i l displacement envelope s t a r t s at 4.5 to 5.5 p i l e diameters below the ground l e v e l . For the l a t e r a l l y loaded p i l e t e s t s , d e n s i f i c a t i o n e f f e c t s may be l e s s s i g n i f i c a n t s i n c e the p i l e behaviour i s dominated by the s o i l CHAPTER 6 63 r e a c t i o n c l o s e to the s o i l surface where the disturbance i s minimum. The t e s t s reported by Oldham(1984), C r a i g (1984, 1985) show that the e f f e c t s of s t r e s s l e v e l d uring the p i l e i n s t a l l a t i o n are important f o r a x i a l l y loaded p i l e s but much l e s s important f o r l a t e r a l l y loaded p i l e s . Therefore the procedure of i n s t a l l i n g p i l e s at the normal s t r e s s c o n d i t i o n and then performing t e s t at a higher s t r e s s l e v e l was employed i n t h i s study. A f t e r p i l e i n s t a l l a t i o n was completed, the loading system, i n c l u d i n g the double a c t i n g p i s t o n and load c e l l was mounted on the s o i l container l i d . The appropriate loading connection was made depending on the t e s t c o n d i t i o n s . The LVDT cores were attached to the p i l e head to measure the corresponding d e f l e c t i o n s . The a i r pressure chamber was then i n s t a l l e d and a l l the i n s t r u c t i o n wires were connected to the data a c q u i s i t i o n systems. 6 .4 SOIL LOADING AND PILE LOADING A f t e r e n c l o s i n g the whole t e s t i n g device, the s o i l loading process was begun by applying a i r pressure i n the a i r chamber and simultaneously i n c r e a s i n g the water i n f l o w to the sand conta i n e r . The pore water pressure was continuously monitored and h y d r a u l i c gradient c a l c u l a t e d . The s o i l loading was stopped on reaching the required gradient. CHAPTER 6 The a i r pressure i n s i d e the pressure chamber pushes back the loading ram i n c r e a s i n g the l a t e r a l p u l l i n g force on the p i l e s i f the h o r i z o n t a l force i s not balanced. A s p e c i a l a i r pressure c o n t r o l system was designed f o r t h i s purpose. The design of the pressure c o n t r o l system has to s a t i s f y the f o l l o w i n g requirements During the s o i l l o a d i n g process i t should a u t o m a t i c a l l y balance the pressure a c t i n g on the loading ram so that the p i l e w i l l stay i n the same p o s i t i o n . A f t e r the s o i l loading i s completed the p i l e s can be loaded very e a s i l y . To s a t i s f y the f i r s t requirement a double a c t i n g a i r - p i s t o n was employed whose p i s t o n area has exact same diameter as the loa d i n g ram connecting to the model p i l e . Thus when the a i r pressure, pressure supplied to the HGST chamber during the g r a v i t a t i o n process, i s connected to the a i r p i s t o n i t balances out the force on the loading ram. When the a i r pressure i n the chamber has reached the target a i r pressure, the a i r pressure i n fr o n t of the double a c t i n g p i s t o n i s reduced. The load i s ap p l i e d by i n c r e a s i n g the a i r pressure i n the back chamber of the two way p i s t o n . 6.5 P I L E H E A D L O A D I N G The l a t e r a l load w a s a p p l i e d to the model p i l e s . The scanning rate of the data w a s 0.5Hz. A l l the t e s t s i n which load CHAPTER 6 bb was a p p l i e d to s i n g l e p i l e were load c o n t r o l l e d . The t e s t s conducted with p i l e groups were displacement c o n t r o l l e d . In the p i l e group the displacement of both the p i l e s at the loading p o i n t was kept equal. CHAPTER 7 66 CHAPTER 7 : RESULTS AND DISCUSSION 7.1 INTRODUCTION This chapter contains the t e s t r e s u l t s of the l a t e r a l l oading of model p i l e s and p i l e groups under c o n t r o l l e d l aboratory environment using the HGST device. This study i s aimed at ev a l u a t i n g the fundamentals of p i l e group response t o s t a t i c and c y c l i c l a t e r a l l o ad under w e l l c o n t r o l l e d s o i l c o n d i t i o n s . 7.2 T e s t i n g S e r i e s The t e s t i n g was conducted i n three s e r i e s of t e s t s . In the SERIES I the s i n g l e p i l e was i n s t a l l e d and loaded h o r i z o n t a l l y . The load was a p p l i e d i n increments and displacements and bending moments were measured. The r e s u l t s of these t e s t s were s t u d i e d to confirm the response of the s i n g l e p i l e . They were also used i n the a n a l y s i s of the p i l e group. In the SERIES I I the p i l e group of two p i l e s was i n s t a l l e d and one p i l e i n the p i l e group was loaded. In t h i s s e r i e s there are various cases depending on the d i r e c t i o n of loading. In CASE I the p i l e i s pushed towards the adjacent p i l e . The distance between two p i l e s i s v a r i e d from 2 to 6 diameters. In the CASE I I the p i l e i s p u l l e d away from the adjacent p i l e and again distance i s v a r i e d from 2 diameters to 6 diameters. In CASE I I I the angle of loading i s CHAPTER 7 b/ changed. In t h i s case the load i s a p p l i e d at an angle of 90 to the center l i n e of the p i l e s . During the SERIES I I I t e s t i n g both the p i l e s i n the p i l e group were loaded and the bending moments f o r the t r a i l i n g p i l e were recorded. The p i l e spacing used was 2d and 4d. The terminology used i n the f i g u r e s i n c l u d e s s e r i e s no., then case no. followed by spacing, e.g. S2C2S4 denotes that the f i g u r e i s f o r s e r i e s 2 (S2), case I I (C2) and p i l e spacing i s 4 diameters (S4). S i m i l a r l y S3C0S4 denotes s e r i e s 3 p i l e spacing of 4 diameters and since there i s only one case the center p o r t i o n denotes CO. 7.2.1 R e p e a t a b i l i t y o f the t e s t r e s u l t s To check the r e p e a t a b i l i t y of the t e s t , three i d e n t i c a l t e s t s on the s i n g l e p i l e under s t a t i c l a t e r a l load were conducted. The r e s u l t s from these t e s t s are given i n f i g u r e s 7.1 to 7.3. Figure 7.1 shows load-displacement response of the s i n g l e p i l e under l a t e r a l load. The f i g u r e shows response at the point of load a p p l i c a t i o n and at the ground l e v e l . The h o r i z o n a l load i s a c t i n g at a distance of 64.0mm above the ground surface ( e c c e n t r i c i t y = 64.0 mm) . The r e s u l t s presented are f o r a h y d r a u l i c gradient of 60. I t can be seen that the load-displacement response of the three t e s t s are quite s i m i l a r i n d i c a t i n g r e p e a t a b i l i t y of the t e s t r e s u l t s . The P-y curves for these three t e s t s f o r the depth of 2 CHAPTER 7 68 diameters below ground l e v e l are given i n f i g u r e 7.2. The P-y curves are developed from the Bending Moment p r o f i l e . The method of c a l c u l a t i n g the P-y curves from the bending moment p r o f i l e was explained i n CHAPTER 4. The P-y curves show some v a r i a t i o n i n the r e s u l t s . This i s because the s o i l pressure i n P-y curves i s obtained by d i f f e r e n t i a t i n g the bending moment p r o f i l e as opposed to the displacement which i s obtained by i n t e g r a t i n g the moment p r o f i l e . The bending moment and shear force p r o f i l e f o r two d i f f e r e n t load cases i s given i n f i g u r e 7.3. I t may be seen that the r e s u l t s from the three t e s t s are i n reasonable agreement. In general, the t e s t s on s i n g l e p i l e s show r e s u l t s that are g e n e r a l l y r e l i a b l e and repeatable. I t should be noted that the accuracy of the t e s t data and the program i s h i g h l y dependent on the h y d r a u l i c gradient as w e l l as the e c c e n t r i c i t y of the loa d i n g point above the ground surface. The load-displacement curves shown i n f i g u r e 7.1 i s the a c t u a l data obtained while the P-y curves shown i n f i g u r e 7.2 are developed from the bending moment p r o f i l e shown i n f i g u r e 7.3. 7.2.2 S e r i e s I (SI) S i n g l e P i l e t e s t i n g r e s u l t s The sand sample was prepared at a r e l a t i v e d ensity of 75% and a h y d r a u l i c gradient of 60. The sample preparation technique and the p i l e i n s t a l l a t i o n method are described i n the CHAPTER 4. A f t e r i n s t a l l a t i o n the s i n g l e p i l e was subjected to the l a t e r a l C H A P T E R 7 69 2 3 4 5 D i s p l a c e m e n t , m m . FIG. 7.1 Load D i sp lacemen t Behav iour 0 0.1 0 .2 0 .3 0 .4 0 .5 D i s p l a c e m e n t ( y - y 0 ) , m m . Figure 7.2 P - ( y - y 0 ) Curve CHAPTER 7 4 0 0 372 3 0 0 + Single Pi le Test HG = 6 0 Test 1 Test 2 Test 3 -e- — 4 0 0 372 3 0 0 cn I 200 100 F o r c e Level 2 F o r c e Level 1 0 70 - 2 0 - 1 0 0 10 20 - 8 0 0 - 6 0 0 - 4 0 0 - 2 0 0 0 200 Shear Fo rce , N. Bend ing Moment , N - m m . Figure 7.3 Bending Moment Pro f i le - S ing le Pile CHAPTER 7 71 load, and the bending moment and displacements recorded. 7 . 2 . 2 . 1 L O A D D I S P L A C E M E N T R E S P O N S E The load-displacement curve of the s i n g l e p i l e at the Ground l e v e l i s given i n f i g u r e 7.4. The c h a r a c t e r i s t i c load-displacement curve i s non-linear w i t h i n c r e a s i n g d e f l e c t i o n s w i t h the load. As the p i l e i s loaded, w i t h the i n c r e a s i n g displacement a gap develops between the p i l e and the s o i l behind the p i l e . This gap increases as the load i s increased. In the t e s t s conducted, la r g e displacements were observed under a p p l i e d load. Due to the la r g e displacements the t e s t was stopped before the u l t i m a t e f a i l u r e load was reached. This shows that i n the t e s t s conducted large displacements and s o i l f a i l u r e occurred before p i l e f a i l u r e , and thus i s a major f a c t o r i n d e c i d i n g the p i l e c a p a c i t y . For the s t r u c t u r a l c a p a c i t y of the p i l e foundation s o i l f a i l u r e i s not a major f a c t o r . But l a r g e displacements play a major r o l e due to accompanying high bending moments. 7 . 2 . 2 . 2 P - ( y - y 0 ) C U R V E Figure 7.5 shows the P vs (y-y 0) curve for the l a t e r a l l o a d t e s t conducted on a s i n g l e p i l e . The t y p i c a l P vs (y-y 0) curve i s a nonlinear curve becoming asymptotic to the (y-y 0) a x i s . The P vs (y-y 0) curve i s the c h a r a c t e r i s t i c curve for the given p i l e and the given s o i l . The f i g u r e shows P vs (y-y 0) curves at CHAPTER 7 72 60 S1C0S0 Single Pi le Test HG = 60 0.5 1 1.5 2 Disp lacement At Ground Leve l , m m . F i g u r e 7.4 L o a d - D i s p l a c e m n t C u r v e 2.5 S 1C0S0 Single Pi le Test HG = 60 D e p t h 1 D D e p t h 2 D D e p t h ' 3 D D e p t h 4 D 0.2 0.3 0.4 0.5 D i s p l a c e m e n t (y— y Q ) , m m . F i g u r e 7 .5 P - ( y - y Q ) C u r v e s 0.6 CHAPTER 7 73 various depths. As seen i n the f i g u r e the i n i t i a l s t i f f n e s s of the curves increases with the depth. 7.2.2.3 BENDING MOMENT AND SHEAR FORCE PROFILE Figure 7.6 shows the shear force and bending moment p r o f i l e along the length of the p i l e . The general bending moment p r o f i l e obtained from the t e s t i s s i m i l a r to the bending moment p r o f i l e given by Davis & Poulos(1981) f o r a long f l e x i b l e p i l e using the e l a s t i c s o l u t i o n . They suggested that the depth of the maximum bending moment developed i s about 0.Id to 0.4d below the ground l e v e l f o r p i l e s subjected t o only h o r i z o n t a l load. In case of p i l e s subjected to only bending moment, the maximum bending moment i s at ground surface. The maximum bending moment observed i n t h i s t e s t program was observed at a depth of about O.ld. I t should be noted that the p i l e was very long with L/d r a t i o of about 50 and the load was a p p l i e d at an e c c e n t r i c i t y of about lOd. This higher depth of the maximum bending moment i s due to the fa c t that the p i l e i s a c t i n g as a f l e x i b l e p i l e as we l l as the load i s ap p l i e d at an e c c e n t r i c i t y . As seen from the f i g u r e 7.6, the bottom h a l f p o r t i o n of the p i l e c o n t r i b u t e s very l i t t l e towards sharing the load, most of the load i s taken by the top h a l f of the p i l e . A lso Figure 7.7 shows the s o i l pressure and p i l e d e f l e c t i o n p r o f i l e along the depth. As expected i t can be seen that as the d e f l e c t i o n s increase the p-y curves near the surface reach the ul t i m a t e strength but at l a r g e r depths the p-y curves have yet CHAPTER 7 7 4 to reach the ult i m a t e strength. This shows that the l o c a l s o i l f a i l u r e has taken place near the surface. I t should be noted that d e s p i t e the l o c a l f a i l u r e t a k i n g place near the surface and larg e d e f l e c t i o n s , the p i l e has not yet reached i t s u l t i m a t e load c a p a c i t y . 7.2.3 S e r i e s I I (S2) P i l e Group Of Two P i l e s ( One P i l e Loaded) Three Cases were considered i n t h i s s e r i e s . 1. When the p i l e i s pushed towards the adjacent p i l e (S2C1). 2. When the p i l e i s pushed away from the adjacent p i l e ( S 2 C 2 ) . 3. When the p i l e i s loaded at r i g h t angle to the adjacent p i l e (S2C3) . In a l l three cases the t e s t s were conducted at a h y d r a u l i c gradient of 60 and the sand sample was prepared at a r e l a t i v e d e n s i t y of 75%. In a l l cases three spacings were used f o r the p i l e group; 2d, 4d, 6d where d i s the p i l e diameter. Only one p i l e was loaded i n the p i l e group of two p i l e s and henceforth the loaded p i l e w i l l be r e f e r r e d to as PILE 1 and the adjacent unloaded p i l e w i l l be r e f e r r e d to as PILE 2. 7.2.3.1 Load Displacement Response Figure 7.8 shows the d e f l e c t i o n of p i l e 2 vs load on p i l e 1. The d e f l e c t i o n curves f o r p i l e 2 are given f o r d i f f e r e n t spacings; 2d, 4d and 6d. As seen i n the f i g u r e the e f f e c t of CHAPTER 7 75 •Legend 372 300 Load 4 N. 16 N. 26 N. 34 N. ' A * o • 200 + ' ( D 100 372 300 + "200 ' CD 100 0 S1C0S0 Single Pile Test HG = 60 - 6 0 - 4 0 - 2 0 0 20 40 60 - 3 0 0 0 - 2 0 0 0 - 1 0 0 0 0 1000 Shear Force, N. Bending Moment, N - m m . F i g u r e 7 . 6 B e n d i n g M o m e n t P r o f i l e - S i n g l e P i l e Legend Load 4 N. 16 N. 26 N. 34 N. 372 300 200 + JZ X 100 372 300 200 100 0 S1C0S Single Pile Test HG = 50 -2 - 1 0 1 - 5 - 4 - 3 - 2 - 1 0 Soil Pressure, N /mm~2 . Displacement, mm. F i g u r e 7 . 7 B e n d i n g M o m e n t P r o f i l e - S i n g l e P i l e CHAPTER 7 7 6 the load on the adjacent p i l e i s n o n l i n e a r . Furthermore, the magnitude of t h i s e f f e c t or i n t e r a c t i o n reduces with i n c r e a s i n g spacing as expected. Davisson (1970) s t a t e d that i f the spacing between two p i l e s i s more than 8d then the p i l e s w i l l have no i n t e r a c t i o n e f f e c t s on each other. As seen from f i g u r e at spacing of 6d the i n t e r a c t i o n e f f e c t i s sm a l l . Figure 7.9 gives load displacement curves f o r the p i l e 1 at spacings 2d, 4d and 6d. I t can be seen that the response of the p i l e becomes s t i f f e r as the spacing between the p i l e s i s reduced. This i n conjunction with f i g u r e 7.8 shows that part of the load a p p l i e d to the p i l e 1 i s shared by p i l e 2. This increased s t i f f n e s s a r i s e s f o r two reasons; f i r s t , the s o i l adjacent to the loaded p i l e i s s t i f f e r due to d r i v i n g of the unloaded p i l e and secondly, the unloaded p i l e i t s e l f has a s t i f f e n i n g e f f e c t on the loaded p i l e . As the distance between the p i l e s increases the load t r a n s f e r r e d decreases as expected. Figure 7.10 gives a comparison between the load displacement response of two p i l e s and the response of the s i n g l e p i l e . The spacing between the two p i l e s i s 2d. Figures 7.11 and 7.12 give curves f o r spacings of 4d and 6d, r e s p e c t i v e l y . I f we compare the displacement of p i l e 1 with the displacement of the s i n g l e p i l e at the same load, as expected displacement of the s i n g l e p i l e i s l a r g e r than the displacement of p i l e 1. I t can also be seen that the d i f f e r e n c e between the two reduces as the spacing between p i l e 1 and p i l e 2 i s increased. In fact at spacing 6d at low load l e v e l s the load-CHAPTER 7 77 L e g e n d S 2 C 1 S 2 S 2 C 1 S 4 S 2 C 1 S 6 • A O HG - 6 0 ^2- 100-(D 8 0 -CL o 6 0 -TJ 4 0 -D O _ J 2 0 -4 S / D = 6 P i l e 1 P i l e 2 0.3 0.4 0.1 0.2 D isp lacement at G.L.( For Pi le 2) , m m . F i g u r e 7 .8 L o a d - D i s p l a c e m e n t C u r v e s - Ad jacen t Pile 100 0 0.5 1 1.5 2 2.5 3 3.5 D isp lacement at G.L.( For Pi le 1), m m . F i g u r e 7 .9 L o a d - D i s p l a c e m e n t C u r v e s - Loaded Pile CHAPTER 7 78 L e g e n d S i n g l e P i l e P i l e 2 P i l e 1 • A O 60 HG = 6 0 S2C1S2 S / D = 2 100 0.5 1 1.5 2 D i s p l a c e m e n t at G . L . , m m . F i g u r e 7 . 1 0 L o a d — D i s p l a c e m e n t C u r v e s o o 0.5 1 1.5 2 2.5 3 D i s p l a c e m e n t a t G.L., m m . F i g u r e 7 . 1 1 L o a d - D i s p l a c e m e n t C u r v e s 2.5 3 .5 CHAPTER 7 7 9 displacement curves for the s i n g l e p i l e and p i l e 1 are very s i m i l a r and only at larg e loads i s there a s l i g h t d i f f e r e n c e between the two. I t should a l s o be noted that t h i s d i f f e r e n c e i s very small compared to the d i f f e r e n c e at spacings 2d and 4d. The comparison of the load-displacement curves for v a r i o u s spacings f or PILE 1 i s given i n f i g u r e 7.13. The load-displacement curve for the s i n g l e p i l e i s a l s o shown. I t can be seen that the e f f e c t of adjacent p i l e presence reduces c o n s i d e r a b l y at a distance of 4 to 6 diameters. The i n t e r a c t i o n f a c t o r s for the p i l e group of two p i l e s were c a l c u l a t e d by using the displacements of PILE 1 and PILE 2. These i n t e r a c t i o n f a c t o r s were compared w i t h the t h e o r e t i c a l i n t e r a c t i o n f a c t o r s obtained from the E l a s t i c theory using Poulos's (1971) s o l u t i o n s . A lso the i n t e r a c t i o n f a c t o r s c a l c u l a t e d from the s o l u t i o n given by Randolph(1981), Sharnouby and Novak (1986) are shown i n the f i g u r e 7.14. I t can be seen that the i n t e r a c t i o n f a c t o r s c a l c u l a t e d from Randolph's s o l u t i o n give the best approximation of the t e s t data. The i n t e r a c t i o n f a c t o r s c a l c u l a t e d by the Sharnouby and Novak method o v e r p r e d i c t the observed response as the spacing between the p i l e s i s increased. The c a l c u l a t i o n of i n t e r a c t i o n f a c t o r s from the theory was explained i n d e t a i l i n Chapter 6. 7.2.3.2 Bending moment and shear force d i s t r i b u t i o n Figure 7.15 shows the experimental bending moment and shear fo r c e p r o f i l e s for PILE 2 at a spacing of 2d for d i f f e r e n t load CHAPTER 7 L e g e n d 140 T-120 100 CD CL 80 i_ O u_ 60 TJ --O 40 .. O _ J 20 ; 0° S 2 C 1S6 HG = 6 0 P i l e 1 P i l e 2 0.5 1 1.5 2 2.5 3 D i s p l a c e m e n t at G . L . , m m . Figure 7 .12 L o a d — D i s p l a c e m e n t C u r v e s 3.5 100 0 0.5 1 1.5 2 2.5 3 3.5 D i s p l a c e m e n t at G .L . ( For P i l e 1 ), m m . Figure 7. 1 3 L o a d — D i s p l a c e m e n t C u r v e s CHAPTER 7 81 o u o c _o u O i_ C L e g e n d E x p t . S h a r n o u b y et . a l . R a n d o l p h P o u l o s ' s 0.6 0.4 0.2 0 3 4 5 6 7 S / D F i g u r e 7 . 1 4 C o m p a r i s o n o f I n t e r a c t i o n C o e f f i c i e n t NOTE :— The I n t e r a c t i o n F a c t o r s a r e c a l c u l a t e d by l o a d i n g a n a d j a c e n t p i le . CHAPTER 7 82 steps. Figure 7.16 shows the p r o f i l e s f o r PILE 2 at a spacing of 4d f o r various loading steps while Figure 7.17 shows the p r o f i l e s at spacing of 6d f o r various loads. As the a p p l i e d h o r i z o n t a l load on PILE 1 increases, the depth of maximum bending moment i n PILE 2 also i n c r e a s e s . I f we compare the three p r o f i l e s at d i f f e r e n t spacings we can observe that the maximum bending moment i n PILE 2 reduces with the i n c r e a s i n g d istance and at a distance of 6d i t i s almost non-existent. Also the shear force i n PILE 2 at a spacing of 4d i s about 40 per cent of that at a spacing of 2d. Thus with the i n c r e a s i n g spacing, the e f f e c t of load on adjacent p i l e , i . e . induced bending moment and shear force, reduce very s i g n i f i c a n t l y . At a spacing of 6d these induced s t r e s s e s are about 10 per cent of the s t r e s s e s at a spacing of 2d. Figure 7.15 shows that the maximum shear force i n PILE 2 occurs above the depth of maximum bending moment. I t can be seen from f i g u r e 7.15 that at a spacing of 2d the shear force generated i n PILE 2 i s almost 20 per cent of the load a p p l i e d on PILE 1 whereas at a spacing of 6d the shear fo r c e i n PILE 2 i s very small compared to the load a c t i n g on PILE 1 ( l e s s than 1 perc e n t ) . Figure 7.18 shows the bending moment and shear force p r o f i l e s f o r PILE 1 at a spacing of 2d. Figure 7.19 and 7.20 shows bending moment and shear force p r o f i l e s at spacings of 4 and 6d f o r PILE 1. From f i g u r e 7.18, i t can be seen that as the spacing between PILE 1 and PILE 2 i s increased although the CHAPTER 7 83 « Legend 16 N. 24 N. 32 N. 40 N - 5 0 5 10 - 4 0 0 - 3 0 0 - 2 0 0 - 1 0 0 0 100 Shear Force, N. Bending Moment, N - m m . F i g u r e 7 . 1 5 B e n d i n g M o m e n t P r o f i l e Legend Load 15 N. 21 N. 32 N. 40 N. S / D = 4 HG = 60 372 372[ Pile 2 S2C1S4 Pile 1 Pile 2 - 4 - 3 - 2 - 1 0 1 2 3 4 Shear Porce, N. 4 0 0 - 3 0 0 - 2 0 0 - 1 0 0 0 100 Bending Moment, N —mm. F i g u r e 7 . 1 6 B e n d i n g M o m e n t P r o f i l e ( S / D = 4 ) CHAPTER 7 84 Legend 0 0.4-0.3-0.2-0.1 0 0.1 0 .20 .30 .4 - 1 5 - 1 0 - 5 0 5 Shear Force, N. Bending Moment, N —mm. F i g u r e 7 . 1 7 B e n d i n g M o m e n t P r o f i l e ( S / D = 6) Legend Load 16 N. 24 N. 32 N. 40 N. Pile 1 S2C1S2 S / D = 2 HG = 60 -40 -20 0 20 40 Shear Force, N. -2000 -1000 0 Bending Moment, N —mm. F i g u r e 7 . 1 8 B e n d i n g M o m e n t P r o f i l e ( S / D o CHAPTER 7 85 maximum bending moment d i d not change, the depth to the maximum bending moment reduced considerably. According to Poulos (1971), the maximum bending moment f o r the p i l e subjected t o moment only i s at the ground l e v e l . Thus as the r a t i o of the a p p l i e d force to the a p p l i e d moment decreases the depth t o the maximum bending moment w i l l s t a r t reducing. In short, the greater the e c c e n t r i c i t y of the a p p l i e d load, the c l o s e r the maximum bending moment i s to the ground surface. In the t e s t s conducted, as the spacing between the two p i l e s was increased, the r e s u l t a n t s t i f f n e s s of l o a d - d e f l e c t i o n response of PILE 1 was reduced. This i s as expected as the s t i f f e n i n g e f f e c t of the adjacent p i l e s a r i s i n g from both d e n s i f i c a t i o n and s t r u c t u r a l r i g i d i t y reduces with spacing. The depth of the maximum bending moment below ground surface decreased with the i n c r e a s i n g spacing. The shear force (SF) and bending moment(BM) p r o f i l e s of PILE 1 and PILE 2 are compared i n / f i g u r e 7.21. I t can be seen that at a distance of 2d the bending moment generated i n PILE 2 i s about 20 per cent of the bending moment i n PILE 1. As seen from the f i g u r e , the value of the bending moment i n PILE 2 i s small compared to that i n PILE 1 but the two bending moment p r o f i l e s are very d i f f e r e n t . Comparison of the p r o f i l e s f o r s i n g l e p i l e and PILE 1 f o r spacings 4d and 6d are given i n f i g u r e s 7.22 and 7.23 r e s p e c t i v e l y . A large amount of reduction can be seen i n the PILE 1 than the s i n g l e p i l e . This can be co n t r i b u t e d to the CHAPTER 7 86 Legend Pile 1 S = 4 D HG = 60 372 300 2 0 0 + cn CD X 100 -60 - 4 0 - 2 0 0 20 40 w - 2 0 0 0 - 1 0 0 0 0 Shear Force, N. Bending Moment, N - m m . Figure 7.19 Bending Moment Profile ( S / D = 4) Legend T o a d 0.5 N. 1.0 N. 2.0 N. 4.0 N. I Pile 1 S2C1S6 ^ D = - 5 § -4 - 2 0 2 4 6 - 2 0 0 - 1 5 0 - 100 - 5 0 0 50 Shear Force, N. Bending Moment, N - m m . F i g u r e 7 . 2 0 B e n d i n g M o m e n t P r o f i l e ( S / D = 6) CHAPTER 7 L e g e n d _oad 16 N. 2 4 N. 3 2 N. 4 0 N. S / D = 2 HG = 6 0 372 300 200 + 'CU X 100 + 0 S 2 C 1S2 40 -20 0 20 40 60 S h e a r F o r c e , N. 372 300 200 "100 0 S 2 C 1S2 -G,-U P ILE 1, P i l e 1 P i l e 2 2000 -1000 0 500 B e n d i n g M o m e n t , N — m m . F i g u r e 7 . 2 1 C o m a p r i s o n Of B e n d i n g M o m e n t P r o f i l e s L e g e n d , , ' L o a d ( N ) . P i l e 1. S i n g l e P i l e 1 4 ZD 3 Z S / D = 4 HG = 6 0 372 300 200 cn 'CD X 100 S 2 C 1 S 4 P i l e 1 P i l e 2 372 300 E 200 CX> X 100 S 2 C 1S4 P i l e 1 P i l e 2 O i l -60 -40 -20 0 20 40 60 -2000 -1000 0 S h e a r F o r c e , N. B e n d i n g M o m e n t , N - m m . F i g u r e 7 . 2 2 C o m p a r i s o n Of B e n d i n g M o m e n t C H A P T E R 7 88 presence of PILE 2. But as seen before, at a spacing of 6d, the PILE 2 i s sharing far l e s s bending moment as compared to a spacing of 4d and even i n that case the r e d u c t i o n i n bending moment i s s i g n i f i c a n t . The only reason for t h i s r e d u c t i o n i n bending moment can be an increase i n the s o i l s t i f f n e s s . This increase i n s t i f f n e s s i s due to the d e n s i f i c a t i o n during the p i l e i n s t a l l a t i o n . Figure 7.24 shows the d e f l e c t i o n and s o i l s t r e s s p r o f i l e s for PILE 2 at a spacing of 2d. The induced d e f l e c t i o n p r o f i l e s for spacings 4d and 6d are given i n f i g u r e s 7.25 and 7.26 r e s p e c t i v e l y . Figures 7.24 to 7.26 show that as the spacing between the p i l e s i s increased the induced d e f l e c t i o n reduces c o n s i d e r a b l y . During the p i l e group t e s t program conducted by Schmidt(1981) , he conducted a study of the e f f e c t of the induced displacement on p i l e response. He used a two p i l e group p r e v i o u s l y subjected to c y c l i c loading and a p p l i e d l oad on one p i l e and measured the displacements and moments i n the other p i l e . He observed that the induced displacement has no r e l a t i o n s h i p w i t h the p i l e head response but as the displacements increased the maximum bending moment i n the p i l e i n creased. I t was a l s o observed that the induced displacement increases w i t h decreasing spacing. Thus c l o s e r the p i l e s are, more the induced displacement due to the p i l e group a c t i o n . The displacement p r o f i l e s for the P i l e 1 at a spacing of 2d are given i n f i g u r e 7.27. Figures 7.28 and 7.29 giv e the displacement p r o f i l e s of P i l e 1 at a spacing of 4d and 6d. I f CHAPTER 7 Load(N) 6 8 12 Pile 1 Single Pile * o • S / D = 6 HG = 60 372 300 200 sz '(D X 100 372 300 200 100 _20^i7r/ 0 " 10~2C7 ~ 3 0 - U1007J^600 - 2 0 0 0 200 Shear Force, N. Bending Moment, N - m m . F i g u r e 7 . 2 3 C o m p a r i s o n Of B e n d i n g M o m e n t Legend /r~. y • -- - S/D = 2 Load 16 N. 24 N. 32 N. 40 N Pile 2 S2C 1S2 0 0 - 1 - 0 . 8 - 0 . 6 - 0 . 4 - 0 . 2 Displacement, mm. F i g u r e 7 . 2 4 D e f l e c t i o n P r o f i l e ( S / D = 2) - 0 .6 -0 .4 -0 .2 0 0.2 0.4 C Soil Pressure, N / m m ~ 2 . CHAPTER 7 90 L e g e n d L o a d 15 N . 2 1 N. 3 2 N . 4 0 N. P i l e 2 S 2 C 1 S 4 S / D - 4 H G = 6 0 3 7 2 c£300 '<u200 X 1 0 0 4 0 P i l e 1 P i l e 2 3 7 2 0 . 4 - 0 . 3 - 0 . 2 - 0 . 1 0 -0.3-0.2-0 .1 0 0 .1 0 . 2 D i s p l a c e m e n t , m m . S o i l P r e s s u r e , N / m m A 2 . Figure 7.25 D e f l e c t i o n P r o f i l e ( S / D = 4) L e g e n d L o a d 6 3 _ N . 8 0 N . 9 0 N . t'^L. H ^ D = _ 6 0 3 5 0 -S 2 C 1S6 3 0 0 2 5 0 } E E 2 0 0 1 5 0 1 0 0 5 0 X . . C L P i l e 1 P i l e 2 0 1 5 -6 . 0 1 - 0 . 0 0 5 0 0 . 0 0 5 - 0 . 0 2 - 0 . 0 1 0 0 . 0 1 D i s p l a c e m e n t , m m . S o i l P r e s s u r e , N / m m I. F i g u r e 7 . 2 6 D e f l e c t i o n P r o f i l e ( S / D 6 CHAPTER 7 91 we compare these displacement p r o f i l e s w i t h the displacement p r o f i l e s of the s i n g l e p i l e at same load, we confirm that at the same load displacement of P i l e 1 i s smaller than that of the s i n g l e p i l e . Thus due to the presence of the adjacent p i l e the l o a d - d e f l e c t i o n response of the P i l e 1 i s s t i f f e r than that of the s i n g l e p i l e . On clo s e r observation, we n o t i c e that the displacement at of the p i l e at the loading p o i n t i s reduced i n far greater amount than at the ground l e v e l . S i m i l a r l y observations can be made i n other cases, although t h i s r e d u c t i o n decreases w i t h i n c r e a s i n g spacing. 7 . 2 . 3 . 3 P-(y-y 0) CURVE Figure 7.30 shows P-(y-y 0) curves for PILE 1 at a spacing of 2d. The curves are shown for various depths. These curves show i n c r e a s i n g s t i f f n e s s w ith i n c r e a s i n g depth s i m i l a r to the s i n g l e p i l e response. But comparing the two responses we f i n d that at a spacing of 2d the response of PILE 1 i s s o f t e r than that of the s i n g l e p i l e . Figure 7.31 gives the P-(y-y 0) curves for spacing of 4d while f i g u r e 7.32 gives P-(y-y 0) curves for a spacing of 6d. I f we compare these responses w i t h that of the s i n g l e p i l e we observe that the response of the PILE 1 at a la r g e r spacing i s s t i f f e r than that of a s i n g l e p i l e . At a small spacing of 2d, the r e s i s t a n c e to the a p p l i e d load i s shared by P i l e 1 , P i l e 2 and s o i l . This f a c t i s a l s o shown by the bending moment p r o f i l e s . In the case of a l a r g e r spacing, most of the r e s i s t a n c e i s shared by only P i l e 1 and the CHAPTER 7 92 L e g e n d L o a d 16 N. 24 N. 3 2 N. 4 0 N. Pi le 1 S2C 1S2 S / D = 2 HG = 60 3 7 2 £300 ^ 2 0 0 | 100 0..L. Pi le 1 Pi le 2 3 7 2 £300 cn ^ 2 0 0 100 + G,L Pi le 1 Pi le 2 0 + 2 1.5 1 0 .5 0 - 0 . 5 - 1 - 1 . 5 Soi l P r e s s u r e , N. 5 4 3 2 1 0 - 1 D i s p l a c e m e n t , m m . F i g u r e 7 . 2 7 D i s p l a c e m e n t P r o f i l e ( S / D = 2 ) e g e n d L o a d 14 N. 20 N. 32 N. Pi le 1 S2C1S4 S / D = 4 HG = 60 3 7 2 3 0 0 . 2 0 0 C7> 'a> X 100 at. Pi le 1 Pi le 2 3 7 2 3 0 0 2 0 0 cn X 1 100 0 Pi le 1 Pi le 2 ..G,L 4 - 3 - 2 - 1 0 D i s p l a c e m e n t , m m . F i g u r e 7 . 2 8 D e f l e c t i o n P r o f i l e ( S / D = 4 ) 1.5 - 1 - 0 . 5 0 0 .5 1 Soi l P r e s s u r e , N / m m A 2 . CHAPTER 7 LOAD 0 . 5 N. 1.0 N. 2 . 0 N. 4 . 0 N. S / D HG 6 6 0 300 E200 J Z IE 100 300 f £200 cn 'CD 100 -0.25-0.2-0.15-0.1-0.05 0 D i s p l a c e m e n t , m m . 0.05 -0.3 -0.2 -0.1 0 0.1 0.2 So i l P r e s s u r e , N / m m A 2 F i g u r e 7 . 2 9 D e f l e c t i o n P r o f i l e ( S / D = 6 ) CHAPTER 7 b»4 s o i l . The s t i f f e r P-y curves imply that the s o i l i s d e n s i f i e d during p i l e i n s t a l l a t i o n . This leads to the c o n c l u s i o n that at the small spacing e f f e c t of d e n s i f i c a t i o n i s small compared to the adjacent p i l e s t i f f n e s s while at l a r g e r spacing s i n c e the adjacent p i l e s t i f f n e s s i s n e g l i g i b l e the e f f e c t of d e n s i f i c a t i o n i s very prominent. 7 . 2 . 3 . 4 C A S E 2 (p = 9 0 ° ) Figure 7.33 compares the load-displacement response of PILE 1 w i t h that of the s i n g l e p i l e . The PILE 1 response i s for CASE 2 i n which the angle between the loading d i r e c t i o n and the l i n e j o i n i n g the p i l e centres i s 90°. The response of the p i l e i s very s i m i l a r to that of the s i n g l e p i l e at smaller loads. At higher loads the PILE 1 response i s s t i f f e r due to the compaction of the s o i l during the i n s t a l l a t i o n of the two p i l e s . Figure 7.34 compares the bending moments i n the two p i l e s for two load cases. As seen from the f i g u r e PILE 2 r e g i s t e r e d zero bending moment. The spacing of the p i l e s was 2d. At spacings 4d and 6d s i m i l a r r e s u l t s were obtained. These shows that the presence of adjacent p i l e has no d i r e c t e f f e c t on the s i n g l e p i l e response. 7 . 2 . 3 . 5 C A S E 3 ((3 = 1 8 0 ° ) In t h i s case, the load-displacement of PILE 1 was s i m i l a r CHAPTER 7 L e g e n d 1.6 1.4 D e p t h 1D 2D 3D 4 D A O D * CN < E E P i l e 1 HG - 6 0 S / D = 2 1.2 + S 2 C 1S2 P i l e 1 P i l e 2 0.1 0.2 0.3 0.4 0.5 0.6 D i s p l a c e m e n t , ( y — yQ ) m m . F i g u r e 7 . 3 0 P - y C u r v e s ( S / D = 2 ) P i l e 1 P i l e 2 0 .1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 D i s p l a c e m e n t , ( y — ) m m . F i g u r e 7.3 1 P - y C u r v e s ( S / D = A\ 0 .7 CHAPTER 7 D e p t h 1D 2D 3D A o n 0.05 0.1 0 .15 D isp lacement , (y — y 0 ) m m . F i g u r e 7 . 3 2 P - y Curves ( S / D 0.2 = 6 ) 70 j 60 -50 -z 40 -TJ a o _j 30 -20 -10 --0 A-P i l e 1 HG = 6 0 S / D = 2 S 2 C 2 S 2 P i l e 1 P i l e 2 —i i—i e g e n d —e— PILE 1 S i n g l e P i l e A n g l e o f l o a d i n g = 9 0 — • 1 • 1 ' 1 -1 2 3 4 5 6 D i s p l a c e m e n t at L o a d i n g P o i n t , m m . F i g u r e 7 . 3 3 Load —Disp lacement Curve CHAPTER 7 97 to that of the s i n g l e p i l e . Furthermore PILE 2 r e g i s t e r e d no e f f e c t , n e i t h e r displacements nor bending moments, due to the loa d a p p l i e d on PILE 1. The comparison of the bending moment p r o f i l e s at two d i f f e r e n t loads i s shown i n f i g u r e 7.35. While i n case 1 the s o i l between the two p i l e s was d e n s i f i e d due to the p i l e i n s t a l l a t i o n , i n t h i s the s o i l i n f r o n t of the PILE 1 showed no e f f e c t s due to the i n s t a l l a t i o n of PILE 2 behind PILE 1. 7.2.4 SERIES I I I (S3) In t h i s s e r i e s both the p i l e s i n the p i l e group are loaded simultaneously. The distance between the p i l e s was v a r i e d from 2d to 4d. The response of the p i l e was compared to both the s i n g l e p i l e as w e l l as the s i n g l e p i l e w i t h the adjacent p i l e . The two p i l e s i n the p i l e group were i n s t a l l e d simultaneously by pushing them i n the same d i r e c t i o n simultaneously. A s p e c i a l p i l e guide was developed for t h i s purpose. 7.2.4.1 Load Displacement Figure 7.36 shows the response of a group of two p i l e s at a spacing of 2d to h o r i z o n t a l load a p p l i e d at an e c c e n t r i c i t y . During the load a p p l i c a t i o n , the displacement of the two p i l e s was kept equal by a r i g i d connection between the two p i l e s . The response of two p i l e s i s al s o shown separately i n the same f i g u r e . The spacing between the two p i l e s i n the p i l e group for CHAPTER 7 98 Legend Load 4 N. 16 N. Pile 1 Pile 7 350 T 300 --250 -• E E 200 --!n cn 150 -• 'cu X 100 -• 50 --0 Pile 2 Pile 1 P = 90 Load Pile 1 Pile 2 -500 0 500 1000 1500 2000 Bending Moment, N —mm. F i g u r e 7 . 3 4 Legend Pile 2 Pile 1 Single B e n d i n g M o m e n t P r o f i l e 372 300 200 CD x 100 372 S / D = 2 HG = 60 Load 300 f .200 '<L> X 100 - 8 0 0 - 6 0 0 - 4 0 0 - 2 0 0 0 200 - 2 0 - 1 0 0 Bending Moment, N - m m . Shear Force F i g u r e 7 . 3 5 B e n d i n g M o m e n t C o m p a r i s o n 10 CHAPTER 7 L e g e n d P i l e 1 P i l e 2 G r o u p S i n g l e . . . . © - -140 120 100 Z 80 1 60 40 20 0 HG = 6 0 S / D = 2 S 3 C 0 S 2 P i l e 1 P i l e 2 0 — — — . -0-"'" 0^"! - CM G .6 4 6 D i s p l a c e m e n t a t L o a d i n g P o i n t , m m . F i g u r e 7 . 3 6 L o a d - D i s p l a c e m e n t C u r v e ( S / D = 2 ) 140 120 100 80 S / D = 4 S 3 C 0 S 4 P i l e 1 P i l e 2 Co 0 2 4 6 8 D i s p l a c e m e n t at L o a d i n g P o i n t , m m . F i g u r e 7 . 3 7 L o a d - D i s p l a c e m e n t C u r v e ( S / D = 4 ) CHAPTER 7 100 t h i s t e s t was 2d. The response of a s i n g l e p i l e subjected to l a t e r a l loads i s a l s o shown i n f i g u r e 7.36. As seen from the f i g u r e , the response of PILE 1 i s s o f t e r than the response of the s i n g l e p i l e . Response of PILE 2 i s much s i m i l a r to that of the s i n g l e p i l e . I t should be noted that most of the load a p p l i e d to the p i l e group i s taken by the PILE 2 (the lead P i l e ) . Figure 7.37 shows the response of the p i l e group w i t h spacing of 4d. I t a l s o shows the response of the i n d i v i d u a l p i l e s . These responses are compared wi t h the response of the s i n g l e p i l e . S i m i l a r to the 2d spacing, the PILE 2 c a r r i e s most of the load a p p l i e d to the p i l e group, but i n t h i s case the percentage of the load c a r r i e d by PILE 1 i s more than the previous case. Also the e f f i c i e n c y of the p i l e group i s more for a spacing of 4d than the spacing of 2d. The e f f i c i e n c y of the p i l e group i s defined as the r a t i o of the maximum load c a r r i e d by the p i l e group to the product of number of p i l e s and the load c a p a c i t y of s i n g l e p i l e . Schmidt (1981) showed that the load c a r r i e d by the f r o n t p i l e i s l a r g e r than the rear p i l e i n p i l e group of two p i l e s . Reese et a l (19 86) during t h e i r experiments on group of l a t e r a l l y loaded p i l e s n o t i c e d that the f r o n t p i l e takes l a r g e r loads and the P-y curve for the rear p i l e i s s o f t e r than that of the s i n g l e p i l e . They explained the overlapping of the pressure zones of the two p i l e s as the cause of t h i s behaviour. According to t h e i r hypothesis, the two pressure bulbs from the CHAPTER 7 101 two p i l e s caused weakening of the s o i l i n between the two p i l e s and thus the rear p i l e c a r r i e d l e s s load than the f r o n t p i l e . Byrne et a l (1986), Yan and Byrne (1990) suggested that casings and platforms can be modelled by c o n s i d e r i n g f r e e f i e l d movements. According to t h i s theory, when a p i l e moves the adjacent p i l e i s subjected to the f r e e f i e l d movements. These movements a f f e c t the behaviour of the adjacent p i l e . P r e v i o u s l y i t has been seen that p u l l i n g adjacent p i l e away has no e f f e c t on the p i l e i n c o n s i d e r a t i o n . But i n t h i s case since the two p i l e s are j o i n e d at the top, thus e n f o r c i n g equal displacements, there are two e f f e c t s . One e f f e c t i s that the fre e f i e l d movements caused by PILE 1 are a c t i n g on PILE 2 and i n reverse movements of PILE 2 are causing a forced free f i e l d movement of PILE 1. This concept i s u t i l i z e d i n analysing the p i l e response i n CHAPTER 8 . 7.2.4.2 P-y CURVES Figure 7.38 shows the P-y curves f o r PILE 1 i n the p i l e group of two p i l e s . The curves are given f o r a spacing of 2d and f o r d i f f e r e n t depths. Figure 7.39 shows the P-y curves f o r PILE 1 f o r a p i l e group of two p i l e s with a spacing of 4d. I f we compare the two f i g u r e s , the response of the PILE 1 i n both the t e s t s i s s i m i l a r . Comparing the response of PILE 1 with that of the s i n g l e p i l e we observe that the response of the PILE 1 i n the p i l e group i s s o f t e r than that of the s i n g l e p i l e . As explained before Reese et a l (1986) suggested that t h i s CHAPTER 7 102 L e g e n d D e p t h 1D 2D 3D 4 D A o n * -0.7 D i s p l a c e m e n t , y ( = ( y - y Q ) + y 0 ) m m . F i g u r e 7 . 3 8 P - y C u r v e s ( S / D = 2 ) 0.7 T — 0®—• 1 • 1 < 1 • 1 • 1 . 1 ^-U . 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 D i s p l a c e m e n t , y ( = (y-yQ.)+yo)> m m -F i g u r e 7 . 3 9 P - y C u r v e s ( S / D = 4 ) CHAPTER 7 103 i s due to the overlapping of the pressure zones form the two p i l e s i n the p i l e group. But as seen from CASE 2, the p i l e i n s t a l l a t i o n c a u s e s d e n s i f i c a t i o n of the s o i l i n between the two p i l e s . Hence t h i s s o f t e n i n g i s due to the f r e e f i e l d displacements imposed by the equal displacement c o n d i t i o n s on the p i l e s i n the p i l e group. 7.2.4.3 Bending moment P r o f i l e The bending moment p r o f i l e for the t r a i l i n g p i l e (PILE 1) i s shown i n f i g u r e 7.40 and f i g u r e 7.41 compares i t w i t h the p r o f i l e of s i n g l e p i l e . The f i g u r e shows the bending moment and shear fo r c e p r o f i l e s for a t r a i l i n g p i l e when both the p i l e s are given same displacements under d i f f e r e n t loads. When a p i l e group i s subjected to l a t e r a l l oad the p i l e group response i s e f f e c t of 1. P i l e - s o i l - p i l e i n t e r a c t i o n 2. P i l e - p i l e c a p - p i l e i n t e r a c t i o n 3. A x i a l push-pull e f f e c t on the p i l e group due to the e c c e n t r i c i t y of the load. In the t e s t s conducted the p i l e head connections were f r e e connections. In t h i s connection, the p i l e head i s allowed to r o t a t e f r e e l y . Due to t h i s s p e c i a l type of connection only p i l e - s o i l - p i l e i n t e r a c t i o n was a f f e c t i n g the group response. As seen i n the p r o f i l e s for the s i n g l e p i l e s the maximum bending moment i s about 3 to 4 diameters below the ground s u r f a c e . In f i g u r e 7.41, i t can be seen that the maximum bending moment i n CHAPTER 7 104 Legend Load 2 N. N. 12 N. 16 N. S = 2 D Pile 1 H G = 60 S3C0S2 372 300 200 sz X 100f 372 300 200 x 100 -20 - 1 0 0 10 20 30 - " 1 5 0 0 - 1 0 0 0 - 5 0 0 0 500 Shear Force, N. Bending Moment, N - m m . F i g u r e 7 . 4 0 B e n d i n g M o m e n t P r o f i l e ( S / D = 2 ) Legend LOAD (N.) 8 12 16 Pile 1 S = 2 D * O • HG = 60 Single Pile E E CD X 372 300^ ,200-100-0 3 0 - 2 0 - 1 0 0 10 20 30 - 1 5 0 0 - 1 0 0 0 - 5 0 0 0 500 Shear Force, N. Bending Moment, N —mm. F i g u r e 7 .4 1 C o m p a r i s o n Of B e n d i n g M o m e n t CHAPTER 7 105 the p i l e remains the same i r r e s p e c t i v e of whether the p i l e was used i n the p i l e group or alone. The only d i f f e r e n c e i s that i n the p i l e used i n p i l e group there i s downward s h i f t i n the maximum bending moment.This s h i f t can be seen i n more prominently i n the shear force p r o f i l e s . In t h e i r study K u l k a r n i et al(1985) subjected a two p i l e group to a l a t e r a l load i n l i n e w i t h the p i l e s . They observed that the bending moment i n the rear p i l e i s much l e s s than that i n the f r o n t p i l e . Their r e s u l t s show that the bending moment i n the rear p i l e i s l e s s than h a l f that of the f r o n t p i l e . According to the e l a s t i c s o l u t i o n , both the p i l e s should c a r r y equal load and the bending moments developed i n both the p i l e s should be equal. Due to the load t r a n s f e r mechanism between two p i l e s observed before i n the Seri e s 2, the rear p i l e c a r r i e s much l e s s load than the f r o n t p i l e . I f we compare the maximum bending moment of the f r o n t p i l e and the rear p i l e at the equal load, we can observe that the both the p i l e s develop equal bending moment. The f i g u r e 7.42 gives the d e f l e c t i o n and s o i l pressure p r o f i l e s of the t r a i l i n g p i l e . Again i t can be seen that the len g t h of the p i l e model below 150mm i s p r a c t i c a l l y i n e f f e c t i v e i n r e s i s t i n g the h o r i z o n t a l load at the top. S i m i l a r l y the bending moment, shear force p r o f i l e s for spacing of 4d are given i n f i g u r e 7.43. When the t r a i l i n g p i l e response of the p i l e group w i t h 4d spacing i s compared wi t h that of the s i n g l e p i l e i n f i g u r e 7.44 as expected there i s a smaller s h i f t between the CHAPTER 7 106 Legend L o a d 9 N. 10 N. 14 N. 16 N. P i le 1 S = 4 D S3C0S4 HG = 60 -20 - 1 0 0 10 20 30 - w 1 5 0 0 - 1 0 0 0 - 5 0 0 0 5 0 0 Shear Force, N. Bending Moment, N - m m . F i g u r e 7 . 4 3 B e n d i n g M o m e n t P r o f i l e ( S / D = 4 ) CHAPTER 7 107 maximum bending moment of the two p i l e s than the p i l e group of spacing 2d. I f f i g u r e s 7.41 and 7.44 are compared, i t can be seen that the d i f f e r e n c e i n depth of maximum bending moment between PILE 1 and s i n g l e p i l e reduces as the spacing i s increased. Also the amount of the negative bending moment developed i n the mid-section of the p i l e i s much l e s s i n the p i l e group than the s i n g l e p i l e . The d e f l e c t i o n and s o i l pressure p r o f i l e s f o r the t r a i l i n g p i l e i n p i l e group of spacing 4d are given i n the f i g u r e 7.45. The f i g u r e 7.4 6 compares the bending moment and shear force p r o f i l e s f o r the SERIES 1, 2, and 3 f o r the p i l e group of spacing 2d. I t can be seen that i n the SERIES 1 and 3 the maximum bending moment i s of the same magnitude while i n the SERIES 2 the bending moment i n the p i l e i s reduced considerably due to the presence of the adjacent p i l e . This i s due to the f a c t t h a t , since i n SERIES 2 the second p i l e i s not loaded, part of the bending moment i s t r a n s f e r r e d to the adjacent p i l e and at the same time, d e n s i f i c a t i o n of the s o i l a l s o reduces the bending moment i n the p i l e . In SERIES 3, although the surrounding s o i l i s d e n s i f i e d , the e f f e c t i s not taken i n t o account since the p i l e i n front (PILE 2) i s al s o moving the same distance (at ground l e v e l ) i n the same d i r e c t i o n . S i m i l a r , observations can be made i n the f i g u r e 7.47 for a p i l e group of spacing 4d. Figure 7.47 compares the bending moment and shear force p r o f i l e s of the P i l e 1 i n a l l the three cases . CHAPTER 7 108 L e g e n d S = 4 D HG = 6 0 372 300 c200 cn 'cu I" 100 1500- 1000 -500 0 500 B e n d i n g M o m e n t , N - m m . F i g u r e 7 . 4 4 C o m p a r i s o n Of B e n d i n g M o m e n t -20 - 10 0 10 20 30 S h e a r F o r c e , N. CHAPTER 7 109 Legend Load 9 N. 10 N. 14 N. 16 N. Pile 1 S = 4 D S3C0S4 HG = 60 372 300 E E ".200 J Z X 100 Pile, .I,., Pile 2 -4 - 3 - 2 - 1 0 - 1 - 0 . 5 0 0.5 Displacement, mm. Soil Pressure, N / m m " 2 . F i g u r e 7.45 D e f l e c t i o n P r o f i l e Legend S3C0S2 S2C1S2 S1C0S0 400-400 300 - ^ 0 0 X 100 - 8 0 0 - 6 0 0 - 4 0 0 - 2 0 0 0 2 0 0 Shear Force, N. Bending Moment, N —mm. S3C0S2 : - Pile Group With Both Piles Loaded S = 2d S2C1S2 : - Pile Group With One Pile Pushed S = 2d S1C0S0 : - Single Pile F i g u r e 7 . 4 6 C o m p a r i s o n Of B e n d i n g M o m e n t CHAPTER 7 7.3 SUMMARY AND CONCLUSIONS 110 This chapter gives the r e s u l t s of the l a t e r a l l o a d t e s t s conducted on the s i n g l e p i l e and group of two p i l e s . The t e s t s were conducted at a h y d r a u l i c gradient of 60 and s o i l comprised of the f i n e Ottawa sand. The t e s t s were conducted i n three s e r i e s SERIES 1 - Si n g l e p i l e loaded h o r i z o n t a l l y SERIES 2 - Si n g l e p i l e loaded h o r i z o n t a l l y w i t h an adjacent p i l e present. SERIES 3 - P i l e group of two p i l e s loaded h o r i z o n t a l l y The r e s u l t s of the t e s t s were compared w i t h the s i n g l e p i l e r e s u l t s . In the s e r i e s 2 the p i l e s were t e s t e d at three angles, 0°,90° and 180°. I t was found that the load i n g i n the 90° or 180° has very l i t t l e e f f e c t on the adjacent p i l e . In both these cases, both the p i l e s showed no e f f e c t of the presence of the adjacent p i l e on e i t h e r the load-displacement response or changes i n s t r e s s c o n d i t i o n s . In case of the 0° of loading, i t was found out that the i n s t a l l a t i o n of adjacent p i l e tends to increase the d e n s i t y of the surrounding s o i l . Due to t h i s e f f e c t the response of the p i l e i n SERIES 2 was s t i f f e r than the s i n g l e p i l e . Since i n SERIES 3 both the p i l e s i n the p i l e group are loaded and the displacements of both the p i l e s are made equal i t was important to n o t i c e the load sharing of the two p i l e s . I t was seen that, the f r o n t p i l e of the two p i l e s shared a l a r g e amount of the CHAPTER 7 111 L e g e n d 4 0 0 S 3 C 0 S 4 S 2 C 1S4 S 1 C 0 S 0 • 3 0 0 "200 cn CD 100 4 0 0 300 j "200 CTi 'CD X 15 - 5 0 5 S h e a r F o r c e 1004 15 - 8 0 0 - 6 0 0 - 4 0 0 - 2 0 0 0 200 N. B e n d i n g M o m e n t , N — m m . F i g u r e 7 . 4 7 C o m p a r i s o n Of B e n d i n g M o m e n t S 3 C 0 S 4 : - Pi le Group With Both P i l es L o a d e d S = 4d S 2 C 1 S 4 : - P i le Group With One Pi le P u s h e d S = 4d S 1 C 0 S 0 : - S ingle Pi le CHAPTER 7 112 load. The response of the f r o n t p i l e was found to be s i m i l a r to the response of the s i n g l e p i l e . The d e n s i f i c a t i o n e f f e c t due to the i n s t a l l a t i o n of adjacent p i l e was not observed for the f r o n t p i l e . In case of the rear p i l e , i t was n o t i c e d that the rear p i l e shares very l i t t l e amount of the t o t a l load a p p l i e d to the group at a small spacing. As the spacing increases, the amount of load shared by the rear p i l e a l s o increases. This may be due to the f a c t that the two p i l e s were subjected to the same displacements. From SERIES 2, i t i s seen that the same rear p i l e showed s t i f f e n i n g e f f e c t s , due to the d e n s i f i c a t i o n of sand during p i l e group i n s t a l l a t i o n . I r r e s p e c t i v e of t h i s e f f e c t , the rear p i l e showed a very response to the p i l e group loads. This i s mainly due to the reason that most of the load a p p l i e d to the s o i l i s taken by the f r o n t p i l e and as the s o i l i n f r o n t of the f r o n t p i l e i s s o f t e r than the s o i l i n between the two p i l e s , i t y i e l d s f i r s t . As soon as t h i s y i e l d i n g s t a r t s , the f r o n t p i l e s t a r t s moving with the s o i l and the rear p i l e and the s o i l mass i n between a l s o s t a r t s moving without a c t u a l l y reaching the y i e l d p o i n t . I t was observed during the loading of the p i l e group that the depth of the maximum bending moment developed i n the p i l e i n c r e a s e s w i t h the decreasing spacing. This i s due to the f a c t that as the spacing decreases the f r o n t p i l e shares the load a p p l i e d on the rear p i l e through the s o i l . Due to t h i s the maximum bending moment i n the f r o n t p i l e i n the p i l e group i s ~1 CHAPTER 7 113 greater than the s i n g l e p i l e and at greater depth. In the next chapter an attempt i s made to p r e d i c t the behaviour of the p i l e i n the p i l e group and to p r e d i c t the bending moments and shear forces i n the p i l e c o r r e c t l y using the LATPILE program. CHAPTER 8 114 C H A P T E R 8 : P R E D I C T I O N O F T H E P I L E GROUP R E S P O N S E 8.1 INTRODUCTION In t h i s chapter, the r e s u l t s from the a n a l y s i s of the p i l e group of two p i l e s using the program LATPILE are compared with the experimental r e s u l t s . The d e t a i l s of the a n a l y s i s are explained below. The program LATPILE i s f i r s t used f o r the s i n g l e p i l e t e s t data. The LATPILE program uses the P-y curve approach to analyze the p i l e . The P-y curves are s p e c i f i e d at various depths, the boundary c o n d i t i o n s are given and then the appropriate loads are a p p l i e d on the p i l e . The program and the concept used i n the a n a l y s i s are discussed b r i e f l y before the d i s c u s s i o n of the p r e d i c t i o n r e s u l t s . 8.2 THE FREE FIELD CONCEPT AND ITS APPLICATION The LATPILE program uses the P-y curve approach f o r a n a l y s i n g the p i l e foundation. In t h i s approach the s o i l system i s replaced by a system of h o r i z o n t a l nonlinear s p r i n g s . The s p r i n g i s attached at one end to the p i l e and at the other end to a free end instead of f i x e d support. Thus free f i e l d movements cause the sp r i n g ends to d e f l e c t r e s u l t i n g i n load and d e f l e c t i o n i n the p i l e s . The r e l a t i o n s h i p between the force and d e f l e c t i o n of the sp r i n g of s t i f f n e s s K i s given by CHAPTER 8 115 P = K y eq. (8 . 1) The displacement of the free f i e l d ends of the springs are assumed to be known. Thus the s o i l r e a c t i o n term i s now given by P = k ( y - y 0 ) eq. ( 8 .2 ) Where P i s the S o i l force per u n i t depth of the p i l e , known as s o i l r e a c t i o n K i s the s o i l s t i f f n e s s c o e f f i c i e n t or the s p r i n g s t i f f n e s s y i s the d e f l e c t i o n of the p i l e r e l a t i v e to i t s i n i t i a l p o s i t i o n . y 0 i s the free f i e l d d e f l e c t i o n , assumed to be known The governing equation becomes El^l+P £ l +k(y-yo)=0 eq. (8.3) dx* ' dx2 ° where E i s the Young's modulus of the p i l e ; I i s the second moment of area of the p i l e about i t s n e u t r a l a x i s ; P x i s the a x i a l force i n the p i l e and x i s v e r t i c a l coordinate. This equation can be r e w r i t t e n as f o l l o w s CHAPTER 8 116 This equation represents a c o n d i t i o n when the s p r i n g ends are f i x e d and the p i l e i s subjected to a l a t e r a l load k y 0. I f the s o i l i s l i n e a r then the s o i l s p r i n g s t i f f n e s s i s constant and since y 0 i s known, the response of the p i l e can be obtained e a s i l y . These d e f l e c t i o n s of the free f i e l d ends of the springs may be due t o ground movement or loads from adjacent p i l e s . I f t h i s concept i s a p p l i e d to the p i l e group a n a l y s i s then i t can be s a i d that the load on one p i l e causes a fre e f i e l d displacement i n the adjacent p i l e which i f determined can be used as the f r e e f i e l d d e f l e c t i o n of the p i l e . Free f i e l d d e f l e c t i o n i s defined as the d e f l e c t i o n at the l o c a t i o n of a p i l e that would occur from loading adjacent p i l e s . Thus the a n a l y s i s of a p i l e w i t h i n a group now reduces to c a l c u l a t i n g the response of the s i n g l e p i l e under i t s a p p l i e d load together with i t s response to the free f i e l d d e f l e c t i o n s a r i s i n g from the loads on the other p i l e s i n the p i l e group. In t h i s chapter an attempt i s made to analyze the p i l e group of two p i l e s using the above concept. 8 . 3 PREDICTION OF PILE RESPONSE The P-y curves developed from the s i n g l e p i l e t e s t r e s u l t s were used i n the LATPILE program. The a n a l y s i s was c a r r i e d out i n three steps as f o l l o w s . In the f i r s t step the response of the s i n g l e p i l e under a h o r i z o n t a l load was compared with the experimental r e s u l t s and C H A P T E R 8 117 i s given i n Figure 8.1. I t was found that LATPILE p r e d i c t s the response of the s i n g l e p i l e very a c c u r a t e l y i f the P-y curves obtained from the experiments are used. In the second step, p i l e response to loads on adjacent p i l e s was analysed. The p i l e displacement, moment and shear for c e p r o f i l e s were obtained from SERIES 2. In the LATPILE a n a l y s i s , the p i l e was subjected to free f i e l d displacement equal to the p i l e displacement observed i n the experiment. The d i f f e r e n c e between the input f r e e f i e l d displacement and the p i l e displacement was very small. The bending moment and shear for c e p r o f i l e s from the a n a l y s i s were compared w i t h the p r o f i l e s obtained from the experiments. Figures 8.2 to 8.6 give comparisons of various load cases and spacings. I t should be noted that although the distance between the p i l e s i s i n c r e a s i n g and the bending moment i s reducing considerably, the LATPILE p r e d i c t i o n s are very good. In the t h i r d step, LATPILE program was used to analyse the response of a s i n g l e p i l e i n group. The p i l e was analysed under a combination of load and free f i e l d displacement. At t h i s p o i n t i t should be remembered that the loads on both the p i l e s are d i f f e r e n t . Therefore the free f i e l d displacement w i l l correspond to a d i f f e r e n t magnitude of load than the a p p l i e d load. 8.3.1 COMPARISON OF BENDING MOMENT The comparison between the experimental r e s u l t s f or the CHAPTER 8 118 L e g e n d E x p e r i m e n t a l — e — L a t p i l e A 400 300 E X 200 t 100 + -800-600-400-200 0 200 B e n d i n g M o m e n t , N — m m . F i g u r e 8 . 1 C o m p a r i s o n Of B e n d i n g M o m e n t F r o m E x p e r i m e n t a n d L a t p i l e F o r S i n g l e P i l e C H A P T E R 8 1 1 9 t r a i l i n g p i l e and s i n g l e p i l e are given i n f i g u r e s 8.7-8.8 w i t h the LATPILE p r e d i c t i o n for the t r a i l i n g p i l e . I t i s q u i t e c l e a r that although the program i s p r e d i c t i n g the maximum bending moment very c l o s e l y the bending moment p r o f i l e along the l e n g t h of the p i l e i s q u i t e d i f f e r e n t from that obtained form the experiment. During the loading of the p i l e i t i s observed that due to the p i l e s o i l gaping the depth of maximum bending moment tends to increase along the p i l e length. This may account for the small discrepancy i n the a n a l y t i c a l r e s u l t s and the experimental r e s u l t s . One more important c o n s i d e r a t i o n i s that the adjacent p i l e i n SERIES 2 showed no e f f e c t when the loaded p i l e was p u l l e d away for the purposes of a n a l y s i s . In the experiment however both the p i l e s were d i s p l a c e d e q u a l l y hence for the purposes of a n a l y s i s i t was assumed that the f r e e f i e l d e f f e c t i n e i t h e r d i r e c t i o n w i l l be same. 8.3.2 LOAD DISPLACEMENT RESPONSE The load displacement curves were used to c a l c u l a t e the i n t e r a c t i o n f a c t o r a which i s then compared w i t h the i n t e r a c t i o n f a c t o r from va r i o u s methods. The comparison i s given i n f i g u r e 7 .14 . The i n t e r a c t i o n f a c t o r s are c a l c u l a t e d using methods based on the e l a s t i c theory. These methods are discussed i n d e t a i l i n CHAPTER 3. The i n t e r a c t i o n f a c t o r s were c a l c u l a t e d for a p i l e group of two p i l e s with the load a p p l i e d at an e c c e n t r i c i t y of CHAPTER 8 120 Expt . La tp i le S = 2 D N = 60 P i l e 2 3 5 0 3 0 0 2 5 0 E E200 J Z . ? 1 5 0 X 100 50 0 L o a d 3 1 . 9 N. • *\ » V , , , 1 3 5 0 3 0 0 2 5 0 E E 2 0 0 JZ . 0 ^ 1 5 0 cu X 100 + 5 0 0 L o a d 3 1 . 9 N. P i l e 1 P i l e 2 - 8 0 - 6 0 - 4 0 - 2 0 0 20 4 0 60 S h e a r F o r c e , N. - 2 5 0 - 1 5 0 - 5 0 0 5 0 3 5 0 3 0 0 2 5 0 E200 J Z . ? 1 5 0 X 100 5 0 0 L o a d 4 0 N. • • ^ \ v • • - • - * / ' (• • B e n d i n g M o m e n t , N —mm F i g u r e 8 . 2 3 5 0 3 0 0 2 5 0 E E200 J Z , ? 1 5 0 cu X 100 5 0 0 L o a d 4 0 N. 1 5 0 - 1 0 0 - 5 0 0 5 0 100 150 - 4 0 0 - 3 0 0 - 2 0 0 - 1 0 0 0 100 S h e a r F o r c e , N. B e n d i n g M o m e n t , N - m m . F i g u r e 8 . 3 CHAPTER 8 121 3 5 0 3 0 0 2 5 0 E ^ 2 0 0 . a i 1 5 0 'CD X 1 0 0 5 0 0 E x p t . L a t p i l e S = 4 D N = 6 0 P i l e 2 3 5 0 -3 0 0 L o a d 4 8 N. / — « *~— *~ \ • / • 1 i > 1 . 1 1 1 1 u - 5 - 4 - 2 0 2 4 5 S h e a r F o r c e , N. - 2 5 0 - 1 5 0 - 5 0 0 5 0 B e n d i n g M o m e n t , N — m m . F i g u r e 8 . 4 - 1 5 - 1 0 - 5 0 5 S h e a r F o r c e , N 10 - 4 0 0 - 3 0 0 - 2 0 0 - 1 0 0 0 100 B e n d i n g M o m e n t , N — m m . F i g u r e 8 . 5 C H A P T E R 8 122 62mm. The e f f e c t of the boundary was taken i n t o c o n s i d e r a t i o n w h i l e c o n s i d e r i n g the i n t e r a c t i o n f a c t o r s . 8.4 SUMMARY In t h i s chapter, the r e s u l t s of the SERIES 2 were used to analyze p i l e groups i n SERIES 2 and 3. In SERIES 2, very good r e s u l t s were obtained, whereas i n SERIES 3 some d i f f e r e n c e was observed although t h i s d i f f e r e n c e was very s m a l l . In both the cases, the induced displacements of the p i l e were obtained from the SERIES 2 and were used as the fre e f i e l d displacements i n LATPILE program. The program c a l c u l a t e d the p i l e displacements and bending moments based on the fre e f i e l d as exp l a i n e d e a r l i e r . The r e s u l t s were remarkably good for the back a n a l y s i s of SERIES 2. The bending moments and the displacement p r o f i l e s of the p i l e were e x a c t l y as recorded during the experiment. In SERIES 3, the s l i g h t d i f f e r e n c e i n the p r o f i l e s of the LATPILE r e s u l t s and the experimental data i s due to the f a c t that i n a d d i t i o n to the free f i e l d imposed on the p i l e , the d e n s i f i c a t i o n of the s o i l i n fr o n t of the rear p i l e has to be taken i n t o account. Since most of the load i s being c a r r i e d by the f r o n t p i l e , and the s o i l ahead of the f r o n t p i l e i s not a f f e c t e d the r e s u l t s of the LATPILE are f a i r l y c l o s e to the experimental data. A more d e t a i l e d study on the a p p l i c a b i l i t y of t h i s method to various cases of p i l e groups i s r e q u i r e d . CHAPTER 8 123 E x p t . L a t p i l e 350 300 250 £ 200 E .9? 150 100 \ 5 0 t S = 6 D HG = 6 0 P i l e 2 L o a d 1 16 .0 N. — i 350 300 250 £ 200 E _c X 150 100 L o a d 1 16 .0 N. 50 Pi le 1 P i le 2 - i — i — h 10 -5 0 5 S h e a r F o r c e , N. 10 -400-300-200-100 0 100 B e n d i n g M o m e n t , N - m m . F i g u r e 8 . 6 CHAPTER 8 124 Trailing Pile single Pile Latpile Prediction 4 0 0 3 0 0 E E 2 0 0 - 4 — ' sz CT CD 100 LOAD 10 N. •J l JG L 4 a •O y « i * Shear Force, N. S = 2 D Pile 1 HG = 60 4 0 0 3 0 0 E E 2 0 0 CT a) X 100 Figure 8.7 - 1 0 0 0 - 7 5 0 - 5 0 0 - 2 5 0 0 2 5 0 Bend ing Momen t , N - m m . Trailing Pile Single Pile Latpile Prediction • • 4 0 0 3 0 0 E E CT ' CD X 2 0 0 100 LOAD 8 N. J O I * \ j\ f 4 0 0 3 0 0 E E 2 0 0 CT '(D X 100 Pile 1 S = 4 D HG = 60 •20 - 10 0 10 20 Shea r F o r c e , N. Figure - 8 0 0 - 6 0 0 - 4 0 0 - 2 0 0 0 2 0 0 Bend ing Momen t , N - m m . C H A P T E R 9 125 C H A P T E R 9 : SUMMARY AND C O N C L U S I O N In t h i s study the p i l e group response to the l a t e r a l load i s s t u d i e d i n the laboratory using the H y d r a u l i c Gradient S i m i l i t u d e T e s t i n g Device. While conducting model t e s t s , i t i s important to conduct the t e s t at f i e l d s t r e s s l e v e l of the s o i l sample so as to get r e a l i s t i c r e s u l t s . The HGS method i s a very e f f e c t i v e way to conduct a model t e s t at f i e l d s t r e s s l e v e l s . The o b j e c t i v e s of the study were to generate a database for the p i l e group response under l a t e r a l loads and study the i n t e r a c t i o n between two p i l e s as w e l l as p i l e - s o i l i n t e r a c t i o n e f f e c t s . I t was found that the h y d r a u l i c gradient t e s t r e s u l t s are repeatable and r e l i a b l e . The H y d r a u l i c Gradient S i m i l i t u d e Method i s a very simple and c o s t - e f f e c t i v e way of conducting model s t u d i e s . The main drawback i s that, i t can be used only for s o i l - s t r u c t u r e s c o n s i s t i n g of uniform sand with h o r i z o n t a l flow boundaries. But even w i t h these r e s t r i c t i o n s a vast number of problems i n c l u d i n g the p i l e groups can be studied very e f f e c t i v e l y . Some of the a p p l i c a t i o n s of the Hydraulic Gradient S i m i l i t u d e modelling technique are as f o l l o w s P i l e group response to c y c l i c l o a d i n g as w e l l as earthquake loading. Response of s i n g l e p i l e and p i l e groups i n l i q u e f i e d m a t e r i a l . C H A P T E R 9 126 E f f e c t s of p i l e d r i v i n g on the p i l e c a p a c i t y and the energy t r a n s f e r during the p i l e d r i v i n g . Tests were conducted on s i n g l e p i l e s , s i n g l e p i l e s i n the presence of adjacent p i l e and p i l e group comprised of two p i l e s . The r e s u l t s from a l l the t e s t s were discussed i n the chapter 7. Tests were conducted w i t h various spacings between the p i l e s and wi t h v a r i o u s angles of loading. From the t e s t s on the s i n g l e p i l e , bending moment, shear f o r c e and d e f l e c t i o n p r o f i l e s were obtained. When the s i n g l e p i l e was loaded i n the presence of adjacent p i l e , i t was found that the adjacent p i l e increases load r e s i s t a n c e by i t s own s t i f f n e s s and by d e n s i f y i n g the s o i l surrounding the p i l e . The e f f e c t of the adjacent p i l e depends on i t s p o s i t i o n r e l a t i v e to the loaded p i l e . When the adjacent p i l e was at 9 0° to the a p p l i e d load or when the adjacent p i l e was away from the d i r e c t i o n of the a p p l i e d load i t was observed that the adjacent p i l e has no e f f e c t on the p i l e response. In the p i l e group t e s t i n g , i t was seen that the t r a i l i n g p i l e shared l e s s load than the lea d i n g p i l e . As the p i l e spacing increased the percentage of load c a r r i e d by the t r a i l i n g p i l e a l s o increased. The maximum bending moment developed i n the l e a d i n g p i l e i s at a lower depth than that of the s i n g l e p i l e . A l s o the maximum bending moment i n l e a d i n g p i l e i s s i m i l a r to that developed i n s i n g l e p i l e . Thus whether the p i l e s are loaded simultaneously or not, lo a d i n g a t r a i l i n g p i l e w i l l cause d e f l e c t i o n of the l e a d i n g C H A P T E R 9 127 p i l e and bending moment w i l l be developed i n the l e a d i n g p i l e as consequence of the load a p p l i e d on t r a i l i n g p i l e . Whereas the loa d i n g of le a d i n g p i l e w i l l not a f f e c t t r a i l i n g p i l e except through p i l e - c a p - p i l e i n t e r a c t i o n . A l l the t e s t r e s u l t s were compared w i t h the r e s u l t s from LATPILE a n a l y s i s . In LATPILE a n a l y s i s P-y curves obtained from the s i n g l e p i l e t e s t were used. LATPILE a n a l y s i s was used to p r e d i c t s i n g l e p i l e response, response of the adjacent p i l e and response of the lead i n g p i l e i n the p i l e group. I t was seen that LATPILE p r e d i c t i o n s and t e s t r e s u l t s agree q u i t e w e l l for s i n g l e p i l e as w e l l as for the adjacent p i l e . In case of the l e a d i n g p i l e i n a p i l e group, although the maximum bending moment p r e d i c t i o n s were good, the bending moment p r o f i l e i s q u i t e d i f f e r e n t than the experimental p r o f i l e . REFERENCE REFERENCES 128 1 A l i z a d e h , M. and Davisson, M.T. - L a t e r a l Load Tests on P i l e s - Arkansas River P r o j e c t , Journal Of S o i l Mechanics and Foundation D i v i s i o n , ASCE, 1970, V o l . 96, SM5, pp. 1583-1604. 2 API—RP2A - Recommended P r a c t i c e f o r Planning, Designing and Const r u c t i n g F i x e d Offshore Platforms. 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