ESTIMATION OF SETTLEMENT OF PILE GROUPS 0

A DISSERTATION Submitted In partial fulfilment of the

requirements for the award of the degree of

MASTER OF TECHNOLOGY in

CIVIL ENGINEERING (With Specialization in Gsotechnical Engineering)

By

VENKATA RAMI REDDY CHALLA

/~ear►i arise

Alt Z.Gi avi

an.2~~-~2•vs! ~

DEPARTMENT OF CIVIL ENGINEERING INDIAN INSTITUTE OF TECHNOLOGY ROORKEE

ROORKEE-247 667 (INDIA)

JUNE, 2005

CANDIDATE'S DECLARATION

I hereby declare that the work presented in this dissertation report entitled

"ESTIMATION OF SETTLEMENT OF PILE GROUPS" submitted in the partial

fulfillment of the requirement for award of the degree of Master of Technology in Civil

Engineering with the specialization in Geotechnical Engineering of the Indian Institute

of Technology Roorkee, Roorkee, is an authentic record of my own work carried out

under the supervision of Dr. G. Ramasamy, Professor, Department of Civil

Engineering, Indian Institute of Technology Roorkee, Roorkee.

I have not submitted the matter embodied in this dissertation for award of any

other degree or diploma.

Date: 30 x̀' June 2005 l Place: Roorkee Venkata Rami RUdy Challa

CERTIFICATE

This is to certify that the above statement made by the candidate is correct to the

best of my knowledge and belief.

Dr. G. Ramasamy

Professor,

Department of Civil Engineering,

Indian Institute of Technology Roorkee,

Roorkee — 247667, India.

i

ACKNOWLEDGEMENT

I sincerely express my deep sense of gratitude to my supervisor Dr. G.

Ramasamy, Professor, Department of Civil Engineering, Indian Institute of Technology

Roorkee, Roorkee, for his expert and valuable guidance, profound advice and persistent

encouragement and help during the completion of this dissertation.

I wish to express my sincere thanks to my teachers of Geotechnical Engineering

Section for their cooperation, teaching and guidance. Also, I would like to thank

Muralidhar Sarabu, M.Tech (CAD) for the help extended to me during my work.

Words fail to express my deep sense of gratitude to my parents for their blessing

and support during my studies.

I also thank all my friends for their direct or indirect support in completing my

dissertation.

Place: Roorkee cLa Dated: 30th June 2005

(Venkata Rami Re dy Challa)

ii

ABSTRACT

Estimation of settlement of pile foundation is generally carried out based on

equivalent raft method, which is empirical in kind. On the other hand, the literature

provides a few sophisticated methods which involve inputting too many soil parameters

which cannot be reliably estimated. Therefore, an attempt has been made to develop a

simple but a rational method of estimating settlement of pile groups based on load

transfer approach as adopted by Hazarika & Ramasamy (2000) for single piles and

equivalent pier method given by Randolph (1994). The method takes into account layered

soil system and makes use of input parameters obtained from usually conducted field

tests such as standard penetration test (SPT) and static cone penetration test (SCPT) in

cohesionless soils and consolidation test in cohesive soils.

The method has been computerized and a user friendly program has been

developed using C++. Using the program, settlement of pile groups has been estimated

for a number of cases and parametric studies have been carried out to bring out the effect

of type of soil and number of piles in a group. Further a few reported case histories have

been compiled and a comparison of predicted and observed settlements has been made.

iii

CONTENTS

Description Page No.

CADIDATE'S DECLARATION i

ACKNOWLEDGEMENT ii ABSTRACT iii

CONTENTS iv LIST OF TABLES vi 1. INTRODUCTION 1

1.0 General 1

1.1 Present work 2 1.3 Organization of dissertation 2

2. LITERATURE REVIEW 3

2.0 Introduction 3 2.1 Single pile 3

2.1.1 Elastic continuum method 3 2.1.2 Finite element Analysis 4

2.1.3 Load transfer method 4 2.2 Pile Groups 5

2.2.1 Equivalent raft method 5 2.2.2 Empirical methods 13 2.2.3 Theoretical methods 14 2.2.4 Load test on pile groups 18 2.2.5 Equivalent pier method 18

3.ESTIMATION OF SETTLEMENT OF PILE GROUPS 21 PROPOSED METHOD

3.0 Introduction 21

3.1 Details of the method 21

3.1.1 Development of Q — z curve 21 3.1.2 Development off— z curve 22

3.2 Procedure 24

VA

4. RESULTS AND DISCUSSIONS 26

4.0 General 26

4.1 Example problem 26

4.2 Case studies 30

4.3 Parametric study 36

4.3.1 Pile group in cohesive soil 36

4.3.2 Pile group in cohesionless soil 39

5. CONCLUSIONS 42

REFERENCES 43

FIGURES 47

V

LIST OF TABLES

No. Description Page No.

Table: 2.1 Steinbrenner's influence factor (I.S:8009 part I) 7

Table: 2.2 Empirical relationship between (E„) and (S.) of soils 7

(Skempton and Bjerrum, 1957)

Table: 2.3 Values of geological factor (pg) 8

(Skempton and Bjerrum, 1957)

Table: 2.4 Value of coefficient `M' for obtaining deformation 11 modulus (Schmertmann, 1970)

Table: 2.5 Approximate relationship between (q~) and (N) 11 (Peck et al., 1974)

Table: 3.1 Values of Ks 23 Table: 3.2 Values of K,, 23 Table: 4.1 Comparison of manually computed and program 27

computed results Table: 4.2 Values of Group ratio with varying B in cohesive soil 36 Table: 4.3 Values of Group ratio with varying B in cohesionless 39

soil

vi

CHAPTER 1 INTRODUCTION

1.0 General There exist many procedures for estimating the settlement behavior of pile

groups, ranging from simple closed form solutions to sophisticated nonlinear finite

element analyses. The mechanism of load transfer in pile groups involves a complex

system interaction of piles, pile cap, and surrounding soil. The process is affected by

many factors such as soil properties, pile group geometry, pile — soil interaction and

interaction between different elements in the group. Due to the difficulty in quantifying

these factors, no method is capable of accounting their effects on the pile group

settlements,

Traditionally, the settlement of a pile group has been estimated by considering an

"equivalent raft". Equivalent raft is considered at two-third depth in the case of friction

piles or at the end of pile group if the piles are end bearing piles.

In most of the available empirical methods, the pile group settlement is related to

the settlement of a single pile, similar to one of those in the group.

Equivalent pier method has been developed as an alternative to the equivalent raft

approach considering the region of soil in which the piles are embedded as an equivalent

continuum, effectively replacing the pile group. The representation of a pile group by an

equivalent pier provides a useful, practical tool for estimating the settlement behavior of

pile groups. The load — settlement response of the equivalent pier can be calculated as for

a single pile. Naturally, the equivalent pier approach gives an estimation of only the

average settlement of the pile group.

The load — settlement behavior of pile group for a pile — soil system can be

obtained from a field load test on pile group, but it is very expensive, time consuming and

that data is useful only for that soil conditions. Because of this, field load tests on group

of piles are not generally carried out except in major projects. Alternatively, one among

the several empirical methods or analytical methods available in the literature are used

for the estimation of load — settlement relationship of the pile groups.

The design load on an axially loaded pile group depends on settlement criteria

rather than bearing capacity criteria. Therefore, estimation of a load — settlement curve

for a given pile — soil system is very important to design pile foundations.

1.1 Present work In the present work an attempt has been made to develop a method to estimate the

load — settlement of pile groups under vertical compressive loading that requires input of

simple geotechnical parameters which can be obtained in routine in-situ and laboratory

tests. The present method of analysis is developed combining equivalent pier method

originally proposed by Randolph (1994) and Hazarika and Ramasamy (2000) method for

single piles making some modifications. This method has been developed and tested with

the help of some case histories, by comparing the estimated settlements with the

measured settlements.

1.2 Organization of the Dissertation

Chapter 2 deals with the literature review on estimation of load — settlement

behavior of pile groups. Some of the methods available in the literature are briefly

discussed in this chapter. Chapter 3 discusses the proposed method of analysis for

estimation of settlement of pile groups. In, chapter 4, a few case histories are discussed

and the results obtained using the proposed method of analysis as well as the

conventional equivalent raft methods are compared. Finally, chapter 5 summarizes this

report along with the conclusions reached in this work.

2

CHAPTER 2 LITERATURE REVIEW

2.0 Introduction

Generally, field pile load tests are conducted to get the load — settlement response

of single piles under axial loads, and these results are extrapolated to estimate the

settlement of pile groups. However load tests are expensive, time consuming , difficult to conduct, and also the results pertain to only the particular pile — soil system as it exist at

the time of test. The settlement calculated from the pile load test is immediate settlement

only, but in case of cohesive soils the settlements are primarily from consolidation of

soils which takes place over a long period of time. So, pile load tests do not consider the

effect of consolidation in the case of cohesive soils. Because of this, generally any one of

the available analytical methods are used for the estimation of load — settlement curves

for the pile groups under axial loading.

This chapter briefly discusses some of the available methods on the estimation of

load — settlement behavior of piles and pile groups.

2.1 Single Piles

The analytical methods available for the evaluation of load — settlement response

of axially loaded piles may be classified into three broad categories.

➢ The Elastic Continuum Method

➢ Numerical Methods, and in particular , the Finite Element Analysis ➢ The Load Transfer Method

2.1.1 Elastic Continuum Method

This method has been used by various investigators (Poulos and Davis, 1968;

Poulos and Davis, 1969; Butterfield and Banerjee, 1971; Randolph and Wroth, 1978) for

studying the response of axially loaded piles. In most of these approaches, a pile is

divided into a number of elements, and a solution is obtained by imposing displacement

compatibility between the pile and adjacent soil for each element of the pile. The pile

displacements are obtained by considering the compressibility of pile under axial

loading. The soil displacements are obtained in most cases by using Mindlin's equations

for displacements within the soil mass caused by loading within soil mass.

This method assumes a linear stress — strain behavior for the pile — soil system,

and the soil mass to be an ideal, homogeneous elastic half space, having constant elastic

parameters E, and is that are not influenced by the presence of pile. Here Es and it are young's modulus and Poisson's ratio of the soil mass respectively.

Limitations

In reality, soils are often non—homogenous with erratic variation of stiffness with

depth. The applicability of this method in such cases is doubtful and may require gross

approximations of pile — soil system that might offset the accuracy of the method.

Further, evaluation of the elastic constants for use in the analysis, require sophisticated

laboratory testing which may not always be readily available or affordable.

2.1.2 Finite Element Analysis

This method has proved to be powerful in tackling complex geotechnical

problems that defy conventional and closed form solutions. It can take into account

factors such as soil layering and non linear stress behavior. The method can also simulate

the process of installation and subsequent loading of the pile.

Limitations

Although finite element analysis are valuable for better understanding of the pile

behavior, they are not very convenient for ready application to solving practical

problems because of the complexity of the analysis and considerable number of

geotechnical parameters required.

2.1.3 Load — Transfer Method

This method for the estimation of load — settlement behavior of axially loaded

piles was originally suggested by Coyle and Reese (1966), and utilizes the soil data

measured from the field tests on instrumented piles and laboratory tests on model piles.

The relevant soil data required in this method are curves relating the ratio of load transfer

and soil shear strength to pile movement. These load transfer curves are usually derived

4

from instrumented pile load tests (Coyle and Reese, 1966; Coyle and Sulaiman, 1967). It

is also possible to generate them theoretically, based on geotechnical properties of soil

deposit (Vijayvergiya, 1977; Kraft et al., 1981; Hazarika and Ramasamy, 2000;) solution

requires the pre — determination of load transfer curves for a particular pile — soil system,

after which an iterative procedure is followed to obtain pile response for a particular

load applied at the pile head.

Recently, this method has gained more popularity because of its adaptability to a

wide variety of pile — soil situations which are normally encountered in practice and also

it requires input of geotechnical parameters which can be reliably obtained from routine

in — situ and laboratory tests.

Limitations

In using the load transfer curves, it is inherently assumed that the movement of

the pile at any point is related only to shear stress at that point and is independent of the

stresses elsewhere on the pile. Thus, no proper account is taken of the continuity of the

soil mass. Because of the disregard to the continuity of the soil mass, this method is

limited to the settlement analysis of single pile.

2.2 Pile Groups 2.2.1 Equivalent Raft Method

For the purpose of estimation of pile group settlement, the pile group is regarded

as an equivalent raft foundation. The depth and dimensions of equivalent raft and amount

of spread of load are governed by the form of pile bearing and soil profile. The spread of

load and depth of equivalent raft for various conditions of pile bearing and soil

conditions are shown in Fig: 2.1(a) as per IS: 8009, part 11 and Fig: 2.1(b) as suggested

by Tomlinson (1977). The soil below Equivalent Raft Foundation (ERF) is considered

for calculation of settlement by taking 2 vertical to 1 horizontal (2V:1H) pressure

distribution.

5

A) Pile group settlement in cohesive soils

According to Skempton and Bjerrum (1957), the total settlement (S) of a pile

group in cohesive soil is the sum of initial elastic settlement and consolidation

settlement. Hence the total settlement is given by following equation

S = S; + S, + Ss (2.1)

Where, S = Total settlement of a pile group

Si = Initial settlement of pile group

S, = Primary consolidation settlement

S, = Secondary consolidation settlement

Case 1: For flexible pile groups

A) Estimation of Elastic Settlement (Si):

Initial elastic settlement takes place immediately after load application and it

varies linearly with the magnitude of load applied.

Initial elastic settlement can be estimated by using the method proposed by

Steinbrenner (1934). According to Steinbrenner (1934), initial settlement for flexible pile

group at the centre of loaded area is obtained by the following expression

M(Si) surface = ~p 2B Ip (2.2)

Si = µd (Si) surface (2.3)

Where, µ = Poisson's ratio of soil layer

(Si)s„rrace= Initial elastic settlement for foundation at ground level (i.e. at surface)

gd = Depth correction factor which can be obtained by using curves devised by

Fox (1948) as shown in Fig: 2.2

I, = Steinbrenner influence factor which can be obtained from Table: 2.1

E„ = Deformation modulus for undrained loading conditions and can be obtained

from stress — strain curve from triaxial or uniaxial compression tests in

laboratory or from plate load test conducted in trial pits. E„ can also be

obtained by empirical relation between E. and undrained shear strength (S„)

as shown in Table: 2.2

0

Table: 2.1 Steinbrenner's influence factor (I.S:8009 part I)

Shape of foundation Flexible foundation (Jr,)

Rigid foundations (Ii,) Centre Comer Average

Circle 1.00 0.64 0.85 0.86

Square 1.12 0.56 0.95 0.82

Rectangle

L/B = 1.5 1.36 0.68 1.20 1.06

L/B = 2 1.52 0.76 1.30 1.20

L/B = 5 2.10 1.05 1.83 1.70

L/B = 10 2.52 1.26 2.25 2.10

L/B = 100 3.38 1.69 2.96 3.40

Table: 2.2 Empirical relationship between undrained deformation modulus (E„) and

undrained shear strength (S„) of soils given by Skempton and Bjerrum (1957)

S.No Type of clay Empirical relationship

I. Under and Normally consolidated soils E„ = 500 S

2. Firm to Stiff clays (O.C.R. <2) E„ = 1000 S~

3. Very stiff clays (O.C.R. > 8) E = 1500 S

B) Estimation of primary consolidation settlement (Se):

According to Skempton and Bjerrum (1957) the primary consolidation settlement

(Se) can be estimated from results of laboratory oedometer tests made on soil sample by

using following expressions:

my = }

(2.4)

Saed = µd my OP AH (2.5)

(Sc)field = Jig Seed (2.6)

Where, el = void ratio corresponding to effective overburden pressure p,

7

e2 = void ratio corresponding to effective overburden pressure plus pressure

increment due to net foundation pressure ( i.e. corresponding to pressure

(pr - Ap)) m„ = Coefficient of volume change

Sced = odeometer settlement for each soil layer at the centre of loaded area

4p = Average effective vertical stress at the centre of loaded area on the soil layer

due to net foundation pressure (q„) at the base of equivalent raft. This can be

obtained by assuming spread of load at 2V: 1 H below base of equivalent raft

level.

AH = Thickness of each layer

(S,)reld = Field value of primary consolidation settlement

µg = Geological factor, which can be taken from the curve derived by skempton

and Bjerrum (1957) as given in Table: 2.3

Table: 2.3 Values of geological factor (µg) established by Skempton and Bjerrum (1957)

S.No Type of clay gg value

1.0-1.2

1. Very sensitive clays (soft alluvial, estuarine

and marine clays) 0.7— 1.0

2. Normally consolidated clays 0.50 — 0.70

3. Over consolidated clays 0.20 — 0.50

4. Heavily over consolidated clays

According to Skempton and Bjerrum (1957) the primary consolidation settlement

can also be obtained by following expressions if values of compression index and initial

void ratios are available.

Socd = ud I C'.AN Jiogio[ po +4Pl (2.7) ] e, Po +

(Sc)tield = µg Soed (2.8)

Where C. = Compression index and can be obtained from laboratory `e' versus `logiop'

curve. However C. can also be obtained from liquid limit (WL) and initial void ratio (ei)

by using following expressions proposed by Terzaghi and Peck (1967) and as per

I.S.8009, part I respectively.

C, = 0.009 (WL - 10%) (2.9)

Cc, = 0.30 (ei-0.27) (2.10)

C) Estimation of secondary consolidation settlement (S5):

Secondary consolidation settlement (Ss) may constitute major part in case of

highly compressible soils and inorganic soils. Secondary consolidation settlement can be

estimated by using expression derived by Raymond and Wahls (1976) after obtaining

requisite data from laboratory odeometer test conducted for a sufficient length of time.

The void ratio (e) versus logio (time) curve or consolidation settlement (or dial gauge

reading) versus logio (time) curve is obtained from laboratory odeometer test. Secondary

consolidation settlement (Ss) is given by

S C' H login t

S— I+ep (tp) (2.11)

Where, C, = Secondary compression index, which is the slope of `e' versus `login (time)'

curve after completion of primary consolidation and can be obtained by

following equation.

C̀ = (f to g, /t) _ Ae, (2.12) giol ) login( 1 l ~l

tp = Time required for the completion of primary consolidation

t, = Service life of proposed structure or any other desired period (measured after

application of structural load)

ep = Void ratio at the time of completion of primary consolidation

9

Aes =eS2 —eg,

Here both void ratios es i and e,2 are taken after completion of primary consolidation.

Case2: For rigid pile groups

Where the pile group is surmounted by a rigid pile cap or if the pile group

supports a rigid superstructure, the pile group can be regarded as being equivalent to a rigid block foundation having a uniform settlement. In this case the settlement is obtained

by following expression

(S)rigid = Rigidity factor x (S)Flexihle (2.13)

Where (S),ig;d = settlement of rigid pile group

(S)neY;bie= settlement of flexible pile group

Under identical conditions, generally the value of rigidity factor is taken as 0.80.

However the rigidity factor is not considered for secondary consolidation settlement.

B) Pile group settlement in cohesionless soils

(a) Schmertmann (1970) method

Settlement of the raft on cohesionless soils based on static cone resistance values

can also be estimated through the method proposed by Schmertmann (1970).

S= C i xC2 xApx

t-lere, lid = Ckd M

Z f= x AZ o Ed

(2.14)

Ap 0.5 5 c, <— 1.0 (2.15)

c2 =1+0.2xlog,o ` o. t

where, t = time in years

Ctid = Static cone resistance

B = Width of loaded area

(2.16)

10

ci = Depth correction factor

c2 = Creep factor (secondary time effect factor)

Ed = Deformation modulus

AZ = Thickness of soil layer

1, = Schmertmann's vertical strain influence factor (Fig: 2.3)

M = A coefficient suggested by Schmertmann (1970). The values of M are shown

in Table: 2.4 Table: 2.4 Value of coefficient 'M' for obtaining deformation modulus proposed by

Schmertmann (1970)

S.No Description of soil Value of M

1 For silts, sandy and slightly cohesive silty sand 2.0

2 For clean fine to medium sands, slightly silty clay 3.5

3 For coarse sands and sands with little gravel 5.0

4 For sandy gravels and gravels 6.0

Schmertmann (1970) has established a simplified curve as shown in Figure: 2.3

for obtaining vertical strain influence factor (IZ) based on elastic half space theory and

referred it as (28— 0.6) curve.

If standard penetration values are available then for settlement computations SPT

values can be converted into static cone resistance values by using simple relationship

proposed by Peck et al (1974). These relationships are indicated in Table: 2.5

'Cable: 2.5 Approximate relationship between static cone resistance (q3 and standard

penetration value (N) given by Peck et al. (1974)

S.No Soil type N (kg/cm2)

I. Silts , sandy silts , slightly cohesive silt sand mixtures 2.0

2. Clean fine to medium sands and slightly silty sands Coarse 3.0 to 4.0

3. sands and sands with little gravel 5.0 to 6.0

4. Sandy gravels and gravels 8.0 to 10.0

(b) De — Beer and Marten's Method

Total settlement of cohesionless soils can be obtained by method proposed by

De — Beer and Marten (1957). De — Beer and Marten used Buismen's formula for

computation of constant of compressibility. According to De — Beer and Marten (1957) the settlement is obtained by

following expressions.

5,. = [.g 1fl[ Po;t%-1' J] X RF XPd (2.17) u

Hence, C = 1.5 Pkd (2.18) 0

Where, C = constant of compressibility

Ckd= static cone resistance

RF = rigidity factor

Po = effective overburden pressure on a layer before applying the foundation

loads.

In case of soil profile with varying static cone resistance value, the average Ckd

values are assigned to different layers, and then computation is done for each layer. The

sum of settlement for all these layers will be the estimated value of settlement for pile

group.

The settlement predicted by De — Beer and Marten's are regarded as somewhat on

higher side. Meyerhof (1965) recommended that the allowable bearing pressures

computed from De — Beer and Marten's method should be increased by 50% for the same

computed settlement this proposal corresponds to assuming that

C = 1.9 Pkd (2.19) 0

C) Pile group settlement in layered soil formation

In layered soil formation the total settlement is obtained by summing up the

settlement of individual layers. The settlement of individual layers can be obtained as per

methods discussed in previously for cohesion and cohesionless soil separately.

12

D) Pile group settlement in/on rock

Pile group settlement may be important in this case of piles are heavily loaded. If

piles are well seated in rock mass then the total settlement is obtained by following

expression.

S = SJ-+ Si (2.20)

Here,

+ L AP (2.21) 2 n

Where Sf= Elastic compression of foundation structure

Si = Immediate or initial settlement at the centre of loaded area and can be

computed by 2.2 and 2.3

p = Average load on each pile

Pb = Average point resistance of each pile

LP = Length of pile

Ep = Modulus of elasticity of pile material

Limitations

Equivalent raft method, gives higher values of settlements of the pile groups than

actual field observed values. Load — settlement behavior of pile groups predicted by this

method are linear, where as actual behavior is non — linear.

2.2.2 Empirical Methods

Most of the empirical methods involve estimating the settlement of a single pile

and extrapolating this for calculation of the group settlement. Among the empirical

methods, those given by Skempton (1953) and Meyerhof (1959) are more popular among

all. These empirical methods are applicable to cohesionless soils only.

13

A) Skempton's method

On the basis of limited number of observations, Skempton (1953) obtained the

variation of settlement ratio Sg/ Si with Hg, where Sg and Si are respectively the settlement

of pile group of width Bg and that of an individual pile, for the same average load Q per

pile in the group. Regression analysis yields

I, _ (SA(222)

S B,

Where Bg = width of pile group in meters

According to I.S.8009 part 11, this formula is applicable to friction piles in cohesionless

soils only.

B) Meyerhof's method

Meyerhof (1959) expressed the settlement ratio for square pile groups driven in sand as

S, _ z (2.23)

S.

( Il+~~

l r 1}

Where, s =Ratio of pile spacing to pile diameter

r= Number of rows in the pile group

Limitations

These methods are not applicable to cohesive soils. Empirical methods are not

applicable to irregular pile groups.

2.2.3 Theoretical Methods

Analytical methods based on the elastic theory have been employed for settlement

analysis of pile groups with some success. These analyses are extensions of the methods

14

for single piles. Basic approach in most of these methods is to estimate the group

settlement ratio of the pile group — soil system defined as

Pile group settlement Group settlement ratio = Settlement of single pile under average

load per pile carried by the group

Other popular approach based on elastic theory is to estimate the influence factors

for all piles in the group and superimposing these factors to get the settlement of pile

group settlement. The interaction factor (a) between two piles i and j in the pile group is

defined as

Additional settlement caused by adjacent pile _ Settlement of pile under its own load

Some of the methods for estimating pile group settlement based on elastic

continuum approach are briefly described in the following section.

A) Interaction factor method

An analytical solution developed by using interaction factor approach, based on

theory of elasticity, for estimating settlement of group of piles. These methods differ in

the way the influence of settlement of a pile or the load on a pile, on the settlement of

adjacent piles is considered. This influence is expressed in terms of interaction factor

between two piles in the group.

In this approach the piles are assumed to be free standing. Thus a pile cap will

only influence the behavior of a group by controlling differential settlement between

different piles in the group.

Interaction factor (a) can be obtained either from the design charts (Poulos,

1968; Poulos and Mattes, 1971) with corrections to account for the effects of finite layer,

enlarged pile base, Poisson's ratio, non uniform soil modulus, effect of slip and effect of

finite compressibility of bearing stratum, effect of sizes of piles for different pile spacing

and stiffness factors, or from the analytical solutions (Randolph and Wroth, 1978; Lee,

1993).

15

The general methodology followed in methods based on interaction factor

approach is as follows.

1. Interaction factor (a) between piles i and j are calculated using either design charts or

analytical solutions.

2. For a group of piles, the interaction factors may be superposed to develop e a

relationship as given by Eq (2.24) for settlement of any pile I (w;), in the group.

w,i = w1 (2.24)

Where,

w, = settlement of single pile under unit head load

Pj = load at head on pile j

= interaction factor between pile I and pile j

(for i j, a = 1.0)

n = total number of piles in the group

3. For equilibrium,

Total load on the group, P = Pi (2.25)

Equations may be written for all piles in the group giving n displacement equations.

The (n+l) equations thus obtained from Eq.2.24 and Eq.2.25 may be solved for two

simple conditions

• Equal load on all piles, corresponding to a loading over a flexible pile cap

• Equal settlement of all piles, corresponding to a perfectly rigid cap on the piles

B) Method by Shen et al. (2000)

Shen et al. (2000) has suggested a practical method to evaluate the settlement of

pile groups, developed through the use of a load — transfer approach to obtain the

response of pile groups embedded in an elastic half space.

It has been observed from the results of a variational approach using elastic half

space model for rigid square pile groups ranging from single piles to 25x25 large pile

groups embedded either in homogeneous soil (p =1.0) or in soil with stiffness increasing

linearly with depth (p = 0.5), that the relationship between the inverse of group settlement

16

ratio (l /R,,) and number of piles (np) when plotted to logarithmic scale was found to be a

straight line for a particular slenderness ratio (1/ro). Here p is the inhomogeneity factor, I

is length of pile and ro is the radius of pile. The rigid pile group settlement ratio for a pile

group having any number of piles can be estimated from the slope of this straight line,

which is obtained from the formula developed for group settlement ratio of 2x2 rigid

square pile groups(RS,4) using load transfer curve method. The pile group settlement ratio

for 2x2 symmetric rigid pile groups can be expressed as

Rs,4 =

2zrpl + 4 ro { 1-v:

2npl 4 +

rocI (1-vs)C,

(2.26)

Where, = 1n 1 r"')

(2.27) l ru

ro = radius of pile

p = inhomogeneity factor = Gin/Gi

01,2. 01 are respectively soil shear modulus at pile mid — depth and at the base.

rm = maximum radius of influence given by

rm = 2.5 1 p (1-vs) + 0.7 s In (1/ro) (2.28)

1= length of pile

v5 = soil Poisson's ratio

? i = t; + 2 In (qn/s) + In (rn,/ 2s) (2.29)

C)= l+ (4rohrs) + (2ro/ 2~es) (2.30)

s = spacing of piles in the group

The group settlement ratio Rsr for a rigid pile group having `np' number of piles thus can

be obtained as

R,= (np)1Og4(",,4'

(2.31)

Limitations

This method is associated with large number of parameters, which are difficult to

find out. Analysis of settlement in these methods is included with difficult computation.

17

2.2.4 Load Tests on Pile Groups Load testing of a pile group is considered the most reliable and acceptable method

of obtaining load — settlement relationship of a pile group because it is the in — situ test.

These involve applying a series of loads on the pile cap and noting the corresponding

settlements. Loads are usually applied by some reaction mechanism, and settlements are

measured by dial gauges.

Limitations Load testing is very difficult to conduct, highly expensive and time consuming.

Further the load — settlement behavior obtained from a particular load test is applicable

only for the pile — soil conditions that exist at the time of test. Hence load testing is rarely

used (only in major projects) for estimating the load — settlement relationship of pile

groups.

2.2.5 Equivalent Pier Method

Equivalent pier (Fig: 2.4) method considers the region of soil in which the piles

are embedded as an equivalent continuum, replacing the pile group by an equivalent pier

(Poulos and Davis, 1980 and Randolph, 1994). The mechanism of load transfer in the

single piles or pile groups involves many interacting factors, such as soil properties,

single pile and pile group geometry, pile cap, surrounding soil, and pile — soil interaction.

Castelli and Michele, (2002) & Castelli and Motta, (2003) developed non — linear

analytical method to predict the behavior of a single pile and pile group under vertical

loads. The evaluation of the non — linear settlement is based on an incremental procedure

taking into account the decrease of the stiffness parameters with increase of the applied

load. The solution derived first for a single pile was extended to the case of pile group,

introducing an equivalent pier interacting with the surrounding soil by means of

hyperbolic load transfer functions. To take into account group action in the soil — pile

interaction, the stiffness of the equivalent pier has been modified. To estimate the

settlement of single pile or a pile group, a procedure derived from a model analyzing the

non — linear settlement behavior of a single pile subjected to axial load is applied. The

load — transfer approach has been simulated by load — transfer functions distributed along

18

the pile shaft and at the base. Load transfer functions for shaft and base are expressed as

below

w() (2.32)

K,, f.

w(z) 9 = 1 w(z) (2.33)

Kb, qn

Where, f = shaft mobilized stress

f, = shear strength at pile shaft

w(z) = corresponding displacement at a given depth `z'

KS;= initial shaft stiffness

q = base mobilized stress

qh = limit unit load at pile base

Kb; = initial base stiffness

As suggested by Randolph (1994) the diameter of the equivalent pier, Deq, for both friction and end — bearing piles, can be taken as

2 AR Dey

Jr

Where, Dcq = diameter of equivalent pier

Ag = plan area of the pile group as a block

The Young's modulus of equivalent pier, Eeq is calculated as

E,y = E, + (E — E, ) A'P Ag

Where, Eeq = Young's modulus of equivalent pier

E, = Average Young's modulus of soil Ep = Young's modulus of piles

A,p = Total cross sectional area of piles in group

Ag = plan area of the pile group as a block

(2.34)

(2.35)

19

For a square group of n piles with diameter D, at spacing s, and an embedded

length 1, the validity of the equivalent pier methods depends on a parameter defined by

Randolph and Clancy (1993), the overall aspect ratio R, given by

R= (in-1+D (2.36)

Randolph and Clancy (1993) showed that the equivalent pier approach was

suitable for R less than 4 and certainly for value less than 2.

Limitations

This method may not be applicable if the overall aspect ratio is greater than 4 and

the spacing of piles in a group is not uniform. Settlement of pile group depends on the

properties of subsoil strata on which it is bearing, but in this method the soil properties up

to pile tip only are considered.

20

CHAPTER 3 ESTIMATION OF SETTLEMENT OF PILE GROUPS -

PROPOSED METHOD

3.0 Introduction

A new method is proposed here based on Hazarika and Ramasamy (2000) method

and equivalent pier method. Some modifications have been made to these two methods

and adopted here, In this method, pile group is converted into an equivalent pier and then

the analysis of pile group is carried out adopting Hazarika and Ramasamy (2000)

method. However, developments of q — z curve and f— z relationships are different from

the Hazarika and Ramasamy (2000) method.

3.1 Details of the Method

The method assumes that a group of piles may be represented by an equivalent

pier as shown in Fig: 2.4. This pier is analyzed in the same way as a single pile is

analyses.

3.1.1. Development of Q—z curve

Q — z curve, which defines the relationship between the load, Q and the

displacement, z at the tip of the pile group is developed based on the properties of soils

below the tip of the piles. As the soil up to a significant depth below the tip of piles may

consists of layers of cohesive and cohesionless soils, settlement in each of these layers is

computed adopting procedures as below and shown in Fig: 3.1

a) Piles resting on sand

Q — z curve is developed by using De - Beer and Marten's (1957) method,

Settlement of each layer is calculated by using Eq: 2.17 and Eq: 2.19 corresponding to

the assumed load at pier tip.

b) Piles resting on clay

e — logp curve obtained from oedometer test is used for cohesive soils to develop

of Q — z curve. Eq: 2.7 is used for calculation of consolidation settlement.

21

3.1.2 Development of f — z curve

The f — z curve is assumed to be same as that of single pile given in Hazarika and

Ramasamy method (2000). The normalized f-z curve given by Vijayvergiya (1977) is

shown in Fig: 3.2. The unit shaft resistance `f' mobilized at any shaft movement `z' is

expressed as a function of `fmax', the maximum shaft resistance by the following non-

linear relationship:

.1= .. 2 2. Z. (3.1)

Where z, = critical movement of the pile segment at which fm. is mobilized, and z:Szs For sands the load transfer function is assumed to remain constant for shaft

movements larger than z,. For clays reduction in f to fmax to a residual value of f, may be

allowed at larger values of z say z,, after which it remains more or less constant.

In the case of the equivalent pier, the shear resistance, along the pier surface is

between the soil enclosed within the pier and soil outside the pier. Further, the shear

displacement along the periphery of the pier may not be uniform. It is likely to be

maximum at the location of the pile and reduces away from the pile. These deviations

from a single pile situation are taken into account as described below.

Estimation of fm„,: (a) For cohesionless soils:

fma,, = K, 6• tanb

(3.2)

Where, K, = Lateral earth pressure coefficient,

cU = Angle of wall friction. i.e. shearing resistance is between soil and

soil.

= Vertical effective pressure at the pile location under consideration

The value of Ks has to be chosen. The value of Ks suggested in the case of single

pile is given in Table: 3.1 to 3.2.

22

Table: 3.1 Values of KS

Installation method KS/Ko

Driven piles, Large displacement 1.00-2.00

Driven piles, Small displacement 0..75-1.25

Bored and cast insitu 0.70-1.00

Jetted piles 0.50-0.70

Table: 3.2 values of Ka

Type of soil Ko

Loose 0.50

Medium dense 0.45

Dense 0.35

(b) For cohesive soils:

fmax = Cu (3.3)

Where, Cu = undrained shear strength of soil

In the case of single pile, the shear displacement between the soil and the pile is

equal to the pile movement. In a pile group, the shear displacement on the surface

enveloping the pile group is not the same as of the pile movement (Fig: 3.4). The shear

displacement reduces away from the pile (Cooke and Price, 1973; Juan etal, 2002; White

and Bolton, 2004). However, not much literature is available to quantify the variation of

shear displacement away from the pile.

The effect of the above is that in the shear resistance along the equivalent pier

surface will not be the same at any given depth below ground level. To account for this a

reduction factor 'Rf' as below may be applied when computing the shear resistance on the

lateral surface of the equivalent pier.

Rr = Average vertical strain of soil around equivalent pier

Vertical strain of soil at pile surface

23

3.2 Procedure

The following procedure is adopted in the analysis of pile group.

1. Pile group is converted into an equivalent pier by using the relation given below

2 AR D y = (3.4)

Where Deq = diameter of equivalent pier

Ag = plan area of the pile group as a block

2. Young's modulus of equivalent pier Eeq is calculated as

A E E,+(E—E..)Ap (3.5)

Where Eeq = Young's modulus of equivalent pier

E5 = Weighted average Young's modulus of soil

Ep = Young's modulus of piles

Alp = Total cross sectional area of piles in group

Ag = plan area of the pile group as a block

3. Assuming the tip of equivalent pier as a raft, settlement at the tip for a range of tip

loads is calculated using De — Beer and Marten's (1957) method for cohesionless

soil layer and e -- logp method for cohesive soil layer. Thus, Q — z curve is

developed.

4. Assume a pile tip movement 'yt' and calculate the tip load 'Qtip' from the Q — z

curve developed in step 3.

5. The Pier is divided into number of convenient segments (Fig: 3.3)

6. Mid point movement (ye) of the bottom segment is estimated. For the first trail,

the mid point movement is assumed to be equal to the tip movement (yt)

7. Using the estimated mid point movement, the shaft resistance is obtained for the

assumed displacement from the f — z curve constructed for the pier — soil system.

Shaft load (S„) transferred by the segment is given by

S„ = f x A g (3.6)

Where A,, = corrected surface area of pier in that segment

Asg AS x Rf (3.7)

N shaft resistance of pier

24

RI = area reduction factor

8. Assuming a linear variation of load distribution in a segment,

(3.8)

9. Now the elastic deformation in the bottom half of the segment is calculated as

C — sy .4E x

(3.9) ey

Here A, Leg are cross sectional area and elastic modulus of pier material respectively

L, = length of the segment considered.

10. New mid point movement is computed for the bottom segment, as:

Yn = 8Y + Yr (3.10)

11. Using the computed new mid point movement, the shaft load of the segment is

calculated using step 7.

12. Shaft load now calculated and previously calculated are compared. If the

difference is not within the specified limit, steps 7 to 12 are to be repeated, until

convergence reached.

13. The steps 6 to 12 are to be repeated for the next segment above the bottom

segment and worked upwards to compute the load (Q) and the settlement (y) at

the pier head.

14. The procedure is to be repeated for different tip movement values and a set of

load - settlement values are to be obtained. The same are to be plotted to give the

load - settlement curve.

A computer program is developed for the above computational procedure. The

program is made in C++.

25

CHAPTER 4 RESULTS AND DISCUSSION

4.0 General The proposed method of analysis has been computerized. This program requires

the user to input various parameters of a pile - soil system under consideration which

include details of subsoil strata such as number of soil layers, depth of water table,

thickness and properties of soil in each layer etc., details of pile group such as number of

piles, length and diameter of piles, spacing of piles, method of pile installation and type

of pile material.

4.1 Example problem The program written for the settlement analysis of pile groups using the proposed

method of analysis has been tested for a few example problems, assuming necessary

field data, and the results obtained from this program have been checked with manually

computed results.

A typical pile group solved is shown in Fig: 4.1. A group of piles in layered soils

is considered. In this program, load — settlement curve of pile group is obtained in three

steps. In the first step, the pile group is converted into an equivalent pier. The second

step involves development of Q — z curve by assuming equivalent raft at the tip of the

piles as explained in chapter 3. Q — z curve developed for this example problem is shown

in Fig: 4.2 Final step is to analyze the equivalent pier to obtain the load and settlement at

the top of the pier (i.e. at the pile cap) using the procedure outlined in Section 3.2. The

estimated load — settlement behavior of the pile group is shown in Fig: 4.3

The problem was solved using manual computation also. The load — settlement

values manually computed and obtained using program are given in Table: 4.1. The

agreement between the values suggests that the computational procedure has been

correctly programmed.

P

Table: 4.1 comparison of manually computed and program computed results

Load on pile group (kN) Settlement (mm)

Manual computations

Obtained using the program

Manual computations

Obtained using the program

4322 4325 1.23 1.24

5536 5537 1.97 1.98

7402 7400 3.88 3.87

7725 7722 4.43 4.40

8295 8291 5.54 5.50

8698 8695 6.66 6.65

9253 9250 9.22 9.20

9372 9369 9.84 9.80

9591 9586 10.92 10.87

9698 9694 11.46 11.40

27

3.5 m

dia =0.5

X

O 0 e 3d

O 0 ± 6

Pile Group

3.5 m

Input data

ZS = 6.5 mm

Pile

Loose sand, iy = 17 kN/m3 2m

K5 =0.7,6=22°,cp=30°

Medium stiff clay, a = 0.7 3m y=18kN/m3,eo=0.75

C„ = 70 kN/m2, C. =0.25

L= 15m Medium stiff clay, a = 0.7 -y= 18kN/m3,eo=0.7S

7m C~=70kN/m2,C,=0.25

t Dense sand, y = 19 kN/ m3 3m K5 0.6, S 24°, cp =36°, Nq 40

/ \Dense sand, y = 19 kN/m3 1

s=0.6,8=24°,cp=36°,Nq =40 2 1

Ckd = 16,000 kN/m2

Fig: 4.1 Example problem

0

Q-z curve

Load, kN 0 500 1000 1500 2000

2 E E 4

E 6

CD ~ 8

U) 10

12

14

Fig: 4.2 Q — z curve for given pile - soil system

2500

0

2

E E

6

U)

10

12

• pile group

Load, kN

2000

4000 6000 8000 10000 12000

Fig: 4.3 Load — settlement curve of given pile soil system

29

4.2 Case studies

To assess the validity of the proposed method, some case studies taken from

literature are analyzed. The predicted and observed settlements are compared.

Case A: piles in medium dense sand (Briaud et al. 1989)

This case history concerns the load test reported by Briaud et al. (1989). A pile

group consisting of five piles was loaded to failure in a medium dense sand. A control

single pile was also loaded to failure as a reference. The piles were closed —end steel

piles driven to a depth of 9.15 m below the ground surface. Arrangement of piles in the

group and soil profile are shown in Fig: 4.4 and 4.5

Given data:

Length of pile below ground Ievel, L = 9.15 m

Outside diameter of pile = 273 mm

Wall thickness = 9.3 mm

Area of pile group, Ag = 2.0535 m2

Total cross sectional area of piles in group, Al = 0.293 m2

Youngs Modulus of soil, E, = 21840 kN/ m2 (Es = 3.5 x Ckd)

Youngs Modulus of pile, Ep = 2.1 x 108 kN/ m2

The above case study is analyzed for different values of reduction factor (Rf) and results

are shown in Fig: 4.6. It is observed that for Rf = 0.7, the load — settlement results agrees

with the observed results.

The load — settlement for the above case is also obtained using equivalent raft at

2/3 L from the top. This estimated load — settlement curve is also shown in Fig: 4.6. It is

found that the equivalent raft method considerably over estimates the settlement.

Case B: piles in overconsolidated clay (O'Neill et al. 1982)

A load test on a group of piles is reported by O'Neill et al. (1982).A pile group

consisting of 9 closed ended steel pipe piles in stiff overconsolidated clays as shown in

Fig: 4.7 was load tested. Load tests were also conducted on single piles for reference.

The pile — soil situation is as shown in Fig: 4.8

Input data:

Length of pile below ground level, L = 13.1 m

Outside diameter of pile = 273 mm

Wall thickness = 9.3 mm

Area of pile group, Ag =3.65 m2

Total cross sectional area of piles in group, A,p = 0.527 m2

Youngs Modulus of soil, E, = 157445 kN/ m2

Youngs Modulus of pile Ep = 2.1 x 106 kN/ m2

The above case study is analyzed for different values of reduction factor (Rf) and the

results are shown in Fig: 4.9.It is observed that for Rf = 0.6, the results are agree well

with the observed results.

The load — settlement for the above case is also obtained using equivalent raft at

213 L from the top. This estimated load — settlement curve is also shown in Fig: 4.9. It is

found that the equivalent raft method considerably over estimates the settlement.

31

Fig: 4.4 Arrangement of piles in group (Case A) Briaud et al. 1989

1. Area of pile group = 1.43 x 1.43 m2 2. Dia of pile = 0.273 m 3. Driven piles

525 m nI Sandy gravel (fill) 7=21 kN/m3

1.5 m Gap

Clean sand, y = 19.25 kN/m3 .9m K I,pp = 35.24°

Clean sand, y = 19.25 kN/m3 K= 1,cp=35.24°

6.75 m

Clean sand, y = 19.25 kN/m3 3.05 m tp = 35.24°, Cka = 8604 kN/m'

Sand with stiff silty clay, 2.1 m y = 20 kN/m3, Ckd = 9240 kN/m2

Serpentine bedrock (fractured)

Fig: 4.5 soil profile and properties for case A

32

0

5

10

15

E20 3 25 E 30 a, 35

40

45

50

Case A

Load, kN

1000 2000

+measured jl —•— Equivalent raft

II

~—•—Rf=1

t

Fig: 4.6 comparison of predicted (for Zs =0.008 m) and observed behavior of pile group.

33

Fig: 43 General test condition (O'Neill et al. 1982)

Pile Cap V

vt i Very stiffclay, 2.6m

2.3m y 20kN/ml,

I Cu _ 150 kN/ m''

L= 13.Im Stiff to very stiff clay,

5.3 m y = 19 kN/nY, C,, = 100 kN/m=

J Silty medium stiff clay, 3 m y= 19kN/m',Cu=85kN/m2

Stiff to very stiff clay, y = 19 kN/m',

Cu = 100 kN/m1

1.2 m Stiff to very stiff clay (CL), y - 19 kN/m', eo = 0.70

C. = 100 kN/m2, C, = 0.03

Stiff to very stiff clay with few dense sand layers 61.7m y = 19kN/m', ea r 0.75,C,=0.03

Fig: 4.8 Soil profile of Case B

3.9 m

34

Case B

Load, RN

2000 4000 6000 8000 10000

Equivalent Raft

u— measured iI E 40 0.4

—Rf=0.6 j

50 —Rf=1

60~

70

Fig: 4.9 comparison of predicted (for Zs =0.015 m) and observed behavior of pile group.

10

20

E 30 «:

35

4.3 Parametric study Behavior of pile group with varying width is studied for size of group varying

from 2 x 2 to 9 x 9 piles. Pile groups in cohesive and cohesionless soils are considered.

Spacing of piles in the group is kept constant as 3 times the diameter of pile. Plots of

variation of group ratio with width of pile group are made. Group ratio is defined as

settlement of pile group for a given load per pile to the settlement of single pile for the

same load on the single pile. Pile group settlement is calculated by the present proposed

method and single pile settlement is calculated by Hazarika and Ramasamy (2000)

method,

4.3.1 Pile group in cohesive soil

To study the effect of width on pile group, a typical soil system shown in Fig:

4.10 is taken and load - settlement behavior of pile groups of size varying from 2 x 2 to

9 x 9 piles is estimated using the proposed method of analysis. In this case spacing of

piles is taken as 3D and kept same for all pile groups. The load on each pile in a group is

taken as 500 kN. Soil strata and details of piles are shown in Fig: 4.10. Variation of

group ratio with B is shown in Fig: 4.11 and values are given in Table: 4.2

Table: 4.2 values of Group ratio (Sg/Si) with varying B in cohesive soil

Pile Spacing = 3D, D = Diameter of Single Pile (0.5 m)

Pile group

Surface area per lm

length of Equivalent

Pier (m2)

Total Load

on the pile

group (kN)

Sg (mm) Si (mm) Sg /S;

2 x 2 7.1 2000 0.99 0.81 1.22

3 x 3 12.41 4500 1.33 0.81 1.64

4 x 4 17.72 8000 1.84 0.81 2.27

5 x 5 23.03 12500 2.72 0.81 3.36

6x 6 28.37 18000 4.95 0.81 6.11

7 x 7 33.68 24500 27.84 0.81 34.37

8 x 8 38.99 32000 66.56 0.81 82.17

9 x 9 44.30 40500 102.74 0.81 126.84

36

Area of pile group = 3.5 x 3.5 mZ C/C spacing = 3D

Pile Crap D = din of single pile = 0.5 rn

Soft clay,

4m y= l 7 kN-/m3, I CU = 45 kN/m2

L= 15m

T Soft clay, 2M y = 17 kN/m3, C„ = 45 kN/m2

Medium to stff clay,

8m -(= 18 kN/m3, eo = 0.7 C„ = 80 kN/m2, C 0.25

Stiff clay, y = 19 kN/m3 'n C, = 200 kN/m2

12 2

Stiff clay, y = 19 kN/m7 eo = 0.6 C = 200 kN/hn2, Cc =0.20

0 m

Fig: 4.10 pile group in cohesive soil

37

140 1

120

100

°_ 80

2 60 a

40

20

0 0 2 4 6 8 10 12

Width, m

14

Group ratio Vs Width

Fig: 4.11 Variation of group ratio with width (B) in cohesive soil

38

4.3.2 Pile group in cohesionless soils

As explained in 4.3.1, the same procedure is adopted in the case of a pile group in

cohesionless soils also. Soil profile and pile characteristics are given in Fig: 4.12. The

variation of group ratio with width is shown in Fig; 4.13 and values are given in Table:

4.3.

Table: 4.3 values of Group ratio (Sg/Si) with varying B in cohesionless soil

Pile Spacing = 3D, D = Diameter of Single Pile (0.5 m)

Pile group

Surface area per lm

length of Equivalent 2

Pier (m)

Total Load on

the pile group

(kN)

SB (mm) Si (mm)

2 x 2 7.I 2000 1.14 1.15 0.99

3 x 3 12.41 4500 1.43 1.15 1.24

4 x 4 17.72 8000 1.75 1.15 1.52

5 x 5 23.03 12500 2.10 1.15 1.83

6 x 6 28.37 18000 3.37 1.15 2.93

7 x 7 33.68 24500 4.58 1.15 3.98

8 x 8 38.99 32000 8.91 1.15 7.75

9 x 9 44.30 40500 17.86 1.15 15.53

It is seen from Fig: 4.11 and 4.13, the group ratio increases with increasing

number of piles in the group. It may be noted that the surface area of the equivalent pier

increases by five to six times and total load increases by 20 times, when the group size is

increased from 2 x 2 to 9 x 9.(Table: 4.2). This implies, in a large group, maximum load

is transferred to the base of the pile group. Further, with increasing width of the

foundation in the case of large groups, the compressible strata also increases. These

factors result in substantial increase in settlement at the base with increasing the size of

the group. This is the reason for increase in group ratio with the increase in pile group

size.

39

Q Area of pile group = 3.5 x 3.5 m2 C/C spacing = 3D

Pile Cap D = dia of single pile = 0.5 m

Loose sand, y = 18 kN/m3

6m 1 Ks =0.7,w=30

Loose sand, y = 18 kN/m3

L = 20m 7.5m K5 =0.7,cp=30

dense sand, y = 18 kN/m3

4.5 m K,=0.6,cp=35°

Dense sand, y = 19 kN/m3 2 K,= 0.5, cp =38°

rDense sand, y = 19 kN/m3 10m

12 Ckd = 12000 kN/m2

Dense sand, y = 19 kiN/m3

10

Cad = 14000 kN/m2

Fig: 4.12 pile group in cohesionless soil

40

18

16

14

12 0

10

Q 8 c7

6

4

2

0 0 2 4 6 8 10

Width, in

12 14

Group ratio Vs Width

Fig: 4.13 variation of group ratio with width (B) in cohesionless soil

CHAPTER 5 SUMMARY AND CONCLUSIONS

Based on the work reported in this dissertation, the following conclusions are drawn.

1. The available methods of settlement computation for pile groups are either empirical

nature or too involved requiring many pile — soil parameters which cannot be easily

obtained.

2. A rational and simple method to estimate load — settlement behavior of pile groups is

developed based on equivalent pier approach suggested by Randolph (1994) and load

— transfer approach suggested by Hazarika and Ramasamy (2000) for single pile.

3. The method developed takes into account layered soil system and requires input of

soil properties which can be readily estimated from usually conducted field and

laboratory tests

4. The method developed has been computerized using C++ language.

5. A few numerical problems and few case histories have been analyzed using the

program. The results of these investigations show that:

i) The proposed method is capable of providing reliable estimate of load

— settlement behavior of pile groups. ii) The equivalent raft method widely adopted in practice may

significantly over estimate the settlement.

42

REFERENCES

1. Briaud, J. L., Tucker, L. M. and Ng, E (1989): "Axially Loaded 5 Pile Group and

Single Pile in Sand", Proceedings of the 12 h̀ International Conference on Soil

Mechanics and Foundation Engineering, Rio de Janeiro, Vol.2, pp. 1121 — 1124.

2. Butterfield, R. and Benerjee, P. K. (1971a): "The Elastic Analysis of

Compressible Piles and Pile Groups", Geotechnique, Vol. 21, No.1, pp. 43 — 60.

3. Butterfield, R. and Benerjee, P. K. (1971b): "The Problem of Pile Group and Pile

Cap Interaction", Geotechnique, Vol.21, No.2, pp. 135— 142.

4. Castelli, F, and Michele, M. (2002): "Simplified Nonlinear Analysis for

Settlement Prediction of Pile Groups", Journal of geotechnical and

Geoenvironmental Engineering, ASCE, Vol.128, No.1, pp 76— 84.

5. Castelli, F. and Motta, E. (2003): "Settlement Prevision of Piles under Vertical

Load", Proceedings of the Institution of Civil Engineers, Geotechnical

Engineering, Vol.156, No. GE4, pp, 183— 191.

6. Cooke, R. W. and Price, G. (1973): "Strains and Displacements around Friction

Piles", Proceedings of the 8th International Conference on Soil Mechanics and

Foundation Engineering, Moscow, Vol. 2, Part I, pp. 53 —60. 7. Coyle, H. M. and Reese, L. C. (1966): "Load Transfer for Axially Loaded Piles

in Clay", Journal of Soil Mechanics and Foundation Engineering Division, ASCE,

Vol.92, No.SM2, pp. 1 — 6.

8. Coyle, H. M. and Sulaiman, I. H. (1967): "Skin Friction for Steel Piles in Sand",

Journal of Soil Mechanics and Foundation Engineering Division, ASCE, Vol.93, No.SM6, pp. 261-278.

9. De Beer, E. and Martens, A. (1957): "Method of Computation of an Upper Limit

for the Influence of the Heterogeneity of Sand Layers on the Settlements of

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43

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375-397.

To

D yi

a) Group of piles supported by skin friction only

04

Sc

IN b) Pile group supported by both skin fr;rt;nn and end bearing

P

0

c) Pile group supported by end bearing only

Fig: 2. l (a) Load — transfer to soil from pile group (I.S:8009 part II)

47

t

h

V1IIiiIII OK2fl7l7C7tC7 t7

riiiiia a) Group of piles supported by skin friction only

1 M

0A

SI

IN b) Pile group supported by both skin f;rr;n„ and end bearing

U

11

Q

c) Pile group supported by end bearing only

Fig: 2.1 (b) Load — transfer to soil from pile group (Tomlinson, 1977)

DEPTH FACTOR

0.5 0.6 0.7 0.8 0-9 1.0

I.

• .

____rae

a ____VA______ ■ ■ ■f 111/ ■ ■ ■ ■■ ■■■ // //■■■■■ ME //i ■■■■■■ =~/I /I■■■■■■

Fig: 2.2 Depth correction factor (Fox, 1948).

Vertical strain factor Iz 0 0.6

RZ

[-

2B • 0.6 curve Fig: 2.3 Vertical strain factor

Cap

If- Deq iiI

Pile Group Equivalent Pier

Fig: 2.4 conversion of pile group into equivalent pier

r,A,.L $.5J.LZ2_7 50 2 05 1

I1

Ile Cap

If— Deq -- ►I '. Equivalent Pier

Cohesionless soil

Pile Group

Cohesive soil j 2 2 L

1 1

Cohesionless soil

Fig: 3.1 procedure development of Q — z curve

51

t•0- f; 1

CURVE FOR Z ZS 0.5 b -C _ PROBABLE f- r CURVE FUR SAND (Z7Zs)

b_d_e tPROSABIE f = CURVE FOR CLAY(Z>Zs)

Z=Zr 0•S t•0

2/h Fig: 3.2 f— z curve (Vijayvergiya, 1977)

52

Q = Applied load Pier

Pier

segments y~ Q1 LE, L2. ....L = Segment lengths Y1, Y2......Y,= Segment movements Qi, Q2.....Qn = Axial forces on

L21 1 S2 --1

Yi segments

WIY S1 , S2.......S. = Skin resistance of

2 segments

4 Yi = Tip movement

_I,Y3

LnI Sn Yn

Pier tip___._____?J '

Fig: 3.3 Dividing of an equivalent pier into convenient number of segments

53

Column

Cap I I Pile Cap

1 1

• ~*f

1 1 Dcq

O 0 0

0 O 0

x Pile Group

Equivalent Pier

Shear displacement z

Section x — x

Fig: 3.4 development of shear resistance and variation of vertical

movement of soil in a pile group

54