lateral group

7/26/2019 Lateral Group

1/71

UNIV RSITY OF H W I LJBR RY

SIMPLIFIED PROCEDURE FOR ANALYSIS

OF LATERALLY LOADED SINGLE PILES AND PILE GROUPS

A THESIS SUBMITTED TO THE GRADUATE DIVISON O TH

UNIVERSITY OF HAWAI / IN PARTIAL FULFILLMENT

O T HE REQUIREMENT S F OR T HE DEGR EE OF

MASTER OF SCIENCE

IN CIVIL ENGINEERING

MAY 2003

y

Brian K.F. Chang

Thesis Committee:

Phillip Ooi Chairperson

Horst Brandes

Peter Nicholson


2/71

ACKNOVVLEDGEMENTS

First I would like to express

y

appreciation to my advisor

r

Phillip Ooi

for his supervision and help

in

all aspects

o

this project I also would like to

acknowledge Geolabs Inc for providing the computer software GROUP which

was used in this study

I would also like to acknowledge Drs Horst Brandes and Peter Nicholson

for reviewing this thesis

Finally I would like to thank my wife Patricia and son Timothy for giving

me their support encouragement and patience throughout my study


3/71

ABSTRACT

Current methods for designing pile groups for lateral loading require a

computer program or extensive manual computations. This research presents a

spreadsheet- or calculator-amenable approach for estimating lateral deflections

and maximum moments

in

single piles and pile groups. The approach for single

piles is

n

extension the characteristic load method, used for predicting

deflections and moments when the pile top

is

at the ground surface. The

proposed method applies to embedded fixed-head piles, which represents most

practical situations. The resulting lateral deflections and moments are less due

to the increased embedment. A simplified procedure to estimate group

deflections n moments was also developed. Termed the Group Amplification

Method GAM , group amplification factors are introduced to amplify the single

pile deflection and bending moment to reflect group effects. This approach

provides good agreement with other generally accepted analytical tools and with

values measured

in

load tests

on

groups fixed-head piles.


4/71

TABLE OF CONTENTS

Acknowledgement. iii

Abstract. iv

~ ~ ~ ~

L

f F

S 0 Igures VIII

Chapter 1: Introduction 1

Chapter 2: Literature Review 2

2 1

Analysis

of

Single Piles Under Lateral Load 2

2.1.1. Evans and Duncan s Procedure 2

2.1.2. Characteristic Load Method CLM) 7

2.1.3. Brettmann and Duncan s Equations 7

2.1.4. LPILE Plus 3.0 for Windows 8

2.1.5. Modified Characteristic Load Method 9

2.2 Analysis

of

Pile Groups Under Lateral Load

11

2.2.1. The Concept of p-multipliers

11

2.2.2. Brown and Bollman s Method 16

2.2.3. Mokwa and Duncan s Group Equivalent Pile Procedure 18

2.2.4. GROUP 4.0 for Windows and FBPier 19

2.3 Limitations

of

the Procedures Described

Chapter 3: Development of Simplified Procedure

for

Analysis of Laterally Loaded

Single Piles and Pile Groups

21


5/71

3 Parametric Study for Single Piles in oh siv Soils 2

3 1 1 Modified Characteristic Load for Single Piles in Cohesive Soils

4

3 1 2 Modified Characteristic Moment for Single Piles in Cohesive

Soils 28

3 1 3 Steps for the Modified Characteristic Load Method 30

3 2 Parametric Study for Pile Groups

in

Cohesive and Cohesionless Soils

32

3 2 1 Group Amplification Method 32

3 2 2 Steps for Simplified Analysis of Laterally Loaded Pile Groups 44

Chapter

4:

Comparison of Predicted with Measured Values from Load Tests

46

4 Case Study 1 Pile Group

in

Cohesive Soils 46

4 2 Case Study 2 Pile Group in Cohesive Soils 50

4 3 Case Study 3 Pile Group

in Cohesionless Soils 53

Chapter 5: Summary and Conclusions 56

References 58


6/71

LIST OF TABLES

able age

Parameters for Equations

2

and 2.2 after Evans and Duncan, 1982 6

2 Constants for equations by Brettmann and Duncan 1996 8

3 Summary of p-multipliers from full scale load tests and centrifuge tests on pile

groups 13

4 Summary of pile types and properties used in this study 22

5 p-y parameters for piles in cohesive soils 23

6

p-multipliers for various pile spacings, pile locations, and soil types 36

7 Configuration, spacing, and sum of p-multipliers for pile groups analyzed 38

8

p-y parameters for piles in cohesionless soils

4

9 Parameters for group amplification factors

4


7/71

Figure

LIST OF FIGURES

Page

1 Dimensionless load-deflection curves for fixed head piles in sand with zero

embedment. 3

2

Dimensionless load-moment curves for fixed head piles in sand with zero

embedment. 3

3 Dimensionless load-deflection curves for fixed head piles in clay with zero

embedment. 4

4 Dimensionless load-moment curves for fixed head piles in clay with zero

embedment. 4

5

p-mUltiplier concept Brown et aI., 1988) 12

6 p-multiplier as a function of pile spacing for leading and first trailing row after

Mokwa and Duncan, 2001) 14

7

p-multiplier as a function of pile spacing for the second and third trailing rows

after Mokwa and Duncan, 2001) 15

8 Brown and Bollman s 1993) method after Hannigan et aI., 1997) 17

9

Dimensionless load-deflection LPILE Plus data points for piles in cohesive

soils with zero embedment 25

10. Dimensionless load-deflection LPILE Plus data points for piles embedded 2

4, 6 and

ft in

cohesive soils 25

11. Modified dimensionless load-deflection LPILE Plus data points for piles

embedded 2

4

6 and

10

ft in cohesive soils 27

12. Dimensionless load-moment LPILE Plus data points for piles in cohesive soils

with zero embedment 27

13. Dimensionless load-moment LPILE Plus data points for piles embedded

2 4

6 and ft in cohesive soils 29

14. Modified dimensionless load-moment LPILE Plus data points for piles

embedded

2

4 6 and

10

ft in cohesive soils 29


8/71

15. Comparison of load versus deflection using GEP and GROUP for a R5C5S3

group of 48-inch-diameter drilJed shafts with zero embedment in soft clay with

Su=0.5ksf 34

16.Comparison

of

load versus deflection using GEP and GROUP for R3C2S3

group

of

48-inch-diameter drilled shafts embedded 4 feet

in

loose sand with

III

=30 34

17.Comparison of load versus maximum moment using GEP and GROUP for a

R5C5S3 group of 48-inch-diameter drilled shafts with zero embedment

in

soft

clay with Su=0.5ksf.. 35

18. Comparison

of

load versus maximum moment using GEP and GROUP for a

R3C2S3 group of 48-inch-diameter drilled shafts embedded 4 feet in loose

sand with

III

=30 35

19. Pile Configuration

in

a R3C2S4 pile group 39

20. Comparison of group deflections using GAM versus GEP for piles

in

cohesive

21. Comparison

of

group moment using GAM versus GEP for piles

in

cohesive

~

22. Comparison

of

group deflections using GAM versus GEP for piles in

cohesionless soils

23. Comparison

of

group moment using GAM versus GEP for piles

in

cohesionless soils

24. Pile test layout for case study 1 a plan view, b and cross-section Rollins

and Sparks, 2002 8

25. Comparison of measured versus predicted deflections using GAM for case

study 1

8

26. Comparison of predicted versus measured bending moments for the Salt

Lake City load test 50

27. Pile test layout for case study 2 Kim and Brungraber, 1976

28. Comparison

of

measured versus predicted deflections using GAM for case

study 2

29. Comparison

of

predicted versus measured bending moment for Bucknell

University load test 53

ix


9/71

30. Pile test layout for case study 3 Huang t aI 2001 55

31. Comparison

o

measured versus predicted deflections using GAM

or

case

study 3 55

x


10/71

CHAPTER 1

INTRODUCTION

Most structures are subject to latera/loads

as

a result wind earthquake

impact waves and lateral earth pressure. If these structures are supported on

deep foundations the foundations have to be designed for lateral loads.

Laterally loaded single piles

and

pile groups should be designed to be safe

against geotechnical failure structural failure and excessive deflections. In

general geotechnical failure seldom governs the design for laterally loaded piles

that are long with respect to its diameter or width. Therefore this study will focus

on

the analyses laterally loaded piles for deflections and structural failure.

This report describes the research

on

developing a simplified method to

analyze fixed head single piles and pile groups subjected to lateral loads. In

Chapter

2

a literature review current state of the art methods for lateral load

analyses of single piles and pile groups is presented. A description of the

simplified procedures developed

in

this study to analyze a single and a group of

fixed head piles is presented

in

Chapter

3

In Chapter 4 three full scale lateral

load tests on groups of fixed head piles are evaluated where the predicted

responses are compared with measured results.


11/71

CHAPTER 2

LITERATURE REVIEW

Articles providing the current state-of-the-art for analyzing laterally loaded

piles and pile groups are summarized based

on

a literature review. Throughout

this section, the term pile includes both driven piles and drilled shafts.

2 1 Analysis Single Piles Under Lateral Load

2 1 1

Evans and Duncan s Procedure

Evans and Duncan (1982) developed a simplified procedure to predict

non-linear behavior

laterally loaded single piles under static loading conditions.

In this approach, dimensionless load-deflection and load-moment curves were

developed for piles

in

cohesive and cohesionless soils. Separate plots were

available for free-

and

fixed-head piles. However, only fixed head piles are

considered since more often than not, piles are used

in

groups that are

connected via a cap. These dimensionless plots are shown

in

Figures 1 through

4

where P is the applied lateral load, M is the maximum moment induced in the

pile due to the lateral load, y is the groundline lateral deflection of the pile and D

is the pile width or diameter. Values of load, moment, and deflection are made

dimensionless by normalizing with a characteristic load, Pc a characteristic


12/71

Evans and Duncan s range 1982)

Brettmann and Duncan s equation 1996)

0.035

.005 1 0.015 0.02 0.025 0.03

y

Figure

Dimensionless load-deflection curves

for fixed head piles in sand with zero embedment

j

I

~

;f/

i I

0.01

o

o

0.014

0.012

0.004

0.002

0.008

a-

c: 0.006

I

i

Evans and Duncan s range

1 9 82 - -]

- - - -Brettmann and Duncan s

e q u a t i o n J 1 ~ 9 6

1

0.014

0.012

1

0.008

a-

-

-

0.006

0.004

0.002

0

0

0 002

0.004 0.006 0.008

0.01

MIMe

Figure 2 Dimensionless load-moment curves

for fixed head piles in sand with zero embedment

3


13/71

Evans and Duncan s range (1982)

Brettmann and Duncan s equation (1996)

i

~

/

,

I

.

e

i

0.06

0.05

0.04

J

a

0.03

002

1

o

0.00

1 0.02

0.03 0.04 0.05

0.06

0.07

Figure 3 Dimensionless l o ~ ~ ~ f l t l o n curves

for fixed head piles

in

clay with zero embedment

Evans and Duncan s range (1982)

- - - .Brettmann and Duncan s equation (1996)

0.06

0.05

0.04

0

a

0.03

0 02

1

0

0

0.005

1

0.015 0.02

0.025

MIMe

Figure 4 Dimensionless load-moment curves

for fixed head piles in clay with zero embedment

4


14/71

moment, e and the pile width or diameter, 0, respectively.

Pc

and

Me

are

expressed as follows:

2.1

)

2.2) .

where

o=

pile width or diameter L)

E

=

Young s modulus of the pile

FL

2

R

1

=

moment of inertia ratio dimensionless)

I

R

J

I,

I = moment of inertia of the pile L

=

moment of inertia of a solid circular cross section of diameter 0 L

nO

-

, 64

2.3)

2.4)

The remaining parameters for the equations are summarized in Table 1.

The behavior of the pile under lateral load is governed by the soil within the top

eight pile diameters. The moist and buoyant unit weights

of

the soil should be

used above and below the water table, respectively. The Evans and Duncan

1982) procedure only applies to piles where the top is

at the ground surface.

5


15/71

Table

1

Parameters for Equations 2 1 and 2.2 (after Evans and Duncan, 1982)

Parameters Sands

Clay

Pc

Mc

Pc

Mc

F=

dimensionless

1

1 1 for plastic

1 or plastic

parameter related to clay

clay

stress-strain behavior o

the soil

1.54 for

1.343 for

brittle clay

brittle clay

m= passive pressure 0.57

0.40 0.683

0.46

exponent

n=

strain exponent

-0.22

-0.15 -0.22

-0.15

up=

representative

up

= CP4>yD

t a n 2 4 5 + ~ / 2

Up = C

pc

Su

passive pressure o soil

(FL-

= dimensionless

Cpc

= dimensionless

modifying factor to

modifying factor to

account for three-

account for three-

dimensional effect o the

dimensional effect

o th

passive wedge

in

front o

passive wedge in front o

the pile = 0

the pile and found to be

4.2 for cohesive soils in

=internal friction angle

their study

o

the soil (degrees)

y= unit weight

o

soil

E5 = strain at which 50

E5 =

0.002 for sands

E5 ranges from 0.004 to

o

the strength

o

the soil

0.020 for plastic clays

is mobilized

6


16/71

2.1.2 Characteristic load Method ClM

The characterist ic load method (Duncan et aI., 1994) is a modif icat ion

of

the Evans and Duncan procedure, where the equations for and

Me

are

simplified as shown

in

Equations (2.5) through (2.8):

For sand

For sand

For clay

For clay

P = 1.57D2fER {Y Dlj) tan

(45 +

lj /2 JO.

7

c

I

ER

I

M =1.33D3(ER {Y Dlj) tan

(45 lj /2 jO.40

c

I

ER

I

P = 7.34D

(ER { ~ j O 6 8

c

I

ER

I

M = 3.860

3

(ER { ~ j 4 6

c

I

ER

I

(2.5)

(2.6)

(2.7)

(2.8)

The parameters have been defined in Section 2.1.1.

2.1.3 Brettmann and Duncan s Equations

Brettmann and Duncan (1996) developed exponential equations for the

dimensionless nonlinear relationships between load-displacement and load-

moment as shown

in

Figures 1 through 4. The equations are as follows:

7


17/71

y/D =

a PIPdb

MIMe

c PIP d

where

a,

b, c and d are summarized in Table 2.

2.9

2.10

Table

2.

Constants for Equations by Brettmann and Duncan 1996

Constant

Fixed-Head Piles in Sand

Fixed-Head Piles in Clay

a 28.8 14.0

b

1.5 1.846

c

2.64 0.78

d 1.3 1.249

2.1.4 LP L Plus 3.0 for Windows

LP L

Plus 3.0 for Windows Reese and Wang, 1997 is commercial

software that can be used to analyze the behavior of a single pile under lateral

load. The program uses a finite difference technique

to

estimate deflection,

shear, bending moment, and soil reaction varying with depth. Soil behavior is

modeled using a series of discrete non-linear springs. The stiffnesses these

springs are characterized using p-y curves, which can be user-defined or

internally generated by the computer program following published

recommendations for various types soils. These p-y curves were developed

based

on

results

full-scale lateral load tests on piles

in

a variety of soils and


18/71

loading conditions. A wide variation pile-head boundary conditions may be

selected in the program. The properties of the pile can also vary as a function

depth. The program also has the capability of considering the non-linear

behavior of concrete piles as a result of cracking.

2.1.5 Modified Characteristic Load Method

Wang 2000) extended the Evans and Duncan 1982) procedure to

estimate deflection and maximum bending moment fixed head piles embedded

below ground surface. Wang s work applies to piles embedded in cohesionless

soils only. Termed the Modified Characteristic Load Method MCLM),

modification factors C

y

and C

m

that account for the effect

pile embedment are

introduced as shown in Equations 2.11) through 2.14).

e

=

eC

m

[

1] 85

0

1 05

Z

.

= 1

y

10D

y

[

1] 3

00 65

Z .

=

1

m 2 y

9

2 11

)

2.12)

2.13)

2.14)


19/71

Wang also proposed modifying Brettmann and Duncan s equations as

follows:

2.15)

2.16)

where P

e

= modified characteristic load

e

=

modified characteristic moment

Z

=

embedment depth

l

y

= total unit weight of soil

Fl-

3

)

y =

effective unit weight soil Fl-

3

)

= buoyant unit weight for submerged soil

=

moist unit weight i f the ground water table is not within the top 8

pile diameters.

As part o f this study. Wang s procedure has been expanded to include

laterally loaded single piles in cohesive soils.

10


20/71

2.2 Analysis Pile Groups Under Lateral Load

Pile groups

can

be divided into two categories:

1.

widely spaced piles which interact only through the pile cap

connection. In these piles, the group response

can

be estimated by

summing the individual pile responses.

2. closely spaced piles are defined as those in which the response an

individual pile is influenced through the adjacent soil by the response

of other nearby piles. This shadowing effect is commonly termed

pile-soii-pile interaction.

This study deals primarily with closely spaced piles, which involves the

majority

pile groups

in

practice.

2.2.1 The Concept of p-multipliers

For a group closely-spaced piles, pile-soil-pile interaction can be taken

into account by introducing reduction factors

to

the soil reaction

p

portion of the

p-y curves for single piles

as

shown

in

Figure 5 Brown et

aI.,

1988). These p

multipliers are typically less than or equal to one. They have been

experimentally derived either from full-scale load tests or from tests

in

a

11


21/71

centrifuge. Reducing the p-value

on

the p-y curve results in a reduction

the

ultimate soil resistance leading to a softening the group response. According

to Brown et

al.

(1988), p-multipliers are approximately constant with depth. The

magnitude of the p-multipliers varies with pile row position, pile spacing and soil

type. Piles in the leading row have the highest p-multipliers. Brown et

al.

(2001)

also indicated construction method (bored versus driven piles) has an influence

on

p-multipliers, the case in point being the Chaiyi Taiwan load test. A summary

p-multipliers obtained from the literature is provided

in

Table 3. Mokwa et al

(2001) plotted p-multipliers as a function of pile spacing

and

row locations

in

four

graphs (Figures 6

and 7 .

p

I r p

u

p p

o

Figure

5.

p-multiplier concept (Brown et

ai.

1988)

y


22/71

Table

3.

Summary of p-multipliers from full scale

load tests and centrifuge tests on

pile

groups

location

Te

Size

PHe

Type Center- Pile

Soil h

DefleCtjon

ulti lier Reference

Type

of

to

Fixity

Type

strength 1st Row 2nd Row 3rd Row

4 th Row 5 th Row

6thRow

7th Row

Pile

Center at Top Parameter

r ups

Spacing (Inches)

Brittany,

Steel H-Pile (d=11.2 ,bf=10.6',) with Meimon et aI.,

Full-scale

3X 2

Side Plates

welded

to Fonna Box

3D

Free-head

Clay

Su -420 pSf 0.0

0.0

0.5

.

1986

France

Section

10.75 SteelPipe Pilewith Wall

1.2 0.7 0.0 0.5

Brown et al.,

Houston,TX

Full-scale 3X3

Thickness= 0.365 & GroutFill

3D Free-head Clay

Su 1500 psf

1967

2.0

0.7

0.5 0.0

Salt lake City, 12 Steel Pipe Pile with

Rollins et aI.,

Full-scale 3X3

3D Free-head Clay

Su 1000 psf 1.0to2.4

0.0

0.0

0.0

1990

U

ConcreteFill

Salt lake City, 12 Steel Pipe

PUe

with

Sparks&

Full-scale

3X 3

3D Fixed-head Clay Similar to Free-Head According to Rollins et al., 1998

Rollins, 1997

U

ConcreteFill

10.75

OD

SteelPipePilewithWall

38

Brown et al.,

Houston, TX

Full-scale x

Thickness= 0.365 &Grout Fill

3D Free-head Sand 1.0to 1.5

0.0

0.0 0.3

1988

Dr> 90

Brown et al.,

2x 3

1.5-m Drilled Shaft

3D

Fixed-head

1.2

0.5

0.0 0.3

2

Chaiyi, Taiwan Full-scale

Sand 0=35

3XO

O.8-m Prestressed Concrete

3D Fixed-head

0.0

0.0

0.7 0.5

0.0

Pile

)

30 X30 Square Prestressed

Ruesta&

Stuart,

FL

Full-scale OXO

ConcretePiles

3D Free-head and

0=32

1.0to3.0

0.8

0.7 0.3

0.3

.

Townsend,

1997

Centrifuge

3X 3

16.9 Pipe P'.e (42.7 fllong)

3D

Free-head and

Dr

=-33

0.65

0.45

0.35

McVayet

at,

1995& Pinto

Centrifuge 3X3 16.9 PipePile (42.7

fllong)

5D Free-head and Dr

=

33

1 0.85 0.7

etal.,1997

Centrifuge 3X3 16.9 Pipe Pile (42.7

fllong)

3D Free-head

and

Dr= 55

0.8 0.0 0.3

Centrifuge 3X3 16.9 Pipe Pile (42.7

ft

long)

5D Free-head and Dr= 55

1

0.85 0.7

Centrifuge 3X3

16.9 Pipe Pile (45 ft long) 3D Free-head

and

Dr=36&55

0.8

0.0

0.3

McVayetal.,

1998

Centrifuge 3XO 16.9 Pipe Pile (45

fl

long) 3D Free-head

and

Dr=36&55

0.8

0.0

0.3 0.3

enlrifllge 3X5 16 9 DO Pipe ile (45

ft

long}

3D Free-head Sand

Dr=36 55

0.8

0.0

0.3 0.2

0.3

.

Centrifuge 3X6 16.9 Pipe Pile(45 fllong)

3D

Free-head

Sand Dr= 36 &55

0.8

0.0

0.3 0.2

0.2

0.3

Centrifuge 3X7 16.9

OD

PipePile (45f1long)

3D Free-head Sand

Dr=36&55

0.8

0.0

0.3 0.2

0.2

0.2

0.3

aThe first number refers to the number of plies ineach r w The second number refers to the number

of

rows of piles inthe group.


23/71

pile spacing, S (diameter)

1 4 5 6 7 8

1 I 1 T M l l 1 T 1 r r r n - n t r ~ m ; o l l l 1 T 1 n 1

Legend fOT PlOts

a

and b

Cox et at

(1984)

centrifuge,soft clay

BroWn

and

Reese (1985)

fun

scale,

stiff

clay

..

Melmonetal.(t986)

full scale, silty clay

Morrison

and Reese (19SB)

-full

scale,

mad

dense sand

Lieng (1989)

19

model, loose sand

o

arowhand Shie (1991)

- finite element analyses

McVay etal.

l995

centrifuge. loose sand

o

McVay

etal.

11 195)

o o n t r i u g ~ med. dense sand

Ruesta and Townsend (1997)

- full scale,loosilfine sand

0 McVayet al. 1998

ool1lrif4ge. med.

dense and

v Rollins

etal.

(1998)

full scale.

clayey silt

- desigl1lines

(a) Leading row.

c cpile spacing, S(diameter)

1 4 5 6 7 8

1.0 .

0.8

J 6

0.8

0.6

v

l >

0.4

>

~

0.2

l >

0.0

(b) Firstfraiflng

row.

0 0

LLU.LWu.u.

................u.u.I..I..I.L.L.U.Iu.u.LL1

S = pile spacingintha direction oflstera//oadlng

Figure 6. p-multiplier as a function

of

pile spacing for leading and first trailing row

(after Mokwa and Duncan. 2001)

14


24/71

cJc

pile sp oing,S (diameter)

3 4 5 6 7 8

1

.0

1TT t rm-,..,.,.,..,,..,.,.,..,.,.,.,., TTT CI T I TMTl 1,

a

Seeomf trailing row.

Legend for plots a .and b

Cox eta (1984)

-centrifuge.

soft

clay

Brown and Reese> 1985

fuU

scale, stiff

clay

Morrison and

Reese 1986

- fUll

scale, med. densesahd

McVay

at

a l

1995

-centrifuge,

[oosesand

o McVayet at. (1995)

-centrifuge. m

dense

sand

Ruesta

andTClWnsend 1997

- full

scale,. loose fine

sand

A McVayet

al. 1998

- centrifuge,

med. dense sand

v

RoUlnsl'lt al.

(1998)

fullscale, clayey silt

- design

lines

o

(b) 3rd and

greater

trailing rows,

etc pile spacing, S(diameter}

1 34

5 6 7 8

1.0 ITTTTTMT1T1TlT1I 1TT 1 rllITl ITTl TTI1

0.8

0.2

0.8

E

l i

0.6

-

S-

0.4

0.2

J

0.6

Ii

i

0.4

,

Figure

7.

p-multiplier as a function

of

pile spacing for the second and third

trailing rows (after Mokwa and Duncan,

2001)

15


25/71

2.2.2 Brown and Bollman s Method

Brown and Bollman 1993) developed a procedure to analyze the behavior

pile groups under lateral load by performing separate p-y analysis for each row

using appropriate values of p-multipliers for each row. The series of p-y analyses

is set up as follows for symmetric pile groups:

1 Determine the p-multiplier for each row according to row position, pile

spacing, and soil type.

2 Perform p-y analyses for one pile in each row using the appropriate p

multiplier for that row

3

Plot the lateral load versus deflection for the pile analyzed in each row see

Figure

8

The lateral load per pile-deflection curve of the pile group can be

estimated by summing the lateral loads for the pile in each row at the same

lateral deflection and diViding this sum by the number of

rows

4. The maximum bending moment

in

the most heavily loaded pile

in

the group

corresponds to the bending moment in the piles

in

the leading

row


26/71

600

Front

Row

Load

Per Pile

Lateral

Load

er Pile, kN

400

3rd

- 4th

Rows

200

Estimated

Pile

Group Deflection

a}

a

25

5 75

5

Pile Head

Deflection mm

Estimated Pile

_

.... Group Deflection

Front Row

2nd

Row

3rd

- 4th

Rows

Maximum

Bending Moment

Per Pile, kN-m

b}

100

a

25 5

75

Pile Head Deflection

mm

Figure

8.

Brown and Bollman s 1993) method after Hannigan et aI., 1997)

7


27/71

2.2.3 Mokwa

and

Duncan Group Equivalent Pile Procedure

Mokwa

and

Duncan 2000 proposed analyzing a group as a single pile in

LPILE. The group equivalent pile is assigned the same structural properties as

the individual pile but the moment

of

inertia is set equal to the sum of the moment

of inertia of all the piles. The p-y curve is modified by using the sum of the p-

multipliers for

all

the piles

in

the group. Then LPILE Plus is used to predict the

lateral group deflection. The bending moment

of

each pile is determined using

equation 2.17

where

M;

=

bending moment

in

pile i

M

gep

=

bending moment computed for the group equivalent pile

N= number of piles

in

the group

Pm; =

p-multiplier for pile i

=

moment

of

inertia

of

pile i

2.17

Pmc

= a multiplier for corner piles = 1 0 1.2 and 1.6 for spacings 3D, =

and::: 10, respectively. Franke, 1988


28/71

2.2.4 GROUP 4.0 for Windows and FBPier

Two state-of-the-art computer programs with the capability for analyzing

pile groups are reviewed in this section. GROUP for Windows Reese and

Wang, 1996 is a commercial program for analyzing groups

vertical or battered

piles. Moment, lateral loads or a combination

the two may be applied to the

group. Possible options

connectivity to the pile cap include fixed, pinned, or

elastically restrained. The program solves by iteration for the nonlinear response

each pile under combined loading, and checks for compatibility

geometry

and equilibrium

forces between the applied external loads and the reactions

each pile head. The load-deflection and load-moment relationships for each pile

in its individual coordinate system are computed by solving nonlinear differential

equations using p-y and t-z curves under lateral and axial loading, respectively.

For closely-spaced piles, the pile-soil-pile interaction can be taken into account

by introducing reduction factors for the p-y curves used for each single pile. The

program can compute the deflection, bending moment, shear,

and

soil resistance

as a function of depth for each pile.

FBPier Bridge Software Institute, 2003 is a more sophisticated non-

linear, finite element analysis, soil-structure interaction program developed at the

University of Florida. The program can be used to perform a complete

substructure design considering both the geotechnical and structural aspects.

The program can be used to analyze single piles, pile groups, pile bents,


29/71

retaining walls, and high mast lighting structures. Analysis capabilities include

combined axial, lateral, and rotation resistance of the piles, pile cap and pier.

The structural model includes both linear and non-linear concrete cracking, steel

yielding capabilities, as well s biaxial interaction diagrams for all sections. It

also allows the use of different pile types within a group.

2.3 Limitation the Procedures Described

The Evans and Duncan procedure and the l cannot be used to predict

the lateral behavior

single piles embedded below the ground surface. The

l can account for pile head embedment but to date, it has only been

developed for single piles in cohesionless soils. n this study, the l is

developed for single piles in cohesive soils. A new simple technique is also

developed

to

analyze the behavior pile groups based on the concept p

multipliers

nd

using the GEP method. This procedure

is

simple enough that it

c n be readily performed in a spreadsheet or using a calculator.


30/71

CHAPTER 3

DEVELOPMENT OF SIMPLIFIED PROCEDURE FOR ANALYSIS OF

LATERALLY LOADED SINGLE PILES AND PILE GROUPS

3

Parametric Study for Single Piles in Cohesive Soils

LPILE Plus 3.0 for Windows was used to perform a parametric study on

the response of laterally loaded fixed head piles in saturated cohesive soils with

different embedment depths. The study included three hundred analyses

generating about 1 700 load cases. The main parameters considered include

pile type pile size undrained shear strength and embedment depth. A range

of

lateral loads was applied to the top of the piles to obtain load deflection and load

moment curves.

Analyses were conducted

on

both driven piles and drilled shafts. Driven

piles analyzed included steel pipe piles steel H piles and precast prestressed

concrete piles. Detail properties of the piles used in the parametric study are

shown in Table

4

Pile diameters or widths analyzed were between 9.7 inches

and 48 inches. The flexural

stiffness

of the piles ranged from 3.31 x 10

to 9 8 X 10

8

kip in

2

. When the pile extreme fiber stresses exceeded the

allowable values the pile failed structurally. These load cases are not included

in the parametric study.


31/71

Table 4 Summary of pile types and properties used in this study

Pile Type Pile Description Pile Width or Area E I

b

Diameter

(inches)

in )

(ksi) (in

Steel H-pile

HP10x42 9.7 12.40 29000 210

Steel H-pile

HP12x74 12.13 21.80

29000 569

Steel H-pile HP14x102 14.01 30.00 29000 1050

Steel Pipe Pile 10o/.-inch-diameter 10.75 8.25 29000 114

Y..-inch-thick wall

Steel Pipe Pile 12o/.-inch-diameter 12.75 14.60 29000 279

318-inch-thick wall

Steel Pipe Pile

14-inch-diameter 14 16.10 29000 373

3/8-inch-thick wall

Precast Prestressed

14-inch-square 14 196.00

4300

3201

Concrete Pile f, =5000psi

Precast Prestressed

14-inch-square 16 256.00

4300

5461

Concrete Pile f, =5000psi

Drilled Shaft

18-inch-diameter 18 254.47

3600

5153

f, =4000psi

Drilled Shaft 24-inch-diameter 24 452.39 3600 16286

f, =4000psi

Drilled Shaft

36-inch-diameter

36

1017.88

3600

82448

f, =4000psi

Drilled Shaft 48-inch-diameter 48 1809.56

3600

260576

f, =4000psi

a E = Young s modulus of pile

b

I

=

moment of inertia of pile

e fe = 28-day compressive strength of concrete


32/71

Four values of undrained shear strength 0.5,

1

2

and

4 ksf) were assumed.

Matlock s 1970) soft clay model was used for cohesive soils with undrained

shear strengths of 0.5 and 1 ksf while Reese

and

Welch s 1975) stiff cohesive

soil model was used for undrained shear strengths of 1 2 and 4 ksf. p-y

parameters for the soils are summarized in Table 5 Both models were used to

analyze cohesive soils with an undrained shear strength of 1 ksf to observe any

differences between

t

two models. A comparison

of

the two models showed

no

major differences when analyzing cohesive soils with an undrained shear

strength of 1 ksf

Table 5 p-y parameters for piles

in

cohesive soils

Soil model

Undrained shear strength

Soil modulus

5

ksf)

pci)

Soft clay 0.5 0 0.02

Soft clay 1

500

0 01

Stiff clay 1

500

0.007

Stiff clay 2 1000

0.005

Stiff clay

2000

0.004

The pile top was embedded at several depths below ground surface.

Embedment depths considered include

0

4 6 and 10 feet.


33/71

3.1.1 Modified Characteristic load for Single Piles in Cohesive Soils

Initially, lPl l analyses were performed for piles with zero embedment to

confirm that the analyses yielded results that are consistent with Brettmann and

Duncan s 1994) equation. The results plotted in Figure 9 show good agreement.

The analyses were then extended to include piles with non-zero embedment and

the results are presented in Figure

10.

Evans and Duncan s characteristic load

for the case of zero-embedment was used to normalize the lateral load. The

figure shows wide scatter, and the Evans and Duncan procedure tends to

overestimate deflection. Thus, as embedment depth increases, the deflection

decreases under the same lateral load indicating that the increase in lateral earth

pressure significantly influences the lateral behavior of piles.

To make the

lM

applicable to the cases with non-zero embedment

depth, the equation for the characteristic load must be modified so that the

calculated load-deflection points all fall on the Evans

and

Duncan trendline. An

embedment correction factor C

y

was developed for the characteristic load Pc to

obtain a better match between the lPl l results and the Evans and Duncan

procedure. The correction factor is applied to the characteristic load as follows:


34/71

LPILE Plus data points Bretlmann and Duncan s equation I

0.16

.14

.12

.10

.06

.04.02

0.08

y

Figure 9 Dimensionless load-deflection LPILE Plus data points for

piles in cohesive soils with zero embedment

0.10 r r ......... .

0.00

_

0.08 -- ,.D

...

o

~ . ~ ~

; i J ~ - - = - - - ; - - 1 - - - - f - - - - - - - - - - - 1

0 05

: + 1 4 ~ - C , d ~ t ~ Q i _ , _ -

. F - - - - - - - - - - - - - - - - - - - j

0.04

__

: l w ~

0.03 ~ ~ ~ _. _ - - - - - - - - - - - - - - 1 - - - - - - - - 1

0.02 t i

0 01 r --- t - -- t - --+--+ ---+--- t --- t - --- I

0.00

J j t j t j I J

0.00

- LPILE Plus data points - Bretlmann and Duncan s equation

I

0.16

.14

.12.10.04 0.06 0.08

y

Figure 10. Dimensionless load-deflection LPILE Plus data points for

piles embedded 2 4 6 and 10 It in cohesive soils

0.12

0.10

0.08

l-

0.06

l-

0.04

0.02

0.00

0.00 0.02


35/71

~ 0 5 J

yD

C

=

1

y

0

where

Pc

=modified characteristic load F)

o = pile diameter or width L)

Z = embedment depth of pile top below ground surface L)

y

=

effective unit weight of soil over top

FL 3)

= buoyant unit weight for submerged soil

=

moist unit weight for soils above the ground water table

u

= undrained shear strength FL 2)

3.1

3.2)

C

y

equals one when the embedment depth

s

zero, is greater than 1.0 for

positive embedment and is not applicable for piles extended above ground.

When the modified characteristic load is used t o normalize the lateral load, t he

revised dimensionless load-defection points all fall within a narrow range close to

the Brettmann and Duncan curve as shown

n

Figure 11.

6


36/71

o LPILE Plus data points - B r e t t m ~ m n : ; ; ~ d Duncan s e q ~ ~ n ]

0.16.14

.12

_ _

0.10.06

.04

.02 0.08

ylD

Figure 11. Modified dimensionless load-


37/71

3.1.2 Modified Characteristic Moment for Single Piles in Cohesive Soils

Using the LPILE results, dimensionless load-moment curves for zero

embedment are plotted in Figure 12. The lateral load is normalized by the

characteristic load, P

e

, while the maximum bending moment

is

normalized by the

characteristic moment, Me. The LPILE data points all fall within a narrow range

illustrating the reliability the Evans and Duncan procedure. Again, the

dimensionless load-moment points for non-zero embedment show poor

agreement as seen

in

Figure

13

where a large scatter can

be

observed.

A correction factor, C

m

, was developed to modify the characteristic

moment,

Me

for non-zero embedment depth as follows:

where

Me

is the modified characteristic moment.

Z

J ~ 0 2

=

1

60D

3.4

3.3


38/71

LPILE Plus data points - Breltmann_llnd Duncan s equation I

0.005

0 01

0.015 0.02 0.025 0.03 0.035 0.04

M Me

Figure 13 Dimensionless load-moment LPILE Plus data points for

piles embedded 2 4 6 and 10 fl in cohesive soils

{

0.12

0.10

0.08

0

0

0.06

0.04

0.02

0.00

0

c;

LPILE Plus data points - Breltmann and Duncan s q u ~ t i ~ r i

0.09

~ r c _

__-_--_----

0.08 1 I L I l : ~ ~ _ _ _ i

0.07 ---- --- i- + - - - - - 1 - - _ l _ - - : o - ~ ; t , , ' ; l - _ l _ - - - - - - 1

0.06

-l---- ------ -- _--f-- A - , j 4 ' ' ' ~ ' ' - - - f - - - + - - - - - - 1

1 1

0.005 0 01 0.015 0.02 0.025 0.03 0.035 0.04

rL 0.05

0 04 -1 - - - - -1 - -_ _

0.03

0.02

0 01

0.00 ~ _ _ _ _ _ _ I _ I _ _ J

o

M Me

Figure 14 Modified dimensionless load-moment LPILE Plus data

points for piles embedded 2 4 6 and 10 fl in cohesive soils

29


39/71

When the modified characteristic load,

Pc

and modified characteristic

moment,

Me ,

are used to normalize the load-moment points for the case non

zero embedment, the scatter diminishes as shown in Figure 14.

3.1.3 Steps for the Modified Characteristic

Load

Method

Steps for analyzing the behavior of laterally loaded piles in cohesive soils

using the MCLM are:

1 Calculate the modified characteristic

load

using Equations 2.1), 3.1), and

3.2).

2 For a given lateral load, P, calculate the dimensionless lateral load PIPe .

3 Use Brettmann and Duncan s Equation 2.9) to estimate the dimensionless

deflection YID corresponding to the dimensionless load from Step 2.

4) Calculate the deflection by multiplying the estimated dimensionless deflection

from Step 3 with the pile width or diameter.

5 Calculate the modified characteristic moment using Equations 2.2), 3.3),

and 3.4).

6 Use Brettmann and Duncan s Equation 2.10) to estimate the dimensionless

moment MIMe corresponding to the value of PIPe from Step 2.

7 Multiply the dimensionless moment from Step 6 with the modified

characteristic moment from the Step 5 to determine the maximum bending


40/71

moment M. Since the pile head is fixed, the maximum bending moment

occurs at the top of the pile.

This method has the following limitations.

1 The MCLM applies only to vertical piles.

2

This study was performed assuming long piles only which are very common

in

practice. This method is not applicable to short piles with low LID ratios.

3 Cases where the pile failed structurally are not included

in

the parametric

study.

4 This method cannot automatically account for nonlinear behavior

reinforced concrete piles after cracking. However, the engineer may

manually reduce the flexural rigidity of the pile to account for this non-linear

behavior.

5 The maximum embedment depth involved

in

this study was 10 feet.

6 Only static lateral loads were considered in this study.

7 The method assumes uniform soil properties within the top 8 pile diameters.

For layered systems, the average properties within the top eight pile

diameters should be used.


41/71

3.2 Parametric Study for Pile Groups

in

Cohesive

and

Cohesionless Soils

3 2 Group Amplification Method

Groups

closely-spaced piles deflect more and are subject to higher

moments compared to single piles for the same load per pile. This is due to pile

soil-pile interaction. The objective

this part of the study was to develop group

amplification factors to amplify the single pile lateral deflection and maximum

moment to values appropriate for the pile group. Termed as the Group

Amplification Method GAM , the pertinent equations are as follows:

where

yg = lateral deflection pile group L

= lateral deflection single pile L

A

y

=deflection amplification factor dimensionless

M

g

=

maximum moment

a pile in pile group F.L

M

s

= maximum moment a single pile F.L

AM = moment amplification factor dimensionless

3.5

3.6


42/71

Amplification factors were developed by running numerous LPILE

analyses to obtain single pile deflections and moments, nd by estimating group

deflections and moments using the group equivalent pile GEP procedure

Mokwa and Duncan, 2000 . The group amplification factors are then obtained

from the ratio of group response to single pile response. The parametric study

was performed for groups of fixed-head piles

in

cohesive and cohesionless soils

with different soil parameters, embedment depths, pile arrangements and lateral

load values. The analyses for cohesive and cohesionless soils were studied

separately. When the pile extreme fiber stresses exceeded the allowable values,

the pile failed structurally. These load cases are not included in the parametric

study.

Before using the GEP procedure, the accuracy the method was first

verified by comparing the results the GEP analyses with those using GROUP.

More cases were analyzed showing good agreement overall but only two cases

are illustrated in Figures 15

nd

16 for load versus deflection, and in Figures 17

nd 18 for lo d versus maximum pile moment. They included a 5 x 5 pile group

in

a soft cohesive soil and a 3 x 2 pile group

in

a loose cohesionless soil. n

general, the two procedures provide close agreement.


43/71

_

GROUP 4.0 data points

e

Group-Equivaient Pile data points

I

1

I

/1

I

- - ,-

6,000

5,000

4,000

\i

:g

3,000

al

2,000

1,000

o

o

1 2 3

4

5

6

lateral deflection inches)

Figure 5 Comparison

of

load versus deflection using GEP and

GROUP for a R5C5S3 group

of

48-inch-diameter drilled shafts with

zero embedment in soft clay with Su=0.5ksf

r=a::GROUP 4.0 data points e GroupECluivalent Pile data points

1.2

.8 1

.64

.2

1,800

-r-----r---.. ..---- ----- ------ ----

1,600 ----j---- -----

_ : ; ~ _ E I _ : : ~ - ' 0 > - - _ 1

1,400 - ~ - - - - - - - - -

j 1,200

c - - - = t = = = i ~ ~ ~ 4 ~ : : : = ~ = = = = ~ = = ~

1,000 -----j---

-0 800

\ I ~ = ~ . ; c \

600 + - - - - - + - - ' - - - . : 9 - ~ + - - - - - - + - -

400 ---/--

200 _

o

o

lateral deflection inches)

Figure 16 Comparison

of

load versus deflection using GEP and

GROUP for R3C2S3 group

of

48-inch-diameter drilled shafts

embedded 4 feet

in

loose sand with

r J =3

34


44/71

I e G R O U P 4.0 data points Group Equivalent P i I ~ d ~ i a p o m t S J

I

i

,

.-::::

; ;

..bP

i

L

V

,

,

3500

3000

2500

2000

-g

1500

Q

1000

500

o

o

500 1000

1500 2000 2500

3000

3500

maximum moment ft-kip

Figure 7 Comparison of load versus maximum moment using GEP

and GROUP for a R5C5S3 group of 48-inch-diameter drilled shafts

with zero embedment in soft clay with S,=0.5ksf

I e

GROUP 4.0 data points Group Equivalent Pile data p o i ~ i S ]

3500 - ------ -----r------ ----- ----r----

3000

---- ---

1 I l

2500 . _ _ .

6000000000000000000

2000

::::

~ ~

L i : = 4 ~ = j

00

t ; ; ; ; ~ 7

0 ~ _ _ _ _ 1

o

maximum moment ft-kip

Figure 8 Comparison of load versus maximum moment using

GEP and GROUP for a R3C2S3 group of 48-inch-diameter drilled

shafts embedded 4 feet in

loose sand with

r


45/71

The following pile spacings and embedment depths were used to develop

the group amplification factors:

1 Pile spacing:

3

4 5 pile diameters or pile widths

2

Embedment depth below ground surface:

0 2,4,6 and

10 feet

p-multiplier values vary with pile spacing, row position with respect to the

direction of loading and soil type. In the GEP procedure, p-multipliers for all the

piles

in

a group are first determined and then added for use in the analyses. p-

multiplier values that were used to develop the group amplification factors are

summarized in Table

6

Table 6 p-multipliers for various pile spacings, pile locations and soil types

p-multipliers

for

groups

in

cohesive p-multipliers for groups

in

cohesionless soils

soils

Rollinsetal.,1998

Pinto

et

aI., 1997

S

Leading row 1st trailing

2nd and Leading row 1st trailing

2nd and

row subsequent row

subsequent trailing

trailing rows

rows

6

0.4

4

8

0.4

3

75 65

65

9

625

5

5 9 86

86

1

85

7

The same set

of

pile and soil properties used

in

the study on single piles

was used in this portion of the study. The pile types used represent a wide range

of flexural rigidities.


46/71

A total of 260 GEP analyses were performed

to

generate 2 200 load cases

for groups

in

cohesive soils. The pile configuration pile spacing and the

corresponding sum of the p-multipliers are summarized in Table 7.

Pile groups are labeled as follows: the first letter R indicates the number

rows the letter C denotes the number columns and the letter 8

represents the pile spacing in terms the number pile diameters. The layout

for pile group R3C284 which consists 3 rows and 2 columns of piles spaced 4

diameters center-to-center

is

shown

in

Figure

19.

A total

eleven group

configurations were analyzed. They include: R1C2 R1C5 R2C1 R2C2 R2C3

R2C4 R3C2 R3C3 R4C4 R5C1 and R5C5.


47/71

Table

7

Configuration, spacing, and sum of p-multipliers for pile groups

analyzed

Group Number Number

of

Dimensionless

m

for

m

forPile Spacing

Designation

of Rows Columns

SID

Cohesive Soils

Cohesionless Soils

R1C2S3 1 2

3

1.2

1.6

R1C2S4

1

2

4 1.5

1.8

R1C2S5 1

2

5

1.8

2

R1C5S3

1

5

3 3

4

R1C5S4 1

5

4

3.75

4 5

R1C5S5 1 5

5

4.5

5

R2C1S3

2

1

3 1

1.2

R2C1S4 2

1

4 1.4

1.525

R2C1S5 2 1

5

1.76

1.85

R2C2S3 2 2 3 2

2 4

R2C2S4 2

2

4 2.8

3.05

R2C2S5 2 2

5

3.52

3.7

R2C3S3

2

3

3 3

3.6

R2C3S4

2 3 4 4.2

4 575

R2C3S5 2 3

5

5.28

5.55

R2C4S3 2

4

3 4

4 8

R2C4S4

2

4

4 5.6

6

R2C4S5 2 2

5

7.04

7.4

R3C2S3 3

2

3 2.8

3

R3C2S4 3

2 4

4

4 5

R3C2S5 3 2 5 5.24

5

R3C2S3 3

2

3 2.8

3

R3C2S4 3

2 4

4

4.05

R3C2S5

3 2

5

5.24

5

R3C3S3

3 3 3 4.2

4 5

R3C3S4 3 3 4

6.15

6.075

R3C3S5 3

3

5 7.86

7.65

R4C4S3 4

4

3 7.2 7.2

R4C4S4 4 4

4

10.8

10.1

R4C4S5

4

4

5

13.92

13

R5C1S3 5 1

3

2.2

2

R5C1S4 5 1 4 3.35 3.025

R5C1S5 5 1

5

4.34

3.95

R5C5S3 5

5

3

10.5

R5C5S4 5 5

4

16.75

15.125

R5C5S5 5

5

5

21.7

19.75


48/71

1 4 1 ~

Column

Column 2

Leading row

D

D

t

First trailing row

D

D

Second trailing row

D

Lateral Load

D

Figure 9 Pile Configuration a R3C2S4 pile group


49/71

For the lateral load behavior

pile groups in cohesionless soils,

approximately 370 GEP analyses were performed to generate 2,880 load cases.

The same pile properties, configurations, embedment depths and pile spacings

for cohesive soils were used for cohesionless soils. Friction angles between 30

and 40 degrees were employed and, both sUbmerged

and

dry conditions were

examined. The p-y parameters for piles in cohesionless soils are summarized

in

Table

Table

p-y parameters for piles

in

cohesionless soils

SUbmerged/Dry

Relative Density

Friction angle Soil modulus Effective unit weight

degrees

pci pel

Loose

3

2

57

Submerged Medium dense 35

6

57

Dense

4

25 57

Loose 3

25 2

Dry Medium dense 35 9 2

Dense 4 225

2

Based on the parametric analyses, the amplification factors A

y

and AM

have the following form:

A

[ ~ J a M 2 s a M 3

M

m

where

4

3.7

3.8


50/71

Ipm = sum p-multipliers for all piles dimensionless

N

pile

= number

piles dimensionless

a

y,

aM1

aM2

and

aM3

=

dimensionless parameters for Equations

7

and

8

Table 9

Table

9 Parameters for group amplification factors

Soil Type Cohesionless Soils Cohesive Soils

0.717 1 31

aM1

0.567 0.475

aM2

1 2

1.194

aM3

0.352 0.421

In

Figures 20 through 23, the predicted values deflection and moment

using the group amplification factor approach are compared with those from the

GEP procedure for pile groups in cohesive and cohesion less soils. It can be

seen that the new approach provides estimates the group response

reasonably well with biases

no more than

and coefficients

determination

all above 0.99.


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3 - - - - - - - - - - - - - - - - - - - - - - - - - - - 0 - - - - - -

3.5.5.5.5

o

o

:? 2.5

;2;

2

l

t---(--{ ------- ';='f-i-

( ) 0.5 ~

Group Deflection using G P in)

Figure 20. Comparison

of

group deflections using GAM versus GEP

for piles

in

cohesive soils

. .

-_ . - - - - - - - I - - - - -

- - - - - - -

1000 1500 2000 2500 3000 3500 4000

Group Moment using GEP kip-tt)

500

4500

,-----,-

4000

+---+---1--

3500

~ - - - - - h Y - : ; = ~ 1 ~ . 0 n : 2 > ? 2 ~ 7 X J - - - - - - - - = k

3000

1 - 1 - - - f R ~ 2 ~ = . : 0 ~ . 9 ~ 9 ~ 8 3 T - I - < t ; ; j

l

.5 2500 - - - - - - - - - - j - - - - - . . . . .::.--+---+------1

lJ

:>


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1.2

~

1 -------I----r--

:;: y

=0.9911x

j

R

2

=

0.9938

C>

0.8

t ~ ~ ~ ~ _ : c : c ; ;

iii

:::l

0.6 +----+----+--

o

8

0 4 ~

a.

:::l

02

:::0

o

0_2

o , . . . . -----

o

0.4

0.6 0.8

1

1.2

Group Deflection using

G P

in

Figure 22_ Comparison of group deflections using

G M

versus G P

for piles in cohesionless soils

y

=0_9978x

R

2

=

0_9982

3500

4000

:;:

j 3000

---- -

C>

2500 - - - - -

.9- 2000 - - - - - - -

Ee.

~ 1500 ---- -- ----;

a.

:::l

1000 - - - - - - . . . . = - - - 1 - - - - - - - - - -

9

500 .l-----;-.. --+----j---+---+--t---+-----j

o

o

500 1000 1500 2000 2500 3000 3500 4000

Group Moment using G P kip-tt

Figure 23. Comparison of group moment using

G M

versus GEP

for

piles

in

cohesionless soils

43


53/71

3.2.2 Steps for Simplified Analysis Laterally Loaded Pile Groups

Steps for analyzing the behavior of laterally loaded pile groups using the

group amplification factor approach are

as

follows:

1 Using the pile and soil properties for the group to be analyzed estimate the

lateral deflection and maximum moment of the single pile following the steps

presented in Section 3.1.3. The lateral load that should be used for the single

pile analysis is the lateral load on the pile group divided by the number

piles

N

pi1e

in

the group.

2 Estimate the p-multipliers for each row

piles based on the center-to-center

spacing and pile

row.

3 Add the p-multipliers for all the piles together LPm .

4 Calculate A

y

and

Am

using Equations 3.7 and 3.8, respectively.

5 Calculate the group deflection yg and maximum pile moment M

g

using

Equations 3.5 and 3.6 respectively.

The limitations for the GAM include:

1. The group amplification factors were developed for pile groups no larger

than 5 x

5.


54/71

ll the piles in each group must

be

identical

3 The piles must

be

uniformly spaced

4

This approach does not provide the load distribution among the piles in the

group nor the maximum moment of each pile with the exception of those

in

the leading

row

5

Torsional effects are not considered

in

this study

45


55/71

CHAPTER 4

COMPARISON OF PREDICTED WITH MEASURED VALUES FROM LOAD

TESTS

Several full-scale lateral load tests on fixed head pile groups have been

reported in the literature Brown et aI 2001; Huang et aI 2001; Kim and

Brungraber, 1976; Mokwa and Duncan, 2000;

Ng

et aI 2001; Rollins and

Sparks, 2002 . The results for three case studies are compared with values

predicted using the procedures developed

in

this study, namely the MCLM and

the

GAM In

general, the lateral loads applied

in

these load tests are either cyclic

incremental or they are performed following a Statnamic load test. This may lead

to a densification of cohesionless soils and a softening cohesive soils.

Nevertheless for the cyclic load tests, the deflections

and

moments from the first

cycle of each load increment should closely approximate those from a static

loading condition, and are therefore useful for validating the analytical tools

developed herein.

4 1

Case Study 1 - Pile Group

in

Cohesive Soils

Rollins and Sparks 2002 performed two series of lateral load tests

on

a

fixed-head pile group at the Salt Lake City International Airport in Utah. A

Statnamic load test was performed to study the lateral response of the pile group


56/71

followed by a conventional static lateral load test. Loads for the static load test

were applied

in

the same direction as the Statnamic loads.

Nine piles, spaced three diameters apart center-to-center, were driven

in

a

3 x 3 arrangement. The piles were embedded in a 4-foot-thick and 9-foot-square

reinforced concrete pile cap. The pile cap was supported on six inches

compacted granular fiJI. One side

the

p l

cap was compacted with granUlar

fi

extending

to

the top of the pile cap (Figure

24)

to provide passive resistance.

The piles consisted

30-foot-long, 12 -inch-OD, 0.375-inch-thick-wall, concrete

filled, closed-end steel pipe piles.

The flexural rigidity (El)

the pile was estimated as follows:

(4.1)

where

and e

are the moment of inertia of the steel pipe and concrete,

respectively, E

e

= 2960 ksi based on fe = 2700 psi)

and

E

s

= 29,000 ksi) are the

Young s modulus

the concrete and steel, respectively. The flexural rigidity

the pile composite was estimated to

be

1.11

x1

0

7

kip-in


57/71

0

,

Ib

o

4

I l l-

B

SHFFrrPIL

BEACTlONWAU.

W36X16ll

Figure

24. Pile

test layout for case study 1

a) plan

view, (b)

and

cross-section (Rollins

and

Sparks, 2002)

Measured Predicted I

.

.,,:

II

_ _

p

,

.

1

[::1Y

Y

V

7

Iii 600

;g, 500

c

g: 400

go 300

e

200

.J 1

a

100

o

0.0 0.5 1.0

1.5

2.0

2.5

3.0

Group Deflection (inches)

Figure 25. Comparison of measured versus predicted

deflections using GAM for case study 1

48


58/71

Subsurface soils at the site consist predominantly of soft clay. The natural

ground water table was reported to

be

immediately below the granular fill.

Rollins and Sparks neglected the soil resistance the top four pile diameters to

account for a gap generated between the pile and the soil as a result the

Statnamic testing. Based

on

this, the clay over the top

12

pile diameters had

an

average undrained shear strength 0.53 ksf. The undrained shear strength was

estimated based

on

triaxial unconsolidated undrained tests, vane shear tests,

and pressuremeter tests.

For this load test, the lateral resistance of the fixed head pile group can be

taken as the sum the pile group and cap resistance. Rollins and Sparks

2002 calculated the cap resistance and added it to the pile resistance at the

same deflection to obtain an overall load-deflection curve. They estimated the

pile group resistance at each value of deflection using GROUP. The pile group

resistance was also estimated using the methods developed

in

this study. The

predicted load-deflection curve compares quite favorably to the actual test results

as

shown in Figure

25

The calculated maximum bending moment did not

compare

as

favorably with the measured values for the piles

in

the leading row

as

shown in Figure

26

This is probably due to rotation the pile cap which led

to a reduction

in

the maximum moment at the pile head. The estimated values

moment are about 79 to 188 percent higher than the measured values.


59/71

I 0 Measured

Predicted

I

l

i

0

I

4 I

.

-

.

~

1

,

,

~

I

I

i

~

I

I

I

i

7

,

i

50

400

350

Ul

9

300

-

Ul 250

0.200


60/71

41 TON J CKS

PILE WITH SLOPE

1

2

3

INDIC TOR TUBE

IeJ IeJ IeJ

2 aD TON J CKS

l

\

3.0

I

l

5

6

'

2

L

2 r 3 0

3

2

Figure 27. Pile test layout for case study 2 Kim and Brungraber, 1976

Eo e ~ u r e d ... Predicted

I

250 - - - - - ---

200 _

J

0 1

0.2

0.3

0.4 0.5

0 -

o

R

:

150 ---- _

>

m

Q

__,.-::--- h e = -

l l

j

Group deflection in

Figure 28 Comparison of measured versus predicted defiections

using GAM for case study 2

51


61/71

the pile was 224.2

in

The pile cap was 4 feet thick

1

feet long and 8 feet

wide.

Subsurface conditions over the top 8 shaft diameters consisted silty

clay with an average undrained shear strength of 2.5 ksf estimated based on

unconfined compression tests and standard penetration test data. The ground

water table

was

reported to be at a depth of

35

feet.

In

this load test the cap was at the ground surface with zero embedment.

As a result the pile cap resistance is not considered significant and the lateral

resistance

can

be considered to be due primarily to the pile group. An axial load

72 kips per pile was applied. The lateral load deflection curve for the group

was estimated using the procedures developed and is compared to measured

values in Figure 28 The measured load deflection curve compares reasonably

with the calculated curve. Note that the measured deflections increased by only

7 percent and measured moments increased by only 42 percent when the load

was doubled. This indicates inconsistency

in

the measurements because these

quantities would increase by a factor two rhigher if the behavior was truly

nonlinear.

The lateral load moment curve for the group was estimated using the

procedures developed and compared to average measured values the piles

in

the leading

row

Figure 29 showed that the estimated maximum bending


62/71

moments are nine percents below

to 5

percent higher than the measured value

for the leading row piles.

[ 0 Measured Moment.. .: .. -Predicted Moment

I

0

i

i

i

c - -

-0

j

/

i

l.e

/

./

35

3

25

g

91 20

5

;;

15

0

.

10

5

o

o

2

40 60

8

100

2

140 160

maximum moment k i p ~ f l

Figure 29. Comparison of predicted versus measured bending

moment for Bucknell University load test

4.3 Case Study 3 - Pile Group

in

Cohesionless Soils

Huang et

al

(2001) and Brown et

al

(2001) reported a full-scale lateral

load test

on

a group of six bored piles reacting against a group of twelve precast

concrete piles for the proposed high-speed rail system project

in

Taipao

Township of Chaiyi County, Taiwan. The bored piles

had

a diameter

59

inches, were 114 feet long, spaced 3 diameters on center and were connected

53


63/71

by a pile cap. The flexural stiffness of the drilled shaft was 2.39 x 10

9

kip-in

2

.

The pile cap was 6.5 feet thick, 72 feet long

and

49 feet wide. Subsurface

conditions over the top 8 shaft diameters consisted loose silty sand with

an

average friction angle of 35 degrees Brown et aI., 2001 . The ground water

table was reported to be at a depth of 3.3 feet. The p-multipliers for the first,

second and third

rows

are 0.5, 0.4 and 0.3, respectively Brown et aI 2001 .

In

this load test, the cap was at the ground surface with zero embedment

Figure 30 . As a result, the pile cap resistance is not considered to be

significant and the lateral resistance can be considered

to

be due primarily to the

pile group. The lateral load-deflection curve for the group is estimated using the

procedures developed and is compared to measured values in Figure 31. It can

be seen that in general, there is good agreement between the estimated

deflections and the measured values. The estimated maximum bending moment

8,850 kip-ft was 23 percent lower than the measured value in the leading row

11,551 kip-ttl. Only one value bending moment was published corresponding

to a lateral load

41 0 kips.


64/71

P Piles

Figure 30. pile test layout for case study 3 Huang et al., 2001

E()

~ ~ s u r e predicted]

I

,

I

;;;w

I

i

I

3000

2500

g

2000

~

1500

1000

-

500

o

0.00

0.20

0.40

0.60 0.80

1.00

1.20

1.40

Group deflection in

Figure

31

Comparison

o

measured versus predicted deflections

using

M

for case study 3

55


65/71

CHAPTER 5

SUMMARY AND CONCLUSIONS

The Modified Characteristic

oad

Method MCLM was developed for

estimating single pile head deflection

and

maximum bending moment for fixed

head piles embedded below ground surface

in

cohesive soils. This simple

procedure requires pile diameter, pile elastic modulus, moment of inertia, pile

head embedment depth, undrained shear strength and soil unit weight as input

parameters. The MCLM provides reliable values of pile deflections and

maximum moments when compared with LPILE Plus.

The Group Amplification Method GAM was developed to predict the

lateral behavior fixed-head pile groups. This procedure was derived based on

the group equivalent pile method proposed

by

Mokwa and Duncan 2000 . The

GAM can be used to amplify the single pile deflection and bending moment to

predict the pile group deflection and maximum moment. The amplification

factors depend

on

the number of piles

in

the group, pile spacing and p

multipliers.

he

p-multipliers depend

on

soil type, pile spacing, pile position

within the group relative to the direction of the applied force and construction

method.


66/71

The GAM conjunction with the MCLM was used to predict the behavior

three full scale pile groups that were load tested These predictions indicate

that the procedures provide estimates

group deflections and moments that are

accurate enough for most practical purposes or they provide results that err on

the side of conservatism


67/71

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