MINISTRY OF EDUCATION MINISTRY OF AGRICULTURE AND

AND TRAINING RURAL DEVELOMENT

VIETNAM ACADEMY FOR WATER RESOURCES

SOUTHERN INSTITUTE OF WATER RESOURCES RESEARCH

BACH VU HOANG LAN

RESEARCH ON THE GROUP EFFECT TO THE

CAPACITY AND SETTLEMENT OF VERTICAL

PILES GROUP

Specialization: Geotechnical Engineering

Code: 62.58.02.11

THESIS OF DOCTOR OF ENGINEERING IN BRIEF

HO CHI MINH City, 2017

The scientific work has been finished at:

SOUTHERN INSTITUTE OF WATER RESOURCES RESEARCH

Advisers: 1. Assoc. Prof. Dr. To Van Lan

2. Prof. Nguyen Cong Man

Reviewer 1: Prof. Dr. Trinh Minh Thu

Reviewer 2: Assoc. Prof. Dr. Nguyen Minh Tam

Reviewer 3: Assoc. Prof. Dr. Le Van Nam

The PhD thesis defends at the assessment committee at the

Southern Institute of Water Resources Research - 658 Vo

Van Kiet Street; Ward 1; District 5; Ho Chi Minh city.

At: 8 AM Date…… month …….. Year 2017

The PhD thesis can be obtained: The National Library or

Southern Institute of Water Resources Research Library

-1-

INTRODUCTION

1. The necessity of this study

Nowadays, pile foundations are widely used in buildings,

bridges, roads and play an important role to structures, which

build on soft soil areas. In Ho Chi Minh city, the large soft soil

areas distribute along the right bank of Saigon river.

When several piles are clustered, it is reasonable to expect

that soil pressures produced from either side friction of point

bearing will overlap. In practice, the capacity of pile group in

cohesive soils is less than the sum of the individual pile capacity.

The reduction of the load capacity and the increased settlement of

the pile group compared to the performance of single pile are

shown by the group efficiency and the settlement ratio. The

question of some concerns is: How to consider group effects

when design the pile foundation in soft soil, to ensure the capacity

and settlement of the pile group. Therefore, the topic “Research

on the group effects to the axial capacity and settlement of

vertical piles group” has scientific and practical significance.

2. Goals of study

The group effects influence on the performance of the pile

groups, which work in the soft clay in Ho Chi Minh City:

- Research for the load distribution on piles; the ultimate value

of unit shaft resistance and the end bearing resistance of each pile

in the groups, which are collected by vertical piles with rigid cap,

under the axial load.

- To define the group efficiency and the settlement ratio of the

pile groups working in soft clay.

- Suggested use the group efficiency and the settlement ratio to

estimate the capacity and the settlement of the pile group from the

static load test result of single pile.

-2-

3. Object and Scope of research

- The group effects of the pile groups with single cap work

under axial load, in the homogeneous soft clay.

- Piles are vertical and having circular section; the pile cap is

rigid and does not contact directly to the ground.

- The number of piles in the group is equal or less than to 16

piles (n≤16), with pile spacing S=3d ÷ 6d (d-pile diameter); the

ratio of pile length and pile spacing in the range [20÷30].

- Ignoring the effect of negative skin friction and the influence

of pile driving on the pile group effects.

4. Purposes of the thesis

(1) Studying the general view solutions of the pile group effects

from foreign and national authors; (2) Research and manufacture

small-scale physical models of single pile and pile groups for

static load tests in the lab and in situ; (3) Analyze the effects of

the pile group from the experiment results, through: the group

efficiency; the settlement ratio; The load distribution on each pile

in the group; the unit shaft resistance and the end bearing

resistance of the different position pile. (4) Applying the

interaction factors theory to analyze the pile group effects; (5)

Using numerical method by Plaxis-3D software to simulate the

static load tests of pile groups. The numerical method results are

used to verify with the experiment results. Constructed the

relationships of settlement ratios and pile number of the group, by

an exponential functions form R=an.

5. Research Method

Experimental method

Theoretical methods.

Numerical method.

-3-

6. New contributions of the thesis

- The results of the thesis make clearly the influences of group

effects on the load sharing in the pile groups with rigid cap: the load

distribution on corner piles are the greater than the load on edge piles

and those of center piles are smallest. The analysis results also show

that: the ultimate value of the unit shaft resistance and the end

bearing resistance of each pile in the group are not constant and

smaller than the corresponding value of the single pile. These values

depend on the interactions between piles and soil.

- Proposed a formula to determine an exponent , which can be

used to calculate the settlement ratio (RS) by the empirical

expression of Fleming et al. (1985).

- Suggest a process for changing pile lengths in the pile group to

improve the performance of the vertical pile group with rigid cap

and working under axial load.

7. The structure of the thesis

Acknowledgements - Preface

Chapter 1: Overview on the piles group effects.

Chapter 2: Using the static pile load tests on the small-scale physical

models to research the piles group effects.

Chapter 3: Application the interaction factors theory to analyze the

group effects of the vertical pile groups under axial load.

Chapter 4: Using the numerical method to analyze the pile group

effects.

Chapter 5: Recommendations

Conclusions and Recommendations

List of Public Scientific Documents

List of References

Appendix

Chapter 1

OVERVIEW ON THE PILES GROUP EFFECTS

-4-

1.1 Outline of the piles group effects

1.2 Equations to determine the piles group effects

1.2.1 Equations of the group efficiency

a. Converse – Labarre equation (1941)

b. Calculation the group efficiency by Feld rule (1943)

c. Sayed and Bakeer equation (1992)

d. Das equation (1998)

1.2.2 Equations of the group settlement ratio

a. Skempton et al. empirical expression (1953)

b. Randolph and Clancy equation (1993)

c. Fleming et al. empirical equation (1985)

1.3 Experimental studies of the pile group effects

1.3.1 Analysis of research results

To evaluate the accuracy of the theoretical equations, we

compared the group efficiencies and settlement ratios, which are

obtained from the experiments results of Barden and Mockton, G.

Dai et al. and from the equations of items 1.2.1 and 1.2.2

1.3.2 Comments

- Almost the equations to calculate the group efficiency and the

settlement ratio only consider the geometry of pile groups,

without considering some parameters, such as: Pile length;

Influence of pile cap (contact or not contact with ground); The

methods to drive piles; The physical mechanical properties of

soil…

- The value of group efficiency and the settlement ratio

calculating by the theoretical equations are not accuracy and not

matching with the corresponding values, which are determined by

the experiment results.

1.4 Regulations to determine the piles group effects in

Vietnam's building codes

-5-

Introduce the regulations of the piles group effects in

Vietnam's building codes, such as: TCXD 205:1998; 22TCN

272:05 and TCVN 10304: 2014.

1.5 Comments of Chapter 1

- The theoretical equations to determine the group efficiency

and the settlement ratio have not taken into all influence

parameters, therefore the value of those are not high accuracy and

sometime not matching with the corresponding values, which are

calculated by the experiment results.

- Equation proposed by Sayed and Bakeer (1992) had new

influence parameters. However, the values of group efficiencies

are not accurate, on some types of soil.

- The regulations of the piles group effects in Vietnam's

building codes do not provide enough information to calculate the

pile group capacity from the static load tests of a single pile.

Goals of study is analysis the pile group effects in soft clay of

Ho Chi Minh City, the purposes of the thesis are: (1) Using some

methods to analyze the group effects to load distribution on pile;

the maximum value of the unit shaft friction and the end bearing

resistance of each pile in the group, the group efficiency and the

settlement ratio of the piles group. (2) Suggestions to use the

group efficiency and settlement ratio to determine the pile group

capability by static load test results of single pile.

Chapter 2

USING THE STATIC LOAD TESTS ON THE SMALL-

SCALE PHYSICAL MODELS TO RESEARCH THE PILES

GROUP EFFECTS

2.1 Basic theories of the static piles load tests

2.1.1. Static piles load test procedure

-6-

The static piles load tests on the small-scale physical models

are used the quick load test program [11] to reduce: Time; Cost;

Avoiding the creep phenomena of soil bed and the residual strains

along pile shaft caused by long-term loading time.

2.1.2. Analysis of the static piles load test results

2.2. Set up the small-scale physical models for pile tests in lab

2.2.1. General

2.2.2. Advantages and disadvantages of small-scale physical

model

Although, the small-scale physical model only describes the

performance of a particular prototype under the gravitation field

of the earth, but it is an useful tool, because: it’s low cost and can

be simulation soil properties, such as: cohesion, friction...

2.2.3. Establishing general equations for series test

The Buckingham's Theorem was used to transfer from any

dimensionally homogeneous equation involving certain physical

quantities to a complete set of dimensionless products.

2.2.4 Basis Theories for scale effects of pile experiments

Applying the scaling laws [28] to determine the minimum value

of pile diameter in the small-scale model is dmin = 5mm, in order

to reduce the errors of shaft friction between the pile-soil. In

practice, pile diameter of physical models was chosen d=16mm to

require the scale effects and easily manufacturing.

Using the formulas by Horikoshi and Randolph (1997) to

calculate the pile cap thickness of tr =25 mm, to satisfy the

assumption of rigid pile cap.

2.2.5. Pile material

The pile model is made of aluminum tubes, because the axial

deformation of piles must has a remarkable value to measure.

-7-

2.2.6. Size of soil container in the lab experiment

To minimize errors, the size of the soil container needs: (1) It has

enough space to avoided some problems due to: boundary effects

and the distribution of soil stress surrounding the piles in group.

(2) The container is not too large, so it is easy to move and to

reconstitute the soil.

Using Plaxis software to determine the distribution of soil stress

surrounding the piles group and combined data of pile

experiments on small-scale models by some authors, the container

size was chosen: 700mm (width)×700mm (length)×800mm (high)

2.2.7. Test Equipment

2.3. Static piles load tests on the physical models in lab

2.3.1. Numbers of pile tests

Static piles load tests were performed on some pile group models:

2x2 piles; 3x2 piles and 3x3 piles. Pile diameter d=16mm; The

ratios of pile length and pile diameter are: L/d=20; 25; 30; Piles

spacing are S= 3d; 4d; 5d and 6d. Each pile group has a maximum

of 3 instrument piles, which lie down on the corner, edge and

center of the pile groups.

2.3.2 Reconstituted soil

Soil bed is reconstituted by compaction method at natural

moisture. The soil is put into the container by layers, then

compacted until it reaches the natural unit weight of the sample.

To easily reconstitute soft clay, clay samples have moisture

content W=[49÷ 52]%; wet unit weight = [15.6÷16.5] kN/m3.

2.3.3 Results of static pile load tests

The relationships between settlements and load of single pile or

load of the pile groups are illustrated in the graphs (Fig. 2.14;

2.15 and 2.16), which obtained by results of pile tests in lab. The

data were determined the utlimate load capacity of single pile and

-8-

pile groups with limited settlement [U] = 8mm and calculate the

values of the coefficient of group () and the ratio of settlement

(RS) of pile groups using equations (2.2) and (2.3).

Hình 2.14. Settlement – Load curves of single pile and 4 piles group

Hình 2.15. Settlement – Load curves of single pile and 6 piles group

Hình 2.16. Settlement – Load curves of single pile and 9 piles group

SETTLEMEMT (mm)

LO

AD

OF

PIL

E G

RO

UP

(N

)

LO

AD

OF

SIN

GL

E P

ILE

(N

)

SETTLEMEMT (mm)

LO

AD

OF

PIL

E G

RO

UP

(N

)

LO

AD

OF

SIN

GL

E P

ILE

(N

)

SETTLEMEMT (mm)

LO

AD

OF

PIL

E G

RO

UP

(N

)

LO

AD

OF

SIN

GL

E P

ILE

(N

)

LO

AD

OF

SIN

GL

E P

ILE

(N

)

LO

AD

OF

PIL

E G

RO

UP

(N

)

SETTLEMEMT (mm)

SINGLE PILE

LO

AD

OF

SIN

GL

E P

ILE

(N

)

LO

AD

OF

PIL

E G

RO

UP

(N

)

SETTLEMEMT (mm)

LO

AD

OF

SIN

GL

E P

ILE

(N

)

LO

AD

OF

PIL

E G

RO

UP

(N

)

SETTLEMEMT (mm)

LO

AD

OF

PIL

E G

RO

UP

(N

)

LO

AD

OF

SIN

GL

E P

ILE

(N

)

SETTLEMEMT (mm)

LO

AD

ON

SIN

GL

E P

ILE

(N

)

LO

AD

OF

PIL

E G

RO

UP

(N

)

SETTLEMEMT (mm)

LO

AD

OF

SIN

GL

E P

ILE

(N

)

LO

AD

OF

PIL

E G

RO

UP

(N

)

SETTLEMEMT (mm)

-9-

2.3.4. Analysis of results

Fig 2.17 and Fig 2.18 show the relationships between the group

efficiency (); the settlement ratios (RS) and S/d ratios, which are

identified from the test results and the formulas of Converse -

Labarre and Randolph - Clancy.

Fig. 2.17. Group efficiency – S/d ratio curves of pile groups

Fig. 2.18. Settlement ratio – S/d ratio curves of pile groups

The pile deformation data were analyzed to determine: the load

sharing on pile and the unit shaft resistance and the end bearing

resistance of each position pile in the groups.

2.4. Static piles load test on small-scale physical models at site

The limitation of pile tests in lab is not accurately simulating

the properties of soft clay and friction between piles and soil.

Therefore, using field tests to prove the research results, which

are collected by experiments in lab.

SE

TT

LE

ME

NT

RA

TIO

S/d RATIO

9 PILES GROUP

SE

TT

LE

ME

NT

RA

TIO

S/d RATIO

6 PILES GROUP

SE

TT

LE

ME

NT

RA

TIO

S/d RATIO

4 PILES GROUP

GR

OU

P E

FF

ICIE

NC

Y

S/d RATIO

4 PILES GROUP

GR

OU

P E

FF

ICIE

NC

Y

S/d RATIO

6 PILES GROUP

GR

OU

P E

FF

ICIE

NC

Y

S/d RATIO

9 PILES GROUP

-10-

2.4.1. Diameter of test pile

The static piles load tests on full-scale model have some

disadvantages: (1). The tests need many mechanical equipment,

so make more expense. (2). The counter-weight causes a

significant increase of the shear resistances of the top soft soil

layer and thus most the pile test results have not reflect the actual

soil conditions at the site. (3). It is difficult to assure the

assumption that the pile group works in homogeneous clay.

Therefore, the research chooses to study small-scale pile group

with pile diameter d= 60mm, satisfy the requirements: (1). The

pile diameter is not too large to simplify: the pile driving and the

static pile load tests. (2). The pile diameter is large enough to

attach the strain gauges inside the pile shaft.

2.4.2. Numbers of pile tests at site

Table 2.9. Numbers of pile tests at site

No. Number

of pile

Pile length

(mm)

S/d

Ratio

L/d

Ratio

Đ1 1 1800 - 30

N4 4 1800 3 30

N9 9 1800 3 30

N16A 16 1800 3 30

N16B 16 Corner Pile Edge Pile Center Pile

3 - 1500 1800 2100

Group N16B has different pile lengths. The test on this group

can be evaluating the effectiveness of changing the piles length.

The total piles length in two groups N16A and N16B are equal.

2.4.3. Detail of piles test and pile cap

Piles test made of steel tube =60 mm with a thickness of 5mm.

Each group has a maximum of three piles with strain gauges were

attached: corner pile; edge Pile and center pile. Each instrument

pile has from 1 to 4 strain gauges depending on the pile length.

-11-

The pile cap is made up some of 800x800x25(mm) steel plates,

which are connected to each other by bolts and fixed to the top of

the pile group.

2.4.4. Apparatus for applying load and measurement system

2.4.5. Soil Condition

2.4.6. Static piles load tests at site

2.4.7 Test Results

Figure 2.37. The curves of – n and RS – n, which analyze from

results of tests in lad and field test

These values of the group efficiencies and the settlement ratios

from the situ test results were compared with those of the lab tests

on groups with the same pile number, S/d ratio and L/d ratio (Fig

2.37), which shows the similar amounts.

2.4.8 Analyses the test results

Analyses the axial deformations of a pile, to determine:

- The load distribution on a pile; the unit shaft friction of each

piece of pile; the end bearing resistance of piles toe.

- In group N16B: The load distribution on the piles is relatively

equal (Fig 2.42); The value of unit shaft friction and the end

bearing resistance are larger than the corresponding values of

piles in group N16A.

()

(RS)

-12-

Hình 2.42. Load sharing on pile - Group settlements curves of

group N9; N16A and N16B

2.5. Conclusions of Chapter 2

The combination and analysis of the results of 39 pile’s tests

in lab and 5 field tests on physical models having conclusions:

- Comparing the group efficiencies, the settlement ratios from

the test results and the corresponding values making from

formulas of Converse-Labarre and Randolph-Clancy, to show that

these values have the same trend in terms of factors: pile number

and pile spacing. The different values of these ratios from two

methods are in the range of [0.1%÷ 18.4%] and [0.09% ÷12.4%]

respectively, because most of the formulas do not take into the

effects of pile length and the physical mechanical properties of

soil.

- The test results point out: Increasing the ratio of pile length

and pile diameter (L/d) to make the decreasing of group

efficiency () and the increasing of settlement ratio (RS) of the

groups with the same pile’s number and pile’s spacing. It shows

that: the effects of the pile length should be considered to analyze

the pile group effects.

The group effects in the pile groups with rigid cap make: the

decreasing of the shaft resistance and toe resistance of the pile in

CORNER PILE

EDGE PILE

CENTER PILE

SETTLEMEMT (mm)

LO

AD

S

HA

RIN

G O

N P

ILE

(k

N)

GROUP N16A

CORNER PILE

EDGE PILE

CENTER PILE

SETTLEMEMT (mm)

LO

AD

S

HA

RIN

G O

N P

ILE

(k

N)

GROUP N16B

CORNER PILE

EDGE PILE

CENTER PILE

GROUP N9

LO

AD

S

HA

RIN

G O

N P

ILE

(k

N)

SETTLEMEMT (mm)

-13-

group; the load sharing on piles are unequal and reducing the pile

efficiency. For the 9 piles groups, the efficiency of center piles

are in the range of [0.34 ÷ 0.56].

Values of the unit shaft friction (fS) and the end bearing

resistance (qp) of pile in groups are smaller than the

corresponding values of the single pile and the arrangement in

decreasing order are: corner piles; edge piles and center piles. It

points that, the maximum value of those are not constant and

depend on the interactions between piles and soil.

The difference value of settlement ratios of the pile groups

having the same piles number, ratio L/d=30 and S/d=3 from pile

tests in lab and in situ are quite small [1.5% ÷ 3.2%]. It shows the

effectiveness of tests on small-scale models in lab.

The static load test results on the group N16A and N16B

show that: the changing pile lengths to reduce the load differential

between piles in the group N16B and increasing the capacity of

group N16B by 12% compared to the corresponding value of

group N16A.

Chapter 3

APPLICATION THE INTERACTION FATORS THEORY TO

ANALYZE THE GROUP EFFECTS ON THE VERTICAL PILE

GROUPS UNDER AXIAL LOAD

3.1 Principles

Analysis the group effects to determine the load distribution

on piles and the settlement ratios of the pile groups. The

interaction factor equation of Randolph and Worth (1978) was

chosen by recommending of Phan Dung and Pender M.J.

3.2 Application the interaction factor equation to analyze

the pile group effects

3.2.1 Establishing work

Using the interaction factor method to analyze performances of

the vertical pile group with cap doesn’t contact to ground, using

-14-

the assumptions: (1). Under the axial load, all piles in the group

have the same settlement; (2) Compressive loading on pile cap

will be completely divided to piles in the group.

3.2.2 Analyzing the pile group effects

Establishing the general equation system based on assumption: all

piles in the group have the same settlement, to calculate: The load

sharing on each pile; The relationship between the settlement of

the group and the load and the value of settlement ratio.

3.2.2.1 Parameters of the piles and soil

Analysis the group effects on some pile groups: 2x2 piles; 3x2

piles; 3x3 piles and 4x4 piles. The parameters of pile material and

soil properties are similar to those of the pile tests in lab (Chapter

2). However, the pile diameter was used 25 times larger than

those in lab tests, which can be reduce some disadvantages of the

experiments on a small-scale model.

3.2.2.2 Results of the analyzing pile group effects

The diagrams (from Fig.3.6. to Fig 3.9.) describe the relationships

between the settlement ratio and pile number in the pile group.

The relationships are approximated by exponential functions of

the form: RS=an.

Figure 3.6. RS – n curves of the

pile groups with ratio S/d=3

Figure 3.7. RS – n curves of

the pile groups with ratio S/d=4

SE

TT

LE

ME

NT

RA

TIO

(R

S)

NUMBER OF PILE (n)

RATIO S/d=4

NUMBER OF PILE (n)

SE

TT

LE

ME

NT

RA

TIO

(R

S)

RATIO S/d=3

-15-

3.3 Conclusions of Chapter 3

- The interactions between the piles and soil cause unequal load

distribution on pile in the group. If pile spacing increases and the

pile length decreases, the piles in group will work more

independently and reducing the load differential between piles.

- The group effects are more significant when increasing the

number of piles: in groups of 9 piles, the load distribution ratio of

corner piles and center piles are [1.28 ÷ 1.16]; [0.55 ÷ 0.33]

respectively and the corresponding values in the groups of 16

piles are [1.5 ÷ 1.37]; [0.57 ÷ 0.49].

- The relationships between the settlement ratio and pile

number are approximated by the exponential function form

RS=an, in the scope of research, the coefficients a is in the range

of [1.04÷0.991] and exponent = [0.466÷0.259].

Chapter 4

USING THE NUMERICAL METHOD TO ANALYZE THE

PILE GROUP EFFECTS

Figure 3.8. RS – n curves of the

pile groups with ratio S/d=5

Figure 3.9. RS – n curves of

the pile groups with ratio S/d=6 S

ET

TL

EM

EN

T R

AT

IO (

RS)

NUMBER OF PILE (n)

RATIO S/d=6

SE

TT

LE

ME

NT

RA

TIO

(R

S)

NUMBER OF PILE (n)

RATIO S/d=5

-16-

4.1 Introduction

Using the numerical models to describe the static load tests on

single pile and pile groups. Plaxis-3D (2013) software is used to

determine the relationship between load - settlement of the static

load tests and the axial force of each pile in the group.

4.1.1 The purpose of the numerical simulation study

4.1.2 Material models of Plaxis-3D software

4.2 Numerical simulation for static pile load tests

4.2.1 Data of pile and soil

In Plaxis software, soil can be simulated by some models, such

as: Mohr-Coulomb; Hardening model. According to [2], [45] the

Soft Soil model (SS) was chosen for studying. The parameters of

the soil are based on the physical properties of the reconstituted

soil in the lab tests (Chapter 2).

Using numerical models to verify the result of the pile group

effect from the experimental method, so that the pile groups are

simulated by large-scale; Pile diameter is 25 times more than the

those of pile in lab tests; Pile diameter d=0.4m. Ratio of pile

lengths and pile diameter: L/d = 20; 25 and 30. The material

properties of the piles and pile cap are same those of values on

pile in lab tests.

4.2.2. Calculation results

Plaxis-3D software is used to simulate the static load tests of the

pile group. From the load - settlement curves and the axial force

graphs of piles, we calculate: (1) Group efficiency and settlement

ratio of each group. (2) Load distribution ratio and efficiency of

each pile. (3) Determining values of the unit shaft friction and the

end bearing resistance of each pile in group.

-17-

Hình 4.4. Load – Settlement curves of single piles

Hình 4.9. Load – Settlement curves of 4 piles group

Hình 4.10. Load – Settlement curves of 6 piles group

SINGLE PILE L/d=25

SE

TT

LE

ME

NT

(m

m)

LOAD (kN)

SE

TT

LE

ME

NT

(m

m)

LOAD (kN)

SINGLE PILE L/d=30

SINGLE PILE L/d=20

SE

TT

LE

ME

NT

(m

m)

LOAD (kN)

4 PILES GROUP L/d=20

LOAD (kN)

SE

TT

LE

ME

NT

(m

m)

4 PILES GROUP L/d=25

LOAD (kN)

SE

TT

LE

ME

NT

(m

m)

4 PILES GROUP L/d=30

LOAD (kN)

SE

TT

LE

ME

NT

(m

m)

LOAD (kN)

SE

TT

LE

ME

NT

(m

m)

6 PILES GROUP L/d=20

LOAD (kN)

SE

TT

LE

ME

NT

(m

m)

6 PILES GROUP L/d=25

LOAD (kN)

SE

TT

LE

ME

NT

(m

m)

6 PILES GROUP L/d=30

-18-

Hình 4.11. Load – Settlement curves of 9 piles group

Hình 4.12. Load – Settlement curves of 16 piles group

4.3 Analysis and comparison of results

4.3.1 Pile Group Effects

In order to assess the compatibility of pile group effects by

different methods, the values of the group efficiency and

settlement ratio of the corresponding groups obtained from:

numerical method; interaction factors theory and experiment

results were compared.

4.3.2 Approximate the settlement ratios by exponential

functions

LOAD (kN)

SE

TT

LE

ME

NT

(m

m)

9 PILES GROUP L/d=30

LOAD (kN)

SE

TT

LE

ME

NT

(m

m)

9 PILES GROUP L/d=25

LOAD (kN)

SE

TT

LE

ME

NT

(m

m)

9 PILES GROUP L/d=20

LOAD (kN)

SE

TT

LE

ME

NT

(m

m)

16 PILES GROUP L/d=30

LOAD (kN)

SE

TT

LE

ME

NT

(m

m)

16 PILES GROUP L/d=25

LOAD (kN)

SE

TT

LE

ME

NT

(m

m)

16 PILES GROUP L/d=20

-19-

Similar to Chapter 3, the relationships of the settlement ratios and

the pile numbers of the group are approximated by exponential

functions form RS=an. These functions are used to set up the

formula for calculating the settlement ratios of the pile groups,

which work in soft clay.

4.4 Conclusions of Chapter 4

- Group effects make the decreasing of shaft resistance and toe

resistance of pile in the group, so these values are smaller than

those of single piles. The maximum values of unit shaft

resistances (fS) of each pile in the group are different and

decreasing in order: corner piles; edge piles; center piles. The

results match the corresponding results obtained by the tests.

- The decreasing of shaft resistance and toe resistance of pile in

the group make the unequal load distribution to the piles. In 9

piles groups, the ratio between the pile load and the average pile

load of each pile in the group are: corner piles [1.30÷1.19]; edge

piles [0.88÷0.96] and center pile [0.30÷0.51].

- The group efficiencies obtained by the numerical method

match to those of test results. The differences of these values

between the two methods are in the range of [0.3% ÷8.2%].

- Comparing the settlement ratio values (RS) between three

methods: theoretical; numerical method and experiments to show

that, there have same trend when taking effect of factors: L/d

ratios; S/d ratios and piles number (n). The differences of

settlement ratio values between the three methods are in the range

of [1.3% ÷ 9.8%].

- The exponential functions form: RS=an is used to represent

the relationship between the settlement ratios (RS) and pile

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number. In scope of study: coefficient a and the exponent

changing in the range: [1.019÷0.987]; [0.437÷0.222] respectively.

Chapter 5

RECOMMENDATIONS

5.1. Proposed formula for determining settlement ratios

5.1.1. The empirical equation of Fleming et al.

Fleming et al. (1985) [24], [47] suggested an empirical

formula to determine the settlement ratio of the pile group:

RS = n

(5.1)

Where, RS – the settlement ratio; n – the number of piles; – an

exponent, which lies between [0.4 ÷ 0.6] for most pile groups.

5.1.2. Comparing the results of calculating the settlement ratio

5.1.3. Proposed formula to determine an exponent

By approximating the relationships between the settlement ratios

and piles number by exponential functions form RS = an in

chapters 3 and 4, with the coefficient a 1. The author proposes

the exponent formulas , which takes into influences of L/d ratios

and S/d ratios to the settlement ratio of the group:

S L0.4 (0.06 ) 0.04

d d

(5.2)

5.1.4. Results of calculations and comparisons

The settlement ratios calculated by equation (5.1) with exponent

determined according by formula (5.2) are compared to those

from experiment results in lab and in situ to show the matching.

Suggest a process for changing the pile lengths to improve the

performance of the pile group

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5.1.5. Introduction

Studies by Chow and Thevendran (1987) shown that using

the pile group with different lengths can be optimizing the

performance of the pile group. The analysis demonstrated that

reducing the load differentials between piles in the pile group

with rigid cap and regarding differentials settlement when pile

caps are flexible. Some authors, for examples: Liew et al. (2002)

[39], Tan et al. [50] used the pile groups with different lengths in

5-storey building in Tinggi Bulit, Malaysia and the 2,500 ton oil

tank in Summatra, Indonesia. It had shown the effectiveness of

changing the pile lengths in the group.

5.2.2. Theoretical basis

Apply the Feld’s rule (1943) to determine the efficiency of each

positional pile in the group.

5.2.3 Assumptions

Using the assumptions: (1). Keeping the pile layout. (2).

Unchanging total of pile length in the group. Redistribute the pile

length according to the principle: decreasing the length (L1) of the

piles in 1st zone, increasing the length of the center piles (L3) in

3rd

zone and keeping the lengths of piles in the middle zone

(L2=L). This process to make the efficiency of the all piles in the

1st zone and 3

rd zone are equal.

5.2.4. Proposed calculation process

To change the length of the piles in the pile group, working

on the order:

(1). From the original pile layout divided into three zones with

different types of pile length, based on the rule: Reducing the

piles length in zone 1st (outside of a group); Increasing the

piles length in zone 3rd

(center of a group) and keeping the

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piles length in zone 2nd

(middle of a group) and determining

the number of piles for each zone.

(2). Using the Feld's rule (1943) to calculate the group efficiency

of the original pile group.

(3). Calculating the pile efficiencies and the load sharing on each

pile in the original pile group by the recommended formulas.

(4). Using the equation (5.7) to determine the load sharing ratio

on each pile in zone 1st and 3

rd of the different- length group.

(5). Calculating the new lengths (L3) and (L1) of piles in

corresponding zones by the formula (5.8) and (5.9).

5.3. Conclusions of Chapter 5

- Proposed expression for an exponent , which is used in the

empirical formula of Fleming et al. (1985) to compute the

settlement ratio. The ratio can be used to estimate the settlement

of a pile group from static load tests result of single pile. The

scope of use: a small pile groups (n≤16 piles) with rigid pile cap,

ratios S/d=[3÷6] ; ratio L/d ≤ 30 and working in soft clay.

- Suggest a process to change the pile lengths of an equal-

length group to improve the performance of vertical pile group

with rigid cap and working under axial load. The process is used

some assumptions: keeping the pile group layout and total pile

lengths of the original group.

CONCLUSTIONS - RECOMMENDATIONS

CONCLUSTIONS

Base on the research results, the thesis makes the conclusions:

1. Group effects in the pile groups with rigid cap cause unequal

load distribution on piles and the value of load on piles

decreases in the order: corner piles, edge piles and center

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piles. These results caused by the decreasing of the unit shaft

resistances and the end bearing resistance of piles in the

group. In study pile groups, the efficiency of the center piles

were in range [0.3÷0.57] compared with those of the single

pile. This phenomenon makes to reduce the performance of

each pile in the groups.

2. The maximum values of the unit shaft friction (fS) and the end

bearing resistance (qp) of pile in groups are not constant and

smaller than the corresponding values of the single pile. It

points that, these values depend on the interactions between

piles and soil.

3. The group efficiencies calculating by the test results and

Converse - Labbare formula are same trends. In groups with

many piles, the group efficiencies making from lab tests are

the smaller than those of value according to the formula. The

different value of the ratios, which conducted by two methods

varied between [0.1% 18.4%]. This points that the effects of

soil properties and pile length should be taken to analyze the

pile groups.

4. The settlement ratios calculating by the test results and the

formula by Randolph and Clancy are same tendency. The

ratios value making from test results are the smaller than those

of value according to the formula, when increased the pile

spacing. The different value of these ratios, which conducted

by two methods varied between [0.09%÷12.4%].

5. Using different pile lengths in a vertical pile groups, which

has rigid cap and works under the axial compression load to

reduce unequal load distribution on each piles and improving

the performance of the pile group.

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RECOMMENDATIONS

Base on group effects research of the vertical pile groups

working in soft clay, the thesis has some recommendations:

1. In the pile groups with rigid cap, the load distribution on the

piles are unequal, the value of load sharing on the corner piles

are larger than those of other piles. Therefore, the group

efficiencies should be taken to check the pile capacity, even if

the load on a pile in a group, which is calculated by formulas

(4) in item 7.1.13 of the Vietnam building code 10304:2014,

hasn’t reached the acceptable capacity of single pile.

2. To design pile foundations working in soft clay from the static

load test results of single pile, it necessary uses the equation

of Fleming et al. with the exponent as defined by the

proposed expression, to estimate the settlement ratios of the

pile group. In groups having many piles, the limit settlement

of single pile in static load test equals 10% of pile diameter or

[Ugh]≤40mm [10] sometimes does not ensure the total

settlement of pile group.

3. The vertical pile groups, with rigid cap working under axial

load may be used the proposed process to change the pile

lengths, to improve the performance of the group.

FURTHER STUDIES OF THESIS

1. Studying group effects of pile group working in multi-layer

soils: piles are driven through soft soil layers and pile toe is in

hard soil.

2. Influence of pile material on pile group effects.

3. Group effects in pile groups with a flexible cap, which is

contacted closely to ground.

LIST OF PUBLIC SCIENTIFIC DOCUMENTS

1. Bach Vu Hoang Lan (2011). “Some accountings on load capacity of

pile’s group”; Vietnam Geotechnical Journal, ISSN-0868-279X.

2. Bach Vu Hoang Lan (2012). “Influence of pile’s length and geo-

stratigraphic structure over the stress distribution rules at the plane

through the tip of precast reinforced concrete pile”; Vietnam

Geotechnical Journal, 3/2012. ISSN-0868-279X. Page: 21-26

3. Bach Vu Hoang Lan (2014). “Vertical stress distribution region of soil

surrounding single pile and pile groups” ; Review of Ministry of

Construction. 2/2014. ISSN-0866-0762; Page: 124-127

4. Bach Vu Hoang Lan (2015). “Using the interaction factor method

analyzes the group effects of vertical pile group under axil load”;

Collection of scientific and technological results of Southern Institute

of Water Resources Research. ISSN: 0866-7292

5. Bach Vu Hoang Lan; Tran Thi Tram (2016). “Research pile group

effects by modeling of axially loaded test”. Review of Ministry of Construction. 6/2016. ISSN-0866-0762. Page: 191-194

6. Bach Vu Hoang Lan; Nguyen Minh Hai (2016). “Analyzing the static

load test of a bored pile in Hotel Des Art Saigon Project”. Proceedings

of the 2nd

National Conference on Transport Infrastructure with Sustainable Development (TISDC 2016); Construction Publishing

House, ISBN 978-604-82-1808-6.

7. L.H.Viet; N. M.Hai; B.V.H.Lan; T.T.Quang. “Field Vane Shear Test

for Thi Vai International Port”. Proceedings of the 2nd

National Conference on Transport Infrastructure with Sustainable Development.

Construction Publishing House, ISBN 978-604-82-1808-6.

8. Bach V. H. L.; Nguyen M. H., Puppala A. J.; Nguyen C. M., (2016).

“Comparing the response of static loading tests on two model pile

groups in soft clay”. Proceedings of the 69th Canadian Geotechnical

Conference, Vancouver, October 2-5; Paper No. 3678, 8 p.

9. Nguyen Minh Hai; Puppala A.J.; Patil U.; Bach Vu Hoang Lan (2016).

“Problems of cycled head- down pile load tests in soft soil region”.

Proceedings of the 3rd

International Conference on “Geotechnics for

Sustainable Infrastructure Development”. Hanoi, Vietnam.

Construction Publishing House, ISBN 978-604-82-0013-8

10. Bach Vu Hoang Lan (2015). “Manufacturing the small-scale physical model to study the capacity of single pile and pile groups”. Science

research of The University of Architecture Ho Chi Minh City. Code:

XD03-NCKH15.