(Luận văn thạc sĩ) a study on bearing capacity of shaft – grouted bored piles and barrettes for high rise in ho chi minh city

To reduce many risks and high costs from installing very long piles, the shaft grouting method has been applied extensively to drilled shafts in the city to increase the resistance of th

VIETNAM NATIONAL UNIVESITY HANOI

VIETNAM JAPAN UNIVERSITY

PHAM THI THUY DUONG

A STUDY ON BEARING CAPACITY OF SHAFT – GROUTED BORED PILES AND

BARRETTES FOR HIGH-RISE

IN HO CHI MINH CITY

MAJOR: INFRASTRUCTURE ENGINEERING

TABLE OF CONTENTS

LIST OF TABLES i

LIST OF FIGURES ii

LIST OF ABBREVIATIONS iv

CHAPTER 1 INTRODUCTION 1

1.1 General Introduction 1

1.2 Necessity of Research 2

1.3 Objective and Scope of Research 3

1.3.1 Objectives of the Study 3

1.3.2 Scope of the Study 4

CHAPTER 2 LITERATURE REVIEW 5

2.1 Principle of the Shaft Grouting Technology 5

2.1.1 Grout Materials and Equipment 5

2.1.2 Construction Procedure 9

2.2 Existing Studies on Shaft-Grouted Piles 12

2.3 Theory for Calculate Bearing Capacity of Drill shaft 16

2.3.1 Method of FHWA (FHWA-NHI-10-016) 16

2.3.2 Method of Vietnam Standard (TCVN10304-2014) 17

2.4 Theory for Converting Strain to Load 19

2.5 Linear Regression Analysis 24

CHAPTER 3 METHODOLOGY 25

3.1 Introduction 25

3.2 The Procedure for Determining Correlation between ru and SPT N60; Correlation between ru and ζ’v 25

3.3 Evaluation of Appropriate Soil Type for Applying Shaft Grouting Technology 27

3.4 The Procedure to Comparison of Shaft Grouted Pile and Plain Pile 30

CHAPTER 4 DATABASE AND ANALYSIS RESULTS 31

4.1 Database of Test Piles 31

4.1.1 List of Projects 31

4.1.2 Geological Conditions 33

4.1.3 Test Pair Piles 35

4.2 The Correlation between ru and SPT N60 36

4.3 The Correlation between ru and Effective Vertical Stress ζʹv 38

4.4 Evaluation the Appropriate Soil Type for Applying Shaft Grouting Technology 39

4.5 Comparison of Shaft Grouted Pile and Plain Pile 41

CHAPTER 5 CONCLUSIONS AND RECOMMENDATIONS 46

5.1 Conclusions 46

5.2 Limitations and Suggestions 46

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REFERENCES 47

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ABSTRACT

In recent years, high-rise buildings have been constructed extensively in Ho Chi Minh City (HCMC) to cope with the increasing demand for living and office spaces Drilled shafts (bored piles) for the high-rise buildings in the city, especially in the central districts along the Saigon river, are often installed up to depths of 70 to 80 m to ensure the bearing capacity To reduce many risks and high costs from installing very long piles, the shaft grouting method has been applied extensively to drilled shafts in the city to increase the resistance of the shafts or to reduce and shaft length with a designated resistance Although the method has been applied extensively, there is still

no comprehensive study on the effectiveness of the shaft grouting method regarding the geological conditions of the city It is very necessary to make a comprehensive study on the effectiveness of the shaft-grouted piles in the city

The effectiveness of the shaft grouting method was evaluated by comparing the ultimate (unit) shaft resistance of shaft-grouted piles with that of plain (not grouted) piles For this, a database of 34 well-instrumented drilled shafts and barrettes from 12 projects in the city was brought into analytical analyses Results from the analyses indicate that the ultimate shaft resistance of shaft-grouted piles in both clayey and sandy soils in general increases approximately 1.8 times that of the plain piles Besides, analyses on suitable soil types indicate that, in general, the stiffer/ denser the soil, is the better the effectiveness of the method The soil has SPT-N larger than 10 (stiff clay, very stiff clay, hard clay, medium dense sand, dense sand, and very dense sand) is suitable to apply the shaft grouting method It was found that long drilled shafts for buildings along the Saigon river can be shorted significantly by applying the shaft grouting method to the lower portion of the piles The shorter grouted piles not only satisfy the required resistance but also help the construction cost up to 10% compared with that for the longer plain ones

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ACKNOWLEDGEMENTS

I would like to express my sincere appreciation to the lecturers of Master of Infrastructure Engineering Program for their help during my undergraduate at Vietnam Japan University (VJU)

First of all, I am very grateful to Dr Nguyen Tien Dung, who guided me to conduct this thesis for the part one year He spent a lot of time telling me complicated issues in geotechnical engineering Not about knowledge, he also taught me valuable lessons about the seriousness and carefulness of scientific research These valuable lessons will follow me throughout the future study

I would like to acknowledge the sincere inspiration from Prof Nguyen Dinh Duc and Prof Hironori Kato Their lectures covered not only specialist knowledge but also the responsibility and mission of a new generation of Vietnam I am grateful to Dr Phan

Le Binh for his support in the last two years since I have studied at Vietnam Japan University Thanks to him, I have learned the professional courtesy of Japanese people

as well as Japanese culture I would also like to acknowledge the staff of Vietnam Japan University, Mr Bui Hoang Tan for their help and support I would also like to Fecon company as well as other members of Fecon‟s lab, where I had 30 meaningful days internship at The laboratory It was very helpful to me

Finally, I want to spend thank my parents and friends for their unflinching support in the tough time Their support, spoken or unspoken, has helped me complete my master thesis

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LIST OF TABLES

Table 2.1 Summary of typical design parameters following author‟s experience 15

Table 3.1 SPT-N value soil property correlations for (a) granular (sandy) soil 28

Table 4.1 The information of projects in Ho Chi Minh city 32

Table 4.2 The information of three test pair piles 35

Table 4.3 The resistance ratio of grouted over not grouted 37

Table 4.4 The resistance ratio of grouted over not grouted 39

Table 4.5 The construction cost saving percentage comparison with plain pile and shaft grouted pile 45

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LIST OF FIGURES

Figure 1.1 The section and details of tested piles from Gouvenot‟s research 3

Figure 2.1 Detail of Tube a manchette 6

Figure 2.2 The land view in the grouting process 7

Figure 2.3 Simulate the grout affected area and the grout section cross 7

Figure 2.4 The grouting diagram CINTAC 15 System – JEANLUTZ 8

Figure 2.5 The grouting machine 8

Figure 2.6 The process to construct the shaft grouted bored pile, barrettes pile 9

Figure 2.7 Details of grouting and instrumentation of Saigon and Song Viet project 10

Figure 2.8 Cross-section and layout of instrumentation 10

Figure 2.9 The process of water cracking (a) and shaft grouting (b) 11

Figure 2.10 Illustration diagram of the grout pipe cross-section, flows paths, the section of the grouted sample 11

Figure 2.11 Variation of gain in load with injection 13

Figure 2.12 The Stocker‟s research result 13

Figure 2.13 The comparison mobilized friction value between the grouted pile and plain pile tests in Hong Kong 14

Figure 2.14 Summary the mobilized shaft resistances of clayey soil (a) and

sandy soil (b) versus N value 15

Figure 2.15 Idealized layering for computation of compression resistances 17

Figure 2.16 Frictional model of unit side resistance for drilled shaft 17

Figure 2.17 The diagram to evaluate p coefficient 19

Figure 2.18 Near pile-head gage level secant stiffness vs measured strain 20

Figure 2.19 Load transfer mechanism for piles, the variation of f(z) with depth 23

Figure 2.20 The mobilized shaft resistance at some strain gauge levels 23

Figure 3.1 Flow chart to evaluate correlation between ru with N60, ζʹv 26

Figure 3.2 Illustration plain pile and grouted pile to evaluate shaft resistance increment 27

Figure 3.3 Flow chart to evaluate suitable soil type 29

Figure 3.4 Flow chart to compare grouted pile and plain pile 31

Figure 4.1 The location of projects in Ho chi minh city 31

Figure 4.2 The soil properties and SPT-N value from data of Ho Chi Minhʹs project 34 Figure 4.3 Illustration of the three test pair piles 36

Figure 4.4 Correlation of ru and N60 for Clayey soil 36

Figure 4.5 Correlation of ru and N60 for Sandy soil 37

Figure 4.6 Correlation of ru and ζʹv for Clayey soil 38

Figure 4.7 Correlation of ru and ζʹv for Sandy soil 38

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Figure 4.8 The correlation of the shaft grouting cost to increase one shaft resistance

unit versus Standard penetration test blow count for clayey soil 40

Figure 4.9 The correlation of the shaft grouting cost to increase one shaft resistance unit versus Standard penetration test blow count for sandy soil 41

Figure 4.10 The load – settlement relation chart of pair 1 (TP-01 and TP-02) 42

Figure 4.11 The load – settlement relation chart of pair 2 (TP-04 and TP-05) 42

Figure 4.12 The load – settlement relation chart of pair 3 (TP1-1 and TP3-1) 43

Figure 4.13 The shaft resistance accumulated of pair 1 (TP-01 and TP-02) 44

Figure 4.14 The shaft resistance accumulated of pair 2 (TP-04 and TP-05) 44

Figure 4.15 The shaft resistance accumulated of pair 2 (TP1-1 and TP3-1) 44

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LIST OF ABBREVIATIONS

A base The cross-sectional area of bearing at the shaft base (m2)

A c Circumference of pile at strain gage

C g Shaft grouting cost

C s Circumference of pile at depth z (m)

c u Undrained shear strength

D Diameter of pile (m)

E s The secant stiffness modulus of pile material (kPa)

E t The tangent stiffness modulus of pile material (kPa)

f L The coefficient depends on the ratio length over diameter

K Coefficient of horizontal soil stress

L Unit length (m)

lc,i Length of pile in clayey soil layer i (m)

l s,i Length of pile in sandy soil layer i (m)

N The number of blows required to penetrate the soil 30cm from Standard

penetration test

N60 The Corrected N-index for 60% efficient energy

Ns,i The average SPT index in sandy soil layer i

n Number of layers providing side resistance

QHL The load at the pile head (kN)

Q SG The load at the strain gauge (kN)

QSG The increment load at the strain gauge (kN)

q BN Nominal unit base resistance (kPa)

R B Nominal base resistance (kN)

R S Nominal side resistance (kN)

r s The unit shaft resistance (kPa)

r s,c Nominal unit side resistance of layers i for clay (kPa)

r s,s Nominal unit side resistance of layers i for sand (kPa)

r u The ultimate unit shaft resistance or fully mobilized unit shaft resistance

(kPa)

zi Thickness of layers i (m)

p The coefficient base on the ratio between undrained shear strength and

average effective stress

β Side resistance coefficient (beta method)

δ Effective stress angle pf friction for the soil shaft interface

 The strain (mm)

ζ Stress (load divided by cross section area)

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ζʹ h Horizontal effective stress (kPa)

ζʹ v Effective vertical stress (kPa)

B Resistance factor for base resistance

S Resistance factor for side resistance

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These days, from the development of science and technology, there are many foundation solutions such as driving and jacking methods; pre-bored precast piling method; drilled shaft The high-capacity deep foundation systems which are used extensively in the world are called under the name drilled shaft or drilled caisson, bored pile, barrettes piles… For construction, the drill shaft is constructed by digging a pillar excavation, install reinforcing cage, and then pouring concrete into the excavation The method is quite effective for bearing large axial, lateral loads and overturning forces In addition, it eliminates the noise and strong ground vibration to avoid affecting surrounding works As well as, it is applied for a variety of different ground conditions For these reasons, drilled shafts become both the technical and economic methods for many construction projects

Drilled shafts are widely applied for highway bridges in seismically active areas because of the flexural strength of a large diameter column of reinforced concrete as well as to avoid reducing the bearing capacity of shallow foundations due to surface soil erosion where installation driving pile might be impossible The construction project applied drilled shafts, for instance: Structural support, Slope stabilization, Earth retention for retaining walls, sound walls, signs or high mast lighting where simple support for overturning loads

On the others hand, the increasing urbanization process is leading to an increase in housing demand However, the limited land fund in the urban area requires high-rise building to expand the space vertically The higher the building, the greater the loaf transferred to the foundation, which requires a higher capacity of the pile A simple

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method to increase the bearing capacity of a pile is increasing the diameter or length of the pile But this solution is quite expensive and difficult to control the quality for piles that are too long There should be an improving bearing capacity of the drilled shaft (bored pile and barrettes piles) more effectively and save the cost for the owner

1.2 Necessity of Research

Based on these limitations of the drilled shaft (bored pile, barrettes pile) many research was conducted study and find out solutions to enhance the bearing capacity of piles is that base grouting and shaft grouting One of the earliest research about shaft grouting

by (Gouvenot and Gabaix, 1975) on 660 mm diameter bored piles showed that “the injection of cement under pressure enables one to increase by 2.5 times the capacity of

a pile sealed under gravity” A similar improvement in friction for shaft grouted sand and clays was reported by (Bruce, 1986), the post-grouting increase in ultimate load of

up to three times in sands and clays on large diameter pile performance Within this research, it is impossible to cover all aspects of drilled shaft foundations therefore, attention is focused on the bearing capacity of shaft grouted bored pile and barrettes for high rise A review of published work of (Littlechild et al, 2000) in the load test program undertaken for Kowloon-Canton Railway Corporation(KCRC) in Hong Kong demonstrate shaft friction capacities measured for shaft grouted barrettes and piles in the completely weathered granite and volcanic achieved a two to three-fold increase when compared with tests without shaft grouting as reported by others…

From previous researches, Shaft grouting technology improves significantly shaft friction of grouted piles compare with the plain (not grouted) piles In addition, the increment ratio depends heavily on geological conditions Recently, this technology is applying extensively in many construction projects in Viet Nam by the main contractors Bachy Soletanche, Bauer Company, Fecon Company, due to the increase

in bearing capacity compared to not grouted piles of the same size However, there are still no technical specifications for the design It is therefore very necessary to make a comprehensive study on instrumented shaft-grouted pile and barrettes to understand the behavior and quantitatively increment of shaft resistance of shaft-grouted piles

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Figure 1.1 The section and details of tested piles from Gouvenot‟s research

(Source: Gouvenot and Gabaix, 1975)

1.3 Objective and Scope of Research

1.3.1 Objectives of the Study

General Objectives

To evaluate the effectiveness of the shaft grouting method in increasing shaft resistance of very long bored piles (drilled shafts) and barrettes in Ho Chi Minh and to suggest appropriate correlations of unit shaft resistance of shaft-grouted piles for

practical design

Specific Objectives:

1 To determine correlations between ultimate unit shaft resistance (ru) and some

parameters such as the corrected SPT N value (N60) and the effective vertical stress

(ζv) for shaft-grouted and not grouted piles in geological conditions at HCMC

2 To determine soil types that are appropriate for applying the shaft grouting method with consideration of the cost-effectiveness

3 To perform a comparative analysis on-resistance of shorter shaft-grouted piles with longer not grouted ones under the same diameters and geological conditions

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1.3.2 Scope of the Study

To obtain the objectives above, this study focuses on the following:

1 Collect existing data in the literature and data from experiments of the supervisor‟s research program in Ho Chi Minh city

2 Perform analytical analyses to obtain the expected outcomes

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CHAPTER 2 LITERATURE REVIEW

2.1 Principle of the Shaft Grouting Technology

The Shaft Grouting technology is the technology solution with the aim to enhance shaft resistance along with the pile The method applied to bored piles and barrettes is similar to the drilled shaft installation but the new method adds injection high-pressure grout after pouring concrete into the borehole within 24 hours The component of the modern grouting system is 50 mm diameter mild steel “Tube à manchettes” pile or called grouting tubes, with manchettes (prefabricated holes) spaced at 1m intervals along with the pile The grouting tubes are attached to the outside of the steel cage by using normal tie wire within the zone of the concrete cover Grouting tubes were generally arranged around the perimeter of the bored piles and barrettes pile as well as tubes extended the full depth of the shaft grout zone Water and grout were injected at

a grouting point by boring/pushing machine

2.1.1 Grout Materials and Equipment

The mixing for grout must ensure flexibility, good viscosity, homogenous It consists

of cement, water, and bentonite which was mixed with proportions as follows:

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In the steel cage was attached the grouting tubes (Tube A Manchette) were equispaced

around the perimeter of piles The grouting tubes consist of mild steel tubes 49-60 mm

external diameters covered by rubber sleeve (one-way valve) which is pre-drilled with

the distance between sleeve from 0.5-1.0 m and 1.0 m from the bottom of the pile

Detail Packer

Figure 2.1 Detail of Tube a manchette (Source: Nicholson, P.G, 2014)

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Figure 2.2 The land view in the grouting process

Figure 2.3 Simulate the grout affected area and the grout section cross

(Source: Sze and Chan, 2012)

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Figure 2.5 The grouting machine

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2.1.2 Construction Procedure

The construction procedure of shaft grouting pile is similar to the construction procedure of drill shaft pile, however the construction process of shaft grouting pile adds two steps: water cracking and shaft grouting The large diameter bored piles and barrettes piles were manufactured by excavating ground through a rotary drilling equipment and rope grab with bentonite and polymer slurry The bentonite and polymer slurry was used to support and stabilize the hole walls The polymer slurry has litter effect on the shaft resistance of pile on some formations but was found a noticeable effect on the other formations when compared with bentonite (Lam.C.et al, 2015) After drilling the designed depth, the reinforcing cages were fabricated

Figure 2.6 The process to construct the shaft grouted bored pile, barrettes pile Grout tubes will be drilled, which are covered by 1 rubber sleeve per 1.0 meter will

be installed on the steel cage prior to an installation called machette After cleaning of drilling hole, rebar cages were installed and concrete was poured The rubber sleeves

of the grout tubes will be opened with water under pressure from 5 to 24 hours after concreting of mass pilings and records will be kept in order to show which sleeves have been successfully “opened” and at what level pressure Shaft grouting work for certain piles will be arranged at least 5 days after concreting time of this pile Figure 2.7 shown for each test pile the location of the strain gauge attached to the reinforcing cages For example, each gage level of PTP1-Saigon center‟s barrettes pile contained two diametrically opposed pairs, gauge A and B, gauge C and D respectively but because of the rectangular shape of the barrettes, the pair did not cover equal areas of the barrette cross-section Each gage level of TP2-Songviet‟s project bored pile

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contained three gage A, B & C which is located in symmetric figure 2.8 The actual placement indicates a quasi-symmetry across the barrette and bored pile center for the gage pairs as placed

a) Saigon center project b) Song Viet project

Figure 2.7 Details of grouting and instrumentation of Saigon and Song Viet project

a) Saigon center project b) Song Viet project

Figure 2.8 Cross-section and layout of instrumentation

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Figure 2.9 The process of water cracking (a) and shaft grouting (b)

Figure 2.10 Illustration diagram of the grout pipe cross-section, flows paths, the

section of the grouted sample

In the water cracking step, the manchette is opened with water under pressure (min

1000 kN/m2- max: 4000 kN/m2) to make flow paths in concrete cover In the first place, the double packer was inserted into the grouting tube at the bottom of the tube The packer was inflated and water was inflected with high pressure to make the crack through the concrete cover This part was carried out within 24 hours after pouring concrete to avoid concrete reaching hardened concrete In the second step, the cement grout was inflected into the grout tube sequentially from the bottom of the tube to the highest manchette position and make the grout zone into the soil Each tube will be grouted by using a grout pump, until the stop with conditions as follow: First, the shaft grout zone is to be measured from 500 mm above the 1st manchette to 500 mm below

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the bottom manchette with target grout volume per manchette is 35 litres/m2 If the target grout volume is not achieved, the side pile will be injected with additional grout

to ensure that the overall minimum average grout takes for mass pilling is greater than

25 liters/m2 The limiting pressure shall be set at 40 bar (4.0 Mpa) or resurgence (grout flowing back up to the surface) is identified

2.2 Existing Studies on Shaft-Grouted Piles

There are a variety of replacement piles that are put into holes dug or augured out of the earth namely: bored piles, barrettes pile, pre-bore H-pile…Most of these pile capacity is assumption generated from tip bearing friction and rock socket friction when the tip pile lay on bedrock However, in some cases the pile lies in the soil and the pile bearing capacity is generated from friction between soil and pile shaft called shaft friction So, the shaft grouting was found to enhance the shaft friction capacity of these piles Many research proves that the friction capacity of the grouted pile is large than 2 to 3 times plain pile (not grouted pile) (Gouvenot and Gabaix, 1975) was first published in 1975 their finding with six shaft grouted piles D660 mm testing in clay, sand that grouted pile increase in shaft friction of 2.5 times the capacity of the normal pile This result was represented from plot correlation QL/QLo, QL is the ultimate bearing capacity after pressure grouting, QLo is bearing capacity before grouting Between 1975 and 1985, Bruce refers to 300 shaft grouted piles of the Jeddah-Mecca Expressway By the way, comparison the grouted pile and not grouted pile through static load test on the same site, same length The article presents the advantage of post grouting both shaft and toe friction that grouting permits increased working load to be utilized Similar the research topic, (Stocker, 1983) arranged grouting for toe and shaft parts The results showed a permanent increase in shaft friction of 1.5 to 3 times that of plain piles in granular soil and cohesive soil However, the limitation of these studies

is that the calculation with the point which did not reach the ultimate statement or

passed the ultimate statement and the SPT-N index is all raw data, leading to

inaccurate results

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Figure 2.11 Variation of gain in load with injection

(Source: Gouvenot and Gabaix, 1975)

(a) Detail of shaft and toe grouting

(b) Skin friction of cast-in-situ bored pile (at a settlement of 10mm) and anchors in non-cohesive

soil Figure 2.12 The Stocker‟s research result

(Source: Stocker, 1983)

A testing program with six piles of large-scale deep foundation carried out for the Kowloon- Canton Railway Corporation, Hong Kong reported by Littlechild (2000), showed shaft friction capacity measured for shaft grouted bore piles and barrettes

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uncorrected mean blow count of SPT It can be seen the frictional capacity of the pile

using the shaft grouting technique can be improved by 2 to 3 times of values attained

by the plain pile Almost the analysis depends on the average SPT-N value or uncorrected mean blow count of SPT leading to inaccurate results

Figure 2.13 The comparison mobilized friction value between the grouted pile and

plain pile tests in Hong Kong (Source: Littlechild, 2000)

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Table 2.1 Summary of typical design parameters following author‟s experience

(Source: Sze and Chan, 2012)

In Vietnam, shaft grouting is developing extensively especially in Ho Chi Minh city However, the technology follows the basic research of (Phan and Pham, 2013) The

research focuses on finding the correlation between shaft resistance (rs) and the mean

SPT-N value to comparing shaft grouted pile and plain pile The research has been

downside from raw SPT-N value data and the value rs was still increasing (not fully mobilized- not ultimate) because all test piles did not fail under applied load An experimental test reported by (Nguyen et al, 2019) showed the correlation between

ultimate unit shaft resistance (ru) with the SPT-N 60 value estimated that the ru value of grouted pile was two times larger than the plain pile for both sandy and clayey soil

Besides, the author emphasized that ru values obtained from β-method recommended

applying well in practice

Figure 2.14 Summary the mobilized shaft resistances of clayey soil (a) and

sandy soil (b) versus N value (Source: Phan and Pham, 2013)

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2.3 Theory for Calculate Bearing Capacity of Drill shaft

2.3.1 Method of FHWA (FHWA-NHI-10-016)

The ultimate bearing capacity of pile have two component side resistance Rs and base

(tip) resistance Rb

∑ ∑

RS,i = nominal side resistance for layer i

ψS,i = resistance factor for side resistance in layer i

n = number of layers providing side resistance,

RB = nominal base resistance

B = resistance factor for base resistance

In layered soil profiles, the total (ultimate) shaft resistance of a pile is calculated as:

∫ ( 2.2)

where

Cs= circumference of pile at depth z For circular pile Cs = πD, for square piles Cs =

4D;

δ = effective stress angle of friction for the soil shaft interface;

D = shaft diameter/ length of square;

zi = thickness of layers i; rs : nominal unit side resistance

K = coefficent of horizontal soil stress (K=ζʹh/ζʹv)

ζʹv = average vertical effective stress over the depth interval z;

ζʹh = horizontal effective stress

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Figure 2.15 Idealized layering for computation of compression resistances

(Source: FHWA-NHI-10-016 Drilled shafts)

Figure 2.16 Frictional model of unit side resistance for drilled shaft

(Source: FHWA-NHI-10-016 Drilled shafts) For convenience:

β = Ktanδ; rs = ζʹv β (2.3)

where β: side resistance coefficient (beta method)

Nominal base resistance is calculated as:

Abase = the cross-sectional area of bearing at the shaft base

qBN = the unit base resistance

2.3.2 Method of Vietnam Standard (TCVN10304-2014)

The allowable capacity for drill shaft follow Architecture institute of Japanese (AIJ):

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rs = nominal unit side resistance

ζʹv = average vertical effective stress over the depth interval z

The unit average shaft resistance in sandy soil layer i

cu,i = undrained shear strength for clayey soil layer i:

fL= the coefficient depends on the ratio h/d (length/diameter) of pile

and with drill shaft fL = 1

p = the coefficient base on the ratio between undrained shear strength and average effective stress, which determined below plot:

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Figure 2.17 The diagram to evaluate p coefficient

(Source: TCVN10304-2014)

Ns,i = the average SPT index in sandy soil layer i

ls,i = length of pile in sandy soil layer i

lc,i = length of pile in clayey soil layer i

2.4 Theory for Converting Strain to Load

Following the Red book (Fellenius, 2020) the strain gauge from the pile provide the value of strain (not load) The measured strains are transferred to load by use of the modulus of the pile material and of the pile cross-sectional area For steel pile, modulus of steel is constant value accurately (20,5x104 MPa) However, the modulus

of the concrete pile not only does range widely but also is a function of the applied stress and strain It is a function of the amount of imposed load, or better stated, of the imposed strain, reducing with increasing stress or strain When the piles have applied load, the plot load- movement follow a curve not a straight line From (Fellenius, 1989) the stress-strain curve can with sufficient accuracy be assumed to follow a second-degree line:

y = ax2+bx+c, where y(stress), x(strain)

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