i

EXPERIMENTAL AND ANALYTICAL INVESTIGATIONS ON

SKIN FRICTION AND END BEARING RESISTANCE OF SINGLE PILE

MD. HASINUR RAHMAN

MASTER OF SCIENCE IN ENGINEERING

(CIVIL & GEOTECHNICAL)

DEPARTMENT OF CIVIL ENGINEERING

BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY

DHAKA, BANGLADESH

DECEMBER 2016

i

EXPERIMENTAL AND ANALYTICAL INVESTIGATIONS ON

SKIN FRICTION AND END BEARING RESISTANCE OF SINGLE PILE

A Thesis

By

Md. Hasinur Rahman

Submitted to the department of Civil Engineering, Bangladesh University of Engineering and Technology

in partial fulfillment of the requirements for the degree of

MASTER OF SCIENCE IN CIVIL ENGINEERING

(CIVIL & GEOTECHNICAL)

DEPARTMENT OF CIVIL ENGINEERING

BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY

DHAKA, BANGLADESH

DECEMBER 2016

ii

iii

iv

DEDICATION

This thesis is dedicated to my parents

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TABLE OF CONTENTS

Page

Title Page i Declaration iii

Dedication iv

Table of Contents v

Acknowledgement viii

Abstract ix

List of Tables xi

List of Figures xii

Notations xv

CHAPTER ONE INTRODUCTION

1.1 General 1

1.2 Objectives of This Study 2

1.3 Outline of Methodology 2

CHAPTER TWO LITERATURE REVIEW

2.1 General 4

2.2 Pile Foundations 4

2.3 Load Transfer Mechanism 5

2.4 Piles in sand 7

2.5 Load Capacity 7

2.6 End Bearing Capacity 8

2.7 Shaft Capacity 17

vi

2.8 Elastic Settlement of Pile Shaft 18

2.9 Allowable Capacity 19

2.10 Static Capacity Using Load- Transfer Load- Test Data. 19

CHAPTER THREE EXPERIMENTAL SETUP

3.1 General 23

3.2 Load Cell Arrangement for Measuring End Resistance 23

3.3 Preparation of Model Concrete Pile 26

3.4 Wooden Box for Model Ground Preparation 31

3.5 Reaction Frame 33

3.6 Spring for Measuring End Resistance 35

3.7 Loading System 36

3.8 Test Procedure 37

3.9 Model Test Schedule 42

CHAPTER FOUR PROCEDURE FOR SEPARATION OF SKIN FRICTION

AND END BEARING AND COMPARISION WITH

MODEL TEST RESULTS

4.1 General 43

4.2 Properties of Sand Used for Model Ground 43

4.3 Static Load Test on Model Concrete Piles 50

4.4 Pile Material Properties Used in Analytical Method 50

4.5 Analytical Method for Separation of Skin Friction and End 51 Bearing

4.6 Effect of Spring in Load-Displacement Response 54

4.7 Result from Model Test 57

vii

4.8 Comparison of Result obtained from Model Tests and Analytical 59 Method

CHAPTER FIVE SUMMARY AND CONCLUSIONS

5.1 Summery 66

5.2 Conclusions 66

5.3 Limitation of the thesis 67

3.4 Recommendation for Future Research 67

REFERENCES 68

APPENDIX-A COMPUTER PROGRAM 71

APPENDIX-B DATA SHEET 79

viii

ACKNOWLEDGEMENT

First, I want to express my deep gratitude to The Almighty and Omnipotent Allah to

enable me to perform this research work.

I am extremely delighted to have the opportunity to explicate my cordial gratitude to

my supervisor Dr. Sarwar Jahan Md. Yasin, Professor, Department of Civil

Engineering, Bangladesh University of Engineering and Technology (BUET), for his

overall supervision, invaluable suggestion and ardent encouragement in every aspect

of my thesis work. His constant guidance, persuasion and above all constructive

criticism helped me immensely to complete the work in time. I want to express my

indebtedness to him for his superbly technical expertise, impromptu answers and

solution to numerous problems.

I am grateful to technical staff of the geotechnical laboratory of BUET for their

continual assistance in laboratory works.

At last, I want to thank my parents, who have provided continuous encouragement,

inspiration and support to me throughout this research project.

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ABSTRACT

In this thesis work, an analytical method is established to separate skin frictional

resistance and end bearing components for a given load on a pile. The method is

based on static load-settlement data and direct shear test data. Three numbers of

model piles of diameter 50 mm, 75 mm and 100 mm, each of length 1000 mm, are

used for laboratory model tests. Each pile is cast in a hole made in a clay soil layer.

This is done to get rough surface of the piles. A wooden box is used to prepare model

ground in the laboratory. The box is 915 mm x 915 mm in cross section and 1676 mm

in height. A reaction frame (consisting of box section, C-channel and rod) is made to

apply load to the test pile using a hydraulic jack. A load cell arrangement with display

monitor is made to measure the pile end resistance directly when a static load is

applied on a model pile. To get pile end force, two springs (one with low stiffness and

the other with relatively high stiffness) are used in the tests. The spring is placed just

below the pile and rested on top of the load cell. Also tests are performed without

spring beneath the pile bottom in which case the pile rested on sand. Pile end bearing

and settlement are recorded when spring is used and these end bearing and settlement

are used as reference to separate end bearing and skin frictional resistance when

spring is not used. The proposed analytical method is based on the mobilized friction

angle. For any given displacement the mobilized friction angle is obtained from a

polynomial equation fitted to the τ/σ vs ε curve as obtained in a direct shear test. The

results of analytical method are compared with those obtained from model tests. The

end bearing for 50 mm, 75 mm and 100 mm diameter piles obtained in model are

found to be respectively 34%, 42% and 28% higher than the end bearing obtained by

the analytical method. However, the skin resistance from analytical method for 50

mm, 75 mm and 100 mm diameter piles are found to be respectively 29%, 33% and

28% larger than the model test values.

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LIST OF TABLES

Table 2.1 Terzaghi (1943) shape factors for various foundations 11

Table 3.1 Reinforcement for rebar cage of model concrete pile 26

Table 3.2 Different end conditions and measurements in the model tests 42

Table 4.1 Properties of the selected sand used in the study 44

Table 4.2 Conditions of shear test specimens 46

Table 4.3 Modulus of Elasticity of Various Soils (Das, 2009) 51

Table 4.4 Comparisons of load on pile head at selected displacement levels

for the 50 mm diameter pile with different end conditions 56

Table 4.5 Comparison between model test and analytical end resistance 63

(50 mm diameter pile) Table 4.6 Comparison between model test and analytical end resistance 63

(75 mm diameter pile)

Table 4.7 Comparison between model test and analytical end resistance 64

(100 mm diameter pile)

Table 4.8 Comparison between model test and analytical skin resistance 64

(50 mm diameter pile)

Table 4.9 Comparison between model test and analytical skin resistance 64

(75 mm diameter pile)

Table 4.10 Comparison between model test and analytical skin resistance 65

(100 mm diameter pile)

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LIST OF FIGURES

Figure 2.1 Typical pile configuration based on pile load carrying capacity 5 (a) end bearing pile, (b) friction pile, (c) compaction pile (modified after Madabhushi et al., 2010). Figure 2.2 General load distribution of a pile. (Das, 2009). 6

Figure 2.3 Ultimate load distribution of pile. (Das,2009). 6

Figure 2.4 Failure surface at pile tip.(Das,2009). 7

Figure 2.5 Bearing capacity failure pattern around the pile tip assumed 9

by Terzaghi (1943)

Figure 2.6 Bearing capacity factors (data from Bowles 1996). 11 Figure 2.7 Point bearing piles. 12 Figure 2.8 Nature of variation of unit point resistance in homogeneous sand. 12 Figure 2.9 Variation of the maximum values of Nq

* with soil friction 13 angle φ’(Meyerhof,1976) Figure 2.10 Bearing capacity factors (data from Bowles 1996) 15

Figure 2.11 Bearing capacity failure pattern around the pile tip assumed 16

by Janbu (1976)

Figure 2.12 Bearing capacity factors (data from Bowles 1996). 16

Figure 2.13 Unit frictional resistance for piles in sand 17 Figure 2.14 A numerical model for an axially loaded pile. 22 Figure 3.1 Load cell arrangement to record pile end load.(a) Schematic 25 diagram of arrangement of component (b) Load cell (c) Display monitor(d) Load cell assembly Figure 3.2 Load cell arrangement calibration. 26 Figure 3.3 Model pile (a) pile cross section (b) pile rebar cage 27 Figure 3.4 Cylindrical hole preparation in clay soil (a) MS pipe (b) pipe driving 28 (c) pipe pull out by lever (d) cylindrical hole

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Figure 3.5 Pile casting.(a) cage in bore hole (b) temping with 10 mm rod 29

Figure 3.6 Piles after pull out from bore hole. 29 Figure 3.7 Piles before model test. 30 Figure 3.8 Part of wooden box. (a) base (b) vertical four sides 32 (c)full box with horizontal ties. Figure 3.9 Reaction frame. (a) base of reaction frame(in plan) (b) & (c) various 34 parts of reaction frame. Figure 3.10 Load- deflection response of spring in incremental load test. 35 Figure 3.11 Test set up to determine end resistance(a)reaction beam and 38~39 proving ring(b) box bottom (c) load cell and MS plate placed (d) small box placed(e) spring placed(f) 127 mm pipe and 10mm circular plate(g) circular hollow MS and pile(h) hydraulic jack (j) vertical four sides(k) wooden plank and deformation dial gauge. Figure 3.12 Schematic Diagram of the Model Pile Test Setup. 41 Figure 4.1 Grain Size Distribution of Sand. 44 Figure 4.2 Shear stress vs shear displacement curve from direct shear 46

test on the sand used for model ground preparation. Figure 4.3 Shear displacemnt vs normal displacement curve from direct 47

shear test on the sand used for model ground preparation.

Figure 4.4 τ/σ vs shear displacement curve for σ=9.3 kPa from direct shear 47

test on sand.

Figure 4.5 τ/σ vs shear displacement curve for σ=18.6 kPa from direct shear 48

test on sand.

Figure 4.6 τ/σ vs shear displacement curve for σ=27.9 kPa from direct shear 48

test on sand.

Figure 4.7 τ/σ vs shear displacement average curve from tests at normal 49 stress on sand. Figure 4.8 τ/σ vs shear displacement curve for three different normal stress 49 and the average curve from direct test on sand.

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Figure 4.9 Shear stress at failure versus normal stress in direct shear test on sand.50 Figure 4.10 Force on each segment of pile 52 Figure 4.11 Load –displacement response in static model test on 55 different end condition for 50 mm diameter pile. Figure 4.12 Load –displacement response in static model test on 55 different end condition for 75 mm diameter pile. Figure 4.13 Load –displacement response in static model test on 56 different end condition for 100 mm diameter pile. Figure 4.14 Load – displacement response for 50 mm diameter pile 57 used softer spring under pile. Figure 4.15 Load – displacement response for 75 mm diameter pile 58 used softer spring under pile. Figure 4.16 Load – displacement response for 100 mm diameter pile 58 used softer spring under pile. Figure 4.17 End resistance – displacement response for 50 mm diameter pile. 60 Figure 4.18 End resistance – displacement response for 75 mm diameter pile. 60 Figure 4.19 End resistance – displacement response for 100 mm diameter pile. 61 Figure 4.20 Skin resistance – displacement response for 50 mm diameter pile. 61 Figure 4.21 Skin resistance – displacement response for 75 mm diameter pile. 62 Figure 4.22 Skin resistance – displacement response for 100 mm diameter pile. 62

xiv

NOTATIONS

Ab Pile base area c' Soil cohesion γ Total unit weight

Nc, Nq, Nγ Bearing capacity factor sc and sγ Shape factor.

q′ Effective vertical stress

φ′

Effective soil friction angle

P Perimeter of the pile section F Unit friction resistance

Qs Skin frictional resistance

K Effective earth pressure coefficient

AP Area of cross section of pile

EP Modulus of elasticity of the pile material

DS Pile diameter

Υ Poisson’s ratio

f1 Standard settlement reduction factor

Iws Influence factor

FS Factor of safety

Cu Coefficient of uniformity Cc Coefficient of curvature Gs Specific gravity σ Normal stress τ Shear stress δ Soil-pile friction angle

1

CHAPTER ONE

INTRODUCTION

1.1 General

An axially loaded pile usually derives its capacity in combination of skin resistance

and end resistance (Bowles, 1988). Thus, in conventional pile design, 'ultimate pile

capacity' is calculated as the sum of 'ultimate skin resistance' and 'ultimate end

resistance'. Allowable load is then determined as 'pile ultimate capacity' divided by

'overall Factor of Safety (FS)' or 'ultimate skin resistance' divided by a FS plus

'ultimate end resistance' divided by a separate FS. However, in static compression

'ultimate pile capacity' is not the linear sum of the 'ultimate skin resistance' and the

'ultimate end resistance'. In reality, ultimate skin resistance is produced at a small

value of relative slip (or pile settlement) between pile and soil whereas ultimate end

resistance is mobilized at a large value of relative slip (Bowles, 1988).

The most reliable method to determine the static load carrying capacity of a pile is the

load test (Morshed, 1991). The detailed load-deformation data obtained from the test

allows more efficient design by reducing the overall-FS through better understanding

of the site-specific properties (Bowles, 1988) but it does not give any idea about skin

friction and end bearing components.

Different codes and practicing engineers suggest various FS to different pile

conditions. For piles up to 600 mm diameter, an overall-FS and for piles larger than

600 mm diameter partial-FS to the ultimate base resistance and shaft resistance are

common (Tomlison, 1993). Use of overall-FS leads to more uncertainties for end

bearing piles but conservative estimates and higher project cost for friction piles (Das,

2009). Generally the global factor of safety ranges from 2.5 to 4.0 (Das, 2009) and

there is scope of cost reduction by applying separate FS for skin resistance and end

bearing.

In order to apply separate FS for skin and end resistance capacity, it is necessary to

determine these components. The static capacity and settlement of a pile can be back

analyzed from load transfer data obtained with strain gages and / or telltales (Bowles,

2

1988). These methods are cumbersome and time consuming. There are some limited

researches to separate the skin friction and end bearing components of static pile

capacity back computed from load transfer data (Fleming, 1992).

From the above discussions, it is revealed that estimation of skin friction and end

bearing and use of partial factor of safety may be desirable in many instances. In this

thesis, a methodology will be established to determine skin friction and end bearing

from pile static load test and the methodology will be verified by model test in sand.

1.2 Objectives of This Study

This research attempted to focus on the following objectives:

a. Establish an analytical method to separate the skin friction and end resistance

components for a given load from static load test data.

b. Conduct static model tests in the laboratory using model concrete piles

embedded in uniform sand deposit with measurement of skin friction and end

resistance.

c. Verify the proposed analytical method using model test results.

1.3 Outline of Methodology

a) An analytical method is established to separate skin resistance and end bearing

components for a given load on a pile. The method is based on static load-

settlement data and direct shear test data.

b) Direct shear tests is performed on collected sand to obtain its stress-strain

characteristics.

c) Axial load tests is conducted in the laboratory on model concrete piles of

length 1000 mm and three different diameters (50 mm, 75 mm, 100 mm). The

piles are embedded in uniform sand deposits (prepared in a test bin) with and

without a spring placed directly beneath the pile. Thus, end bearing for

different settlement of pile head is directly measured.

3

d) Estimation of skin friction and end bearing for the model piles are made using

the proposed analytical method. The results of analytical method are compared

with those obtained from model tests.

4

CHAPTER TWO

LITERATURE REVIEW

2.1 General

This research attempts to find an analytical method that will enable separation of skin

resistance and end bearing components for a given load on a pile. The method will be

based on static load-settlement data and direct shear test data. To separate skin

resistance and end bearing components of a pile, need to load transfer mechanism and

parameters governing the load carrying of pile is very important. Relevant

information from literature review is presented in this chapter.

2.2 Pile Foundations

Pile foundations are commonly used in engineering practice to carry the loads from

heavy structures such as multi-storied buildings, bridges, highways, embankments, to

the underlying soil safely without stability or settlement problems. Piles are used in

situations when the bearing capacity of soil is low, proper bearing stratum is not

available at shallow depth and shallow foundations are not practical or economical.

Extensive growth of offshore energy resources and development of high-rise

structures, highlight the need for using pile foundations with higher capacities and

deeper penetrations. (Chandrasekaran et al. 1978, Bowles 1996, Katzenbach et al.

2000, Overy 2007, Madabhushi et al. 2010, Doherty and Gavin 2011).

Pile foundations can be classified by different criteria such as pile material (i.e., steel,

reinforced concrete piles, or wood), method of installation (i.e., driven, jacketed or

bored piles), and load carrying mechanism of the pile. Based on the load carrying

mechanism, piles can be categorized as follows:

• End bearing piles: pile end resistance plays significant role in this group to

transfer the load of superstructure through the water or weaker soils to strong

stratum.

5

• Friction piles: vertical distribution of the superstructure load to the lower stratum

by means of pile shaft friction which is sometimes called as floating piles.

• Compaction piles: rather than load carrying approach, piles can be used to

compact the soil. Through using these piles the loose, granular soil would

become denser. Normally a steel tube is derived into the ground which replaces

the tubular volume by forming a sand pile from granular materials.

• Tension piles: in case of superstructures which are subjected to lateral loads such

as wind, wave, and earthquake, these pile can be utilized to neutralize the pull-

out forces.

Fig. 2.1 illustrates different pile types based on pile load carrying mechanism.

Fig. 2.1 Typical pile configuration based on pile load carrying capacity (a) end

bearing pile, (b) friction pile, (c) compaction pile (modified after Madabhushi et al., 2010)

2.3 Load Transfer Mechanism

The load transfer mechanism from a pile to the soil is complicated.

If the load on the pile is gradually increased at the ground surface, the pile and

surrounding soil is deformed and the soil pile interface is stressed. Part of this load is

6

resisted by the side friction developed along the shaft and part by the soil below the

tip of the pile (Das, 2009). General load distribution of a pile is shown in Fig.2.2.

Q

Q1

Q2

Fig. 2.2 General load distribution of a pile (Das, 2009)

If the load Q on pile top is gradually increased maximum frictional resistance (Qs)

along the pile shaft is fully mobilized when the relative displacement between the soil

and the pile is about 5 to 10 mm, irrespective of the pile size diameter length. But the

maximum point resistance (QP) is not mobilized until the tip of the pile has moved

about 10% to 25% of the pile width (diameter). The lower limit is applicable to driven

pile and the upper limit is applicable to bored pile. Distribution of ultimate load of

pile is shown in Fig.2.3. This explanation indicates that QS is developed at a much

smaller pile displacement compared with the point resistance, QP.

Fig. 2.3 Ultimate load distribution of pile (Das, 2009)

7

Pile foundations are deep foundations and the failure surface at ultimate load in the

soil at the pile tip (a bearing capacity failure caused by QP) is like that shown in

Figure 2.4. The triangular zone, , is developed at the pile tip,which is pushed

downward without producing any other visible slip surface. In dense sands and stiff

clayey soils, a radial shear zone, , is partially developed.

Fig. 2.4 Failure surface at pile tip (Das,2009)

2.4 Piles in Sand

It is well known in the literature that the pile base bearing capacity contribution of

single piles is dominant in sandy type of soils in comparison with the shaft carrying

capacity (Miura 1983, Yasufuku and Hyde 1995, Ohno and Sawada 1999, Manandhar

and Yasufuku 2012). Determination of the independent contribution of base resistance

of single pile from field tests is difficult. Due to this reason, it will be valuable to

provide an analytical approach to separate skin friction and end bearing resistance of

single pile in sands.

2.5 Load Capacity

The single piles ultimate carrying capacity can be estimated from the combined

contribution of the shaft and base resistance. The axial load capacity of a single pile is

typically expressed using the relationship below:

( 2.1)

where, Qu = single pile ultimate bearing capacity

Qb = pile base resistance

Sbu QQQ

8

Qs = shaft friction resistance of the pile

2.6 End Bearing Capacity

The analytical approach to analyze and estimate the static pile bearing capacity was

investigated by several investigators (Terzaghi 1943).Their work was mainly based on

failure mechanism for single pile foundations which has established a benchmark for

future works (Chandrasekaran et al., 1978). Following the same approach, several

different solutions were proposed by various researchers (Meyerhof 1951, Hansen

1970, Janbu 1976, Vesic 1977, Coyle and Castello 1981). In this section some of the

conventional methods proposed for estimation of single pile base capacity are briefly

reviewed.

Method Proposed by Terzaghi (1943)

Terzaghi (1943) proposed a method for determining the bearing capacity of shallow

foundation which can be extended for estimation of the pile base resistance. Figure

2.5 illustrates the proposed bearing capacity failure pattern around the pile tip. The

soil above the pile base is assumed as an equivalent surcharge, q. The shear strength

of the overburden soil is ignored and its weight is only considered. This failure

mechanism indicates the downward movement of the volume I and consequently

displacement of soil outward and upward (i.e., volume II, III, II', and III') with the

failure surfaces ending at the pile tip level.

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Fig. 2.5 Bearing capacity failure pattern around the pile tip assumed by Terzaghi

(1943)

The soil mass is divided by two planes into three zones with different shear patterns.

The plane ad inclines toward the left at an angle of α (i.e., α = 45◦ - ϕ/2) to the

horizontal line and the other plane ac toward the right at an angle of 45◦ + ϕ/2. The

zone (I) indicate the active Rankine state and also zones (III) and (III') represent the

passive Rankine state. The two active and passive Rankine zones are divided by a

zone of radial shear.

The general form of Terzaghi (1943) equation for estimating the base bearing capacity

of single piles is a superposition of influence of soil cohesion, c', overburden pressure,

q, and the soil unit weight, γ, which is determined using limit equilibrium (Zhu and

Michalowski, 2005) method and is given as below:

(2.2) )

21( /

sBNNqsNcAQ qccbb

10

where, Ab = pile base area, c' = soil cohesion, q = surcharge load, γ = total unit weight

of soil, B = pile diameter, Nc, Nq, and Nγ = bearing capacity factors, sc and sγ = shape

factors.

The bearing capacity factors can be estimated using the following relationships:

245cos

aN2

q

(2.3)

1)cot(NN qc (2.4)

1)cos

k(

2tanN 2

pyγ

(2.5)

Where, a = a coefficient related to the internal angle of friction,

Figure 2.6 expresses the relationship between the bearing capacity factors and the

angle of internal friction angle, ϕ'. The bearing capacity factors Nc and Nq have been

calculated using analytical method assuming the soil weightless by various

investigators (Terzaghi 1943, Meyerhof 1951, Vesic 1973). These studies estimate the

bearing capacity factors Nc and Nq with small differences and approximately the

same. However, there is a large scatter in estimated values of the bearing capacity

factor Nγ by different researchers, which highlights the analytical uncertainty

associated with this parameter (Ukritchon et al., 2003).

The shape factors used in Terzaghi (1943) equation are defined in Table 2.1. These

shape factors were proposed based on empirical or semi-empirical considerations

using the test data of Golder et al. (1941). These shape factors are introduced as shape

modifiers to convert the bearing capacity factors from plain strain to axisymmetric

conditions.

11

Fig. 2.6 Bearing capacity factors (Bowles 1996)

Table 2.1 Terzaghi (1943) shape factors for various foundations

Terzaghi (1943) did not take into account the contribution of matric suction towards

the bearing capacity of soils; hence, using the conventional method will be

conservative for soils that are in a state of unsaturated conditions.

Method Proposed by Meyerhof (1976)

Meyerhof (1976) proposed a method for determining the bearing capacity of pile

foundation which can be extended for estimation of the pile base resistance. Meyerhof

noticed that the unit point resistance, qp, of a pile in sand generally increase with the

depth of embedment in the bearing stratum and reaches a maximum value at an

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embedment ratio of Lb/D=(Lb/D)cr where, D=pile diameter and Lb =depth of

penetration into bearing stratum. In a homogeneous soil Lb is equal to the actual

embedment length of the pile, L (Figure 2.3). Where a pile has penetrated into a

bearing stratum, Lb<L ( Figure 2.7). Beyond the critical embedment ratio, (Lb/D)cr, the

value of qp remains constant (qp=ql). The variation of qp with L/D is shown in Figure

2.8 for the case of a homogeneous soil, L=Lb.

Fig. 2.7 Point bearing piles.

UUHFI Unit point resistance

L/D=Lb/D

Fig.2.8 Nature of variation of unit point resistance in homogeneous sand.

13

According to Meyerhof’s method for sand, the pile tip resistance is given by:

*qpppp NqAqAQ

(2.6)

where, q = effective vertical stress at the level of the pile tip

Nq*= bearing capacity factors

The variation of Nq* with soil friction angle φ′ is shown in Fig. 2.9. The limiting value of APqp

is given below

lqANqAQ p*

qpp (2.7)

The Limiting point resistance is

tanN0.5pq *qal (2.8)

where

pa = atmospheric pressure (100 KN/m2)

φ′ = effective soil friction angle of the bearing stratum.

Fig.2.9 Variation of the maximum values of Nq* with soil friction angle φ′ (Meyerhof,1976)

14

Method Proposed by Hansen (1970)

This method is an extension of the Meyerhof (1951) work on the effect of footing

base on bearing capacity. This method allows any D/B (i.e., embedment depth to

foundation diameter ratio) and consequently can be used for both shallow and deep

foundations. Hansen (1970) proposed that all the loads applying on the foundation are

combined into one resultant with two components: (і) V, which is normal to the base

of the foundation and (іі) H, which is in the base. The intersection of these two

components is called load center. The general form of the equation proposed by

Hansen is:

(2.9)

The bearing capacity factors Nc , Nq′ and Nγ can be estimated using the equations as

below:

)2

(45taneN 2πtanq

(2.10)

1)cot(NN qc (2.11)

)1)tan(1.41.5(NN qγ (2.12)

The relationship between the bearing capacity factors and the angle of internal friction

is shown in Figure 2.10.

In order to calculate the depth factor (i.e., dc and dq) Hansen proposed the following

equations:

BD0.4tan1d

BD)2tansin(12tan1d

1c

1q

1{BD

(2.13)

where: D = pile embedment depth, B = pile diameter.

The Hansen (1970) method will be conservative for unsaturated soils.

BNdNqdcNAQ qqccbb 2

1

15

Method Proposed by Janbu (1976)

The failure mechanism proposed by Terzaghi (1943) leads to conservative results as

the assumed mechanism is not consistent with the actual ground movement

(Meyerhof, 1948). The height of the failure surface for deep foundation will not end at

the pile base level. Estimating the height of the failure surface with respect to pile

base level which indicates the level where the shearing strength of the soil is

mobilized becomes uncertain. In an attempt to alleviate this uncertainty, Janbu (1976)

extended the previous analysis of plastic equilibrium of a surface footing to deep

foundations. Figure 2.11 illustrates the failure mechanism proposed by Janbu (1976).

The zone of plastic equilibrium increases as a function of pile diameter from pile base

level up to a limiting height (usually 6 to10 pile diameter). The central zone ABC

below the pile base remains in an elastic state of equilibrium and acts as a part of the

foundation. Two other zones are generated at the ultimate bearing capacity, namely; a

radial shear zone, BCD, inclines toward the right at an angle of ψ (ψ varies from 60º

in soft compressible to 105º in dense soil) and a mixed shear zone, BDE, where the

shear changes between the limits of radial and plane shear. Janbu proposed the

following equation for single pile base resistance estimation

(2.14)

Fig. 2.10 Bearing capacity factors (data from Bowles 1996)

NBdNqdNcAQ qqccbb 2

1

16

The bearing capacity equation is of the same form as the Terzaghi (1943) equation;

however, the bearing capacity factors N'q and N'c are calculated using recommended ψ

values for different types of soil. The bearing capacity factor N'γ is same as Hansen

(1970) method. The variation of bearing capacity factors with the angle of internal

friction, φ', is shown in Figure 2.12.

Fig. 2.11 Bearing capacity failure pattern around the pile tip assumed by Janbu (1976)

Fig. 2.12 Bearing capacity factors (data from Bowles 1996).

17

2.7 Shaft Capacity

Meyerhof (1976) proposed that the pile shaft resistance is fully mobilized along the length of the pile-soil interface. The pile shaft capacity is commonly can be estimated as:

QS = ∑pΔLf (2.15)

where

P = perimeter of the pile section

ΔL= incremental pile length over which p and f are taken to be constant

F = unit friction resistance at any depth.

The nature of variation of f in the field is approximately as Fig.2.13.

Fig.2.13 Unit frictional resistance for piles in sand

The equation which was used in this research to calculate skin frictional resistance are given below:

Qs=Kσ′tan(0.8φ)pL (2.16)

Where, Qs = skin frictional resistance

K = effective earth pressure coefficient and for bore pile,K=(1-sinφ)

φ = angle of internal friction for any shear displacement.

P = pile perimeter

L = pile length within embedded soil.

18

2.8 Elastic Settlement of Pile Shaft

The total settlement of a pile under a vertical working load is given by

Se=Se(1)+Se(2)+Se(3) (2.17)

Where

Se(1)=elastic settlement of pile

Se(2)=settlement of pile caused by the load at the pile tip.

Se(3)=settlement of pile caused by the load transmitted along the pile shaft

For the elastic material, the deformation of the pile shaft can be evaluated in accordance with the fundamental principles of mechanics of materials, as

ppe EA

PLS )1( (2.18)

where

P = load carried by pile point under working load condition

L = length of pile

AP = area of cross section of pile

EP = modulus of elasticity of the pile material

The settlement of a circular pile caused by the load carried at the pile tip is commonly expressed as (Fleming, 1992)

12

BB

e(2) )fν(1DEq

4πS (2.19)

where

EB = modulus of elasticity of the soil below the pile point.

q = applied base pressure.

DB = pile diameter

υ = Poisson’s ratio=0.3

f1 = standard settlement reduction factor related to foundation depth=0.8

19

The settlement of a pile caused by the load carried by the pile shaft is expressed as below (Das, 2009):

ws2

S

wse(3) I )μ(1

ED

pLQS

(2.20)

where QWS = load carried by frictional(skin) resistance under working load condition P = perimeter of the pile Iws = influence factor

The influence factor, Iws has a simple empirical relation (Vesic,1977):

(2.21)

2.9 Allowable Capacity

After determination of ultimate capacity of a pile by summing the point bearing

capacity and the frictional resistance, a reasonable factor of safety should be used to

obtain the total allowable load for each pile. The general equation for allowable load

is given below:

FSQQ u

all (2.22)

where,

Qall = allowable load carrying capacity of each pile load carrying capacity of each pile load carrying capacity of each pile

FS = factor of safety

The range of general factor of safety used for pile foundation is 2.5 to 4.

2.10 Static Capacity Using Load- Transfer Load- Test Data

The static capacity and settlement of a pile can be back – computed from load transfer

data (Bowles, 1988). They are obtained from field tests on instrumented piles and

laboratory tests on model pile. The pile-capacity computation can be made by hand or

by computer (Coyle and Reese, 1966; Bowles, 1974). Only three to five pile segments

need in practical for hand calculations. Conceptually, the computation is based on the

numerical model (Bowles, 1982) shown in Fig. 2.14.

DL.3502Iws

20

This numerical procedure consists of the following steps.

1. The pile is divided into a number of segments considering stratified layers and

related load transfer curves as guides.

2. A small tip displacement ( zp) is assumed. 3. From this Zp ,the total tip resistance (Qp) is computed. Applying a soil spring

with a modulus of subgrade reaction Ks

psPp ZkAQ (2.23)

where PA = tip area of pile

Ks may also be estimated using suitable p-z (tip resistance) curve

4. The slip (average displacement) of the bottom segment is then computed.

Initially, zp is assumed as zero. From an appropriate t-z (shear resistance)

curve, the skin stress (t) corresponding to this Zp is obtained. Thus the axial

load at the top of the segment (segment 3) is obtained as:

333P3 t*P*LQQ ( 2.24)

Where Pi = perimeter of segment i

Li = length of segment i

Now the segment slip is computed using Eq.2.25 and a new skin stress is

obtained as:

33

33pP3 E2A

L*)Q(Qzz

(2.25)

Ai = cross sectional area of segment i.

Ei= modulus of elasticity of segment i.

5. The procedure is repeated until slip used and slip computed is in satisfactory convergence.

With convergence in the last segment, the procedure is continued to the next

segment (segment 2) above. Initially, the slip of the new segment is assumed to

be equal to the slip (Z3) of the last segment below. From this slip, the

corresponding skin stress is obtained and the pile load (Q2) at the top of the new

21

segment is computed. Now, the slip ( 2Z ) of the new segment is revised using

Eq. 2.26

22

23232 E2A

L*)Q(Qzz (2.26)

Again the procedure is repeated till suitable convergence is obtained. Thereafter, it is repeated on the next segment above and so on.

6. Finally , the ultimate pile load (at top of the top most segment) is obtained as:

iiiP10 tPLQQQ (2.27)

Q1= Q0

N1

22

L1

z1 t1

Q2

Q2

L2

z2 t2

Q3

Q3

L3

z3 t3

Qp

Fig.2.14. A numerical model for an axially loaded pile.

CHAPTER THREE

EXPERIMENTAL SETUP

3.1 General

N2

N2

23

This research work attempts to focus on the load-displacement response and separate

the skin frictional resistance and end bearing resistance of axially loaded pile in sand.

Model piles of three different diameters and under two different end conditions are

studied. Setup consisted of load cell arrangement, concrete piles (50 mm, 75 mm and

100 mm diameter), wooden box (915 mm by 915 mm in cross section and 1675 mm

in height to contain the model ground, hydraulic jack, deformation dial gauge,

proving ring etc. The components of the experimental setup are described below.

3.2 Load Cell Arrangement for Measuring End Resistance

A load cell arrangement was prepared to measure the pile end resistance directly

when a static load is applied on the model pile. A spring was used under pile bottom

to create soil like environment i.e to allow deformation/pile settlement. Actually the

stiffness of the load cell is quite high. So if the pile bottom is placed directly on the

load cell, then there would be small/negligible deformation/settlement of the pile

bottom. The load cell arrangement had four parts (Fig. 3.1):

a. Bottom frame

b. Top frame

c. Load cell

d. Monitor

The dimensions of bottom frame were 616 mm by 460 mm in cross section and it was

made using (38mm x 38mm x 5mm) steel. Additional two angles were provided at the

middle in the long direction. This size was chosen so that applied load can be easily

transferred to the base. A 10 mm thick steel plate was attached to the additional angles

that supported the load cell. The top frame was placed on the load cell. The outer

dimension of the top frame was (380 mm x 210mm) and was made of steel angle

(38mm x 38mm x 5mm). This dimension was chosen according to the diameter of the

largest model concrete pile and arrangement. The concrete pile rested directly on a

plate attached to the top of the spring. The spring was encased in a mild steel (MS)

pipe section. The diameter of the plate attached to the spring was such that it could

move vertically inside the MS pipe without significant friction. This arrangement was

necessary to keep the spring free from soil.

24

A load cell was used to make load cell arrangement. The load cell capacity was 15

kN. Load cell of this capacity was decided on the basis of analytical ultimate capacity

of the largest model pile.

A digital display monitor was connected to the load cell. To observe pile end force,

the display monitor was kept outside of wooden box when spring was used under the

pile bottom. The calibration curve is shown in Fig. 3.2 of the load cell, at any stage of

the test the load at pile tip could be obtained for the display.

Load cell Top frame

10 mm plate Bottom frame

25

(a)

(b)

(c)

Wire for display monitor 10mm plate Bottom frame Load cell Top frame

(d)

Fig. 3.1 Load cell arrangement to record pile end load (a) Schematic diagram of

arrangement of components (b) Load cell (c) Display monitor (d) Load cell assembly.

26

Fig. 3.2 Load cell arrangement calibration.

3.3 Preparation of Model Concrete Pile

Pile reinforcement/ Rebar cage

Three numbers of model concrete piles of diameter 50 mm, 75 mm and 100 mm were

used in this research work. Each pile length was 1000 mm. Rebar cages were made

for each pile using wire reinforcement. Different size of GI wires was used as bars

and ties and these are shown in table 3.1. Cross section and rebar cage of each pile is

shown in Fig 3.3.

Table 3.1 Reinforcement for rebar cage of model concrete pile

Sl. No

Model pile diameter (mm)

Main bar Spiral diameter (mm)

Spiral spacing (mm) Diameter

(mm) Nos.

01 50 3 4 2 50

02 75 5 4 2 50

03 100 5 4 2 50

27

(a)

(b)

Fig. 3.3 Model pile (a) pile cross section (b) pile rebar cage

Cylindrical Hole Preparation

A model pile was prepared by casting concrete in a cylindrical bore hole made in a

clay soil layer. This is done to get rough surface of the pile. An MS pipe of 75 mm

outer dia and SS pipes of 50 mm and 100 mm outer dia were used to make bore hole

for three sizes of model piles. A hammer was used to insert the pipes into the soil. A

10 mm thick circular plate was kept on top of the pipe to apply the hammer blow.

Initially bottom 1/3 of the pipe was driven into the soil by hammer blow. Then the

pipe was pulled out and both the hole and the pipe were cleaned. Then 2/3 of the pipe

rebar cage for 75 mm

pile

rebar cage for 50 mm

pile

rebar cage for 100 mm

pile

28

was driven in the same hole. It was again pulled out and cleaned. The same procedure

was followed in the 3rd stage to complete the hole. Finally the pipe was manually

pulled out from soil using a lever system. Hole preparation process is shown in

Fig.3.4

(a) (b)

(c) (d)

Fig. 3.4 Cylindrical hole preparation in clay soil (a) MS pipe (b) pipe driving (c) pipe pull out by lever (d) cylindrical hole

Fresh Concrete Preparation

For concrete preparation, 3/16 inch downgraded stone chips were used as coarse aggregate. Sylhet sand were used as fine aggregate. The mix ratio was

1 (cement):1 ½ (sand):2 (stone chips).

100 mm dia pipe

75 mm dia pipe

50mm dia pipe

10 mm circular plate

Lever

Cylindrical hole

29

Concrete Casting

After preparation of bore hole, rebar cage was inserted into the hole. Before concrete

casting, bore hole was cleaned. Fresh concrete was poured into the bore hole. During

concrete pouring into the bore hole, a 10 mm diameter rod was used for temping.

(a) (b)

Fig. 3.5 Pile casting.(a) cage in bore hole (b) temping with 10 mm rod

Pile Pull Out and Curing

After pile casting, water was poured on the ground around the pile every day to keep

the surrounding soil wet to facilitate curing of the pile concrete. After 7 days, piles

were pulled out from ground. Before pull out, the soil was excavated to a depth to

prevent pile breakdown. Then the pile was kept under water in a house for 28 days.

Fig. 3.6 Piles after pull out from bore hole.

Temping rod

30

Pile End Treatment

Both ends of a pile were uneven after it was pulled out from ground. Both ends were

later smoothened using concrete cutter. The cylindrical surface of the pile was rough

as shown in Fig.3.7

Fig. 3.7 Piles before model test.

Smooth surface Rough surface

31

3.4 Wooden Box for Model Ground Preparation

A wooden box was made to prepare model ground in the laboratory. The dimensions

of the box were 915 mm by 915 mm in cross section and 1675 mm in height. The

cross sectional size was chosen so that the load cell arrangement and pile could be

easily placed inside the wooden box and there would be no interference between the

walls of the wooden box and the failure zone around the pile. The zone in which the

soil will be affected by either installation of the pile or loading varies with soil density

and pile installation method, but it is reported in the range of 3 to 8 pile diameters

(Mhaidib, 2006). The sides of the wooden box (915 mm) used in the present study is

more than 4 pile diameter in the horizontal direction. There was also more than 4 pile

diameter clearance in the vertical direction beneath the base of the model pile.

Therefore, it was expected that there would be no/insignificant effect of the boundary

on the observed soil-pile response in the model tests.

The base and the vertical four sides of the box were not completely fixed. They were

kept separate and could be assembled into a box. This is because if the sides of the

box were prefixed, then it would be difficult to place the load cell arrangement, pile

and hydraulic jack setup inside the box. The bottom part (base) of the box was 1067 x

1067 mm and it was larger than box cross-sectional area. A 152mm high wooden

guide frame was placed on the bottom part to encase the four vertical sides. The

bottom guide frame also provided lateral support to the vertical sides against lateral

sway due to lateral earth pressure when the box was filled with sand. A load cell

arrangement was placed at the centre of the base when it was intended to measure the

load at the pile tip. The load cell arrangement was attached to a display monitor

(placed outside of the box) with a wire. After preparation of the base of the box and

load cell arrangement (when required), the vertical sides were put in place and kept in

position. There were horizontal tie rods/braces at three different heights around the

wooden box to hold the sides of the box against the lateral pressure for the soil.

Various parts of box are shown in Fig.3.8.

32

(a)

(b) (c)

Fig. 3.8 Part of wooden box. (a) base (b) vertical four sides (c) full box with

horizontal ties.

Wooden guide frame

915 mm

915 mm

1067 mm x 1067 mm

Vertical four sides

Horizontal ties

Hole for wire

Bottom part

33

3.5 Reaction Frame

In model test, the reaction frame is very important. Load is applied on the top of the

pile by jacking against the reaction frame. In actual field tests reaction frame may be

made from sand bag or reaction pile. The reaction frame used in the model tests was

made from steel sections (box section and C-channel) and rod.

A C-channel ISLC200 (200 X 75) was placed horizontally in the bottom of reaction

frame. The length of bottom C-channel was 1524mm. Four holes were made on top of

the C-channel to connect four rods (vertically). Each rod length was 2438 mm and the

rods were fully threaded.

A steel box section (reaction beam) was placed horizontally on the upper part of the

rods using four nuts. The height of the reaction beam could be adjusted using the nuts.

Reaction beam was made from two C-channel (ISLC200) by welding and length of

reaction beam was 1524 mm. Four pieces C-channel (75 mm x 50 mm) were attached

to the bottom C-channel in the horizontal plane to distribute the weight of the sand

filled box over a wide area. The length of each of these C-channels (75 mm x 50 mm)

wer 610 mm.

34

C-channel(75X50)

(a)

C200 (200 X 75) C- (75 X 50)

(b) (c)

Fig. 3.9 Reaction frame. (a) base of reaction frame(in plan) (b) & (c) various parts of reaction frame.

C-channel ISLC200 (200 X 75)

Vertical rods

Tie rods Reaction beam

100mm x100mm hole

Lateral support

35

3.6 Spring for Measuring End Resistance

Two types of springs (one relatively softer and the other stiffer) were used under the

pile in tests in which measurement of end resistance was made. In an actual pile, the

side friction is gradually mobilized as the pile settles. If there is no settlement there

will be no friction. Settlement of the pile also causes the end bearing to mobilize to

ultimate value. A very stiff spring below the pile will make it an end bearing pile

where as a very soft spring will make the pile frictional one. Also response of actual

sand layer beneath a pile is nonlinear where as that of the spring is linear. Thus, it was

planned to see the effect of spring stiffness on the observed load-settlement response.

Two springs with different stiffness were therefore used. The stiffness of the spring

can be seen from the calibration curves (Fig.3.10). The stiffness of the springs are 55

KN/m and 270 KN/m. Pile end resistance was transferred through the spring to the

load cell and the force was displayed on the monitor.

Fig. 3.10 Load- deflection response of spring in incremental load test.

36

3.7 Loading System

A hydraulic jack was used to apply load on the model pile. The capacity of the

hydraulic jack was 3 metric ton. The hydraulic jack was operated manually. Total

applied load was obtained from the proving ring reading. Calibration chart of proving

ring was used to get load from proving ring data. The load was applied in increments

of 0.157 kN up to the load of 0.294 kN and in increment 0.294 kN beyond 0.314 kN

load. The pile end resistance was recorded from the display monitor.

37

3.8 Test Procedure

Model test was conducted in the laboratory on model RCC piles installed in a model

ground using incremental loading procedure. The tests were performed under two

different end conditions of piles. In one case a spring was placed under the pile

bottom and in the other case the pile bottom rested in sand layer. Test setup for first

case are shown in Fig.3.11 and also schematic diagram in Fig.3.12.The steps followed

for model tests conducted with spring below pile bottom stated below.

i. At first, the reaction frame with its base and vertical rods was set up.

ii. Proving ring was connected to the reaction beam using nuts and bolts.

iii. The reaction beam was leveled.

iv. The bottom part of the wooden box was placed on the C-channel base.

v. Load cell arrangement was placed on the bottom part of the box.

vi. Display monitor was connected with load cell arrangement and it was kept

outside of the box.

vii. A rectangular MS plate (10 mm thick) was placed on load cell arrangement. A

pipe where diameter was larger than the spring was attached with MS plate.

The pipe was necessary to prevent lateral displacement of spring.

viii. Another small box was placed on the MS plate to prevent sand from entering

into the load cell arrangement.

ix. The spring was placed in the center of the MS plate.

x. A 127 mm diameter pipe was placed on the MS plate to cover the spring and

the bottom of the pipe was covered with foam to prevent entering of sand

around the spring.

xi. A 10 mm circular plate was placed on the spring. The circular plate could just

move vertically inside the pipe without much friction.

xii. A circular hollow MS plate was plate on pipe (127 mm diameter) to prevent

sand from entering into the pipe. The size of hole of plate was larger than

model pile diameter.

xiii. The pile was placed on the circular plate. Bottom of the pile was surrounded

by a circular sheet of foam. The foam sheet was necessary to hold the sand in

38

position as the bottom steel plate moved downward with the settlement of the

pile.

xiv. A circular plate was placed on top of pile.

xv. Hydraulic jack was placed on the upper circular plate and made in contact to

the proving ring.

xvi. Vertical four sides of wooden box were placed.

xvii. Horizontal tie rods/braces around the wooden box were placed.

xviii. Sand was poured into the box from a container with perforated bottom. The

height of fall of the sand above the sand surface in box was always maintained

as 915 mm.

xix. After pouring sand to the desired level, the top surface of the sand was leveled

by straight edge.

xx. A wooden plank was placed horizontally in the box above the sand surface to

support deformation dial gauge.

Fig. 3.11 Test set up to determine end resistance (a) reaction beam and proving ring

(b) box bottom (c) load cell and MS plate placed (d) small box placed

Continued..

Box bottom

Reaction beam

Proving ring

MS plate 10mm thick Small box

a b

c d

39

Fig. 3.11 Test set up to determine end resistance (e) spring placed (f) 127 mm pipe and 10mm circular plate (g) circular hollow MS and pile (h) hydraulic jack (j) vertical four sides (k) wooden plank and deformation dial gauge.

spring

foam 127 mm dia pipe

10 mm circular plate

Hollow plate

Hydraulic jack

Wooden plank

Deformation dial gauge

Vertical sides

e d

g h

j k

40

The steps followed when model test was conducted with pile bottom resting on sand

are stated below.

i. The reaction frame, with its base and vertical rods, was set up.

ii. Proving ring was connected to the reaction beam using nuts and bolts.

iii. The reaction beam was leveled.

iv. The bottom part of the wooden box was placed on the C-channel base.

v. Vertical four sides of wooden box were placed.

vi. Horizontal tie rods/braces around the wooden box were placed.

vii. Sand was poured into the box from a container with perforated bottom. The

height of fall of the sand above the sand surface in box was always maintained

as 915 mm. Sand was poured up to a height of 457 mm in the box.

viii. Pile was placed on deposited sand.

ix. A circular plate was placed on top of pile.

x. Hydraulic jack was placed on the upper circular plate and made in contact to

the proving ring.

xi. Sand was poured to the desired level. The top surface of the sand was leveled

by straight edge.

xii. A wooden plank was placed horizontally in the box above the sand surface to

support deformation dial gauge.

41

Fig. 3.12 Schematic Diagram of the Model Pile Test Setup.

42

3.9 Model Test Schedule

A total of nine model tests were performed in the laboratory. Table 3.2 shows the end

condition of the piles and measurement in these tests.

Table 3.2 Different end conditions and measurements in the model tests

Sl.No End condition No. of Test Remark

01 With stiffer

spring

03 Total load, end resistance and pile

head deflection was measured

02 With softer

spring

03 Total load, end resistance and pile

head deflection was measured

03 Without spring 03 Total load and pile head deflection

was measured

43

CHAPTER FOUR

PROCEDURE FOR SEPARATION OF SKIN FRICTION AND END

BEARING AND COMPARISION WITH MODEL TEST RESULTS

4.1 General

This thesis work attempts to establish an analytical method to separate skin frictional

resistance and end bearing resistance of axially load pile. The proposed analytical

method is presented in this chapter. To verify the analytical method, laboratory model

tests on piles of three different diameters (50 mm, 75mm and 100 mm) and under two

different end conditions (with spring and without spring directly beneath the pile)

were performed. Three different diameters of model RCC concrete piles were made in

the field. Test on model pile was performed within a model ground. The model

ground was prepared within a box deposited with uniform sand through a perforated

bottom of container and the height of fall of the sand above the sand surface in box

was always maintained as 915 mm. Preparation of model ground is described in the

earlier chapter. In this chapter, the model pile test results are presented in two

sections. In the first section, the test results related to the conventional soil properties

and direct shear test results are presented. The direct shear test result (τ/σ vs shear

displacement) is used for analytical method. In the second section, test results of

model pile along with analytical method are presented. The skin frictional resistance

and end bearing resistance thus obtained from model tests are compared with those

obtained by analytical method.

4.2 Properties of Sand Used for Model Ground

The basic soil properties of the sand used in model ground preparation were

determined through a series of tests.

Grain size distribution and specific gravity

River sand was used in the laboratory to prepare model ground. The sand was

obtained from a local supplier. In order to determine the grain size distribution of the

44

selected sand, representative sample was collected from the whole batch of sands. The

soil samples were air-dried for 24 hours and sieve analysis test was conducted on sand

following the ASTM D422 (1994) standard procedures. The specific gravity of the

selected soils was measured using the ASTM D854-10 (1994).The grain size

distribution of the sand is shown in Figure 4.1. The key parameters derived from the

tests are summarized in Table 4.1. The sand is classified as poorly graded (SP) sand

according to the unified soil classification system.

Table 4.1 Properties of the selected sand used in the study

Soil property Value

D60, mm 0.23

D30, mm 0.18

D10, mm 0.10

Coefficient of uniformity, Cu 2.3

Coefficient of curvature, Cc 1.41

Specific gravity, Gs 2.67

M.I.T Classification

Course Medium Fine Coarse Medium Fine

ClaySiltSandGravel

0

10

20

30

40

50

60

70

80

90

100

0.0010.010.1110

PER

CE

NT

FIN

ER

(℅)

GRAIN SIZE(mm)

SIEVE ANALYSIS

Fig.4.1 Grain size distribution of sand.

45

Density of Sand Bed

In the model pile tests, sand bed was prepared by pouring sand from a container with

perforated bottom. The height of fall of sand was maintained as 915 mm. The average

density of the sand thus obtained was about 14 kN/m³.

Result of Direct Shear Test on Sand

The shear strength parameter of sand is the angle of internal friction, This

parameter was determined by using the conventional direct shear test. The angle of

internal friction, was found as 36.3° (Fig. 4.9). Tests were conducted on test

specimens under different normal stress. The normal stresses used were 9.3 kPa, 18.6

kPa and 27.9 kPa. Conditions of the test specimens are summarized in Table 4.2.

Shear displacement vs shear stress and shear displacement vs normal displacement

plots obtained from the test are shown in Fig. 4.2 to Fig 4.8 at three normal stress. To

verify the proposed analytical method for separation of skin friction and end bearing it

is required to obtain the mobilized friction angle at any shear displacement. Therefore

to get mobilized friction at any shear displacement, polynomial equations were fitted

to the τ/σ vs shear displacement curve plot. Fitted polynomial equations are given

below.

(S>=0 & S<=0.872) (4.1)

(S>0.872 & S<=2.286) (4.2)

(S>2.286) (4.3)

S=shear displacement in mm

0.3270.303S0.062S2

0.716

1.45S0.9374S2

46

Table 4.2 Conditions of shear test specimens

Specimen No.

Water content, %

Dry unit wt, kN/m3

InitialVoid ratio

Normal stress, σ

(τ/σ)f max

φf

Shear displacement at failure

1 0.36 14 0.86 9.3 0.67 34 2.7 2 0.37 14 0.85 18.6 0.76 37 2.7 3 0.35 14 0.86 27.9 0.72 36 2.7

*φf=tan-1(τ/σ)f

Fig 4.2 Shear stress vs shear displacement curve from direct shear test on the sand

used for model ground preparation.

47

Fig 4.3 Shear displacemnt vs normal displacement curve from direct shear test on the sand used for model ground preparation.

Fig 4.4 τ/σ vs shear displacement curve for σ=9.3 kPa from direct shear test on sand.

48

Fig 4.5 τ/σ vs shear displacement curve for σ =18.6 kPa from direct shear test on

sand.

Fig 4.6 τ/σ vs shear displacement curve for σ =27.9 kPa from direct shear test on

sand.

49

Fig 4.7 τ/σ vs shear displacement average curve from tests at normal stress on sand.

Fig 4.8 τ/σ vs shear displacement curve for three different normal stress and the

average curve from direct test on sand.

50

Figure 4.9: Shear stress at failure versus normal stress in direct shear test on sand.

4.3 Static Load Test on Model Concrete Piles

Model piles of three different diameters installed in a model ground in the laboratory

with two different end conditions were tested under static compression loading. In the

model tests the load –displacement responses were recorded. Also the tip resistance

was measured in some of the tests. The skin friction was determined as the difference

between the applied load and the measured end resistance. The skin friction resistance

and end bearing resistance obtained from the laboratory model tests are compared

with those obtained by the analytical approach.

4.4 Pile Material Properties Used in Analytical Method

Three model concrete piles were made with mix ratio of 1 (cement): 1 ½ (sand):

2(stone chips) by volume. Each pile length was 1000 mm with the diameters of 50

mm, 75 mm and 100 mm. Concrete strength of pile, modulus of elasticity of the pile

material (Ep) and modulus of elasticity (Es) of soil needed for analytical method for

separation of skin friction and end bearing from static load test data were not directly

51

determined by laboratory tests. Instead these values were taken from available data or

calculated using available empirical equations. The concrete strength cf =3000 psi is

used in analytical method. The Young’s modulus of elasticity of the pile material (Ep)

is found as 21525553 KN/m2 using equation cc f57000E psi where cf is

psi.(Nilson et al., 2003). Das (2009) the value of soil-pile friction angle (δ) varies

from 0.5φ to 0.8 φ. However, Armaleh and Desai (1987) noted that δ is usually

smaller than φ. In this research, 0.8 φ is used as soil-pile friction angle. The modulus

of elasticity of various soil is shown in Table 4.3 (Das, 2009).

Table 4.3 Modulus of Elasticity of Various Soils. (Das, 2009)

Type of soil Modulus of elasticity, Es (Mpa) Poisson’s ratio,µs Loose sand 10.5-24.0 0.2-0.40 Medium dense sand 17.25-27.60 0.25-0.40 Dense sand 34.5-55.20 0.30-0.40 Silty sand 10.35-17.25 0.20-0.40 Sand and gravel 69.00-172.50 0.15-0.35 Soft clay 4.1-20.7 Medium clay 20.7-41.4 0.2-0.50 Stiff clay 41.4-96.6

4.5 Analytical Method for Separation of Skin Friction and End Bearing

An analytical method is attempted to separate skin frictional resistance and end

bearing resistance from a static model test on single pile. In this method, a pile is

divided into several segments ( length of each segment need not be equal) and force

equilibrium of each segment is considered starting from the top most segment and

transferring the unbalanced load to the consecutive lower segment. Such segmental

method also proposed by Bowles (1974a) and it is an iterative method. But proposed

analytical method is load incremental method. A computer program (appendix-A) is

written to separate skin friction and end bearing from a given load and settlement. The

analytical method will be verified using model test result. The steps involved in using

the analytical method are presented below.

52

1. Pile is divided into n number of segments as shown in Fig 4.10

Pile head settlement of first segment S Q applied load on first segment

Elastic deformation of segment 1 L1

Δ1 Δq1

Q1

Pile head settlement of second segment S1 Q1 applied load on second segment

Elastic deformation of segment 2 L2

Δ2 Δq2

Q2.

Pile head settlement of first segment Sn-1 Qn-1 applied load on n segment

Ln

Δn Δqn

Qn

Fig 4.10 Force on each segment of pile.

N1

N2

N3

53

2. Skin frictional resistance (Δq1) of first segment is determined and it is

obtained from the following equation. The same equation is used for

successive segments also.

(4.4) or (4.5) where,

k=Earth pressure coefficient and for bored pile k= 1-sin φ

γ=unit weight of soil and this value is obtained from laboratory test, KN/m3

z=depth of soil under consideration, m

p=perimeter of model pile, m

L1= length of first segment, m

φ = angle of internal friction, degree

3. Point load (Q1) on the bottom of the first segment is obtained by deduction of skin frictional resistance (calculated in step 2) from total applied load (Q) on top of the segment.

4. Settlement (Δ1=Δe1+Δt1) of first segment for elasticity of pile and load transmitted along the pile shaft is determined and it is obtained from the following equation

(Das, 2009) (4.6)

where, Ap= area of first segment of pile, m2

Ep= The modulus of elasticity of the pile material (Ep), kPa .

(4.7)

where, D(m)=Diameter of model pile

ES (kN/m2)= modulus of elasticity of soil.

µs =Poission’s ratio of soil. =0.3 is used for this model.

Iws=influence factor and this is obtained from below equation

(Vesic,1977) (4.8)

)(tan 11 pLkq

11 )8.0tan()sin1( pLzq

10002

)()( 111

ppe EA

LQQmm

1000)1()()( 2

1

11 wss

St I

ED

pLQmm

DLIws135.02

54

5. Settlement for subsequent segment is then calculated by deduction of settlements of all previous segments from the total settlement. The load on next segment is obtained by deduction of frictional force of all previous segments from the total applied load on pile.

6. If the value of calculated point load on any subsequent segment is zero or negative then the total applied load is resisted by frictional force along the pile shaft. If the value of point load is greater than zero, then extra load will be applied to the next segment and it is continued up to the nth segment.

.

4.6 Effect of Spring in Load-Displacement Response.

Two types of spring one relatively stiffer and the other are relatively softer were used

to measure the end resistance in model pile load tests. The load-displacement

responses in these tests obtained are shown in Fig. 4.11 to Fig. 4.13. As expected,

using the softer spring, the curve shifted to left than when stiffer spring was used. The

load-displacement response of softer spring appears to be nearer to the actual load-

displacement response. Table 4.4 compares the loads on pile head corresponding to

the settlements of 5 mm, 10 mm, 15 mm and 20 mm for the 50 mm diameter pile with

three different end conditions. A non linear spring that could produce a load –

displacement response identical to the one without spring, would have been ideal.

Such a spring is not available. However observing Fig. 4.11 to Fig. 4.13 and Table

4.4, it is considered that the softer spring produced a response close to that when sand

exists below the pile tip.

55

Fig.4.11 Load- displacement response in static model test on different end condition for 50 mm diameter pile.

Fig.4.12 Load- displacement response in static model test on different end condition for 75 mm diameter pile.

56

Fig.4.13 Load- displacement response in static model test on different end condition for 100 mm diameter pile.

Table 4.4 Comparison of load on pile head at selected displacement levels for the 50

mm diameter pile with different end conditions

Pile diameter (mm)

Pile head deflection(mm)

Total applied load on pile (kN) Without spring Softer spring Stiffer spring

50 5 0.42 0.52 1.47 10 0.59 0.83 2.81 15 0.73 1.08 3.93 20 0.88 1.31 5.14

57

4.7 Result from Model Test

Model piles of three different diameters, under static loading and with two different

end conditions were tested in the laboratory. In the model tests the load -displacement

response was recorded. Also the tip resistance was measured for three model piles

using softer spring at pile bottom. Pile end bearing and settlement are recorded when

spring is used and these end bearing and settlement are used as reference to separate

the end bearing and skin frictional resistance when spring is not used. The skin

friction was then determined as the difference between the applied load and measured

end resistance. The load-displacement response and end bearing resistance of model

piles are shown in Fig 4.14 to Fig.4.16.

Fig.4.14 Load - displacement response for 50 mm diameter pile used softer spring under pile.

58

Fig.4.15 Load - displacement response for 75 mm diameter pile used softer spring under pile.

Fig.4.16 Load - displacement response for 100 mm diameter pile used softer spring under pile.

59

4.8 Comparison of Result Obtained from Model Tests and Analytical Method

End bearing resistance of 50 mm, 75 mm and 100 mm diameter piles obtained in

model test and these separated by analytical method are listed in Table 4.5 to Table

4.7 and analytical and model test end bearing are shown in Fig.4.17 to Fig.4.19.Skin

frictional resistance of 50 mm, 75 mm and 100 mm diameter piles for model test and

analytical method are listed in Table 4.8 to Table 4.10 and analytical and model test

skin friction are shown in Fig.4.20 to Fig.4.22. The model test end bearing for 50 mm,

75 mm and 100 mm diameter piles are found to be 34%, 42% and 28% higher than

the analytical end bearing. However, the analytical skin resistance for 50 mm, 75 mm

and 100 mm diameter piles are found to be respectively 29%, 33% and 28% larger

than the model test values.

60

Fig.4.17 End resistance - displacement response for 50 mm diameter pile.

Fig.4.18 End resistance - displacement response for 75 mm diameter pile.

61

Fig.4.19 End resistance - displacement response for 100 mm diameter pile.

Fig.4.20 Skin resistance -displacement response for 50 mm diameter pile.

62

Fig.4.21 Skin resistance -displacement response for 75 mm diameter pile.

Fig.4.22 Skin resistance -displacement response for 100 mm diameter pile.

63

Table 4.5 Comparison between model test and analytical end resistance (50mm diameter pile).

Sl. No

Total applied pile load (kN)

Model test end bearing

(kN)

Analytical end bearing

(kN)

Variation between model test and analytical(% of model test result)

Average variation

01 0.16 0.06 0 38

34

02 0.31 0.16 0.07 29 03 0.47 0.31 0.23 17 04 0.63 0.57 0.38 30 05 0.79 0.86 0.54 41 06 1.1 1.12 0.7 38 07 1.26 1.44 0.86 46

Table 4.6 Comparison between model test and analytical end resistance (75mm

diameter pile). Sl. No.

Total applied pile load

(kN)

Model test end bearing

(kN)

Analytical end bearing

(kN)

Variation between model test and analytical(% of

model test result)

Average variation

01 0.16 0.04 0 25

42

02 0.31 0.15 0 48 03 0.47 0.28 0.03 53 04 0.63 0.49 0.19 48 05 0.79 0.7 0.34 46 06 1.1 0.91 0.5 37 07 1.26 1.26 0.82 35

64

Table 4.7 Comparison between model test and analytical end resistance (100mm diameter pile).

Sl. No

Total applied pile load

(kN)

Model test end bearing

(kN)

Analytical end bearing

(kN)

Variation between model test and analytical(% of model test result)

Average variation

01 0.16 0.015 0 9

28

02 0.31 0.077 0 25 03 0.47 0.185 0 39 04 0.63 0.31 .03 44 05 0.79 0.46 0.19 34 06 1.1 0.62 0.34 25 07 1.26 0.94 0.66 22

Table 4.8 Comparison between model test and analytical skin resistance (50 mm

diameter pile). Sl. No.

Total applied pile load

(kN)

Model test skin resistance

(kN)

Analytical skin resistance

(kN)

Variation between model test and analytical(% of analytical result)

Average variation

01 0.16 0.09 0.16 45

29 02 0.31 0.159 0.24 26 03 0.47 0.163 0.24 16 04 0.63 0.061 0.24 28

Table 4.9 Comparison between model test and analytical skin resistance (75 mm diameter pile).

Sl. No.

Total applied pile load

(kN)

Model test skin resistance

(kN)

Analytical skin resistance

(kN)

Variation between model test and analytical(% of analytical result)

Average variation

01 0.16 0.12 0.16 25

33

02 0.31 0.16 0.31 48 03 0.47 0.19 0.44 53 04 0.63 0.14 0.44 48 05 0.79 0.09 0.44 44 06 1.1 0.04 0.44 36

65

Table 4.10 Comparison between model test and analytical skin resistance (100 mm

diameter pile).

Sl. No.

Total applied pile load

(kN)

Model test skin resistance

(kN)

Analytical skin resistance

(kN)

Variation between model test and analytical(% of analytical result)

Average variation

01 0.16 0.14 0.16 13

28

02 0.31 0.24 0.31 22 03 0.47 0.29 0.47 38 04 0.63 0.32 0.6 44 05 0.79 0.32 0.6 35 06 1.1 0.33 0.6 25 07 1.26 0.32 0.6 22

66

CHAPTER FIVE

SUMMARY AND CONCLUSIONS

5.1 Summary

In this thesis attempts were made to develop an analytical method that may be used to

separate skin frictional resistance and end bearing components for a given load on a

pile in a static model test. The method is based on static load-settlement data and

direct shear test data. In the proposed analytical method the pile is divided into a

number of segments. The side friction in each segment is calculated using mobilized

friction angle. The mobilized angle of internal friction for any displacement is

obtained from fitted polynomial equation to τ/σ vs shear displacement plot. To verify

the analytical method, three numbers of models concrete piles of diameter 50 mm, 75

mm and 100 mm were made. Static model test were conducted on these piles in a

model sand bed. To measure the end bearing resistance two types of springs (one

relatively softer and the other relatively stiffer) is used beneath the model piles along

with a load cell. A display monitor directly provided the load recorded by the load

cell. The analytical results are compared with the model test results.

5.2 Conclusions

Based on the investigation presented here, the following conclusions can be drawn:

i. An experimental setup is made to separate end bearing resistance and skin

frictional resistance from static model test.

ii. An analytical method is proposed to separate the end bearing resistance and

skin frictional resistance for a given load in a static model test on a pile

embedded in sand.

iii. The model test end bearing for 50 mm, 75 mm and 100 mm diameter piles are

found to be 34%, 42% and 28% higher than the analytical end bearing.

iv. The analytical skin resistance for 50 mm, 75 mm and 100 mm diameter piles

are found to be respectively 29%, 33% and 28% larger than the model test

values.

67

5.3 Limitation of the Thesis.

The limitation of the thesis which has affected the result is given below:

Linear spring is used in this thesis but soil is non linear.

The static model test is conducted in a laboratory model sand bed which may

not represent the field sand layers. As per example, the effect of cementation,

ageing and over consolidation ratio may not represented by the sand bed used

in the study.

The modulus of elasticity of pile and sand used in analytical method was not

directly measured. Empirical equation was used for modulus of elasticity of

pile concrete. The modulus of elasticity of sand was taken from reference

value obtained from literature.

5.4 Recommendation for Future Research.

The present study focused only on piles embedded in sand layer. Further study

may be conducted for piles in purely clay layer, silty-clay layer and layered

soils.

The proposed analytical method for separation of end bearing and skin friction

for a given load in a static model test may be verified using field load test data.

Further study may be conducted using spring of various stiffness at the pile

bottom

68

REFERENCES

Al-Mhaidib, A. I. 2006, Influence of shearing rate on interfacial friction between sand and steel. Engineering Journal of the University of Qatar, Vol.19, 2006 , pp (from Internet).

ASTM D1143 / D1143M- 07 (2013), Standard Test Methods for Deep Foundations Under Static Axial Compressive Load.

ASTM D854-10. 1994c. Standard test method for specific gravity of soils. ASTM Standards, ASTM International, West Conshohocken, PA, USA, 4(8): 80-83.

Bowles, J.E. (1974), Analytical and Computer Methods in Foundation Engineering, McGraw-Hill Book Co., INC. N Y, 519 pp.

Bowles, J. E. (1988), Foundation Analysis and Design., McGraw-Hill, New York, 4th Edition.

Bowles, J.E. (1996), Foundation Analysis and Design., The McGraw-Hill Companies INC. New York, USA.

Coyle, H.M and L.C.Reese(1966), Load Transfer of Axially Loaded Piles in Clay,JSMFD,ASCE, vol.92,SM 2, March,pp. 1-26

Chandrasekaran, V., Garg, K.G. and Prakash. C. (1978), Behavior of isolated bored enlarged base pile under sustained vertical loads. Japanese Society of Soil Mechanics and Foundation Engineering, 18(2): 1-15.

Coyle, H.M. and Castello, R.R. (1981), New design correlations for piles in sand. Journal of the Geotechnical Engineering Division, 107(7): 965-986.

Das, B.M (2009), Principles of Foundation Engineering., Cenagage Learning India Private Limited, 6th Edition.

Doherty, P. and Gavin, K. (2011), The shaft capacity of displacement piles in clay: a state of art review. Geotechnical and Geological Engineering, 29(4): 389-410.

Fleming, W. G. K. (1992).”A New Method for Single Pile Settlement Prediction and Analysis,” Geotechnique, Vol. 42, No.3. pp.411-425.

Golder, H.Q., Fellenius, W., Kogler, F., Meischeider, H., Krey, H. and Prandtl, L. 1941. The ultimate bearing pressure of rectangular footings. Journal of the ICE, 17(2): 161-174.

Hansen, J.B. (1970). A revised and extended formula for bearing capacity. Danish Geotechnical Institute, Copenhagen, Bul. 28(21).

69

Janbu, N. 1976. Static bearing capacity of friction piles. In Proceedings of European Conference on Soil Mechanics and Foundation Engineering. 1(2): 479-488

Katzenbach, R. Arsalan, U. and Moormann, C. (2000), Piled raft foundation projects in Germany. Design applications of raft foundations, 323.

Madabhushi, G., Knappett, J. and Haigh, S. (2010), Design of pile foundations in liquefiable soils. Imperial College Press, 57 Shelton street Covent Garden, London, UK.

Nilson,A.H.,Darwin.D. and Dolan.C.W(2003), Design of Concrete Structures., McGraw-Hill, Singapore, 13th Edition.

Overy, R. (2007), The use of ICP design methods for the foundations of nine platforms installed in the UK North Sea. Offshore Site Investigation and Geotechnics Confronting New Challenges and Sharing Knowledge.

Meyerhof, G.G. (1951), The ultimate bearing capacity of foundations. Géotechnique. 2(4): 301-332.

Meyerhof, G.G. (1976), Bearing capacity and settlement of pile foundation. Journal of Geotechnical Engineering, ASCE, 102(3): 195-228.

Miura, N. (1983), Point resistance of piles in sand. Technology reports of the Yamaguchi University, 3(2): 129-139.

Morshed, J. (1991), “Prediction of Load Deformation Behaviour of Axially Loaded Piles in Sand”, M.Sc. Thesis, Department of Civil Engineering, BUET.

Manandhar, S. and Yasufuku, N. (2012), Analytical model for the end bearing capacity of tapered piles using cavity expansion theory. Advance in Civil Engineering.

Ohno, S. and Sawada, S. (1999), Bearing capacity of piles in sands with different crushabilities under various stress conditions. In Proceedings of 11th Asian Regional Conference on Soil Mechanics and Geotechnical Engineering, 1: 249-252.

Sew, G.S., Chin, T.Y. & Shong, L.S., “A Brief Guide to Design of Bored Piles Under Axial Compression –A Malaysia Approach”, Gue & Patners Sdn, Kuala Lumpur, Malaysia

Terzaghi, K. (1943), Analytical soil mechanics. J., 57 Shelton street Covent Garden, London, UK.

Tomlinson, M. J. (1993), Pile Design and Construction Practice. Taylors & Francis, 4th Edition.

Ukritchon, B., Whittle, A.J. and Klangvijit, C. 2003. Calculations of bearing capacity factor using numerical limit analyses. Journal of Geotechnical and Geoenvironmental Engingeering, 129(5): 468-474.

70

Vesic, A.S. (1977). Design of Pile Foundation, National Cooperative Highway Research Program. Synthesis of Highway Practice No. 42, Transportation Research Board, Washington, D.C.

Yasufuku, N. and Hyde, A.F.L. (1995), Pile end-bearing capacity in crushable sands. Géotechnique, 45(4): 663-676.

71

APPENDIX-A

COMPUTER PROGRAM

#include<iostream>

#include<cmath>

#include <fstream>

using namespace std;

main()

{

float sval,tval,delbyfi,delbytheta;

float pe1, se1, fi, sdel, gama, l, D,Es, area, elas,ttlseg;

float pi=3.1416;

//for input

ifstream in("input.txt"); // input

if(!in) {

cout << "Cannot open input.txt file.\n";

return 1;

}

char title[100];

float val;

in >>title>> val;

ttlseg = val;//total segment

72

in >>title>> val;

l = val;//segment length

in >>title>> val;

area = val;//pile area

in >>title>> val;

elas = val;//Elasticity of pile materials

in >>title>> val;

Es = val;//Elasticity of soil

in >>title>> val;

pe1 = val;//External load

in >>title>> val;

se1 = val;//Settlement

in >>title>> val;

gama = val;//soil unit weight,

in >>title>> val;

D = val;//diameter, D(m)

in.close();

//end for input

ofstream out("output.txt"); // output, normal file

if(!out) {

cout << "Cannot open test.txt file.\n";

return 1;

}

73

//out << "Ra " << 9.9 << endl;

//out << "Ta " << 9.9 << endl;

//out << "Md " << 4.8 << endl;

float Iws = 2+.35*sqrt(l/D);

float X = (D/(Es*pi*D*l))*(1-0.3*0.3)*Iws;

int j;

float tq=0,L=0;

float tsj=0;

float prevdpj=0;

for(j=1;j<=ttlseg;j++)

{

if(se1>=0 && se1<=0.872)

{

delbyfi = -(0.9374*(se1*se1))+(1.45*se1);

}

else if(se1>0.872 && se1<=2.286)

{

delbyfi = -(.0625*(se1*se1))+(.3035*se1)+0.3275;

}

else if(se1>2.286)

{

delbyfi = 0.716;

}

74

fi = atan(delbyfi)*(180/3.1416);//fi // converted into degree

sdel = 0.8*fi;//theta // converted into degree

//calculate degree to radian

fi = fi*(3.1416/180);

sdel = sdel*(3.1416/180);

sval=sin(fi);

tval=tan(sdel);

float q;

/*

cout<<endl;

cout<<"sval: "<<sval<<endl;

cout<<"tval: "<<tval<<endl;

cout<<endl;

cout<<"q:"<<q<<endl;*/

L=L+l;

q = (1-sval)*gama*L*tval*(D*pi*l);

tq=tq+q;

float dpj = pe1-tq;//pj //- er jaigai + disi

//out<<endl;

//out<<"dp"<<j<<" : "<<dpj<<endl;

// calculating Sj;

75

float f,up,dwn,div,sj;

if(j==1)

{

f=dpj+pe1;

}else{

f=dpj+prevdpj;

}

prevdpj=dpj;//for storing current dpj for next loop.

up = f*(l*1000);

dwn = 2*area*elas;

div=up/dwn;

sj=se1- (tsj+(div+q*X*1000));//sj

tsj = tsj+sj;

// out<<endl<<"SE"<<j<<" : "<<sj<<endl;

//out<<endl;

// theoritical end bearing

float send=sj;

float Db=D;

float fcof=.85;

float nw=.3;

float endup,enddwn;

endup=4*area*Es*send;

enddwn=pi*Db*(1-(nw*nw))*fcof*1000;

76

float pend = endup/enddwn;

float endb = pe1-tq;//

if(j!=ttlseg)

{

if(dpj<.001 & sj<.0001)

{

//out <<"Go to next load increament. Total external force resisted by

frictional force."<<endl;

out<<"Frictional force = "<<tq<<endl;

//have to show the value of Q.

break;

}else

{

//out<<"Go to next segment"<<endl;

//have to next function (p,s)//

se1=sj;

}

}else

{

if(dpj<.001 & sj<.0001)

{

//out<<"Go to next load increament. Total external force resisted by

frictional force."<<endl;

out<<"Frictional force = "<<q<<endl;

}

else

{

77

//out<<"External force resisted by frictional force"<<endl;

//end of testing using for statement

if(pend==endb)

{

out<<" Output ";

out<<endl;

out<<"------------------------------------------------------------------------

----------";

out<<endl;

out<<"Frictional force |" <<"End bearing from load test |"<<"End

bearing analytical |"<<"Remarks"<<endl; //<<tq<<endl;

//out<<"End bearing from load test = "<<endb<<endl;

//out<<"End bearing analytical= "<<pend<<endl;

out<<tq<<" |" <<endb<<" |"<<pend<<"

|"<<"Ok"<<endl;

}

else{

out<<" Output ";

out<<endl;

out<<"------------------------------------------------------------------------

----------";

out<<endl;

out<<"Frictional force |" <<"End bearing from load test |"<<"End

bearing analytical |"<<"Remarks"<<endl; //<<tq<<endl;

//out<<"End bearing from load test = "<<endb<<endl;

//out<<"End bearing analytical= "<<pend<<endl;

78

out<<tq<<" |" <<endb<<" |"<<pend<<"

|"<<"Not Ok"<<endl;

}

}

}

}

out.close();

return 0;

}

79

APPENDIX-B

DATA SHEET

Table B1: Data Sheet of Stiffer Spring

SI. No

Stand gauge

reading

Deflection Proving ring reading Load

in mm Test-01

Test-02

Test-03

Avg. KN

1 0 0 0 0 0 0 0.0 0.01 2 100 0.1 2.54 19 23 23 22 0.57 3 200 0.2 5.08 47 50 50 49 1.28 4 300 0.3 7.62 74 77 77 76 1.99 5 400 0.4 10.16 101 104 105 103 2.70 6 500 0.5 12.7 128 131 131 130 3.39 7 600 0.6 15.24 155 158 158 157 4.10 8 700 0.7 17.78 181 185 184 183 4.78 9 800 0.8 20.32 208 212 212 211 5.49 10 900 0.9 22.86 236 240 240 239 6.22 11 1000 1 25.4 264 268 268 267 6.95

Table B2: Data Sheet of Softer Spring

SI. No

Stand gauge

reading

Deflection Proving ring reading Load Load

in mm Test-01

Test-02

Test-03 Avg. Ib KN

1 0 0 0 0 0 0 0.0 2 0.01 2 100 0.1 2.54 5 3.5 4.5 4.3 27 0.12 3 200 0.2 5.08 10 9 9.5 9.5 57 0.26 4 300 0.3 7.62 15.5 14 15 14.8 89 0.40 5 400 0.4 10.16 21 19 20 20.0 119 0.53 6 500 0.5 12.7 26.5 24.5 25 25.3 150 0.67 7 600 0.6 15.24 32 30 31 31.0 183 0.82 8 700 0.7 17.78 38 36 37 37.0 218 0.97 9 800 0.8 20.32 43.5 41.5 42.5 42.5 250 1.12 10 900 0.9 22.86 49 47 48 48.0 282 1.26 11 1000 1 25.4 54.5 53 53.5 53.7 315 1.41

80

Table B3: Data Sheet of Sieve Analysis

Sieve No

Sieve opening in mm

Wt. sieve in g

Wt. sieve+soil in g

Wt.soil retained in g

Percent retained

Cumulative Percent retained

Percent finer

4 4.76 521.6 521.6 0.0 0.0 0.0 100 8 2.38 492.8 492.8 0.0 0.0 0.0 100 16 1.18 426.4 426.5 0.1 0.1 0.1 99.9 30 0.60 402.6 402.8 0.2 0.2 0.3 99.7 50 0.30 375.7 387.3 11.6 11.6 11.9 88.1 100 0.15 351.1 419.3 68.2 68.2 80.1 19.9 200 0.075 350.5 363.5 13.0 13.0 93.1 6.9 pan 363.9 370.8 6.9 6.9 100.0

100

Table B4: Data Sheet of Specific Gravity Test

Determination No 1 2 3 Bottle No. S-34 S-35 S-36 Wt.of bottle+Water+Soil, W1 in g 372.8 376.9 378.3 Temperature T in C 27.5 27.5 27.5 Wt.of bottle+Water, W2 in g 341.4 345.6 346.9 Wt.of dish in g 34.5 34.5 34.5 Wt.of dish + dry soil in g 84.5 84.5 84.5 Wt.of bottle + dry soil in g 143 147.4 148.3 Wt.of bottle in g 93 97.4 98.3 Wt.of dry soil Ws in g 50 50 50 Specific Gravity of Water GT at T'C 0.9964 0.9964 0.9964 Specific Gravity of soil Gs 2.68 2.66 2.68 Specific Gravity of soil Gs = 2.67

81

Table B5: Data Sheet to Determine Angle of Internal Friction of Specimen-01

Elapsed time, min.

Shear dial 0.001

in.

Shear disp- lacement, in

Normal dial 0.001

in.

Normal disp- lacement, in

Proving dial 0.0001

in.

Shear Force load, lbs.

Shear Stress τ, kPa

τ/σ

0.00 0 0.000 378 0.000 0 0.00 0.00 0 0.25 16 0.016 376 0.002 8 2.53 3.55 0.382 0.50 34 0.034 374 0.004 11 3.47 4.88 0.525 0.75 52 0.052 373 0.005 12 3.79 5.32 0.573 1.00 72 0.072 372 0.006 13 4.10 5.76 0.621 1.25 90 0.090 374 0.004 13.5 4.26 5.99 0.644 1.50 106 0.106 372 0.006 14 4.42 6.21 0.668 1.75 126 0.126 373 0.005 14 4.42 6.21 0.668 2.00 146 0.146 373 0.005 14 4.42 6.21 0.668

Table B6: Data Sheet to Determine Angle of Internal Friction of Specimen-02

Elapsed time, min.

Shear dial 0.001 In/div.

Shear disp- lacement, in

Normal dial 0.001 in

Normal disp- lacement, in

Proving dial 0.0001 in.

Shear Force load, lbs.

Shear Stress

τ, kPa

τ/σ

0.00 0 0.000 315 0.000 0 0.00 0.00 0.000 0.25 17 0.017 311 0.004 20 6.31 8.87 0.477 0.50 35 0.035 310 0.005 24 7.58 10.64 0.573 0.75 54 0.054 310 0.005 28 8.84 12.42 0.668 1.00 72 0.072 311 0.004 30 9.47 13.30 0.716 1.25 90 0.090 312 0.003 31 9.79 13.75 0.740 1.50 106 0.106 313 0.002 32 10.10 14.19 0.764 1.75 126 0.126 314 0.001 32 10.10 14.19 0.764 2.00 143 0.143 314 0.001 32 10.10 14.19 0.764

Table B7: Data Sheet to Determine Angle of Internal Friction of Specimen-03

Elapsed time, min.

Shear dial 0.001 in/div.

Shear disp- lacement, in

Normal dial 0.001 in

Normal disp- lacement, in

Proving dial 0.0001 in.

Shear Force load, lbs.

Shear Stress

τ, kPa

τ/σ

0 0 0.000 363.0 0 0 0.00 0.00 0.000 0.25 16 0.016 359.0 0.004 29 9.16 12.86 0.461 0.5 34 0.034 357.0 0.006 35 11.05 15.52 0.557

0.75 51 0.051 356.5 0.0065 39 12.31 17.29 0.621 1 72 0.072 356.0 0.007 43 13.58 19.07 0.684

1.25 90 0.09 356.0 0.007 44 13.89 19.51 0.700 1.5 106 0.106 356.0 0.007 45 14.21 19.95 0.716

1.75 125 0.125 356.0 0.007 45 14.21 19.95 0.716 2 142 0.142 359.0 0.004 45 14.21 19.95 0.716

82

Table B8: Data Sheet for 50mm diameter Model Pile with Softer Spring.

Sl.No Proving ring, Reading (Div)

Total Load on pile

Dial gauge reading, (Div)

Deflection End force

Frictional force

kN mm kN kN 1 0 0.00 0 0.0 0.00 0.00 2 5 0.16 15 0.3 0.03 0.12 3 10 0.31 94 2.3 0.08 0.23 4 15 0.47 182 4.3 0.17 0.30 5 20 0.63 275 6.6 0.27 0.36 6 25 0.79 389 9.3 0.38 0.40 7 30 0.94 510 12.1 0.51 0.43 8 35 1.10 653 15.5 0.68 0.42 9 40 1.26 800 19.0 0.84 0.41 10 50 1.57 1060 25.1 1.16 0.41 11 60 1.89 1322 31.2 1.47 0.41 12 70 2.20 1610 38.0 1.83 0.37 13 80 2.51 1918 45.2 2.21 0.31 14 90 2.83 2200 51.7 2.60 0.23 15 100 3.14 2500 58.7 2.99 0.15

83

Table B9: Data Sheet for 50mm diameter Model Pile with Stiffer Spring

Sl.No Proving ring, reading(Div)

Total Load on pile

Dial gauge reading,

(Div)

Deflection End force

Frictional force

kN mm kN kN 1 0 0.00 0 0.00 0.00 0.00 2 5 0.16 14 0.31 0.03 0.13 3 10 0.31 48 1.08 0.09 0.23 4 15 0.47 73 1.60 0.16 0.31 5 20 0.63 100 2.15 0.25 0.38 6 25 0.79 128 2.69 0.35 0.43 7 30 0.94 153 3.16 0.46 0.48 8 35 1.10 181 3.69 0.57 0.53 9 40 1.26 209 4.23 0.68 0.58 10 50 1.57 270 5.35 0.95 0.62 11 60 1.89 341 6.67 1.25 0.64 12 70 2.20 410 7.95 1.55 0.65 13 80 2.51 472 9.07 1.83 0.68 14 90 2.83 530 10.06 2.14 0.69 15 100 3.14 600 11.32 2.47 0.68 16 110 3.46 668 12.54 2.79 0.67 17 120 3.77 736 13.72 3.13 0.64 18 130 4.09 820 15.31 3.47 0.61 19 140 4.40 865 15.92 3.81 0.59 20 150 4.72 951 17.57 4.14 0.58 21 160 5.03 1050 19.38 4.58 0.45

Table B10: Data Sheet for 50mm diameter Model Pile without Spring.

Sl.No Proving ring,reading (Div)

Total Load on pile

Dial gauge reading,(Div)

Deflection

KN mm 1 0 0.00 0 0.0 2 5 0.16 50 1.27 3 10 0.31 120 3.05 4 15 0.47 238 6.05 5 20 0.63 438 11.13 6 25 0.79 667 16.94 7 30 0.94 865 21.97 8 35 1.10 1115 28.32 9 40 1.26 1400 35.56 10 50 1.57 2500 63.50

84

Table B11: Data Sheet for 75mm diameter Model Pile with Softer Spring.

Sl.No Proving ring,reading (Div)

Total Load on pile

Dial gauge reading, (Div)

Deflection End force

Frictional force

kN mm kN kN 1 0 0.00 0 0.00 0.00 0.00 2 5 0.16 8 0.20 0.03 0.13 3 10 0.31 50 1.1 0.08 0.24 4 15 0.47 126 3.0 0.13 0.34 5 20 0.63 230 5.5 0.23 0.40 6 25 0.79 326 7.8 0.33 0.45 7 30 0.94 445 10.6 0.45 0.49 8 40 1.26 700 16.7 0.69 0.57 9 50 1.57 923 22.0 0.93 0.64

10 60 1.89 1184 28.0 1.28 0.61 11 70 2.20 1425 33.6 1.62 0.58 12 80 2.51 1686 39.7 1.96 0.55 13 90 2.83 1915 44.9 2.35 0.47 14 100 3.14 2180 51.0 2.75 0.40 15 110 3.46 2391 55.8 3.10 0.36

85

Table B12: Data Sheet for 75mm diameter Model Pile with Stiffer Spring.

Sl.No Proving ring, reading (Div)

Total Load on pile

Dial gauge reading,

(Div)

Deflection End force Frictional force

kN mm kN kN 1 0 0.00 0 0.0 0.00 0.00 2 5 0.16 2 0.04 0.01 0.15 3 10 0.31 10 0.16 0.06 0.26 4 15 0.47 20 0.32 0.12 0.35 5 20 0.63 46 0.86 0.20 0.43 6 25 0.79 68 1.26 0.29 0.49 7 30 0.94 97 1.84 0.39 0.55 8 40 1.26 160 3.08 0.62 0.64 9 50 1.57 217 4.14 0.86 0.71 10 60 1.89 270 5.06 1.13 0.76 11 70 2.20 329 6.14 1.39 0.81 12 80 2.51 390 7.25 1.67 0.85 13 90 2.83 454 8.41 1.96 0.87 14 100 3.14 520 9.62 2.26 0.89 15 110 3.46 570 10.34 2.60 0.86 16 120 3.77 626 11.24 2.93 0.84 17 130 4.09 699 12.5 3.31 0.78 18 140 4.40 765 13.58 3.68 0.72 19 150 4.72 825 14.53 4.04 0.67 20 160 5.03 885 15.46 4.41 0.62 21 170 5.34 959 16.76 4.78 0.57 22 180 5.66 1025 17.85 5.15 0.51

86

Table B13: Data Sheet for 75mm diameter Model Pile without Spring.

Sl.No Proving ring,reading(Div)

Total Load on pile

Dial gauge reading,(Div)

Deflection

kN mm 1 0 0.00 0 0.0 2 5 0.16 30 0.76 3 10 0.31 110 2.79 4 15 0.47 200 5.08 5 20 0.63 350 8.89 6 25 0.79 500 12.70 7 30 0.94 650 16.51 8 40 1.26 900 22.86 9 50 1.57 1200 30.48 10 60 1.89 1700 43.18 11 70 2.20 2500 63.50

87

Table B14: Data Sheet for 100mm diameter Model Pile with Softer Spring.

Sl.No Proving ring, reading(Div)

Total Load on pile

Dial gauge reading, (Div)

Deflection End force

Frictional force

kN mm kN kN 1 0 0.00 0 0.00 0.00 0.00 2 5 0.16 4 0.09 0.00 0.15 3 10 0.31 34 0.80 0.04 0.27 4 15 0.47 74 1.73 0.10 0.38 5 20 0.63 122 2.82 0.17 0.46 6 25 0.79 180 4.18 0.25 0.54 7 30 0.94 230 5.32 0.33 0.61 8 40 1.26 355 8.21 0.51 0.75 9 50 1.57 527 12.26 0.71 0.86 10 60 1.89 691 16.11 0.90 0.98 11 70 2.20 883 20.58 1.16 1.04 12 80 2.51 1080 25.14 1.44 1.07 13 90 2.83 1232 28.54 1.73 1.10 14 100 3.14 1410 32.61 2.02 1.13 15 110 3.46 1692 39.27 2.33 1.13 16 120 3.77 1917 44.45 2.67 1.10 17 130 4.09 2150 49.81 3.02 1.07 18 140 4.40 2417 56.01 3.38 1.02 19 150 4.72 2642 61.18 3.73 0.99 20 160 5.03 2909 67.26 4.17 0.86

88

Table B15: Data Sheet for 100mm diameter Model Pile with Stiffer Spring.

Sl.No Proving ring, Reading (Div)

Total Load on pile

Dial gauge reading, (Div)

Deflection End force

Frictional force

kN mm kN kN 1 0 0.00 0 0 0.00 0.00 2 5 0.16 2 0.03 0.01 0.15 3 10 0.31 8 0.16 0.03 0.28 4 15 0.47 27 0.54 0.09 0.38 5 20 0.63 48 0.92 0.19 0.44 6 25 0.79 77 1.54 0.26 0.53 7 30 0.94 99 1.99 0.31 0.63 8 40 1.26 150 3.02 0.49 0.77 9 50 1.57 210 4.27 0.66 0.91 10 60 1.89 268 5.34 0.88 1.00 11 70 2.20 321 6.31 1.14 1.06 12 80 2.51 380 7.35 1.42 1.09 13 90 2.83 444 8.61 1.70 1.13 14 100 3.14 492 9.36 1.96 1.18 15 110 3.46 555 10.37 2.31 1.15 16 120 3.77 620 11.44 2.67 1.10 17 130 4.09 688 12.58 3.09 1.00 18 140 4.40 740 13.45 3.43 0.97 19 150 4.72 806 14.47 3.78 0.94 20 160 5.03 862 15.27 4.17 0.86 21 170 5.34 920 16.18 4.51 0.83 22 180 5.66 1001 17.72 4.91 0.75

89

Table B16: Data Sheet for 100mm diameter Model Pile without Spring.

Sl.No Proving ring, reading(Div)

Total Load on pile

Dial gauge reading, (Div

Deflection

kN mm 1 0 0.00 0 0.0 2 5 0.16 10 0.25 3 10 0.31 50 1.3 4 15 0.47 120 3.0 5 20 0.63 200 5.1 6 25 0.79 300 7.6 7 30 0.94 400 10.2 8 40 1.26 610 15.5 9 50 1.57 800 20.3 10 60 1.89 1020 25.9 11 70 2.20 1300 33.0 12 80 2.51 1750 44.5 13 90 2.83 2400 61.0