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RAPID PULLOUT TEST OF SOIL NAIL

OOI POH HAI

NATIONAL UNIVERSITY OF SINGAPORE

2006

RAPID PULLOUT TEST OF SOIL NAIL

OOI POH HAI (B.Eng. (Hons), UTM)

A THESIS SUBMITTED

FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

DEPARTMENT OF CIVIL ENGINEERING

NATIONAL UNIVERSITY OF SINGAPORE

2006

i

Acknowledgments

I would like to express my sincere gratitude and appreciation to my supervisor,

Assoc. Prof. Dr. Tan Siew Ann, for his invaluable advice throughout this study. I am

grateful for his relentless efforts in helping to overcome the difficuities encountered

during the course of this research program.

I would like to thank my friend, Mr. William Cheang, for spending time

clarifying doubts I had and providing me with the background information regarding

this project.

I would like to thank all colleagues and technicians from Geotechnical

Laboratory for providing assistance throughout this project.

I would like to thank the examiners of this thesis for their valuable and

constructive comments which helps to improve the quality of this thesis.

At last, I would like to thank my parents for their kind support and

encouragement.

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Table of Contents

Page

Acknowledgements i

Table of Contents ii

Summary vi

List of Tables viii

List of Figures ix

List of Symbols

xvi

Chapter 1: Introduction 1

1.1 Problem Background 1

1.2 Literature Review 5

1.2.1 Dynamic Testing Techniques 5

1.2.1.1 Low Strain Integrity test 6

1.2.1.2 High Strain Dynamic test 7

1.2.1.3 Rapid Test 10

1.2.1.4 Testing Technique for Dynamic Pullout Test of

This Study

15

1.2.2 Dynamic Shaft Resistance 16

1.3 Problem Definition 19

1.4 Objectives and Scope 21

Chapter 2: Descriptions of Experiments 29

2.1 Introduction 29

2.2 Pullout Box 29

2.3 Quasi Static Pullout Machine 31

2.4 Impulse Hammer 32

2.4.1 Working Mechanism 32

2.4.2 The Characteristic of Impulse Load 35

iii

2.5 Instrumentations 35

2.5.1 Load Cell 35

2.5.2 Linear Motion potentiometer 36

2.5.3 Strain Gauge 37

2.5.4 Data Acquisition System 40

2.6 Nail 41

2.6.1 Dimension and Material 41

2.6.2 Types of Nail Surface 41

2.6.2.1 Preparation of Nail Surface 42

2.6.2.2 Normalized Roughness Rn 43

2.7 Sand 45

2.7.1 Basic Properties 45

2.7.2 Direct Shear Test 46

2.7.3 The Construction of Sand Medium 51

2.8 Experimental Program 54

Chapter 3: Quasi Static Pullout Test 84

3.1 Introduction 84

3.2 The Plot of Load Displacement Curve 84

3.2.1 Repeatability of Test Results 85

3.3 Quasi Static Pullout Response 86

3.3.1 Rough Nail 86

3.3.2 Smooth Nail 89

3.4 Quasi Static Load Distribution Curve 90

3.5 Peak Quasi Static Pullout Strength and Restrained Dilatancy

Effect

90

3.6 Quasi Static Reload Test 96

3.7 Concluding Remarks 98

Chapter 4: High Energy Rapid Pullout Test 112

4.1 Introduction 112


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4.3 Pre Peak Rapid Pullout Response of Rough Nail 115

4.3.1 Pre Peak rapid Pullout Stiffness 115

4.3.2 Peak rapid Pullout Strength 116

4.3.3 The Causes of Improvements in Pre Peak Rapid Pullout

Response

119

4.3.4 Rapid Load Distribution Curve 126

4.4 The ‘Actual’ Damping Coefficient 127

4.5 Post Peak Softening Behaviour of Rough Nail 134

4.6 Rapid Pullout Response of Smooth Nail 139

4.7 Quasi Static Reload Test 141


Chapter 5: Low Energy Rapid Pullout Test 174



5.3 Pullout Response of Low Energy Rapid Pullout Test 176

5.4 Successive Low Energy Rapid Pullout Tests 178

5.5 Succeeding Quasi Static Pullout Test 179

5.6 Modified Unloading Point Method 180


Chapter 6: Discussion on Spring and Dashpot Model 192


6.2 Reviews on Available Shaft Models Appiled to Pile 192

6.3 Modelling of Rapid Pullout Response of Rough Nail 197

6.3.1 Model with Constant Pre Failure Stiffness 199

6.3.2 Model with Weaken Zone Hyperbolic Spring 201


Chapter 7 Conclusions 212


7.2 Findings of this Study

212

v

7.3 Implications on the Development of Rapid Pullout Test of Soil

Nail

216

7.4 Recommendations for Future Research 219

References 221

Appendix A 234

Appendix B 244

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Summary

The main purposes of this research project were to investigate the pullout

response of soil nail under rapid loading condition and to clarify the potential of rapid

pullout test as a supplementary test method to assess the quasi static pullout response

of soil nail. The rapid loading condition is referred to the loading condition similar to

‘Statnamic’ pile load test. These purposes were achieved by conducting a series of

large scale laboratory rapid and quasi static pullout tests on horizontal nails embedded

in dry clean sand. To conduct the laboratory rapid pullout tests, a spring based

impulse hammer was designed and built in this research project.

Results of these experiments showed that the influence of loading rate on

pullout response is highly dependent on the roughness condition of nail surface. For

rough nail, although the pre peak rapid pullout response was generally similar to the

pre peak quasi static pullout response in trend, the pre peak pullout stiffness and peak

pullout strength of rapid pullout test were higher than those of corresponding quasi

static pullout test. These variations were found to be in direct proportion to nail

diameter and were identified to be most probably caused by the mobilization of

radiation damping effect. ‘Actual’ damping coefficient mobilized in these tests,

defined by the difference in load between equivalent quasi static and rapid load

displacement curves divided by nail’s velocity, was not a constant but decrease with

the increase in pullout displacement. Restrained dilatancy effect mobilized in rapid

pullout test is also found to be almost similar to that mobilized in quasi static pullout

test.

In contrary, the rapid pullout response of smooth nail was virtually identical to

the corresponding quasi static pullout response with negligible damping effect.

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For low energy rapid pullout tests which the nails were not loaded to complete

pullout failure, the unloading point, the point of maximum displacement and zero

velocity on rapid load displacement curve, was observed to coincide with the

corresponding quasi static load displacement curve. By using this unique

characteristic of the unloading point, ‘Modified Unloading Point Method’ was

suggested to predict the equivalent quasi static pullout response from low energy

rapid pullout test result by simple interpretation procedures. Besides, it is also

observed that the quasi static pullout response of a nail was not adversely affected by

the conduct of preceding rapid pullout test as long as the peak quasi static pullout

capacity was not exceeded. This observation suggests the capability of low energy

rapid pullout test to be applied as an inspection test method for working nail.

At the end of this thesis, discussion on modeling by spring and dashpot model

was presented. Experiences and concepts learned from the modelling of dynamic pile

shaft resistance were applied to model the high energy rapid pullout response of rough

nail. It is found that although current knowledge learned from dynamic pile shaft

modelling can simulate the rapid pullout response of rough nail reasonably well,

equivalent quasi static pullout response derived from the simulation results is

generally disagree with the experimental quasi static pullout response. More research

works are needed before spring and dashpot model can be conveniently used in

routine interpretation of field soil nail rapid pullout test results in future.

As a conclusion, the use of rapid pullout test as a supplementary test method

to assess the quasi static pullout response of soil nail seems to be feasible if the results

of rapid pullout test are interpreted by a proper interpretation method.

viii

List of Tables

Table 1.1 Suggestion on the minimum number of in-situ pullout tests required for

assessment of soil nail design parameters, by the French National

Research Project Clouterre (1991).

Table 1.2 Characteristics of different pile testing methods (after Holeyman,

1992).

Table 1.3 The relationship between dynamic and static shaft resistance in contact

with clay.

Table 2.1 Normalized Roughness Rn of nail surfaces.

Table 2.2 Descriptions and results of direct shear tests.

Table 2.3 Descriptions and results of sand density calibration tests.

Table 2.4 The details of test series conducted in these experiments.

Table 2.5 The details of pullout tests conducted under each test series.

Table 3.1 Summary of quasi static pullout tests results.

Table 4.1 Summary of high energy rapid pullout tests results for test series on

rough nail.

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List of Figures

Figure 1.1 The working mechanism of soil nail.

Figure 1.2 Typical setup of quasi static soil nail pullout test.

Figure 1.3 Typical result of low stain integrity test of a defective pile.

Figure 1.4 Typical result of high strain dynamic test on pile.

Figure 1.5 Comparison of load displacement curve of pile between high strain

dynamic test and static test (after Chow, 1999).

Figure 1.6 Comparison of load distribution curve of pile between high strain


Figure 1.7 Example result of stress wave matching method

Figure 1.8 Comparison of load displacement curve of pile between rapid test and

static test (after Chow, 1999).

Figure 1.9 Comparison of load distribution curve of pile between rapid test and


Figure 2.1 (a) The pullout box and (b) the steel frame that reduced the length of

pullout box from 2 m to 1.1 m.

Figure 2.2 Cross section of pullout box.

Figure 2.3 Reflection of circularly propagated stress wave by the square pullout

box.

Figure 2.4 The displacement controlled quasi static pullout machine.

Figure 2.5 Connection between pulling arm and connection rod.

Figure 2.6 Picture of impulse hammer.

Figure 2.7 Cross section of impulse hammer.

Figure 2.8 Steps of impulse generation, (a) compression of spring ‘A’, (b)

projecting of impact ram toward spring ‘B’, (c) collision of impact ram

with spring ‘B’.

Figure 2.9 Close view of mechanical lock.

Figure 2.10 Comparison of impulse load generated by the impulse hammer with

and without ‘Polyfoam’ on the impact face of spring ‘B’.

x

Figure 2.11 Calibration result of static load cell.

Figure 2.12 Static calibration result of potentiometer ‘T’.

Figure 2.13 Dynamic calibration result of potentiometer ‘T’.

Figure 2.14 Installed strain gauge.

Figure 2.15 Setup of (a) static strain calibration test, and (b) dynamic strain

calibration test.

Figure 2.16 Static strain calibration result of nail with surface sand glued by coarse

sand, for strain gauges installed at (a) 0.25 m, and (b) 0.45 m from nail

head.

Figure 2.17 Dynamic strain calibration results for nail with surface sand glued by

coarse sand, with impulse load imposed at (a) nail head, and (b) nail

end.

Figure 2.18 Close view of (a) C surface, (b) F surface, (c) P surface and (d) U

surface.

Figure 2.19 Surface profiles of F surface measured at three random locations.

Figure 2.20 Surface profiles of P surface measured at three random locations.

Figure 2.21 Surface profiles of U surface measured at three random locations.

Figure 2.22 Particle distribution curve of coarse sand and fine sand.

Figure 2.23 Shear stress – normal stress relationship of direct shear test results.

Figure 2.24 Result of direct shear tests with dense coarse sand medium.

Figure 2.25 Comparison of direct shear test results between DCs-C test (90% Id)

and MCs-C test (82% Id).

Figure 2.26 Results of direct shear tests with dense fine sand medium.

Figure 2.27 The motion of sand hopper during sand pluviation process.

Figure 3.1 The load displacement curves of DCs-S25C test series measured at 0

m, 0.25 m and 0.45 m from nail head, (a) quasi static pullout test; (b)

quasi static reload test.

Figure 3.2 The load displacement curves of DCs-S45C test series measured at nail

head, (a) quasi static pullout test; (b) quasi static reload test.

xi

Figure 3.3 The load displacement curves of MCs-S25C test series measured at 0



Figure 3.4 The load displacement curves of DCs-S25F test series measured at 0



Figure 3.5 The load displacement curves of DCs-S45F test series measured at 0



Figure 3.6 The load displacement curves of DCs-L25F test series measured at 0

m, 0.4 m, 0.8 m and 1.2 m from nail head, (a) quasi static pullout test;

(b) quasi static reload test.

Figure 3.7 The load displacement curves of DFs-S25F test series measured at 0 m,

0.25 m and 0.45 m from nail head, (a) quasi static pullout test; (b)


Figure 3.8 The load displacement curves of DCs-S22U test series measured at nail


Figure 3.9 The load displacement curves of DCs-S25P test series measured at nail


Figure 3.10 Comparison of quasi static load displacement curves of test series with

rough nail embedded in dense coarse sand medium.

Figure 3.11 Comparison of quasi static load displacement curves of DCs-S25C test

series and MCs-S25C test series.

Figure 3.12 Load distribution curves of quasi static pullout tests on rough nail.

Figure 3.13 The relationship between ratio of friction coefficient µ at peak and nail

diameter, (a) between DCs-S25C test series and DCs-S45C test series;

and (b) between DCs-S25F test series and DCs-S45F test series.

Figure 4.1 Load displacement curves of high energy rapid pullout tests of DCs-

S25C test series measured at 0 m, 0.25 m and 0.45 m from nail head.


S45C test series.

Figure 4.3 Load displacement curves of high energy rapid pullout tests of MCs-

S25C test series measured at 0 m, 0.25 m and 0.45 m from nail head.


S25F test series measured at 0 m, 0.25 m and 0.45 m from nail head.

xii




L25F test series measured at (a) 0 m and 0.4 m from nail head, and (b)

0.8m and 1.2 m from nail head.

Figure 4.7 Load displacement curves of high energy rapid pullout tests of DFs-



S22U test series.


S25P test series.

Figure 4.10 The influence of inertia effect on rapid pullout response of (a) DCs-

S25C test series, (b) DCs-S25P test series, and (c) DCs-S22U test

series.

Figure 4.11 Comparisons of peak quasi static pullout strength, peak rapid pullout

strength and ‘analytical’ peak pullout strength of DCs-S25C test series,

DCs-S25F test series, DFs-S25F test series and MCs-S25C test series.

Figure 4.12 Comparison of rapid and quasi static load distribution curves of test

series on rough nails.

Figure 4.13 ‘Actual’ damping coefficient of DCs-S25C test series.

Figure 4.14 ‘Actual’ damping coefficient of DCs-S45C test series.

Figure 4.15 ‘Actual’ damping coefficient of MCs-S25C test series.

Figure 4.16 ‘Actual’ damping coefficient of DCs-S25F test series.

Figure 4.17 ‘Actual’ damping coefficient of DCs-S45F test series.

Figure 4.18 ‘Actual’ damping coefficient of DCs-L25F test series.

Figure 4.19 ‘Actual’ damping coefficient of DFs-S25F test series.

Figure 4.20 Comparison of ‘actual’ damping coefficient between DCs-S25C test

series and DCs-S25F test series.



Figure 4.22 Comparison of ‘actual’ damping coefficient between DCs-S25F test

series and DCs-L25F test series.

xiii


series and DCs-S45C test series (normalized to 25 mm nail diameter).

Figure 4.24 Comparison of ‘actual’ damping coefficient between DCs-S25F test

series and DCs-S45F test series (normalized to 25 mm nail diameter).

Figure 4.25 Load distribution curves of residual rapid pullout strength.

Figure 4.26 Comparison of load displacement curve and velocity displacement

curve of DCs-S25C-2-RH test.


curve of DCs-S45C-2-RH test.


curve of MCs-S25C-2-RH test.


curve of DCs-S25F-2-RH test.


curve of DCs-S45F-2-RH test.


curve of DCs-L25F-2-RH test.


curve of DFs-S25F-2-RH test.

Figure 4.33 Shear band model by Oda and Kanzama (1998).

Figure 4.34 Postulation on shear band evolution mechanism of rough nail – sand

interface in (a) quasi static pullout test, and (b) rapid pullout test.

Figure 4.35 Comparison of quasi static reload test results conducted after the high

energy rapid pullout test and quasi static pullout test.

Figure 5.1 Load displacement curves of low energy rapid pullout test, DCs-S25C-

3-RL.

Figure 5.2 Load displacement curves of low energy rapid pullout test, DCs-S25F-

3-RL.

Figure 5.3 Load displacement curves of low energy rapid pullout test, DCs-S45F-

3-RL.

Figure 5.4 Load displacement curves of low energy rapid pullout test, DCs-L25F-

3-RL

xiv

Figure 5.5 Load displacement curves of low energy rapid pullout test, DFs-S25F-

3-RL.

Figure 5.6 ‘Actual’ damping coefficient of DCs-S25F-3-RL test.

Figure 5.7 ‘Actual’ damping coefficient of DCs-S45F-3-RL test.

Figure 5.8 ‘Actual’ damping coefficient of DCs-L25F-3-RL test.

Figure 5.9 Comparison of derived and experimental quasi static curves of DCs-

S25C test series.


S25F test series.


S45F test series.


L25F test series.

Figure 5.13 Comparison of derived and experimental quasi static curves of DFs-

S25F test series.

Figure 6.1 Dynamic shaft resistance models proposed by (a) Smith (1960), (b)

Randolph and Simon (1986), and (c) El-Naggar and Novak (1994).

Figure 6.2 Comparison of simulated load displacement curves by multiple

element wave equation model and single element lumped mass model.

Figure 6.3 Approximation of non linear hyperbolic load displacement response by

constant stiffness matched at particular pullout stage.

Figure 6.4 Load displacement curves of DCs-S25C test series simulated by the

model with constant pre failure stiffness, compare to the experimental

results.

Figure 6.5 Damping coefficient predicted by the model with constant pre failure

stiffness, compare to the experimental ‘actual’ damping coefficient

(DCs-S25C test series).

Figure 6.6 Load displacement curves of DCs-S25C test series simulated by the

model with weaken zone hyperbolic spring, compare to the

experimental results.

Figure 6.7 Damping coefficient predicted by the model with weaken zone

hyperbolic spring, compare to the experimental results (DCs-S25C test

series).

xv

Figure 6.8 Velocity of shaft node and outer field soil medium simulated by model

with weaken zone hyperbolic spring, for DCs-S25C test series.

Figure 6.9 Load displacement response of DCs-S45C test series simulated by the

model with weaken zone hyperbolic spring, compare to the

experimental results.

xvi

List of Symbols

a Acceleration

ao Dimensionless frequency

C Damping coefficient

Cul

Damping coefficient at the unloading point.

c Damping coefficient (per unit length)

c* ‘Actual’ damping coefficient (per unit length)

d Diameter of shaft / nail

D50 Mean particle size of sand

e Void ratio

f Apparent ratio of friction coefficient

Gm Shear modulus of high strain weaken zone

Gmi

Initial shear modulus of high strain weaken zone

Gs Shear modulus of soil

Id Relative density of soil

J*

Loading rate factor

Js Smith’s damping factor

K Pullout stiffness

Ko Horizontal earth pressure at rest

Ksi Initial quasi static pullout stiffness

Ksp Secant pullout stiffness at peak of quasi static pullout response

k Stiffness coefficient of shaft resistance (per unit length)

kst Tangent stiffness of quasi static pullout response (per unit length)

L Length of pile

xvii

Le Effective nail length

M Mass of nail

Nw Wave Number

Pd Dynamic impulse load (before subtraction of inertia effect)

Pr Rapid load (after subtraction of inertia effect)

Prmax

Maximum rapid load (after subtraction of inertia effect)

Prp Peak rapid pullout strength (after subtraction of inertia effect)

Prres

Rapid residual pullout strength (after subtraction of inertia effect)

Prul

Rapid load at the unloading point (after subtraction of inertia effect)

Ps Static load

Psp Quasi static peak pullout strength

Psreload

Maximum quasi static reloading pullout strength

pd Dynamic shaft resistance (per unit length)

pd(u) Limiting dynamic shaft resistance (per unit length)

ps Static shaft resistance (per unit length)

ps(u) Limiting static shaft resistance (per unit length)

Rmax Maximum distance between highest peak and lowest through of a surface

profile within a length equal to D50 of sand in contact

Rn Normalized roughness

Rncri

Critical normalized roughness

r Radius of shaft / nail

r1 Radius of weaken zone

td Loading duration of impulse load

u Displacement

up(r)

Displacement at peak rapid pullout strength

xviii

up(s)

Displacement at peak quasi static pullout strength

uul

Displacement at the unloading point

Vp Longitudinal Wave Speed

Vs Shear wave (distortional) speed

v Velocity

vmax

Velocity at the point of maximum rapid load

αp Ratio of peak rapid pullout strength to peak quasi static pullout strength

β Correlation factor between static tangent stiffness and ‘actual’ damping

coefficient

∆e Elastic elongation of model nail.

∆v Relative velocity between shaft and adjacent soil

δ’ Interface friction angle

δ’r Rapid interface friction angle

δ’s Static interface friction angle

φ’ds Direct shear friction angle of soil

φ’ps Plane strain friction angle of soil

Λ Relative Wave Length

µ Ratio of friction coefficient

ρs Dry density of sand medium

ρg Density of sand particles

σ’n(p) Mean effective normal stress on nail shaft at peak pullout stage

σ’n(i) Initial mean effective normal stress on nail shaft

σ’v Effective vertical stress

σ’o Mean effective confining stress

xix

∆σ’ Increment of effective normal stress

τo Shear stress of soil adjacent to shaft

τf Ultimate shear stress

ω Angular frequency of loading

ψ Dilatancy angle

Chapter 1: Introduction

1.1 Problem Background

In recent years, soil nailing technique has been widely accepted by the

industry as an effective and economic reinforcement method to stabilize natural slope

or excavation face. In this technique, a number of discrete reinforcement elements are

installed near horizontally into the reinforced ground in grid pattern. The presence of

these discrete reinforcement elements essentially restrict the degree of stress relief of

the ground by holding the active zone of unstable soil wedge to the stable passive

wedge at the back (Figure 1.1).

Although there are a number of soil nail design methods available today, such

as the methods proposed by Shen et.al., (1978), Stocker et.al. (1979), Schlosser,

(1982) and Juran et.al., (1990), all of these methods emphasize the important role of

shaft resistance at nail - soil interface. The contribution of bending resistance has been

found to be fairy insignificant in common application of soil nail especially when

large lateral movement of the soil nailed structure is undesirable. Gassler (1990)

stated that the contribution of bending resistance is minimal and in second order when

compared to the role of shaft resistance, and can reasonably be ignored in the design.

The French National Research Project Clouterre (1991) also stated that although the

consideration of bending resistance may be beneficial for ductile reinforcement at

failure, its contribution is usually less than 15 % and most of the resistance is

contributed by shaft resistance. Jewell and Pedley (1992) concluded from laboratory

test that bending or shear resistance mobilized in nail is modest when compared with

that due to shaft resistance. Kenny and Kawai (1996) by finite element analysis also

arrived at the same conclusion. All of these results strengthen the importance of shaft

resistance in soil nail design.

Due to the importance of nail- soil shaft resistance, reliable assessment of

shaft resistance is crucial for a safe and economical soil nailing design. Although

design charts that correlate the limiting shaft resistance with soil types (French

National Research Project Clouterre, 1991) and analytical equilibrium equations that

calculate the limiting shaft resistance from basic soil properties and stress boundary

conditions (Schlosser, 1982, Jewell, 1980) were proposed, in-situ pullout test still

appears to be the most reliable and straightforward method to directly assess the

limiting shaft resistance of an installed nail including its load displacement

characteristic. Several soil nail design codes, such as the Euro code, the FHWA code

and the ‘Recommendations Clouterre’ (French National Research Project Clouterre,

1991) have stressed the importance of in-situ pullout test and stated that in-situ

pullout test must be conducted in every soil nailing work although the limiting shaft

resistance has been predicted by other methods. Inspection (acceptance) pullout test

must also be conducted to examine the as-constructed performance of working nails.

Table 1.1 tabulates the minimum number of in-situ pullout tests suggested by the

French National Research Project Clouterre (1991) for reliable assessment of soil nail

design parameters, depending on the area covered by each soil type. The French

National Research Project Clouterre (1991) also specifies that for each soil type and

each excavation stage, minimum 5 inspection tests shall be conducted for the first

1000 m2 of soil nailed area, and adds 1 test for every additional 200 m

2. Additional

inspection tests are also needed for suspicious working nails. Based on the

suggestions by the French National Research Project Clouterre (1991), the total

number of in-situ pullout tests required for a soil nailing site with highly

heterogeneous soil profile such as the tropical residual soil would be particularly high.

As an example, for a site consists of 3 different soil types covering 1000 m2 each, the

minimum number of in-situ pullout tests required for the assessment of soil nail

design parameters is 27 (based on Table 1.1, 9 test per 1000m2) and the minimum

number of inspection tests required for confirmation of as-constructed performance of

working nails is 15 (5 tests per 1000 m2). In total, the minimum number of in-situ

pullout tests required is as high as 42. Additional inspection tests would also be

needed if unforeseen soil condition such as localized soft soil pocket is revealed

during the installation process.

Nowadays, the only available in-situ soil nail pullout test method is quasi

static pullout test. In this method, quasi static pullout load is applied to nail head

either at constant slow displacement rate (displacement controlled test) or at constant

small load increment (force controlled test). A typical setup of quasi static pullout test

is shown in Figure 1.2. A rigid reaction frame is raised on the sloping ground to

transfer and support the pullout load exerted in the test. This reaction frame is usually

supported at four corners either by concrete pads or existing wall facing. Bearing

capacity of these supports must be sufficient enough to bear the maximum pullout

load anticipated for the test. These supports must also be placed as far as possible

from the nail to minimize the transfer of additional stresses to nail – soil interface

which will affect the pullout test result. But on the other hands these supports can not

be placed too far away from the nail to ensure the rigidity and stability of the whole

setup.

It has to be said that raising this reaction frame on sloping ground is in fact

quite tough and challenging because the slope angle of soil nailed structure is

normally very steep or even at 90o. Sometimes days will be needed to prepare the

slope surface for proper sitting of this reaction frame, especially for slope with weak

surface ground. The pullout test itself normally will take about half to one day

depending on the size of load increment or pullout rate of the test.

As has been discussed before, the total number of pullout tests needed for a

soil nailing work may be quite high especially for site with highly heterogeneous soil

profile. Therefore, the time consumed by pullout tests is sometimes impractically long.

Moreover, construction of soil nailed structure adopts top – down sequence. If the

working performance of soil nails installed for a particular excavation stage still can

not be confirmed because pending for the result of inspection tests, the excavation of

following stage shall not be on halt. Consequently, this may result in delay of

construction, or the worst causes the reduction in the number of inspection tests to

compensate the lost in time, which either is undesirable.

In view of this, idea to explore the feasibility of using dynamic pullout test as

a supplement to the conventional quasi static pullout test was recently initiated in the

National University of Singapore. It has to be stressed that dynamic pullout test is not

intended to replace the conventional quasi static pullout test which still appear to be

the most reliable and straightforward method to assess the static nail – soil shaft

resistance. Dynamic pullout test is intended to be used as a supplementary test method

that after being calibrated by equivalent quasi static pullout test results, it may be used

as part of the whole in-situ pullout test scheme, especially the inspection test. This

will reduce the number of quasi static pullout tests required, and will eventually save

the testing time (and hence construction time) while keeping the total number of

pullout tests to a reasonable number.

The application of dynamic pullout test technique to soil nail is a novel

attempt. Therefore, as the first step to the development, it is necessary to investigate

the dynamic pullout response of soil nail and the feasibility of this method by

laboratory test with well controlled test conditions before applying it to the more

expensive and complicated field trial. This forms the basis of study presented in this

thesis.

However, although the application of dynamic pullout test on soil nail is a new

attempt, dynamic testing technique has been widely applied to assess the compression

capacity of pile for the past few decades. Hence, a review on the types of dynamic

testing techniques that have been applied to pile and the experiences on behaviour of

dynamic shaft resistance of piles would be valuable. The review on types of dynamic

testing technique may help to determine the type of dynamic testing technique that

will be adopted for the newly initiated dynamic soil nail pullout test and facilitate the

design of a suitable impulse hammer to conduct the dynamic pullout test in this study.

1.2 Literature Review

In this section, the experience of dynamic testing on pile, emphasising on the

characteristics of each dynamic testing techniques and the behaviour of dynamic shaft

resistance of pile, are presented and reviewed.

1.2.1 Dynamic Testing Techniques

Nowadays, dynamic testing techniques that have been applied to pile can be

grouped into three categories, the low strain integrity test, high strain dynamic load

test and rapid test. Table 1.2 summarizes the main characteristics of these dynamic

testing techniques and compare them with the characteristics of conventional static

load test of pile (Holeyman, 1992). It has to be noted that the rapid test is termed as

kinetic test in the original paper by Holeyman (1992) but the terms ‘kinetic test’,

‘rapid test’ or the commercial name ‘Statnamic test’ all referred to the same type of

dynamic testing technique. A review on the characteristics and behaviours of these

dynamic testing techniques is given below, including the limited experiences of

utilizing the dynamic compression test result to predict the tension capacity of pile.

1.2.1.1 Low Strain Integrity Test

In low strain integrity test, the pile head is knocked by a small hand held

hammer to send a low strain impulse wave down the pile. The loading duration of this

impulse wave is relatively short, usually in the range of 0.5 ms to 2 ms only (Table

1.2). The relatively short impulse duration of this test is essential to ensure good depth

resolution of test result.

The basic working mechanism of this test is the detection of early wave

reflection caused by pile defects. For non defective pile, the impulse wave will only

be reflected by pile toe and the reflected wave will only arrive at pile head after a time

period of 2L/Vp (L = pile length, Vp = longitudinal wave speed of pile). While, the

existence of pile defects will induce changes in pile impedance and subsequently

cause the early reflection of impulse wave. The reflected wave caused by pile defects

will arrive at pile head by time shorter than 2L/Vp (Rausche et.al., 1992). Figure 1.3

shows typical low strain integrity test result of a defective pile. This result clearly

shows the distinctive difference of reflected wave caused by pile defects and pile toe

Because the strain level of impulse wave applied in low strain integrity test is

usually very small, soil resistance is unlikely to be mobilized in this test. Hence, this

method is clearly inapplicable for the development of dynamic soil nail pullout test

that aims to predict the pullout strength. However, this test method may be applied to

examine the integrity and length of installed nail. But these subjects are not the

purposes of this study.

1.2.1.2 High Strain Dynamic test

In high strain dynamic test, a high strain compressive impulse wave is

generated by the impact of a heavy drop hammer on pile head. The impulse wave then

propagates down the pile to mobilize the soil resistance. The mobilization of soil

resistance will result in wave reflection that propagates in direction opposite to the

incident wave. Once this reflected wave arrives at the pile head, it will cause the

separation of particle velocity trace and force trace as shown in Figure 1.4.

By referring to Table 1.2, the relative wave length Λ, defined by Holeyman

(1992) as the ratio of impulse wave’s travelling length to twice the pile length (Eq.

1.1), of high strain dynamic test is in the range of 0.1 – 1.

L

tV dp

2=Λ (1.1)

with Vp = longitudinal wave speed in nail’s body, td = loading duration, L = length of

pile.

This means that in typical high strain dynamic test, the travelling duration

taken by an impulse wave to travel to pile toe and reflected back again to pile head is

longer than the loading duration of impulse wave. In other words, stress wave

propagation phenomenon exists in the high strain dynamic test. This is the reason why

the load displacement response of pile in high strain dynamic test is very different

from the load displacement response of equivalent static test (Figure 1.5) (Chow,

1999). The distribution of axial load in high strain dynamic test is also very different

from that of static test (Figure 1.6). Hence, the prediction of equivalent static load

displacement response of pile from the high strain dynamic test result can only be

achieved by relatively complicated and non straightforward procedures. Nowadays,

the most popular interpretation method of high strain dynamic test result is the stress

wave matching method (Rausche et.al., 1972).

In stress wave matching method, either the velocity trace or force trace

measured in field is used as the input parameter to simulate the high strain dynamic

test by one dimension wave equation model. In the simulation process, the parameters

of soil resistance along the pile are varied until acceptable matched is obtained

between the measured and computed pile dynamic response. The equivalent static

load displacement response is then derived by considering the stiffness resistance

(spring) only. Figure 1.7 shows an example of stress wave matching result. In this

example, the force trace was used as the input value while the velocity trace was the

target of matching. The accuracy of this method is mainly dependent on the accuracy

of dynamic soil resistance modelling of the wave equation model.

The first model of dynamic soil resistance was proposed by Smith (1960).

Smith (1960) idealized the dynamic soil resistance by spring and dashpot that

simulate the displacement dependent stiffness resistance and the velocity dependent

damping resistance respectively. After that, several improvements on this spring and

dashpot model have been suggested to improve its accuracy. Randolph and Simon

(1986) and Lee et.al. (1988) replaced the purely empirical spring and dashpot

coefficients of Smith’s model by analytical solutions that correlate the spring and

dashpot coefficients to basic soil properties. Later, attempts to incorporate the

existence of weaken zone around pile shaft were also made by several researchers

such as Mitwally and Novak (1988) and El-Naggar and Novak (1994). The existence

of weaken zone around pile shaft has been identified to reduce the radiation damping

resistance (Novak and Sheta, 1980). Detailed discussions on these spring and dashpot

models for dynamic shaft resistance will be given in Chapter 6.

Despite the stress wave matching method has been widely applied since its

introduction, Poulos (1998) commented that the prediction of static pile response by

this method is just a best fit prediction obtained through trial and error procedure only.

The main disadvantage of stress wave matching technique is the non-uniqueness of its

solution, which means that different set of soil parameters may still lead to

considerable matched of the measured and computed dynamic response. Therefore,

the accuracy of this method depends a lot on the experience and knowledge of the

engineer. This disadvantage can be seen from the results of prediction activity

reported by Holeyman et.al. (2000) which showed that the percentage of variation in

ultimate pile capacity predicted by different parties from the same set of high strain

dynamic test result was as high as 100 %.

To the author’s knowledge, although high strain dynamic test technique has

been extensively applied to conduct pile dynamic compression test, only one attempt

to apply this technique on dynamic tension test is available. This attempt was reported

by Klingberg and Wong (1996). But unfortunately due to the technical limitation of

their apparatus, full mobilization of tension capacity was not achieved in their

dynamic tension test. Tension capacity predicted by their dynamic tension test was

only 46 % of tension capacity resulted from equivalent static tension test. After that,

no further attempts are reported on the application of high strain dynamic tension test

probably due to the difficulty to develop an apparatus capable of supplying sufficient

dynamic tension energy. Hence, nowadays tension capacity of pile is usually

estimated from total shaft resistance of equivalent high strain dynamic compression

test by applying a reduction factor of 0.75 - 0.8 (Randolph, 2000 and Martel and

Klingberg, 2004). This reduction factor is applied to account for the variation in

mobilization characteristic of shaft resistance between compression test and tension

test. However, this method requires accurate separation of shaft resistance from the

total compression resistance of pile. Although this can be achieved by the stress wave

matching method that models the shaft and toe resistance independently, sometimes

the outcomes is arbitrary due to the non uniqueness of stress wave matching result

(Middendorp and van Weele, 1986), particularly for the case with high shaft

resistance near to pile toe.

1.2.1.3 Rapid Test

Rapid test technique is a relatively recent development by the collaboration

works of Canada and the Netherlands (Middendorp et.al., 1992 and Bermingham

et.al,. 1994). This technique is usually known by its commercial name ‘Statnamic’

test. In some region, rapid test is also known as kinetic test.

The main characteristic of rapid test is the lengthening of impulse duration to

an extent that is sufficient to eliminate the influence of stress wave propagation

phenomenon. Holeyman (1992), Middendorp and Biefield (1995), Nishimura et.al.

(1998) and Chow (1999) suggested that the relative wave length (Eq. 1.1) of a rapid

test should exceed the minimum value of 5 - 10. This means that the impulse duration

of rapid test should be at least 5 - 10 times longer than the traveling period needed by

the impulse wave to be reflected back to pile head again. It has to be noted that the

suggestions by Middendorp and Biefield (1995), Nishimura et.al. (1998) and Chow

(1999) were reported in the form of wave number Nw which is exactly twice the value

of equivalent relative wave length.

For a commercial rapid test on pile (Statnamic test), the typical impulse

duration is in the range of 50 ms to 200 ms (Table 1.2), significantly larger than the

impulse duration used in high strain dynamic test. However, rapid test is still

considered as a category of dynamic tests because its loading duration is still

significantly shorter than that of static test.

Although in the commercial rapid test on pile (Statnamic test), the downward

compressive impulse wave is generated by the upward acceleration of a huge mass

induced by explosion, the impulse wave needed for a rapid test in fact can be

generated by any method as long as the duration of the generated impulse wave is

long enough to exceed the minimum relative wave length required to achieve the

rapid loading condition. As an example, Matsumoto et.al. (2004) has invented an

innovative rapid test method by attaching an additional soft spring and damper on pile

head. In this innovative method, the impulse wave is generated by the impact of drop

hammer on pile head similar to that in high strain dynamic test, but the duration of the

generated impulse wave was lengthen by the additional soft spring and damper to

meet the requirement of rapid loading condition. The load displacement response of

pile tested by this innovative method was shown to be similar to that of the

commercial rapid test.

Figure 1.8 plots the typical load displacement result of rapid test on pile.

When compared to the result of high strain dynamic test (Figure 1.5), it is clearly seen

that the rapid load displacement response of pile is similar to the static load

displacement response in trend. Besides, the load distribution curve of rapid test and

static test is also similar to each other in trend (Figure 1.9). These characteristics of

rapid test are the results of minimal influence of stress wave propagation in rapid test

due to longer impulse duration. These characteristics are the merits of rapid test when

compared to high strain dynamic test which is highly influenced by stress wave

propagation phenomenon. The stiffer and stronger rapid load displacement response

observed in Figure 1.8 is mainly attributed to the mobilization of damping effect

(Middendorp et.al., 1992). Besides, the unloading point, the point on rapid load

displacement curve with maximum displacement and zero velocity (Figure 1.8), is

also observed to coincide with the static load displacement curve. It is because the

damping resistance mobilized at the unloading point is negligible due to zero velocity

of this point.

The similar in trend of both rapid and static load displacement response and

the unique characteristic of the unloading point offer the possibility of deriving

equivalent static load displacement response from rapid test result with simple and

straightforward interpretation procedures, such as by the ‘Unloading Point Method’

proposed by Horvath et.al. (1995) and Kusakabe and Matsumoto (1995). In this

method, after the subtraction of inertia resistance, a constant damping coefficient Cul

is first calculated by Eq. 1.2 shown below:

max

max

v

PPC

ul

rrul −= (1.2)

with Prmax

= maximum rapid load, Prul

= rapid load at the unloading point, vmax

=

velocity at the point of maximum rapid load.

The equivalent static load displacement curve is then constructed by applying

Eq. 1.3 shown below to the measured rapid load displacement curve.

iuli

r

i

s vCPP −= (1.3)

with Psi = equivalent static load at point i, Pr

i = rapid load at point i after subtraction

of inertia effect, vi = velocity of point i.

Since the first introduction of ‘Unloading Point Method’, this method has been

widely applied to interpret the rapid pile test result and is found to usually result in

reasonably good prediction of equivalent static load displacement response. However,

the ‘Unloading Point Method’ also has its disadvantage. This method only treats the

measured rapid load displacement curve without any proper modeling of shaft and toe

resistance.

Therefore, attempts to model the rapid pile test response by spring and dashpot

model were also made. Kato et.al. (1998) and Chow (1999) proposed the use of

lumped mass models that model the shaft and toe resistance separately. In their

method, the spring and dashpot coefficients of the shaft and toe models are adjusted

until acceptable matched between simulated and measured rapid pile response is

obtained. However, the use of these lumped mass models requires the pile to behave

as rigid body and the distribution of shaft resistance along the pile shaft also needs to

be fairly uniform. Therefore, the use of one – dimensional wave equation model was

also attempted by several researchers (El Naggar and Novak, 1992, Ochiai et.al., 1996,

Asai et.al., 1997, Nishimura et.al., 1998) and has been reported to obtain reasonably

good results. The use of one dimensional wave equation model has the advantages of

being able to model the non uniform distribution of shaft resistance along the pile and

the pile does not need to behave as rigid body. However, Matsumoto et.al. (1997)

pointed out that allowance for the difference in drainage condition between rapid test

and static test must be provided for proper prediction of equivalent static load

displacement response from rapid test result. Besides, Hayashi et.al. (1998) pointed

out that back analysis of rapid pile response by wave equation model is non unique

and insensitive to the variation in distribution of shaft resistance along the pile and the

variation in proportion of contribution by toe resistance. These shortcomings are

mainly due to the nature of low depth resolution of rapid test. However, Hayashi et.al.

(1998) also stated that the uniqueness of rapid pile load test simulation can be

enhanced if measurements of axial body load along the pile are available.

The use of finite element method to interpret the rapid pile test result was also

attempted lately. The advantage of this method is more realistic modelling of

surrounding soil medium by more sophisticated soil model. Besides, the contribution

of radiation damping effect also evolves naturally in the finite element calculation

without the need of any external treatment. Horikoshi et.al. (1998) and Matsumoto

(1998) used the finite element method to simulate rapid pile test response and has

claimed to achieve reasonably good agreement. However, the use of finite element

method to back analyze the rapid pile test result is still tedious work and unpopular as

it requires much longer computational time.

In the author’s knowledge, no attempt has being made to apply the rapid test

technique to tension or pullout test that mobilizes the shaft resistance in tension only.

Although the tension capacity of pile may also be deduced by the method proposed by

Randolph (2000) and Martel and Klingberg (2004) for high strain dynamic test, which

the tension capacity be equated to the total shaft resistance mobilized in compression

test factored by a reduction factor of 0.8, this method is likely to be unreliable and

inaccurate. This is because the separation of shaft resistance from the total

compression resistance of pile is even more difficult for rapid test due to the low

depth resolution of this test.

1.2.1.4 Testing Technique for Dynamic Pullout Test of This Study

Among the dynamic testing techniques presented above, the low strain

integrity test is obviously irrelevant to the dynamic pullout test developed in this

study because shaft resistance is unlikely to be mobilized in this test due to the low

strain level.

Although both the high strain dynamic test and rapid test are capable of

mobilizing the shaft resistance, rapid test is preferred for dynamic pullout test

developed in this study. It is mainly because the load displacement response of rapid

test is more akin to the static load displacement response and the interpretation of

rapid test result is more straightforward. These characteristics of rapid test are

preferred for this study that appears to be the first attempt to investigate the dynamic

pullout response of soil nail. The results of rapid pullout test may provide direct

observation on the characteristic of shaft resistance when subjected to transient

impulse load. In contrast, the load displacement response of high strain dynamic test

is very different from the static load displacement response due to the influence of

stress wave propagation. The characteristic of dynamic shaft resistance of high strain

dynamic test can only be approximately and indirectly assessed through back analysis

by a suitable wave equation model, which depends a lot on the capability and

accuracy of shaft model used in the back analysis.

Therefore, rapid test is chosen as the dynamic test technique for the dynamic

pullout test developed in this study. Hereafter in this thesis, the dynamic pullout test

and dynamic pullout response will be directly termed as “rapid pullout test” and

“rapid pullout response” to more precisely reflect the loading condition of this test.

1.2.2 Dynamic Shaft Resistance

In this section, findings of past laboratory studies on the loading rate

dependency of shaft resistance will be presented and reviewed.

Dayal and Allen (1975) studied the influence of loading rate on ultimate shaft

resistance of pile by penetrating a small scale penetrometer into homogeneous soil

sample at constant penetration velocity. Their results showed that for dry sand, the

loading rate had an insignificant influence on the ultimate shaft resistance. In contrast,

the ultimate shaft resistance of pile embedded in clay was found to be approximately

correlated with penetration velocity by a non linear logarithmic equation shown in

Table 1.3. Dayal and Allen (1975) observed that the viscous coefficient KL in this

logarithmic equation decreased with the increase in soil strength.

Heerema (1979) conducted a dynamic test that simulates the unit shaft

resistance of pile by a piece of steel plate. In the test, the steel plate was pressed on

the surface of a soil sample at constant normal pressure and sheared along the

interface at constant velocity. From the test results, Heerema (1979) concluded that

for dry sand the ultimate shaft resistance was virtually independent of velocity while

for clay the relationship between ultimate shaft resistance and velocity can be best

fitted by a non linear power function (Table 1.3).

Litkouhi and Poskiti (1980) examined the relationship between ultimate shaft

resistance and loading rate by penetrating a modelled steel pile into clay sample at

constant penetration velocity. They also found that the ultimate shaft resistance of pile

embedded in clay can be correlated with penetration velocity of pile by a non linear

power function (Table 1.3). They also indicated that the loading rate factor J* in this

equation was decreasing with the increase in undrained shear strength of soil, which is

in agreement with the observation by Dayal and Allen (1975).

Lepert et.al. (1988) and BenAmar et.al. (1991) studied the loading rate

dependency of ultimate shaft resistance by driving a steel pile into homogeneous soil

sample. By taking the shaft resistance as the difference in axial body load measured

between two successive axial strain measurement points, the shaft resistance of test

with dry sand medium was found to be independent of velocity (Lepert et.al., 1988)

while the shaft resistance of test with clay was found to be non linearly correlated

with pile velocity by an exponential function (BenAmar et.al., 1991) (Table 1.3).

Chin and Seidel (2004) studied the loading rate dependency of clay – structure

interfaces by a dynamic shearing device that is almost similar to the device of direct

shear test. In their studies, three types of surface roughness were considered: the

smooth steel surface, the smooth concrete surface and the rough concrete surface.

Their results indicated that the ultimate shaft resistance of clay – structure interface

can be correlated by the exponential function proposed by BenAmar et.al. (1991) for

all types of surface roughness considered in their experiment.

From the experiences of past laboratory tests on loading rate dependency of

shaft resistance presented above, a general conclusion can be drawn. For dry sand, the

ultimate shaft resistance is virtually unaffected by the velocity. While for clay, the

ultimate shaft resistance is highly influenced by velocity with a non linear logarithmic,

exponential or power function.

However, detailed reviews of these past experimental experiences reveal that

the surfaces of shaft considered by all of these experiments, except those by Chin and

Seidel (2004), were metal surface. Potyondy (1961), Pedley (1991) and Frantzen

(1998) showed that the interface friction angle of metal surface is normally lower than

the friction angle of soil in contact. This is because the dominant failure mode of this

surface is the sliding failure along the interface and this type of surface was

categorized as smooth surface by Uesugi and Kishida (1986) and Hu and Pu (2004).

The behaviour of smooth surface is very different from the behaviour of rough surface.

The failure plane of rough surface is usually formed within the adjacent soil mass and

its interface friction angle is usually limited and equal to the friction angle of soil in

contact (Uesugi and Kishida, 1986). From the experience of Schlosser and Elias

(1978), Jewell (1980) and Frantzen (1998), the surface of in-situ grouted nail and

ribbed driven nail is most likely ‘the rough surface’ as the interface strength of these

nail are widely found to be identical to the shear strength of soil medium in contact.

Hence, the use of laboratory test results with smooth metal surface to predict the

loading rate dependency of these rough nails is questionable.

Although three types of surfaces were considered by Chin and Seidel (2004) in

their experiments, no clear conclusion on the influence of surface roughness on the

extent of loading rate dependency of ultimate shaft resistance was shown in their

paper. They only stated that the loading rate dependency of these surfaces was fairly

similar to each other in trend. Besides, only clay was considered in their experiments.

The possible influence of surface roughness on the loading rate dependency of rough

surface in contact with sandy soil was not reported. Moreover, the roughness

conditions of the surfaces considered in their experiments were not described

quantitatively such as by the normalized roughness Rn proposed by Uesugi and

Kishida (1986). Hence, reference to their result is quite difficult and uncertain.

Besides, all of the reviewed literature only reported the results on ultimate

shaft resistance without mentioning the influence of loading rate on load displacement

response. A good understanding of loading rate dependency on load displacement

response is important for the interpretation of rapid pullout test result because the

aims of rapid pullout test are not on the prediction of ultimate pullout capacity only

but also on the prediction of equivalent static load displacement response.

1.3 Problem Definition

Recently, rapid test has been used substantially in the pile testing industry, but

no experience on the application of this testing method to tension test that mobilizes

only the shaft resistance in tension is available. Although the tension or pullout

capacity of a geotechnical structure such as pile or soil nail may be deduced from the

equivalent rapid compression test result by taking the tension capacity as the total

shaft resistance mobilized in compression test factored by a reduction factor, the

result is arbitrary and non unique. This is mainly caused by the difficulty in accurate

separation of shaft resistance from the total pile compression resistance due to the low

depth resolution of rapid test result. Although some attempts have been made to

separate the total compression resistance of rapid compression test to shaft and toe

resistance (Hayashi et.al., 1998)), the outcomes are very dependent on the nature of

spring and dashpot model used in the back analysis. The characteristic of dynamic

shaft resistance deduced from the back analysis of rapid compression test is not a

physical measurement result but just an approximated result that depends a lot on the

nature of the shaft model. Any characteristics of dynamic shaft resistance that are

unforeseen or not considered by the shaft model will be misinterpreted or remain

undetected. Hence, rapid test in tension that enables the direct assessment of shaft

resistance is needed if good prediction of tension or pullout capacity as well as its

load displacement behaviour is targeted.

From the experimental results presented above on the loading rate dependency

of ultimate shaft resistance, it is noticed that most of these experiments were

conducted on smooth surface. It has been discussed before that the interface

behaviour of smooth surface and rough surface is far different from each other due to

the difference in mode of interface failure (Section 1.2.2). Hence, the use of these

experimental results to describe the pullout behaviour of rough nails such as the in-

situ grouted nail and ribbed driven nail is doubtful, especially for nails embedded in

sandy soil that has been shown to have negligible loading rate effect when in contact

with smooth metal surface. Moreover, the loading rate dependency of load

displacement behaviour of shaft resistance was not addressed by any of the

experimental works presented above. As a conclusion, the currently available

experimental results are still inadequate to provide confident description of the rapid

pullout behaviour of soil nail, especially for rough nails.

Besides, the influence of loading rate on restrained dilatancy effect is also

never being assessed before. Restrained dilatancy is an important mechanism that

influences the pullout capacity of rough soil nail embedded in dense dilative soil

(Schlosser, 1982). In the mobilization of dilative interfacial shaft resistance, soil

adjacent to shaft (within weaken zone) tends to dilate but this dilation tendency is

restrained by the surrounding relatively undisturbed soil medium. As a consequence,

additional circumferential compression pressure is induced by the surrounding soil

medium to elastically compress the weaken zone to compensate the plastic dilation

tendency. This additional compression pressure will then be transferred to the nail –

soil interface as an enhancement in normal stress, and finally increase the interfacial

shaft resistance. Restrained dilatancy effect is an important characteristic that must

also be mobilized in rapid pullout test if the rapid pullout test result is to be applied

for the prediction of equivalent quasi static pullout response. Detailed discussions on

restrained dilatancy effect will be given in Section 3.5 of Chapter 3.

1.4 Objectives and Scope

In view of the inadequacy of knowledge of rapid pullout response, a series of

large scale laboratory tests were conducted in this study to provide high quality data

for the physical observation on the rapid pullout response of soil nail and to compare

it with the corresponding quasi static pullout response.

The objectives of these experiments were:

• To investigate the pullout response of soil nail including its load displacement

characteristics under rapid loading condition. The influence of loading rate is

assessed by comparing the rapid pullout test results to the corresponding quasi

static pullout test results under the same test conditions.

• To examine the influence of surface roughness, nail diameter and effective

nail length on rapid pullout response of soil nail.

• To assess the mobilization characteristic of radiation damping effect in a rapid

pullout test.

• To evaluate the loading rate dependency of restrained dilatancy effect which is

an important mechanism that influences the pullout capacity of soil nail.

• To explore the potential of rapid pullout test as an alternative method to assess

the quasi static pullout response of soil nail.

• To evaluate the quasi static pullout response of soil nail after the conduct of

preceding rapid pullout test. This is important for the assessment of the

potential of rapid pullout test as an inspection test method that shall not

adversely affect the working performance of tested nail.

In these experiments, only dry sand medium was considered. The main reason

for this is to avoid the influence of viscous damping effect in order to focus the

investigations on radiation damping effect and loading rate effect only.

Besides, to avoid the random error of test conditions caused by the installation

of soil nail, pre buried nail installed in-place before the construction of soil medium

was used for all tests. The consistency of test conditions among tests is crucial for

these experiments to make the comparison of rapid and quasi static pullout results

sensible. Moreover, only nails installed horizontally were considered.

The findings of this study may serve as a basis for the development of a field

scale in-situ rapid pullout test capable of predicting the quasi static pullout behaviour

of soil nail. It needs to be stressed that this study only aims to investigate the

feasibility of rapid pullout test from a geotechnical perspective.

The author has to admit that currently the economical competitiveness of field

scale rapid pullout test still can not be assessed. It is because the cost of a field scale

rapid pullout test depends a lot on the mechanism and system applied, which are both

still an unknown. The laboratory scale apparatus used in these experiments may not

be applied to field scale test because of the large difference in impact energy needed.

It has to be said that the apparatus for field scale rapid pullout test is much

complicated and requires large input from mechanical engineering specialist.

However, due to the time saving in rapid pullout test, it is believed that the ‘final cost’

of a rapid pullout test will be lower than a quasi static pullout test.

Tab

le 1

.1:

Su

gges

tio

n o

n t

he

min

imum

num

ber

of

in-s

itu p

ull

out

test

s re

quir

ed f

or

asse

ssm

ent

of

soil

nai

l des

ign p

aram

eter

s, b

y t

he

Fre

nch

Nat

ional

Res

earc

h P

roje

ct C

loute

rre

(199

1).

m2 o

f ar

ea

No.

m2 o

f ar

ea

No.

Up t

o 8

00

6

4000 t

o 8

000

15

800 t

o 2

000

9

8000 t

o 1

6000

18

2000 t

o 4

000

12

16000 t

o 4

0000

25

Tab

le 1

.2:

Ch

arac

teri

stic

s o

f d

iffe

ren

t pil

e te

stin

g m

ethods

(aft

er H

ole

yman

, 1992).

L

ow

Str

ain

In

tegri

ty

Tes

t

Hig

h S

train

Dyn

am

ic

Tes

t R

ap

id T

est

Sta

tic

test

Mas

s of

Ham

mer

0.5

– 5

kg

2000 -

10000 k

g

2000 -

5000 k

g

N/A

Pil

e P

eak

Str

ain

2 -

10 µ

str

500 -

1000 µ

str

1000 µ

str

1000 µ

str

Pil

e pea

k V

elo

city

1

0 –

40 m

m/s

2000 -

4000 m

m/s

500 m

m/s

10

-3 m

m/s

Pea

k F

orc

e 2

– 2

0 k

N

2000 -

10000 k

N

2000 –

10000 k

N

2000 –

10000 k

N

Forc

e D

ura

tio

n

0.5

– 2

ms

5 –

20 m

s 50 –

200 m

s 10

7 m

s

Pil

e A

ccel

erat

ion

50 g

500 g

0.5

– 1

g

10

-14

g

Pil

e D

isp

lace

men

t 0.0

1 m

m

10-

30 m

m

50 m

m

> 2

0 m

m

Rel

ativ

e W

ave

Len

gth

Λ #

0.1

1.0

10

10

8

# Λ

= t

dV

p/2

L, w

ith

, t d

= l

oad

ing d

ura

tion, V

p =

longit

udin

al w

ave

spee

d o

f pil

e, a

nd L

= p

ile

len

gth

T

able

1.3

: T

he

rela

tio

nsh

ip b

etw

een d

ynam

ic a

nd s

tati

c sh

aft

resi

stan

ce i

n c

onta

ct w

ith c

lay.

Ori

gin

ato

r R

elati

on

ship

bet

wee

n D

yn

am

ic a

nd

Sta

tic

Sh

aft

Res

ista

nce

Dayal

& A

llen

(1

97

5)

(

)s

Lc

cDV

VK

qq

/lo

g1

/+

=

qcD

=

unit

dynam

ic c

on

e re

sist

ance

qc

=

unit

dynam

ic c

on

e re

sist

ance

at

low

est

pen

etra

tion r

ate

Vs

=

low

est

pen

etra

tion v

elo

city

(1.3

mm

/s)

KL

=

Vis

cous

coef

fici

ent

Hee

rem

a (1

97

9)

2.0

32

Va

a+

=τ

a 2 &

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Figure 1.1: The working mechanism of soil nail.

Figure 1.2: Typical setup of quasi static soil nail pullout test.

Passive Active

Nail

Figure 1.3: Typical result of low stain integrity test of a defective pile.

Figure 1.4: Typical result of high strain dynamic test on pile.

Figure 1.5: Comparison of load displacement curve of pile between high strain


High strain

dynamic test

Static test

Wave reflection

caused by pile

toe

Wave reflection

caused by pile

defect

2L/c

Figure 1.6: Comparison of load distribution curve of pile between high strain dynamic

test and static test (after Chow, 1999).

Figure 1.7: Example result of stress wave matching method.

High strain dynamic test

Static test

Figure 1.8: Comparison of load displacement curve of pile between rapid test and


Figure 1.9: Comparison of load distribution curve of pile between rapid test and static

test (after Chow, 1999).

Unloading point

Rapid test

Static test

Point of maximum

rapid load

Rapid Static

Dep

th (

m)

Chapter 2: Descriptions of Experiments

2.1 Introduction

In Chapter 1, the need to perform an experimental study on the pullout

response of soil nail under rapid loading condition was emphasized, and was

determined as the main activity in this research project. In view of the lack of

experiences on this subject, laboratory test was more preferred than field test because

the consistency of test conditions in laboratory test is more controllable. The

consistency of test conditions is essential for this study to make the comparison of

rapid and quasi static pullout test results sensible.

In this chapter, the setup of laboratory rapid pullout test and quasi static

pullout test will be discussed in detail, especially on the impulse hammer that was

designed and built in this research project to conduct the laboratory rapid pullout test.

The details of experimental program that describes the test conditions of all pullout

tests conducted in these experiments will also be given at the end of this chapter.

2.2 Pullout Box

The dimension of this steel pullout box was 1m in width, 1m in height, and 2

m in length. But in most of the tests, the length was adjusted to 1.1 m by fixing an

additional rigid steel frame to the rear part of the 2 m long steel box (Figure 2.1). The

facing of this steel frame was made of 25 mm thick Plywood with surface laminated

by a thin layer of smooth ‘Formica’ sheet.

Figure 2.2 shows the side view cross section of this pullout box together with

the nail and instruments that have been installed in place. A circular instrumentation

chamber was created behind the front wall to house a dynamic load cell and a pair of

linear motion potentiometers (Figure 2.2). These instruments were located in this

manner because the measurement of impulse load and pullout displacement should be

taken as close as possible to the nail head to minimize the error caused by inertia

effect or elongation of any connection parts existed in between the nail head and the

energy source.

To eliminate the adverse influence of rigid front wall, a 100 mm long sleeve

was attached to the end of instrumentation chamber as shown in Figure 2.2. The inner

diameter of this sleeve was chosen to be at least 15 mm larger than the outer diameter

of soil nail. The use of sleeve to eliminate the influence of rigid front wall was

illustrated by Palmeira and Milligan (1989) and has been widely applied to pullout

tests of Geogrid and soil nail by Farrag et.al. (1993), Franzen (1998), Chang et.al.,

(2000) and etc. The effectiveness of this 100 mm long sleeve in eliminating the rigid

front wall effect of these experiments will be shown later in Chapter 3 by the results

of quasi static pullout tests.

With the maximum outer diameter of nails considered in these experiments as

45 mm, the rigid side wall of this pullout box was at least 11 times of nail diameter

away from the nail center. This distance should be sufficient to avoid the boundary

side wall effect. This is supported by the experience of Ekstrom (1989) on driven pile

test which indicated the influence of stress distribution only reached about 5 times of

pile diameter from the pile center.

In the event of rapid pullout test, consideration should also be given to the

reflection of shear wave by the rigid side wall. By taking the small strain shear wave

velocity of sand medium used in these experiments as 100 m/s - 110 m/s (Table 2.3),

time period required for a shear wave to travel across the 0.5 m thick of sand medium

and reflected back again to the nail is round 9 ms – 10 ms. This time period is smaller

than the loading duration of impulse load applied to rapid pullout tests of these

experiments, which is typically in the range of 25 ms - 30 ms. This comparison seems

to suggest the inevitable influence of shear wave reflection. However, due to the

difference between the pattern of shear wave propagation (circularly away from the

nail) and the square shape of pullout box (Figure 2.3), most of the shear wave would

not hit the rigid side wall at right angle. Thus, it is postulated that most of the

reflected waves would not be directly reflected back to the nail, but will be reflected

at direction further away from the nail (Figure 2.3). As a result, the intensity of

reflected waves that travel back to the nail would be greatly reduced. The

effectiveness of square container in dispersing and minimizing the reflection of

circularly propagated stress wave was also observed by Lenke et.al. (1991) in their

centrifuge tests.

2.3 Quasi static pullout machine

The quasi static pullout tests of these experiments were performed by the slow

speed displacement controlled pullout machine shown in Figure 2.4. Throughout the

experiments, the pullout rate was fixed at 0.006 mm/s, the lowest pullout rate

achievable by this machine.

The pulling arm of this pullout machine was connected to the end of

connection rod (and hence the nail since another end of this connection rod was

connected to nail head) by an adapter shown in Figure 2.5. A static load cell was

installed in between the pulling arm and the connection rod to measure the quasi static

pullout load. In rapid pullout test, this connection was detached.

2.4 Impulse hammer

In conjunction with this research project, a spring based impulse hammer was

designed and built. This impulse hammer is capable of imposing a clean and smooth

tensile impulse load directly on nail head to conduct the laboratory rapid pullout tests.

This impulse hammer is a novel invention that has never been used in any dynamic

testing work.

Figure 2.6 and Figure 2.7 show the picture and the cross section side view of

this impulse hammer. The main body of this impulse hammer consists of two springs

(spring ‘A’ and spring ‘B’), an impact ram, an impulse receiver and a connection rod

that connects the impulse receiver to nail head. The stiffness of spring ‘A’ and spring

‘B’ was 14 kN/m and 75 kN/m respectively. This impulse hammer was directly

mounted on the front wall of pullout box.

2.4.1 Working Mechanism

The basic working mechanism of this impulse hammer is essentially identical

to the working mechanism of conventional pile driving by drop hammer. The impulse

load is exerted by the impact of a high speed traveling impact ram on the targeted

structure. However, due to the horizontal orientation of soil nail, the impact must also

take place horizontally in line with the axis of soil nail. Besides, the duration of

impulse load must also be long enough to achieve the rapid loading condition which is

the targeted loading condition of these experiments. The generated impulse load must

also be clean and smooth to avoid the adverse influence of unwanted high frequency

oscillation. The final impulse load that imposed on nail head must also be in the form

of tensile load to conduct pure pullout test. All of these factors have been taken into

account in the design of this impulse hammer.

To conduct a rapid pullout test by this impulse hammer, the required impulse

energy is first generated in the form of spring potential energy by compressing the

impact ram against spring ‘A’ as shown in Figure 2.8a. The impact ram is then locked

in position by a pair of mechanical locks, the clip - like components mounted on both

sides of this impulse hammer (Figure 2.6). Figure 2.9 shows close-up view of a

mechanical lock together with its mounting bar. Multiple mounting holes were

fabricated along the mounting bar to allow for adjustment of mechanical lock’s

location so that the level of potential energy stored in spring ‘A’ can be easily

adjusted according to the level of energy required by a particular rapid pullout test.

In the execution of rapid pullout test, the impact ram is released by simply

pressing the lever arm of the mechanical locks. The potential energy of spring ‘A’ is

then converted into kinetic energy and projecting the impact ram toward spring ‘B’

(Figure 2.8b). The movement of impact ram was guided by six guide rods as shown in

Figure 2.6 and Figure 2.7. To minimize the dissipation of kinetic energy through

frictional resistance between the moving impact ram and guide rods, the contacts sat

on bearing balls.

Subsequently, the impact ram collides with spring ‘B’ to generate a impulse

load (Figure 2.8c). The generated impulse load is then transferred to nail head in the

form of tensile load through the connection rod that runs through the hollow center of

this impulse hammer and connects the impulse receiver to nail head (Figure 2.7). In

the design of this impulse hammer, the spring ‘B’ was designed to function as a

‘cushion’ that reduces the peak impulse load and elongate the impulse duration. The

use of spring as a ‘cushion’ to reduce the peak impulse load and elongate the impulse

duration has been tried and proved workable by Matsumoto et.al. (2004) with their

newly invented innovative rapid pile load test method.

However, as can be seen from Figure 2.10, the impulse load generated by this

impulse hammer with spring ‘B’ only suffered from low amplitude oscillation with

frequency that is obviously higher than the frequency of generated impulse load. This

oscillation was probably caused by the ‘hard’ impact that took place in between the

steel impact ram and the steel front cap of spring ‘B’. This oscillation can be

eliminated by attaching a 5 mm thick ‘Polyfoam’ sheet to the front cap of spring ‘B’,

as shown by the smooth resulting impulse load shown in Figure 2.10.

The end cap of spring ‘B’ was designed to just ‘touch’ the impulse receiver

without any mechanical joint. With this design, the propagation of compressive load

from the end of spring ‘B’ to impulse receiver is allowed but any existence of tensile

load will automatically detach this contact. The main purpose of this design is to

minimize the influence of recoil by spring ‘B’. The connection between impulse

receiver and connection rod was designed as the ‘bolt and nut’ connection to make it

perfectly tight. A ‘loose’ connection tends to vibrate in an impact event and may

cause unwanted oscillation on the resulting impulse load.

From Figure 2.7, it is seen that the end of connection rod protrudes

approximately 20 mm from the face of impulse receiver. The time period for a

longitudinal wave to travel from the impulse receiver to this end and reflected back

again is only 6 µs (with longitudinal wave speed in steel as 5000 m/s). This time

period is much shorter than the typical loading duration of impulse load considered in

these experiments, which was around 25 ms – 30 ms. therefore, the reflection of

longitudinal wave by the end of connection rod should not cause significant influence

on the characteristic of tensile impulse load transferred to nail head.

2.4.2 The Characteristic of Impulse Load

The traces of impulse loads that were generated by this impulse hammer in

these experiments are plotted in Appendix A and Appendix B. From these plots, it can

be seen that the characteristic of these impulse loads were approximately the same.

The loading duration of this impulse was around 27 ms, with approximately 8 ms of

rise time and 19 ms of fall time. Although these parameters slightly differ from test to

test, the differences were marginal. The dominant loading frequency was found as

approximately 35 Hz by Fast Fourier Transform (FFT) analysis. The level of peak

impulse load was mainly determined by the level of spring potential energy stored in

spring ‘A’ (and hence the compressed length of spring ‘A’) before test.

With the typical loading duration of impulse loads applied to these

experiments as 27 ms, the corresponding relative wave length defined by Eq. 1.1 for

rapid pullout tests with 0.75 m and 1.65 m of effective nail length was 90 and 41

respectively (with compression wave speed vp of steel nail = 5000 m/s). These relative

wave lengths are significantly larger than the lower boundary value of 10 proposed by

Holeyman (1992) for the validity of rapid loading condition. Therefore, it is

reasonable to say rapid loading condition with minimal influence of stress wave

propagation was achieved by all rapid pullout tests of these experiments.

2.5 Instrumentations

2.5.1 Load cell

The static load cell was a strain gauge based load cell, INTERFACE SML

series, with 100 Ibf (approximately 2200 N) of tension capacity. The calibration factor

of this load cell was deduced by loading this load cell in tension with dead weight.

The calibration result is shown in Figure 2.11.

In quasi static test, the static load cell was installed in between the connection

rod and the pulling arm of pullout machine (Figure 2.5). In rapid pullout test, the

static load cell was detached.

The dynamic load cell used to measure the tensile impulse load was a

piezoelectric based force sensor, DYTRAN 1051V3. The tension capacity of this

dynamic load cell was 100 Ibf (approximately 2200 N). The resonant frequency of

this dynamic load cell was 75 kHz, which is much higher than 35 Hz, the dominant

loading frequency of these experiments. The calibration of dynamic load cell can only

be carried out by the manufacturer with special equipment. For this device, the

calibration factor was given by the manufacturer as 404 N/V with 1 % of non-linearity.

The age of this calibration result was less than one year throughout the whole

experimental period.

The dynamic load cell was fixed in between the connection rod and the nail

head as shown in Figure 2.2.

2.5.2 Linear Motion Potentiometer

In these experiments, both the quasi static and rapid pullout displacements of

nail head were measured by a pair of linear motion potentiometers. These

potentiometers were conductive plastic based. The maximum stroke of these

potentiometers was 25 mm with 1 % of non-linearity.

These potentiometers were mounted on the inner wall of instrumentation

chamber with their moving stroke firmly tied to the flanges projected from nail shaft

(Figure 2.2). The pair of potentiometers, measuring the pullout displacement of top

and bottom of nail shaft, was termed as potentiometer ‘T’ and potentiometer ‘B’

respectively.

The accuracy and sensitivity of these potentiometers were calibrated under

both static and dynamic conditions. Figure 2.12 plots the static calibration result for

potentiometer ‘T’. Considering the pullout displacement required to mobilize the peak

pullout strength is usually in the range of a few millimeters, the response of this

potentiometer to displacement step as small as 0.1 mm was examined and is found to

be fairly linear and accurate (Figure 2.12). In this calibration, the initial stroke

position of potentiometer was made as similar as possible to that in actual pullout tests

to eliminate the non-uniformity error, if any. The static calibration factor for

potentiometer ‘T’ and potentiometer ‘B’ determined by this method was 0.24

mm/V/V and 0.26 mm/V/V respectively.

In dynamic calibration test, the dynamic motion of a trial rapid pullout test

was measured by a potentiometer and an accelerometer at the same section. Figure

2.13 compares the displacement, velocity and acceleration trace recorded by

potentiometer ‘T’ and accelerometer. The static calibration factor determined earlier

was applied to the output of this potentiometer. All differentiation and integration

involved to derive the curves in Figure 2.13 was calculated by ‘Dplot’, a graphical

calculus software. Figure 2.13 shows that the measurements by potentiometer and

accelerometer were well match to each other, justifying the use of potentiometer to

measure the pullout displacement of rapid pullout tests.

2.5.3 Strain Gauge

Semiconductor strain gauges (KYOWA KSP-2-120-E4) were installed along

the body of sand glued nail to measure the axial body load in quasi static and rapid

pullout tests. For nail with 0.75 m of effective length, two pairs of strain gauges were

installed at location 0.25 m and 0.45 m from nail head (the terms ‘nail head’ is

referred to point A in Figure 2.2, which is the point where the nail first in contact with

surrounding sand medium). While for nail with 1.65 m of effective length, three pairs

of strain gauges were installed at location 0.4 m, 0.8 m and 1.2 m from nail head. The

effective gauge length of this strain gauge is only 2 mm. The short effective gauge

length of this strain gauge makes it suitable for the measurement of dynamic strain

because the duration for a longitudinal wave to travel across the effective gauge

length was only 0.4 µs (longitudinal wave speed of steel = 5000 m/s), merely 0.0015

% of 27 ms, the typical impulse duration of these experiments. This point is important

for the measurement of dynamic strain because the strain output from a strain gauge is

actually the average strain within the effective gauge length. If the variation of strain

within the effective gauge length is too large, the details of variation in strain with

time may be undetected.

At each strain measurement point, a pair of strain gauges was installed on nail

surface by CN glue at opposite sides of nail shaft in direction parallel to the axial axis

of nail. To avoid the influence of cable on pullout response, all cables were hidden

inside the hollow nail body. The cables were welded to the connection terminals of

strain gauges through 5 mm diameter holes as shown in Figure 2.14. The installed

strain gauges were covered by a thin layer of silicon rubber to protect it from damage.

Each pair of installed strain gauges were connected to a pair of dummy strain gauges

installed outside the nail to form a complete Wheatstone bridge circuit.

The calibration factor for each pair of installed strain gauges was deduced by

calibration test conducted under both static and dynamic loading conditions. The

calibration test was carried out after the nail surface had been treated as necessary to

form the desired surface roughness condition.

In the static calibration test, the upper end of nail was fixed by hanging it on a

rigid supporting frame while its lower end was loaded by the dead weight of steel

plates (Figure 2.15a). Since the upper end of test nail was virtually in fixed end

condition, the axial load distribution along the nail body should be uniform and

equated to the imposed dead weight. By using this assumption, the calibration factor

of each pair of strain gauges was deduced. Figure 2.16 shows the calibration results

for nail with surface sand glued by coarse sand (D50 = 0.7 mm). From Figure 2.16, the

calibration factor for both pairs of strain gauges installed at distance 0.25 m and 0.45

m from nail head was deduced as 1007 N/V and 1134 N/ respectively. The response

of these strain gauges to axial force was found to be fairly linear.

The setup of dynamic calibration test is shown in Figure 2.15b. It was

modified from the setup of static calibration test by attaching the spring ‘B’ of

impulse hammer to the end of hanger. A dynamic force sensor was installed in

between the lower end of nail and the upper end of hanger to measure the impulse

load. In the calibration test, a circular steel plate was dropped on spring ‘B’ to

generate an impulse load. The output of each pair of strain gauges (in voltage) was

then multiplied by their corresponding calibration factors deduced from the static

calibration test, and was compared to the measurement of dynamic force sensor.

Figure 2.17a shows the dynamic calibration results for nail with surface sand glued by

coarse sand (D50 = 0.7 mm). From this figure, it can be seen that the measurements by

dynamic force sensor and both pairs of strain gauges were fairly close to each other,

justifying the capability of these strain gauges to measure dynamic strain. This result

also suggests that the response of these strain gauges to static strain and dynamic

strain was fairly similar. The influence of inertia effect on this dynamic calibration

test was also checked by measuring the acceleration of nail head, and it was found to

be negligible since the upper end of nail was in fixed end condition and the

extensibility of the nail was negligible.

To ensure that the response of strain gauges to dynamic strain was unaffected

by the loading direction, dynamic calibration test was repeated by reversing the

direction of nail. The result is plotted in Figure 2.17b. It showed that the response of

installed strain gauges to dynamic strain was virtually unaffected by the loading

direction.

These calibration procedures were repeated on every pairs of strain gauges

used in these experiments. It is found that the calibration factors of all pairs of strain

gauges determined from static calibration tests worked well in the measurement of

dynamic strain

2.5.4 Data Acquisition System

The data acquisition system consists of an oscilloscope and an amplifier. The

output signals (in form of voltage) of all instruments were real time monitored and

recorded by a digital oscilloscope. The sampling rate was set to 0.5 Hz for quasi static

pullout tests while was set to 20 kHz for rapid pullout tests. High frequency electrical

noise was filtered by the built-in filtering function of oscilloscope. The filtering

frequency was set to 10 Hz and 50 kHz for quasi static pullout tests and rapid pullout

tests respectively. Because the signals from static load cell and strain gauges were

very small, usually in the range of a few milliVolt, there were amplified by 300 times

and 100 times respectively before being transmitted to oscilloscope.

2.6 Nail

2.6.1 Dimension and Material

All nails used in these experiments were made of hollow circular stainless

steel pipe, except for ‘sand papered’ nail which the material was changed to

aluminium because the stainless steel surface is too hard to be roughened by sand

paper. To make the aluminium pipe as rigid as the stainless steel pipe, the cross

section area of aluminium pipe was chosen to be approximately three times of the

cross section area of stainless steel pipe, as the modulus of aluminium is

approximately three times lower than that of stainless steel.

Hollow circular pipes with outer diameter of 22 mm and 42 mm were used.

The wall thickness of nail with 22 mm of outer diameter was 0.8 mm, while the wall

thickness of nail with 42 mm of outer diameter was 1 mm. For the aluminium pipe, to

make its axial stiffness comparable with the 22 mm diameter stainless steel pipe, its

outer diameter was chosen as 25 mm with 2 mm of wall thickness. After the treatment

of nail surface by sand glued technique, the final outer diameter of sand glued nail

became 25 mm and 45 mm respectively. The effective nail length (the length of nail

that is in contact with surrounding soil medium and contributes to pullout resistance)

was 0.75 m for most series of tests except for one series which the effective nail

length was increased to 1.65 m.

2.6.2 Types of Nail Surface

Four types of nail surface were considered in these experiments, there were:

1. Surface sand glued by coarse sand (D50 = 0.7 mm), C surface.

2. Surface sand glued by fine sand (D50 = 0.12 mm), F surface.

3. Surface roughened by sand paper, P surface.

4. Untreated smooth stainless steel surface, U surface.

The close-up view of these nail surfaces are shown in Figure 2.18. For ease of

discussion, only the abbreviation of surface type will be quoted hereafter.

2.6.2.1 Preparation of Nail Surface

The sand glued surfaces (C surface and F surface) were prepared by applying

a layer of slow setting ‘ARALDITE’ on the surface of a stainless steel pipe (on the

effective length only), and then the pipe was pressed and rolled thoroughly on sand

mass with desired D50 until the whole effective nail length was covered by a uniform

layer of sand particles. After that, the nail was left for 24 hours for the ‘ARALDITE’

to set. As can be seen from Figure 2.18a and Figure 2.18b, the resulting sand glued

surface formed by these procedures was fairly uniform. The spots on these sand glued

surfaces where strain gauges were installed are also seen in Figure 2.18a and Figure

2.18b. It is observed that the surface of these spots was almost level with the adjacent

nail surface, implies that the existence of stain gauges on these sand glued surfaces

should not generated any error on the pullout test result.

In the preparation of P surface, the aluminium pipe was first wrapped around

by a sand paper (grade no. 2). The sand paper was then firmly griped by hand while

the pipe was rotated in a constant direction for approximately ten rounds. The

resulting scar on nail surface was in the direction perpendicular to pullout direction.

This procedure was repeated until similar scar was formed on the surface of whole

effective nail length. To ensure the uniformity of surface roughness and to eliminate

any workmanship error, the whole roughening process was done by the same person.

Figure 2.18c shows the resulting P surface. It can be seen that the surface produced by

the abovementioned procedures is fairly uniform.

The U surface was merely a stainless steel pipe with untreated surface. A

close-up view of this surface is shown in Figure 2.18d.

2.6.2.2 Normalized Roughnes Rn

In order to quantify the roughness condition of nail surface, the concept of

normalized roughness proposed by Uesugi and Kishida (1986b) was adopted. The

normalized roughness was defined as:

50

max

D

RRn = (2.1)

with Rmax = relative height between the highest peak and the lowest trough of surface

profile over a length equal to D50 of sand in contact.

In this study, the profiles of F surface, P surface and U surface were measured

by a high precision surface roughness meter at three random locations along the nail

surface over a distance of 3 mm. The measured surface profiles are shown in Figure

2.19 to Figure 2.21. The profile of C surface was not measured because the height of

its asperities had exceeded the measurable range of the surface roughness meter.

In the calculation of Rmax of each surface profile shown in Figure 2.19 to

Figure 2.21, the surface profile was first divided into several segments with length

equates to the D50 of sand in contact (D50 = 0.7 mm for all type of surfaces, D50 = 0.1

mm for F surface only). The Rmax of a surface profile was then taken as the average of

Rmax of all segments within the same surface profile.

Table 2.1 shows the Rmax and Rn of each surface profile shown in Figure 2.19

to Figure 2.21. The Rmax of U surface shown in Figure 2.21 was just approximated

because the asperities height of these surface profiles was too small to be measured. It

is observed that the Rn of similar nail surface was quite consistent, implies that the

roughness condition of nail surface prepared by the methods described before is fairly

uniform. The Rn of F surface, P surface and U surface in contact with coarse sand was

approximately 0.2, 0.03 and 0.003 respectively, and the Rn of F surface in contact

with fine sand was around 1. Although the profile of C surface was not measured, its

Rn may be deduced from the experience on of F surface. The Rn of F surface in

contact with fine sand was around 1, suggesting that the Rn of a sand glued surface

may be equal to 1 when in contact with sand that has D50 similar to the D50 of sand

particles glued on its surface. Therefore, the Rn of C surface in contact with coarse

sand was estimated as 1.

By utilizing the normalized roughness Rn, the nails can be further categorized

into ‘rough nail’ and ‘smooth nail’. Uesugi and Kishida (1986a) and Uesugi and

Kishida (1986b) illustrated that the interface strength was proportional to the

normalized roughness until the critical normalized roughness Rncri

. After that point,

the interface strength was independent of normalized roughness. Yoshimi and Kishida

(1981), Uesugi and Kishida (1986a) and Jewell (1989) pointed out that the maximum

attainable interface strength of rough surface with Rn > Rncri

was limited by the shear

strength of soil in contact. Yoshimi and Kishida (1981), Uesugi et.al. (1988), and Hu

and Pu (2004) through direct measurement of sand particles movement in interface

test demonstrated that majority of the interface displacement of rough surface (Rn >

Rncri

) was the shear deformation of soil mass in contact with the surface, and the

failure plane was formed within the adjacent soil mass. In contrast, the interface

displacement of smooth surface (Rn < Rncri

) was mainly contributed by the sliding

displacement of sand particles on the interface, and the failure plane was formed

along the interface.

From the literature review, the critical normalized roughness Rncri

does not

appear to be a constant but a variable that depends on sand type. The results of

interface test by Uesugi and Kishida (1986b) showed that the Rncri

for Toyoura sand,

Fujigawa sand and Seto sand was roughly 0.15, 0.1 and 0.07 respectively. Hu and Pu

(2004) proposed 0.1 as the Rncri

for Yongdinghe sand. The difference in Rncri

of

difference type of sands may be attributed to the difference in roughness, angularity

and mineralogy of sand particles.

Although the Rncri

for the sands used in these experiments was unknown, but

from the limited past experiences, the Rncri

seems to be within the range of 0.07 – 0.15.

Thus, the nails with C surface and F surface with Rn ≥ 0.15 can be reasonably

categorized as rough nail; while, the nails with P surface and U surface with Rn ≤ 0.03

can be categorized as smooth nail.

2.7 Sand

The sand medium of these experiments were formed by poorly graded clean

dry sand. The basic properties (particle size distribution, maximum density and

minimum density) and friction angle of these sands were obtained by standard

laboratory tests.

2.7.1 Basic Properties

The particle distribution curves of both sands used in these experiments,

termed as coarse sand and fine sand, are plotted in Figure 2.22. Both of these sands

can be categorized as poorly graded sand because their particle size distribution

curves were obviously concentrated within a narrow range only. The D50 of coarse

sand and fine sand was 0.7 mm and 0.12 mm respectively.

The maximum density of sands was determined by the vibrating table method

suggested by ASTM D 4253. In this method, a standard mold filled up with sand

sample (~ 2830 cm3 in volume) is subjected to a vibration of 0.5 mm in double

amplitude at 50 Hz for 12 minutes while surcharge pressure of 13.8 kPa is loading on

the surface of sand sample. The final sand density after the vibration is taken as the

maximum density. The maximum density of coarse sand and fine sand was 1655

kg/m3 and 1720 kg/m

3 respectively.

The minimum density of sands was determined by the shaking method

suggested by ASTM D 4254. In this method, a 2 liters cylinder filled with 1 kg of

sand sample is shook up and down rapidly and the final sand density is taken as the

minimum density. The minimum density of coarse sand and fine sand was determined

as 1400 kg/m3 and 1430 kg/m

3 respectively.

2.7.2 Direct Shear Test

The friction angles of sand and sand – nail interface were determined by

conventional 100 mm x 100 mm direct shear test. For direct shear test on sand – nail

interface, the lower halve of direct shear box was replaced by an aluminium block

with surface that has been treated by the same method used to form the nail surface as

described before.

Although soil stresses along the shear plane of direct shear test is likely to be

non-uniform due to the influence of rigid boundary, Potts et.al. (1987) demonstrated

by finite element analysis that these stresses are actually fairly uniform at the stage of

peak shear stress. Uesugi and Kishida (1986b) compared the results of simple shear

test and direct shear test on sand steel interface and showed that the results of both

tests, especially in terms of peak and residual interface friction angles, were quite

close to each other. Therefore, direct shear test was adopted to determine the friction

angle of sand and sand – nail interface of these experiments.

The sand sample of direct shear tests was prepared by air pluviation method,

the same method used to prepare the sand medium of pullout test. The details of the

preparation procedures will be discussed later in Section 2.7.3.

Table 2.2 shows the details of each series of direct shear tests. In each series of

direct shear tests, three levels of normal stress, 17 kPa, 32 kPa and 57 kPa, were

considered. For the convenience of discussion, a code is assigned to each series of

direct shear tests as shown in Table 2.2. The code consists of two terms. The first term

describes the sand properties. The second term describes the surface type for direct

shear interface test, or the sand properties for direct shear sand – sand test. As an

example, the DCs-F test stands for the direct shear interface test between dense course

sand and surface sand glued by fine sand. While, the DCs-DCs test stands for the

direct shear sand – sand test on dense coarse sand. The details of this coding system

are given as the footnote in Table 2.2.

Figure 2.23 plots the curves of peak and residual shear stress vs. normal stress

of every series of direct shear tests. From this figure, the peak friction angle and

residual friction angle of every series of direct shear tests were deduced and given in

Table 2.2.

Figure 2.24 compares the direct shear test results (the curves of shear stress vs.

horizontal displacement and the vertical displacement vs. horizontal displacement) of

tests with dense coarse sand medium. Figure 2.25 compares the direct shear test

results of MCs-C test to DCs-C test to examine the influence of sand density. Figure

2.26 compares the direct shear test results of tests with dense fine sand medium. The

normal stress of tests plotted in Figure 2.24, 2.25 and 2.26 was 32 kPa. From the plots

of vertical displacement vs. horizontal displacement in Figure 2.24 to Figure 2.26, the

maximum dilatancy angle ψ of every direct shear tests were deduced and given in

Table 2.2.

From Figure 2.24 and Table 2.2, the peak and residual friction angle of DCs-

DCs test, DCs-C test and DCs-F test appears to be nearly identical. This observation

is reasonable since C surface (sand glued by coarse sand) and F surface (sand glued

by fine sand) are both categorized as rough surface by their normalized roughness Rn.

It has been discussed in Section 2.6.2.2 that the interface strength of rough surface is

limited by the shear strength of adjacent soil mass because the failure plane is likely

to be formed within the adjacent soil mass. From Figure 2.24, it is also seen that the

horizontal displacement required to achieve the peak shear stress of DCs-DCs test was

twice of those required by DCs-C test and DCs-F test. This observation seems to

suggest that the thickness of shear zone in DCs-DCs test was almost twice the

thickness of shear zone in DCs-C test and DCs-F test.

In term of dilatancy, Figure 2.24 shows that the maximum vertical

displacement achieved by DCs-DCs test was almost twice the maximum vertical

displacement achieved by DCs-C test and DCs-F test. This observation again suggests

the thickness of shear zone of DCs-DCs test was almost twice the thickness of shear

zone of DCs-C test and DCs-F test. Although the DCs-F test seems less dilative when

compared to DCs-C test, the difference was unclear concerning the error involved in

the measurement of vertical displacement as the top cap was rotating in direct shear

test due to non uniform distribution of soil stresses (Jewell, 1989). It has to be stressed

that the accuracy of dilatancy angle deduced by the vertical displacement of direct

shear test is inaccurate as had been illustrated by Palmeira (1987) that the dilatancy

angle deduced by this method is likely to be underestimated by as high as 6o.

Figure 2.24 also plots the direct shear interface test results of DCs-P test and

DCs-U test on smooth surface. The maximum shear stress achieved by these tests was

obviously lower than those achieved by DCs-C test and DCs-F test on rough surface.

From the shear stress vs. horizontal displacement curves, both of these tests exhibited

very stiff loading response until reaching their maximum shear stress. After that, the

maximum shear stress of both tests was kept constant for further increase in interface

displacement. From the vertical displacement vs. horizontal displacement curve

shown in Figure 2.24, DCs-P test is seen to exhibit slight dilative response with 1.8o

of maximum dilatancy angle. This result agrees with the simple shear test result on

smooth steel interface with normalized roughness Rn of 0.05 reported by Hu and Pu

(2004) (The Rn of P surface was approximately 0.03). For DCs-U test, no dilative

response was observed.

By comparing the results of MCs-C test to DCs-C test which are varied only in

sand density (Table 2.2 and Figure 2.25), it can be seen that despite the decrease in

relative sand density from 90 % to 82 %, the change in peak interface friction angle

was marginal, only slightly reduced from 38.9o

to 37.0o. This result is comparable to

the direct shear interface test results on interface between Leighton Buzzard sand and

sand glued surface reported by Tei (1993), which the peak interface friction angle was

only dropped from 39o to 36

o with the decrease of relative density from 90 % to 81 %.

In term of dilatancy, Figure 2.25 shows that the MCs-C test appears to be less dilative

than DCs-C test, with the maximum dilatancy angle dropped from 11.3o to 8.0

o (Table

2.2).

From Figure 2.26 that compares the results of DFs-DFs test to DFs-F test, it is

seen that the peak and residual shear stress of both tests were comparable. The

maximum dilatancy angles of these tests were also identical (Table 2.2). These results

are reasonable since the F surface (sand glued by fine sand) was also categorized as

rough surface when in contact with fine sand (Table 2.1 and Section 2.6.2.2). The

horizontal displacement required to mobilize the peak shear stress and the maximum

vertical displacement of DFs-DFs test were also almost twice of those attained by

DFs-F test.

Jewell (1989) discussed the difference between plane strain friction angle and

direct shear friction angle, and had proposed the analytical solution shown below (Eq.

2.2) to calculate the plane strain friction angle from direct shear friction angle.

( )ds

ds

ps'tantan1cos

'tan'sin

φψψ

φφ

+= (2.2)

with φ’ps = plane strain friction angle of soil, φ’ds = direct shear friction angle of soil,

and ψ = dilatancy angle.

By using Eq. 2.2, the peak plane strain friction angle of dense coarse sand with

90 % of relative density (DCs-DCs test) and dense fine sand medium with 95 % of

relative density (DFs-DFs test) was calculated as 35.6o and 37

o respectively. Although

the results of direct shear sand – sand test on medium dense coarse sand with 82 % of

relative density was not available, the plane strain friction angle of this sand medium

can be calculated from the results of MCs-C interface test. This is because the

comparison of DCs-DCs test and DCs-C test reveals that the peak friction angle and

maximum dilatancy angle deduced from direct shear interface test with rough surface

are fairly similar to those of direct shear sand – sand test with identical sand medium.

With this assumption, the peak plane strain friction angle of medium dense coarse

sand medium with 82 % of relative density was calculated from the results of MCs-C

test as 34.5o. These peak plane strain friction angles will be utilized later in this thesis

to calculate the coefficient of horizontal stress at rest Ko by the Jaky’s formula.

2.7.3 The Construction of Sand Medium

In these experiments, sand mediums were constructed by the air pluviation

method, which the clean dry sand is pluviated in air from a sand hopper positioned at

certain pluviation height. The homogeneity and consistency of sand mediums

prepared by this method has been shown by Miura and Toki (1982), Presti et.al. (1993)

and Fretti et.al. (1995). It has to be stressed that a new sand medium was constructed

for every pullout tests conducted in these experiments.

The consistency of sand mediums in every pullout tests was the essence of

these experiments because the results of quasi static pullout test and rapid pullout test

will be compared to deduce the influence of loading rate on pullout behaviour of soil

nail. Since the consistency and homogeneity of density of loose sand was

comparatively harder to be controlled than dense sand (Presti et.al., 1993), only dense

sand medium was considered in this study. This is acceptable since most of the

application of soil nailing technique is in dense to medium dense natural ground.

The sand hoppers used in these experiments were modified from a normal

water pail, by drilling a series of circular holes on its base. The holes were arranged in

rectangular grid pattern with 15 mm of center to center distance. The diameter of

holes was 5 mm for sand hopper used to prepare the coarse sand medium, and was 1

mm for sand hopper used to prepare the fine sand medium.

In the preparation of coarse sand mediums, two levels of pluviation height, 1

m and 0.3 m, were considered. In the pluviation process, the sand hopper was hung on

a crane at the desired pluviation height and moved about in a forward and backward

motion as shown in Figure 2.27 to form a leveled sand layer. This method is almost

similar to the method proposed by Fretti et.al. (1995) that has been shown to produce

consistent and homogeneous soil medium. The sand hopper was constantly filled up

to at least half of its depth. The lift height of each layer of sand was approximately

0.03 m. After a layer of sand was formed, the pluviation height was adjusted again to

the desired height for the construction of next layer of sand.

In the preparation of fine sand mediums, only one level of pluviation height, 1

m, was considered. The preparation procedures were the same as the procedures used

to prepare the coarse sand mediums.

The density of sand mediums constructed by the procedures mentioned above

was calibrated by a large container with approximate dimension of 0.4 m length x 0.3

m width x 0.45 m height. The exact volume of this container was deduced as 0.0525

m2 by water replacement method. In the calibration test, this container was first

placed inside the pullout box and then a sand medium was constructed by the

procedures described above. After the container was fully covered by sand, it was dug

out carefully and the weight of sand medium inside was measured. Together with the

volume of container measured previously, the density of sand medium inside the

container was deduced. The reason to use large container in this calibration test was to

minimize the errors that may be caused by the rigid container wall and the inaccuracy

in measurement of volume and sand mass.

The sand density calibration results are shown in Table 2.3. Three calibration

tests were done for each combination of sand type and pluviation height. The density

of sand mediums constructed by similar combination of sand type and pluviation

height were found to be comparable to each other, implies that the sand mediums

prepared by this method are pretty consistent and repeatable. The density of coarse

sand medium constructed with 1 m and 0.3 m of pluviation height was approximately

1625 kg/m3

and 1602 kg/m3 respectively, corresponding to 90 % and 82 % of relative

density. For fine sand medium constructed with 0.1 m of pluviation height, the density

was approximately 1700 kg/m3, corresponding to 95 % of relative density.

In Table 2.3, the void ratio e and small strain shear wave velocity Vs of sand

mediums are given as well. The void ratio was calculated by Eq. 2.3, while the small

strain shear wave velocity was calculated by the empirical equation (Eq. 2.4)

proposed by Hardin and Richart (1963) for dry clean sand.

1−

=

s

ge

ρ

ρ (2.3)

with ρg = density of sand particles, assumed as 2650 kg/m3; and ρs = dry density of

sand medium.

( )3.0

'35.536.11 oo eG σ−= (2.4)

with σ’o = mean effective confining stress, calculated as [(1+Ko)/2]σ’v, with Ko = 1-

sinφ’ps (Jacky’s formula) and σ’v = effective overburden stress.

It has to be noted that in these experiments, nail was fixed in-place before the

construction of sand medium. Although the existence of nail may cause the ‘shading

effect’ that affects the density of sand medium constructed below the nail, this

procedure is still preferred than installing the nail after the sand medium has been

constructed up to the nail level. It is because disturbance on sand medium below and

adjacent to the nail level is virtually inevitable in the nail installation process if sand

medium is constructed up to the nail level beforehand. Besides, this disturbance is

likely to be a random error that may differ from test to test, unlike the error caused the

‘shading’ effect that would most likely be a systematic error that is consistent in every

tests.

In the laboratory soil nail pullout tests conducted by Tei (1993), the nail was

mentioned to be installed after the sand medium had been constructed up to a ‘certain

level’, but no clear definition on ‘certain level’ was given. However, it is postulated

that the sand level must be at some distance below the nail level to avoid the

disturbance of nail installation. Thus, the ‘shading’ effect may still exist on sand

medium adjacent to and below the nail that was constructed after the nail had been

installed in place. Since the sand medium adjacent to nail is the most influential

medium to pullout response, the error of installing the nail after sand medium has

been constructed up to a ‘certain level’ or before the construction of sand medium

might be similar.

2.8 Experimental Program

Table 2.4 shows the detailed descriptions of all series of pullout tests

conducted in these experiments. In this table, a code is assigned to each test series to

ease the presentation and discussion of experimental results in this thesis. The code

consists of two terms. The first term describes the properties of sand medium. The

second term describes the properties of nail. By taking the DCs-S25C test series as an

example, the first term DCs indicates the sand medium of this test series was dense

coarse sand; while the second term S25C indicates the nail of this test series was 0.75

m in effective length (short), 25 mm in diameter and the nail surface was sand glued

by coarse sand. The details of this coding system are given as the footnote of Table

2.4.

The varying parameters that were considered in these experiments were as

below:

1) Nail Surface

Four types of nail surfaces, termed as C surface (sand glued by coarse sand), F

surface (sand glued by fine sand), P surface (roughened by sand paper) and U

surface (untreated smooth stainless steel surface) were considered to investigate

the influence of surface roughness on both quasi static and rapid pullout tests.

2) Nail Diameter, d

Two diameter sizes, 25 mm and 45 mm, were considered for nails with C

surface and F surface to examine the influence of nail diameter on pullout

behaviour, especially its influence on restrained dilatancy effect and radiation

damping effect.

3) Effective Nail Length, Le

Effective nail length is defined as the length of nail in contact with

surrounding soil medium that contributes to total shaft resistance. The effective

nail length of all series of tests was 0.75 m, except for DCs-L25F test series

(Table 2.4) where the effective nail length was increased to 1.65 m. The main

purpose to have a test with longer effective nail length was to study the influence

of effective nail length on the characteristic of axial body load distribution along

the nail under both quasi static and rapid loading conditions, which may indirectly

indicate the existence of any rigid front wall effect and reveal the influence of

effective nail length on the mobilization characteristic of damping resistance. It

has to be noted that both nails with 0.75 m and 1.65 m of effective nail length

behaved as rigid body in these experiments as can be seen later by the pullout test

results due to relatively rigid nail body and low overburden pressure (and hence

low interfacial resistance).

4) Particle Size

In these experiments, coarse sand medium was used for most series of tests.

With the D50 of coarse sand as 0.7 mm, the minimum ratio of nail diameter d to

mean particle size of sand D50 was around 36, which had exceeded the minimum

requirement of 30 suggested by Ovensen (1979) to avoid the particle size effect.

However, Foray et.al. (1998) with their results on tension pile tests suggested that

the ratio of d/D50 should exceed 200 in order to effectively eliminate the particle

size effect. But detailed examination of their discussion reveals that the particle

size effect referred by them was actually the restrained dilatancy effect which was

not intended to be eliminated in these experiments. Thus their results were be

irrelevant to these experiments.

However, as a measure of precaution to ensure the minimal influence of

particle size effect on the observations made in these experiments, DFs-S25F test

series was created (Table 2.4). In this test series, the sand medium was formed by

fine sand with D50 = 0.12 mm. The d/D50 ratio of this test series was as high as

208, slightly exceeded the minimum value suggested by Foray et.al. (1998). The

pullout results of this test series, especially on the influence of loading rate on

pullout response, will then be compared qualitatively to the results of DCs-S25F

test series, to identify any significant variation in influence of loading rate

between these test series. The DCs-S25F test series had test conditions that were

similar to DFs-S25F test series except the mean particle size of sand medium and

hence the d/D50 ratio. The d/D50 ratio of DCs-S25F test series was 36.

5) Relative Density, Id

For tests with nail embedded in coarse sand, sand medium with relative

density of 82 % (MCs-S25C test series) and 90 % (DCs-S25C test series) were

considered. The purpose of this variation was to indirectly examine the

characteristic of restrained dilatancy effect under both quasi static and rapid

loading condition because the restrained dilatancy effect is highly affected by the

density of surrounding sand medium.

The overburden pressure on the center line of nail was kept constant at

approximately 7.3 kN/m2

for all series of tests. The overburden pressure was induced

by the dead weight of sand fill only. The height of sand fill depended on the unit

weight (the density) of sand medium that have been determined in Section 2.7.3.

Table 2.5 shows the pullout mode of every pullout tests that were conducted

under each test series. From this table, it can be seen that under each test series, at

least two quasi static pullout tests and two high energy rapid pullouts were conducted.

One low energy rapid pullout test was also conducted for every test series except the

DCs-S45C test series, the DCs-S25P test series and the DCs-S22U test series. The

term ‘high energy’ and ‘low energy’ mentioned in this thesis was a relative term that

represents the energy level of impulse load compared to the pullout strength of nail. In

high energy rapid pullout test, the nail was loaded to complete pullout failure; while

in low energy rapid pullout test, the peak impulse load was well below the peak

pullout strength of nail and thus complete pullout failure did not occurred in this test.

Before a rapid pullout test, type of the test (‘high energy’ or ‘low energy’) can be

roughly determined by setting the input energy to be higher or lower than the

threshold energy needed to attained the estimated peak rapid pullout strength Psp. The

threshold energy can be approximately assessed by energy principle as 1/2Pspu

p(s) with

Psp the estimated peak rapid pullout strength and u

p(s) the pullout displacement

required to achieve the peak rapid pullout strength.

The compressed length of spring ‘A’ in millimeter that stored the spring

potential energy for rapid pullout test was also shown in Table 2.5.

The sequence of a pullout tests was conducted under each test series followed

exactly the sequence shown in Table 2.5. Under each test series, both of the quasi

static pullout tests were purposely arranged to be the first and the last pullout test. The

purpose of this arrangement was for the possibility to indirectly evaluate the variation

of nail surface throughout a series of tests. If the condition of nail surface was not

severely altered throughout a series of tests, the results of the first and the last quasi

static pullout tests should be fairly identical to each other. It has to be noted that this

deduction is only true if the condition of sand medium was constant for both of the

quasi static pullout tests, which was likely true for these experiments as has been

discussed in Section 2.7.3 that the density of sand medium constructed by the air

pluviation procedures is highly consistent and repeatable.

Similar to test series, a code is also assigned to each pullout test to ease the

discussion in the following section of this thesis (Table 2.5). The code for pullout test

is basically an extension to the code for test series by adding another two terms at its

end. These additional terms indicates the sequence of the pullout test be conducted

under its test series and the mode of pullout test. As an example, the DCs-S25C-2-RH

test stands for the second pullout test that was conducted under the DCs-S25C test

series and this pullout test was a high energy rapid pullout test. The details of this

coding system are given as the footnote of Table 2.5.

Quasi static reload tests were directly conducted after each quasi static pullout

tests and rapid pullout tests. In this thesis, reload tests will be referred by adding a ‘-r’

at the end of code for their preceding pullout tests. As an example, the reload test that

was conducted after the DCs-S25C-1-S test will be referred as DCs-S25C-1-S-r test.

Tab

le 2

.1:

No

rmal

ized

Ro

ugh

nes

s R

n o

f nai

l su

rfac

es

Su

rface

ty

pe

Rm

ax

* (

D50 =

0.7

mm

)

(mm

) R

n#(D

50 =

0.7

mm

)

Rm

ax*(D

50 =

0.1

2 m

m)

(mm

) R

n# (

D50 =

0.1

2 m

m)

0.1

1

0.1

6

0.1

1

0.8

5

0.1

5

0.2

1

0.1

2

1

San

d g

lued

by f

ine

sand,

F s

urf

ace

0.1

3

0.1

9

0.1

1

0.8

5

0.0

19

0.0

27

0.0

24

0.0

34

Roughen

by s

and

pap

er,

P s

urf

ace

0

.021

0.0

3

0.0

02

+

0.0

03

0.0

02

+

0.0

03

Untr

eate

d s

mo

oth

stai

nle

ss s

teel

surf

ace,

U s

urf

ace

0.0

02

+

0.0

03

* R

ma

x=

max

imu

m h

eigh

t b

etw

een

th

e hig

hes

t pea

k a

nd l

ow

est

trou

gh o

f su

rfac

e pro

file

alo

ng a

dis

tance

equ

al t

o D

50.

# R

n =

norm

aliz

ed r

ou

gh

nes

s =

(R

ma

x /

D5

0)

+ A

ppro

xim

ated

fro

m t

he

surf

ace

pro

file

s sh

ow

n i

n F

igu

re 2

.21.

T

able

2.2

: D

escr

ipti

on

s an

d r

esu

lts

of

dir

ect

shea

r te

sts

Fri

ctio

n a

ngle

(o)

Tes

t C

od

e*

Sa

nd

med

ium

R

elati

ve

den

sity

of

san

d, I d

(%

) S

urf

ace

typ

e P

eak

Res

idual

Dil

ata

ncy

an

gle

, ψ ψψψ

(o)

Dir

ect

shea

r sa

nd

– s

an

d t

est

DC

s-D

Cs

Den

se c

oar

se s

and

90

- 39.4

31.0

12.0

DF

s-D

Fs

Den

se f

ine

sand

95

- 41.8

30.9

14.0

Dir

ect

shea

r in

terf

ace t

est

DC

s-C

D

ense

co

arse

san

d

90

San

d g

lued

by c

oar

se s

and

38.9

30.8

11.3

MC

s-C

M

ediu

m d

ense

co

arse

san

d

82

San

d g

lued

by c

oar

se s

and

37.0

30.7

8.0

DC

s-F

D

ense

co

arse

san

d

90

San

d g

lued

by f

ine

sand

38.2

30.5

10.5

DC

s-P

D

ense

co

arse

san

d

90

Roughen

by s

and p

aper

28.3

-

1.8

DC

s-U

D

ense

co

arse

san

d

90

Sm

ooth

sta

inle

ss s

teel

surf

ace

16.4

-

-

DF

s-F

D

ense

fin

e sa

nd

95

San

d g

lued

by f

ine

sand

41.1

30.7

12.0

* T

he

det

ails

of

cod

ing s

yst

em

D

C

s -

C

Den

sity

sta

te o

f sa

nd

•

D =

den

se

•

M =

med

ium

den

se

S

an

d t

ype

•

Cs

= c

oar

se s

and

•

Fs

= f

ine

sand

Su

rface t

ype f

or

dir

ect

shear

inte

rface t

est

•

C =

san

d g

lued

by c

oar

se s

and

•

F =

san

d g

lued

by f

ine

sand

•

P =

rough

en b

y s

and p

aper

•

U =

sm

ooth

sta

inle

ss s

teel

surf

ace

or

San

d t

ype f

or

dir

ect

shear

san

d –

san

d t

est

•

DC

s =

den

se c

oar

se s

and

•

DF

s =

den

se f

ine

sand

Tab

le 2

.3:

Des

crip

tio

ns

and

res

ult

s o

f sa

nd d

ensi

ty c

alib

rati

on t

ests

.

San

d T

yp

e P

luv

iati

on

Hei

gh

t (m

) D

ensi

ty (

kg/m

3)

Mea

n

Den

sity

, ρ ρρρ

s

(kg/m

3)

Rel

ati

ve

den

sity

,

I d (

%)

Void

rati

o, e*

Sm

all

Str

ain

Sh

ear

Wave

Sp

eed

, V

s (m

/s)#

1624.7

6

1625.5

2

1

1627.6

2

1625

90

0.6

3

104

1602.2

4

1601.4

8

Coar

se s

and

(D

50 =

0.7

mm

)

0.3

1603.3

8

1602

82

0.6

6

102

1706.2

8

1707.4

7

Fin

e sa

nd

(D

50 =

0.1

2 m

m)

1

1703.7

1705

95

0.5

5

110

* e

= (

ρg/ρ

s)-1

, w

ith

ρg

≈ 2

65

0 k

g/m

3

# V

s =

(11.3

6-5

.35e)

σ’ o

0.3, w

ith

σ’ o

= m

ean e

ffec

tive

confi

nin

g s

tres

s. (

Har

din

and R

ichar

t, 1

963).

Tab

le 2

.4:

Th

e d

etai

ls o

f te

st s

erie

s co

nduct

ed i

n t

hes

e ex

per

imen

ts.

Tes

t S

erie

s *

R

ela

tiv

e d

ensi

ty

of

san

d, I d

(%

)

San

d t

yp

e

Eff

ecti

ve

Nail

Len

gth

, L

e (

m)

Nail

Dia

met

er,

d (

mm

)

Su

rface

typ

e

DC

s-S

25

C

90

C

oar

se s

and

0.7

5

25

San

d g

lued

by c

oar

se s

and

DC

s-S

45

C

90

C

oar

se s

and

0.7

5

45

San

d g

lued

by c

oar

se s

and

MC

s-S

25

C

82

C

oar

se s

and

0.7

5

25

San

d g

lued

by c

oar

se s

and

DC

s-S

25

F

90

C

oar

se s

and

0.7

5

25

San

d g

lued

by f

ine

sand

DC

s-S

45

F

90

C

oar

se s

and

0.7

5

45

San

d g

lued

by f

ine

sand

DC

s-L

25

F

90

C

oar

se s

and

1.6

5

25

San

d g

lued

by f

ine

sand

DF

s-S

25

F

95

F

ine

sand

0.7

5

25

San

d g

lued

by f

ine

sand

DC

s-S

25

P

90

C

oar

se s

and

0.7

5

25

Roughen

ed b

y s

and p

aper

DC

s-S

22

U

90

C

oar

se s

and

0.7

5

22

Sm

ooth

sta

inle

ss s

teel

* T

he

codin

g s

yst

em o

f te

st s

erie

s

D

C

s -

S

2

5

C

Den

sity

sta

te o

f sa

nd

• D

= d

ense

• M

= m

ediu

m d

ense

Sa

nd

typ

e

• C

s =

co

arse

san

d

• F

s =

fin

e sa

nd

Eff

ecti

ve n

ail

len

gth

• S

= 0

.75 m

• L

= 1

.65 m

Nail

dia

mete

r

in m

m

S

urf

ace t

ype

• C

= s

and g

lued

by c

oar

se s

and

• F

= s

and g

lued

by f

ine

sand

• P

= r

ough

ened

by s

and p

aper

• U

= u

ntr

eate

d s

mooth

st

ainle

ss

st

eel

Tab

le 2

.5:

Th

e d

etai

ls o

f p

ull

ou

t te

sts

conduct

ed u

nder

eac

h t

est

seri

es.

Tes

t S

erie

s *

P

ull

ou

t T

est

#

Mod

e of

Pu

llou

t T

est

Co

mp

ress

ed l

ength

of

spri

ng ‘

A’

(mm

)

DC

s-S

25C

-1-S

Q

uas

i S

tati

c

-

DC

s-S

25C

-2-R

H0

Hig

h E

ner

gy R

apid

45

DC

s-S

25C

-3-R

L

Low

En

erg

y R

apid

15,3

0♦

DC

s-S

25C

-4-R

H

Hig

h E

ner

gy R

apid

45

DC

s-S

25

C

DC

s-S

25C

-5-S

Q

uas

i S

tati

c

-

DC

s-S

45C

-1-S

Q

uas

i S

tati

c

-

DC

s-S

45C

-2-R

H

Hig

h E

ner

gy R

apid

70

DC

s-S

45C

-3-R

H

Hig

h E

ner

gy R

apid

70

DC

s-S

45

C

DC

s-S

45C

-4-S

Q

uas

i S

tati

c

-

MC

s-S

25C

-1-S

Q

uas

i S

tati

c

-

MC

s-S

25C

-2-R

H

Hig

h E

ner

gy R

apid

45

MC

s-S

25C

-3-R

H

Hig

h E

ner

gy R

apid

45

MC

s-S

25

C

MC

s-S

25C

-4-S

Q

uas

i S

tati

c

-

DC

s-S

25F

-1-S

Q

uas

i S

tati

c

-

DC

s-S

25F

-2-R

H

Hig

h E

ner

gy R

apid

45

DC

s-S

25F

-3-R

L

Low

En

erg

y R

apid

30

DC

s-S

25F

-4-R

H

Hig

h E

ner

gy R

apid

45

DC

s-S

25

F

DC

s-S

25F

-5-S

Q

uas

i S

tati

c

-

Tab

le 2

.5 c

on

tin

ue

Tes

t S

erie

s *

P

ull

ou

t T

est

#

Mod

e of

Pu

llou

t T

est

Co

mp

ress

ed l

ength

of

spri

ng ‘

A’

(mm

)

DC

s-S

45F

-1-S

Q

uas

i S

tati

c

-

DC

s-S

45F

-2-R

H

Hig

h E

ner

gy R

apid

70

DC

s-S

45F

-3-R

L

Low

En

erg

y R

apid

45

DC

s-S

45F

-4-R

H

Hig

h E

ner

gy R

apid

70

DC

s-S

45

F

DC

s-S

45F

-5-S

Q

uas

i S

tati

c

-

DC

s-L

25

F-1

-S

Quas

i S

tati

c

-

DC

s-L

25

F-2

-RH

H

igh E

ner

gy R

apid

70

DC

s-L

25

F-3

-RL

L

ow

En

erg

y R

apid

60

DC

s-L

25

F-4

-RH

H

igh E

ner

gy R

apid

70

DC

s-L

25

F

DC

s-L

25

F-5

-S

Quas

i S

tati

c

-

DF

s-S

25F

-1-S

Q

uas

i S

tati

c

-

DF

s-S

25F

-2-R

H

Hig

h E

ner

gy R

apid

45

DF

s-S

25F

-3-R

L

Low

En

erg

y R

apid

15,3

0♦

DF

s-S

25F

-4-R

H

Hig

h E

ner

gy R

apid

45

DF

s-S

25

F

DF

s-S

25F

-5-S

Q

uas

i S

tati

c

-

DC

s-S

25P

-1-S

Q

uas

i S

tati

c

-

DC

s-S

25P

-2-R

H

Hig

h E

ner

gy R

apid

15

DC

s-S

25

P

DC

s-S

25P

-3-R

H

Hig

h E

ner

gy R

apid

15

Tab

le 2

.5 c

on

tin

ue

Tes

t S

erie

s *

P

ull

ou

t T

est

#

Mod

e of

Pu

llou

t T

est

C

om

pre

ssed

len

gth

of

spri

ng ‘

A’

(mm

)

DC

s-S

25

P

DC

s-S

25P

-4-S

Q

uas

i S

tati

c

-

DC

s-S

22U

-1-S

Q

uas

i S

tati

c

-

DC

s-S

22U

-2-R

H

Hig

h E

ner

gy R

apid

15

DC

s-S

22U

-3-R

H

Hig

h E

ner

gy R

apid

15

DC

s-S

22

U

DC

s-S

22U

-4-S

Q

uas

i S

tati

c

-

* F

rom

Tab

le 2

.4.

# T

he

codin

g s

yst

em o

f p

ull

ou

t te

st

DC

s-S

25

C

- 1

-

S

Test

seri

es

(fro

m

Ta

ble

2.4

)

Sequ

en

ce o

f th

e

test

was

con

du

cte

d

un

der

th

e t

est

seri

es

Type o

f pu

llou

t te

st

• S

= q

uas

i st

atic

• R

H =

hig

h e

ner

gy r

apid

• R

L =

low

ener

gy r

apid

♦ T

wo s

ucc

essi

ve

low

en

erg

y r

apid

pu

llout

test

s w

ere

condu

cted

.

(a)

(b)

Figure 2.1: (a) The pullout box and (b) the steel frame that reduced the length of

pullout box from 2 m to 1.1 m.

Fig

ure

2.2

: S

ide

vie

w o

f pull

out

box

.

Str

ain g

ages

Dyn

amic

load

cel

l Lin

ear

moti

on

pote

nti

om

eter

Sle

eve

0.2

m

0.1

m

1.1

m /

2 m

Co

nn

ecti

on

ro

d (

to

imp

uls

e re

ceiv

er)

0.55 m 0.45 m

A

Imp

uls

e

ham

mer

Alu

min

ium

pin

Fig

ure

2.2

: C

ross

sec

tion

of

pull

out

box

.

Figure 2.3: Reflection of circularly propagated stress wave by square pullout box.

Figure 2.4: The displacement controlled quasi static pullout machine.

Direction of incident stress wave

Direction of reflected stress wave

Square

pullout box

Circular

nail

Figure 2.5: Connection between pulling arm and connection rod.

Figure 2.6: Picture of impulse hammer.

Static load

cell

Pulling arm

Adapter

Guide rod Impact

ram

Spring ‘A’ Spring ‘B’

Mechanical

locks

Fig

ure

2.7

: C

ross

sec

tion

of

impuls

e ham

mer

.

Imp

uls

e re

ceiv

er

Connec

tion r

od

Spri

ng ‘

A’

Spri

ng ‘

B’

Guid

e ro

d

Impac

t ra

m

Bas

e pla

te T

o n

ail

hea

d

(a)

(b)

(c)

Figure 2.8: Steps of impulse generation, (a) compression of spring ‘A’, (b) projecting

of impact ram toward spring ‘B’, (c) collision of impact ram with spring ‘B’.

Figure 2.9: Close view of mechanical lock.

Mechanical

lock

Mounting bar

0 10 20 30Time (ms)

0

40

80

120

160

Lo

ad

(N

)

With Polyfoam

Without Polyfoam

Figure 2.10: Comparison of impulse load generated by the impulse hammer with and

without ‘Polyfoam’ on the impact face of spring ‘B’.

0

200

400

600

800

1000

1200

0 2 4 6 8 10

Output (V)

Lo

ad

(N

)

107.8

1

Figure 2.11: Calibration result of static load cell.

Figure 2.12: Static calibration result of potentiometer ‘T’.

0 0.01 0.02 0.03 0.04 0.05Time (s)

0

0.002

0.004

0.006

0.008

0.01

Dis

pla

ce

me

nt (m

)

0 0.01 0.02 0.03 0.04 0.05Time (s)

0

0.1

0.2

0.3

0.4

0.5

Ve

locity (

m/s

)

0 0.01 0.02 0.03 0.04 0.05Time (s)

-40

-20

0

20

40

Accele

ratio

n (

m/s

2)

Potentiometer

Accelerometer

Figure 2.13: Dynamic calibration result of potentiometer ‘T’.

0

1

2

3

4

5

6

7

0 0.5 1 1.5 2 2.5

Output (V)

Dis

pla

cem

en

t (m

m)

0

0.5

1

1.5

2

0 0.2 0.4 0.6 0.8

Figure 2.14: Installed strain gauge

Figure 2.15: Setup of (a) static strain calibration test, and (b) dynamic strain

calibration test.

Supporting frame

Nail with strain

gauges

Dynamic

load cell

Adapter

Spring ‘B’ Dead

weight

Falling

dead

weight

Strain

gauge

Connection

terminal Hole for cable to

pass through

(a) (b)

Figure 2.16: Static strain calibration result of nail with surface sand glued by coarse

sand, for strain gauges installed at (a) 0.25 m, and (b) 0.45 m from nail head.

0 10 20 30 40Time (ms)

0

100

200

300

400

Lo

ad

(N

)

0 10 20 30 40 50Time (ms)

0

100

200

300

400

Lo

ad

(N

)

Dynamic load cell

Strain gauges at 0.25 m from nail head

Strain gauges at 0.45 m from nail head

(a)

(b)

Figure 2.17: Dynamic strain calibration results of nail with surface sand glued by

coarse sand, with impulse load imposed at (a) nail head, and (b) nail end.

0

100

200

300

400

500

600

0 0.1 0.2 0.3 0.4 0.5 0.6

Output (V)

Lo

ad

(N

)

1007

1

0

100

200

300

400

500

600

0 0.1 0.2 0.3 0.4 0.5 0.6

Output (V)

Lo

ad

(N

) 1134

1

(a)

(b)

(c)

(d)

Figure 2.18: Close view of (a) C surface, (b) F surface, (c) P surface and (d) U

surface.

Strain gauge

Figure 2.19: Surface profiles of F surface measured at three random locations.

Figure 2.20: Surface profiles of P surface measured at three random locations.

50µm

15µm

200µm

200µm

Figure 2.21: Surface profiles of U surface measured at three random locations.

0102030405060708090

100

0.01 0.1 1 10

Particle Size, mm

Perc

en

tag

e p

ass,

%

Coarse

sand

Fine

sand

0.12 0.7

Figure 2.22: Particle distribution curve of coarse sand and fine sand.

5 µm

200 µm

DCs-DCs DCs-C

DCs-F MCs-C

DFs-DFs DFs-F

DCs-U DCs-P

Figure 2.23: Shear stress – normal stress relationship of direct shear test results.

y = 0.6006x

y = 0.8219x

0

10

20

30

40

50

0 20 40 60

Normal stress (kPa)

Sh

ear

str

ess

(kP

a)

y = 0.5961x

y = 0.8075x

0

10

20

30

40

50

0 20 40 60

Normal stress (kPa)

Sh

ear

str

ess

(kP

a)

y = 0.5926x

y = 0.7862x

0

10

20

30

40

50

0 20 40 60

Normal stress (kPa)

Sh

ear

str

ess (

kP

a)

y = 0.5899x

y = 0.7611x

0

10

20

30

40

50

0 20 40 60

Normal stress (kPa)

Sh

ear

str

ess (

kP

a)

y = 0.2949x

0

5

10

15

20

0 20 40 60

Normal stress (kPa)

Sh

ea

r s

tre

ss

(k

Pa

)

y = 0.5384x

0

10

20

30

40

0 20 40 60

Normal stress (kPa)

Sh

ea

r s

tre

ss

(k

Pa

)

y = 0.5988x

y = 0.8948x

0

10

20

30

40

50

60

0 20 40 60

Normal stress (kPa)

Sh

ear

str

ess (

kP

a)

y = 0.5936x

y = 0.8737x

0

10

20

30

40

50

60

0 20 40 60

Normal stress (kPa)

Sh

ear

str

ess (

kP

a)

0 2 4 6 8 10

Horizontal displacement (mm)

0

10

20

30S

he

ar

stre

ss (

kPa

)

0 2 4 6 8 10

Horizontal displacement (mm)-0.4

0

0.4

0.8

1.2

Ve

rtic

al d

isp

lace

me

nt (

mm

)

DCs-C DCs-F

DCs-P DCs-U

DCs-DCs

Figure 2.24: Result of direct shear tests with dense coarse sand medium.

0 2 4 6 8


0

10

20

30

Sh

ea

r st

ress

(kP

a)

0

0.2

0.4

0.6

0.8

Ve

rtical d

ispla

ce

me

nt (m

m)

82% relative density

90% relative density

Figure 2.25: Comparison of direct shear test results between DCs-C test (90 % Id) and

MCs-C test (82 % Id).

0 2 4 6


0

10

20

30

Sh

ea

r st

ress

(kP

a)

0

0.2

0.4

0.6

Ve

rtical d

ispla

ce

me

nt (m

m)

DFs-F

DFs-DFs

Figure 2.26: Results of direct shear tests with dense fine sand medium.

Figure 2.27: The motion of sand hopper during sand pluviation process.

Impulse

hammer

Front of

pullout box

Motion of sand hopper

Chapter 3: The Quasi Static Pullout Test

3.1 Introduction

A good understanding of the characteristic of quasi static pullout response will

greatly facilitate the interpretation of rapid pullout test results in the next chapter. In

this chapter, the quasi static pullout response of nails with different surface roughness

conditions will be examined in detail, focusing on load displacement characteristic,

peak pullout strength and the degree of restrained dilatancy effect.

In the discussion, the nails are categorized into ‘rough nail’ and ‘smooth nail’

according to the normalized roughness Rn of nail surface as pointed out in Section

2.6.2.2 of Chapter 2. The nails with C surface (sand glued by coarse sand) and F

surface (sand glued by fine sand) are categorized as rough nail while the nails with P

surface (roughened by sand paper) and U surface (untreated stainless steel surface) are

categorized as smooth nail.

3.2 The Plot of Load Displacement Curve

The quasi static load displacement curves of every test series are plotted as

plots (a) in Figure 3.1 to Figure 3.9. Both of the identical quasi static pullout tests that

were conducted under each test series are plotted together in the same figure for clear

examination of any variation in between tests. A new sand medium was prepared for

every pullout tests conducted in these experiments.

For pullout tests under DCs-S25C test series, MCs-S25C test series, DCs-

S25F test series, and DCs-S45F test series, measurements of axial body strains were

made along the nail by strain gauges at points 0.25 m and 0.45 m from nail head.

While for pullout tests under DCs-L25F test series with 1.65 m of effective nail length,

the strain measurements were made at points 0.4 m, 0.8 m and 1.2 m from nail head.

The strain measurement results, after being converted into axial body load by

multiplying the voltage output of strain gauges with the calibration factors determined

in Section 2.5.3, are also plotted together with their corresponding load displacement

curve (measurement at nail head by load cell).

The load displacement curves of quasi static reload tests that were conducted

directly after the primary quasi static pullout tests are plotted as plot (b) in Figure 3.1

to Figure 3.9. The scale of load axes (vertical axes) of plot (a) and plot (b) in these

figures were made identical for easier comparison of maximum reloading strength to

the corresponding peak and residual quasi static pullout strength.

3.2.1 Repeatability of Test Results

From Figure 3.1 to Figure 3.9, it can be seen that the load displacement curves

and the axial body load vs. pullout displacement curves of both quasi static pullout

tests under the same test series were well matched to each other with minor

differences. This observation indicates that the test conditions, including the

conditions of sand medium and nail surface, of these pullout tests were fairly identical

and repeatable.

The consistency of sand medium constructed by the air pluviation procedures

applied to these experiments has been shown by the results of sand density calibration

test presented in Section 2.7.3. These calibration tests showed that all sand samples

constructed by the same air pluviation procedures and conditions were consistent and

virtually identical to each other. The consistency of sand medium formed by air

pluviation method was also illustrated by several researchers such as Miura and Toki

(1982), Presti et.al. (1993) and Fretti et.al. (1995).

It has been mentioned in Section 2.8 of Chapter 2 that both of the quasi static

pullout tests were conducted as the first and the last pullout test under each test series

(Table 2.5). Thus, the consistency and the repeatability of these quasi static pullout

test results imply that the roughness condition of nail surface was not severely

degraded throughout the series of tests. This means that the condition of nail surface

was virtually consistent for all pullout tests under the same test series, including the

high energy and the low energy rapid pullout tests which were conducted in between

that two quasi static pullout tests (Table 2.5). This deduction is important because the

comparison between quasi static pullout test and rapid pullout test is only sensible if

the condition of nail surface is identical in both quasi static and rapid pullout tests.

3.3 Quasi Static Pullout Response

3.3.1 Rough Nail

The quasi static load displacement curves of all series of tests on rough nail

are presented in Figure 3.1 to Figure 3.7. It can be seen from these figures that the

shape of these load displacement curves were identical: with hyperbolic load

displacement response up to the peak pullout stage and then followed by softening

behaviour in the post peak region. Clear peak pullout strength was attained in all tests.

The shape of these load displacement curves is typical for rough nail embedded in

dense dilative soil (Schlosser and Elias, 1978, Franzen, 1998).

The pullout displacement up(s)

required to achieve the peak quasi static pullout

strength of all series of tests on rough nail are given in Table 3.1. For test series with

coarse sand medium (DCs-S25C test series, DCs-S45C test series, DCs-S25F test

series, DCs-S45Ftest series and MCs-S25C test series), the up(s)

were approximately

in the range of 2.5 mm to 3.5 mm. While for test series with fine sand medium (DFs-

S25F test series), the up(s)

was only 1.3 mm, significantly lower than the up(s)

of tests

with coarse sand medium. This result implies that the up(s)

for rough nails embedded in

dense sand is highly influenced by the mean particle size of sand medium.

Figure 3.10 compares the load displacement curves of DCs-S25C-1-S test,

DCs-S45C-1-S test, DCs-S25F-1-S test and DCs-S45F-1-S test. It is important to note

that the initial stiffness Ksi of these curves were in good agreement to each other, and

the curves only started to diverge when approaching their peak quasi static pullout

strength. It is interesting to observe that the load displacement curves of DCs-S25C-1-

S test and DCs-S45F-1-S test that had nearly identical peak quasi static pullout

strength were approximately matched to each other, despite the variation in surface

roughness and nail diameter. Besides, the point of peak quasi static pullout strength of

these tests can also be traced by a straight line from the origin, the stiffness of this

straight line, which can be termed as the secant stiffness at peak Ksp. The similar of

initial stiffness and secant stiffness at peak of these tests suggests that the pre peak

quasi static load displacement stiffness of rough nail embedded in the same dense

sand medium is mainly affected by the level of peak pullout strength but less

influenced by nail diameter. The high influence of peak pullout strength in turn

suggests the important role of restrained dilatancy effect because the difference in

peak quasi static pullout strength between the tests compared in Figure 3.10 is found

to be mainly contributed by the restrained dilatancy effect (Section 3.5). Similar

observation was also made from the soil nails pullout test results reported by Tei

(1993) and pile tension test results reported by Lehane et.al. (2005).

Figure 3.11 compares the load displacement curves of DCs-S25C-1-S test and

MCs-S25C-1-S test. It can be seen that both curves started to diverge from the

beginning of pullout response (in relative to the response of tests compared in Figure

3.10), and the point of peak pullout strength of both tests can not be joined by a

straight line from the origin. This means that the initial stiffness and secant stiffness at

peak of both tests are dissimilar despite the small variation in sand density.

Comparatively the initial stiffness and secant stiffness at peak of MCs-S25C-1-S test

were smaller than those of DCs-S25C-1-S test (Figure 3.11). This observation

suggests the significant influence of sand density on the pullout stiffness.

In Figure 3.1 to Figure 3.7, except Figure 3.2, the axial body load

measurements made along the nails by strain gauges are also plotted. From the curves

of axial body load versus pullout displacement of nail head, it is revealed that the

shape and the pullout displacement required to achieve the peak pullout stage of these

curves were very similar to those of corresponding load displacement curves

measured at nail head. These observations suggest that the nails, even for nail with

1.65 m of effective nail length (DCs-L25F test series), were stiff enough to behave as

rigid body in the pullout and the extensibility of the nails was relatively insignificant

to cause the lag (in terms of nail head pullout displacement) in mobilization of shaft

resistance along the nails (Gurung et.al., 1999).

Beyond the peak pullout stage, softening behaviour was observed. However,

residual pullout strength that is constant with the increase in pullout displacement was

not clearly achieved by these quasi static pullout tests as the post peak pullout

response was still in gentle decreasing trend at the end of these tests, even the post

peak pullout displacement was as high as 15 mm (DCs-S25C-5-S test in Figure 3.1).

Further increase in pullout displacement was not allowed in these experiments due to

the limited measuring range of potentiometers. This response agrees with the post

peak pullout behaviour of ribbed steel bar embedded in dense sand observed by

Schlosser and Elias (1978) and the tension pullout response of 40 mm diameter rough

model pile embedded in dense sand observed by Alawneh et.al. (1999).

3.3.2 Smooth Nail

The quasi static load displacement curves of test series with smooth nail

surface, the DCs-S22U test series (U surface, untreated smooth stainless steel) and the

DCs-S25P test series (P surface, roughened by sand paper) are plotted in Figure 3.8

and Figure 3.9 respectively. From these figures, the load displacement behaviour of

smooth nails is observed to be totally different from the load displacement behaviour

of rough nails. Clear peak pullout stage and post peak softening behaviour which were

common for tests on rough nail surface were not observed at all in the results of tests

on smooth nail.

The pullout displacement required to achieve the maximum pullout strength of

DCs-S22U test series was very small, only approximately 0.5 mm (Figure 3.8), which

was much smaller than the pullout displacement required to achieve the peak pullout

strength of rough nail embedded in similar sand medium. After reaching the

maximum pullout strength, the load displacement curve of DCs-S22U test series

became a plateau with constant pullout strength. This behaviour is opposite to the

softening behaviour observed in tests on rough nail (Figure 3.1 to Figure 3.7), but

agrees well with the results of direct shear test on U surface (Section 2.7.2).

For DCs-S25P test series with P surface (Figure 3.9), the quasi static load

displacement behaviour at small pullout displacement (< 0.5 mm) was quite similar to

the behaviour of DCs-S22U test series. However, after approximately 1 mm of pullout

displacement, the load displacement behaviour of DCs-S25P test series had turned

into hardening behaviour with its pullout strength continually increased with the

increase in pullout displacement. The hardening rate (in terms of pullout displacement)

was fairly constant up to 11 mm of pullout displacement, the end of the test.

3.4 Quasi Static Load Distribution Curve

The load distribution curves of axial body load measured along the nail are

extracted from Figure 3.1 to Figure 3.7 (except Figure 3.2) and plotted in Figure 3.12

for pullout stages corresponding to 50 % and 100 % of peak quasi static pullout

strength. These plots clearly show that the load distribution curves of all series of tests

were fairly linear even for test series with 1.65 m of effective nail length (DCs-L25F

test series). The linearity of these load distribution curves again suggests that all nails

considered in these experiments behaved as rigid body in pullout tests.

Besides, the linearity of load distribution curve also indicates minimal

influence of rigid front wall on the pullout response because it indirectly shows the

uniform distribution of unit shaft resistance along the nails irregardless of distance

from the rigid wall in front (Farrag et.al., 1993).

3.5 Peak Quasi Static Pullout Strength and Restrained Dilatancy Effect

The peak or maximum quasi static pullout strength, the apparent ratio of

friction coefficient f and the ratio of friction coefficient µ. of all series of tests are

given in Table 3.1. The f and µ were defined by Eq. 3.1 to Eq. 3.3 (Milligan and Tei,

1998). Since the peak or maximum pullout strength of both quasi static pullout tests

conducted under the same test series were nearly identical, only the average peak

pullout strength of both tests is given in Table 3.1. For DCs-S25P test series, the

maximum pullout strength was taken as the pullout load mobilized at maximum

pullout displacement recorded in the test because clear peak or maximum pullout

strength was not observed.

)(' ine

p

s

dL

Pf

σπ= (3.1)

( )v

o

in

K'

2

1' )( σσ

+= (3.2)

'tanδµ

f= (3.3)

with, p

sP = peak quasi static pullout strength; d = nail diameter; Le = effective nail

length; Ko = Jaky’s formula for coefficient of earth horizontal pressure at rest, 1-

sinφ’ps; δ’ = peak interface friction angle (Table 2.2), φ’ps = peak plane strain friction

angle of sand medium (Table 2.2), and σ’v = initial effective vertical stress.

From Table 3.1, it can be seen that the ratio of friction coefficient at peak of

every series of tests on rough nail had exceeded unity, which implies that the peak

pullout strength of rough nail in these experiments had exceeded the analytical peak

pullout strength estimated based on interface friction angle by the equilibrium

equation shown below.

'tan' )( δσπ inedLP = (3.4)

with d = nail diameter, Le = effective nail length, σ’n(i) = initial mean effective normal

stress, and δ’ = peak interface friction angle (from Table 2.2).

The ratio of friction coefficient at peak that is larger than unity was also

observed by Schlosser and Elias (1978), Guilloux et.al. (1979), Cartier and Gigan

(1983), Ignold (1983), Heymann (1993) and Milligan and Tei (1998) on the pullout

response of planar reinforcement or soil nail embedded in dense dilative soil. This

phenomenon was also observed by Horvath and Kenney (1980), Stewart and Kulhawy

(1981) and Jardine and Chow (1996) on the interfacial shaft resistance of pile.

Schlosser (1982) attributed this phenomenon to the restrained dilatancy effect.

Restrained dilatancy effect is generated by the restraining effect of relatively

undisturbed outer field soil medium on the dilative response of high strain weaken

zone adjacent to interface. This restraining effect enhances the normal stress acting on

interface and subsequently enhances the interfacial resistance. This hypothesis is

supported by the direct physical measurements on enhancement of interfacial

effective normal stress in pullout, reported by the French National Research Project

Clouterre (1991) on soil nail and ground anchor, Johnston and Romstad (1989) on

Geogrids and Stewart and Kulhawy (1981) on uplift drilled shaft.

The enhancement in normal stress caused by restrained dilatancy effect was

also observed by Guilloux et.al. (1979), Sobolevsky (1995), and Evgin and Fakharian

(1996) on laboratory direct or simple shear tests with constant normal stiffness.

Guilloux et.al. (1979) recorded an increase in normal stress up to 14 times of the

initial normal stress when the normal displacement of a direct shear test was fully

restrained. Sobolevsky (1995) studied this phenomenon by the dilatometer, a device

that similar to direct shear test but with controllable normal stiffness. Sobolevsky

(1995) demonstrated that the enhancement in normal stress was increasing with the

increase in normal stiffness. Similar observation was also made by Evgin and

Fakharian (1996) on constant stiffness simple shear interface tests for surface with

0.05 in normalized roughness Rn.

From Table 3.1, it is seen that the ratio of friction coefficient at peak, which is

an indicator to the degree of restrained dilatancy effect, was affected by the surface

roughness. This can be seen by comparing the ratio of friction coefficient at peak of

DCs-S25C test series, DCs-S25F test series, DCs-S25P test series and DCs-S22U test

series, which indicates the progressive decrease in ratio of friction coefficient at peak

from 3.76 to 1.1 with the decrease in normalized roughness of nail surface from 1 to

0.003. The high ratio of friction coefficient at peak of DCs-S25C test series and DCs-

S25F test series is reasonably due to the dilative behaviour of C surface and F surface

as has been demonstrated by the direct shear interface test results (DCs-C test and

DCs-F test) reported in Figure 2.24.

The ratio of friction coefficient at peak of DCs-S22U test series that was close

to unity indicates minimal influence of restrained dilatancy effect on the pullout

response of this smooth nail. This is reasonable since the results of direct shear test

with U surface (DCs-U test) shown in Figure 2.24 showed non-dilative behaviour.

For DCs-S25P test series, the ratio of friction coefficient at peak was 1.71.

This result indicates that restrained dilatancy effect was also mobilized in the quasi

static pullout tests of nail with P surface although P surface was categorized as

smooth surface by its normalized roughness (Rn = 0.03). This observation is supported

by the results of direct shear interface test on P surface (DCs-P test) in Figure 2.24,

which indicates small dilative behaviour of P surface with 1.8o of maximum dilatancy

angle.

It has to be noted that the mobilization of restrained dilatancy effect is

progressive in nature because the dilative response of interface is progressively

mobilized with the increase in pullout displacement (shear strain). Therefore, the

enhancement in mean effective normal stress on nail shaft caused by restrained

dilatancy effect is also progressive in nature. This may consequently lead to gradually

increasing of pullout strength with the increase in pullout displacement although the

basic interfacial strength under constant normal stress is constant or with gentle

softening response, which is the case for interface between dense course sand and P

surface (DCs-P test, Figure 2.24). Hence, the hardening response of DCs-S25P test

series may be mainly attributed to restrained dilatancy effect. It needs to be mentioned

that the hardening response of DCs-S25P test series should not be attributed to

densification effect of surrounding soil in the pullout process as the sand medium was

initially in dense state with relative density as high as 90 %.

This deduction can be supported by the results of simple shear interface tests

on steel surface with Rn = 0.05 reported by Evgin and Fakharian (1996). Their results

showed that when free vertical displacement was allowed in the simple shear interface

test (without restrained dilatancy effect), the response of this interface test displayed

clear peak shear strength and continued by gentle softening behaviour. However,

when the vertical displacement was partially or fully restricted (with restrained

dilatancy effect), the response of this interface became hardening behaviour without

peak shear strength and the final shear strength achieved in this interface test was

significantly higher than the peak shear strength achieved by the test with allowance

of free vertical displacement.

The comparison of ratio of friction coefficient at peak between DCs-S25C test

series and MCs-S25C test series in Table 3.1 also reveals that the ratio of friction

coefficient at peak was also influenced by the density of sand medium, as the ratio of

friction coefficient has decreased from 3.76 (DCs-S25C test series) to 3.00 (MCs-

S25C test series) with the small decrease in relative sand density from 90 % to 82 %.

This is reasonable since the interface behaviour between medium dense course sand

(Id = 82 %) and C surface is shown to be less dilative than the interface behaviour

between dense course sand (Id = 90 %) and C surface (Figure 2.25 and Table 2.2).

The ratio of friction coefficient at peak of DCs-L25F test series with 1.65 m of

effective nail length is also observed to be nearly identical to the ratio of friction

coefficient at peak of DCs-S25F test series with 0.75 m of effective nail length (Table

3.1). This result indicates the independence of ratio of friction coefficient on effective

nail length, which implies that the enhancement in normal stress (and hence the shaft

resistance) is evenly distributed along the nail. Besides, the independence of ratio of

friction coefficient on effective nail length also implicitly implies the minimal

influence of rigid front wall effect on the measured pullout response, as described by

Palmeira and Milligan (1989).

By comparing the ratio of friction coefficient at peak of DCs-S25C test series

to DCs-S45C test series and DCs-S25F test series to DCs-S45F test series in Table 3.1.

It is revealed that the ratio of friction coefficient at peak was decreasing with the

increase in nail diameter. As an example, the increase in nail diameter from 25 mm

for DCs-S25C test series to 45 mm for DCs-S45C test series caused the decrease of

ratio of friction coefficient at peak from 3.76 to 2.60. This observation accords with

the results of Milligan and Tei (1998) on laboratory soil nail pullout tests. Besides,

similar observation was also made by Stewart and Kulhawy (1981) and Jardine and

Chow (1994) on interfacial shaft resistance of pile embedded in dense dilative sand.

The relationship between nail diameter and ratio of friction coefficient at peak

observed in these experiments can also be described by the empirical solution

proposed by Jardine and Chow (1996) and the analytical solution proposed by Luo

(2001). From their solutions, the relationship between ratio of friction coefficient µ

and nail radius r is found to be (µ -1)∝ 1/r. The points of (µ-1) at peak of DCs-S25C

test series, DCs-S45C test series, DCs-S25F test series and DCs-S45F test series are

plotted in Figure 3.13a and Figure 3.13b versus nail diameter, together with the line of

(µ -1)∝ 1/r. It is seen that the relationship between ratio of friction coefficient at peak

and nail diameter of these experiments seems to obey the 1/r rule proposed by Jardine

and Chow (1996) and Luo (2001).

3.6 Quasi Static Reload Test

The load displacement curves of quasi static reload tests which were

conducted directly after the primary quasi static pullout tests are plotted as plot (b) in

Figure 3.1 to Figure 3.9 for each test series. In the plots for DCs-S25C test series,

MCs-S25C test series, DCs-S25F test series, DCs-S45F test series and DCs-L25F test

series which were instrumented with strain gauges, the axial body load measurements

made along the nail are also plotted.

For all test series on rough nail (Figure 3.1 to Figure 3.7), the load

displacement curves of reload tests displayed stiffer load displacement response when

compared to the load displacement curves of their preceding quasi static pullout tests.

The pullout displacement required to mobilize the maximum reloading pullout

strength was only in the range of 0.5 mm. After reaching the maximum reloading

pullout strength, the reloading pullout response became a plateau with constant

pullout strength.

From Figure 3.1 to Figure 3.7, it can be seen that although the maximum

reloading pullout strength of a reload test was slightly lower than the least post peak

pullout strength attained by its preceding quasi static pullout test, this difference is

marginal. This small difference in pullout strength may be caused by the situation that

residual pullout stage was not sufficiently achieved by the preceding quasi static

pullout test due to the limited pullout displacement allowed in these experiments.

However, it may be postulated that the maximum reloading pullout strength would

eventually be achieved by the preceding quasi static pullout test if longer pullout

displacement is allowed. In fact, the least post peak pullout strength attained by DCs-

S25C-5-S test with 15 mm of post peak pullout displacement was already fairly close

to the maximum pullout strength attained by its succeeding reload test (Figure 3.1). It

is interesting to note that the reloading behaviour was not severely affected by the

level of post peak pullout displacement experienced by the preceding quasi static

pullout test. This can be seen from Figure 3.1 that the maximum reloading pullout

strength as well as the reloading load displacement response of reload tests conducted

after the DCs-S25C-1-S test and the DCs-S25C-5-S test were nearly identical, though

the maximum post peak pullout displacement experienced by their preceding quasi

static pullout tests were 5 mm and 15 mm respectively. But this could only be true if

the peak pullout stage has been sufficiently exceeded.

For DCs-S22U test series (Figure 3.8), the initial reloading pullout response is

seen to be very stiff with virtually negligible pullout displacement until the maximum

reloading pullout strength was attained. The reloading response then became plateau

with constant maximum pullout strength. The maximum reloading pullout strength of

these reload tests were virtually equal to the maximum pullout strength attained by

their preceding quasi static pullout tests.

For DCs-S25P test series (Figure 3.9), the initial reloading pullout response

was also very stiff with virtually negligible pullout displacement. However, after the

reloading strength had exceeded the maximum pullout strength attained by its

preceding quasi static pullout test, the reloading response turned into hardening

behaviour with hardening rate that was similar to the hardening rate of its preceding

quasi static pullout test.

3.7 Concluding Remarks

The quasi static pullout response of soil nails is observed to be highly

influenced by the roughness of nail surface. For nail with C surface (sand glued by

course sand) and F surface (sand glued by fine sand), which were both categorized as

rough nail by their normalized roughness Rn, the quasi static pullout response

exhibited non linear load displacement response until the peak pullout stage and then

followed by post peak softening response. For nail with U surface, the initial quasi

static pullout response was very stiff until reaching its maximum pullout strength, and

then the load displacement response became a plateau with constant pullout strength.

For nail with P surface, the pullout response is seen to attain the hardening behaviour

after approximately 0.5 mm of stiff initial pullout response.

The quasi static pullout response of rough nail and sand papered nail are found

to be influenced by restrained dilatancy effect. The restrained dilatancy effect

enhanced the pullout strength by as high as 3.76 times (DCs-S25C test series) in these

experiments.

Tab

le 3

.1:

Su

mm

ary o

f q

uas

i st

atic

pu

llout

test

s re

sult

s.

Tes

t se

ries

Pu

llo

ut

dis

pla

cem

ent

req

uir

ed t

o a

ttain

the

pea

k o

r m

ax

imu

m p

ull

ou

t st

ren

gth

us(

p) (

mm

)

Pea

k o

r m

axim

um

pu

llou

t st

ren

gth

Psp

(N

)

Ap

pare

nt

rati

o o

f

fric

tion

coef

fici

ent

f

at

pea

k

(Eq

. 3.1

)

Rati

o o

f fr

icti

on

coef

fici

ent

µ µµµ a

t p

eak

(Eq

. 3.3

)

DC

s-S

25C

3

930

3.0

4

3.7

6

DC

s-S

45C

3

.5

1080

2.1

0

2.6

0

MC

s-S

25C

3

700

2.4

6

3.0

0

DC

s-S

25F

2

.5

670

2.3

8

2.7

8

DC

s-L

25

F

2.5

1500

2.4

2

2.8

3

DC

s-S

45F

3

980

1.8

7

2.4

2

DF

s-S

25F

1

.3

950

3.4

4

3.6

3

DC

s-S

22U

0

.5

90

0.3

2

1.1

DC

s-S

25P

-

280*

0.9

1*

1.7

1*

* m

easu

red a

t 1

1 m

m o

f p

ull

ou

t d

isp

lace

men

t, t

he

max

imum

pull

out

dis

pla

cem

ent

reco

rded

in D

Cs-

S25P

tes

t se

ries

.

04

812

16

20

Pu

llo

ut d

isp

lace

me

nt (

mm

)

0

200

400

600

800

10

00

Load (N)

00

.51

1.5

22.5

Pu

llo

ut d

isp

lace

me

nt (m

m)

0

20

0

40

0

60

0

80

0

100

0

Load (N)(a

)(b

)

DC

s-S

25

C-1

-S, 0

m

DC

s-S

25

C-1

-S, 0

.25

m

DC

s-S

25

C-1

-S, 0

.45

m

DC

s-S

25

C-5

-S,

0m

DC

s-S

25

C-5

-S,

0.2

5m

DC

s-S

25

C-5

-S,

0.4

5m

DC

s-S

25C

-1-S

-r,

0m

DC

s-S

25C

-1-S

-r,

0.2

5m

DC

s-S

25C

-1-S

-r,

0.4

5m

DC

s-S

25

C-5

-S-r

, 0

m

DC

s-S

25

C-5

-S-r

, 0

.25m

DC

s-S

25

C-5

-S-r

, 0

.45m

Fig

ure

3.1

: T

he

load

dis

pla

cem

ent

curv

es o

f D

Cs-

S25C

tes

t se

ries

mea

sure

d a

t 0 m

, 0.2

5 m

and 0

.45 m

fro

m n

ail

hea

d,

(a)

qu

asi

stat

ic p

ull

out

test

; (b

) quas

i st

atic

rel

oad

tes

t.

04

812

Pu

llo

ut d

isp

lace

me

nt (m

m)

0

400

800

12

00

Load (N)

00

.40.8

1.2

1.6

Pu

llo

ut d

isp

lace

me

nt (m

m)

0

40

0

80

0

120

0

Load (N)

DC

s-S

45

C-1

-S

DC

s-S

45

C-4

-S

DC

s-S

45C

-1-S

-r

DC

s-S

45C

-4-S

-r

Fig

ure

3.2

: T

he

load

dis

pla

cem

ent

curv

es o

f D

Cs-

S45C

tes

t se

ries

mea

sure

d a

t nai

l hea

d, (a

) quas

i st

atic

pull

out

test

; (b

) quas

i st

atic

rel

oad

tes

t.

(a)

(b)

02

46

81

0

Pu

llo

ut d

isp

lace

me

nt (

mm

)

0

20

0

40

0

60

0

80

0

Load (N)

00

.51

1.5

22

.5

Pu

llo

ut d

isp

lace

me

nt (

mm

)

0

20

0

40

0

60

0

80

0

Load (N)

(a)

(b)

MC

s-S

25

C-4

-S-r

, 0

m

MC

s-S

25

C-4

-S-r

, 0

.25

m

MC

s-S

25

C-4

-S-r

, 0

.45

m

MC

s-S

25C

-1-S

-r,

0m

MC

s-S

25C

-1-S

-r,

0.2

5m

MC

s-S

25C

-1-S

-r,

0.4

5m

MC

s-S

25

C-4

-S,

0m

MC

s-S

25

C-4

-S,

0.2

5m

MC

s-S

25

C-4

-S,

0.4

5m

MC

s-S

25

C-1

-S,

0m

MC

s-S

25

C-1

-S,

0.2

5m

MC

s-S

25

C-1

-S,

0.4

5m

F

igu

re 3

.3:

Th

e lo

ad d

isp

lace

men

t cu

rves

of

MC

s-S

25C

tes

t se

ries

mea

sure

d a

t 0 m

, 0.2

5 m

and 0

.45 m

fro

m n

ail

hea

d,

(a)

qu

asi

stat

ic p

ull

out

test

; (b

) quas

i st

atic

rel

oad

tes

t.

02

46

8

Pu

llo

ut d

isp

lace

me

nt (m

m)

0

200

400

600

800

Load (N)

01

23

4

Pu

llo

ut d

isp

lace

me

nt (m

m)

0

20

0

40

0

60

0

80

0

Load (N)

(a)

(b)

DC

s-S

25

F-5

-S-r

, 0

m

DC

s-S

25

F-5

-S-r

, 0

.25

m

DC

s-S

25

F-5

-S-r

, 0

.45

m

DC

s-S

25

F-1

-S-r

, 0

m

DC

s-S

25

F-1

-S-r

, 0

.25

m

DC

s-S

25

F-1

-S-r

, 0

.45

m

DC

s-S

25

F-5

-S, 0

m

DC

s-S

25

F-5

-S, 0

.25

m

DC

s-S

25

F-5

-S, 0

.45

m

DC

s-S

25

F-1

-S, 0

m

DC

s-S

25

F-1

-S, 0

.25

m

DC

s-S

25

F-1

-S, 0

.45

m

Fig

ure

3.4

: T

he

load

dis

pla

cem

ent

curv

es o

f D

Cs-

S25F

tes

t se

ries

mea

sure

d a

t 0 m

, 0.2

5 m

and 0

.45 m

fro

m n

ail

hea

d,

(a)

qu

asi

stat

ic p

ull

out

test

; (b

) quas

i st

atic

rel

oad

tes

t.

02

46

Pu

llo

ut d

isp

lace

me

nt (

mm

)

0

200

400

600

800

10

00

Load (N)

00.4

0.8

1.2

1.6

2

Pu

llo

ut d

isp

lace

me

nt (m

m)

0

200

400

600

800

10

00

Load (N)

(a)

(b)

DC

s-S

45

F-5

-S,

0m

DC

s-S

45

F-5

-S,

0.2

5m

DC

s-S

45

F-5

-S,

0.4

5m

DC

s-S

45

F-1

-S, 0

m

DC

s-S

45

F-1

-S, 0

.25m

DC

s-S

45

F-1

-S, 0

.45m

DC

s-S

45

F-5

-S-r

, 0

m

DC

s-S

45

F-5

-S-r

, 0

.25

m

DC

s-S

45

F-5

-S-r

, 0

.45

m

DC

s-S

45

F-1

-S-r

, 0

m

DC

s-S

45

F-1

-S-r

, 0

.25

m

DC

s-S

45

F-1

-S-r

, 0

.45

m

Fig

ure

3.5

: T

he

load

dis

pla

cem

ent

curv

es o

f D

Cs-

S45F

tes

t se

ries

mea

sure

d a

t 0 m

, 0.2

5 m

and 0

.45 m

fro

m n

ail

hea

d,

(a)

qu

asi

stat

ic p

ull

out

test

; (b

) quas

i st

atic

rel

oad

tes

t.

02

46

Pu

llo

ut d

isp

lace

me

nt (m

m)

0

40

0

80

0

12

00

16

00

Load (N)

00

.40

.81

.21

.6P

ullo

ut d

isp

lace

me

nt (

mm

)

0

40

0

80

0

12

00

16

00

Load (N)

(a)

(b)

DC

s-L

25

F-5

-S,

0m

DC

s-L

25

F-5

-S,

0.4

m

DC

s-L

25

F-5

-S,

0.8

m

DC

s-L

25

F-1

-S,

0m

DC

s-L

25

F-1

-S,

0.4

m

DC

s-L

25

F-1

-S,

0.8

m

DC

s-L

25

C-1

-S,1

.2m

DC

s-L

25

C-5

-S,1

.2m

DC

s-L

25

F-5

-S-r

, 0

m

DC

s-L

25

F-5

-S-r

, 0

.4m

DC

s-L

25

F-5

-S-r

, 0

.8m

DC

s-L

25

F-1

-S-r

, 0

m

DC

s-L

25

F-1

-S-r

, 0

.4m

DC

s-L

25

F-1

-S-r

, 0

.8m

DC

s-L

25

C-1

-S-r

,1.2

mD

Cs-L

25

C-5

-S-r

,1.2

m

Fig

ure

3.6

: T

he

load

dis

pla

cem

ent

curv

es o

f D

Cs-

L25F

tes

t se

ries

mea

sure

d a

t 0 m

, 0.4

m,

0.8

m a

nd 1

.2 m

fro

m n

ail

hea

d,

(a)

quas

i st

atic

pull

out

test

; (b

) quas

i st

atic

rel

oad

tes

t.

01

23

4

Pu

llou

t dis

pla

ce

me

nt (

mm

)

0

20

0

40

0

60

0

80

0

10

00

Load (N)

00

.40

.81

.21

.62

Pu

llo

ut d

isp

lace

me

nt (m

m)

0

20

0

40

0

60

0

80

0

100

0

Load (N)(b

)(a

)

DF

s-S

25

F-5

-S,

0m

DF

s-S

25

F-5

-S,

0.2

5m

DF

s-S

25

F-5

-S,

0.4

5m

DF

s-S

25

F-1

-S,

0m

DF

s-S

25

F-1

-S,

0.2

5m

DF

s-S

25

F-1

-S,

0.4

5m

DF

s-S

25

F-5

-S-r

, 0

m

DF

s-S

25

F-5

-S-r

, 0

.25

m

DF

s-S

25

F-5

-S-r

, 0

.45

m

DF

s-S

25

F-1

-S-r

, 0

m

DF

s-S

25

F-1

-S-r

, 0

.25

m

DF

s-S

25

F-1

-S-r

, 0

.45

m

Fig

ure

3.7

: T

he

load

dis

pla

cem

ent

curv

es o

f D

Fs-

S25F

tes

t se

ries

mea

sure

d a

t 0 m

, 0.2

5 m

and 0

.45 m

fro

m n

ail

hea

d,

(a)

qu

asi

stat

ic p

ull

out

test

; (b

) quas

i st

atic

rel

oad

tes

t.

00

.40

.81

.21

.6

Pu

llo

ut d

isp

lace

me

nt (m

m)

0

20

40

60

80

10

0

Load (N)

DC

s-S

22

U-1

-S

DC

s-S

22

U-4

-S

00.2

0.4

0.6

0.8

Pu

llou

t d

isp

lace

me

nt (m

m)

0

20

40

60

80

10

0

Load (N)

DC

s-S

22

U-1

-S-r

DC

s-S

22

U-4

-S-r

(a)

(b)

F

igu

re 3

.8:

Th

e lo

ad d

isp

lace

men

t cu

rves

of

DC

s-S

22U

tes

t se

ries

mea

sure

d a

t nai

l hea

d, (a

) quas

i st

atic

pull

out

test

; (b

) quas

i st

atic

rel

oad

tes

t.

04

812

Pu

llo

ut d

isp

lace

me

nt (

mm

)

0

100

200

300

Load (N)

DC

s-S

25

P-1

-S

DC

s-S

25

P-4

-S

01

23

4

Pu

llo

ut d

isp

lace

me

nt (m

m)

0

100

200

300

Load (N)

DC

s-S

25P

-1-S

-r

DC

s-S

25P

-4-S

-r

F

igu

re 3

.9:

Th

e lo

ad d

isp

lace

men

t cu

rves

of

DC

s-S

25P

tes

t se

ries

mea

sure

d a

t nai

l hea

d, (a

) quas

i st

atic

pull

out

test

; (b

) quas

i st

atic

rel

oad

tes

t.

(a)

(b)

0 2 4 6 8 10 12

Pullout displacement (mm)

0

400

800

1200

Lo

ad

(N

)

DCs-S25C-1-S

DCs-S45C-1-S

DCs-S25F-1-S

DCs-S45F-1-S

Ksi Ks

p

Figure 3.10: Comparison of quasi static load displacement curves of test series with

rough nail embedded in dense coarse sand medium.

0 2 4 6 8 10


0

200

400

600

800

1000

Lo

ad

(N

)

DCs-S25C-1-S

MCs-S25C-1-S

Ksi Ks

p

Figure 3.11: Comparison of quasi static load displacement curve of DCs-S25C test


0 0.2 0.4 0.6 0.8

Distance from nail head (m)

0

200

400

600

800

1000A

xia

l b

od

y lo

ad

(N

)

0 0.2 0.4 0.6 0.8


0

200

400

600

800

Axia

l b

od

y lo

ad

(N

)

0 0.2 0.4 0.6 0.8


0

200

400

600

800

1000

Axia

l b

od

y lo

ad

(N

)

0 0.2 0.4 0.6 0.8


0

200

400

600

800

Axia

l b

od

y lo

ad

(N

)

0 0.2 0.4 0.6 0.8


0

200

400

600

800

1000

Axia

l b

od

y lo

ad

(N

)

0 0.4 0.8 1.2 1.6 2


0

400

800

1200

1600

Axia

l b

od

y lo

ad

(N

)

DCs-S25C-1-S

DCs-S25F-1-S

MCs-S25C-1-S

DCs-L25F-1-S DFs-S25F-1-S

DCs-S45F-1-S

100 % of Psp

50 % of Psp

Figure 3.12: Load distribution curves of quasi static pullout tests on rough nail.

00.5

1

1.52

2.53

3.5

44.5

5

0 20 40 60 80

Nail diameter (mm)

(µ−

1)

(µ−

1)

(µ−

1)

(µ−

1)

(a)

0

0.5

1

1.5

2

2.5

3

3.5

4

0 20 40 60 80

Nail diameter (mm)

(µ−

1)

(µ−

1)

(µ−

1)

(µ−

1)

(b)

Figure 3.13: The relationship between ratio of friction coefficient µ at peak and nail

diameter, (a) between DCs-S25C test series and DCs-S45C test series; and (b)

between DCs-S25F test series and DCs-S45F test series.

∝ 1/r

∝ 1/r

Chapter 4: High Energy Rapid Pullout Test

4.1 Introduction

In this chapter, the results of high energy rapid pullout tests are presented and

discussed in detail. The loading rate effect on pullout response of soil nail is assessed

by comparing the rapid pullout test results with the corresponding quasi static pullout

test results presented in Chapter 3. The mobilization characteristic of radiation

damping effect in rapid pullout test is also addressed. The term ‘high energy’ in this

thesis is referred to the condition which the imposed tensile impulse load was high

enough to exceed the pullout strength of the nail and cause complete pullout failure.

The results of quasi static reload test conducted after the high energy rapid

pullout test are also presented in this chapter to assess the influence of preceding rapid

pullout test on quasi static reloading behaviour.

The traces of impulse load, rapid axial body load, displacement, velocity and

acceleration in time domain of all high energy rapid pullout tests are plotted in

Appendix A. As has been discussed in Section 2.4.2 of Chapter 2, loading duration of

impulse load applied to every rapid pullout tests in these experiments was around 27

ms, with approximately 8 ms of rise time and 19 ms of fall time (although these

parameters slightly differ from test to test, the differences were marginal). The

dominant loading frequency was approximately 35 Hz by FFT analysis. The

corresponding relative wave length defined by Eq. 1.1 was 90 and 41 respectively for

tests with 0.75 m and 1.65 m of effective nail length. These relative wave lengths are

significantly larger than the lower boundary value of 10 proposed by Holeyman (1992)

for the validity of rapid loading condition.


The load displacement curves of all high energy rapid pullout tests conducted

are plotted in Figure 4.1 to Figure 4.9 according to test series. Rapid load

displacement curves plotted in these figures are the curve of ‘net’ rapid soil response,

with inertia effect had been subtracted by Eq. 4.1 below. In Eq. 4.1, the pullout

acceleration of nail head is taken to represent the acceleration of whole nail. This

assumption is valid only if the nail behaves as rigid body in pullout, which is true for

these experiments as has been demonstrated by the results of quasi static pullout tests

in Chapter 3. The inertia effect involved in these experiments was found to be

relatively insignificant for tests on rough nail (C surface and F surface) because the

pullout strength of rough nail was a lot higher than the additional resistance caused by

inertia effect. However, inertia effect was quite significant for tests on smooth nail (U

surface and P surface) with low pullout strength, as illustrated in Figure 4.10.

MaPP dr −= (4.1)

with Pr = ‘net’ rapid soil response, Pd = dynamic impulse load, M = total mass of nail

body plus any connection accessories that existed after the force measurement point,

and a = acceleration of nail head.

Similar to the presentation of quasi static pullout test results, the results of

both high energy rapid pullout tests under the same test series are plotted together to

examine the repeatability and consistency of rapid pullout tests. It has to be reminded

that new sand medium was prepared for every pullout tests (except the reload tests).

As observed from Figure 4.1 to Figure 4.9, the load displacement curves of both high

energy rapid pullout tests under the same test series are well matched to each other.

This observation together with the repeatability and consistency of quasi static pullout

tests reported in Section 3.2.1 of Chapter 3 leads to the conclusion that the condition

of nail surface was rather consistent throughout each series of test.

For better examination of the influence of loading rate on pullout behaviour,

the results of quasi static pullout tests presented in Chapter 3 are also re-plotted in

Figure 4.1 to Figure 4.9 together with their corresponding rapid pullout test results.

Since the results of both quasi static pullout tests under a test series were highly

identical, only one quasi static pullout test result is plotted here for each test series.

The axial body load measurements made by strain gauges along the nail of

DCs-S25C test series, MCs-S25C test series, DFs-S25F test series, DFs-S45F test

series and DFs-L25F test series are also plotted in Figure 4.1 – Figure 4.7 (except

Figure 4.2) together with corresponding rapid load displacement curve measured at

nail head. Similar to the plots of rapid load displacement curve, the plotted curves of

rapid axial body load vs. nail head pullout displacement in Figure 4.1 to Figure 4.7

(except Figure 4.2) are the curve of ‘net’ rapid soil response calculated by Eq. 4.1, by

taking the Pd in Eq. 4.1 as the axial body load measured by strain gauges in rapid

pullout tests and M as the total mass of nail body after the point of strain measurement.

From these figures, it is seen that the shape of axial body load vs. nail head pullout

displacement curves was almost identical to the shape of corresponding load

displacement curve measured at nail head. This observation implies that the nails also

behaved as rigid body in rapid pullout tests as no lag (in terms of nail head pullout

displacement) in mobilization of rapid axial body load along the nail was observed.

4.3 Pre Peak Rapid Pullout Response of Rough Nail

4.3.1 Pre Peak Rapid Pullout Stiffness

From Figure 4.1 to Figure 4.7, it is clearly observed that although the shape of

pre peak rapid load displacement curves was approximately similar to that of

corresponding quasi static load displacement curves, the pre peak pullout stiffness

rapid pullout tests was obviously higher than that of corresponding quasi static pullout

test. The pullout displacement required to mobilize the peak rapid pullout strength

(up(r)

) also seemed smaller than that required to mobilize the peak quasi static pullout

strength (up(s)

). As an example, the pullout displacement required to mobilize the peak

rapid pullout strength of DCs-S25C-2-RH test was approximately 2 mm, while the

pullout displacement required to achieve the peak quasi static pullout strength of

corresponding DCs-S25C-1-S test was around 3 mm (Figure 4.1). It has to be noted

that despite the difference in between up(r)

and up(s)

, the quasi static pullout load

mobilized at up(r)

was in fact rather close to the corresponding peak quasi static pullout

strength with less than 5 % in variation (Figure 4.1 to Figure 4.7). This is because the

variation in quasi static pullout load was quite minimal in vicinity of the point of peak

quasi static pullout strength.

The stiffer pre peak load displacement behaviour of rapid pullout tests was not

only observed on the load measurement made at nail head but also on the axial body

load measurement made along the nail (Figure 4.1 to Figure 4.7 except Figure 4.2).

This observation implies that the stiffer pre peak behaviour of rapid pullout tests is a

characteristic contributed by the mobilization of shaft resistance along the nail under

rapid loading condition. Besides, this phenomenon appears not to be influenced by the

particle size effect (d/D50) as the same phenomenon is also observed on DFs-S25F test

series (Figure 4.7) with d/D50 ratio as high as 208, slightly exceeds the highest

minimum d/D50 ratio that had ever been suggested to eliminate of particle size effect

(Randolph and House, 2001).

By comparing the results of test series with different nail diameter, such as

between DCs-S45C test series (Figure 4.2) and DCs-S25C test series (Figure 4.1) or

between DCs-S45F test series (Figure 4.5) and DCs-S25F test series (Figure 4.4), it

can be seen that the enhancement in pre peak rapid pullout stiffness became more

pronounced with the increase in nail diameter, suggesting the remarkable influence of

nail diameter on rapid pullout behaviour. However, the influences of other parameters

such as the roughness of nail surface, effective nail length and sand density on rapid

pullout behaviour are not clearly shown in the plot of load displacement curve in these

figures but the influences of these parameters will be assessed later in this chapter.

4.3.2 Peak Rapid Pullout Strength

From Figure 4.1 to Figure 4.7, it is clear that the peak rapid pullout strength

was higher than the corresponding peak quasi static pullout strength especially for

tests with larger nail diameter. Same as the enhancement in pre peak pullout stiffness,

the improvement in peak rapid pullout strength was not only observed on load

measurement made at nail head but also on the axial body load measurements made

along the nail by strain gauges. This observation again indicates that this

improvement in peak rapid pullout strength should be a basic characteristic of shaft

resistance of rough interface under rapid loading condition. This phenomenon is also

observed on DFs-S25F test series with d/D50 ratio as high as 208, implies that this

phenomenon should not be caused by the particle size effect.

The improvement in peak rapid pullout strength observed in these experiments

appears to be controversial when compared with the experimental results reported by

Dayal and Allen (1975), Heerema (1979) and Lepert et.al. (1988) who showed that

the shaft resistance of pile shaft in contact with clean dry sand was independent of

loading rate. However, detailed examination on their experiments revealed that the

surface of model pile shaft used by them was smooth steel surface. Thus, their

experimental results cannot be compared directly with the results on rough surface of

these experiments. This is because the mobilization characteristic of interfacial

resistance of rough surface and smooth surface has significant difference, as has been

shown by the results of interface tests reported by Yoshimi and Kishida (1981),

Uesugi and Kishida (1986) and Hu and Pu (2004). It will be shown later in Section

4.6 of this chapter that the maximum pullout strength of nails with smooth surface (P

surface and U surface) was independent of loading rate, which is in good agreement

with the results of Dayal and Allen (1975) and Heerema (1979) because the surface

conditions of smooth P surface and U surface were more closer to the surface

condition of smooth steel surface considered by Dayal and Allen (1975), Herrema

(1979) and Lepert et.al. (1988)) in their experiments.

Table 4.1 lists the peak rapid pullout strength Prp

of all test series on rough

nails. As the peak rapid pullout strength of both high energy rapid pullout tests under

the same test series was fairly identical, only the average value of both tests is given

in Table 4.1. The peak quasi static pullout strength Psp

given in Table 3.1 is also

reproduced in Table 4.1 for clearer comparison. The ratio of peak rapid pullout

strength to peak quasi static peak pullout strength αp is also calculated for each series

of tests in Table 4.1. It has to be noted that the pullout velocity at the point of peak

rapid pullout strength of all test series considered in Table 4.1 was fairly identical to

each other, with the range lied in between 0.4 m/s to 0.5 m/s only. Therefore, direct

comparison of peak rapid pullout strength between these test series is valid because

any error caused by the variation in pullout velocity would be very minimal.

From the αp ratio given in Table 4.1, it is observed that the percentage of

improvement in peak rapid pullout strength was unaffected by surface roughness

(within the range of rough surface), effective nail length, sand density and sand type

but was significantly affected by nail diameter. The αp ratio of test series with 25 mm

of nail diameter (DCs-S25C series, DCs-S25F test series, MCs-S25C test series, DCs-

L25F test series and DFs-S25F test series) was within the range of 1.09 - 1.12, while

the αp ratio of test series with 45 mm of nail diameter (DCs-S45C test series and DCs-

S45F test series) was within the range of 1.2 - 1.22. These results indicate that the

percentage of improvement in peak rapid pullout strength is nearly in direct

proportion to nail diameter.

The similar of αp ratio of DCs-S25C test series, DCs-S25F test series, MCs-

S25C test series and DFs-S25F test series shown in Table 4.1 also indirectly and

broadly suggests that the influence of restrained dilatancy effect on rapid pullout

response is fairly similar to that on quasi static pullout response. This context is best

illustrated by the bar chart shown in Figure 4.11 that compares the peak quasi static

pullout strength Psp, the peak rapid pullout strength Pr

p and the ‘analytical’ peak

pullout strength estimated by Eq. 3.4 based on interface friction angle (without

restrained dilatancy effect) side by side for these test series. From Figure 4.11, it is

seen that the variation in ‘analytical’ peak pullout strength between these test series

was marginal. This is because the peak interface friction angle of nail – sand interface

of these test series was quite similar to each other as can be seen from the direct shear

interface test results shown in Table 2.2. The obvious variation in peak quasi static

pullout strength of these test series has been discussed to be mainly contributed by the

difference in degree of restrained dilatancy effect (Section 3.5 in Chapter 3).

Therefore, the obvious variation in peak rapid pullout strength between these test

series that followed closely the trend of variation in peak quasi static pullout strength

broadly suggests that the influence of restrained dilatancy effect on both quasi static

pullout test and rapid pullout test would be quite identical.

The possibility of minor variation in restrained dilatancy effect between quasi

static pullout test and rapid pullout test that appears as a possible cause to the

enhancement in pre peak rapid pullout stiffness and improvement in peak rapid

pullout strength will be discussed in next section.

4.3.3 The Causes of Improvements in Pre Peak Rapid Pullout Response

In the author’s opinion, there are three possible causes that may contribute to

the improvements in pre peak rapid pullout stiffness and peak rapid pullout strength

of rough nails that were observed in these experiments: (a) the improvement in

interfacial friction properties, (b) the improvement in restrained dilatancy effect and (c)

the mobilization of damping resistance. All of these possible causes will be examined

here to identify the most likely cause or causes.

In the discussion below, the improvements in pre peak rapid pullout stiffness

and peak rapid pullout strength of test series with varying nail diameters will be

compared qualitatively without considering the variation in pullout velocity between

these tests. This is reasonable as has been mentioned before that the pullout velocity

experienced by these tests before the peak rapid pullout stage were fairly identical to

each other (Appendix A). Therefore, the influence of variation in pullout velocity on

the validity of this comparison is minor.

(a) Improvement in Interface Friction Properties

The only past experiences that studied the behaviour of rapid or dynamic

interfacial shaft resistance for shaft embedded in clean dry sand are the experiments

by Dayal and Allen (1975), Hereema (1979) and Lepert et.al. (1988), but their results

cannot be compared to the results of rough nails of these experiments due to the

difference in basic mobilization characteristic between rough surface and smooth

surface (Uesugi et.al., 1988). However, since the failure of rough surface is likely to

be formed within the adjacent soil mass and the interface strength of rough surface is

bounded and equal to the shear strength of adjacent soil mass (Jewell, 1980, Uesugi

and Kishida, 1986), the experiences on rapid soil test may be applied to approximate

the behaviour of rough interface under rapid loading condition. As the sand medium

considered in these experiments consists of dry dense sands, only the experiences of

rapid test on dry dense sands are discussed here.

Casagrande and Shannon (1949) appears to be the first to study the rapid shear

strength of dry dense sand. Their results showed that the increase in loading rate

caused approximately 10 % of increase in peak shear strength. However, Whitman

and Healy (1962) with huge numbers of results on rapid Triaxial tests on Ottawa sand

indicated that the influence of loading rate on peak shear strength of dry dense sand

was quite minimal, with less than 1o of variation in peak friction angle. Whitman and

Healy (1962) attributed the increase in peak shear strength observed by Casagrande

and Shannon (1949) to the inaccuracy of load measurement device under rapid

loading condition. Schimming et.al. (1966) conducted a study on the friction angle of

soil under rapid loading condition with a modified direct shear setup. Their results

also showed that the influence of loading rate on peak and residual friction angle of

dry dense sand was virtually negligible. The loading rate independence of residual

friction angle of dry sand was also observed by Hungr and Morgenstern (1984) on

high velocity ring shear tests.

From these limited past experiences, the influence of loading rate on rapid

shear strength of dry dense sand seems quite minimal. Since the interface strength of

rough surface is bounded and equal to the shear strength of its adjacent soil mass, the

minimal influence of loading rate on shear strength of dry dense sand lead to the

conclusion that the influence of loading rate on interface strength of rough nails is

also quite minimal.

Besides, from the analytical equilibrium equation for peak pullout strength

(P=πdLeσ’n(p)tanδ’), the ratio of peak rapid pullout strength to peak quasi static

pullout strength (the αp ratio in Table 4.1) can be written as below:

s

r

spne

rpne

pdL

dL

'tan

'tan

'tan'

'tan'

)(

)(

δ

δ

δσπ

δσπα == (4.2)

with σ’n(p) = mean effective normal stress on nail shaft at peak pullout stage, r'δ =

rapid interface friction angle, and s'δ = static interface friction angle

From Eq. 4.2, it is observed that the αp ratio should be constant and

irregardless of nail diameter if the improvement in peak rapid pullout strength is

caused by the improvement in interface friction angle only. However, from the

comparison of αp ratio of DCs-S25C test series to DCs-S45C test series and DCs-

S25F test series to DCs-S45F test series (Table 4.1), it is clearly seen that the αp ratio

was significantly higher for test series with 45 mm of nail diameter (DCs-S45C test

series and DCs-S45F test series) when compared to those of test series with 25 mm of

nail diameter (DCs-S25C test series and DCs-S25F test series). In addition, the degree

of improvement in pre peak rapid pullout stiffness was also noticed to be more

pronounced for test series with 45 mm of nail diameter (compare Figure 4.2 to Figure

4.1 and Figure 4.5 to Figure 4.4).

Therefore, the improvement in interface friction properties under rapid loading

condition appears not to be the main cause for the improvement in pre peak pullout

stiffness and peak pullout strength observed in these experiments for tests on rough

nails.

(b) Improvement in Restrained Dilatancy Effect

Restrained dilatancy effect is a mechanism that causes the enhancement of

normal stress on dilative interface which eventually results in enhancement of

interfacial strength (Schlosser, 1982). Detailed explanations of this effect are given in

Section 3.5 of Chapter 3.

From the description of restrained dilatancy effect by Schlosser (1982), it is

clear that the main factor controlling the degree of restrained dilatancy effect is the

dilative behaviour of interface. Therefore, the discussion on the similarity of

restrained dilatancy effect under rapid and quasi static loading condition should be

based on the loading rate dependency of the dilative behaviour of interface. Since the

dilative behaviour of rough interface is mainly caused by the dilative behaviour of

high strain weaken zone adjacent to interface, the loading rate dependency of dilative

behaviour of rough interface can be deduced from the loading dependency of dilative

behaviour of soil.

However, results on loading rate dependency of dilative or volume change

behaviour of sand are very rare probably due to the difficulty and inaccuracy of

dilatancy or volume change measurement under rapid loading condition. The only

data available to the author is the results by Whitman and Healy (1962). In their paper,

the excess pore pressure generated in undrained Triaxial test of dense sand under

static and rapid test condition was found to be nearly identical, indicated that the

dilatancy behaviour of dense sand would be independent on loading rate.

The independence of dilatancy behaviour of dense sand on loading rate may

also be indirectly deduced from the results of rapid shear strength which appears

easier and more accurate to be measured. Theoretically, the peak shear strength of

dense sand is contributed by the basic inter-particle friction properties and the

dilatancy behaviour of the sand bulk. Therefore, the independence of shear strength of

dense sand on loading rate shown by Whitman and Healy (1962) and Schimming et.al.

(1966) also implicitly indicated the independence of dilatancy behaviour of sand bulk

on loading rate, provided the inter-particle friction angle is constant with loading rate,

which is shown to be true by Horn and Deere (1962).

Hence, from these limited available information, the dilatancy behaviour of

rough interface also seems to be unaffected by the loading rate. Consequently, it

appears that the degree of restrained dilatancy effect mobilized in quasi static and

rapid pullout test would be fairly similar, and suggests that this is not a likely cause

for the stiffer pre peak pullout stiffness and higher peak pullout strength of rapid

pullout response.

The irrelevance of restrained dilatancy effect to the improvements in pre peak

rapid pullout stiffness and peak rapid pullout strength may also be seen from the

proportionality of these improvements with nail diameter. The influence of restrained

dilatancy effect has been widely found to be inversely proportional to nail diameter by

experimental study (Tei, 1993), and analytical study (Luo, 2001) as well as by the

results of quasi static pullout test conducted in these experiments (Chapter 3). Thus, if

the improvements in pre peak rapid pullout stiffness and peak rapid pullout strength is

caused by the enhancement in degree of restrained dilatancy effect, the degree of

these improvements would be less pronounced for tests with larger nail diameter.

However, the results of these experiments show that the improvement in peak rapid

pullout strength was obviously more pronounced for tests with larger nail diameter.

From Table 4.1, the αp ratio of test series with 45 mm nail diameter (DCs-S45C test

series and DCs-S45F test series) was almost twice the αp ratio of test series with 25

mm nail diameter (DCs-S25C test series and DCs-S25F test series). Besides, the

improvement in pre peak rapid pullout stiffness was also seen to be more pronounced

for tests with larger nail diameter (compares Figure 4.2 to Figure 4.1 and Figure 4.5 to

Figure 4.4).

(c) Mobilization of Damping Effect

There are mainly two types of damping effects: viscous damping effect and

radiation damping effect. Viscosity damping effect is caused by the viscosity

properties of surrounding soil, which appears irrelevant to these experiments since the

soil mediums considered in these experiments were dry dense sands with minimal

viscosity properties. Radiation damping is caused by the radiation of stress wave from

the loading source. The radiation damping effect is always present and is identified as

the main damping source for a pile dynamic event (Smith and Chow, 1982).

Therefore, it is reasonable to deduce that radiation damping effect should also be

present in the rapid pullout response of these experiments.

From the analytical solution of radiation damping coefficient suggested by

Novak et.al. (1978), damping coefficient of radiation damping resistance is

proportional to shaft diameter. This characteristic of radiation damping appears to

agree well with the characteristic of improvements in pre peak rapid pullout stiffness

and peak rapid pullout strength which were fairly proportional to nail diameter. The

proportionality of improvement in peak rapid pullout strength to nail diameter can be

seen from the αp ratio given in Table 4.1, which shows that the αp ratio of test series

with 45 mm of nail diameter (DCs-S45C test series and DCs-S45F test series) was

almost twice the αp ratio of test series with 25 mm of nail diameter (DCs-S25C test

series and DCs-S25F test series). The direct proportionality of improvement in pre

peak pullout stiffness will be shown later in Section 4.4 of this chapter.

From the discussion above, it seems reasonable to deduce that the

improvements in pre peak rapid pullout stiffness and peak rapid pullout strength are

mainly caused by the mobilization of radiation damping effect. The influences of

variation in interface friction properties and restrained dilatancy effect are found to be

minimal. The influence of radiation damping effect has been widely suggested and

accepted by the industry of dynamic pile load test as the main damping source that

enhances the dynamic pile resistance (Smith and Chow, 1982), especially for cases

with non-viscous soil medium.

Since the failure of rough interface is mainly caused by the shear failure of soil

mass adjacent to the interface, the deduction that the improvement in peak rapid

pullout strength of rough nail is caused by the mobilization of radiation damping

resistance seems reasonable because the shear failure of soil is mainly controlled by

the amount of shear strain experienced. Hence, at the moment the limiting shear strain

of the adjacent soil mass is attained, the total resistance that experienced by the

interface should be the sum of the displacement dependent stiffness resistance (strain

effect) and the velocity dependent damping resistance (strain rate effect).

The influence of radiation damping effect on shaft resistance was also

considered by Wong (1988) in his formulation of dynamic shaft model for pile. In the

modeling of dynamic shaft resistance by spring and dashpot analogy, Wong (1988)

suggested that the failure of shaft resistance should be limited by the stiffness

resistance (spring) alone instead of by the sum of stiffness and damping resistance.

With this arrangement, the possibility for total dynamic shaft resistance to exceed the

limiting static shaft resistance is allowed by this model even the limiting shaft

resistance is equal for both dynamic and static cases.

4.3.4 Rapid Load Distribution Curve

The rapid load distribution curves of rough nails (after subtraction of inertia

effect by Eq. 4.1) are plotted in Figure 4.12 at pullout stages corresponding to 50 %

and 100 % of peak rapid pullout strength. To assess the difference in between the

rapid load distribution curves and quasi static load distribution curves, the quasi static

load distribution curves mobilized at similar level of pullout displacement are also

plotted in Figure 4.12.

From Figure 4.12, the rapid load distribution curve is found to be fairly a

straight line, similar to the characteristic of quasi static load distribution curve. This

observation shows the insignificant influence of stress wave propagation on rapid

pullout tests of these experiments. Chow (1999) illustrated that the shape of rapid load

distribution curve is only similar to the shape of static load distribution curve if the

influence of stress wave propagation is minimal. This observation was expected since

the relative wave length of rapid pullout tests conducted in these experiments is at

least 41 (Section 2.4.2), well beyond 10, the lower boundary value suggested by

Holeyman (1992) for the elimination of stress wave propagation phenomenon.

Besides, the linearity of rapid load distribution curve also suggests the rigid body

behaviour of nails in rapid pullout tests, even for tests with 1.65 m of effective nail

length.

Although the shape of both quasi static and rapid load distribution curves was

similar to each other, the rapid load distribution curve was obviously steeper than the

quasi static load distribution curve. This is reasonable due to the additional

contribution by radiation damping resistance to the shaft resistance of rapid pullout

tests. The difference in terms of load between both rapid and quasi static load

distribution curves is seen to linearly decrease with distance from nail head,

suggesting that the unit damping resistance mobilized in rapid pullout test was

uniformly distributed along the nail. The uniformity of unit damping resistance

deduced here also implicitly indicates the minimal influence of rigid chamber wall

presence at 100 mm in front of the nail head (the front end of nail in contact with

surrounding soil) on the mobilization of damping resistance. It is because the unit

damping resistance of front part of nail would be different from the unit damping

resistance of rear part of nail if significant influence of rigid front wall effect is

present.

4.4 The ‘Actual’ Damping Coefficient

The improvements in pre peak rapid pullout stiffness and peak rapid pullout

strength of rough nails has been discussed to be most likely induced by the

mobilization of radiation damping resistance. In order to quantify the radiation

damping resistance that was mobilized in each rapid pullout test on rough nails of

these experiments, the ‘actual’ damping coefficient defined by Eq. 4.3 was calculated.

The ‘actual’ damping coefficient is defined as the product of difference between rapid

pullout load and quasi static pullout load mobilized at similar pullout displacement, in

terms of per unit length, divided by the pullout velocity of nail head.

e

i

i

s

i

r

Lv

PPc

−=* (4.3)

with c* = ‘actual’ damping coefficient (per unit length); Pri = rapid load at point i; Ps

i

= quasi static load at point i; and vi = pullout velocity at point i; Le = effective nail

length.

In the calculation of ‘actual’ damping coefficient by Eq. 4.3, the displacement

dependent stiffness coefficient of rapid pullout response is assumed to be identical to

that of corresponding quasi static pullout response. This assumption may be supported

by the results of low energy rapid pullout tests that will be presented and discussed in

Chapter 5 later. The unloading point of low energy rapid pullout response with zero

velocity (and hence mobilized only the displacement dependent stiffness resistance at

that point) is observed to approximately fall on the corresponding quasi static pullout

response (Figure 5.1 – Figure 5.5), infers the virtually identical of stiffness coefficient

of both rapid and quasi static pullout tests.

Figure 4.13 – Figure 4.19 plot the curves of ‘actual’ damping coefficient

versus pullout displacement for all high energy rapid pullout tests on rough nail of

these experiments. It has been widely accepted that the existence of high strain

weaken zone adjacent to nail shaft will reduce the radiation damping effect (Novak

and Sheta, 1980). The evolution of high strain weaken zone is progressive in nature

that evolves with the increase in shear strain level of weaken zone (and hence the

pullout displacement in the context of pullout test). Hence, it is anticipated that

‘actual’ damping coefficient calculated by Eq. 4.3 which is mainly governed by

radiation damping effect will exhibit certain relationship with pullout displacement.

‘Actual’ damping coefficient was also calculated from axial body load to

examine the distribution of damping effect along the nail. In the calculation of ‘actual’

damping coefficient from axial body load, Le in Eq. 4.3 was taken as the length of nail

after the axial body load measurement point.

The axis of pullout displacement (x - axis) of Figure 4.13 – Figure 4.19 is only

limited to peak rapid pullout stage because after that, the pullout response has turned

into drastic softening behaviour that mostly involves the mechanism of shear band

evolution, a mechanism that is totally different from the radiation damping effect.

From Figure 4.13 – Figure 4.19, it is seen that although the curves of ‘actual’

damping coefficient calculated from the load measurement made at nail head and

several strain measurement points along the nail appears to be quite scattered, they

seem to fall in a band with finite thickness. This observation implies the uniformity of

unit damping resistance distributed along the nail. It has to be noted that there is no

clear relationship between the position of an ‘actual’ damping coefficient curve with

its load measurement location. As an example, from Figure 4.13, the highest ‘actual’

damping coefficient curve of DCs-S25C-2-RH test was the curve deduced from

pullout load measured at nail head (DCs-S25C-2-RH, 0 m); while the highest ‘actual’

damping coefficient curve for of DCs-S25C-4-RH test was the curve deduced from

axial body load measured at 0.45 m from nail head (DCs-S25C-4-RH, 0.45 m). The

rather scattered appearance of ‘actual’ damping coefficient curve may be attributed to

the nature of Eq. 4.3 that would exaggerate the small error in rapid and quasi static

load measurement and the small error in velocity differentiated from displacement

trace. It is also noted that the distribution of ‘actual’ damping coefficient at small

pullout displacement (< 0.4 mm) seems severely scattered and unreliable, most

probably caused by the relatively low pullout load of this region that reduce the

sensitivity of load cell or strain gauges in capturing the real variation between rapid

pullout load and quasi static pullout load.

From Figure 4.13 – Figure 4.19, the curves of ‘actual’ damping coefficient is

decreasing with the increase in pullout displacement. This result agrees with the

observations made by Ealy and Justason (2000) on rapid load test results of pile

groups. As has been mentioned before, this characteristic of ‘actual’ damping

coefficient is mainly attributed to the progressive evolution of high strain weaken

zone around nail shaft due to strong non linearity of soil behaviour. The existence of

high strain weaken zone which is less stiff than the relatively undisturbed outer field

soil medium may cause relative velocity between nail shaft and outer field soil

medium. From the suggestions by Novak and Sheta (1980), El-Naggar and Novak

(1992) and Khaled (2000), the outer field soil medium is the main soil medium that

contributes to the total radiation damping resistance because the mass of thin weaken

zone is comparatively minimal when compared to the mass of outer field soil medium.

However, in common setup of rapid pullout test such as in these experiments, the only

measurable velocity is the velocity of nail shaft. Hence, the ‘actual’ damping

coefficient calculated by using the velocity of nail shaft (Eq. 4.3) is not the basic

damping properties of soil but the ‘apparent’ damping properties taking into account

the variation between the velocity of nail shaft and the velocity experienced by outer

field soil medium. The reduction in shear modulus of high strain weaken zone will

increase the extent of relative velocity between nail shaft and outer field soil medium

and finally lead to the decrease in ‘actual’ damping coefficient.

It is well understood that the development of high strain weaken zone is in a

progressive manner that can be fitted by a hyperbolic curve. Therefore, the relative

velocity between nail shaft and outer field soil medium grows with the increase in

pullout displacement and consequently causes the progressive decrease in ‘actual’

damping coefficient.

From the results of these experiments, ‘actual’ damping coefficient is also

found to correlate reasonably well with the tangent stiffness of corresponding quasi

static load displacement curve by the following equation:

t

skdc β=* (4.4)

with β = correlation factor, d = shaft diameter, kst = tangent stiffness of corresponding

quasi static load displacement curve (per unit length).

The curves of ‘actual’ damping coefficient calculated by the above equation

are also plotted in Figure 4.13 – Figure 4.19, together with their corresponding

experimental results. It is observed that the trend of these calculated curves agrees

reasonably well with the experimental results. The close correlation between

equivalent quasi static tangent stiffness and ‘actual’ damping coefficient implicitly

verifies the anticipation that non constant characteristic of ‘actual’ damping

coefficient is mainly induced by the development of high strain weaken zone, which

is also the main contributor to the non linear hyperbolic behaviour of quasi static load

displacement response. The correlation factor β is also found to fall within a narrow

range of 35 to 42 for test series with dense coarse sand medium (DCs-S25C test series

– Figure 4.13, DCs-S45C test series – Figure 4.14, DCs-S25F test series – Figure 4.16,

DCs-S45F test series – Figure 4.17 and DCs-L25F test series – Figure 4.18), 25 for

test series with medium dense coarse sand medium (MCs-S25C test series – Figure

4.15) and 45 for test series with dense fine sand medium (DFs-S25F test series –

Figure 4.19). However, more results are needed before general conclusion and

recommendation on this correlation factor β can be drawn.

It has to be stressed that the conclusion of ‘actual’ damping coefficient is

decreasing with pullout displacement does not violate the basic velocity dependent

principle of damping resistance. It is because in the calculation of ‘actual’ damping

coefficient by Eq. 4.3, velocity has been considered as a denominator in this equation.

The resultant ‘actual’ damping coefficient should be a constant if damping resistance

mobilized in a rapid pullout test of soil nail is purely dependent on velocity alone.

In Figure 4.20, the band of ‘actual’ damping coefficient of DCs-S25C test

series is compared to that of DCs-S25F test series, and both of these bands are seen to

match with each other quite well. Although the band of ‘actual’ damping coefficient

of DCs-S25F test series seemed slightly lower than that of DCs-S25C test series, the

difference was uncertain and quite negligible if compared to the thickness of the error

band. This observation seems reasonable since both nails with C surface (sand glued

by coarse sand) and F surface (sand glued by fine sand) are categorized as rough nail

with their pullout response be mainly determined by the properties of surrounding soil

medium. This can be seen from the equal of initial pullout stiffness and secant pullout

stiffness at peak of quasi static pullout response of both test series (Figure 3.10).

While, Figure 4.21 compares the band of ‘actual’ damping coefficient of MCs-

S25C test series to that of DCs-S25C test series. This figure reveals that the band of

‘actual’ damping coefficient of MCs-S25C test series was more obviously lower than

the band of DCs-S25C test series. This result seems logical since the density of sand

medium in MCs-S25C test series (Id = 82 %) was lower than the density of sand

medium in DCs-S25C test series (Id = 90 %). The lower sand density of MCs-S25C

test series may reduce the stiffness of weaken zone. This can be indirectly seen from

the lower initial pullout stiffness and secant pullout stiffness at peak of MCs-S25C

test series when compared to those of DCs-S25C test series (Figure 3.11). The lower

stiffness of weaken zone may increase the relative velocity between nail shaft and far

field soil medium and consequently decrease the ‘actual’ damping coefficient

calculated by Eq. 4.3.

Figure 4.22 compares the bands of ‘actual’ damping coefficient of DCs-S25F

test series and DCs-L25F test series. It is seen that the ‘actual’ damping coefficient of

DCs-L25F test series was approximately matched with the band of DCs-S25F test

series. This observation again suggests the uniformity of unit damping resistance

distributed along the nail.

Figure 4.23 to Figure 4.24 plot the comparison of ‘actual’ damping coefficient

of DCs-S25C test series to DCs-S45C test series and DCs-S25F test series to DCs-

S45F test series. In these figures, the ‘actual’ damping coefficients of test series with

45 mm nail diameter (DCs-S45C test series and DCs-S45F test series) are normalized

to 25 mm nail diameter. It is clearly seen that after the normalization, the ‘actual’

damping coefficients of test series with different nail diameter appear to fall in the

same band, suggesting the direct proportional relationship between nail diameter and

‘actual’ damping coefficient. This result agrees with the analytical solution by Novak

et al. (1978) which suggested the direct proportion of radiation damping coefficient to

shaft diameter. This observation also to some extent justifies the deduction that the

stiffer pre peak rapid pullout stiffness and higher peak rapid pullout strength are

mainly caused by radiation damping effect.

4.5 Post Peak Softening Behaviour of Rough Nail

Similar to the post peak behaviour of quasi static pullout tests, the post peak

behaviour of rapid pullout tests also exhibited softening behaviour with pullout load

decreasing with the increase in post peak pullout displacement. However, the

softening rate (in terms of pullout displacement) of post peak rapid pullout response

was obviously much steeper than the softening rate of post peak quasi static pullout

response. As can be seen from Figure 4.1 to Figure 4.7, the post peak rapid pullout

response generally attained the well defined residual pullout stage after approximately

2 mm of post peak pullout displacement irregardless of nail diameter, effective nail

length, surface roughness (rough surface only) and sand density. In contrary, well

defined residual pullout stages was not clearly attained by the quasi static pullout tests

even the post peak pullout displacement was as high as 15 mm (DCs-S25C-5-S,

Figure 3.1).

It has to be noted that the variation in post peak pullout behaviour between

rapid pullout test and quasi static pullout test appears to be an intrinsic characteristic

of interfacial shaft resistance under different loading rates as this variation was not

only observed on pullout load measured at nail head but also on axial body load

measured along the nail body by strain gauges. Besides, the distribution of residual

rapid pullout strength along the nail was also fairly linear as shown in Figure 4.25,

implies that the distribution of residual rapid pullout strength along the nail body is

fairly uniform.

Besides, this variation in post peak pullout behaviour also should not be

influenced by the particle size effect. It is because this characteristic was also

observed on DFs-S25F test series (Figure 4.7) with d/D50 ratio as high as 208, slightly

exceeded the highest d/D50 ratio that has ever been proposed to eliminate the particle

size effect (Randolph and House, 2001).

From the comparison of load displacement curves and velocity displacement

curves plotted in Figure 4.26 to Figure 4.32 for all series of tests on rough nails,

sudden rise in pullout velocity (the point circled in these figures) was generally

observed in vicinity of the sharp turning point on the rapid load displacement curve

where residual rapid pullout stage was first achieved (though it was rather unclear for

MCs-S25C test series (Figure 4.28) and DCs-S25F test series (Figure 4.29)). This

sudden rise in pullout velocity suggests the abrupt ‘detachment’ of nail from

surrounding sand medium once the residual rapid pullout stage has been achieved.

From the comparison of load displacement curve and velocity displacement

curve (Figure 4.26 to Figure 4.32), the residual rapid pullout strength is also seen to

be unaffected by the substantial change in pullout velocity after the sharp turning

point, implies that the effect of damping resistance is virtually ceased in the residual

rapid pullout stage. Therefore, the residual rapid pullout strength may be merely

contributed by the residual friction angle of nail – sand interface. This observation

again suggest the total de-coupling of the motion of nail from the surrounding soil

medium after the residual rapid pullout stage has been attained.

Table 4.1 listed the residual rapid pullout strength Prres

attained by all series of

tests on rough nails. The ratio of friction coefficient at residual rapid pullout stage was

also calculated and given in Table 4.1. The ratio of friction coefficient at residual

rapid pullout stage was calculated by Eq. 3.1 – Eq. 3.3, by replacing the Psp in Eq. 3.1

to Prres

and equating the interface friction angle δ’ in Eq. 3.2 to the residual interface

friction angle of corresponding interface test (Table 2.2). The use of static residual

interface friction angle to represent the rapid residual interface friction angle is

reasonable since Schimming et.al. (1966) and Hungr and Morgenstern (1984) have

shown that the residual friction angle of dry dense sand was independent of loading

rate.

In Table 4.1, the ratio of friction coefficient at peak of quasi static pullout tests

given in Table 3.1 is also reproduced for comparison. From the comparison, it is

interesting to reveal that the ratio of friction coefficient at residual rapid pullout stage

was fairly identical to the ratio of friction coefficient at peak of corresponding quasi

static pullout tests with variation less than 10 %. This observation implies that the

evolution of rapid pullout stage from peak to residual is mainly contributed by the

evolution of interface friction angle, and the increase in mean effective normal stress

caused by restrained dilatancy effect is minimal between the peak and residual rapid

pullout stages. This statement was made under the assumption that the ratio of friction

coefficient at peak of rapid pullout test can be approximated by the ratio of friction

coefficient at peak of corresponding quasi static pullout test. This assumption seems

valid since the improvements in pre peak rapid pullout response has been discussed to

be most probably contributed by the radiation damping effect, and the quasi static

pullout load mobilized at the point of peak rapid pullout strength (at similar pullout

displacement) was quite close to the corresponding peak quasi static pullout strength

with less than 5 % in variation (Figure 4.1 – Figure 4.7).

The maximum reloading pullout strength Psreload

attained by the quasi static

reload tests presented in Section 3.6 is also re-produced in Table 4.1. It is worth to

note that the residual rapid pullout strength was fairly identical to the maximum

reloading pullout strength, with variation less than 11 %. Since it was anticipated in

Chapter 3 that the maximum reloading pullout strength may be eventually attained by

the primary quasi static pullout test if longer pullout displacement was allowed in the

test, the residual rapid pullout strength may be taken as an approximation to the

residual quasi static pullout strength that will be mobilized at large pullout

displacement.

In the author’s opinion, the difference in post peak softening behaviour of

rapid and quasi static pullout response is postulated to be caused by the difference in

nature of shear band evolution under rapid and quasi static loading conditions.

The evolution of shear band in rough interface tests was observed by Yoshimi

and Kishida (1981), Uesugi et.al. (1988) and Hu and Pu (2004). Their observations

showed that the form of obvious shear band was only initiated after the point of peak

shear strength. After that, the deformation of adjacent sand medium was observed to

concentrate within a thin shear band with finite thickness. The form of shear band

around rough reinforcement in quasi static pullout tests was also observed by Jewell

(1980), Tei (1993) and Otani et.al. (2001). Jewell (1980) and Otani et.al. (2001)

demonstrated that the form of shear band was dominantly initiated after the stage of

peak pullout strength. The thickness of shear band formed around the rough planar

reinforcement with sand glued surface was measured as approximately 20 times of

D50, the mean particle size of sand by Jewell (1980) and Tei (1993).

Oda and Kazama (1998) proposed a model as shown in Figure 4.33 to describe

the evolution of shear band under static load. According to this model, the post peak

softening behaviour is mainly contributed by the buckling of sand particle columns.

The progressive buckling of particle columns may gradually reduce the axial capacity

of these columns and eventually the shear capacity of shear band. At last, once the

limiting rotational resistance across particle contacts required to hold the highly bent

column structure in stable has been exceeded, the particle columns may collapse to

enter the residual shear stage. The rotational resistance across particle contacts was

identified by Oda and Kazama (1998) as the main key controlling the evolution of

shear band and hence the post peak softening behaviour. Although this model was

created to describe the evolution of shear band in Triaxial sand sample, it should be

applicable to describe the evolution of shear band along rough interface since the

failure plane of rough interface is likely to be formed within the adjacent sand mass.

By referring to this model, the evolution of shear band along the nail – sand

rough interface under quasi static load is visualized as Figure 4.34a. Initially the

particle column is assumed to tilt at 45o from the nail – sand interface, in direction

parallel to the direction of major principle stress of soil adjacent to reinforcement

suggested by Luo (2001). The thickness of shear band is chosen as 20 sand particles

according to the observation by Jewell (1980) and Tei (1993). With the increase in

post peak pullout displacement, the particle column is visualized to gradually buckle

and bend, and at last collapse once the limiting rotational resistance across particle

contacts is exceeded (Figure 4.34a).

However, it is postulated that the fully buckling of particle columns in quasi

static test (Figure 4.34a) may not happen in rapid test due to the additional inertia

resistance of sand particles. The presence of inertia resistance may increase the

resistance of particle columns to buckling. Thus, higher rotational moment propagated

from the nail – soil interface is needed in order to buckle the column structure.

However, the limiting rotational moment that can be propagated across adjacent

particles is controlled by the limiting rotational resistance across the particle contacts,

which is independent of loading rate (Horn and Deere, 1962). Therefore, the column

structures has a tendency to collapse due to the lack of limiting rotational resistance

across particle contacts before the fully buckling structure similar to quasi static test

(Figure 4.34a) is formed. Hence, the height of buckled particle column of rapid test

may be significantly shorter than that of quasi static test. Figure 4.34b visualized the

postulation of shear band evolution in rapid test. From Figure 4.34, it is clear that

shorter height of buckled particle column results in smaller relative displacement

required to cause the collapse of column structure, and hence smaller relative

displacement required to achieve residual stage.

4.6 Rapid Pullout Response of Smooth Nail

The rapid load displacement curves (‘net’ rapid soil response with inertia

effect has been subtracted by Eq. 4.1) of tests series on smooth nails, the DCs-S22U

test series (untreated smooth stainless steel surface) and the DCs-S25P test series

(surface roughened by sand paper), are plotted in Figure 4.8 and Figure 4.9, together

with the corresponding quasi static load displacement curves reproduced from Figure

3.8 and Figure 3.9.

From Figure 4.8 and Figure 4.9, it is seen that the rapid load displacement

response of smooth nails was well matched with the corresponding quasi static load

displacement response. This observation implies that the influence of radiation

damping effect on rapid pullout response of smooth nails was minimal and negligible.

This phenomenon may be explained by the characteristic of smooth surface pointed

out by Yoshimi and Kishida (1980), Uesugi et.al. (1988) and Hu and Pu (2004). From

their observation, the shear deformation of soil mass in contact with smooth surface is

very minimal and the sliding displacement along the interface appears to be the

dominant contributor to the total interface displacement. The failure of smooth surface

is also most likely to occur along the interface as opposed to within the adjacent soil

mass for rough surface. In other words, there is large discontinuity in between the

motion of smooth surface and the adjacent soil medium. Since the radiation damping

effect is caused by the inertia of surrounding soil medium to dynamic shear

deformation (propagation of shear stress) (Randolph, 1991), the negligible radiation

damping effect of smooth nails is reasonable as the shear deformation of surrounding

medium is very minimal if compared to the sliding displacement along the interface.

In other words, the increase in dynamic shear stiffness of surrounding sand medium

caused by radiation damping effect is very minimal and negligible when compared to

the total interface displacement that mainly contributed by sliding displacement along

interface that is unaffected by radiation damping effect.

The negligible damping resistance of DCs-S25P test series (Figure 4.9) is

quite surprising as the nail – sand interface behaviour of P surface was slightly

dilative with maximum dilatancy angle of 1.8o (Table 2.2). A possible explanation to

this phenomenon is the dilative behaviour of P surface may not be caused by the

dilative behaviour of adjacent dense sand but is mainly contributed by the movement

of sand particle to overrides the asperities of P surface. The observation by Hu and Pu

(2004) showed that the normal displacement and shear displacement of sand particles

in interface test on surface with normalized roughness Rn = 0.05 (close to 0.03 of P

surface) was virtually ceased at distance about 1 - 2 particle size from the interface,

and majority of the total interface displacement was also contributed by sliding

displacement along interface. This observation implies that the dilative response of

this interface should be mainly induced along the interface, not within the adjacent

sand mass.

From the comparison of rapid and quasi load displacement curves of DCs-

S25P test series in Figure 4.9, the hardening rate, in terms of pullout displacement, is

seen to be identical for both rapid and quasi static pullout tests. Since the hardening

behaviour of DCs-S25P test series is probably caused by restrained dilatancy effect as

has been discussed in Chapter 3 by referring to the results of Evgin and Fakharian

(1996), the identical hardening rate of rapid and quasi static pullout tests infers that

restrained dilatancy effect mobilized in both tests would be nearly the same.

4.7 Quasi Static Reload Test

Quasi static reload tests were directly conducted after each high energy rapid

pullout test. The load displacement curves of these reload tests are plotted in Figure

4.35. To examine the influence of loading mode of its preceding pullout test on the

quasi static reloading behaviour, load displacement curves of reload tests directly

conducted after quasi static pullout test are also plotted in Figure 4.35 for comparison.

In these figures, only the code of reload tests is referred. The details of this coding

system were described in Section 2.8.

It has to be mentioned that quasi static reload tests were not conducted after

the high energy rapid pullout tests of DCs-S25F test series because the final pullout

displacement of these high energy rapid pullout tests had exceeded the limiting

displacement allowed by the setup of this experimental (to protect the linear motion

potentiometer) and had been stopped by a damper positioned at distance

approximately 20 mm from the front end of connection rod. Thus, no allowance of

pullout displacement was available for the conduct of succeeding quasi static reload

test. Besides, as the nail had been stopped by damper at the end of high energy rapid

pullout test, the nail had been severely disturbed and the results of any reload tests

conducted afterward are meaningless.

From Figure 4.35, the load displacement response, especially the maximum

reloading strength, of quasi static reload test conducted after high energy rapid pullout

tests was observed to be virtually identical to the corresponding reload tests conducted

after quasi static pullout test, though the post peak pullout response of high energy

rapid pullout test and quasi static pullout test was significantly different. The slightly

softer reloading response of some reload tests conducted after the high energy rapid

pullout tests would be mainly caused by the inevitably slight disturbance of nail in the

preparation of quasi static pullout test setup (the mount of static load cell and

connection rod to the pulling arm of pullout machine). It is because this softer

reloading response appears to be a random response that was not seen in every reload

tests conducted after the high energy rapid pullout test. Anyway, this minor

discrepancy is negligible as it only cause small shift, at most 0.2 mm of pullout

displacement, on the reloading load displacement curve.


For tests on rough nail, the load displacement response of rapid pullout test is

generally similar to the quasi static load displacement response in trend. However, the

pre peak pullout stiffness and peak pullout strength of rapid pullout test were higher

than those of corresponding quasi static pullout test. These differences in pre peak

pullout response between rapid pullout test and quasi static pullout test is found to be

proportional to nail diameter and is deduced to be most probably caused by radiation

damping effect. ‘Actual’ damping coefficient, defined as the difference in load

between corresponding quasi static and rapid load displacement curves divided by

velocity of nail shaft (Eq. 4.3), of soil nail rapid pullout test is observed to decrease

with the increase in pullout displacement. Restrained dilatancy effect mobilized in

rapid pullout test is also found to be almost similar to that mobilized in quasi static

pullout test. The softening rate (in terms of pullout displacement) of post peak

softening behaviour of rapid pullout test was also higher than that of corresponding

quasi static pullout test. This variation is postulated to be caused by the basic

difference in shear band evolution under both rapid and quasi static loading conditions.

In contrary, the rapid pullout response of smooth nail was virtually identical to

the corresponding quasi static pullout response with minimal damping effect.

Therefore, the results of high energy rapid pullout test of smooth nail can be

directly taken as a good estimation to the equivalent quasi static pullout response

without any treatment. While, the results of high energy rapid pullout test of rough

nail may need certain treatment to subtract the contribution of damping resistance

from the rapid pullout test results and to achieve a reasonable estimate of equivalent

quasi static pullout response. A possible interpretation method for these purposes is

back analysis by simple spring and dashpot model.

Tab

le 4

.1:

Su

mm

ary o

f h

igh

en

erg

y r

apid

pull

out

test

res

ult

s fo

r te

st s

erie

s on r

ough n

ail.

Pea

k p

ull

ou

t st

ren

gth

R

ati

o o

f fr

icti

on

coeff

icie

nt,

µ µµµ

Tes

t S

erie

s R

ap

id P

rp

(N)

Qu

asi

sta

tic

Psp

(N)

Resi

du

al

rapid

pu

llou

t st

ren

gth

Prre

s (N

)

Maxim

um

qu

asi

stati

c r

elo

adin

g

stre

ngth

Psre

load (

N)

α αααp

#

At

peak q

uasi

stati

c p

ull

ou

t

stage

At

resi

du

al

rapid

pu

llou

t st

age

DC

s-S

25C

1

02

0

93

0

630

680

1.0

9

3.7

6

3.5

1

DC

s-S

45C

1

30

0

10

80

800

880

1.2

0

2.6

0

2.6

1

MC

s-S

25C

7

80

7

00

500

500

1.1

1

3.0

0

2.7

2

DC

s-S

25F

7

50

6

70

500

510

1.1

2

2.7

8

2.7

7

DC

s-L

25

F

16

50

1

50

0

1150

1300

1.0

9

2.8

3

2.9

0

DC

s-S

45F

1

20

0

98

0

800

800

1.2

2

2.4

2

2.6

4

DF

s-S

25F

1

05

0

95

0

600

600

1.1

0

3.6

3

3.3

4

# α

p =

Prp

/ P

sp

02

46

810

Pu

llo

ut d

isp

lace

me

nt (m

m)

0

40

0

80

0

12

00

Load (N)

DC

s-S

25

C-2

-RH

, 0m

DC

s-S

25

C-2

-RH

, 0.2

5m

DC

s-S

25

C-2

-RH

, 0.4

5m

DC

s-S

25

C-1

-S, 0

m

DC

s-S

25

C-1

-S, 0

.25m

DC

s-S

25

C-1

-S, 0

.45m

DC

s-S

25

C-4

-R,

0m

DC

s-S

25

C-4

-RH

, 0.2

5m

DC

s-S

25

C-4

-RH

, 0.4

5m

H

Fig

ure

4.1

: L

oad

dis

pla

cem

ent

curv

es o

f hig

h e

ner

gy r

apid

pull

out

test

s of

DC

s-S

25C

tes

t se

ries

mea

sure

d a

t 0 m

, 0.2

5 m

an

d 0

.45 m

from

nai

l hea

d.

02

46

810

12

14

Pu

llo

ut d

isp

lace

me

nt (m

m)

0

40

0

80

0

120

0

Load (N)

DC

s-S

45C

-2-R

H

DC

s-S

45C

-3-R

H

DC

s-S

45C

-1-S

Fig

ure

4.2

: L

oad

dis

pla

cem

ent

curv

es o

f hig

h e

ner

gy r

apid

pull

out

test

s of

DC

s-S

45C

tes

t se

ries

.

04

81

216

Pu

llo

ut d

isp

lace

me

nt (m

m)

0

200

400

600

800

Load (N)

MC

s-S

25

C-2

-RH

, 0m

MC

s-S

25

C-2

-RH

, 0.2

5m

MC

s-S

25

C-2

-RH

, 0.4

5m

MC

s-S

25

C-1

-S,

0m

MC

s-S

25

C-1

-S,

0.2

5m

MC

s-S

25

C-1

-S,

0.4

5m

MC

s-S

25

C-3

-R, 0

m

MC

s-S

25

C-3

-RH

, 0

.25

m

MC

s-S

25

C-3

-RH

, 0

.45

m

H

Fig

ure

4.3

: L

oad

dis

pla

cem

ent

curv

es o

f hig

h e

ner

gy r

apid

pull

out

test

s of

MC

s-S

25C

tes

t se

ries

mea

sure

d a

t 0 m

, 0.2

5 m

an

d 0

.45 m

from

nai

l hea

d.

02

46

810

12

14

16

18

Pu

llou

t d

isp

lace

me

nt (

mm

)

0

200

400

600

800

Load (N)

DC

s-S

25

F-2

-RH

, 0m

DC

s-S

25

F-2

-RH

, 0.2

5m

DC

s-S

25

F-2

-RH

, 0.4

5m

DC

s-S

25

F-1

-S, 0

m

DC

s-S

25

F-1

-S, 0

.25m

DC

s-S

25

F-1

-S, 0

.45m

DC

s-S

25

F-4

-R, 0

m

DC

s-S

25

F-4

-RH

, 0

.25m

DC

s-S

25

F-4

-RH

, 0

.45m

H

Fig

ure

4.4

: L

oad

dis

pla

cem

ent

curv

es o

f hig

h e

ner

gy r

apid

pull

out

test

s of

DC

s-S

25F

tes

t se

ries

mea

sure

d a

t 0 m

, 0.2

5 m

an

d 0

.45 m

from

nai

l hea

d.

02

46

8

Pu

llou

t d

isp

lacem

en

t (m

)

0

40

0

80

0

12

00

Load (N)

DC

s-S

45

F-2

-RH

, 0

m

DC

s-S

45

F-2

-RH

, 0

.25

m

DC

s-S

45

F-2

-RH

, 0

.45

m

DC

s-S

45

F-1

-S,

0m

DC

s-S

45

F-1

-S,

0.2

5m

DC

s-S

45

F-1

-S,

0.4

5m

DC

s-S

45

F-4

-R,

0m

DC

s-S

45

F-4

-RH

, 0

.25

m

DC

s-S

45

F-4

-RH

, 0

.45

m

H

Fig

ure

4.5

: L

oad

dis

pla

cem

ent

curv

es o

f hig

h e

ner

gy r

apid

pull

out

test

s of

DC

s-S

45F

tes

t se

ries

mea

sure

d a

t 0 m

, 0.2

5 m

an

d 0

.45 m

from

nai

l hea

d.

02

46

8P

ullo

ut d

isp

lace

me

nt (

mm

)

0

40

0

80

0

12

00

16

00

Load (N)

DC

s-L

25

F-2

-RH

, 0m

DC

s-L

25

F-2

-RH

, 0.4

m

DC

s-L

25F

-1-S

, 0

m

DC

s-L

25F

-1-S

, 0

.4m

DC

s-L

25

F-4

-R, 0

m

DC

s-L

25

F-4

-RH

, 0.4

m

H

Fig

ure

4.6

: L

oad

dis

pla

cem

ent

curv

es o

f hig

h e

ner

gy r

apid

pull

out

test

s of

DC

s-L

25

F t

est

seri

es m

easu

red a

t (a

) 0 m

and 0

.4 m

fro

m

nai

l hea

d, an

d (

b)

0.8

m a

nd 1

.2 m

fro

m n

ail

hea

d

(a)

02

46

8P

ullo

ut d

isp

lace

me

nt (m

m)

0

20

0

40

0

60

0

80

0

Load (N)

DC

s-L

25

F-2

-RH

,

DC

s-L

25

F-2

-RH

, 1.2

m

DC

s-L

25

F-1

-S,

DC

s-L

25

F-1

-S,

1.2

m

DC

s-L

25

F-4

-R,

DC

s-L

25

F-4

-RH

, 1.2

m

H0

.8m

0.8

m 0

.8m

Fig

ure

4.6

conti

nue

(b)

04

812

Pu

llo

ut d

isp

lace

me

nt (m

m)

0

40

0

80

0

120

0

Load (N)

DF

s-S

25F

-2-R

H,

0m

DF

s-S

25F

-2-R

H,

0.2

5m

DF

s-S

25F

-2-R

H,

0.4

5m

DF

s-S

25F

-1-S

, 0

m

DF

s-S

25F

-1-S

, 0

.25m

DF

s-S

25F

-1-S

, 0

.45m

DF

s-S

25

F-4

-R, 0

m

DF

s-S

25

F-4

-RH

, 0.2

5m

DF

s-S

25

F-4

-RH

, 0.4

5m

H

Fig

ure

4.7

: L

oad

dis

pla

cem

ent

curv

es o

f hig

h e

ner

gy r

apid

pull

out

test

s of

DF

s-S

25F

tes

t se

ries

mea

sure

d a

t 0 m

, 0.2

5 m

and 0

.45 m

from

nai

l hea

d.

00

.40

.81.2

1.6

2

Pu

llou

t d

isp

lace

me

nt (m

m)

0

20

40

60

80

100

Load (N)

DC

s-S

22

U-2

-RH

DC

s-S

22

U-3

-RH

DC

s-S

22

U-1

-S

Fig

ure

4.8

: L

oad

dis

pla

cem

ent

curv

es o

f hig

h e

ner

gy r

apid

pull

out

test

s of

DC

s-S

22U

tes

t se

ries

.

02

46

81

0P

ullo

ut d

isp

lace

me

nt (m

m)

0

10

0

20

0

30

0

Load (N)

DC

s-S

25P

-2-R

H

DC

s-S

25P

-3-R

H

DC

s-S

25P

-1-S

Fig

ure

4.9

: L

oad

dis

pla

cem

ent

curv

es o

f hig

h e

ner

gy r

apid

pull

out

test

of

DC

s-S

25P

tes

t se

ries

.

0 2 4 6 8 10


0

200

400

600

800

1000

Load (N

)

0 2 4 6


0

50

100

150

200

250

Load (N

)

0 1 2 3 4 5


0

40

80

120

Load (N

)

with inertia

without inertia

Figure 4.10: The influence of inertia effect on rapid pullout response of (a) DCs-S25C

test series, (b) DCs-S25P test series, and (c) DCs-S22U test series.

(a) (b)

(c)

With inertia effect, Fd

Without inertia effect, Fd-Ma (Eq. 4.1)

0

200

400

600

800

1000

1200

DCs-S25C DCs-S25F DFs-S25F MCs-S25C

Test series

Pu

llo

ut

loa

d (

N)

'Analytical' (Eq. 3.4) Quasi static Rapid

Figure 4.11: Comparisons of peak quasi static pullout strength, peak rapid pullout

strength and ‘analytical’ peak pullout strength of DCs-S25C test series, DCs-S25F test

series, DFs-S25F test series and MCs-S25C test series.

0 0.2 0.4 0.6 0.8


0

400

800

1200

Axi

al lo

ad

(N

)

0 0.2 0.4 0.6 0.8


0

200

400

600

800

Axia

l lo

ad

(N

)

0 0.2 0.4 0.6 0.8


0

400

800

1200

Axia

l lo

ad

(N

)

0 0.2 0.4 0.6 0.8


0

200

400

600

800

Axi

al lo

ad

(N

)0 0.2 0.4 0.6 0.8


0

400

800

1200

Axia

l lo

ad

(N

)

Rapid at 50 % of Prp

Rapid at 100 % of Prp

Quasi static at 50 % of Prp

Quasi static at 100 % of Prp

0 0.4 0.8 1.2 1.6 2


0

400

800

1200

1600

2000

Axia

l lo

ad

(N

)

DCs-S25C-2-RH

DCs-S45F-2-RH

DCs-L25F-2-RH

MCs-S25C-2-RH

DCs-S25F-2-RH

DFs-S25F-2-RH

Figure 4.12: Comparison of Rapid and quasi static load distribution curves of test series

on rough nails.

0 0.4 0.8 1.2 1.6 2


0

400

800

1200

1600

'actu

al'

da

mp

ing

co

effc

ien

t (N

s/m

/m) DCs-S25C-2-RH, 0m

DCs-S25C-2-RH, 0.25m


DCs-S25C-4-RH, 0m



Eq. 4.4, β = 38

Figure 4.13: ‘Actual’ damping coefficient of DCs-S25C test series.

0 1 2 3


0

1000

2000

3000

4000

5000

'actu

al'

da

mp

ing

co

effcie

nt (

Ns/m

/m)

DCs-S45C-2-RH

DCs-S45C-3-RH

Eq. 4.4, β = 42

Figure 4.14: ‘Actual’ damping coefficient of DCs-S45C test series.

0 0.5 1 1.5 2 2.5

Pullout displacement (mm)-400

0

400

800

1200

1600

'actu

al'

da

mp

ing

co

effc

ien

t (N

s/m

/m) MCs-S25C-2-RH, 0m

MCs-S25C-2-RH, 0.25m


MCs-S25C-3-RH, 0m



Eq. 4.4, β = 25

Figure 4.15: ‘Actual’ damping coefficient of MCs-S25C test series.

0 0.4 0.8 1.2 1.6 2


0

400

800

1200

1600

'act

ua

l' d

am

pin

g c

oe

ffcie

nt (

Ns/m

/m) DCs-S25F-2-RH, 0m

DCs-S25F-2-RH, 0.25m


DCs-S25F-4-RH, 0m



Eq. 4.4, β = 35

Figure 4.16: ‘Actual’ damping coefficient of DCs-S25F test series.

0 1 2 3


0

1000

2000

3000

4000

'actu

al'

da

mp

ing

co

effcie

nt (N

s/m

/m) DCs-S45F-2-RH, 0m



DCs-S45F-4-RH, 0m



Eq. 4.4, = 37

Figure 4.17: ‘Actual’ damping coefficient of DCs-S45F test series.

0 0.4 0.8 1.2 1.6 2


0

400

800

1200

1600

'actu

al'

da

mp

ing

co

effc

ien

t (N

s/m

/m)

DCs-L25F-2-RH, 0m

DCs-L25F-2-RH, 0.4m

DCs-L25F-2-RH, 0.8m

DCs-L25F-2-RH, 1.2m

DCs-L25F-4-RH, 0m

DCs-L25F-4-RH, 0.4m

DCs-L25F-4-RH, 0.8m

DCs-L25F-4-RH, 1.2m

Eq. 4.4, β = 35

Figure 4.18: ‘Actual’ damping coefficient of DCs-L25F test series.

0 0.4 0.8 1.2 1.6 2


0

1000

2000

3000

'actu

al'

da

mp

ing

co

effcie

nt (N

s/m

/m) DFs-S25F-2-RH, 0m

DFs-S25F-2-RH, 0.25m


DFs-S25F-4-RH, 0m



Eq. 4.4, β = 45

Figure 4.19: ‘Actual’ damping coefficient of DFs-S25F test series.

0 0.4 0.8 1.2 1.6 2 2.4Pullout displacement (mm)

0

400

800

1200

1600

'act

ua

l' d

am

pin

g c

oe

ffici

en

t (N

s/m

/m) DCs-S25C

DCs-S25F

Figure 4.20: Comparison of ‘actual’ damping coefficient between DCs-S25C test series

and DCs-S25F test series.


0

400

800

1200

1600

'act

ua

l' d

am

pin

g c

oe

ffic

ien

t (N

s/m

/m)

DCs-S25C

MCs-S25C


and MCs-S25C test series.


0

400

800

1200

1600

'act

ua

l' d

am

pin

g c

oe

ffici

en

t (N

s/m

/m)

DCs-S25F

DCs-L25F

Figure 4.22: Comparison of ‘actual’ damping coefficient between DCs-S25F test series

and DCs-L25F test series.

0 0.5 1 1.5 2 2.5Pullout displacement (mm)

0

400

800

1200

1600

'actu

al'

da

mp

ing

co

effic

ien

t (N

s/m

/m)

DCs-S25C

DCs-S45C


and DCs-S45C test series (normalized to 25 mm nail diameter).


0

400

800

1200

1600

'act

ua

l' d

am

pin

g c

oe

ffici

en

t (N

s/m

/m)

DCs-S25F

DCs-S45F

Figure 4.24: Comparison of ‘actual’ damping coefficient between DCs-S25F test series

and DCs-S45F test series (normalized to 25 mm nail diameter).

0 0.2 0.4 0.6 0.8


0

200

400

600

800

Axia

l lo

ad

(N

)

0 0.2 0.4 0.6 0.8


0

100

200

300

400

500

Axia

l lo

ad

(N

)

0 0.2 0.4 0.6 0.8


0

200

400

600

Axia

l lo

ad

(N

)

0 0.2 0.4 0.6 0.8


0

100

200

300

400

Axia

l lo

ad

(N

)

0 0.2 0.4 0.6 0.8


0

200

400

600

800

Axia

l lo

ad

(N

)

0 0.4 0.8 1.2 1.6 2


0

400

800

1200

Axia

l lo

ad

(N

)

DCs-S25C-2-RH

DCs-S45F-2-RH

Dcs-L25F-2-RH

MCs-S25C-2-RH

DCs-S25F-2-RH

DFs-S25F-2-RH

Figure 4.25: Load distribution curves of residual rapid pullout strength.

0 2 4 6 8 10Pullout displacement (mm)

0

200

400

600

800

1000

Lo

ad

(N

)

0

0.2

0.4

0.6V

elo

city (m

/s)

Figure 4.26: Comparison of load displacement curve and velocity displacement curve of

DCs-S25C-2-RH test.

0 4 8 12Pullout displacement (mm)

0

400

800

1200

1600

Lo

ad

(N

)

0

0.2

0.4

0.6

0.8

Ve

locity

(m/s

)


DCs-S45C-2-RH test.

Rapid pullout load Pullout velocity


0 4 8 12 16Pullout displacement (mm)

0

200

400

600

800

1000

Lo

ad

(N

)

0

0.2

0.4

0.6

0.8

1

Ve

locity

(m/s

)


MCs-S25C-2-RH test.


0

200

400

600

800

Lo

ad

(N

)

0

0.2

0.4

0.6

0.8

1

Ve

locity (m

/s)


DCs-S25F-2-RH test.




0

400

800

1200

1600

Lo

ad

(N

)

0

0.1

0.2

0.3

0.4

0.5

Ve

locity

(m/s

)


DCs-S45F-2-RH test.

0 1 2 3 4 5


0

400

800

1200

1600

2000

Lo

ad

(N

)

0

0.1

0.2

0.3

0.4

0.5

Ve

locity

(m/s

)


DCs-L25F-2-RH test.




0

400

800

1200

Lo

ad

(N

)

0

0.2

0.4

0.6

0.8

Ve

locity

(m/s

)


DFs-S25F-2-RH test.


Figure 4.33: Shear band model by Oda and Kanzama (1998).

Figure 4.34: Postulation on shear band evolution mechanism of rough nail – sand

interface in (a) quasi static pullout test, and (b) rapid pullout test.

Thickness of

shear band

Nail

Evolution of shear band

Sand particle

Sand

(a)

Thickness of

shear band

Nail

Evolution of shear band

Sand particle

Sand

(b)

0 0.4 0.8 1.2Pullout displacement (mm)

0

200

400

600

800

Lo

ad

(N

)

DCs-S25C-2-RH-r

DCs-S25C-4-RH-r

DCs-S25C-1-S-r

DCs-S45C-2-RH-r

DCs-S45C-1-S-r

0 0.4 0.8 1.2 1.6Pullout displacement (mm)

0

200

400

600

800

1000

Lo

ad

(N

)

DCs-S45F-2-RH-r

DCs-S45F-4-RH-r

DCs-S45F-1-S-r


0

200

400

600

800

1000

Lo

ad

(N

)

Figure 4.35: Comparison of quasi static reload test results conducted after the high energy

rapid pullout test and quasi static pullout test.

0 0.2 0.4 0.6 0.8Pullout displacement (mm)

0

20

40

60

80

100

Lo

ad

(N

)

DCs-S22U-2-RH-r

DCs-S22U-3-RH-r

DCs-S22U-1-S-r

0 0.4 0.8 1.2Pullout displacement (mm)

0

200

400

600

Lo

ad

(N

)


0

400

800

1200

1600

Lo

ad

(N

)

DFs-S25F-2-RH-r

DFs-S25F-4-RH-r

DFs-S25F-1-S-r

DCs-L25F-2-RH-r

DCs-L25F-4-RH-r

DCs-L25F-1-S-r

Figure 4.35 continue


0

100

200

300

Lo

ad

(N

)

DCs-S25P-2-RH-r

DCs-S25P-3-RH-r

DCs-S25P-1-S-r

Figure 4.35 continue

Chapter 5: Low Energy Rapid Pullout Test

5.1 Introduction

In high energy rapid pullout tests presented in Chapter 4, nails were loaded to

complete pullout failure to mobilize the full rapid pullout response including the pre

peak and the post peak pullout stages. However, in the field, the condition of

complete pullout failure may not be achieved due to the limited capacity of impulse

hammer to impose adequate pullout energy. Occasionally, the condition of complete

pullout failure may be even undesirable if the planned pullout test is an inspection test.

Therefore, there is a need to study the pullout response of nails when loaded by lower

energy level that less than adequate to cause complete pullout failure.

In these experiments, low energy rapid pullout tests were performed on rough

nail only because the minimum energy level of the impulse hammer used in these

experiments was still too high to avoid the complete failure of smooth nail. Anyway,

since it has been shown by the results of high energy rapid pullout test that the rapid

pullout response of smooth nail was virtually identical to its quasi static pullout

response with minimal damping effect, it is reasonable to say that the low energy

rapid pullout response of smooth nail would also be equal to its corresponding quasi

static pullout response.

As usual, only the code of test series and pullout tests will be quoted in this

chapter. The details of the coding system are given in Table 2.4 and Table 2.5. For

pullout tests that consists of two successive low energy rapid pullout tests, the first

and the second low energy rapid pullout tests will be distinguished by adding ‘1’ and

‘2’ at the end of test code. As an example, the first and second rapid pullout tests of

DCs-S25C-3-RL test are termed as DCs-S25C-3-RL1 test and DCs-S25C-3-RL2 test

respectively.

The traces of impulse load, rapid axial body load, displacement, velocity and

acceleration in time domain of all low energy rapid pullout tests are plotted in

Appendix B. As has been discussed in Section 2.4.2 of Chapter 2, loading duration of

impulse load applied to every rapid pullout tests in these experiments was around 27

ms, with approximately 8 ms of rise time and 19 ms of fall time (although these

parameters slightly differ from test to test, the differences were marginal). The

dominant loading frequency was approximately 35 Hz by FFT analysis. The

corresponding relative wave length defined by Eq. 1.1 was 90 and 41 respectively for

tests with 0.75 m and 1.65 m of effective nail length. These relative wave lengths are

significantly larger than the lower boundary value of 10 proposed by Holeyman (1992)

for the validity of rapid loading condition.


The low energy rapid load displacement curves of all test series on rough nails

(except the DCs-S45C test series) are plotted in Figure 5.1 to Figure 5.5. For DCs-

S25C test series and DFs-S25F test series which consist of two successive low energy

rapid pullout tests with increasing energy level, the results of these successive low

energy rapid pullout tests are plotted in the same figure. As before, the plotted load

displacement curves are the curves of ‘net’ rapid soil response after the subtraction of

inertia effect by Eq. 4.1.

In Figure 5.1 to Figure 5.5, the load displacement curve of succeeding quasi

static pullout tests conducted after the low energy rapid pullout tests are also plotted

to examine the influence of low energy rapid pullout test on the behaviour of quasi

static pullout tests conducted afterward.

Besides, the load displacement curves of quasi static pullout tests presented in

Chapter 3 are also reproduced in Figure 5.1 to Figure 5.5 for each test series. As usual,

although there were two quasi static pullout tests conducted under each test series,

only one is plotted here because the results of both quasi static pullout tests were

nearly identical.

5.3 Pullout Response of Low Energy Rapid Pullout Test

From the load displacement curve of low energy rapid pullout tests plotted in

Figure 5.1 to Figure 5.5, it can be seen that the load displacement path of low energy

rapid pullout tests was generally following the load displacement path of

corresponding quasi static pullout test, though the rapid pullout response was always

stiffer than the quasi static pullout response. The stiffer rapid pullout response can be

attributed to the mobilization of damping resistance, as has been discussed in the

previous chapter with the results of high energy rapid pullout test. In fact, for tests

with very low pullout energy such as DCs-S25C-3-RL1 test (Figure 5.1) and DFs-

S25F-3-RL1 test (Figure 5.5), the loading response of these low energy rapid pullout

tests were approximately matched with their corresponding quasi static load

displacement curves with minimal damping effect. It is because the maximum pullout

velocity of these tests was very small, less than 0.05 m/s.

The ‘actual’ damping coefficient of pre peak pullout response of low energy

rapid pullout tests (DCs-S25F-3-RL, DCs-S45F-3-RL and DCs-L25F-3-RL) was also

calculated by Eq. 4.3 and plotted in Figure 5.6 to Figure 5.8. In these figures, the

‘actual’ damping coefficient of corresponding high energy rapid pullout tests was also

plotted for comparison. It is seen that the ‘actual’ damping coefficient of low energy

rapid pullout tests was generally fall within the ‘actual’ damping coefficient of

corresponding high energy rapid pullout tests, despite the clear difference in pullout

velocity between low energy and high energy rapid pullout tests (Compares between

Appendix A and Appendix B). This observation indicates that the damping effect

mobilized in both low energy and high energy rapid pullout tests is nearly identical

and supports the hypothesis that the difference in pre peak pullout response between

rapid pullout test and quasi static pullout test is mainly contributed by the velocity

dependent damping resistance.

After the point of peak rapid pullout load, the rapid load displacement

response started to decrease in load while the pullout displacement is still increasing

until the unloading point. The unloading point is defined as the point on rapid load

displacement curve where maximum pullout displacement is first attained. From the

comparison of displacement trace and velocity trace in Figure B1 – Figure B5

(Appendix B), the unloading point is also seen to approximately coincide with the

point of zero velocity. This characteristic of the unloading point is essential because at

this point, only the displacement dependent stiffness resistance is mobilized as the

velocity dependent damping resistance is negligible due to zero pullout velocity.

From Figure 5.1 to Figure 5.5, the unloading point is seen to approximately

fall on the quasi static load displacement curve irregardless of nail diameter and

effective nail length. This observation suggests the possibility to utilize this unloading

point for the prediction of equivalent quasi static pullout response from low energy

rapid pullout test result. Besides, the coincidence of the unloading point with quasi

static load displacement curve also implicitly indicates the stiffness coefficient of

rapid pullout tests was nearly identical to that of quasi static pullout tests, which leads

to the deduction that the characteristics of restrained dilatancy effect and interfacial

shaft resistance that dominantly influenced the stiffness coefficient are virtually

unaffected by the variation in loading rate between quasi static and rapid tests. The

coincidence of unloading point with quasi static load displacement curve was also

observed on the response of rapid test on pile (Middendorp et.al., 1992).

After the unloading point, it is seen that the load displacement curve had

turned into a very stiff unloading response with virtually zero unloading displacement

for the first two third of decrease in pullout load (Figure 5.1 – Figure 5.5). Most of the

unloading displacement only occurred after the nail had been fully unloaded. This

very stiff unloading response caused the existence of a plateau with virtually constant

maximum pullout displacement on displacement trace (Figure B1 – Figure B5,

Appendix B). It has to be stressed that the unloading point must be taken as the first

point where the maximum pullout displacement is first met. The use of other points

along the plateau of maximum pullout displacement is unreasonable because these

points are mainly influenced by the unloading response.

5.4 Successive Low Energy Rapid Pullout Tests

For DCs-S25C-3-RL test and DFs-S25F-3-RL test, two successive low energy

rapid pullout tests with increasing pullout energy were conducted. The load

displacement curves of these tests are plotted in Figure 5.1 for DCs-S25C-3-RL test

and in Figure 5.5 for DFs-S25F-3-RL test.

From Figure 5.1 and Figure 5.5, it can be seen that after the rapid pullout load

of a succeeding rapid pullout test exceeded the maximum rapid pullout load

experienced by its preceding rapid pullout test, the load displacement curve of this

succeeding rapid pullout test turned smoothly to retrace and continue the rapid load

displacement path left behind by its preceding rapid pullout test. Both of these

successive low energy rapid pullout tests formed a complete unloading – reloading

loop that is similar to the unloading – reloading characteristic of quasi static pullout

test. Therefore, in future, the low energy rapid pullout test may be utilized to examine

the unloading - reloading characteristic of installed nail such as those expected to

resist cyclic loading.

5.5 Succeeding Quasi Static Pullout Test

The load displacement curve of succeeding quasi static pullout tests that were

conducted after the low energy rapid pullout tests are also plotted in Figure 5.1 to

Figure 5.5 for each test series.

From these figures, it is seen that the load displacement curve of these

succeeding quasi static pullout tests gradually curved to retrace the path of quasi static

load displacement curve reproduced from Chapter 3, and both were well matched to

each other after the pullout load at the unloading point of preceding low energy rapid

pullout tests had been exceeded. These characteristics seemed unaffected by the level

of rapid pullout load at the unloading point of their preceding low energy rapid

pullout tests as long as the rapid pullout load at the unloading point was well below

the corresponding peak quasi static pullout strength. As an example, these

characteristics were also observed in DCs-L25F-3-RL test (Figure 5.4) although the

rapid pullout load at the unloading point of this low energy rapid pullout test was

1450 N, only slightly lower than 1500 N, the peak quasi static pullout strength of this

test.

These results on succeeding quasi static pullout tests suggest that quasi static

pullout response of a nail is not adversely affected by the conduct of preceding low

energy rapid pullout tests. Therefore, the technique of low energy rapid pullout test

could be implemented as an inspection test method to evaluate the pullout response of

a working nail without adversely affecting its working performance.

5.6 Modified Unloading Point Method

In previous section, the low energy rapid pullout curve has been shown to

approximately coincide with the quasi static load displacement curve at its unloading

point. This unique characteristic of the unloading point shed a light on the possibility

to predict the equivalent quasi static pullout response of a nail from its low energy

rapid pullout response through a simple iterative procedure.

This unique characteristic of the unloading point has been widely utilized to

predict the equivalent static response of pile from the result of rapid test on pile by

using the ‘Unloading Point Method’ proposed and described by Horvath et.al. (1995)

and Kusakabe and Matsumoto (1995). In these ‘Unloading Point Method’, the

difference in rapid load (after subtraction of inertia effect) between the unloading

point and the point of maximum rapid load is assumed to be fully contributed by

damping resistance. With this assumption, a damping coefficient is calculated and is

usually assumed to be constant throughout the rapid test to deduce the equivalent

static response (Section 1.2.1.3, Chapter 1).

However, the assumption of constant damping coefficient appears improper

for the interpretation of soil nail rapid pullout test result since ‘actual’ damping

coefficient as defined by Eq. 4.3 of a soil nail rapid pullout test has been shown to be

a variable that decreases with the increase in pullout displacements (Section 4.4). In

addition, the assumption of equal static load mobilized at both the unloading point and

the point of maximum rapid load is also invalid for low energy rapid pullout tests.

From Figure 5.1 to Figure 5.5, it is clearly seen that the quasi static pullout load

mobilized at the point of maximum rapid pullout load was obviously smaller than the

quasi static pullout load mobilized at the unloading point.

In view of these shortcomings, the ‘Unloading Point Method’ was modified to

allow for variation in stiffness and damping coefficients. In this modified method, the

first reference stiffness coefficient is deduced from the unloading point (point ‘ul’)

which has zero damping resistance by Eq 5.1 below.

ul

ulrul

u

PK = (5.1)

with Prul

= rapid load at the unloading point after subtraction of inertia effect, uul

=

pullout displacement at the unloading point.

Then, the stiffness coefficient of the preceding point Kul-1

is equal to Ku1

(Eq. 5.2).

ulul KK =−1 (5.2)

with this assumption, the damping coefficient of point ‘ul-1’ Cul-1

is deduced by Eq.

5.3 below.

1

111

1

−

−−−

− −=

ul

ululul

rul

v

uKPC (5.3)

with vul-1

= pullout velocity at point ‘ul-1’.

Subsequently, the damping coefficient of point ‘ul-2’ Cul-2

is equal to Cul-1

as shown in

Eq. 5.4, and the stiffness coefficient of point ‘ul-2’ Kul-2

is then deduced by Eq. 5.5.

12 −−=

ululCC (5.4)

2

222

2

−

−−−

− −=

ul

ululul

rul

u

vCPK (5.5)

These procedures are continued for point ‘ul-3’, ‘ul-4’ ….. until the beginning of

rapid pullout test to determine the stiffness and damping coefficients in alternate

manner. The equivalent quasi static load displacement curve is then constructed by

multiplying the deduced stiffness coefficient with pullout displacement. It needs to be

reminded that the above equations are only applicable for nails that virtually behave

as rigid body in pullout because the distribution of pullout displacement and pullout

velocity are assumed to be uniform along the nail in this method.

The ‘Modified Unloading Point Method’ described above is nearly similar to

the modified initial stiffness method proposed by Matsumoto et.al. (1994) to interpret

the results of rapid test on pile, with the only difference on the determination of the

first reference stiffness coefficient. In the method proposed by Matsumoto et.al.

(1994), the first reference stiffness coefficient is determined from the initial stiffness

of rapid pile response which is mainly induced by the dead weight of rapid test setup.

However, this procedure appears to be inapplicable for rapid pullout test because the

statically induced initial stiffness is not seen in rapid pullout response as the nails

were not statically loaded at all before the conduct of rapid pullout tests of these

experiments.

The ‘Modified Unloading Point Method’ described above was applied on the

results of low energy rapid pullout tests shown in Figure 5.1 to Figure 5.5, and the

derived quasi static load displacement curves are compared to the experimental quasi

static load displacement curves in Figure 5.9 to Figure 5.13. It has to be noted that the

‘Modified Unloading Point Method’ was only applied up to the unloading point. This

is because after the unloading point, the unloading response is very stiff with virtually

no decrease in pullout displacement and zero in velocity. This may causes ill

conditioning on Eq. 5.3 with velocity as the denominator. For DCs-S25C-3-RL test

(Figure 5.9) and DFs-S25F-3-RL test (Figure 5.13), only the second low energy rapid

pullout tests were treated by this ‘Modified Unloading Point Method’ because the

influence of damping effect on the first low energy rapid pullout response was

minimal due to low in pullout velocity.

From Figure 5.9 to Figure 5.13, it can be seen that the derived quasi static load

displacement curves seemed more or less matched with the experimental quasi static

load displacement curves, though the derived curves appeared slightly less stiff and

less non linear when compared to the experimental curves. This small discrepancy

may be attributed to the nature of this method that determines the stiffness and

damping coefficients in alternate manner, which may not be accurate enough to

capture the variation of these coefficients with pullout displacement. However, under

the circumstance that experimental quasi static load displacement response is

unknown, the derived quasi static load displacement curve should be sufficient

enough to serve as an approximation to the actual quasi static load displacement

response. Another point needed to be stressed is the simplicity of this method which

can be applied shortly after the conduct of low energy rapid pullout test on the spot.

Therefore, the ‘Modified Unloading Point Method’ is a promising method for fast

prediction of quasi static load displacement response of nail from low energy rapid

pullout test.


The most important characteristic of low energy rapid pullout response is the

coincidence of low energy rapid load displacement curve with its corresponding quasi

static load displacement curve at the unloading point. With this unique characteristic

of the unloading point, a ‘Modified Unloading Point Method’ was proposed to predict

the equivalent quasi static load displacement curve of a nail from its low energy rapid

pullout test result with simple procedures. This method is found to work well on the

results of low energy rapid pullout test of these experiments.

Besides, the basic characteristics of quasi static pullout response are seen not

to be adversely affected by the preceding low energy rapid pullout tests. This

observation suggests that low energy rapid pullout test can be applied as an inspection

test method to examine the pullout response of a working nail without adversely

affecting its working performance.

0 1 2 3 4


0

200

400

600

800

1000

Lo

ad

(N

)

DCs-S25C-3-RL1

DCs-S25C-3-RL2DCs-S25C-3-RL-r

DCs-S25C-1-S

Figure 5.1: Load displacement curves of low energy rapid pullout test, DCs-S25C-3-

RL.

0 1 2 3 4


0

200

400

600

800

Lo

ad

(N

)

DCs-S25F-3-RL DCs-S25F-3-RL-r

DCs-S25F-1-S

Figure 5.2: Load displacement curves of low energy rapid pullout test, DCs-S25F-3-

RL.

0 1 2 3 4


0

400

800

1200

Lo

ad

(N

)

DCs-S45F-3-RL DCs-S45F-3-RL-r

DCs-S45F-1-S

Figure 5.3: Load displacement curves of low energy rapid pullout test, DCs-S45F-3-

RL.

0 1 2 3 4


0

400

800

1200

1600

Lo

ad

(N

)

DCs-L25F-3-RL DCs-L25F-3-RL-r

DCs-L25F-1-S

Figure 5.4: Load displacement curves of low energy rapid pullout test, DCs-L25F-3-

RL

0 0.5 1 1.5 2 2.5


0

200

400

600

800

1000

Lo

ad

(N

)

DFs-S25F-3-RL1

DFs-S25F-3-RL2

DFs-S25F-3-RL-r

DFs-S25F-1-S

Figure 5.5: Load displacement curves of low energy rapid pullout test, DFs-S25F-3-

RL.

0 0.4 0.8 1.2


0

400

800

1200

1600

'actu

al'

da

mp

ing

co

effcie

nt (N

s/m

/m)

High energy rapid

DCs-S25F-3-RL

Figure 5.6: ‘Actual’ damping coefficient of DCs-S25F-3-RL test.

0 0.4 0.8 1.2


0

1000

2000

3000

4000

5000

'actu

al'

da

mp

ing

co

effcie

nt (N

s/m

/m)

High energy rapid

DCs-S45F-3-RL

Figure 5.7: ‘Actual’ damping coefficient of DCs-S45F-3-RL test.

0 0.4 0.8 1.2 1.6


0

400

800

1200

1600

2000

'actu

al'

da

mp

ing

co

effcie

nt (

Ns/

m/m

)

High energy rapid

DCs-L25F-3-RL

Figure 5.8: ‘Actual’ damping coefficient of DCs-L25F-3-RL test.

0 0.5 1 1.5 2 2.5 3 3.5Pullout displacement (mm)

0

200

400

600

800

1000

Lo

ad

(N

)

Derived quasi static

Rapid (DCs-S25C-3-RL2)

Quasi static (DCs-S25C-1-S)

Figure 5.9: Comparison of derived and experimental quasi static curves of DCs-S25C

test series.

0 0.5 1 1.5 2 2.5 3Pullout displacement (mm)

0

200

400

600

800

Lo

ad

(N

)


Rapid (DCs-S25F-3-RL)

Quasi static (DCs-S25F-1-S)

Figure 5.10: Comparison of derived and experimental quasi static curves of DCs-

S25F test series.

0 0.5 1 1.5 2 2.5 3 3.5Pullout displacement (mm)

0

200

400

600

800

1000

Lo

ad

(N

)


Rapid (DCs-S45F-3-RL)

Quasi static (DCs-S45F-1-S)

Figure 5.11: Comparison of derived and experimental quasi static curves of DCs-

S45F test series.

Figure5.12: Comparison of derived and experimental quasi static curves of DCs-L25F

test series.

0 0.5 1 1.5 2 2.5 3 3.5 4Pullout displacement (mm)

0

400

800

1200

1600

Lo

ad

(N

)


Rapid (LSF-3-RL)

Quasi static (LSF-1-S)


Rapid (DCs-L25F-3-RL)

Quasi static (DCs-L25F-1-S)

0 0.5 1 1.5 2 2.5 3 3.5 4Pullout displacement (mm)

0

200

400

600

800

1000

Lo

ad

(N

)


Rapid (DFs-S25F-3-RL2)

Quasi static (DFs-S25F-1-S)

Figure5.13: Comparison of derived and experimental quasi static curves of DFs-S25F

test series.

Chapter 6: Discussion on Spring and Dashpot Model

6.1 Introduction

In this chapter, modelling of rapid pullout response of rough nail by spring and

dashpot model is discussed. As has been mentioned in Chapter 4, back simulation of

high energy rapid pullout test results of rough nail is needed to subtract damping

resistance and derive the equivalent quasi static pullout response. Spring and dashpot

model appears to be a possible approach for this purpose.

At the beginning of this chapter, a brief review on the development of spring

and dashpot model for dynamic pile shaft resistance is presented. Experiences and

concepts applied to these shaft models will provide some valuable guidelines on

proper modelling of rapid pullout response of rough nail, which previous experiences

are apparently lacking.

In this chapter, only modelling of pre peak pullout response was considered. It

is because post peak pullout response is mainly affected by the evolution of shear

band (Section 4.5) that obviously differs from the mechanism of damping resistance.

6.2 Reviews on Available Shaft Models Applied to Pile

Figure 6.1a shows the first dynamic shaft model proposed by Smith (1960) for

pile. This model simulates the displacement dependent stiffness resistance and

velocity dependent damping resistance by a pair of parallel spring and dashpot. The

limiting static shaft resistance is modeled by a plastic slider in series with the spring.

Smith (1960) suggested the dynamic shaft resistance pd can be approximated as

( )vJpp ssd += 1 (6.1)

with pd = dynamic shaft resistance, ps = static shaft resistance, Js = Smith’s damping

factor, and v = shaft velocity.

Implicitly, Smith (1960) correlated the damping coefficient to stiffness

coefficient by an empirical factor of Js. Rausche et.al. (1994) suggested the Smith’s

damping factor Js of shaft resistance to be 0.164 s/m for sand and 0.656 s/m for clay.

The Smith’s model suffers from several limitations (Randolph, 1991). Firstly,

the damping modelling in Smith’s model does not explicitly consider the radiation

damping effect which has been well accepted as the main damping source in pile

dynamic event (Smith and Chow, 1982). Secondly, the determination of Smith’s

damping factor is fully empirical without any rational link to conventional soil

properties. In view of this, revised shaft models incorporating the plane strain

analytical solution of radiation damping for vertical shaft embedded in radially

homogeneous elastic soil medium (Novak et.al., 1978) were proposed by Randolph

and Simon (1986) and Lee et.al. (1988). In these models, spring coefficient k and

damping coefficient c (in terms of per unit length) are related to conventional soil

properties by equations shown below:

sGk 75.2= (6.2)

ssGrc ρπ2= (6.3)

with Gs = shear modulus of soil. r = shaft radius, and ρs = density of soil.

The main difference between the R-S model (Randolph and Simon, 1986) and

the NUS model (Lee et.al., 1988) lies in the definition of limiting shaft resistance. In

the R-S model, limiting shaft resistance is defined by the sum of spring and dashpot

resistance by placing the plastic slider in between the lumped mass and the pair of

spring and dashpot (Figure 6.1b). While, the NUS model defines the limiting shaft

resistance by the spring resistance alone by placing the plastic slider in line with

spring (Figure 6.1a). Lee et.al. (1988) claimed that definition of limiting shaft

resistance of the NUS model is more logical since limiting shaft resistance is mainly

controlled by the level of shear strain experienced by the adjacent soil alone. Lee et.al.

(1988) also mentioned that once the limiting shaft resistance is achieved by the spring,

dashpot in the NUS model will be numerically disconnected to simulate the ceasing of

radiation damping effect.

The influence of loading rate on limiting shaft resistance is explicitly

considered in the NUS model by the power function suggested by Coyle and Gibson

(1970) (Eq. 6.4). Loading rate effect is also simulated by the R-S model by a power

function that is almost similar to Eq. 6.4 with the only difference being the

replacement of shaft velocity v in Eq. 6.4 by the relative velocity between shaft and

adjacent soil ∆v. The loading rate effect was proposed by Randolph and Simon (1986)

to be visualized as an additional viscous dashpot placed in parallel with the plastic

slider as shown in Figure 6.1b.

( )N

usud vJpp*

)()( 1+= (6.4)

with pd(u) = limiting dynamic shaft resistance, ps(u) = limiting static shaft resistance, J*

= loading rate factor, and v = shaft velocity, N = 0.2.

However, the existence of high strain weaken zone adjacent to shaft is not

considered in all of the abovementioned models. The shear modulus of this weaken

zone is significantly lower than the shear modulus of relatively undisturbed outer field

soil medium due to the strong non linearity of soil behaviour. The neglect of weaken

zone is likely to lead to overestimation of radiation damping effect (Mitwally and

Novak, 1988). To cope with this discrepancy, Mitwally and Novak (1988) proposed

to determine the spring and dashpot coefficients by the plane strain analytical solution

of radiation damping for vertical shaft embedded in radially inhomogeneous soil

medium (Novak and Sheta, 1980). In this analytical solution, the existence of high

strain weaken zone adjacent to shaft is simulated by a finite radius weaken zone in

between shaft and outer elastic soil medium. In their paper, Mitwally and Novak

(1988) considered two definitions of limiting shaft resistance, by placing the plastic

slider in line with spring similar to the NUS model (Figure 6.1a), and by placing the

plastic slider in between the lumped mass and the pair of spring and dashpot similar to

the R-S model (Figure 6.1b). Both definitions were shown to work equally well in the

modelling of dynamic and rapid pile load test result in their paper.

The major discrepancy of the M-N model (Mitwally and Novak model) is on

the need to pre-determine a constant Gm/Gs ratio (Gm = shear modulus of weaken zone,

Gs = shear modulus of outer field soil medium) in the simulation. The pre-

determination of a constant Gm/Gs ratio is illogical since the weakening of soil within

the weaken zone is progressive in manner and is evolving throughout the loading

process.

In view of this, El-Naggar and Novak (1994) proposed another shaft model

(the E-N model) that is capable of simulating the progressive evolution of high strain

weaken zone. In this model, the surrounding soil medium is divided into weaken zone

and outer field soil medium (Figure 6.1c). The progressive weakening of weaken zone

is modeled by a non linear spring defined by the hyperbolic relationship shown as Eq.

6.5 below. The initial shear modulus of weaken zone Gmi in Eq. 6.5 is equated to shear

modulus of outer field soil medium Gs. A viscous dashpot is also proposed to be

placed in parallel with the non linear spring to model the rate effect. A plastic slider

defining the limiting shaft resistance is placed in between shaft node and weaken zone.

p =

−

−

o

o

i

m

r

r

G

η

η

π

1ln

2

1

u

with p = shaft resistance, Gmi = initial shear modulus of weaken zone, r1 = radius of

weaken zone, r = radius of shaft, u = shaft displacement, ηo = τo/τf, τo = shear stress

of soil adjacent to shaft, and τf = ultimate shear stress.

The outer field soil medium of this model is assumed relatively undisturbed

and remained elastic and homogeneous. The stiffness and damping coefficients of this

medium are determined by Eq. 6.2 and Eq. 6.3 respectively. The limiting shaft

resistance of this model is accounted for by a plastic slider placed between lumped

mass and weaken zone (Figure 6.1c). The loading rate effect is also explicitly

considered by Eq. 6.4.

Although all of the abovementioned dynamic shaft models are originally

proposed to model pile shaft response in high strain dynamic pile load test (usually

known as PDA test), attempts to apply these shaft model to simulate rapid pile load

test response have been explored by several researchers either in the form of full wave

equation model (El Naggar and Novak, 1992, Ochiai et.al., 1996, Asai et.al., 1997,

Nishimura et.al., 1998) or in the form of simplified single lumped mass model (Kato

(6.5)

et.al., 1998). These limited published experiences generally reported that these

dynamic shaft models are also reasonably good in simulating the shaft resistance of

rapid pile load test.

6.3 Modelling of Rapid Pullout Response of Rough Nail

From the reviews on dynamic pile shaft models presented above, an

approximate picture of spring and dashpot model capable of modelling the rapid

pullout response of rough nail can be drawn. It should consists of a lumped mass that

simulates the mass of nail, a pair of parallel spring and dashpot that respectively

simulates the displacement dependent stiffness resistance and velocity dependent

damping resistance (radiation damping) of soil, and a plastic slider that simulates the

limiting shaft resistance. The need to incorporate an additional spring between the

pair of parallel spring and dashpot and shaft node to simulate the existence of high

strain weaken zone will be assessed later. The modelling of rate effect by the power

function (Eq. 6.4) can be reasonably ignored here because viscous damping is

insignificant in these experiments with nail embedded in non viscous clean dry sand.

To simulate the pullout test results of these experiments, single element

lumped mass model is found adequate. This is because all nails used in these

experiments are very rigid with insignificant extensibility effect. The negligible

influence of extensibility effect in these experiments can be seen from the virtually

identical in shape of pullout load and axial body load (versus nail head displacement)

measured along the nail (Figure 4.1 to Figure 4.7) and the linearity of axial load

distribution curves (Figure 4.11). These characteristics imply that shaft resistance was

mobilized simultaneously along the nail in the pullout, which is a clear indication of

negligible extensibility effect (Gurung et.al., 1999). Progressive failure of shaft

resistance caused by extensibility effect does not apply to these experiments.

The very rigid behaviour of nails in these experiments can also be seen from

the fact that maximum elastic elongation of the model nails ∆e is only 0.3 mm when

subjected to their corresponding peak pullout strength exerted in these experiments,

under the most extreme condition of one-end-fixed. Actual elastic elongation of nail

in pullout will be lower due to dissipation of pullout load to surrounding soil medium

through shaft resistance. But even under this extreme one-end-fixed condition, the 0.3

mm elastic elongation of nail is still relatively insignificant when compared to the

pullout displacement needed to mobilize the peak pullout strength of rough nail in

these experiments.

Influence of stress wave propagation phenomenon was also minimal in these

experiments because the relative wave length Λ of all rapid pullout tests was larger

than 10 (Section 2.4.2), the lower boundary value proposed by Holeyman (1992) for

the validity of rapid loading condition. Hence, progressive mobilization and failure of

shaft resistance caused by stress wave propagation does not apply to these

experiments.

The correctness of using single element lumped mass model to simulate the

rapid pullout test results of these experiments can be seen from Figure 6.2. This figure

shows that load displacement curves of DCs-S25C test series simulated by both single

element lumped mass model and multiple elements wave equation model are well

matched to each other under both static and rapid loading conditions. In these

simulations, shaft model with constant pre failure stiffness and plastic slider in line

with spring (Figure 6.1a) was applied. The nail was discretized into 75 nail elements

in the multiple elements wave equation model. Input parameters of shaft model

applied to these simulations are the same as the parameters applied to produce the

‘best matched’ simulated curve in Figure 6.4 that will be discussed in Section 6.3.1

below.

Hence, the use of single element lumped mass model to simulate the pullout

response of rough nail considered in these experiments is reasonable.

6.3.1 Model with Constant Pre Failure Stiffness

In the review of dynamic pile shaft models presented above, models with

constant pre failure stiffness (Figure 6.1a and 1b), such as the Smith model (Smith,

1960), the R-S model (Randolph and Simon, 1986) and the NUS model (Lee et.al.,

1988) are commonly applied. However, intuitively the use of this concept is

inappropriate for pullout response of rough nail because of the highly non-linear

hyperbolic load displacement response of rough nail as observed in these experiments

(Figure 3.1 to Figure 3.7) and reported by other researchers (Schlosser and Elias, 1978

and Heymann, 1992). As illustrated in Figure 6.3, the value of this constant pre failure

stiffness can only represent the secant stiffness of particular pullout stage such as the

initial pullout stage (kini), the pullout stage at 50 % of peak pullout strength (k50), the

pullout stage at 75 % of peak pullout strength (k75), the pullout stage at peak pullout

strength (k100) and etc.

Figure 6.4 plots the simulation results of DCs-S25C test series by the constant

pre failure stiffness model. The simulated rapid load displacement curve (after

subtraction of inertia effect) was produced by adjusting the stiffness coefficient of this

model until the best matched with corresponding experimental result had achieved. In

this model, damping coefficient was calculated from stiffness coefficient by Eq. 6.6

below. Eq. 6.6 is derived from the analytical solution of stiffness coefficient (Eq. 6.2)

and damping coefficient (Eq. 6.3), by substituting Gs=k/2.75 from Eq. 6.2 into Eq. 6.3.

Plastic slider that defines the limiting shaft resistance was placed in line with the

spring (Figure 6.1a). This placement of plastic slider is more sensible because it

explicitly allows the enhancement of dynamic limiting shaft resistance by radiation

damping effect, which is an important characteristic of rapid pullout response of

rough nail observed in these experiments.

skrc ρ8.3= (6.6)

with c = damping coefficient (per unit length), r = shaft’s radius, k = stiffness

coefficient (per unit length), ρs = density of soil.

From Figure 6.4, the simulated rapid pullout response (after subtraction of

inertial effect) seems to reasonably match the experimental result. However, the main

deficiency of this model lies in the equivalent static load displacement response

derived from the simulation result. Equivalent static pullout response of DCs-S25C

test series derived from the ‘best matched’ simulated rapid pullout response is also

plotted in Figure 6.4, compared against the corresponding experimental results. Since

the pre failure stiffness coefficient of the shaft model is constant, the predicted

equivalent static load displacement response is essentially a straight line that

obviously differs from the non linear hyperbolic behaviour of experimental results. It

has to be stressed again that the experimental non linear hyperbolic pullout response

can not be predicted by this model even when full multiple elements wave equation

model was considered (Figure 6.2). This is because the experimental non linear

hyperbolic behaviour is the intrinsic behaviour of shaft resistance and not the

consequence of extensibility effect or progressive shaft resistance failure.

From Figure 6.4, it is clearly shown that the peak static pullout strength

predicted by the simulation result is lower than the actual peak static pullout strength

achieved in the experiments. The main explanation for this error is that Eq. 6.3 (and

hence Eq. 6.6) tends to overestimate the damping coefficient. Figure 6.5 compares the

constant damping coefficient calculated by Eq. 6.6 with the experimental ‘actual’

damping coefficient (Eq. 4.3) of DCs-S25C test series. This figure obviously shows

that the calculated damping coefficient is consistently larger than the band of

experimental ‘actual’ damping coefficient, and the error become more serious with

the increase in pullout displacement because the decrease in damping coefficient with

pullout displacement is also not predicted at all by this model. The reason for this

discrepancy in damping coefficient prediction is mainly due to the fact that the

existence of high strain weaken zone adjacent to shaft is not considered in the

formulation of Eq. 6.3, which has been widely recognized by researchers in pile

dynamic modelling such as Novak and Sheta (1980), Mitwally and Novak (1988) and

El-Naggar (2001).

6.3.2 Model with Weaken Zone Hyperbolic Spring

The main setbacks of model with constant pre failure stiffness presented above

are the neglect of non linear hyperbolic characteristic of shaft resistance and high

strain weaken zone formed adjacent to shaft. Both of these setbacks may be solved by

adopting the approach proposed by El-Naggar and Novak (1994) in the E-N model

(Figure 6.1c), where an additional spring with non linear hyperbolic behaviour is

inserted in between shaft node and outer field soil medium. In this model, the stiffness

and damping coefficients of outer field soil medium are calculated by Eq. 6.2 and Eq.

6.3 respectively assuming this soil medium is relatively undisturbed and remained in

elastic region throughout the mobilization of shaft resistance. The hyperbolic

behaviour of weaken zone spring is related to the shear modulus of outer zone by Eq.

6.5. This model has been used to simulate rapid pile load test response by El-Naggar

and Novak (1994) and was reported to achieve reasonable agreement with measured

field test results.

Figure 6.6 plots the simulation results of DCs-S25C test series by this model.

The simulated rapid load displacement curves (after subtraction of inertia effect) in

Figure 6.6 are produced by assuming r1/ro in Eq. 6.5 as 2, a reasonable value

suggested by Nogami and Chen (1995), and by changing the shear modulus Gs in Eq.

6.5 until the best matched with experimental rapid load displacement curve was

achieved. The simulated rapid pullout response is seen to reasonably well match with

the experimental result.

Equivalent static pullout response derived from this ‘best-matched’ simulated

rapid pullout response is also shown in Figure 6.6. This figure indicates that the

derived static pullout response agrees reasonably well with the experimental results,

although the whole matching process was purely achieved by matching the rapid load

displacement response only. The advantages of this model lie in its more sensible

modelling of high strain weaken zone, by simulating the weaken zone as a non linear

hyperbolic spring. This method not only enable the model to capture the non linear

hyperbolic static load displacement response but also enable the model to implicitly

capture the non linear decrease of ‘actual’ damping coefficient with shaft

displacement. ‘Actual’ damping coefficient is the damping coefficient experienced by

the shaft, defined as the difference in load between equivalent rapid and quasi static

load displacement curves divided by the shaft’s velocity (Eq. 4.3). Figure 6.7 plots the

‘actual’ damping coefficient of DCs-S25C test series predicted by this model

compared against those derived from experimental results. ‘Actual’ damping

coefficient predicted by this model is derived by applying Eq. 4.3 on equivalent rapid

and static load displacement curves simulated by this model. This figure shows that

although only a constant damping coefficient is inputted in this model (for dashpot at

the outer field soil medium, Figure 6.1c), the resultant ‘actual’ damping coefficient is

non constant and decrease with pullout displacement.

The characteristic of non constant ‘actual’ damping coefficient predicted by

this model is attributed to the incorporation of additional hyperbolic weaken zone

spring and the assumption of (radiation) damping resistance is fully contributed by

outer field soil medium where the only dashpot is placed (Figure 6.1c). With the

increase in pullout (shaft) displacement, tangent stiffness of weaken zone hyperbolic

spring is decreasing, causing gradual growth in relative motion (relative velocity for

the case of dynamic / rapid loading) between shaft node and outer field soil medium.

Figure 6.8 shows the difference in velocity of shaft node and outer field soil medium

extracted from the simulation results plotted in Figure 6.6. It is clearly seen that the

difference in velocity between shaft node and outer field soil medium is progressively

increase with pullout displacement. The velocity of shaft node is also consistently

higher than the velocity of outer field soil medium. As damping resistance of this

model is assumed to be fully contributed by outer field soil medium, velocity of outer

field soil medium is the velocity that actually influences the amount of damping

resistance mobilized by the model. While, velocity of shaft which is in fact the only

measurable velocity in a pullout test is applied in the calculation of ‘actual’ damping

coefficient (Eq. 4.3). Since the velocity of shaft node is consistently higher than the

velocity of outer field soil medium (Figure 6.8), ‘actual’ damping coefficient

calculated from velocity of shaft node will be consistently lower than the constant

damping coefficient inputted for dashpot at outer field soil medium. The higher the

relative velocity between shaft node and outer field soil medium, the lower will be the

calculated ‘actual’ damping coefficient. It has been shown in Figure 6.8 that relative

velocity between shaft node and outer field soil medium is increasing with pullout

displacement. Hence it is expected that ‘actual’ damping coefficient predicted by this

model is decreasing with pullout displacement, which agrees with the experimental

observations.

However, Figure 6.7 also reveals that actual’ damping coefficient predicted by

this model is generally being under-predicted especially when approaching the peak

rapid pullout stage. The predicted ‘actual’ damping coefficient has decreased to near

zero at peak rapid pullout stage but the experimental results shows a minimum value

was attained at this stage. This is because when approaching the limiting shaft

resistance, tangent stiffness of the weaken zone hyperbolic spring becomes close to

zero. Full detachment of shaft node and outer field soil medium is also predicted by

the free sliding of plastic slider at constant resistance when limiting shaft resistance is

attained (Figure 6.1c). Experimental results presented in Chapter 4 disagree with these

characteristics since the experimental results clearly shows that full detachment

between nail shaft and surrounding soil medium only happened after the pullout

response has attained its post peak residual rapid pullout strength (Section 4.5).

Moreover, full detachment at peak rapid pullout stage also implies that enhancement

in peak rapid pullout strength by radiation damping resistance is not allowed by this

model, which is obviously in opposition to the experimental results.

This discrepancy will result in under prediction of ‘actual’ damping coefficient

mobilized at peak rapid pullout stage and eventually leads to over prediction of

equivalent peak static pullout strength, as can be seen from Figure 6.6. This error

becomes more significant for cases with high radiation damping effect, such as for

test series with larger nail diameter (DCs-S45C test series – Figure 6.9) that has

higher radiation damping effect because radiation damping effect is proportional to

shaft diameter (Novak et.al., 1978).

It has to be stressed that this discrepancy is unlikely to be solved by the power

function (Eq. 6.4) proposed by Coyle and Gibson (1970) for loading rate effect, which

is visualized as a viscous dashpot within weaken zone (Figure 6.1c). It is because the

modelling of loading rate effect by Eq. 6.4 is mainly for the modelling of viscous

damping effect (Randolph, 1991), which is not applicable to these experiments using

only dry clean sands. Wong (1988) and Deeks and Randolph (1992) suggested the J*

for sand can be ignored as it is as low as 0.1.


In this chapter, shaft model with constant pre failure stiffness which is

commonly used to simulate dynamic shaft resistance of pile is found unsuitable for

the modelling of rapid pullout response of rough nail mainly due to its characteristics

of constant pre failure stiffness and the neglect of high strain weaken zone formed

around the shaft. By inserting an additional hyperbolic spring between shaft node and

outer field soil medium, the non linear load displacement response of rough nail can

be reasonably simulated. Non linear trend of ‘actual’ damping coefficient that

decreases with pullout displacement is also implicitly simulated by this model.

However, due to the behaviour of this additional hyperbolic spring that its tangent

stiffness is approaching zero when close to the limiting shaft resistance, ‘actual’

damping coefficient is generally under predicted by this model. This discrepancy will

leads to over prediction of equivalent peak static pullout strength.

Hence, generally, more research works are needed for accurate modelling of

rapid pullout response of rough nail by spring and dashpot model before the model

can be conveniently used in routine interpretation of field rapid pullout test results in

future.

Figure 6.1: Dynamic shaft resistance models proposed by (a) Smith (1960), (b)

Randolph and Simon (1986), and (c) El-Naggar and Novak (1994).

Dashpot Spring

Plastic

slider

Lumped mass

Radiation

dashpot Spring

Plastic

slider

Lumped mass

Viscous

dashpot

(a) (b)

Radiation

dashpot

Spring

Plastic

slider

Lumped mass

Viscous

dashpot

Spring Outer field

soil medium

Weaken zone

Shaft

(c)

0 0.4 0.8 1.2 1.6 2Pullout displacement (mm)

0

400

800

1200

Pu

llout

loa

d (

N)

Multiple elements - static

Single element - static

Multiple elements - rapid

Single element - rapid

Figure 6.2: Comparison of simulated load displacement curves by multiple element

wave equation model and single element lumped mass model.

Pullout displacement

Pu

llo

ut

loa

d

k ini k 50k 100k 75

Figure 6.3: Approximation of non linear hyperbolic load displacement response by

constant stiffness matched at particular pullout stage.


0

400

800

1200

Pu

llou

t lo

ad

(N

)

Rapid - experimental (DCs-S25C-2-RH)Rapid - simulated

static - experimental (DCs-S25C-1-S)Static - simulated

Figure 6.4: Load displacement curves of DCs-S25C test series simulated by the model

with constant pre failure stiffness, compare to the experimental results.

0

200

400

600

800

1000

1200

1400

1600

0 0.5 1 1.5 2


'Actu

al' d

am

pin

g c

oeff

icie

nt

(Ns/m

/m)

Eq. 6.6

Figure 6.5: Damping coefficient predicted by the model with constant pre failure

stiffness, compare to the experimental ‘actual’ damping coefficient (DCs-S25C test

series).

Simulated Experimental


0

400

800

1200

Pu

llou

t lo

ad

(N

)

Rapid - experimental (DCs-S25C-2-RH)Rapid - simulated

static - experimental (DCs-S25C-1-S)Static - simulated


with weaken zone hyperbolic spring, compare to the experimental results.

0

200

400

600

800

1000

1200

1400

1600

0 0.5 1 1.5 2


'Actu

al' d

am

pin

g c

oeff

icie

nt

(Ns/m

/m)

Figure 6.7: Damping coefficient predicted by the model with weaken zone hyperbolic

spring, compare to the experimental results (DCs-S25C test series).

Simulated Experimental


0

0.2

0.4

0.6

Ve

locity (

m/s

)

Shaft node

Outer field zone

Figure 6.8: Velocity of shaft node and outer field soil medium simulated by model

with weaken zone hyperbolic spring, for DCs-S25C test series.


0

400

800

1200

1600

Pullo

ut lo

ad

(N

)

Rapid - simulated Rapid - experimental (DCs-S45C-2-RH)

Static - simulated Static - experimental (DCs-S45C-1-S)


with weaken zone hyperbolic spring, compare to the experimental results.

Chapter 7: Conclusions

7.1 Introduction

The experimental works presented in this thesis aimed to provide information

on the pullout response of soil nail subjected to rapid loading condition. The

relationship between rapid pullout response and the corresponding quasi static pullout

response was studied. This information is valuable for the evaluation of the potential

of rapid pullout test as a supplementary pullout test method to assess the quasi static

pullout response of soil nails, which eventually aims to reduce the numbers of

conventional quasi static pullout test needed for a particular site and hence save the

construction time. Interpretation procedures capable of deriving the equivalent quasi

static pullout response from rapid pullout test result was also discussed at the end of

this thesis based on the results of these experiments.

7.2 Findings of this Study

Firstly, it is observed from the experimental results that the influence of

loading rate on pullout response is highly dependent on the roughness condition of

nail surface. For rough nail, although the rapid load displacement response was fairly

similar to the quasi static load displacement response in trend, the pre peak pullout

stiffness and peak pullout strength of rapid pullout test (after subtraction of inertia

effect) was stiffer and stronger than those of corresponding quasi static pullout test.

The reasons for these enhancement in rapid pullout response was identified as the

mobilization of damping resistance, which is mainly the radiation damping resistance

for these experiments with non viscous dry dense sand. ‘Actual’ damping coefficient,

defined as the difference in load between equivalent pre peak quasi static and rapid

pullout response at the same pullout displacement divided by pullout velocity (Eq.

4.3), was observed to decrease with the increase in pullout displacement. This

characteristic is most probably caused by the progressive weakening of high strain

weaken zone adjacent to nail shaft. ‘Actual’ damping coefficient was observed in

direct proportion with nail diameter and effective nail length but less influenced by

the variation in surface roughness within the vicinity of ‘rough surface’.

For smooth nail, the influence of loading rate on pullout response was very

minimal as the load displacement curves of rapid pullout test (after subtraction of

inertia effect) and quasi static pullout test of smooth nail were virtually identical. This

behaviour is logical because the shear deformation of surrounding soil mass for

smooth interface has been observed to be relatively minimal when compared to the

sliding displacement along shaft interface. Therefore, the enhancement in shear

stiffness of surrounding soil medium caused by radiation damping effect is

insignificant when compared to the total interface displacement that is dominantly

contributed by the sliding displacement along interface.

It is also observed that for rough nail, the post peak pullout response of rapid

pullout test showed drastic softening behaviour with softening rate (in terms of

pullout displacement) that was significantly higher than the softening rate of

corresponding quasi static pullout test. This phenomenon was postulated to be caused

by the variation in evolution of shear band between rapid pullout test and quasi static

pullout test. Once the post peak rapid pullout response of rough nail achieved the

residual pullout stage, abrupt ‘detachment’ of nail from surrounding soil medium had

occurred as can be seen from the sudden rise in pullout velocity. After that, the rapid

pullout response was virtually unaffected by the variation in pullout velocity, which

means that radiation damping effect virtually ceased in residual rapid pullout stage.

The residual rapid pullout strength also seemed to be comparable with the maximum

reloading pullout strength of quasi static reload test conducted after the quasi static

pullout test or high energy rapid pullout test.

For low energy rapid pullout tests with energy level lower than that required to

cause complete pullout failure of nail, the unloading point of rapid pullout response

(after subtraction of inertia effect) with maximum pullout displacement and zero

pullout velocity was coincident with the corresponding quasi static load displacement

curve. This characteristic is in accordance with the characteristic of the unloading

point of rapid compression test of pile. From this characteristic of the unloading point,

the “Modified Unloading Point Method’ capable of deriving equivalent quasi static

load displacement curve from a low energy rapid pullout test result with simple and

straightforward interpretation procedures was proposed in this thesis. The unloading –

reloading loop formed by successive low energy rapid pullout tests with increasing

pullout energy was also quite identical to the unloading - reloading loop of quasi static

pullout test, which implies that low energy rapid pullout test may also be applied to

cyclic pullout test. The quasi static pullout response is also observed to be not

adversely affected by the conduct of preceding low energy rapid pullout test. This

suggests that the use of low energy rapid pullout test as an inspection test method for

working nails is feasible.

From the results of these experiments, the variation in loading rate between

rapid and quasi static pullout tests seems does not result in significant variation of

mobilized restrained dilatancy effect. Restrained dilatancy effect is a mechanism that

leads to the enhancement of normal stress on dilative shaft interface, caused by the

restraint of relative undisturbed surrounding medium to the dilative tendency of

interface, which eventually results in enhancement of interface strength. The fairly

identical of restrained dilatancy effect in both quasi static and rapid pullout tests can

broadly be seen from the fairly similar levels of peak rapid pullout strength (after

subtraction of inertia effect) and peak quasi static pullout strength achieved by each

series of tests on rough nail. The quasi static pullout response of rough nail was highly

influenced by restrained dilatancy effect which is estimated to enhance the peak quasi

static pullout strength of rough nail by as much as 3.76 times in these experiments.

Therefore, the fairly similar levels of peak pullout strength of rapid pullout and quasi

static pullout test are only possible if the rapid pullout response was also influenced

by nearly similar degree of restrained dilatancy effect. The enhancement in pre peak

rapid pullout stiffness and peak rapid pullout strength has also been discussed in this

thesis to be unlikely caused by the variation in restrained dilatancy effect. These

improvements in rapid pullout response were observed to be in direct proportion to

nail diameter while the retrained dilatancy effect has been widely proven either

experimentally or analytically to be in inverse proportion to nail diameter.

Furthermore, the unloading point of low energy rapid pullout test which was the point

with zero damping resistance was coincident with the corresponding quasi static load

displacement curve. This suggests that the stiffness coefficient of rapid pullout test

was virtually identical to that of quasi static pullout tests. Since the quasi static pullout

response of rough nail was highly influenced by restrained dilatancy effect, the

similarity in stiffness coefficient between rapid pullout test and quasi static pullout

test implicitly indicates that similar levels of restrained dilatancy effect were

mobilized in both tests. By combining all of those observations presented above, it

would be reasonable to say that the restrained dilatancy effect mobilized in rapid

pullout test is fairly similar to that in quasi static pullout test.

In the last part of this thesis, discussion on modeling of high energy rapid

pullout response of rough nail by spring and dashpot model was presented. Generally,

it is found that although current knowledge learned from dynamic pile shaft modelling

can simulate the rapid pullout response of rough nail reasonably well, equivalent

quasi static pullout response derived from the simulation results is generally disagree

with the experimental quasi static pullout response. Shaft model with constant pre

failure stiffness is found unsuitable to describe the quasi static pullout response of

rough nail. This is mainly due to its basic characteristic of constant pre failure

stiffness which clearly differs from the highly non linear hyperbolic behaviour

observed in these experiments. This discrepancy may be approximately addressed by

inserting an additional hyperbolic spring between shaft node and outer field soil

medium. The insertion of this additional hyperbolic spring is observed to not only

reasonably simulate the non linear behaviour of pre failure pullout stiffness, but also

approximately simulate the behaviour of non linear ‘actual’ damping coefficient that

decreased with pullout displacement. However, in comparison to the experimental

results, ‘actual’ damping coefficient simulated by this model was generally under-

predicted especially when approaching the limiting shaft resistance This discrepancy

will lead to over estimation of equivalent peak static pullout strength derived from a

rapid pullout test result.

7.3 Implications on the Development of Rapid Pullout Test of Soil Nail

Generally, the use of rapid pullout test to assess quasi static pullout response

of a soil nail is feasible provided the rapid pullout test result is correctly interpreted by

a suitable interpretation method.

For test on smooth nail, the equivalent quasi static pullout response can be

reasonably equated to the rapid pullout response after subtraction of inertia effect.

This is because the influence of radiation damping resistance is found to be quite

minimal for test with smooth nail.

For test on rough nail that is not loaded beyond the peak pullout strength (low

energy rapid pullout test), the equivalent pre peak quasi static pullout response can be

acceptably derived from the rapid pullout test result by the simple and straightforward

‘Modified Unloading Point Method’ proposed in this study. This method is modified

from the ‘Unloading Point Method’ that has been widely applied to interpret the rapid

compression or lateral load test result on piles.

While, for rough nail loaded to complete pullout failure (high energy rapid

pullout test), back simulation of rapid pullout response is needed to estimate and

subtract the contribution of damping resistance. Back simulation of rapid pullout

response by spring and dashpot model was discussed in Chapter 6 of this thesis. It is

generally found that more data are needed, especially on the modeling of non linear

‘actual’ damping coefficient observed in these experiments, before spring and dashpot

model can be used conveniently as a routine interpretation procedure for high energy

rapid pullout test results of rough nail. The use of the ‘Modified Unloading Point

Method’ on high energy rapid pullout test result is impossible due to the absence of

point with zero velocity along the pre peak rapid pullout response.

The results on rough nail of this study can be applied to in-situ grouted nail

and ribbed driven nail. The failure of these rough nails has been observed to occur

within the soil mass adjacent to nail shaft (Schlosser and Elias, 1978 and Jewell,

1980), which is in accordance to the behaviour of rough nail used in this study. It is

because the dominant surface asperities of these rough nail is usually much coarser

than the mean particle size of surrounding soil medium. Driven nail with smooth

material surface may behave as ‘rough’ nail or ‘smooth’ nail depends on the mean

particle size of surrounding soil medium (the crushed particle if particle crushing

effect caused by installation process is significant). The nail will behave as ‘rough

nail’ if mean particle size of surrounding soil medium is small in relative to asperities

of nail surface to results in normalized roughness Rn > Rncri

, with Rncrit

the critical

normalized roughness. On the other hand, the nail will behave as ‘smooth nail’ if

mean particle size of surrounding soil medium is large in relative to asperities of nail

surface to results in normalized roughness Rn < Rncri

. The categorization of roughness

condition by normalized roughness Rn was discussed in detailed in Section 2.6.2.2 of

this thesis.

In future field scale test, rapid pullout test can be designed to be a ‘high

energy’ test or ‘low energy’ test depends on the purpose of the test, by setting the

input energy higher or lower than the threshold energy needed to attained the

estimated peak rapid pullout strength. The threshold energy can be approximately

estimated by energy principle as 1/2Pspu

p(s), with Ps

p the estimated peak rapid pullout

strength and up(s)

the pullout displacement required to achieve the peak rapid pullout

strength. The correctness of this calculated threshold energy depends a lot on the

accuracy of estimated Psp and u

p(s). However, wrong estimation of test type does not

affect the usefulness of the test result. If a ‘low energy’ test is planned but the test

result turned out to be a ‘high energy’ test, this means the pullout capacity of the nail

has been overestimated. In another way, if a planned ‘high energy’ test ends up to be a

‘low energy’ test means that the pullout capacity of the nail has been underestimated.

Both cases will still provide valuable information on the pullout response of tested

nail.

It has to be stressed that the observations and conclusions made in this thesis

are only for nails embedded in soil with minimal viscosity effect, such as sandy soil or

low plasticity residual soil. For nails embedded in high plasticity clayey soil, the

contribution of viscous damping effects should be taken into account. One possible

way to cope with this problem is to incorporate the non linear equation proposed by

Wong (1988) that correlates the ultimate dynamic shaft resistance with velocity.

Besides, nails considered in these experiments were placed horizontally. In

practice, nails will be installed at certain angle, normally < 20o to the horizontal. This

small angle is anticipated to slightly increase the inertia effect in rapid pullout

response. Further research is needed on this subject.

Although the tensile impulse load applied to conduct the rapid pullout test of

these experiments was generated by the spring based impulse hammer, the tensile

impulse load can be generated by any mechanism as long as the generated tensile

impulse load is smooth and has relative wave length larger than 10 (Holeyman, 1992)

to achieve rapid loading condition with minimal stress wave propagation influence.

The problem of ‘rebound’ must also be taken into account in the design of impulse

hammer to ensure that only one impulse load is sent to the nail in every test.

Otherwise, the interpretation of result will become very complicated if multiple

impulse loads are sent into the nail.

7.4 Recommendations for Future Research

Several areas of future research are recommended as below:

1. Study the rapid pullout response of nail embedded in other soil medium such as

residual soil or clayey soil. The viscosity effect of clayey soil is postulated to

enhance the contribution of damping resistance even for test with smooth nail.

2. Study the effect of soil nail’s extensibility on rapid pullout response, especially on

the mobilization characteristic of damping effect. This study also has to aim for

determination of threshold boundary where rigid body assumption is valid.

3. Study the rapid pullout response of nail installed at an angle to the horizontal.

Inertia effect in rapid pullout response of the non horizontal nail is anticipated to

be higher.

4. Physical observation on the behaviour of surrounding soil medium in rapid pullout

test by X-ray or CT scan technique. These observations are helpful to validate the

explanation and postulation that have been made in this thesis for the rapid pullout

response of soil nail.

5. Study the analytical relationship between ‘actual’ damping coefficient and tangent

stiffness of corresponding non linear load displacement curve. This may be done

by adopting the analytical solution of radiation damping for inhomogeneous soil

medium reported by El-Naggar (2000) in the frequency domain.

6. Development and conduct of field scale rapid pullout test. The importance of this

study is to investigate and verify the characteristics of rapid pullout response of

nail embedded in natural ground condition that is much more complex than the

‘controlled’ ground of laboratory test.

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Mechanics and Foundation Engineering Division, ASCE, vol. 86, pp. 35-61.

Smith, I.M. and Chow, Y.K. (1982), “Three Dimensional Analysis of Pile

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Int. Conf. on Numerical Methods in Offshore Piling,

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Appendix A: Results of High Energy Rapid Pullout Tests in Time

Domain

0 10 20 30

Time (milliseconds)

0

200

400

600

800

1000

Imp

uls

e lo

ad

(N

)

0 10 20 30

Time (milliseconds)

0

0.002

0.004

0.006

0.008

0.01

Pu

llo

ut d

isp

lace

me

nt (m

m)

0 10 20 30

Time (milliseconds)

0

0.2

0.4

0.6

Pu

llo

ut v

elo

city

(m

/s)

0 10 20 30

Time (milliseconds)

-200

-100

0

100

200

Pu

llo

ut a

cce

lera

tio

n (

m/s

2)

DCs-S25C-2-RH

DCs-S25C-4-RH

0 10 20 30

Time (milliseconds)

0

200

400

600

800

1000

Imp

uls

e lo

ad

(N

)

nail head 0.25 m 0.45 m

DCs-S25C-2-RH DCs-S25C-4-RH

Figure A1: The impulse load (with inertia effect), pullout displacement, velocity and

acceleration trace of high energy rapid pullout tests of DCs-S25C test series in time

domain.

0 10 20 30 40

Time (milliseconds)

0

400

800

1200

1600

Imp

uls

e lo

ad

(N

)

0 10 20 30 40

Time (milliseconds)

0

4

8

12

16

Pu

llo

ut d

isp

lace

me

nt (m

m)

0 10 20 30 40

Time (milliseconds)

0

0.4

0.8

1.2

Pu

llo

ut ve

loci

ty (

m/s

)

0 10 20 30 40

Time (milliseconds)

-600

-400

-200

0

200

400

Pu

llou

t a

cce

lera

tion

(m

/s2)

DCs-S45C -2-RH

DCs-S45C-3-RH


acceleration trace of high energy rapid pullout tests of DCs-S45C test series in time

domain.

0 10 20 30 40

Time (milliseconds)

0

200

400

600

800

1000

Imp

uls

e lo

ad

(N

)

0 10 20 30 40

Time (milliseconds)

0

4

8

12

16

Pu

llou

t d

isp

lace

me

nt (m

m)

0 10 20 30 40

Time (milliseconds)

0

0.2

0.4

0.6

0.8

1

Pu

llo

ut ve

loci

ty (

m/s

)

0 10 20 30 40

Time (milliseconds)

-200

-100

0

100

200

300

Pu

llou

t acc

ele

ratio

n (

m/s

2)

MCs-S25C-2-RH

MCs-S25C-3-RH

0 10 20 30 40

Time (milliseconds)

0

200

400

600

800

1000

Imp

uls

e lo

ad

(N

)


MCs-S25C-2-RH MCs-S25C-3-RH


acceleration trace of high energy rapid pullout tests of MCs-S25C test series in time

domain.

0 10 20 30 40

Time (milliseconds)

0

200

400

600

800

Lo

ad

(N

)

0 10 20 30 40

Time (milliseconds)

0

4

8

12

16

20

Pu

llo

ut d

isp

lace

me

nt (m

m)

0 10 20 30 40

Time (milliseconds)

0

0.2

0.4

0.6

0.8

1

Pu

llou

t ve

locity

(m

/s)

0 10 20 30 40

Time (milliseconds)

-200

-100

0

100

200

Pu

llo

ut a

cce

lera

tion

(m

/s2)

DCs-S25F-2-RH

DCs-S25F-4-RH

0 10 20 30 40

Time (milliseconds)

0

200

400

600

800

Lo

ad

(N

)


DCs-S25F-2-RH DCs-S25F-4-RH


acceleration trace of high energy rapid pullout tests of DCs-S25F test series in time

domain.

0 10 20 30

Time (milliseconds)

0

400

800

1200

Lo

ad

(N

)

0 10 20 30

Time (milliseconds)

0

2

4

6

8

Pu

llo

ut d

isp

lace

me

nt (m

m)

0 10 20 30

Time (milliseconds)

0

0.1

0.2

0.3

0.4

0.5

Pu

llo

ut ve

loci

ty (

m/s

)

0 10 20 30

Time (milliseconds)

-200

-100

0

100

200

Pu

llo

ut a

cce

lera

tio

n (

m/s

2)

DCs-S45F-2-RH

DCs-S45F-4-RH

0 10 20 30

Time (milliseconds)

0

400

800

1200

Lo

ad

(N

)


DCs-S45F-2-RH DCs-S45F-4-RH


acceleration trace of high energy rapid pullout tests of DCs-S45F test series in time

domain.

0 10 20 30

Time (milliseconds)

0

400

800

1200

1600

2000

Lo

ad

(N

)

0 10 20 30 40

Time (milliseconds)

0

2

4

6

8

Pu

llo

ut d

isp

lace

me

nt (m

m)

0 10 20 30 40

Time (milliseconds)

0

0.2

0.4

0.6

Pu

llo

ut ve

locity

(m/s

)

0 10 20 30 40

Time (milliseconds)

-200

-100

0

100

200

300

Pu

llo

ut a

cce

lera

tio

n (

m/s

2)

DCs-L25F-2-RH

DCs-L25F-4-RH

0 10 20 30

Time (milliseconds)

0

400

800

1200

1600

2000

Lo

ad

(N

)

nail head 0.4 m 0.8 m 1.2 m

DCs-L25F-2-RH DCs-L25F-4-RH


acceleration trace of high energy rapid pullout tests of DCs-L25F test series in time

domain.

0 10 20 30

Time (milliseconds)

0

400

800

1200

Lo

ad

(N

)

0 10 20 30

Time (milliseconds)

0

4

8

12

16

Pu

llou

t d

isp

lace

me

nt (m

m)

0 10 20 30

Time (milliseconds)

0

0.2

0.4

0.6

0.8

Pu

llou

t ve

loci

ty (

m/s

)

0 10 20 30

Time (milliseconds)

-200

-100

0

100

200

Pu

llou

t a

cce

lera

tio

n (

m/s

2)

DFs-S25F-2-RH

DFs-S25F-4-RH

0 10 20 30

Time (milliseconds)

0

400

800

1200

Lo

ad

(N

)


DFs-S25F-2-RH DFs-S25F-4-RH


acceleration trace of high energy rapid pullout tests of DFs-S25F test series in time

domain.

0 10 20 30 40

Time (milliseconds)

0

40

80

120

Imp

uls

e lo

ad

(N

)

0 10 20 30 40

Time (milliseconds)

0

1

2

3

4

5

Pu

llo

ut d

isp

lace

me

nt (m

m)

0 10 20 30 40

Time (milliseconds)

0

0.1

0.2

0.3

Pu

llo

ut ve

loci

ty (

m/s

)

0 10 20 30 40

Time (milliseconds)

-40

-20

0

20

40

60

Pu

llou

t a

cce

lera

tio

n (

m/s

2)

DCs-S22U-2-RH

DCs-S22U-3-RH


acceleration trace of high energy rapid pullout tests of DCs-S22U test series in time

domain.

0 10 20 30 40

Time (milliseconds)

0

50

100

150

200

250

Imp

uls

e lo

ad

(N

)

0 10 20 30 40

Time (milliseconds)

0

2

4

6

8

Pu

llo

ut d

isp

lace

me

nt (m

m)

0 10 20 30 40

Time (milliseconds)

0

0.1

0.2

0.3

0.4

0.5

Pu

llo

ut ve

loci

ty (

m/s

)

0 10 20 30 40

Time (milliseconds)

-80

-40

0

40

80

120

Pu

llou

t a

cce

lera

tio

n (

m/s

2)

DCs-S25P-2-RH

DCs-S25P-3-RH


acceleration trace of high energy rapid pullout tests of DCs-S25P test series in time

domain.

Appendix B: Results of Low Energy Rapid Pullout Tests in Time

Domain

0 10 20 30 40

Time (milliseconds)

0

100

200

300

400

Lo

ad

(N

)

0 10 20 30 40 50

Time (milliseconds)

0

0.4

0.8

1.2

Pu

llo

ut d

isp

lace

me

nt (m

m)

0 10 20 30 40 50

Time (milliseconds)-0.04

0

0.04

0.08

0.12

0.16

Pu

llou

t ve

loci

ty (

m/s

)

0 10 20 30 40 50

Time (milliseconds)

-40

-20

0

20

40

Pu

llou

t acc

ele

ratio

n (

m/s

2)

DCs-S25C-3-RL1

DCs-S25C-3-RL2

0 10 20 30 40

Time (milliseconds)

0

200

400

600

800

Lo

ad

(N

)


DCs-S25C-3-RL1 DCs-S25C-3-RL2

Figure B1: The impulse load (with inertia effect), pullout displacement, velocity and

acceleration trace of low energy rapid pullout tests of DCs-S25C-3-RL in time

domain.

0 10 20 30 40 50

Time (milliseconds)

0

200

400

600

800

Imp

uls

e lo

ad

(N

)

0 10 20 30 40 50

Time (milliseconds)

0

0.4

0.8

1.2

1.6

Pu

llo

ut d

isp

lace

me

nt (m

m)

0 10 20 30 40 50


0

0.05

0.1

0.15

0.2

Pu

llo

ut ve

loci

ty (

m/s

)

0 10 20 30 40 50

Time (milliseconds)

-60

-40

-20

0

20

40

60

Pu

llo

ut a

cce

lera

tion

(m

/s2)



acceleration trace of low energy rapid pullout tests of DCs-S25F-3-RL in time

domain.

0 10 20 30 40 50

Time (milliseconds)

0

200

400

600

800

Imp

uls

e lo

ad

(N

)

0 10 20 30 40 50

Time (milliseconds)

0

0.4

0.8

1.2

Pu

llou

t dis

pla

ce

me

nt (m

m)

0 10 20 30 40 50


0

0.05

0.1

0.15

0.2P

ullo

ut v

elo

city

(m

/s)

0 10 20 30 40 50

Time (milliseconds)

-80

-40

0

40

80

Pu

llou

t acc

ele

ratio

n (

m/s

2)



acceleration trace of low energy rapid pullout tests of DCs-S45F-3-RL in time

domain.

0 10 20 30 40 50

Time (milliseconds)

0

400

800

1200

1600

Imp

uls

e lo

ad

(N

)

0 10 20 30 40 50

Time (milliseconds)

0

0.4

0.8

1.2

1.6

2

Pu

llo

ut d

isp

lace

me

nt (m

m)

0 10 20 30 40 50


0

0.1

0.2

0.3

Pu

llo

ut ve

locity (

m/s

)

0 10 20 30 40 50

Time (milliseconds)

-80

-40

0

40

80

120

Pu

llo

ut a

cce

lera

tio

n (

m/s

2)

nail head 0.4 m 0.8 m 1.2 m


acceleration trace of low energy rapid pullout tests of DCs-L25F-3-RL in time

domain.

0 10 20 30 40

Time (milliseconds)

0

100

200

300

400

500

Imp

uls

e lo

ad

(N

)

0 10 20 30 40 50

Time (milliseconds)

0

0.2

0.4

0.6

0.8

Pu

llo

ut d

isp

lace

me

nt (m

m)

0 10 20 30 40 50


0

0.04

0.08

0.12

Pu

llou

t ve

loci

ty (

m/s

)

0 10 20 30 40 50

Time (milliseconds)

-40

-20

0

20

40

Pu

llo

ut a

cce

lera

tio

n (

m/s

2)

DFs-S25F-3-RL1

DFs-S25F-3-RL2

0 10 20 30 40 50

Time (milliseconds)

0

200

400

600

800

1000

Imp

uls

e lo

ad

(N

)


DFs-S25F-3-RL1 DFs-S25F-3-RL2


acceleration trace of low energy rapid pullout tests of DFs-S25F-3-RL in time

domain.