Improving Techniques and Practices on the Geotechnical Centrifuge. Including literature review

University of NottinghamDepartment of Civil Engineering

Department of Civil Engineering

Improving techniques and practices on

the Geotechnical Centrifuge at the

University of Nottingham

An investigative report by Jonathon Simons

May 2010

The is an investigative report submitted in part consideration of the

degree of MEng (Honours) in Civil Engineering

University of Nottingham

Module: H24A04


This dissertation contains 13500 words, including the

text captions for the figures, tables and plates.

Removing these captions the word count drops below

13000 words


ABSTRACT

The University of Nottingham has one of only a handful of geotechnical

centrifuges in the UK. This is a investigative report aimed at improving practices

and techniques currently used in centrifuge testing. This report is individual to

the University of Nottingham, and the Nottingham Centre of Geomechanics. The

developments brought about by this report will hopefully complement future

work on the centrifuge and the refinement of the techniques and processes will

enable more accurate and precise modelling.

The report consists of several static loading centrifuge tests and differing g-

levels and comparing the results of these experiments to investigate and

improve the practices already in place.

This report and the experimentation within provides a base for all future work

carried out at this centrifuge. The scope for supplementary work to the report is

immense such as investigations into foundation design of buried structures or

effects of weather on embankments causing landslips and precautionary

methods that can be taken.

ACKNOWLEDGEMENTS


Firstly, I would like to take this opportunity to express my gratitude and

appreciation to my tutor, Dr Dave Reddish, who has not only supervised this

project but has been a constant source of help and advice.

My thanks also to Mr Craig Cox, who helped me immensely on the analysis of the

results and MatLab programming. I am very grateful for him taking time out from

his own work to assist me with mine. He was extremely helpful and was always

willing to share his knowledge and experience with me.

I would also like to thank Dr Alec Marshall who always made himself available to

quickly and precisely answer any questions I had. I wish him all the best with his

new career at the University of Nottingham.

I would also like to thank Dr Rick Munro. His comments and advice on the interim

dossier report were invaluable when it came to writing this report.

Finally, a thank you to my parents, who’s never ending support and

encouragement helped me to stay focused and motivated and whose belief in

me has never waned.

TABLE OF CONTENTS

ABSTRACT............................................................................................................... i

ACKNOWLEDGEMENTS........................................................................................... ii


TABLE OF CONTENTS............................................................................................ iii

LIST OF FIGURES..................................................................................................vii

LIST OF TABLES..................................................................................................... ix

LIST OF PLATES......................................................................................................x

1. INTRODUCTION............................................................................................1

1.1. Introduction...............................................................................................1

1.2. Aims..........................................................................................................1

1.3. Objectives.................................................................................................2

1.4. What is a centrifuge..................................................................................2

1.5. Centrifuge principles.................................................................................2

1.6. Outline of Report.......................................................................................5

2. LITERATURE REVIEW....................................................................................6

2.1. Introduction...............................................................................................6

2.2. Developments in Centrifugal technology..................................................6

2.3. Theories of Soil Behaviour in a Centrifuge................................................8

2.4. Scale Effects in Modelling Using a Centrifuge.........................................11

3. EQUIPMENT AND APPARATUS.....................................................................13

3.1. The Centrifuge Facility............................................................................13

3.2. Plane strain box......................................................................................15

3.3. Material...................................................................................................15

3.4. Ultimate Bearing capacity of the Soil......................................................16

3.4.1. General Shear...................................................................................17

3.4.2. Local Shear.......................................................................................17

3.4.3. Punching Shear.................................................................................18

3.4.4. Failure Mechanism in these experiments..........................................19

3.4.5. Calculating Ultimate Bearing Capacity.............................................22

3.5. Additional apparatus...............................................................................26

4. METHODOLOGY..........................................................................................26

4.1. Preliminaries...........................................................................................27


4.2. Pluviating the sand..................................................................................27

4.3. Preparing to test the model....................................................................32

4.4. Testing....................................................................................................33

4.5. Analysis of test........................................................................................33

4.6. Experimental Errors................................................................................34

4.6.1. Boundary conditions.........................................................................34

4.6.2. Particle grain size increasing............................................................35

4.6.3. Plate is not infinitely long..................................................................35

5. USE OF MATLAB IN CENTRIFUGE MODELLING............................................36

5.1. Introduction.............................................................................................36

5.2. Technical Introduction.............................................................................36

5.3. PIV Analysis.............................................................................................36

5.4. Use of MatLab in GeoPIV analysis...........................................................38

5.5. Getting Results from the GeoPIV analysis...............................................38

5.6. Possible source of error in the analysis...................................................40

5.6.1. Non co-planarity of the CCD and target............................................40

5.6.2. Radial and Tangential lens distortion................................................42

5.6.3. Refraction through viewing window..................................................42

5.6.4. CCD pixel non-squareness................................................................42

5.7. Performance of GeoPIV...........................................................................43

6. TESTING & RESULTS...................................................................................45

6.1. Test One..................................................................................................45

6.1.1. Test arrangement.............................................................................45

6.1.2. The positioning of the plates............................................................47

6.1.3. Results..............................................................................................48

6.2. Test Two..................................................................................................49

6.2.1. Preparation.......................................................................................49

6.2.2. Results..............................................................................................50


6.3. Test Three...............................................................................................51

6.3.1. Preparation.......................................................................................51

6.3.2. Results..............................................................................................52

6.4. Test Four.................................................................................................53

6.4.1. Lighting.............................................................................................53

6.4.2. Perspex.............................................................................................54

6.4.3. Changes to Experimentation Method................................................56

6.4.4. Test Procedure..................................................................................59

6.4.5. Results..............................................................................................59

7. DISCUSSION...............................................................................................61

7.1. Improvements in testing.........................................................................61

7.2. What is happening in the soil..................................................................61

8. FURTHER STUDY.........................................................................................62

8.1. Foundation design and limits..................................................................62

8.2. Tunnel & buried structures......................................................................63

8.3. Further improvements to centrifuge modelling.......................................63

8.3.1. Investigation into the effect of grain size..........................................63

8.3.2. Frictional effects of Perspex and walls of plane strain box...............64

8.4. Investigations into geotechnical structures.............................................64

8.5. Non geotechnical investigations.............................................................64

9. REFERECENCES..........................................................................................65

10. BIBLIOGRAPHY............................................................................................66

10.1. Book Sources.......................................................................................66

10.2. Internet sources...................................................................................67

APPENDIX A.........................................................................................................69

Risk assessment Chart......................................................................................70

Additional Information......................................................................................71

Checklist...........................................................................................................74

COSHH Assessment Form (2 Pages).................................................................75


APPENDIX B.........................................................................................................77

Diary................................................................................................................. 78

APPENDIX C.........................................................................................................85

Ballistic Pendulum.............................................................................................86

APPENDIX D.........................................................................................................87

Matlab List of Commands.................................................................................88

LIST OF FIGURES

1 - Introduction

Figure 1-1.......................................................................................................................................3

Stages of a hammer throw

Figure 1-2.......................................................................................................................................4


A diagram showing the forces on an object as it travels on a circular orbit

2- Literature Review

Figure 2-1.......................................................................................................................................9

Stress at a point below a point load.

Figure 2-2.....................................................................................................................................10

Stress at a point below a strip foundation.

Figure 2-3.....................................................................................................................................11

Contours of equal vertical stress beneath a foundation in a semi-infinite elastic

solid defined by the Boussinesq equation

3 - Equipment and Apparatus

Figure 3-1.....................................................................................................................................14

Schematic of Geotechnical Centrifuge at the University of Nottingham showing

all main components

Figure 3-2.....................................................................................................................................15

Schematic of Plane Strain box, showing internal dimensions

Figure 3-3.....................................................................................................................................18

Three shear failure modes for soil

Figure 3-4.....................................................................................................................................20

Nature of failure in soil with relative density of sand Dr and Df/R

4 - Methodology

Figure 4-1.....................................................................................................................................29

Figure illustrating the drop height

Figure 4-2.....................................................................................................................................30

Side view of the plane strain box, side view of hopper. An illustration of the

pluviation technique


Figure 4-3.....................................................................................................................................31

Side view of Plane strain box, end view of hopper. An illustration of the refined


5 - USE OF MATLAB IN CENTRIFUGE MODELLING

Figure 5-1.....................................................................................................................................37

Showing the evaluation of two subsequent images to find correlations in soil

texture

Figure 5-2.....................................................................................................................................41

Displacement vectors of the soil including the camera distortion

Figure 5-3.....................................................................................................................................41

Displacement vectors of the soil after being scaled up and compensating for

camera distortion

6 - Testing and Results

Figure 6-1.....................................................................................................................................49

Contour plot of displacement of magnitude 50-g. First Test

Figure 6-2.....................................................................................................................................51

Contour plot of displacement of magnitude 80-g. Second Test

Figure 6-3.....................................................................................................................................52

Figure showing displacement vectors from of magnitude 80-g. Third Test

Figure 6-4.....................................................................................................................................55

Contour plot of displacement, magnitude 80-g. Data from second test

Figure 6-5.....................................................................................................................................57

Mylar sheet

Figure 6-6.....................................................................................................................................58

Showing movement of control points due to camera distortion

Figure 6-7.....................................................................................................................................60


Fourth test. Contour plot of displacement, Magnitude 100-g.

Figure 6-8.....................................................................................................................................60

Fourth test. Contour plot of displacement with use of Mylar sheet, Magnitude

100-g.

LIST OF TABLES

Table 2-1......................................................................................................................................13


solid defined by the Boussinesq equation

LIST OF PLATES

4 - Methodology

Plate 4-1.......................................................................................................................................28

Picture of the pluviating room, with metal hopper and extractor fan

Plate 4-2.......................................................................................................................................28

Picture of the hopper showing the end plate

5 - USE OF MATLAB IN CENTRIFUGE MODELLING

Plate 5-1.......................................................................................................................................39


Comparison of soil at 1-g and 100-g

6 - Testing and Results

Plate 6-1.......................................................................................................................................54

Comparison between old and new lighting

Plate 6-2.......................................................................................................................................55

Image of Perspex sheet, notice large scratch across centre of sheet and many

other marks and imperfections


1. INTRODUCTION

1.1. Introduction

For any construction project, a sound knowledge of the ground conditions is

important to ensure the safety of any constructions against soil failure. Since the

soil will be the ultimate foundation material, investigations into how the ground

will react to increased dead and live loads are essential.

Geotechnical centrifuge testing offers a means of modelling complex 2 & 3

dimensional problems under well controlled and repeatable conditions.

Centrifuge testing is unique compared with conventional geotechnical testing as

there is the ability to change the gravitational field of the model and hence the

limiting factors, without running separate experiments. This flexibility allows a

small model, which can be tested in the centrifuge, to represent a much larger

prototype in the field. This concept of scaling is covered in more detail in

sections 2.3 and 2.4 of this report.

This project will involve using the centrifuge to statically test a sand model, to

investigate the stresses and strains at increasing g-levels and the effects a

foundation has on soil strata below. The model will consist of a metal plate which

will be placed on layers of sand to represent an infinitely long strip foundation.

This plate will be cut to size and accurately weighed in order to be a

representative of a real life situation when taken to a higher g-level. This could

be the foundation of a building acting on the ground, and by increasing the

weight on the plate a large structure can be modelled.

1.2. Aims

To investigate how centrifuge experimentation techniques can be

improved at the University of Nottingham.

To study how stresses and strains develop in a homogenous soil sample

and how these results can be applied to a construction situation

~ 1 ~


1.3. Objectives

Investigate quality of current centrifugal techniques by comparing results

with existing centrifuge theory.

Research previous investigations in centrifuge technology and consider

previous work when designing and testing the model

Construct and test a model under static loading

Suggest trial improvements and compare the results of these tests against

previous tests

Consider how testing could further be improved and what further work

could be carried out

1.4. What is a centrifuge

A geotechnical centrifuge is a machine with an arm that transects the centre of

the machine with one end of the arm capable of holding a model which is

counterweighted at the other end. The centrifuge is often powered by an electric

motor, which allows the arm to rotate about the vertical axis of the machine. The

centrifuge can rotate at very high speeds causing large centrifugal forces to act

on the model, which has the effect of increasing the gravitational field acting at

the sample. This can be used, with the scaling laws described in section 2.4, to

produce a scaled model of a real life situation.

1.5. Centrifuge principles

A centrifuge works in the same way and uses the same principle as an athlete

who takes part in the hammer throw event. In the figure below, the hammer

thrower represents the centrifuge and the motor, his arms are the centrifuge

arms and the hammer is the model. As in the centrifuge, as the hammer thrower

spins, the hammer can ‘swing-up’ around a pivot point, the throwers’ hand, from

~ 2 ~


an initial stationary position, see figure 1-1(a), to a position where the hammer is

completely horizontal figure 1-1(c) and in line with the throwers’ arm.

The phenomenon of centrifugal force is caused by inertia from Newton’s first law

of motion, which is defined by the Oxford English Dictionary (2010) as:

“That property of matter by virtue of which it continues in its existing state,

whether of rest or of uniform motion in a straight line, unless that state is altered

by an external force”

a. b. c.

Figure 1-1

Stages of a hammer throw. Left (a): hammer is at rest, Centre (b) : hammer

starts to take flight, Right (c) : Hammer in full swing

In centrifuge modelling and the hammer throw, the direction of the object is

constantly changing, which figure 1-2 attempt to demonstrate. At any time in the

orbit, if released the object would continue on its instantaneous direction of

travel which is always tangential to the curvature of the orbit.

~ 3 ~


Figure 1-2

A diagram showing the forces on an object as it travels on a circular orbit

Centrifugal force is the force acting directly outwards from the centre and is

equal and opposite to the centripetal force, which is the force acting towards the

centre of the orbit. Centripetal force can be calculated from the mass of the

object, its velocity and the radius of the orbit by the equation,

F=mv2

rEq. 1-1

Where; m = mass of object

v = velocity

r = radius of curvature

~ 4 ~

INSTANTANEOUS

VELOCITY AND

DIRECTION

CENTRIFUGAL

FORCE

CENTRIPITAL

FORCE

ANGULAR

VELOCITY

ORBIT PATH

OBJECT


since v=rω, (Eq. 1-1) becomes;

F=mr ω2 Eq. 1-2

Where; ω = angular velocity

The size of this centrifugal force can be changed by changing the angular

velocity of the centrifuge. An increase in the centrifugal force is directly

proportional to the increase in g-level at the model.

1.6. Outline of Report

This reports aims to inform the reader about centrifuge technology and

techniques. The literature review, Section 2, gives the reader a background into

the history of centrifuge and some of the principles behind the soil mechanics

and principles involved in the testing.

Then a more general introduction to the specific facility available to the

University of Nottingham and an introduction into the materials and processes

involved in centrifuge testing and analysis, sections 3, 4 and 5.

Sections 6 and 7 describe the individual tests done, the results achieved and a

discussion on these results.

Section 8 completes the report with a set of recommended further work and

study that could be carried out to supplement this report.

Sections 9 and 10 include all the references cited in the text and a list of

additional reading material on topics discussed within this report.

Appendices A, B, C, D and E are provided to supplement the main text

~ 5 ~


2. LITERATURE REVIEW

2.1. Introduction

Centrifuge modelling in short, allows an accurate representation of stress and

strain trends of a much larger structure than the one being modelled. This is

achieved by using the appropriate scaling laws (section 2.4) and assumptions

and equations set out by Boussinesq (section 2.3). Below is a brief history of the

centrifuge and how it developed (section 2.2).

2.2. Developments in Centrifugal technology

It is possible that centrifuge technology spawned out of a similar but different

invention.

Benjamin Robins (1707 – 1751) was an English military engineer who was

influenced by Newton’s laws of physics and among other things, invented the

ballistic pendulum see Appendix C. He carried out work on a ‘whirling arm

apparatus’ to determine drag forces in the air, a machine which looked strangely

familiar to what we would call a centrifuge today.

The next major step towards the modern centrifuge was made by a man named

Antonin Prandtl, a German who has the first recorded practical use of a

centrifuge in 1864, when he used a spinning rotary arm to separate cream from

milk.

In 1869, a French man by the name of Eduoard Phillips published two papers on

the subject of centrifuge technology. The first of which, (Phillips 1869a),

recognised the limitations of contemporary elastic theory and advocated model

testing of structures, especially bridges, to centrifugal forces of 50 gravities. He

introduced scaling relationships and examined several different scenarios,

concluding with the case where self-weight body forces are significant. The first

paper Phillips wrote, he considered only quasi-steady problems of analysis and

design, but later in the same year (Phillips 1869b) he extended his work to

~ 6 ~


dynamic effects. He concluded that, in the centrifuge, inertial time scaling is the

same as linear scaling, which is commonly accepted by today's centrifuge

modellers. Although Phillips had the correct idea of a ‘modern’ geotechnical

centrifuge, he seemed to be ahead of his time.

Even after the publishing of his papers, there is no recorded use of a centrifuge

used for modelling of this kind until 1931, when Phillip Bucky used a centrifuge

to assess the integrity of mine roof structures. He constructed a small scaled

model of the mine structure and accelerated it until failure. Bucky's work

continued for many years, albeit on a small scale, but he lead the way for many

more to carry on his work, providing the base for the increase of centrifuge work

in the United States.

Whilst work was progressing at a slow rate in Europe and the United States, huge

technological advances were being made in the USSR. G.I. Pokrovskii and I.S.

Fiodorov, two Russian centrifuge pioneers, both published papers in 1933 and

presented them at the first ICSMFE (International Conference of Soil Mechanics

and Foundation Engineering) in 1936. Due to the Second World War and

subsequent cold war, their work was largely unknown to the west until the 8th

meeting of the ICSMFE historically held in Moscow by Pokrovskii in 1973. Here

the extent of soviet expertise in the field became apparent. The soviet scientists

had extensive work on underground explosions and the extent of cratering and

ground transmission of vibrations. These were obviously withheld from the west

due to their military implications, but also revealed at the conference was the

advances they made in non-military centrifugal technology.

Progression was also happening across the rest of the world. In the United States

by U.S. Bureau of Mines and the University of Missouri, in Japan by M. Mikasa,

and notably in the United Kingdom by Andrew Schofield whose work was as

valuable as the Russian's. After an increased awareness of centrifuge research

illustrated at the 7th and 8th meetings of the ICSMFE, an international technical

committee was set up to promote activity in the field of centrifuge, headed by

Schofield.

~ 7 ~


The geotechnical centrifuge has been, and always will be an integral part of the

design stage and is now a worldwide essential machine. This is demonstrated no

better than at the 14th meeting of the ICSMFE hosted in 1994 in Singapore which

resulted in publication of about 130 papers by more than 280 authors from 20

countries on six continents.

2.3. Theories of Soil Behaviour in a Centrifuge

Elastic theory is the driving principle in centrifugal technology, first investigated

in this context by Phillips in 1869. He recognised the possibilities and advantages

of testing in such a way and developed the scaling relationships described below

(section 2.4). Static centrifugal testing is based on principle of elastic theory in

soil. This theory was developed by Boussinesq in 1885, who assumed that the

soil could be represented as a semi-infinite, homogeneous, isotropic mass. He

determined an equation to calculate the vertical stress, at any point below a

point load on a soil as;

σ z=3Q

2 π z2 { 1

1+( rz )2 }52

Eq. 2-2

Where;

- Q is the point load at the location of application

- r is the horizontal distance to the point of interest from the point of

applied load, Q

- z is the vertical depth of the point of interest

- σz is the vertical stress at the point of interest

- Axis-symmetric case

~ 8 ~


Figure 2-2

Stress at a point below a point load. R.F. Craig (1997), p163

Figure 2.1 shows the horizontal and vertical stresses at the point of interest, X,

when point load Q, is applied.

This and subsequent equations all make the core assumption that the stress is

independent of Poisson’s ratio and the modulus of elasticity, as long as the

material is homogeneous and isotropic.

As stated above, this equation is specific to point loads. To generate the

equation that is relevant for the experiment described in this report, it is

necessary to integrate the point source loads over the particular area required.

This generates the following equations, which show the vertical and horizontal

stress respectively.

σ z=qπ

{α+sin α cos (α+2 β ) } Eq. 2-3

σ x=qπ

{α−sin α cos (α+2β ) } Eq. 2-4

Where;

~ 9 ~


- q is the uniform pressure on a strip area of width B and infinite

length

- α and β are angles in radians defined in the diagram below

Figure 2.2 shows the horizontal and vertical stresses at any point below a strip

foundation of width B and infinite length, with a uniform pressure, q.

Figure 2-3

Stress at a point below a strip foundation. R.F. Craig (1997), p166

Boussinesq’s equations can be used to calculate the vertical stress at all points

in the vicinity of the foundation. These are plotted in the figure below (Figure

2.3), with the contours representing lines of equal vertical stress intensity. The

vertical stress contour of value 0.2q is described as the bulb of pressure.

Boussinesq equations also demonstrate that the further away the point of

interest is from the position of applied load, i.e. increased z or r and

subsequently larger α and β, the smaller the stress intensity is. This agrees with

figure 2.3, where nearer to the sides and edges the smaller the stress intensity

is, which relates to increasing values of z and r.

Above distances from the point of load where the stress is less than 10% or 0.1q,

the change in stress is such that the stresses become negligible.

~ 10 ~


Figure 2-4


solid defined by the Boussinesq equation (Herndon 1990)

2.4. Scale Effects in Modelling Using a Centrifuge

Phillips first developed the appropriate scaling relationships between model and

prototype when testing in a centrifuge after recognising ‘the significance of self

weight body forces in a number of different situations’, (Taylor 1995). It is

important to realize that the small model in the geotechnical centrifuge

experiences the same physical effects as a large prototype in the earth’s

gravitational field. This is because all the material properties, aside from the self

weight, remain the same, regardless of the gravity level in the centrifuge,

(Schofield 1990). For example, as any stress intensity increases due to the

increase in gravities in the centrifuge, the same proportional increase can be

~ 11 ~


expected for the prototype in the field. Consequently, this emphasises the

importance of scaling the model’s linear dimensions to correspond with the

prototypes dimensions when the model is placed under the specified gravity

level in the centrifuge. The linear dimensions of the prototype must be reduced

by a factor of n, where the centrifugal acceleration is n gravities. The model is

built to ensure stress similarity between model and corresponding prototype.

Therefore, if at a gravity level n, the stresses at depth hm of the model, will be

identical to the corresponding stress at depth hp of the prototype, assuming

similarity between the physical dimensions of the model and prototype.

hp=nhm Eq. 2-5

If the soil being tested has a specific density ρ and the centrifuge is accelerated

to experience n times the earth’s gravity, g, then σvm, the vertical stress in the

model at a depth of hm, is calculated according to the formula;

σ vm= ρgnhm Eq. 2-6

using (Eq. 2-4) then;

σ vm=σvp Eq. 2-7

Where; σ vp= ρghp

This shows that the stress in both the prototype and the model will be identical

Table 2.1 below shows the scaling laws for each parameter derived from

dimensional analysis.

~ 12 ~


Table 2-1

Centrifugal scaling laws obtained from Soft Soil Engineering, C.F. Lee et al.

(2001), cross referenced with a presentation by the Japanese Geotechnical

Society (1998) and Geotechnical centrifuge technology, R. N. Taylor 1995

Scaling Laws

Parameter Scale (prototype : model)

Length 1 : 1/nArea 1 : 1/n2

Volume 1 : 1/n3Stress 1 : 1Strain 1: 1

Density 1: 1Unit Weight 1 : n

Gravity 1 : nMass 1 : 1/n3Force 1 : 1/n2Time 1 : 1/n2

where n is the scale factor in G

3. EQUIPMENT AND APPARATUS

3.1. The Centrifuge Facility

The geotechnical centrifuge is part of the Nottingham Centre of Geomechanics

(NCG) at the University of Nottingham. It is a 50g-T modular beam centrifuge

with a 2.0 metre platform radius, designed and installed by Broadbent & Sons

Ltd (Huddersfield, UK). The centrifuge is capable of rotating up to 280 times per

minute creating model accelerations of up to 150-g. The facility is enclosed in a

0.5 metre thick concrete chamber and the data recording and analysis is done in

a separate room with remote connection to the centrifuge’s onboard computers.

~ 13 ~


Figure 3-1 show a schematic of the centrifuge with all major components

labelled.

During testing the model will be attached to the swing cradle, which is hinged to

the centrifuge ‘arm’ at the clevis. The swing cradle is able to pivot about this

point and will ‘swing up’ during testing so that it is in horizontal alignment with

the rest of the arm. This is necessary as the scaling effects of centrifuge testing

act radially out from the vertical axis, meaning that if the swing cradle did not

‘swing up’ then the centrifugal forces would act horizontally through the side of

the soil sample rather than down through the plate.

Figure3-5

Schematic of Geotechnical Centrifuge at the University of Nottingham showing

all main components

~ 14 ~


3.2. Plane strain box

The centrifuge can accommodate different models for different tests. The testing

carried out as part of this study requires the use of the plane strain box shown in

figure 3-2. The plane strain box has internal dimension of 700mm length x

400mm depth x 200mm width, although this width gets reduced by 4mm when

the required sacrificial Perspex sheet is installed. The box is made from hardened

steel and is designed for the purpose of withstanding the high forces

experienced during centrifuge testing.

Figure 3-6

Schematic of Plane Strain box, showing internal dimensions

3.3. Material

The chosen soil material is Leighton Buzzard Fraction C sand and the plates are

cut from steel.

A simple pouring test was carried out on the sand by Aslam 2006, which involved

measuring the height and width of a pile of sand to find the natural friction

angle. This was found to be 35°. This value represents a quite loose state of the

~ 15 ~

Viewing window

Internal Height,

400mm

Internal Length,

700mm

Internal Width,

200mm


sand, and probably slightly lower than what would be expected in the field, and

in the experimentation included in the report. Direct shear tests on Leighton

Buzzard Fraction C by Simoni and Houlsby (2006) gave values of nearer 45°.

The unit weight of the sand is 16.7kN/m3. Further material properties are

calculated in the next section of this report.

The steel plates are of approximate density 7800 kg/m3 and are cut to suit the

model and experimental requirements.

3.4. Ultimate Bearing capacity of the Soil

The ultimate bearing capacity of a soil is defined as the ultimate load that the

soil can support before it fails. In other words it is the ability that the soil has to

support the loads that are imposed on it, and is denoted by the term (q f). The

bearing capacity is a function of the soil properties and influenced by the size

and weight of the structure above it.

In general, the recognised bearing capacity for sands ranges from <100 kN/m2

for loose sand up to values >300 kN/m2 for dense sands (Craig 1997). The

bearing capacity for this particular soil is calculated in this section.

The metal plate used for the experiments in this project represents an infinitely

long, strip footing, with b / L equal to zero, where b and L represent width and

length of the plate respectively. Since the plate is assumed to be infinitely long,

then there are three recognised failure mechanisms for the supporting soil.

General Shear

Punching Shear

Local Shear

3.4.1.General Shear

(See in figure 3-3(a))

~ 16 ~


In general shear, total rupture occurs of the soil immediately below the

foundation and in the locality of the failure. The soil immediately below the

foundation is displaced as the foundations moves into the soil. The failure

surfaces propagate from the failure zone beneath the foundation to the ground

surface. The soil in these new failure zones are forced upwards and outwards, by

the movement of the foundation into the ground, in a process known as heaving

or bulging. Heaving occurs on both sides of the foundation at first, but only of

one side as the soil reaches failure. This caused tilting or twisting of the

foundation as the soil reaches its plastic limits with q => q f. This type of failure is

abrupt and catastrophic and will occur in incompressible (dense or stiff) soils

such as hard clay. Due to the suddenness of the failure, q f is well defined on the

Pressure-Settlement curve.

3.4.2.Local Shear

(See figure 3-3(b))

Local shear can be described as a mix of punching and general shear failure. It

consists of the same well defined shear failure zone beneath the footing like

punching shear, but also shows slight heaving and lateral displacement in

surrounding soil. This is because the failure surfaces are not well defined and do

not reach the ground surface to cause heaving as in general shear. Large

settlements only occur directly below the foundation and as the load, q,

approaches the failure load, qf, partial plasticity develops in the failure zones of

the soil which can lead to minor tilting. This failure is gradual and q f is not well

defined on the Pressure-Settlement curve. It can occur in loose or silty sands and

in weak clay. Local shear often acts as a transitional stage between general and

punching shear failure.

3.4.3.Punching Shear

(See figure 3-3(c))

~ 17 ~


Punching shear does not develop the same shear planes as in general shear and

there is little lateral soil displacement and no heaving of the surrounding ground.

The failure zone is located directly below the foundation and the shearing

extends up to the perimeter of the foundation. The soil undergoes compression

with the greatest compression occurring directly below the foundation and

dissipates with increased depth. This type of failure is not catastrophic and only

occurs at high pressures. It generally occurs in soils with low compressibility

(loose soils) such as sand. Due to the type of failure, it is not readily recognised,

apart from large settlements of the foundation into the ground

Figure 3-7

Three shear failure modes for soil

(a) General Shear Failure, (b)Local Shear Failure, (c)Punching shear failure

In all three of the cases, the dotted line represents the ground surface with the

solid grey lines representing the shear failure planes.

3.4.4.Failure Mechanism in these experiments

The mechanism of failure at ultimate load is determined by several factors.

Properties of the supporting soil such as strength and compressibility as well as

the depth, length, breadth and nature of the foundation. Work carried out by

~ 18 ~


Vesic (1973) on the ultimate failure mechanisms in sand, explains in detail these

factors and there effects on the type of failure caused by a shallow foundation.

His work was summarised by Som and Das (2004).

Figure 3-4 shows the nature of the soil failure at ultimate load with regards to the

relative densities.

In this case, R is the hydraulic radius and is defined as

R= AP

Eq. 3-8

Where;

A=Area of Foundation=BL

P=Perimeter of foundation=2¿)

Therefore;

R= BL2(B+L)

Eq. 3-9

Figure 3-8

~ 19 ~


Nature of failure in soil with relative density of sand Dr and Df/R. Som and Das (2004)

This is where Df is the depth of the foundation below surface and Dr is the

relative density of the sand. From figure 3-4, it is apparent that above a D f / R

value of about 18, the soil will fail by punching shear, regardless of the density of

the sand. The relative density is expressed as a percentage and is a measure of

the soils density with respect to the densest and loosest possible soil conditions.

As the relative density nears 100% it indicates a very dense compact soil,

whereas values nearer to 0%, indicate a very low density loose material.

Relative density, Dr can be expressed as

Dr=emax−e0emax−emin

x100% Eq. 3-10

Where;

emax = Maximum Voids Ratio (soil in its loosest condition)

emin = Minimum Voids Ratio (soil in its densest condition)

e0 = Natural Voids Ratio of the soil or condition in question

For the experiments in this report, Df = 0 (depth of footing below ground

surface), and hence Df / R =0.

Work carried out by Aslam (2006) on Leighton Buzzard Fraction C, determined

the Maximum and Minimum Densities and from these, a minimum and maximum

void ratio can be calculated

Minimum density (Loose sample)

ρ d,min = 1.47 Mg/m3

with a corresponding maximum void ratio of;

emax = 0.80

Maximum Density (Dense sample)

~ 20 ~


ρ d,max = 1.707 Mg/m3

with a corresponding minimum void ratio of;

e min = 0.55

Where;

e ¿Gs γwρbulk

−1 Eq. 3-11

Full explanation and test procedure can be found in R. Aslam, Centrifuge

Modelling of Reinforced Piled Embankments (2006), 1st year PhD report for the

University of Nottingham.

Values of e0 can be calculated from the weight of the samples that were tested

on the centrifuge. Knowing the dimensions of the plane strain box and the mass

of the sand to be tested, the density of the sample in question can be calculated

using eq. 3-5 with results from the tests

ρ=MV

= 58.6 kg

0.0357m3=1641.46 kgm-3 Eq. 3-12

And from the density, the void ratio of the sample can be found using (Eq. 3-4)

❑0=2.65×10001641.46

−1=0.614

Calculating Dr, using Eq. 3-3

Dr=emax−e0emax−emin

x100%=0.80−0.6140.80−0.55

x 100%=74.4

From figure 3-2 this indicates that the soil failure is most likely to occur by local

shear failure.

~ 21 ~


3.4.5.Calculating Ultimate Bearing Capacity

Understanding the failure mechanisms gives a better understanding of how the

soil will fail and sub sequentially, how better to design future tests. The failure

mechanism defines how the soil will fail, the next section will explain when the

soil should theoretically fail. The bearing capacity, qf, or the ability of the soil to

resist the loads applied to it was derived by Terzaghi (1967) as,

qf = c Nc sc + D Nq + 0.5 B N s Εq. 3-13

where,

a) Bearing capacity factors;

Nq = exp ( tan ∅) tan2 (450 + ∅ /2)

Nc = (Nq - 1) cot ∅ (For ∅ > 0 )

= 5.14 (For ∅ = 0) (Jumikis 1966)

N = 1.8 (Nq -1) tan ∅ by Hansen (1968)

Note: ∅ is the friction angle of the soil

b) Shape factors:

sc = 1 + 0.20 B / L …………………………….……………. (∅ ≠ 0

conditions)

sc = [1 + 0.20 B / L] [1 + 0.3 (D / B)0.25 ] ….. (∅ = 0 conditions,

saturated clays)

s = 1 - 0.2 (B / L) ………………… (B / L = footing width to length

ratio)

s = 0.6 ………………… (circular footing)

c) Other Factors

B = Width of Plate

C = Cohesion Coefficient of Soil

D = Depth of Footing Below Surface

~ 22 ~


It is customary to take B / L = 0 for a strip footing, and B / L = 1 for a square

footing. In this report, the metal plate acts as a strip footing, therefore B / L = 1,

where L => ∞.

For use in these experiments, Terzaghi’s equation simplifies to,

qf = 0.5 Β Ν s Eq. 3-14

This is due to;

c Nc sc = 0

For a granular, non cohesive soil, such as sand, c = 0

Since the plate is acting as a strip footing, B / L = 0 and therefore, Sc = 1

Hence value of Nc is irrelevant

and

D Nq = 0

The plate is not buried and is on top of the surface, therefore D = 0

Hence the values of and Nq are irrelevant

The term s can also be removed as;

s = 1

B / L ≡ 0, therefore s = (1 – 0) = 1

This equation give the bearing capacity in soil property terms of friction angle, ∅,

unit weight, , and the width of the plate, b, all of which are known.

Therefore a calculation can be made for the bearing capacity of the soil at 1-g

and using the scaling laws, the bearing capacity at an arbitrary g-level, say 100-

g,

At 1-g. = 16.7 kN/m3

B = 0.055 m

∅ = 350

~ 23 ~


Ν=1.8×(N q+1) tan∅

Where;

Nq=e (tan∅ )× tan2(45 °+∅2

)

Nq = 33.29

Ν = 48.02

q f=0.5×16.7×0.055×48.02

q f=26.062 kN/m2

At 100-g, using the scaling laws in section 2.4

= 16.7100

=¿ 0.167 kN/m3

B = 0.055×100=5.5 m

∅ = 350 which is an unchanged material property

∅ is constant, therefore Nq and hence Ν are unchanged

∴qf=0.5×0.167×5.5×48.02

q f=26.062kN/m2

This means that the bearing capacity of the soil is the same at 100-g as it is at 1-

g. At first this answer seems incorrect, but it makes sense when considering

what actually happens during centrifuge testing. Bearing capacity of the sand

depends on two variables, the linear dimensions of the plate and the unit weight

of the sand, both of which, need to be scaled according to the change in g-level.

The scaling laws discussed in section 2.4 show the appropriate factors to be

~ 24 ~


applied to each variable are 1/n and n for the linear dimensions and unit weight

respectively. This means, that if the prototype has a linear dimension of 1 then

the corresponding linear dimension of the plate in the model has a length of 1/n

where n is the g-level. Similarly for the unit weight, if the prototype has a unit

weight of 1, then the model must have a unit weight of n. This second statement

is one of the major disadvantages of centrifuge testing. It states that as the

centrifuge is in flight, the increase in g-level does not only increase the apparent

size and weight of the plate, it also increase the apparent size of the sand grains

and net strength of the soil sample. The increase in the strength of the soil is

inversely proportional to the rate of the apparent increase in the size of the

plate. This is demonstrated in the above equations as the increase in plate size ,

n, is essentially multiplied by the decrease in unit weight, 1/n, giving an overall

scale factor to be applied to the bearing capacity of 1. Note this is ‘model to

prototype transformation’, therefore the ratios are the inverse of the ‘prototype

to model transformation’. This inaccuracy in centrifuge testing will be discussed

in more detail in section 4.6.

It is still possible to fail the soil using this simple test but would require a large

force, acting on the plate. Therefore this type of static loading test using the

centrifuge is not ideal for simulating large structures. It would be much more

efficient to add a hydraulic ram to force the plate down at the same time as the

centrifuge was in motion. This way, it would be possible to have a large applied

load which is not dependant on the gravitational field acting on the model.

3.5. Additional apparatus

When working and performing tests in the laboratory, hard cap boots and

laboratory coats need to be worn. In addition, when pluviating the sand to build

the model, the fan assisted ventilation mask must be worn to ensure that no

sand or dust particles come in contact with the eyes, nose or mouth.

~ 25 ~


4. METHODOLOGY

This section will explain how the test is set up and how to achieve results from

the analysis. Accompanying this methodology is a risk assessment for the

preparation of the model, see Appendix A.

4.1. Preliminaries

Before testing and the construction of the model, all screws need to be secured

on the plane strain box. The box needs to be empty and the sacrificial Perspex

sheet needs to be installed. Both of the Perspex sheets need to be polished to

remove any marks and minor scratches that could distort the PIV analysis. The

plane strain box now needs to be put onto the hydraulic trolley so that it can be

transported and weighed. The hydraulic trolley has a built in scale which can give

the weight of the box in kg. This should be noted for comparison with the weight

of the plane strain box after pluviation, so the mass of sand can be calculated

and since the internal dimensions of the box are known, the density of the model

can be calculated also.

4.2. Pluviating the sand

Pluviating the sand is important to ensure that the model is as homogeneous and

isotropic as possible. Pluviation is a method by which the sand is poured into the

plane strain box in even layers and from a constant drop height so that the sand

is compacted evenly across the whole model. Pluviating minimises any stresses

or strains to be induced on the system prior to experimentation. The hopper is

specially designed with a sieve-like base which is covered by a removable end

plate. Once the end plate is removed, the sand can pour out of the holes in the

base of the hopper uniformly and at a constant rate.

~ 26 ~

PULLEY SYSTEM USED TO WINCH HOPPER INTO POSITION

HOPPER

EXTRACTOR FAN


The pluviating or pouring of the sand model takes place in the designated

pluviating room, see plates 4-1 and 4-2 for pictures of the pluviating room and

hopper respectively. To pluviate the sand, the hopper is lowered to the ground

and filled with more than enough sand than is required. This is done to ensure

that the hopper does not run out of sand half way through the pluviation. This is

an issue as it both introduces errors into the experiment and for health and

safety reasons (to fill the hopper requires standing on a kick stool and lifting

bags of sand to the height of the hopper). Stopping and starting the pluviation

could cause stratification of the sand causing it to be non-homogeneous and

adversely affect the experiment.

Plate 4-1

Picture of the pluviating room, with metal hopper and extractor fan

~ 27 ~

HOPPER

END PLATE(NOT YET REMOVED)

DROP HEIGHT

HOPPER

PLANE STRAIN BOX


Plate 4-2

Picture of the hopper showing the end plate

Once the hopper is raised, the wooden rests are moved into position in the

pluviating room, providing a place to rest the plain strain box, whilst pluviating.

This is required so that the plane stress box is raised off the floor which allows it

to be easily removed after pluviation is finished. The pulley system is used to

raise the hopper to the calculated drop height, which is defined as the distance

between the base of the hopper to the base of the plane strain box, see figure 4-

1.

~ 28 ~

MOVEMENT OF HOPPER HOPPER

END PLATE (OUT)

PLANE STRAIN BOX

SAND


Figure 4-9

Figure illustrating the drop height

The pluviation is started by removing the end plate. The original technique used

on this project was to take the end plate fully out so that the sand was being

released from the entirety of the base. This resulted in a pluviating technique

moving the hopper side to side. This technique caused a build up of sand in the

centre of the model, as figure 4-2 attempts to demonstrate.

Figure 4-10

Side view of the plane strain box, side view of hopper. An illustration of the


Consequently, the pluviating method was altered so that the sand was more

evenly distributed. This was achieved by rotating the hopper by 90° and only

removing the end plate part of the way. See figure 4-3.

~ 29 ~

MOVEMENT OF HOPPER

END PLATE (PARTIALLY OUT)

PLANE STRAIN BOX

SAND


Figure 4-11

Side view of Plane strain box, end view of hopper. An illustration of the refined


Although this method would take longer as the rate at which the sand is filling

the box is less, it gives a more even layer thickness and distribution of sand.

Once the sand is to the required height, the end plate is re-inserted, stopping the

flow of the sand. The plane strain box is removed by using the hydraulic trolley

and the hopper is lowered to the ground.

~ 30 ~

HOPPER


4.3. Preparing to test the model

Whilst the model is on the hydraulic trolley, the weight of the plane strain box

and sand can once again be recorded. Weighing the box serves two purposes.

Firstly for calculation of the density of the sample and secondly to assess

whether the counterweight on the centrifuge needs to be moved, the heavier the

model the further away the counter weight needs to be. The plane strain box

then needs to be loaded onto the swing cradle of the centrifuge and securely

fastened down with the bolts. Loading is done using the stacker which can only

be used by an appropriately qualified technician. Once the model is securely

fastened, all centrifuge components are checked to ensure they are working. The

following are some of the routine checks that need to take place before testing

can begin.

Check camera is working and connections are secure

Check that the lighting is securely fastened and illuminate viewing window

sufficiently

Attach and securely fasten all equipment to centrifuge

Tie down all loose wires so they cannot work loose during testing and

either obstruct the view of the camera or cause connections to break.

Ensuring the wires have sufficient slack to accommodate the increased

distance between the model and the centre of the centrifuge. As the swing

cradle moves up to its horizontal position.

The g-level experienced at the model is produced by different speeds of the

centrifuge. The faster the centrifuge travels, the greater the angular velocity,

which produces a higher centrifugal force and hence a larger apparent

gravitational field is created at the model. The centrifuge input is in revolutions-

per-minute (rpm), and these need to be calculated for each g-level that the

centrifuge is to be taken to for each test.

4.4. Testing

~ 31 ~


Once the centrifuge is set and all equipment is secured to the centrifuge and all

components are working correctly, the test can begin. An initial image is taken,

which is at 1-g to give a reference image for the others to be evaluated against.

Once the image has been captured, the quality of the image is assessed by

visual inspection to see if there is sufficient detail in the image for the PIV

analysis to detect specific regions of textured soil. The centrifuge is then started

by inputting the rpm value for the first g-level to be tested, in the case of this

report, this was always 10-g. Once the centrifuge has reached this value with no

fluctuations in rpm, the next image can be recorded. This process is repeated at

every 10-g until the required g-level is reached.

The centrifuge motor is then turned off and the centrifuge slows down to a stop.

Once it has fully stopped, the plane strain box is removed and placed on the

wooden rests. The box is emptied and cleaned so that it is ready for use for the

next test.

4.5. Analysis of test

Please see appendix D for full MatLab command list and terminologies

All the images are automatically stored in a folder, which is assigned by the

operator prior to the first image captured. The analysis implements MatLab

modules to analyse each image and to track regions of specific textured sand

through a series of images. This is explained in detail in section 5. This section

aims to provide a brief explanation of the stages carried out in the analysis.

Create the mesh

A mesh is created which divides the primary images up into rows and columns of

square patches. These patches are where the GeoPIV will search for regions of

textured soil.

Run the GeoPIV

The GeoPIV requires two input files, one being the mesh that has just been

created and the other being a launcher file which is set up by the operator and

instructs the GeoPIV.

~ 32 ~


Track movements of control points

Control points are marked onto the Perspex sheet and do not move during the

experiment. If these appear to move through the images then the operator

knows that there is distortion of the camera lens. Tracking these movements and

then removing them from the soil displacement data gives the true displacement

of the soil

Interpolate any erroneous results

Any result that obviously is an error, caused by localised disruptions in the

viewing window or otherwise can be removed and interpolated in MatLab.

Plot the results

A contour plot can be produced which shows the movement of specific regions of

soil, showing trends in displacements and the influence of the plate(s).

4.6. Experimental Errors

4.6.1.Boundary conditions

Error introduced by boundary conditions refers to the interaction between sand

grains and the walls of the Plane Strain Box. The sand grains adjacent to the

boundaries (walls) ‘feel’ a frictional force restricting the movement of the grains.

The frictional force is proportional to the force that the grains exert of the walls,

hence at higher g-levels, the frictional force is greater. It is for these reasons that

there are regions of sand left unanalysed. The frictional force will not affect the

sand towards the centre of the model and therefore will not affect the results.

The Perspex sheet is polished before testing in order to try and reduce the

frictional effect of the sheet on the sand. Although, its effect is minimal anyway

due to the Perspex having a relatively low friction coefficient.

4.6.2.Particle grain size increasing

~ 33 ~


Centrifuge testing relies on the scaling laws to allow a scaled model to represent

a prototype in the field. It would be sensible to also assume that these same

scaling laws would have an effect on the sand particles. If the centrifuge was

taken up to n-g, then the sand particles would resemble a particle N times their

own actual size and weigh n2 their own actual physical weight. This would

represent more of gravel than sand.

This is an unfortunate effect of centrifuge modelling. Although there is no effect

on the stress / strain properties of the material. This effect is much more

apparent when experimenting with gravel as the scaling effect on the already

large grained material introduces other distorting factors. Inter-particle friction

and interaction causes the model to act different to the continuous soil that

would be found in the prototype in the field.

4.6.3.Plate is not infinitely long

The assumption is that the plate is acting like an infinitely long strip foundation.

In reality, it is not and the ratio b / L, which should be zero is actually 0.25. This

has the effect of increasing the calculated bearing capacity as the load is spread

over a wider region of soil.

5. USE OF MATLAB IN CENTRIFUGE MODELLING

5.1. Introduction

In order to evaluate the strains produced when the soil is subjected to increasing

loads, there needs to be an appropriate method of comparing the soil samples

from one g-level to the next. Physical strain tests whilst the centrifuge was in

motion would be impractical, and stopping the centrifuge to perform tests would

~ 34 ~


be pointless as the majority of the strains would be elastic and dissipate when

the weight of the load was equal only to the weight of the plate with no scaling

effects. Tests would also be intrusive and disturb the soil sample so that it may

not show true stress strain properties. However, it is possible to record small

deviations and displacements in the soil sample and convert these into strains.

5.2. Technical Introduction

Soil displacement data is derived by processing a series of sequential images

taken at regular g-level intervals, from 1 to a nominal value of N gravities.

Images are captured and stored remotely during a test. Analysis of the results is

carried out using software called GeoPIV developed by Dave White et al at

Cambridge University. GeoPIV is a suite of programs designed to run in the

MatLab environment. The software implements Particle Image Velocimetry (PIV)

in a manner suited to geotechnical testing to determine the displacement field of

an area of soil.

5.3. PIV Analysis

The PIV analysis operates by tracking a specific region of soil texture or

arrangement of soil particles throughout a series of images. It works by dividing

up an initial image into a mesh of patches and tracking the movement of specific

textured soil in each of the patches through the series of images. In the context

of this project the primary image is the soil at 1-g state, when the machine is

stationary. The software searches within the next image in the series to

determine the new location of each patch. A parameter is passed to the software

to instruct it to search only within a given area for the new location of a patch

with matching regions of soil texture. For a particular patch, this area of the

image is analysed to find the highest correlation of texture within the search

area which corresponds to the displacement of the patch of soil. The process is

illustrated in Figure 5-1.

~ 35 ~


Figure 5-12

Showing the evaluation of two subsequent images to find correlations in soil

texture

Where;

SMAX : is the maximum distance that the search patch increases by to find

corresponding regions of similar texture

Image 1: Shows the first image in the sequence, in the context of this

project it would correspond to the lowest g-level

Image 2: Shows the second image in the sequence, in the context of this

project it would correspond to an incrementally higher g-level

Search patch 1: the area which the GeoPIV looks in for soil of

corresponding texture that was found in Patch 1

The texture of the soil can be recognised in a number of ways. The soil in this

project is Leighton Buzzard fraction C sand which has a natural distinctive

texture in the form of different coloured sand grains, but regions could also be

identified by different light and shadow formations between adjacent grains

when illuminated.

The process of comparing a patch on the primary image to a larger patch on the

secondary image is repeated for the entire mesh. This produces a complete list

~ 36 ~


of trajectories and displacements for all similar textures of soil throughout the

test sample.

5.4. Use of MatLab in GeoPIV analysis

To run the analysis of the series of images, MatLab uses a number of programs

written specific for GeoPIV analysis. These programs are initiated by certain

command lines when entered on the MatLab command screen and designed

specifically to run in the MatLab environment.

5.5. Getting Results from the GeoPIV analysis

The MatLab module requires two input files (a launcher and an initial mesh file)

which are prepared in ASCII format by the user. In short, the launcher file

contains the input variables for each PIV analysis and the initial mesh file

contains the locations of the initial mesh of patches. The GeoPIV analysis

produces output files which are also in ASCII format, which can be manipulated

by the user in MatLab or a spreadsheet to produce displacement data and hence

soil strains.

After the running the GeoPIV program a set of results and displacements are

given in pixels in a ‘(u,v) co-ordinate system’ where u and v are the axis of the

image. This is known as image-space. This data needs to be converted to

physical dimensions of mm or in an ‘(x,y) co-ordinate system’, which is known as

object -space.

In essence, this transformation is a very simple process whereby a constant

scale factor can be applied across the surface of the soil and all measurements

can be scaled up or down according to the quality of the camera. For example, in

the case of the experiments detailed in this report, this scale factor is roughly 5

pixels to every 1mm. This simple scaling procedure does however require a set

of assumptions to be made. It assumes that there are no distortions or errors

~ 37 ~


associated with the camera, the lens, the viewing window and assumes

regularity and squareness of the pixels.

It is unreasonable to make these assumptions for this project in order to get the

accuracy required. Plate 5-1 below clearly illustrates camera lens distortion.

Movement Caused by distortion

of the camera lens

Plate 5-3

Comparison of soil at 1-g and 100-g. Left: Image of soil sample at 1-g, Right: Image of soil at 100-g

The bolts in the image are securely fastened in place and do not move position

during the test, but appear to move on the image. Also notice at the top of the

image, it is possible to see the top of the plane strain box at 100-g, whereas in

the 1-g image it is not there. This is caused by vertical and rotational distortion

of the camera lens and/or CCD set-up. The CCD is an internal element of the

camera and will be explained under ‘Non co-planarity of the CCD and target’.

There are other distortional errors in the image, some which are apparent and

can be observed, such as refraction of the lighting equipment in the Perspex

viewing window as well as some which cannot be detected by visual observation,

without close inspection.

~ 38 ~


5.6. Possible source of error in the analysis

5.6.1.Non co-planarity of the CCD and target

This refers to the normals of the CCD and target being on parallel planes. The

CCD or Charge- Coupled Device is a light sensitive chip in the camera, which

converts light into an analogue signal, which gets converted into a digital image,

which is observed on the computer screen. The dimensions of the CCD are

represented in pixels a ‘(u,v) co-ordinate system’ which directly correspond to

the u and v axis on the image. The face of the CCD should be vertical and so

should the viewing window. Therefore the normal’s of both of these planes

should be parallel. If the equipment is correctly assembled at the start of the

experiment then this should be the case, but as the experimentation begins and

the centrifuge spins the normal’s to the two surfaces can become misaligned.

The camera and its components experience increased self weight, in the same

way that the model does. This can cause the CCD and lens system to move out

of alignment especially as the centrifuge reaches higher g-levels. Since the

experiments completed in this report reach g-levels of up to 100-g, then this

becomes a significant source of error. The result of this error is to give a set of

data which has much higher displacement vectors of the soil than is actually

occurring. The increase in displacement can be very large as the two figures

below show.

~ 39 ~


Figure 5-13

Displacement vectors of the soil including the camera distortion

Figure5-14

Displacement vectors of the soil after being scaled up and compensating for

camera distortion

This figure shows how the movement of the camera is much larger than the

displacement of the soil. This has the effect of masking the true soil

displacements which are not easily detected without compensating for the

distortion. In these tests, the movement of the camera resulted in a recorded

displacements of up to 25 times the actual displacement of the soil.

5.6.2.Radial and Tangential lens distortion

Radial lens distortion is a feature of the camera lens whereby the light rays

coming from the target are deflected radially from the lens normal. This causes

problems for the CCD in trying to detect the exact origin of the source of the

light as it has become scattered. A second error arises when the camera has

more than one lens for the light to pass through. If the multiple lenses do not

~ 40 ~


have the same centres of curvature then the light rays will not be collinear which

creates a decentring distortion. This has both a radial and tangential distortions.

5.6.3.Refraction through viewing window

Much like looking at an object underwater where it seems closer to the surface

and at a different position to where it actually is. This is caused by light

diffraction through the medium, in the case of these experiments, this will be

through the Perspex viewing window. The degree of diffraction depends on the

thickness and diffractive index of the Perspex and the inclination of the incidence

rays.

5.6.4.CCD pixel non-squareness

This is small error that can be corrected by one stage in the image-space to

object-space transformation. It refers to the pixels of the CCD not being perfectly

square but only requires a simple linear scaling factor which can be applied

across the whole image.

Digital camera are prone to suffer significant internal distortion from the sources

above and therefore the broad assumptions that we detailed earlier, which

ignored these errors, cannot be used. The simple scaled transformation from

image-space to object-space cannot be used and a more detailed transformation

is required. A 14 parameter transformation is therefore used, developed from

work done by Heikkila and Silven (1997). This complex transformation attempts

to model every possible form of image distortion and correct them. This

transformation can be divided into six sets of parameters detailed in ‘Soil

deformation measurement using Particle Image Velocimetry (PIV) and

photogrammetry’ by White et al. (2003). These are;

1) Camera pose: six parameters to describe the translation and rotation

between the image-space and object-space coordinate systems.

~ 41 ~


2) Focal length, f

3) Principal point, (uo, vo): the pixel coordinates of the intersection of the

optical axis and the CCD plane

4) Radial lens distortion, (two parameters k1, k2)

5) Tangential lens distortion, (two parameters p1, p2)

6) CCD pixel squareness (α)

In addition to these parameters, the refractive index and thickness of any

viewing windows are included in the transformation.

5.7. Performance of GeoPIV

The performance of GeoPIV can be analysed by considering the accuracy and

precision of the results. Accuracy is defined as the systematic difference

between a measured quantity and the true value, whereas precision is defined

as the random difference between multiple measurements of the same quantity.

In general, the accuracy of the PIV analysis depends on the ability to convert

from image-space to object-space correctly. Errors arise when the conversion

ratios between image- and object- space are ignored.

To ensure that the answers that the PIV analysis produces are accurate it is

important to set the search zone to a large enough range to ensure that the

displacements of textured sand are within the boundaries of the search area, i.e.

GeoPIV cannot detect a region of sand outside of the area in which it is looking

for it.

The precision of the PIV analysis can be effected by a number of things;

a) The test patch size

b) Soil type / appearance

c) Movement distance (whether pixel size is greater or smaller than

displacements)

From work carried out by White et al. (2001a) and more extensively White (2002)

and Take (2002), it was found that the precision of the PIV analysis has a strong

correlation to patch size and less effected by the image content. Although a

~ 42 ~


larger patch size leads to improved precision, the number of measurement

points that can be contained within a single image is reduced. Larger patches

‘smear’ the displacement field in areas of high strain gradient. A compromise is

necessary.

Leapfrog is simple function of the GeoPIV analysis which dictates to the program

which two images to compare. The analysis run on this project uses the most

common Leapfrog value of one. This means that the GeoPIV will compare image

one with image two, image two with image 3, image (x) with image (x+1) etc.

until the final image is reached. For example, if leapfrog was set to two then the

GeoPIV would compare image one with image three, image two with image four,

image (x) with image (x+2) etc. until the final image. Leapfrog can be changed

to observe different trends in the soil deformation in this way

The performance of the PIV analysis can be link credited to the ability of the

user. Poor input images to GeoPIV will result in poor and incorrect output

displacement values. Simple precautions should be taken such as ensuring that

the image that has been captured is of good quality and not blurred or unfocused

and that the viewing surface is not sufficiently scratched or damaged to interfere

with the recorded displacements of the sand behind it.

6. TESTING & RESULTS

6.1. Test One

6.1.1.Test arrangement

In this experiment, the sand was pluviated to a height of 350mm. This height

was chosen so that the height of the sand and plate combined, did not exceed

the height of the box. The plane strain box has internal height of 400mm, and

leaving this 50mm gap was more than sufficient for the height of the plate as

well as having room to accommodate an extra weight on top of the plate in sub

sequent experiments if needed. The width of the plates was then determined

from knowing this height and using the graph of contours of equal vertical strain

~ 43 ~


derived by using the Boussinesq equation, (figure 2.3). By assuming that all

strains that are less than 10% of the maximum strain are negligible (Herndon

1990) and that the footing is infinitely long, the maximum depth of the sand can

only be approximately 6.3 times the width of the footing, b. This led to the

maximum footing width being,

350mm=6.3×b∴b=350mm6.3

=55.56mm

Therefore the first plate was cut to 55mm width.

One of the aims of the first experiment was to evaluate the possibility of running

two plates per experiment, so that twice the number of results could be attained

per experiment. Using again the contour plot and still assuming less than 10%

strain was negligible, a horizontal distance can be calculated for the region of

sand affected by the plate to this strain intensity. From the graph, at a horizontal

distance of approximately 2.1 b from the centre of the plate, the strain never is

greater than 10% of the total. Therefore, the contour line at 10% intensity is

approximately 4.2b wide. The internal length of the plane strain box is 700 mm,

and again, the boundary effects of the walls need to be avoided hence, a 50 mm

region of sand is given at each wall so that the boundary effects are exerted on

this region, which will not be used in the analysis. The resulting effective length

of plane strain box is,

700mm−(2×50mm )=600mm

If the first plate is 55mm wide, then the remaining region of unaffected sand is,

600mm−(4.2×55mm )=369mm

hence, the maximum width of the second plate could be

369mm4.2

=87.86mm

~ 44 ~


Although, the maximum width has already been defined as 55.56mm, so this

plate size cannot be used. The width of the second plate is an arbitary35mm,

which allows for 7% negligible strains in the vertical direction

Dept hof boxWidt hof plate

=350mm35mm

=10

∴dept hof box=10bcorresponds ¿≈0.07q

and less than 1% in the horizontal direction.

Region of unnaffected sandWidt hof plate

=369mm35mm

=10.54

∴widt hof sand=10.54b correspond ¿≈0.01q

6.1.2.The positioning of the plates

The position of the plates were calculated so that they were in the optimum

position for recording the results. This was as close to the centre of the

experiment as possible, without either plate severely affecting the displacement

vector field of the other. The distances were calculated by assuming that at less

than 10% strain intensity, the effects were negligible. Hence the distance

between the plates had to be at least,

2.1×b (first plate )+2.1×b(second plate)

¿>minimumdistance between plates=2.1×55mm+2.1×35mm

¿189mm

The minimum distance between the plates, imposed by the boundary conditions

(leaving a 50mm region of ‘unaffected’ sand) is,

~ 45 ~


2.1×b (first plate )+b( first plate )

2+2.1×b(second plate)+

b(second plate )

2

¿>maximumdistancebetween plates=2.1×55mm+ 55mm2

+2.1×35mm+ 35mm2

¿300mm

Note: the b2

term is introduced as the width of the area enclosed by the contour

lines is measured from the middle of the plate.

Each of the plates will be 30mm closer to the centre than the furthest possible

position they can be placed. This will aid the analysis, as the displacement

results will suffer from less distortion and error the closer they are to the centre

of the viewing window.

6.1.3.Results

The first test was run to investigate the viability of running two plates

simultaneously and to understand what kind of results future experiments should

yield. For this reason the centrifuge was only taken to 50-g as the test was only

to assess the trend and patterns of the results. With only the self weight of the

plates acting on the soil, small displacements were expected, but still showing

general trends and contours of equal stress. Figure 6-1 shows the contour plot

after the PIV analysis was run. There is little evidence that either plate caused

any additional settlement in the soil and the plot shows pretty uniform

settlement across the whole sample, caused by the increased self weight of the

sand which is getting compressed under its own weight at increased g-levels.

The lighter blue areas, representing displacements of between 0.06 and

0.08mm, could be caused by the presence of the plates as each area

corresponds to the position of each plate. Although, the difference in

displacements between these areas and the rest of the sample is so small, that

assuming this may be incorrect.

~ 46 ~


The red area of the plot at [x,y (525,75)] is caused by either a distortion caused

by either an imperfection on the Perspex or reflection from one of the LED’s. The

red area just above this is caused by an excess of sand that has built up on one

side when levelling the surface. Before the test, this was noticed but it was not

thought that it would affect the results of the testing. This was a correct

assumption, as although the plot looks dramatic, the red regions correspond to a

soil movement of only 0.18mm, which is a very minor movement. It can also be

noticed that below approximately 200mm depth, there is virtually no movement

of the sand.

Figure 6-15

Contour plot of displacement of magnitude 50-g. First Test

It is apparent from this test that the self weight of the plates alone is not

sufficient to cause any significant displacement of the sand.

6.2. Test Two

6.2.1.Preparation

In preparing the second test there was no need to re-pluviate the sand as the

displacements were small and hence sand deformations were still completely

~ 47 ~


elastic as the sand had been taken nowhere near to its failure point. The result of

this is the sand sample returned to its original state, with no residual strains.

Since the first test yielded such small displacements, additional weights were

added to the plates in an attempt to create larger displacements in the sand. The

additional weights were an extra 2.000kg on the 55mm plate and an extra

1.000kg on the 35 mm plate. The mass of these weights were weighed with

accuracy to three decimal places, so that the exact weight of the system was

known. The two plates were reinserted in the same position as they were as

there was no indication of interaction between the strain vectors of the two

plates in the first experiment. The additional weights were attached to a foam

pad with a strong adhesive material which was then securely attached to the

plate using the same adhesive. When attaching the weights to the plates, it is

important to ensure that the weights were perfectly central so no torsion effects .

For this test the centrifuge was taken to 80-g to increase the apparent weight

and dimensions of the plate (with the additional weight attached). The centrifuge

could still not be taken to its limits or to 100-g as expected due to a new piece of

equipment installed on the centrifuge that had not been tested to that g-level.

6.2.2.Results

The resulting contour plot from the PIV analysis is shown in figure 6-2. The plot

shows regions of soil displacement that are much larger than the previous

experiment, but still small as the max displacement is only 0.2mm. Due to these

larger soil displacements, the imperfections in the viewing window are more

clearly seen. These are the dark blue regions shown in figure 6-2 as the sporadic

blue patches above 200mm on the Y-axis and the large blue region below this

point shows little or no movement. This shows that with the current weight on

the plate, no significant strains are developing in the soil at depth.

~ 48 ~


Figure 6-16

Contour plot of displacement of magnitude 80-g. Second Test

6.3. Test Three

6.3.1.Preparation

The first two tests yielded very poor results, which was due to the force caused

by the weight and the plates being small, even at increased g-levels. It was

obvious that picking up basic strain patterns and trends with small weights was

difficult and to achieve this, larger weights needed to be added. The sand was

re-pluviated in case the previous test caused any residual strains to remain in

the soil and an larger weight was prepared. The additional weight to be placed

onto the plate was 5.000kg, again measured precisely and the smaller plate was

removed. Only having one plate on this test allowed the plate to be placed

directly in the centre of the plane strain box, without it interfering with the

results of another plate.

~ 49 ~


6.3.2.Results

The analysis of this test was only run over the top half of the sample as below

this point, only very minor displacements are observed. This would aid the

analysis and produce a better contour plot as the deviation between the

maximum and minimum displacements would be smaller. With increased depth,

the change in magnitude of displacements get smaller hence displaying the

slight change in size would require a more complex plot. The resulting

displacement vectors are shown in figure 6-3, which does show larger vectors

directly beneath the plate which becomes smaller with increased distance from

the plate, which is what would was expected.

Figure 6-17

Figure showing displacement vectors from of magnitude 80-g. Third Test

6.4. Test Four

~ 50 ~


Test 3 produced much better results with larger displacements showing the

trends that were expected in the literature review. Although, there is many

distorted regions caused by poor lighting and imperfections in the viewing

window. The aim of the fourth test was to improve on these results by improving

the experiment set-up and quality of analysis.

6.4.1.Lighting

The results from the previous test showed patches of inconsistency where the

LED lights were reflecting of the Perspex. The reflection of the LED’s severely

distorted several patches on the image and sub sequentially, damaged the

ability of the GeoPIV analysis to run accurately at these points. Prior to this

experiment, the results have been interpolated in the MatLab environment or

removed completely if the interpolation was unsuccessful. In general, the

disturbance caused by lights has been derogatory to results of the experiments.

Therefore for this test, a new lighting rig was installed with the aim to minimise

the disturbance caused by the light on the results. Instead of the LED lights,

three fluorescent tubes were installed to get a more even distribution of light.

Difference combinations of the lighting were set up and photographed, as if the

experiment was running. The combination which gave the most detail and

textured sand was chosen. This was a combination of a 22 Watt fluorescent bulb

along the base of the model, and two 9 Watt fluorescent bulbs attached to the

top of the front of the box. On each side there are three, 1 Watt, high intensity

LEDs, which were the same ones that were used in the previous experiments.

The lighting in this arrangement provided a much more even illumination of the

viewing window compared to previous experiments.

~ 51 ~


Plate 6-4

Comparison between old and new lighting. Left: an image from first experiment,

Right: an image from fourth experiment with new lighting set up

6.4.2. Perspex

Further to the improvements in the lighting was the changing of the sacrificial

Perspex sheet. This sheet is only a few millimetres thick and installed to save the

thicker, more expensive sheet of Perspex behind it. The sacrificial Perspex sheet

is likely to become scratched from sand and equipment inside of the box and is

designed to be quick and easy to replace. Plate 6-2 shows an image of the

Perspex sheet and figure 6-4 shows the result of using the scratched sheet in the

GeoPIV analysis.

~ 52 ~


Figure 6-18

Contour plot of displacement, magnitude 80-g. Data from second test

Plate 6-5

Image of Perspex sheet, notice large scratch across centre of sheet and many

other marks and imperfections

The regions circled in red on plate 6-2 and figure 6-4 show the scratch on the

Perspex and the result of the scratch in the analysis.

The new Perspex sheet had a new set of control points mapped onto it. These

control points were at approximately 100mm centres, starting at 50mm from the

sheet edge. This change in the number and positioning of the control points

gives an increased number of control points in the centre of the sheet, which

should allow for a greater accuracy when modelling movements of the control

points, as there is naturally less distortion at the centre of the image than at the

edges. Also, the camera can be zoomed in to capture a smaller area of the soil,

with the aim of increasing accuracy, and still include control points in the image.

The ultimate aim of using a new Perspex sheet is to eliminate disturbance

caused by the scratches across the viewing window.

~ 53 ~


6.4.3.Changes to Experimentation Method

The analysis of these test results were run twice, once using the conventional

methods and secondly with a new method of tracking the control points

introduced by Dr Alec Marshal a new lecturer at the University of Nottingham

with expertise in geotechnical centrifuge technology. This technique used a

Mylar sheet, which is a very precise grid of 3mm diameter, circular dots with

centres exactly 6mm apart. See figure 6-5.

Array of 480 3 mm diameter dots, located at exact 6 mm centres

Figure 6-19

Mylar sheet

This grid of dots is very precise and can be used to accurately give all positions

of control points from one reference point. One of the control points, normally a

corner point, is labelled (0,0) in object-space, (x,y) coordinates in mm, and all

other control points are referenced to this one point. By knowing the exact

position of one control point in object-space, when tracking the control point’s

precise movement distances can be established. The exact position of the

reference control point in image-space can be determined in pixels, from an

image at 1-g, when the centrifuge is stopped and there is no camera lens or CCD

~ 54 ~


distortion. This point in pixels can then be called (0,0) in object space in physical

(x,y) coordinates. After the centrifuge testing, the position of the reference

control point at higher g-levels can be found in pixels. Knowing the original

position and the final position of the reference control point in pixels, and the

original position in (x,y) coordinates, the final position of the control point can be

found in (x,y) coordinates, in mm. This same procedure can be implemented for

all the control points, as the original positions are all know down to an accuracy

of 0.001mm provided by the Mylar sheet. The position of all the control points

are reference back to the first control point and so can all the image-space pixel

distances.

The advantage of doing this process is that all movements of the camera lens

and CCD components can be modelled in all directions. The MatLab program is

designed to compensate for the both rotational and transverse movements of

the camera lens and CCD by calculating both a transverse and rotational

components of the movement of the control points.

Note, the actual position of the control points does not move, it is only the

apparent position that changes on the images due to distortion.

Figure 6-6 attempts to show this.

Figure 6-20

Showing movement of control points due to camera distortion

~ 55 ~

x , u

y , v


The solid circular dots in the figure show the original position of the control

points and the dashed circular dots show the apparent position on the last image

of the image series. The movements have been exaggerated for demonstration

purposes.

In conclusion, the Mylar sheet should increase the precision and accuracy of the

experiment by reducing error induced by camera lens and CCD distortion. It

achieves this by allowing the operator to deduce an accurate conversion factor

for the image-space to object-space transformation.

6.4.4.Test Procedure

The sand was only pluviated up to a height of 280mm. This was to avoid

interference from the reflection caused by the new lighting arrangement. This

depth of sand was sufficient for the test as from analysing previous test results it

is apparent that the displacements and hence the soil strains quickly dissipate

with depth. This meant that boundary effects of the base of the plane strain box

would not influence the displacement results. The plate was placed in the centre

of the box due to the light disturbance still caused by the LED at the edge of the

viewing window (see Plate 6-2). This LED disturbance at the edge of the viewing

window was out of the anticipated region of high stress and in a region where

the GeoPIV analysis would not be running so this would not be a problem.

The centrifuge was taken up to 100-g for this experiment to fully test the

changes made to the set-up and analysis in order to achieve the strain patterns

that have been expected.

6.4.5. Results

As discussed, the test results were analysed twice, once by the conventional

method, the same as the previous test and once using the accurate positions of

the control points.

~ 56 ~

x-axis, mm

x-axis, mm

y-a

xis, m

m

y-a

xis, m

m


Figures 6-6 and 6-7 show the contour plots for the data from test four, analysed

firstly without and then with the exact positions of the control points, using the

Mylar sheet. The contour lines or lines of equal stain on figure 6-7 are very well

defined and there are very few erroneous results. The plot resembles what was

expected in section 2.3 of the literature review and figure 2-3, which shows

contours of equal vertical stress beneath a foundation in a semi-infinite elastic

solid defined by the Boussinesq equation.

Figure 6-21

Fourth test. Contour plot of displacement, magnitude 100-g.

~ 57 ~


Figure 6-22

Fourth test. Contour plot of displacement with use of Mylar sheet, magnitude

100-g.

The small, circular dark blue regions on figure 6-8 are the locations of the control

points, which were not removed from this plot.

7. DISCUSSION

7.1. Improvements in testing

The improvements in the results comparing test one to test four are vast.

Compared to figure 6-1 (from the first test), figure 6-8 (from the fourth test)

shows much more well defined contours of equal strain. This is much closer to

what was expected from the research, see section 2.3 and figure 2-3, where the

maximum displacement vectors and hence strains are found directly beneath the

plate which dissipate with depth and distance.

7.2. What is happening in the soil

~ 58 ~


What was expected to be observed was the soil moving towards failure passing

through elastic stage to a plastic failure. The results actually showed something

slightly different to this. As the g-level was increased, to simulate a larger weight

being placed on the soil, the net strength of the soil also increased on a linear

scale, this concept is further discussed in section 3.5 and section 4.6.2. This

meant that any increase in force by increasing the g-level was counteracted by

an equivalent increase in soil strength. Therefore to fail the soil by this method

would require the load equal to the bearing capacity of the soil to be placed on

the model prior to the start of testing. The centrifuge could then be spun up to

recreated the same dimensions of a prototype.

The displacements seen here are most possibly all elastic and would dissipate

when the centrifuge was stopped. Therefore the weights added in these test

have been insufficient to cause shear failure in the soil. The displacements

observed are caused by the settlement or consolidation of the soil and the

presence of the plate intensifies the process which causes larger displacements

under the plate.

Although the net strength of the soil increases with the g-level and the soil is not

failing, the strain patterns are still valid for a prototype geotechnical situation.

Since the strain properties of soil at any g-level has a scale factor of one, the

strain vectors model the same strains that would be found in the field.

In many of the tests, the displacement vectors dissipated at much shallower

depth than was expected. This could be due to the frictional boundary effects of

the Perspex on the sand grains or due to the fact that the plate is not infinitely

long as assumed in the calculations. The ratio b / L should equal zero for the

infinitely long case but in actual fact, it only equals approximately 0.25. This

would have the effect of making the displacements smaller and hence be more

easily dissipated throughout the soil. This change in assumption would also

increase the calculated bearing capacity of the soil, meaning that even if the

sand was statically loaded with the value calculated in section 3.4, the soil might

not reach its failure criterion.

~ 59 ~


8. FURTHER STUDY

The tests carried out in this report are very basic and the main focus has been on

improving the testing procedure and analysis of the results. Therefore the scope

for further work on this project is immense. This section aims to highlight and

briefly explain the tests that could be carried out supplementary to this project.

8.1. Foundation design and limits

Ultimately, the base of any buildings foundation is the ground soil and the

foundations to a building are paramount to the strength and the survival of that

building. Therefore the effects of foundations on the soil with all associated loads

need to be well understood. Modelling a building’s foundation in the centrifuge

with dynamic loading can accurately represent real-life conditions and help

engineers understand the effect that the foundation has on the soil. It was

discovered in this report that simple static loading is not sufficient for this.

8.2. Tunnel & buried structures

Deep buried structures, such as pipelines and tunnels experience huge forces

acting on them from the weight of the soil above. The strength of the buried

structure need to be able to resist these forces and remain structurally stable.

LVDT’s (linear variable differential transformer) and the conventional PIV analysis

discussed in this report can be used as well as monitoring the distortion from

inside the buried structure using strain gauges.

8.3. Further improvements to centrifuge modelling

~ 60 ~


The extent that the experimental errors highlighted in this report have on the

results is not fully known. There are improvements which could have been

investigated which have not been covered.

8.3.1.Investigation into the effect of grain size

By testing different sized sand grains at different g-levels, it is possible to

examine what effect the grain size of the sand under the same conditions. This

could be done by testing a larger grain size sand at a lower g-level, with a larger

plate size and weight with a smaller grain size sand at a higher g-level with a

smaller plate size and weight. The strain contours should be similar and could be

compared to expected strain patterns

8.3.2.Frictional effects of Perspex and walls of plane strain box

This can be investigated by running the regular PIV to capture displacements at

the viewing window and installing LVDT’s to record soil movement in the sample

at varying depths from the centre of the plane strain box. By comparing the

displacement results, it is possible to evaluate the interference caused by the

boundaries.

Further to this, different materials instead of the Perspex sheet could be used or

applying a lubricating material to the face of the Perspex to try and reduce the

sheet friction.

8.4. Investigations into geotechnical structures

An embankment, cliff or hillside could be modelled and investigations into failure

zones caused by environmental influences such as rain, heat or ice. Investigation

could include inducing landslips in hills or excess settlement caused by

~ 61 ~


weakened wet embankments. Also the use of geogrids, grouting or retaining

walls could be investigated for these cases.

8.5. Non geotechnical investigations

The geotechnical centrifuge is a multipurpose facility and is not only restricted to

geotechnical investigations. The scale effects would still apply if modelling a

structural member of a building or simple structure. Using dynamic loading and a

range of analysis, such as the PIV analysis, strain gauges or LVDT could be used

to model the twisting, bending or distortion of a steel beam.

9. REFERECENCES

Craig, R. F. 1997. Soil Mechanics 6th Ed. Chapman & Hall.

Craig, W. H. 2001.The Seven Ages of Centrifuge Modelling. University of

Manchester.

Hansen, J. B. 1968. A revised extended formula for bearing capacity, Danish

Geotechnical Institute Bulletin, No. 28

Herndon, R. L. 1990. Engineering and Design - Settlement Analysis. U.S. Army

Corps of Engineers.

Jumikis A. R. 1966. Thermal Soil Mechanics. Rutgers University.

McCarthy, D. F. 1998. Essentials of Soil mechanics and Foundations, 5 th Ed.

Prentice Hall.

Simoni, A. and Houlsby G. T. 2004. The direct shear strength & dilatancy of sand-

gravel mixtures. Springer Netherlands.

~ 62 ~


Som, N. N. and Das, S. C. 2004. Theory and Practice of Foundation Design.

Prentice-Hall

Taylor, R.N. 1995. Geotechnical Centrifuge Technology. Chapman & Hall.

Terzaghi, K. and Peck, R. B. 1967. Soil Mechanics in Engineering Practice, 2nd

Ed. John Wiley and Sons,

Vesic, A. S. 1973. Analysis of ultimate loads on shallow foundations . Duke

University

White D. J, et al. 2003. Geotechnique 53, No. 7.

White D.J. and Take W.A. 2002. Particle Image Velocimetry (PIV) software for use

in geotechnical testing. Cambridge University Engineering Department (CUED).

http://www.hammerthrow.com. 2005. Youth Handbook. Date accessed

23/03/2010

10. BIBLIOGRAPHY

10.1. Book Sources

Atkinson, M.F. 2004. Structural Foundations Manual 2nd Ed. Spon Press.

Bowles, J.E. 1988. Foundation Analysis and Design, 4th Ed. McGraw Hill.

Calabar A. F. et al. 2009. Constitutive modelling of Leighton Buzzard sands using

genetic programming. Springer-Verlag London.

Ellis, E.A. et al. 1994. Centrifuge and Analytical Studies of Full Height Bridge

Abutment on Piled Foundation Subjected to Lateral Loading. Cambridge

University Engineering Department (CUED).

Japanese Geotechnical Society. 1998. CD-ROM Library on Geotechnical

Centrifuge

~ 63 ~


Lee, C. F. et al. 2001. Soft Soil Engineering. Swets and Seitelinger B. V.

Madabhushi, S. P. G. 1994. Stress wave propagation in a centrifuge model

Meguid, M.A. et al. 2007. Physical modelling of tunnels in soft ground: A review.

McGill University.

Milovic, D. M. and Tournier, J. P. 1971. Stresses and displacements due to

rectangular load on a layer of finite thickness, Soils and Foundations Volume 11.

Japanese Geotechnical Society.

Reddish, D. J. et al. Centrifuge modelling of rock cavity collapse mechanisms.

Schofield, A. N. 1998. Geotechnical centrifuge development corrects Terzaghi’s

errors., Cambridge University Engineering Department (CUED), (lecture to the

Tokyo Conference of TC2, 23 September 1998).

Turner, P. Geotechnical Centrifuges. www-g.eng.cam.ac.uk, 199?

Valsangkar, A.J. 1987. An Experimental investigation of factors affecting

penetration resistance in granular soils in centrifuge modelling. Cambridge

University Engineering Department (CUED).

3rd World Congress on Industrial Process Tomography, Canada 607

Use of ERT in a Geotechnical Centrifuge

Friederike K Günzel, Colin J Fyfe, Michael C R Davies, C. R.

Coelho, P. A. L. F. et al. 2003. Boundary effects in dynamic centrifuge modelling

of liquefaction in sand deposits. University of Washington.

~ 64 ~


10.2. Internet sources

University of Bolton. Stress under applied loads.

http://data.bolton.ac.uk/staff/phm2/files/Sem2/J2%20PJ3%20Geotechnics/Stress

%20and%20Found%20Dist%20Session%2002%20V1.00%20Feb2009.pdf.

Accessed January 2010

http://eprints.brighton.ac.uk/1655/01/Banff_paper.pdf.

http://www.atypon-link.com/TELF/doi/pdf/10.1680/geot.53.7.655.37392?

cookieSet=1 -

http://www.earth.cardiff.ac.uk/research/geoenvironment/pace/CH31/

GeotechnicalCentrifugeModelling.htm

http://www.geotech.cv.titech.ac.jp/~cen-98/Library/. Accessed October 2009.

Harris, C. and Leutchg, M. Geotechnical Centrifuge Modelling - Scaled Physical

Modelling In The Geotechnical Centrifuge.

http://www.geotech.cv.titech.ac.jp/~cen-98/Library/3_EQUIPM/3_2_IMPO/

SCALING1.HTM. Acessed January 2010

~ 65 ~


APPENDIX A

~ 66 ~


Risk assessment Chart

1 - Individual 2 - Group 3 - school

2. Construction of Model

3. Loading Payload

Manual Handling 2 Use stacker

All staff in control room while test in progress

Dust / Sand - respitory

2 Restrict activity to enclosed room with extractor to outside. Operator to wear powered respirator

Dust / Sand - eyes 2 Restrict activity to enclosed room with extractor to outside. Operator to wear powered respirator

Personnel inside chamber during use

3 Physical inspection of chamber

Loss of element of package through roof apperature

2 Metal grill to contain secondary impact

Noise 2

Low

Low

Low

Low

Low

Low

1

2

2

1

1

1

Authorised Operator

Authorised Operator

Authorised Operator

Authorised Operator

UoN Authorised Supervisor, Authorised Operator

Low 2 Broadbent & Sons Ltd.

Low 2 UoN Authorised Supervisor, Authorised Operator

Authorised Operator

1. Operation of Centrifuge

Failure of Machine - Structural elements, rotor, swing, machine

3

Detachment of Payload

3 Assure box screws are fully tightened and box is attached securely to swing

Controlled Design of Machine

Action ByPeople Endangered

Task Hazard(s) Harm Rating Control Measures Likliness

~ 67 ~


Additional Information

This is a checklist to accompany the risk assessment forms, detailing activities that do

not fit into one of the listed categories or to give more detail on the safety risks and

precautionary measures

Payload

Checked by authorised approver

Mass of payload within operational limits of machine; 500kg

Payload securely fastened to swing

Counterweight positioned at required distance from crossbar

DAS

Physical inspection that cables and hoses correctly terminated in cabinet

Physical inspection that DAS doors are closed and locked

Machine and chamber

Physical inspection that no personnel are present in chamber before the doors are

locked and the machine is turned on.

Physical inspection that there are no loose objects in the chamber and that there are

not hanging objects on the arm

Chamber door closed and locked before experimentation begins

CCTV cameras functioning correctly

~ 68 ~


During Test

Never leave machine unattended. If it is necessary to leave the area, arrange suitable

and authorised ‘cover’. This includes toilet breaks

Stop test if any unusual circumstances start occurring. Never be in doubt

Model

Ensure model and model box can be taken to the required g-level without any

structural failure

Ensure model is concurrent to design and assumptions

If any external elements are being used, ensure that they have been tested to

withstand forces that are to be expected at the required g-level

Calculations

Approved by authorised approver

State calculated payload mass, Mp, (kg)

State calculated effective radius, Rp, (kg)

State calculated payload, MpRp, (kg)

State theoretically ideal counterweight position x, (mm)

State actual counterweight position x, (counterweight to crossbar), (mm)

~ 69 ~


Note: Before the running of any experiment, check with authorised supervisors that

machine is fully operational and that no faults or possibilities of any part machine

failing are known of and that the machine is safe to run.

~ 70 ~


Checklist

~ 71 ~


COSHH Assessment Form (2 Pages)

~ 72 ~


~ 73 ~


APPENDIX B

~ 74 ~


Diary

Week Commencing 5th October 2009

Although I had not settled on a firm project title, I started to preliminary

research into Geotechnical Centrifuge Modelling

I was attending all of the timetabled lectures until I had decided which

ones to enrol on for the coming year


Met with my tutor, Dr Dave Reddish to discuss how to approach the

project and started to discuss possible project titles. I wanted to do

something different from what was offered so that my work was of more

use than something that had been already done.

Dr Reddish provided me with a paper, ‘Centrifuge Modelling of Rock

Cavity Collapse Mechanisms’ which he himself had part written.

I continued my research into Geotechnical centrifuge and loaned three

books out from the library on soil mechanics and the foundations


Continued research into centrifugal theory and mechanics of foundations

on soil

Met with Dr Reddish and suggested project title which were we both happy

for me to proceed with. The title was ‘The effect of strip foundations on a

homogeneous soil sample using the static loading in the Geotechnical

Centrifuge’.

Wrote preliminary aims and objectives and writing up some of the

literature that I had read


Met with Dr Reddish early who introduced me to Mr Craig Cox, who would

be assisting me with the centrifuge testing

Dr Reddish and I discussed the research that I had found and what results

I was expecting and trying to prove. Discussed in particular the Bousinesq

equations.

~ 75 ~


Discussed with Mr Cox the procedure in centrifuge testing and got to fully

understand the testing process. Also got my first exposure to the

machinery and equipment that I would be using

Wrote up a preliminary aims and objectives and drafted a title page

Week Commencing 2th November 2009

Continued with research and writing the literature review. Found several

Google book references such as ‘Geotechnical Centrifuge Technology’ by

R. N Taylor

Arranged a date with Mr Cox for when I could build and test the first

experiment so that I would have a set of results for the Viva

Designed the first test, calculated the size of the plates and required

depth of the sand

Met with Dr Kim Elliot to try and get a reasonable weight to simulate a

medium sized building and an approximate size of the foundations. Used

the information provided in design the first test


Pluviated the sand for the first model to be tested later in the week. Had

to Pluviate the sand twice as first time I did not feel that the sand was as

evenly distributed as it could be and that it might adversely affect the

results of the test.

Finalised dossier for hand-in date and presented it to Dr Reddish so that

he could give me his opinion on it

During the meeting, we also discussed the progress of the testing

Towards the end of the week, I ran the first experiment


Ran the analysis on the results from the test and began to evaluate the

results for inclusion in the Viva

Met with Mr Cox and after analysing results and realising why they did not

yield the result that I was expecting, I quickly designed the and arranged

to run another test for later in the week

Prepared for the Viva and produced the powerpoint presentation and

presentation prose to learn

After the Viva, I ran the second test and started the analysis

~ 76 ~



Continued the analysis of test two and evaluated the results

During this week, I spent a lot of time on the coursework for the Coastal

and Business modules


Now that I had general understanding of the processes involved in

centrifuge testing I started to write an initial methodology

Week Commencing 7th December 2009

Was away for personal reasons and therefore could not work on project

Week Commencing 14th December 2009 – 25th January 2010

During these weeks, no progress was made on the dissertation as they

were designated to revision for my January exams

Week Commencing 25th January 2010

After the exams period was over, I re-read through the research that I had

acquired and the interim dossier. I was grateful to Dr Rick Munro for

providing such good feedback on my interim dossier.

Spoke with both Dr Reddish and Mr Cox to become re-acquainted with the

project and experimentation

Week Commencing 1st February 2010

During this week I researched in depth past papers on centrifugal

technology

I wrote up the changes to the interim dossier as suggested by Dr Munro

Week Commencing 8th February 2010

Met with Mr Cox to discuss possible times to run the next test.

Unfortunately, due to his own commitment and other users of the

centrifuge I was not able to run a test this week. He kindly agreed to

explain to me fully how the analysis works and the commands that need

to be input. I was keen to be able to run the analysis by myself by the end

of the project

~ 77 ~


Looked over previous tests and started to design for the third test

Continued to expand on the interim dossier in preparation for submission

in the final report

Week Commencing 15th February 2010

Met with Dr Reddish to discuss progress on the report

Received an email from Mr Cox containing two very useful documents on

the GeoPIV software. Started to read through these and understand

exactly how the analysis worked

Week Commencing 22nd February 2010

Started to write up a report about how MatLab was used in the analysis of

the tests

Designed the third test

Arranged to run the third test the following week when there was an

appropriate time

Week Commencing 1st March 2010

Met with Dr Reddish to discuss progress on project. Showed him the

MatLab piece that I had written and explained that I had made all the

changes to my interim dossier. Also discussed the results that I had

already achieved and what I wanted to achieve in the rest of the project.

Pluviated the model and ran the third test

Started the analysis

Week Commencing 8th March 2010

Continued the analysis of the third test

Had geology coursework due in this week which consumed a lot of the

time that I had set aside for project work

Completed the analysis and discussed results with Mr Cox


In order to improve analysis, a new lighting system was bought and

started to be installed on the centrifuge. There were many problems in

setting up the lights with the right distribution of light evenly across the

~ 78 ~


whole screen. Photos were taken to assess the quality of each

combination.

Pluviated the sand for the fourth test in preparation for whenever the

lighting rig was fully set-up

Modified methodology and combined all my work that I had done for the

final report

Also started to write up the testing procedure for each individual test

Week Commencing 22nd March 2010

During this week, a lot of time was dedicated to other coursework

commitments, such as business, geology and soil mechanics

Met up with Mr Cox to run the test. The final light was being installed but it

got cracked when securing it to the centrifuge. Had to postpone test while

a new light was bought. Sub sequentially a metal plate was attached to

the light case and small wooden block were placed under the plate so that

the light was not in direct contact with the centrifuge.

When the lighting was finally ready and when the test ran, it had to be

quickly stopped due to problem with the centrifuge. These included,

o The camera disconnecting from the computer

o Lighting cables coming unplugged as insufficient slack had been

given to adjust for increased distance to model during test

o The test was again postponed for the following week


Met with tutor and explained problem that I had experienced during

testing. A decision was made to change the title of the project to

‘Improving techniques and practices on the Geotechnical Centrifuge at the

University of Nottingham and the Nottingham Centre for Geomechanics’.

The fourth test was finally run

Further researched into the soil properties in preparation for further write

up

Started writing the introduction section explaining what a centrifuge is and

its uses

Week Commencing 5th April 2010

~ 79 ~


Analysis of fourth test. I attempted to run the MatLab without instruction

for Mr Cox with varying success. I was remotely logging in to the

centrifuge from another computer as there were other people using the

centrifuge.

During this week, I first met Dr Alec Marshall. He introduced the concept of

using a Mylar sheet in the PIV analysis to accurately plot the control point

positions.

Finished the introduction sections for the final report


I arranged a meeting with Dr Marshall so that I could understand fully the

advantages of using the Mylar sheet and how it was used in the analysis.

Also discussed general progress on the project and the quality of the

results that I had already got.

Was waiting for Dr Marshall to provide the exact positions of the control

points so that the analysis could be run with again with these positions

known

Calculated and wrote up the Bearing Capacity of the soil section and

continued work on the methodology. Also continued the write up on the

individual tests

After Dr Marshall provided the control point locations, the analysis of the

fourth test was run again yielding some very positive results.

At the end of this week, whilst transferring files between the University

computer and my home, my USB flash drive broke and I lost all the work

that I had done up to this point, apart from the interim dossier. I informed

the University but unfortunately it was a matter that they could do nothing

about. I sent the USB off to a data recovery company to see if it was

repairable. I continued work regardless and wrote up the results of the

tests.


Found out that the USB was irreparably damaged and that I had to rewrite

all that I had lost. Managed to recover a few documents which came to

about a fifth of what I had previously written.

Began rewriting what I had lost

Met with Dr Reddish to discuss final approach to project

~ 80 ~


Spoke with Mr Cox to investigate the possibility of running another test,

but again, unfortunately it was difficult to arrange a time before the hand-

in date of this report


Met with Dr Reddish who looked over work that I had rewritten and was

able to give me prompt feedback

Continued to write report and was able to almost finish and proof read

over the weekend

Week Commencing 3rd May

Added final documents to the report

Finishes and hand in

~ 81 ~


APPENDIX C

~ 82 ~

Before Collision:Bullet has a mass, m , velocity, v and momentum, p= mv.Block has mass, M, velocity, V =0 and therefore no momentum

Instant of Collision:Combined bullet and block mass, m+M, an unknown velocity, but has momentum equal to that of the bullet before collision, p=mv.

After Collision:Pendulum swings up and kinetic energy is turned into potential energy. Height of ‘swing up’ and oscillation time can be measured and a momentum, p calculated.


Ballistic Pendulum

A ballistic pendulum harnesses the concept of conservation of momentum which

Benjamin Roberts used to ascertain for the first time the velocity of a bullet. The

experiment was very simple, a shot of known mass was fired from a musket into

pendulum of known mass. Using conservation of momentum and the period of

the oscilation, Roberts was able to calculate the momentum of the pendulum

which would be equal to the momentum of the bullet, before the collision. The

velocity of the bullet is then easily calculated. The figure below attempts to

explain how a ballistic pendulum works.

~ 83 ~


APPENDIX D

~ 84 ~


Matlab List of Commands

This list of commands is specific for use in testing using the Centrifuge at the

University of Nottingham. All MatLab commands appear with >> before the

command which is input to MatLab.

Before starting the analysis, ensure that the directory is correct by typing,

>>cd C:\GeoPIV

Collect all the images in the same folder, does not have to be the above

directory and label them image_01 to image_xx. Modify the launcher file to

coincide with the series of images to be analysed and the mesh to be created.

e.g.

Create the mesh of patches in which the PIV analysis will search for the regions

of textured sand.

>>GeoMESHuv8(‘Name of new MESH’, size of square patch, separation of patch)

E.g. GeoMESHuv8(‘example_mesh.txt’, 50, 50)

This prompts the operator to select the first image in the series and create the

mesh on this image. Once the mesh has been completed press the return key.

Run the GeoPIV analysis on the series of images. Ensure that the launcher file

and mesh file are in the C:\GeoPIV folder and that the MatLab is also in this

directory.

~ 85 ~

Name of Mesh to load. (Just created)

Size of the area around the patch in the

succeeding image to search for regions of similar

textured sand

Range of images to run analysis over

Directory location of images


>>GeoPIV8

This command prompts the operator for the launch file, which should be

prepared prior to testing and when selected, the PIV analysis then starts to run.

Once the analysis has finished, a series of PIV outfiles will be created in the form

of ASCII text files for each translation between subsequent images. This data

needs to be extracted and combined for analysis. Change back to the C:\GeoPIV

directory and run

>> uvdata=consolidate8

This extracts the data from the ASCII files and stores it under the variable name

uvdata. This data then needs to be compensated for camera movements and

distortional errors. Produce copies of the whole series of images, in the same

directory that they are and give all the copies the prefix or suffix cp. This is to

ensure that the PIV outfiles for the first analysis are not overwritten. To

compensate for distortional effects, the control points need to be tracked. This is

done with the command

>>conpoint_patch(‘Name of control point’, file name of first image, patch size,

number of points)

E.g. conpoint_patch(‘example_meshcp.txt’, C:\GeoPIV\images\image1.jpg, 20,

20)

This brings up the image specified in the command line. Zoom in to the first

control point and click in the centre of it. Zoom out and repeat this process for all

the control points.

Then run the GeoPIV analysis on the movement of these control points. The

launcher file needs to be modified to cover the new range of images (with the

prefix of suffix cp) and to apply the new mesh (e.g. example_meshcp.txt) and

saved with a name to that effect (e.g. geoPIV_launcher_examplecp.txt). Again

ensure that the MatLab is in the C:\GeoPIV directory

>>GeoPIV8

This will prompt the operator to select the launcher files which is has just been

created. After the analysis has completed, it will have produced another set of

~ 86 ~


PIV outfiles for the control points. The data needs to be extracted from these

files.

>>cpdata=consolidate8

The lens movements now need to be removed from the original data.

>>uvdatac=camera_pos_comp2d09(uvdtata,cpdata)

This removes the control point movements from the soil displacement data. To

interpolate and erroneous results use

>>uvdatac=geoWILDcc1(uvdatac, image x, image x+1, scale factor)

E.g. uvdatac=geoWILDcc1(uvdatac, 1, 2, 5)

Repeat this stage, removing all wild vectors from the each image translation.

Using the command,

qquvdatac(first image, last image, scale factor)

E.g. qquvdatac(1, 11, 10)

the displacement vectors from the first to the last image can be viewed. This can

give the operator a good indication of how successful the test has been and an

indication on the quality of the results.

The final stage is to produce a contour plot of the results

>>uvcontour

Terminology

MESH and PATCHES

A Mesh is a grid of patches.

GRAVITY

1-g or 1 gravity corresponds to the normal gravitational pull of the earth (9.81ms -

2)

~ 87 ~


PHOTOGRAMMETRY

Photogrammetry is the making of precise measurements from photographs

ASCII

ASCII (American Standard Code for Information Interchange) is the most common

format for text files in computers and on the Internet. In an ASCII file, each

alphabetic, numeric, or special character is represented with a 7-bit binary

number (a string of seven 0s or 1s). 128 possible characters are defined.

UNIX and DOS-based operating systems use ASCII for text files. Windows NT and

2000 uses a newer code, Unicode. IBM's S/390 systems use a proprietary 8-bit

code called EBCDIC. Conversion programs allow different operating systems to

change a file from one code to another.

(definition from:

http://searchcio-midmarket.techtarget.com/sDefinition/0,,sid183_gci211600,00.h

tml#)

~ 88 ~

Date post:	27-Jul-2015
Category:	Documents
Upload:	stoneagecaveman
View:	449 times
Download:	3 times

Improving Techniques and Practices on the Geotechnical Centrifuge. Including literature review

Documents