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Investigation of the Collapse Mechanism of Open Eaied Piles during Instaltation
June 1996 G.Kramer
Geotechnical Laboratory Delft University ofTechnology
Investigation of the Collapse Mechanism of Open Ended Piles during Installation
Author: G. Kramer
By order o f Shell Intemational Exploration & Production B .V.
Supervisors:
Prof dr.ir. A Verrui j t
Dr.ir . H.G.B. Allersma
Dr. ir. C . W . M Sitters
Ir. R.A.W. Dubbers
Ir. K . G . Bezuyen
De l f t University o f Technology,Faculty o f C i v i l Engineering,
Department o f Hydraulic and Geotechnical Engineering,
Section o f Geomechanics,
the Netherlands
De l f t University o f Technology,Faculty o f C i v i l Engineering,
Department o f Hydraulic and Geotechnical Engineering,
Section o f Geomechanics,
the Netherlands
Del f t University o f Technology,Faculty o f C i v i l Engineering,
Department o f Hydraulic and Geotechnical Engineering,
Section o f Geomechanics,
the Netherlands
Shell Intemational Exploration & Production
De l f t University o f Technology,Faculty o f C i v i l Engineering,
Department o f Hydraulic and Geotechnical Engineering,
the Netherlands
G. Kramer
Geotechnical Report Hr. 404
I f a man w i l l begin w i t h certainties
he shall end in doubt
but i f he w i l l be content to begin wi th doubt
he shall end i n certainties.
Francis Bacon, 1561-1626
A computer lets you make more mistakes faster than any
other invention in human history,
w i th the possible exceptions o f handguns and tequila.
Mi tch Ratl i ffe , in "Technology Review", A p r i l 1992
Look for fellow-travellers on your journey o f l i fe .
Although they sometimes might not please you or even hurt your feelings,
they w i l l be a comfort to travel w i th most o f the time and
are worth a thousand times more than the most precious diamond.
G. Kramer, 1996
Preface
Preface
This report contains the results o f investigations on the collapse mechanism o f open ended large diameter piles
during installation, done in the period o f September 1995 to June 1996. This study is done as a graduation
project at De l f t University o fTechnology by order o f Shell Intemational Exploration & Production B . V . which
is located in R i j swi jk , the Netherlands. I have chosen this subject as my thesis project because o f t h e unfamil iar i
ty o f t h e problem and because o f the combination o f experiments and theory.
I have experienced that it can be very d i f f i cu l t to reach the point that you want to reach when you start w i th a
project. Several factors have their influence on this unpleasant though unavoidable fact. Time always seems too
short to examine everything as thoroughly as wanted. When I started wi th this project some nine months ago, I
did not know that m y point o f view could change so often in a short period. Several times I believed to have
found an answer for the problem. Often it then seemed that the problem was even more complex than thought. A
better solution then had to be found. This so-called process o f two steps forward one step back has f m a l l y lead to
more msight in the problem and an improved point o f view.
I would like to seize the opportunity to thank the people who have helped and supported me during my graduati
on time. Special thank I would like to give to prof.dr.ir. A . Verrui j t , dr.ir H.B.G. Allersma, dr.ir. C . W . M . Sitters
and ir. R .A.W. Dubbers for guiding me through the whole project. Furthermore I would like to thank the people
o f the Geotechnical Laboratory: Han de Visser who helped me preparing the experiments; Ab Mensinga fo r
making the beautiful photo's o f t h e experknental results and Joop van Leeuwen for mul t ip ly ing my thesis report.
Thanks as we l l for all the other persons wi th whom I could discuss my experimental results and theoretical
models and who gave me an enjoyable graduation time.
Many thanks I owe to my friends and fami ly who supported me during my study at De l f t University o fTechno
logy, both in good and in bad times. L i f e would have been much more complicated i f it had been without you
all.
Del f t , June L996
G. Kramer III
Summary
Summary
The open-ended large diameter piles, used by Woodside Offshore Petroleum Ltd . as foundation for the offshore
pla t form in Goodwyn-A, Australia, experienced deformations during their installation. The cause o f this
deformation was not clear as they were never observed before. Pile tips seemed to have obtained a sort o f peanut
shape deformation.
The Geotechnical Laboratory was asked to do experimental research to see i f the observed peanut shape was
reproducible and to find out which parameters were o f influence on the deformation process. Next to this
investigation, a proposed theoretical model had to be vahdated which could explain the pile's collapse mecha
nism. The influence o f t h e so-called D/t-ratio, which shows the pile diameter divided by the wa l l thickness, was
given a major role as parameter o f influence and thus needed to be investigated thoroughly.
A parameter study was started. Scaled open-ended piles were driven in a soil sample which was placed wi th in a
pressure vessel. Various cell pressures could be imposed on the soil sample. Piles could thus be driven m the soil
under varying soil stresses.
Tt appeared that an ini t ia l damage always had to be given to the pile tip to obtain deformation during pile driving
i f a certain amount o f cell pressure was placed on the soil sample. I t seemed that a guiding system, used to ease
the entrance o f a pile in the pile sleeve, could be the cause o f this ini t ial damage. The pile sleeves were used to
batter the piles in the soil by around 1.5 degrees to avoid piles would touch at greater depth.
Much time was spent on the development o f a usable geomettical model that could reproduce the shape o f the
pile i f certain measured values were used as input. Next to this, a new model had to be developed which could
explain the pile-soil interaction during pile driving.
A model was made in which soil and pile behaviour is represented by springs having certain stiffnesses.
Formulas w i th which these rigidities could be calculated were made wi th the aid o f the existing formulas fo r
'Stresses in Tunnel Linings ' by A . Verrui j t .
A final test series was done in which piles having various D/t-ratios were given certain init ial damages. The cell
pressure needed to obtain plastic pile deformation was looked at. I t seemed that the gradient wi th in the init ial
deformation o f the pile tip had a major influence. Piles having larger gradients required less cell pressure to
deform.
Finally, a comparison was made between the theoretical calculated values for the maximum radial deformation
and the experimental results. Piles for which the calculated radial deformation exceeded a certain value always
seemed to be deformed further in the experiments. I t can thus be concluded that the proposed model can
determine very roughly whether a pile w i l l deform during driving or not.
G. Kramer IV
Layout of the report
Layout of the report
Chapter 1 describes the common use o f open-ended large diameter piles, the why and how o f their use for
Goodwyn-A and the used method o f installation. Chapter 2 gives the analysis o f the available Shell data. B y this,
facts are mentioned that might be o f use in understanding the cause o f the deformation o f t h e pile. In Chapter 3,
the pile deformation model as proposed by Shell reviewed. Chapter 4 describes the used equipment and materi
als. Both the test set up for the pile-soil interaction and the test set up for the investigation o f t h e initial damage
are presented as we l l as the used scaled open-ended piles. The first part o f the research period was spent on the
investigation o f parameters o f influence on the deformation process. The division o f these parameters in groups
and the way they influence the process is described in Chapter 5. The deformation o f the pile during the f i rs t part
o f t h e installation process is described in Chapter 6. Two models are presented which show the possibility o f t h e
occurrence o f an ini t ial pile tip damage during this part o f the installation. Two mathematical descriptions for the
deformation behaviour o f a pile under an extemal load are presented in Chapter 7. One o f these models is
modelled m a program that calculates elastic energy and plastic work within a pile. The experimental results o f
the tests in which an init ial damage was given to a pile t ip are presented in Chapter 8 as wel l as a comparison
between the experunental and theoretical results. Chapter 9 presents a model for the elastic pile-soil interaction
behaviour during driving. The place the various parameters o f influence have wi th in the model is given as how
their values can be calculated. The description o f experiments done to determine the pile-soil interaction durmg
dr iving are given in Chapter 10. A comparison between the experimental results and the theoretically calculated
values for the maximum radial pile deformation is given in Chapter 11. Conclusions and recommendations are
given in Chapter 12.
The appendices are presented in a separate volume as the total o f pages otherwise would become too much.
Tests done for the parameter study are given in Appendix 1. The available Shell data is given in Appendix 2.
Appendix 3 presents the theories behind the test series on init ial damage. The solution for the ovalisation o f a
tunnel is given in Appendix 4. Appendix 5 gives the calculation o f the stiffnesses for pile and soil wi th the aid o f
the software programme Maple V . These stiffnesses are used in the pile-soil interaction model o f Chapter 9.
Appendix 6 shows various pile tip shapes obtained after the driving tests. Appendix 7 gives the charts in which a
comparison is made between the experimental resuhs and the theoretical calculated values fo r the maximum
radial deformation. Calculations are as we l l presented out o f which the influence o f t h e various parameters can
be obtained. The computer programmes that were written fo r the various research parts are presented in Appen
dix 8. Appendix 9 f ina l ly gives the test results o f the measurements done for the init ial damage tests.
G. Kramer V
Table of Contents
Table of Contents
Lessons o f l i fe
Preface
Summary
Layout o f the report ^
Table o f Contents V I
Introduction
1 Open-ended large diameter piles 1
1.1 The use o f open-ended large diameter piles 1 1.2 The foundation piles o f the Goodwyn A platform in Australia 1
1.3 Method o f installation 2
2 Analysis o f available Shell data 4
3 Shell model o f pile ovalisation during driving 6
3.1 Pile behaviour during driving 6
3.2 V i e w on the model 7
3.2.1 Init ial pile shape 7
3.2.2 Soil behaviour 7
3.2.3 Pile behaviour 8
4 Used materials and equipment 9
4.1 The pressure vessel 9
4.2 The scaled open-ended piles 13
4.3"Pile tip deformer 16
4.3.1 Elliptic/oval deformer 16
4.3.2 Local initial deformer 17
5 Study on parameters o f influence 18
5.1 Soil Parameters 18
5.2 Pile parameters 18
5.3 Effect o f t h e parameters on the deformation process 19
5.4 Conclusions 22
6 Deformation behaviour o f piles during installation 23
6.1 Probable cause o f the mitial damage 23
6.2.1 Load on a pile t ip, model I 24
6.2.2 Load on a pile tip, model I I 25
6.3 M i n i m u m load needed to obtain failure o f material 26
6.4 A n example o f pile tip deformation 27
6.4.1 Model I 27
6.4.2 Model I I 27
6.5 Shape o f the init ial damage 27
6.5.1 The angle a wi thin the pile's damage 28
6.6 Conclusions 28
G. Kramer VI
Table of Contents
7 Model for the deformation behaviour o f a pile under an extemal load 32
7.1 Geometric modellmg for the shape o f t h e pile during loading 32
7.2 Model I , elliptical top - elliptical bottom damage o f the pile tip 33
7.2.1 Max imum and minimum values for various lengths 33
7.2.2 Init ial damage in the lateral direction 34
7.3 Model I I , Circular top - elliptical bottom damage of the pile tip 35
7.3.1 Cross section at the pile tip 36
7.3.2 Model ing o f damage m lateral pile length 39
7.4 Numerical model for behaviour model I 41
7.4.1 Discretisation o f a distorted pile 41
7.4.2 Determination o f the strain in a pile part 41
7.4.3 Behaviour o f pile part under pressure 42
7.4.4 Calculation o f plastic work and elastic energy 43
7.4.4.1 Plastic work 43
7.4.4.2 Elastic energy 44
7.5 Extemal work 45
8 Comparison o f experimental and theoretical results o f pile-loading system 46
8.1 H o w to determine and deal wi th hysterisis 46
8.2 Influence o f various stamps on shape o f pile t ip during loading 47
8.3 Obtained test results 48
8.3.1 Hysteresis and Young modulus 48
8.3.2 Load displacement curves o f initial deformation tests 49
8.4 Graphical display o f calculated values f rom the numerical model 50
8.5 Deformed lengths as function o f load 52
8.6 Difference in calculated plastic work 53
8.7 Conclusions 53
9 Model on elastic pile-soil interaction during driving 54
9.1 Shape of init ial damage 54
9.2 Determination o f the rigidities o f pile and soils 55
9.2.1 Soil w i th in the pile 56
9.2.2 Soil outside the pile 57
9.2.3 Pile Stiffness K.iu 58
9.3 Calculation o f the Young modulus for soils 59
9.4 Pile-soil interaction model 60
9.4.1 Stresses in springs 61
9.4.2 The equilibrium o f stress increment 62
9.4.3 Combining o f the two soil rigidities in the equilibrium equation 63
9.4.4 Factor 1.6 wi th in the equilibrium equation 64
9.5 Determination o f maximum deformation wi th a given penefration length 64
9.5.1 Ratio o f h ove rd 64
9.5.2 Check on position pile and soil parameters wi th in h/d-equation 65
9.6 Example o f calculated radial damage 65
9.7 Graphical output 66 9.8 Plastic instead o f elastic behaviour during penetration 69
9.9 Conclusions 70
G. Kramer VII
Table of Contents
10 Experiments on pile-soil interaction during driving 71
10.1 Introduction 71
10.2 Test procedures 71
10.3 The angle a wi th in the ini t ial damage 72
10.4 Results o f pile-soil interaction tests 73
10.5 Graphical output for various parameter combinations 77
10.6 Importance and clear influence o f a parameter value on test result 79
10.7 Conclusions 81
11 Comparison o f pile-soil interaction model and data obtained f r o m experiments 82
11.1 Introduction 82
11.2 Proposed comparison method 82
11.3 Comparison o f theoretical values and experimental results 82
11.4 Influence o f the parameters on the process 85
11.5 Difference in needed ini t ia l cell pressure 87
11.6 Conclusions 88
12 Conclusions and recommendations 89
12.1 Conclusions 89
12.2 Recommendations 90
12.2.1 Recommendations on the experimental part o f the graduation project 90
12.2.2 Recommendations on the theoretical part o f the graduation project 91
12.2.3 Recommendations on the construction o f an o i l platform w i t h the same foundation type . . . 91
References 92
G. Kramer VIII
Offshore platform Goodwyn-A, Australia
G. Kramer
Introduction
Introduction
For the foundation o f the Goodwyn-A oi l platform (see page I X ) at the North-West side o f Australia, open-
ended large diameter piles were used. The calcareous nature o f the soil made i t impossible to use normal driven
piles. The Goodwyn-A piles exist o f two parts, a primary and an insert pile. The primary pile is first driven into
the soil. Hereafter the soil wi th in and over some depth below the pile is removed. The insert pile w i th a smaller
diameter than the primary pile, is placed through the primary pile. Concrete blocks are pre-installed wi th in the
insert pile to l imi t hydratation heat from the setting grout. Finally the insert pile is connected to the surrounded
soil by filling the pile w i t h grout.
Dur ing the removal o f the soil wi th in the primary piles almost every primary pile was found collapsed over
some length from the tip o f t h e pile. The pile tips were deformed into a peanut shape. Because o f t h e deformati
on, placement o f t he insert piles through the primary piles was not possible.
A n assignment has been given by Shell to the Departtnent o f Hydraulic and Geotechnical Engineering, Section
o f Geomechanics, De l f t University o f Technology, to examine the cause o f the observed deformations. Experi
ments were to be carried out to reproduce the observed failure mechanism. The research on the subject is done to
obtain a code requirement for the ratio o f diameter over wal l thickness.
G. Kramer X
Chapter 1
1 Open-ended large diameter piles
1.1 The use of open-ended large diameter piles
Open-ended large diameter piles are used in cases where the loading conditions require large diameters to be
driven to large penetration depth in order to obtain sufficient bearing capacity. The piles are open ended because
large hammer energy is required to drive the piles to the required depth. Closed ended piles w i l l require even
more hammer energy.
Open-ended piles are widely used in the offshore industry. They can be found as foundations fo r steel jackets
and tension leg platforms (see Fig. 1.1), as conductor piles for o i l or gas wells and as anchor piles. In the past
years, open-ended large diameter piles were also used onshore as the foundation o f bridges (Jamuna Bridge,
Bangladesh, Fugro Engineers B . V . ) .
1.2 The foundation piles ofthe Goodwyn-A platform in Australia
Open-ended large diameter piles were also used for the foundation o f the Goodwyn-A platform in Australia. The
soil in this area mainly consists o f carbonate sand and calcarenite, graded f r o m weakly to strongly cemented.
Load capacity mechanism o f this soil can be compared wi th a Dutch rusk in which a pencil is being pushed. Part
o f t h e rusk surrounding the pencil breaks in smaller pieces thus reducing the load capacity o f the rusk. The same
occurs i f a pile is driven in calcareous soil. This behaviour made it impossible to use normal driven piles.
A pile was developed to obtain sufficient load capacity. This pile exists o f two parts, a primary and an insert
pile. The primary part had a length o f 133m, a diameter o f 2.65m, a wal l thickness o f 0.045m and a weight o f
520 ton (in air). The insert pile had a length o f 80.5m, a diameter o f 2.0m, a wal l thickness o f 0.05m and a
weight o f 185 ton (in air). For each jacket leg, a total o f f ive primary and insert piles were to be placed. This
means a total o f twenty primary piles. Appendix 2 gives an overall picture o f stratigraphy, the used piles and
their positioning around the jacket legs.
Fig. 1.1 Pipe piles in the offshore industry
G. Kramer 1
Chapter1
1.3 Method of installation
Piles are horizontally transported to their place o f destination (see Fig. 1.2). This has to be mentioned to prevent
the thought o f a possible pile tip deformation resuUing from o f on shore handling. Before the piles penefrate the
soil, they have to be lowered in the water (see Fig. 1.3). This process is done accurately to prevent damage to the
piles during stabbing.
Fig. 1.2 Transportation of piles in water Fig. 1.3 Lowering of primary pile
Fig. 1.4 Moment of contact between primary pile and pile sleeve
Fig 1.5 Penetration of primary pile in soil
The primary piles are battered in the soil by around 1.5 degrees to avoid the piles to touch each other as they
have a tendency to get closer to each other during driving. To batter the piles under the right angle and direction,
the piles need to be guided by pile sleeves. The sleeves have a diameter o f 2.85m, only 0.20m more than the
primary pile. The top o f t h e pile sleeve has a cone to make enfrance o f the primary pile easier (see Fig. 1.4). To
prevent the pile from getting stuck in the space between the jacket leg and the cone construction, a frame o f
pipes, the so-called bumper was attached to the jacket leg (see appendix 2, page 6).
G. Kramer 2
Chapter 1
After the driving o f the primary pile to the desired depth, the soil inside it and for some 65m under its tip is
removed. Hereafter the insert pile is lowered through the prunary pile. The insert pile is aheady f i l l ed wi th
precast concrete segments (see Fig. 1.6). The empty space wi th in the insert pile and between the soil mass and
the insert pile is f i l l ed w i t h grout.
Jacket leg
Cone construction
Raked pi le sleeve
Pr imary pile
Insert pile
Fig 1.6 Overview of raked pile sleeve, primary pile and insert pile
Certain matters, however, delayed the mstallation process significantly. When the soil was removed from wi th in
the primary piles, it seemed that almost every primary pile was deformed to some extent. The insert piles could
not be placed as a resuh. As the reason fo r the deformation was not known, investigations were started to find
the mechanism that lead to the observed deformations.
G. Kramer 3
Chapter 2
2 Analysis of available data
Sonar surveys were employed to obtain information about the shape o f the deformed piles. The data, obtained
f r o m these surveys, showed some remarkable facts. Appendix 2 w i l l provide the reader wi th the available data.
The page number at which information can be found wi thm the appendix, is given after each remark between [ ] .
1] No clear connection is found between the orientation o f the deformation and the direction in which the pile is
driven [6 and verbal information];
2] The size o f the f m a l pile deformation shows a very large range [9.. 12];
3] A connection can be found between the size o f the fma l pile tip deformation and the lateral length over
which this deformation is found [9.. 12];
4] Most o f the piles obtamed a sort o f peanut shaped deformation [9.. 12];
5] Maximum pile deformation is always found at the pile tip [9.. 12];
6] The path leading to the f m a l deformation shape can be divided in various deformation shape steps. The
various steps can be found at various levels above the pile tip [9.. 12];
7] Considering the soils , two layers can be found that have a much higher peak shear stress (kPa) than the other
layers [3] .
From these facts, f o l l o w m g proposals and/or conclusions are given:
A d 1] The piles might obtain their initial damage through three parts o f the guidmg system: the bumper, the
sleeve cone or the sleeve pile. I f rotation o f the pile during its mstallation is disregarded, the fo l lowing
can be concluded: N o orientation could be found between the direction o f the deformation and the
dr iv ing direction. This makes it highly likely that the sleeve cone causes the pile tip to deform as it is
the only part w i t h no clear orientation. The primary pile can hit the sleeve cap at any place. The other
two parts o f the guiding system have a clear orientation. I f one o f these parts had been hh, a clear
connection would have been found between the direction o f the ini t ial deformation and their cause.
A d 2] I t can be expected that larger initial damages w i l l lead to larger fma l deformations i f all other facts are
constant during installation. Proof o f this can be found in chapter 10 in which the experimental results
w i l l be treated. The primary pile can hit the sleeve cone anywhere. A constant lowering speed is
maintained for all piles. The size o f the surface o f contact or initial distortion depends on the impact
during contact w i th the sleeve cone. As this impact varies for each pile, each pile w i l l obtain a
different size o f ini t ial distortion. Some piles might not even obtain any initial distortion at all i f no
contact occurs between the sleeve cap and the primary pile. Such piles w i l l not deform at all .
A d 3] Next to the size o f the inhial damage, the angle o f inclination wi th in the init ial damage w i l l probably
influence the way in which deformation occurs. A larger angle o f inclination w i l l lead to less
deformed lateral pile length.
A d 4] Many pile tips obtained peanut shape deformations. The completely closed pile tips might have had a
peanut shapes in an earlier stage o f the deformation process. Other shapes seem to occur as wel l .
G. Kramer 4
Chapter 2
A d 5] This pomt is obvious as the pile w i l l incur initial damage at its tip and not m the middle.
A d 6] This is one o f the most important pomts as the history o f loading condition and the shape o f the initial
distortion can be found back in the shape o f the deformed pile. Taking pile B4-2 at page 12 as
example, various deformation shapes can be found at different cross-sections o f the pile. The top o f
the pile st i l l has its circular shape as deformation has not yet entered that level. A t some level, the pile
loses its circular shape and some deformation is found. Another shape, which looks like a cashew nut,
is found at a higher lateral level o f the pile (level = zero at pile t ip) . This cashew nut shape might
show that mit ial distortion occurred only at one side o f the pile t ip. This side w i l l walk 'ahead' in
phase on the opposite side as deformation o f the opposite side is the result o f the init ial distortion at
the other side. As the mitial distorted side moves inwards, the pile w i l l flatten. This causes the
undistorted opposite side o f the pile tip to move inwards.
A d 7] The shear stiffness o f the soil probably influences the rate o f the deformation process. I f no shear
stiffness is present (e.g., l iquid), the pile w i l l not deform. I f rock has to be penetrated, piles w i l l
deform at a max imum rate. I t can be assumed that a larger stiffness o f the soil w i l l lead to a larger
radial displacement considering al l other factors o f influence unchanged.
The points mentioned above have been investigated in experiments done on scaled-down open-ended piles. The
results o f these experiments are discussed in fo l lowing chapters.
G. Kramer 5
Chapter 3
3 Shell model of pile ovalisation during driving
3.1 Pile behaviour during driving
The scope o f work which was provided by Shell (see Appendix 2) included a model for the pile ovalisation
durmg dr ivmg (see Fig. 3.1 and Fig. 3.2). Both the soil and the pile are considered in the model.
Slip circles in the soil around the pile cause extemal work Eei on the pile. The soil plug wi th in the pile causes
external work as wel l . Both extemal works lead to ovalisation o f the pile. The outside extemal work ( I ) can
be written as
] E = xCs = - T i r D ^ c j ) (3.1)
in which: x is the shear stress in the soil
C is the circumference o f the slip circle;
s is the length o f the displacement;
D is the diameter o f the slip circle, which is the same as the pile diameter;
(|) is the angle o f rotation.
The inside extemal work ( I I ) can be written as
= (3.2)
m which: i is the shear stress in the soil;
Y is twice the rotation angle (j);
A is the area wi th in the pile;
D is the diameter o f the pile;
(j) is the angle o f rotation.
G. Kramer 6
Chapter 3
Besides extemal work in the soil, intemal work can be found in the pile wal l . As plastic behaviour is assumed to
occur in the pile wal l f r o m the mmute the pile starts to deform, mtemal work is written as:
E. = 2M^(t) = = 2 r a^(t) = ^t^o^^ (3.3)
The situation is stable i f the intemal work is larger or at least the same as the extemal work. This gives
= ^ . (3.4)
or:
1 , 2 - - 4 -r^o^cj) = - i xDHc t ) (3.5)
The criterion for dr iving shoe thus becomes:
i x ( - ) ^ ( - ) < 1 (3.6)
W i t h the shear stress in the soil and the pile sizes and strength known, Eq. 3.6 shows whether pile or soil w i l l
deform.
3.2 View on the model
The way in which the model describes the pile and soil behaviour during loading is given by an energy balance.
The initial pile shape w i l l be discussed in Par. 3.2.1. Soil behaviour w i l l be discussed in Par. 3.2.2 and the pile
behaviour in Par. 3.2.3.
3.2.1 Initial pile shape
In i t ia l damage is assumed in the given model. N o particular pile t ip shape is included. The influence o f initial
damage on the pile behaviour during dr iving however needs to be investigated. The shape o f the inhial damage
in lateral direction has to be considered as wel l , as this parameter seems to have large influence on the minimum
required cell pressure to obtain plastic deformation.
3.2.2 Soil behaviour
Slip circles are used to f i n d the amount o f extemal work o f the soil around the pile. I f an ini t ial ly distorted pile
tip peneh-ates the soil, soil pressure w i l l be build up against the curved pile wal l . Evenhially when too much
pressure occurs in the soil, a slip circle might occur. The arrows in Fig. 3.2 indicate the shear forces acting on
the rotating soil mass and not the direction o f movement.
Not much can be said about the way soil behaviour wi th in the pile is simulated as many not yet investigated
effects have to be taken into account.
G. Kramer 7
Chapter 3
3.2.3 Pile behaviour
The model considers only the fiilly plasticised zone o f the pile, immediately w i l l behave plastical wi th plastic
hinges occurrmg on the places where most stram is obtained. Elastic pile behaviour is neglected. Regarding the
crherion given for the ini t ial stability o f the pile tip, elastic mstead o f plastic behaviour has to be used. The stress
wi th in in the pile wal l has to be calculated fo r the moment the pile wants to deform. B y this means, the intemal
work can be calculated and compared wi th the extemal work and a conclusion can be drawn on the pile
behaviour during driving.
G. Kramer 8
Chapter 4
4 Used materials and equipment
4.1 The pressure vessel
To simulate in-situ soil conditions during driving, the Geotechnical Laboratory has buil t a pressure vessel (see
Fig. 4.1). W i t h i n the vessel there are a sealed rubber hose on the inner wall and a circular rubber seal at the
bottom. The pressure vessel is made in such way that both horizontal (cell) pressure and vertical (bottom)
pressure can be imposed on the soil sample. Only cell pressure is used in the tests done in the research done for
this thesis. No additional vertical pressure is imposed on the soil sample during a l l the experiments.
Pile hammer
\Cell pressure
Fig. 4.1 Pressure vessel used in the experiments
Dry sand is placed in the vessel. The use o f dry sand instead o f wet sand allows higher effective shesses and
hence increases the simulation depth. The annuli are filled wi th compressed air. A maximum pressure o f 4.0 bar
(kg/cm^) can be achieved. Pressure meters show the amount o f cell and/or bottom pressure placed on the sand.
Eq. 4.1 gives the formula that can be used to hanslate bar cell pressure into depth below groundlevel.
depth - ^^*c^llpfessure*g
K * y' 0 • drysoil
(4.1)
I f for example a y'drysoii o f 16 kN/m^ ,a K-value o f 0.5 and a g-value o f 9.81 m/s^ are used, Eq. 4.1 would become
98.1 *cellpressure depth (4.2)
4 bar would then be comparable wi th a depth below groundlevel o f about 50m. Through a hole in the l i d o f t h e
vessel, a pile can be pushed or driven into the soil sample. The height o f t h e vessel measures 0.67m, the outer
diameter 0.30m. The diameter o f the hole (5 cm) is small enough to influence the pressure in the sand only over
a small hemisphere. The diameter o f this hemisphere is estimated maximum one to one and a half times the
diameter o f the hole. Overview pictures are given in Fig. 4.2 to Fig. 4.4.
G. Kramer 9
Fig. 4.2 Overall view of the experimental setup in which driving or pushing of a pile oan be simulated
G. Kramer 10
Chapter 4
Fig. 4.3 Pressure vessel and pile with driving installation
G. Kramer 11
Chapter 4
Chapter 4
4.2 The scaled open-ended piles
Model piles had to be made that could be used m scaled tests. These piles have to comply wi th f o l l o w m g terms:
- the elastic and plastic behaviour o f the material has to be comparable to the behaviour o f steel under the
same loading conditions;
- the piles must be able to resist the axial load caused by the pile hammer durmg dr ivmg and/or pushmg;
- the piles need to have a varymg diameter over wal l thickness ratios'. Adjust ing this ratio has to be easy and
mexpensive; - the costs o f t h e model piles have to be kept as low as possible as many piles are requhed for the experunents.
A pipe was found which met most o f these terms. The pipe material exists o f an inner layer o f brass and an outer
layer o f chromium. The outer layer is removed in a lathe to yield a solely brass pile. The behaviour o f the piles
strongly depends on the alloy used.
The properties o f chart 4.1 were sent by the German factory m which the piles were produced.
Material brass Composhion
Mass portions in %
Abbreviation Number Cu Z n A l Fe N i Pb Sn Remainder
Density
CuZn40 2.0360 mm.
max
59.5
61.5
Rest
0.05 0.2 0.3 0.3 0.2 0.2
8.4
Material brass
Abbreviation Number
Wal l
thickness
(mm)
Yie ld
Strength
(N/mm^)
0.2%-Strain
L i m h
(N/mm')
Strain at
Failure
%
min .
Hardness
H B
CuZn40 2.0360
P .08 no prescribed values
1 f\ . lU Up to 10 mm. J t u « OOA T C OA
F41 .26 up to 10 min. 410 min . 220 20 115
F47 .30 up to 5 min . 470 min. 350 11 140
Chart 4.1 Material qualities
The material has a good warm and cold transformation capacity and can bend easily.
To detect which o f t h e numbers .08,. 10,.26 or .30 fits on the piles used in the tests, addhive tests were done to
determme yield strength and the strain at failure. Four tests were done using a draw-bench. Fig. 4.5 to 4.8 show
the load-displacement curves resultmg from the tests. The vertical lines in Fig. 4.6, 4.7 and 4.8 were meant to
show the unloading curve. Due to hysteresis o f the displacement measure equipment, this Ime became vertical
instead o f showing a gradient.
G. Kramer 13
Chapter 4
Load
Displacement
Fig. 4.5 Load-displacement curve yield test 1
Load
Displacement
Fig. 4.6 Load-displacement curve yield test 2
Load Load
Displacement Displacement
Fig. 4.7 Load-displacementcurve yield test 3 Fig. 4.8 Load-displacement curve yield test 4
Divis ion o f load F at rupture by pile surface A gives the yie ld strength. This leads to the results as given in chart
4 . 2 .
Name test Outer
Diameter
(mm)
W a l l
Thickness
(mm)
Pile
Surface
(mm' )
Max imum
Load
(kN)
Y i e l d
Strength
(N/mm' )
Shength
at Rupture
(N/mm' )
Failure
Strain
(%)
yield test 1 31.6 0.3 27.6 16.2 560 586 12
yield test 2 31.6 0.3 27.4 16.6 575 606 -
yield test 3 31.7 0.35 33 16.8 465 509 -
yield test 4 31.75 0.375 33.7 20.5 525 608 7.6
Chart 4.2 Calculated Yield Strengths
In the calculation o f the yield strength, the pile surface at the moment o f yie ld has to be used as constriction
might occur. No clear rupture shape was observed. The piles instead ruptured like the peel o f an orange. To
calculate the Strength at Rupture, the smallest pile diameter and wa l l thickness were measured to determine the
pile surface. The large scatter in calculated yield strengths as calculated in test 3 might be the result o f the
strange way o f rupture. Resuhs o f the tests however show that the piles used all have a yield strength higher than
the yie ld strength known for brass F47 and number 2.0360.30 (see chart 4.1). The yield strength that w i l l be
used in future calculations, is the average o f the four calculated yield strengths. This gives a value o f 530
N / m m ' .
G. Kramer 14
Chapter 4
stress sigma [N/mm''2]
The material seems to behave almost ideal plastic as almost no hardening occurs during the tensile tests. Steel
has the capacity to obtain more hardening during a tensile test. Fig. 4.9 shows the stress-strain curves for various
typed o f steel. A higher steel quality leads to a smaller horizontal plateau.
Piles used for offshore purposes are often made o f high quality steels. The
behaviour o f the brass scaled piles can be considered as the behaviour o f a
high strength steel as both material mis the horizontal platform in their
stress-strain path. Both material show a clear failure strain as wel l .
The hardening behaviour o f the piles is different. Brass piles harden less
than steel piles. Plastic deformation o f the brass piles w i l l be easier than
plastic deformation o f steel piles because o f this.
strain 6 [%] coucludcd that the use o f brass scaled piles instead o f steel scaled Fig 4.9 Stress-strain path for various steel . acceptable for the determination o f the failure mechanism, qualities ^
Fig. 4.10 Experimental setup in which pile oan be given an initial distortion
G. Kramer 15
Chapterj
4.3 Pile tip deformer
4.3.1 Elliptic/oval deformer
To observe the effect o f a pile t ip hit t ing an object, an experimental setup was developed (see Fig. 4.10 and Fig.
4.11). This setup made it possible to make init ial distortions in the pile tips. As the load on the pile tip increases,
this w i l l cause the pile t ip to deform. Measurements can be done on this tip deformation. The measured values
can be used as input for a computer model. In this way, deformation can be visualized and elastic and plastic
deformation areas wi th in the pile can be shown. Chapter 8 w i l l discuss the tests done wi th the pile tip deformer
and the results obtained by the tests.
Fig. 4.11 Loading equipment by whicli process is simulated
Q. Kramer 16
Chapter 4
4.3.2 Local initial deformer
Another tool could be used to make small reproduceable local initial distortions in a pile. Fig. 4.12 shows this
device [Allersma 1]. A pile t ip is placed over a metal mould. A n indentation is made in the plug to enable
deformation o f the pile t ip. A rod can now be l i f ted below which a die is attached. I f the rod is pushed
downwards, the die w i l l h i t the pile tip thus creating a local init ial distortion. The dimensions o f this distortion
depend on the amount o f load placed on the rod and the shape o f the mould.
Two types o f inhial distortions can now be made. The first one, an elliptic/oval inhial distortion is made wi th the
tool f igured in Fig. 4.10 and Fig. 4.11. The second one, a local initial distortion, is created wi th the tool
displayed in Fig. 4.12.
Adjustable stop
Fig. 4.12 Tool, used to make local initial distortions
G. Kramer 17
Chapter 5
5 Study on parameters of influence
I f a new phenomenon needs to be described in a theoretical model, a parameter study can be very useful. In this
study parameters o f mfluence can be identified as wel l as the way m which they influence the process. To obtain
an idea o f what leads to pile deformation durmg driving, several tests were done on the scaled piles mentioned in
Chapter 4. A report was made after four months o f investigation in which the results o f t h e parameter tests were
presented. This report has been slightly rewritten and can now be found in Appendix 1. While describing the
mfluence o f t h e various parameters, the experunents given in Appendix 1 w i l l be referred to.
The parameters can roughly be divided in a tree as drawn m Fig 5.1
Parameters of Influence
1
Pile parameters j Soil parameters
Material parameters
Pressure parameters
1
Material parameters
Shape/dimensional parameters
Fig. 5.1 Division of parameters in groups
The soil and pile parameters w i l l be, respectively, described in Par. 5.1 and Par. 5.2. Theh effect on the process
is described in Par 5.3. Conclusions w i l l be given in Par. 5.4.
5.1 Soil Parameters
The soil parameters are divided in material parameters and pressure parameters. The material parameters
describe the soil used in the sample in which a pile is driven. North Sea sand is used as soil sample in the
experiments o f Appendix 1. The kind o f soil in which driving w i l l take place probably affects the behaviour o f
an open-ended pile during this driving. Next to the material parameters, pressure parameters w i l l probably have
influence on the process. I f a higher pressure is placed on the soil sample, the sample w i l l react much stiffer.
Stiffer behaviour o f t h e soil sample leads to an increased Young modulus o f the sample.
5.2 Pile parameters
The pile parameters are divided into two groups. The material parameters include the Young modulus, the
Poisson's ratio and the yield strength o f the pile. Both have their influence on the process. The second group
mcludes the dimensions o f t h e pile, the diameter, the wal l thickness and the inhial distortion o f the pile tip or the
enthe pile.
Chapter 5
5.3 Effect ofthe parameters on the deformation process
Chart 5.1 shows the various parameters mentioned in Par 5.1 and Par. 5.2. The first column gives the
parameters. The thhd column gives the effect a parameter value increase or decrease has on the pile
deformation. The fourth column gives the number(s) o f Appendix 1 experiment(s) in which the parameter is
investigated. I f no specific research was done on a parameter, a hyphen [-] is printed.
The parameter values are compared wi th a siUiation m which the pile and soil parameters are chosen in such a
way that the pile w i l l deform during driving.
Name parameter Increase or decrease of value or change of material
Effect of this change on the pile deformation
Experiments done in which influence of the parameter can
be found
A ] Ini t ial distortion increase more deformation 2 A 1 , 2 A 2 , 2 B 1 ,
3 ,4 , 8, 10
A ] Ini t ial distortion
decrease less or no deformation
2 A 1 , 2 A 2 , 2 B 1 ,
3 ,4 , 8, 10
B] Gradient wi thm init ial
pile tip distortion
increase various deformation
shapes 2 B 1 , 7 , 10
B] Gradient wi thm init ial
pile tip distortion decrease various deformation
shapes or no
deformation at al l
2 B 1 , 7 , 10
C] Soil in sample
clay instead o f sand or
loosely packed instead
o f dense
- all
D] D/t-ratio
increase more deformation -D] D/t-ratio
decrease less or no deformation -
E] Pressure on sample
increase more deformation
1 ,2B1,2B2, 6, 8, E] Pressure on sample decrease less or no deformation
1 ,2B1,2B2, 6, 8,
F] Young's modulus pile
increase
(steel instead o f brass)
less or no deformation
3 ,6 F] Young's modulus pile decrease
(tempering o f the pile or
copper instead o f brass)
more deformation 3 ,6
G] Dr iv ing depth
increase more deformation
-G] Driv ing depth decrease less or no deformation
-
Chart 5.1 Effect of various parameters on deformation behaviour of pile during driving
A d A , B ] The performed experiments show an initial distortion is needed to obtain pile deformation during
dr iv ing. Inhia l distortion however is not enough; a min imum gradient has to be present wi th in the
inhial distortion. The gradient is described as the maximum radial deformation divided wi th the lateral
deformed pile length.. Even very large inhial distortion without a gradient w i l l not cause deformation
o f the pile during driving. This gradient w i l l be considered more thoroughly in Chapter 9. A larger
inhial distortion wi th a gradient w i l l lead to a larger final pile deformation.
G. Kramer 19
Chapter 5
ad C] I t is not really known what effect a change o f soil might have on the deformation behaviour o f a pile.
Hardly any theory can be found on this subject. Some tests have been done to determme the plugging
effect o f the soil column wi th in the pile. Plugging o f the sand column seems to depend on the
conditions surrounding the pile. No plugging occurred in the calcareous soils. Tests wi th dry sand
give the same resuh; hardly any plugging occurred. As considering the effect o f plugging is very
d i f f i c u h and as experimental resuhs have shown that hardly any plugging occurs, the effect w i l l be
neglected.
ad D] Piles w i t h a smaller D/t ratio needed more cell pressure to obtain plastic deformation. A n increasing
D/t-ratio w i l l resuh in a less s t i f f pile. As the inhial distortion w i l l easily enlarge in a less s t i f f pile,
more deformation is to be expected m piles driven over the same length. Many experiments have to
be done to check the exact relationship between the minimum required D/t-ratio and the inhial
distortion o f the pile t ip. Not enough tests have been done on pile to find this exact relationship.
ad E] Another parameter that has to be taken into account is the Young modulus o f the soil. This modulus
represent the stiffness o f the soil. I f the soil stiffiiess increases, so does the pile deformation. Lowering
o f a pile in fo r example water (Young modulus = 0) w i l l result in no deformation at all . I f the pile
would be driven in solid rock (Young modulus = « ) , maximum deformation w i l l occur during
dr iv ing. A n increasing cell pressure leads to an increment o f the Young's modulus and thus to stiffer
sample behaviour. A pile wi th a particular inhial pile tip distortion w i l l deform more i f more ceh
pressure is placed on the sample.
ad F] A larger Young modulus o f the pile leads to stiffer pile behaviour. More load has to be placed on the
pile to obtain the same deformation as the one that w i l l occur in a pile w i th a lower Young's modulus.
ad G] Dur ing the first months o f research, no attention was paid to the pile dr iving length. Only after a new
model was designed which had to describe the pile-soil interaction behaviour, h seemed that the
dr iv ing length had a major influence on the deformation behaviour o f the pile. I f the circumstances
enabled the pile to deform during driving, the size o f the deformation seemed to increase wi th an
increasing dr ivmg length. Plastic deformation can only occur i f the maximum elastic strain is
exceeded. Some driving length is needed to obtain this shain. I f this dr iving length is not exceeded,
no deformation w i l l be found when the pile is taken out o f the soil sample. Increasing the driving
length w i l l then probably result in observable plastic deformation.
Various pile shapes were observed after driving o f the piles in the soil sample. Fig. 5.2 and Fig. 5.3 show the
shapes obtained for the piles used in the parameter determination phase. The text below the pile refers to the
name o f the experiment.
Many parameters have an influence on the deformation o f a pile during driving. Initial distortion is the main key
m the process. Without inhial distortion, deformation w i l l not occur under any circumstances. I f init ial distortion
is present, soil parameters w i l l determine the load present on a pile. It depends on the pile parameters whether
this load w i l l lead to pile deformation or not. Fig. 5.4 shows how the parameters might be related to each other
in determining whther or not a pile would collapse. It is clear that one specific parameter can already determine
i f a pile w i l l deform or not during driving.
G. Kramer 20
Chapter 5
Chapter 5
Initial damage present
Yes
1 Gradient present |
Yes
Young's modulus of soil large enough | -
Yes
1 D/t-ratio large enoughr
Yes
lYoung's modulus of pile low enougl}-
Yes
1 Enough driving depth availableh
Yes
Pile deformation possible I
No
No
No
No
No
No
Pile deformation not possible
Fig. 5.4 The way in which parameters might lead to pile deformation
I f e g , values are known for the init ial distortion, the gradient and Young's modulus o f the soil, combinations o f
values'can be found for the unknown parameters for which a pile w i l l not collapse. A 3D-figure is made in
which three axes represent three conditions, e.g., the D/t-ratio, the gradient o f the init ial distortion and the
Young's modulus o f t h e soil. A n area w i l l be found in which deformation w i l l always occur (see Fig 5.5).
Y o u n g ' s modulus soi l ^ ^ ^ ^ ^ ^ ^^^^
Fig. 5.5 3D-picture with three conditions on the axes and imaginary
shape of failure area
5.4 Conclusions
Many parameters seem to have influence on the deformation process o f a pile during driving. Penetration o f a
pile having an ini t ial distorted pile tip causes stress wi th in the soil. I f these stresses become too large, the pile
w i l l start to deform. The size o f the deformation depends on the driving depth and the gradient o f the inhial
distortion. Combmations o f these condhions can be found which w i l l always lead to deformation o f the pile
during driving.
G. Kramer 22
Chapter 6
6 Deformation behaviour of piles during installation
This chapter considers the way m which mhial damage might occur m a pile during its installation. During part
o f the installation process the pile is slowly lowered m the water and fmal ly placed in the sleeve pile. I t should
be mentioned that in this part no contact between pile and soil occurs. Par. 6.1 gives the cause o f the init ial
damage. Par. 6.2. deals w i th the mechanism wi th which the load on the pile, resuhing f r o m the contact wi th the
sleeve cone can be calculated. Par 6.3 gives the equation wi th which the mmhnum load needed to obtain plastic
deformation m a pile can be calculated. Par. 6.4 gives the calculations made for an example pile. In Par. 6.5 a
proposal is presented for the shape o f the pile and hs tip that w i l l be driven m the soil. Par. 6.6 gives the
conclusions o f t h e mvestigations as reported in this chapter.
JACKET LES f
^ 2 « 8 0 i AHTI-ROTATIHG
Fig. 6.1 Guiding equipment for the installation of a pile
6.1 Possible cause ofthe initial damage
To incline a pile under the right angle and in the right direction, it has to be guided by a sleeve. The sleeve
consists o f two parts. The first part is a pile sleeve through which the primary pile can slide during driving. This
pile has a diameter o f 2.85m, only 0.20m more than the primary pile. The second part is called the sleeve cone.
This cone is placed on top o f the pile sleeve to ease entrance o f the primary pile (see Fig. 6.1). To prevent the
pile from touching the jacket leg, a bumper frame was attached to the jacket leg.
Experiments done in the pressure vessel have shown that scaled open-ended piles w i l l not deform durmg driving
without initial pile tip damage (see Appendix 1). Almost every primary pile in Goodwyn showed considerable
deformation after dr iving (see Appendix 2, page 9 to 11). This suggests inhial pile tip damage. As can be seen in
Fig. 6.2, some parts o f the guiding equipment might have contributed to the init ial damage.
G. Kramer 23
Chapter 6
During descendance, tlie pile can hit either the bumper, the cone construction, the pile sleeve or a combination
o f these. This depends on the accuracy at which the primary pile is descended. The pile thus might obtain its
inhial damage through three parts o f the guiding system: the bumper, the sleeve cone or the pile sleeve. I f
rotation o f the pile during installation is neglected, fo l lowing can be said. No clear orientation could be found
between the place o f the mhial pile t ip damage and the drivmg direction o f the pile. This lack o f orientation
makes i t highly presumable that the sleeve cone causes the pile tip to deform as this guiding part is the only part
present over 360 degrees.
— -Primary pile
^^^^^^^^^^^^^^^^l^umper
Sleeve Jacket leg
cap
b o
\Pile sleeve
Fig. 6.2 Easier entrance in pile sleeve because of sleeve cone
The primary pile can h h the sleeve cone at any place. The other two parts o f the guiding system have a clear
orientation. I f one o f these parts had been hit, a clear connection would have been found between the direction
o f the init ial deformation and their cause.
6.2.1 Model for load on a pile tip
Another approach o f the situation can be obtained, i f the energy wi th in a pile during descending is looked at.
Before the pile hhs the sleeve cone, the energy wi th in the pile consists o f kinetic energy. A t the moment o f
contact, this kinetic energy partly changes into another shape, for instance spring energy. Three possible ways o f
contact are known, elastic, elastic-plastic and f u l l y plastic (see Fig. 6.3). A model is made which is based on
three assumptions:
1] the pile wal l can be schematized as a spring having a r igidi ty K ;
2] all the kinetic energy w i l l become spring energy;
3] elastic-plastic behaviour w i l l not be taken into account. I f the maximum elastic strain is exceeded in a pile
part, the pile part w i l l be regarded as plastic deformed.
The f i rs t step is a rotation o f the coordinate system over an angle p and a hansformation o f the center to the
point o f contact between pile tip and sleeve cone (see Fig. 6.4). The second step is the determination o f the
stiffness o f the pile. For the stiffness o f the pile, Eq. 6.1 is used. How this stiffness was obtained, w i l l be
explained in Chapter 9.
3 E ,t' K„ = ^ [N/m'] (6.1)
pile 8 ( - l + v ) ( l + v ) ( i - v ' ) /? '
G. Kramer 24
Chapter 6
The Stiffness is given in N/m^ and has to be translated in N / m to be o f use. This is done as fol lows.
Eq. 6.2 gives the maximum moment wi th in a pile part.
^ 0 = (6.2)
Omax gives the maxhnum stress within the pile part, and t gives the wall thickness.
The maximum moment wi th in a cross-section o f a pile can also be written as
M„ =0 .318 Fi?^,^ (6.3)
in which Rpn^ gives the pile radius and F the point load on the cross section [13] .
Substituting o f Eq. 6.2 in Eq. 6.3 and rewrit ing gives an equation for as a funct ion o f R, F and t.
2 , (6.4)
3
The maximum stress a^^ can as wel l be written as
" » a . = ^ p . 7 . * « (6.5)
in which KpHe is the pile stiffness (Nm"^) as given in Eq. 6.1 and u the displacement.
Substitution o f Eq. 6.4 m Eq. 6.5 gives F as a function o f Kpn^, RpHe and t.
, = „ (6.6) 0.318 R^,^
F can as wel l be written as
F = K i l e « (6.7)
The required K'pn^ (Nm"') can now be written as a function o f the known value o f Kpn^. This gives
, (6.8)
0.318 i?^,.
G. Kramer 25
Chapter 6
Situation A Situation B
v,= X ms'' Vj = 0
Fig. 6.3 Fully elastic (A) and fully plastic (B) behaviour during contact
The velocity Vy' is given by
Fig. 6.4 Translation and rotation of co-ordinate system
V ' = V *cosP (6.9)
The thhd step is to detemiine the displacement Uy.. This can be found from Eq. 6.3. K^^^* represents the stiffness
in N / m .
7 - / = i / c . u;^ (6.10)
Substitution o f Eq. 6.9 m Eq. 6.10 and rewrit ing gives the equation for displacement Uy.
m
\ u^' = V C O J P (6.11)
The radial pile displacement u^ can be obtained from u by multiplication wi th sinp. This gives
u = vco^p sinP
pile
(6.12)
I f this radial displacement exceeds some maximum value, plasticity w i l l occur wi th in the pile t ip. Par. 6.4 gives
an example in which the Goodwyn-A pile parameters are used in calculating the radial displacement.
6.3 Minimum load needed to obtain failure of material
The resulting horizontal point load can cause local inhial damage i f the maximum load the pile tip can bear is
exceeded. For the maximum load fo l lowing formula is found (see appendix 2, page 15).
F„ = 0 / V 2 (6.13)
in which a is the yield sfrength o f the material and t the wal l thickness o f the pile.
G. Kramer 26
Chapter 6
Fig. 6.5 sliows tiie way in w l i i c l i a point load P creates damage on the edge o f a f la t plate.
Fig. 6.5 Point load on the edge of a flat plate
6.4 An example of pile tip deformation
As example, the parameters o f the open-ended piles used for Goodwyn-A w i l l be taken. Fol lowing values are
found for the piles and the guiding system:
Outer Diameter Pile: 2.65 m ;
Wal l Thickness Pile: 0.045 m;
Weight Pile: 520000 kg;
Yie ld stress Pile: 420 MPa;
Young modulus: 210 GPa;
Poisson's ratio: 0.3;
Descending velocity: 0.25 ms"' (estimated);
Angle P: 70° (es thna ted) .
A critical load o f 1.2*10'' N or 120 tons is found using Eq. 6.13. As the pile weights 520 tons, h seems
assumable that the pile could have obtained dsome kind o f init ial damage during lowering.
The pile stiffness as calculated wi th Eq. 6.1 and Eq. 6.8 has a value o f 9000 Nm"' . I f all parameter values are
substituted in Eq. 6.5, a displacement u, o f 0.61m is found. The relative radial deformation is given by the radial
displacement divided by the pile radius. A relative radial deformation o f about 46% is calculated for this case in
which al kinetic energy was disspated by the pile. I t can be assumed that this is enough to obtain the required
plastic behaviour.
Even i f only 30% o f the kinetic energy would be dissipated by the pile, thus creating an ini t ial damage, still
some 0.33m o f radial displacement is to be expected. This still seems enough to obtain a plastic zone wi th in the
pile tip.
G. Kramer 27
Chapter 6
6.5 Shape of the initial damage
The shape in which the pile w i l l deform during its installation depends mainly on the shape o f the touched
object. A theory that supports this idea is the collapse theory by Prof Vreedenburgh (1960) (see Appendix 3).
Hertz' theory o f contact forces between two bodies might as wel l be o f help in understanding and dealing wi th
the problem, even though the given example uses massive bodies instead o f a cylinder (see Appendix 3).
Fig. 6.6 Initial shape of the pile tip Fig. 6.7 Elliptical new shape of Fig 6.8 Collapsing of pile tip pile tip as a result of load increasing
Fig. 6.9 Load distribution on the pile tip
Fig. 6.10 Initial shape of the pile tip
Fig. 6.11 Circular surface of contact as a result of load increasing
Fig 6.12 Increasing surface of contact (exaggerated)
Fig 6.13 Load distribution on the pile tip
Fig. 6.14 Initial shape ofthe pile tip
Fig. 6.15 Local damage as a result of load increasing
Fig. 6.16 Increasing damage with increasing load (exaggerated)
Fig. 6.17 Load distribution on the pile tip
The collapse theory shows a distinct connection between the load placed on a cylinder or hol low pile and the
obtained shape o f this cylinder or hollow pile. It can be seen that a difference o f shape o f the pushing object
results in a different load distribution. Pushing wi th for instance a plane plate (see Fig. 6.6 to Fig. 6.9) on a
chcular object w i l l resuh m a smaller surface o f contact. The loaded area w i l l thus be smaller and a higher peak
value o f the load at the top o f the pile tip w i l l be a result as the total load (see Fig. 6.11).
Using a circular curved plate (see Fig 6.10 to 6.13) w i l l lead to a larger loaded area over which a distribution
wi th a smaller peak value can be found (see Fig 6.13). I f a sharp pointed pushing shape is used, the load w i l l
have a high peak value (see Fig. 6.16) and a small surface (see Fig. 6.14 to 6.17).
Tests in which the shape o f the pushing object was varied have been done on various pile tips. Shapes varying
f rom plane plate to sharp pomted ones were used. I f a plane plate is used, the pile tips seem to collapse as shown
in Fig. 6.8 to 6.11. The circular shape o f the pile tip gradually becomes more elliptic and even obtains a cashew
nut shape.
G. Kramer 28
Chapter 6
I f a circular shape as shown in Fig. 6.10 to 6.13 is used, the pile tends to obtain a large surface o f contact and
eventually two hmges occur, one at each side o f the pile t ip. A sharp pointed shape as the one shown m Fig . 6.14
to Fig. 6.17 leads to local damage o f the pile tip, thus leaving a large part o f the pile t ip undeformed.
In lateral pile dhection, the distorted shape gradually duninishes and the pile regains its original circular shape at
some lateral length. More about the executed tests and the obtained results can be found in chapter 8.
6.5.1 The angle a o f the pile's damage
A maximum angle over which the damage is bent can be found. This maximum angle occurs at the location o f
the maximum load. This is at the centre o f the bent pile tip. The size o f the angle can be described as the
arctangent o f the radial displacement 11 or 12 divided by the longitudinal damaged length h (see Fig. 6.18).
Fig. 6.18 Angle a within initial damage Fig. 6.19 Angle a within initial damage Fig. 6.20 Angle a within initial damage
A difference is made in the description o f the tangential distorted length a,b and c I f the size o f t h e elliptical
inhial damage has to be described, both the smallest and longest radius are given. I f the size o f a local damage
has to be described, the tangential length p and the radial length q are given. The angle a can be found at all four
sides o f an elliptical distorted pile tip (see Fig. 6.18). T w o o f the sides are transformed over a length Ij toward
the center o f t h e pile and two o f the sides are transformed over a length away f r o m the center o f t h e pile (see
Fig. 6.18). Chapter 7, which deals wi th the modelling o f inhial damages in a pile, w i l l specify the various
lengths.
Fig. 6.21 and Fig. 6.22, showing the pile in undeformed and in deformed situation, prove this conclusion can be drawn.
6.6 Conclusions
Although the model that calculates the radial displacement is a simple one, the resuh shows that inhial damage of the pile t ip can occur.
I f the pile hits the sleeve cone, h w i l l most l ikely obtain a damage as shown in Fig. 6.10 to 6.12 as the shape o f the sleeve cone is circular.
G. Kramer 29
Fig. 6.21 Undeformed pile tip as no load has yet been placed on it
G. Kramer 30
Fig. 6.22 Deformation of pile tip as in Fig. 6.11
G. Kramer 31
Chapter 7
7 Model for the deformation behaviour of a pile under an external load
In various tests tlie tips o f model piles deformed. A model is required to describe this deformation as a function
o f the inhial and physical condhions. In Chapter 6, h is already mentioned that various shapes may occur. The
shape o f t h e damage mainly depends on the shape o f the stamp used to deform the pile t ip. Dur ing tests various
dimensions o f the deformed shape can be measured at various loading conditions. These sizes can be used in the
development o f a geometric model. Two models are made. One o f which is used in the comparison between
model and test resuhs. I t should be emphasized that the models only count for situations in which a load is
placed on the pile. I f the cause o f the deformation (read the load on the pile t ip) is removed, all the elastic energy
wi th in the pile w i l l disappear and only plastic deformation remains.
7.1 Geometric modelling for the shape of the pile during loading
Two different shapes o f pile deformation are investigated and used in a model. The idea behind the two shapes
w i l l be explained. The equations needed to determine the exact shape, given measured values as input, w i l l be
given. Dur ing the experhnents done on piles, two different shapes were observed. The fu-st shape, model I , an
almost elliptical damage o f the pile t ip, occurs i f the radius o f the circular shape, used to deform the pile tip,
does not d i f fe r very much trom the outer radius o f the pile. The finst shape is modeled in Par. 7.2. The second
shape, model I I , a circular upper pile tip part that turns into an elliptical lower pile tip part via two plastic hinges,
was observed i f dies w i th larger radii were used. In the most extreme case, pushing wi th a plane plate on the
upper part o f a pile tip, damage o f the pile t ip was clearly visible. The second shape is modeled in Par. 7.3.
I f the sleeve cone (see Fig. 7.1) is looked at, the pile was subject to various loading conditions as these depend
on the location o f contact between pile tip and sleeve cone.
side-view sleeve cone
Fig. 7.1 Sleeve cone with various radii at various altitudes
Model 1 can best be used for the small ratio's o f R ieeve/RpUee- Model I I might has to replace model I in case o f
larger ratio's o f R i ev/Rpiiee as the first model might not have enough accuracy.
Many tests were done w i t h apparently relative small ratio's o f RpHe/Rsieeve. The ratio was not known during the
execution o f most o f the tests as the idea o f a sleeve cone causing the inhial damage was developed quite late in
the study. Because o f this, a model was developed, which might only be accurate enough for small ratio's o f Rpne
over Rsieevecone Pst. 7.2 w l l l show the way in which this model was designed. To have a more accurate model a
start has been made in developing a model for the larger radii o f the sleeve cone. This model is given in par. 7.3.
I t should be clearly stated that both models contain assumed shapes. I t was tried to find a shape that could
describe the observed pile tip shapes during deformation at best.
G. Kramer 32
Chapter 7
7.2 Model I , elliptical top - elliptical bottom damage of the pile tip
The model exists o f two ellipses; a horizontal one covering the damage o f the top part o f the pile t ip and a
vertical one covermg the damage over the bottom part o f t h e pile t ip (see Fig. 7.2).
Pile tip top
^ j i e w ^
/ a \ a \
\ \ ' ƒ
\ p i l e /
> X Pile tip bottom
Fig. 7.2 Shape of pile tip with elliptical top and bottom
The cartesian equation for an ellipse is:
] — + — = 1 with a>b a' 6 '
(7.1)
7.2.1 Maximum and minimum values for various lengths
The measured values are all min imum or maximum values as they are found at the pile t ip at which the new pile
shape has hs maxhnum damage. In the next paragraph, the way in which the shape o f the inhial damage can be
found in the pile, is described. As was said before, the value o f a and the sum o f (b+c), which w i l l be called (d)
have to be obtamed f r o m experiments.
To determine the new shape o f the pile tip, another equation is needed. The equation fo r preservation o f
circumference w i l l be used. The circumference o f an ellipse is given by
O = 2na a - b
1 - v/ith a>b 2a^
As only ha l f o f the circumference is needed, the circumference is divided by two. The circumference for the
upper ellipse thus becomes
O = na upper A
with a>b (7.3) la'
In the same way, an expression for the circumference o f the lower ellipse is found
O, = nc lower \
c ' - a ' 1 - with c>a
2 c ' (7.4)
G. Kramer 33
Chapter 7
Preservation o f circumference gives
O + O, = mr ., upper lower pile
(7.5)
and tlius
no. 1 - ^1-:^ . no 2 a '
1 - = 2.r pile (7.6)
W i t h d = b+c, Eq. 7.6 can now be rewritten in such a way that c can be calculated knowing a, d and R^ÜJ.
1 - c,' - ^ Ida - c ' ^ ^
2 a ' 1 -2R (7.7)
The value for c can be determmed iteratively. W i t h c known, the value for b can be found.
The various radi i can best be described in polar coordinates. Eq. 7.8 and Eq. 7.9 are used to determine the
correlation between the radius o f a point and its polar coordinate for the upper ellipse.
è ' x ' + a V ' = a ' è ' (7.8)
X = r*cos(j) y = r*sm<^ (7.9)
Substitutmg Eq. 7.9 in Eq. 7.3 and rewrhmg gives Eq. 7.10.
r = abs ( upper "
a^b'
^ è'cos'cj) + a'sin'(|) (7.10)
The same can be done in the determination o f the correlation between the radius o f a point and hs polar coordi
nate for the lower ellipse. This gives Eq. 7.11.
^ c'cos'tj) + a'sin'4) ) (7.11)
7.2.2 Initial damage in the lateral direction
The initial damage can be found over some laterally deformed length h (see page 29). This length is measured in
the experiments. The values o f length a, b, c and e are known at length h from the pile t ip. A t this point the pile
has its original chcular shape. This means that dimensions a, b, and c all have the same value Rpn^ and that 'e '
becomes zero As linearity is assumed fo r the way initial damage can be found over the lateral pile length h, Eq.
7.12 is found for the mcrease o f length a in lateral direction.
= Kae- ^ (7.12) I
G. Kramer 34
Chapter 7
Linearity is also assumed for tlie decrease o f lengtii d. Tliis gives
dix) = (2r ,, -d^J^ + rf,
Values for a and d can now be found for all points in the lateral direction o f the pile. Because a and d are
determined for each pomt, length b and c as wel l as the new radius fo r each point are determmed.
7.3 Model I I , C ircu lar top - elliptical bottom damage of the pile tip
For the modeling o f t h e damaged pile t ip , certain dimensions should be known to determine the new Cartesian x-
and y - values for all the points situated on the new shape. During the experiments, three o f these are quite
shnple to measure. These are (see Fig. 7.4):
1. the maximum horizontal length 2a between the deformed points;
2. the maximum vertical length d between the deformed points;
3. the horizontal length 21 between the boundary points o f the line o f contact.
A certain shape has to be defined at which certain geomehic rules can be applied. The shape chosen can be
divided m two parts (see Fig. 7.5):
1. a circular upper part, the radius o f which is the same as the radius o f the shape used to lay a load on the pile
tip (see Fig. 7.6);
2. an elliptical lower part (see Fig. 7.6). The radius o f the points siUiated on this ellipse depends on theh
location wi th regard to the center o f the ellipse.
W i t h this known, an equation has to be found which can determine the Cartesian coordinates o f each point o f the
ellipse. Fig. 7.6 shows the overall picture in which all the used lengths and angles and their denominations are
given.
Fig. 7.3 Deformation ofthe pile tip as a Fig. 7.4 Lengths measured during experi- Fig 7.5 Shape ofthe pile tip with a circular result ofthe loading conditions ment at various loads upper part and elliptical lower part
As the lengths are measured at the pile tip, this cross section w i l l be taken. The way in which this damage
continues over the lateral direction o f the pile w i l l be discussed in Par. 7.3.2.
The values o f both the lateral and the two radial distorted lengths are considered known as we l l as the horizontal
length between the boundary points o f the line o f contact at the pile tip.
G. Kramer 35
Chapter 7
7.3.1 Cross section at the pile tip
Fig. 7.6 Overall picture of the various lengths and angles used by the model
Fol lowing relations between the various lengths can be found:
d = b + c + f (7.14)
(7.15)
(7.16)
(7.17)
(7.18)
b ^ c = f - (R,^^, - ^ r I , - I') (7.19)
Fol lowmg relations can be found for the determination o f the angles as a funct ion o f t h e lengths:
271 / Y = atan^
360 c + b + g -) (rad) (1.20)
G. Kramer 36
Chapter 7
Tl = atan{ —) {rad) 360 /
(7.21)
I t can be seen that, i f lengths b and c are known, the coordinates o f the entire shape are known.
Preservation o f chcumference can be useful in calculating the value o f b.
With the angle o f y and R|„,j known, Eq. 7.22 gives for the length o f the line o f contact
O. (7.22)
The equation for the circumference o f an ellipse wi th sides a and b and a>b is given by
O „. = 2-Ka ellipse /<
1 -g ' - b-
la^ (7.23)
The chcumference o f t h e undistorted pile shape is given by
Op„e = ^^Rplle (7.24)
Fig. 7.7 Elliptical shape between two angles 6
I t is found that the remaining circumference for the elliptical shape is the difference between Opü^ and 0„pp„. This
remaining circumference is not equal to the total circumference o f an ellipse as the elliptic shape starts at an
angle ri° and finishes at an angle (-ri)° (see Fig. 7.7).
The midpoint equation o f an ellipse is given by
(7.25)
Eq. 7.25 can be rewritten in polar coordinates. This gives the radius as a funct ion o f angle 6
m = a^b'
^ 6 W 9 + a 'cos '0 ^ è W e + fl'cos'0 (7.26)
G. Kramer 37
Chapter 7
Next Step in tlie determination o f the chcumference o f an ellipse between two angles is the solvmg of the
mtegral
[ (R(Q)*d)dQ (7.27)
The solution for the prhnhive o f Eq. 7.27 is stepwise given in Eq. 7.28 to 7.38 The first step is to f ind the
prhnhive o f the radius R(6) . In Analyse, J.H.J. Almer ing e.a., the primitive o f Eq. 7.28 is given by
( ^ = In ( ;c + ^ / ^ ^ ^ ' ) (a e S l ^ (7.28)
This function seems to be the same as the funct ion found for R ( ö ) i f R(6) is slightly rewritten. Rewrhmg gives
RiQ) - & = ^ (7.29)
sjbhm^Q + a 'cos 'e ^b\l - cos'6) + a'cos^O
Rewritmg o f t h e denominator gives
^,(0) = ^ = ^ (7.30)
\lb^ + ( a ' - Ö') cos'e \Jb^ + e 'cos 'e
Wi th
(7.31)
mtegration o f Eq. 7.30 gives
Km.se (^) = * In ( X + s/x' + a' ) (7.32)
Rewriting o f x to
* = y ^ W ö (7.33)
leads to
R ... = * In ( \le 'cos '0 + sje^cos^Q + ö ' ) (7.34) P prim
Rewrit ing o f c' gives
Kmpse , = * ( \ / (a ' - 6 + \ / (a ' - è ' ) c o s ' 0 + b^ ) (7.35)
G. Kramer 38
^ Chapter 7
or simplified
^ellipse = ab * \n i cosQ\J(a^ - b^) + \J{a^ - è ' ) c o s ' 6 + fe' ) with a > 0, b > 0, 0<e<7t (7.36)
W i t h the prhnitive o f the function R(6) known, the second step in solving the length o f the elliptic circumferen
ce is partial integration o f Eq. 7.27.
I f f ( x ) and g(x) can be both differentiated, then equation 7.37 can be used in solving the integral o f f (x)g ' (x)dx.
[Ax)g 'ix)dx = Ax)g(x) -[Ax)g(x)dx (7.37)
R(e) w i l l be seen as g(x) and 6 as f (x ) . The solution for the chcumference o f an ellipse between two angles is
given by equation 7.38.
Oempse = 2(, a'b'
è W e + a ' c o s ' e d - ab *ln (cos6
The one thing that remams is the substitution o f an angle r\ after which the chcumference o f the elliptical part o f
the pile shape is known. For angle r|, Eq. 7.21 is substituted as boundary condition in Eq. 7.38. For length b, Eq.
7.18 is substituted in Eq. 7.14. Rewrhing o f Eq. 7.14 gives
b - d - (R,^, - f L ~ T ^ ) - c (7.39)
Substitution o f both Eq. 7.21 and 7.39 in Eq. 7.38 gives an equation in which length c is the only unknown. This
length can now be calculated heratively. W i t h c known, b can be calculated as wel l . The x- and y- values o f all
the pomts can now be determined taking the center o f the circular top o f the pile tip as center o f the x-y-plane.
7.3.2 Modeling of damage in lateral pile length
Another assumption has to be made to make modeling in lateral pile direction a little easier. Fol lowing is
assumed: the maximum horizontal and vertical length wi th in the shape o f the pile tip w i l l increase and decrease
Imearly over the lateral distorted length to their inhial values o f 2*Rpj|e (see Fig 7.8).
Length a w i l l decrease linearly unti l it obtains its original value Rpn at the end o f the lateral distorted length.
This leads to the Eq. as described in Eq. 7.40.
1 «(^) = Ku,p - ^p,7.)(l - ^ ) ^ Rp.u (7.40)
This gives, for z = 0, an a(0) o f apjiedp and fo r z = h an a(h) o f RpHe
Length f is assumed to decrease linearly over the lateral distorted length h to a value o f zero. This gives
] A^) = /p,7.«p(l - f) (7.41)
G. Kramer 39
Chapter 7
Fig. 7.8 View of damage in lateral pile direction
Length c is assumed to increase linearly over the lateral distorted length h unt i l h obtains its original value RpHe.
This gives
(7.42)
Length b is assumed to increase linearly over the lateral distorted length h unti l i t obtains hs original value Rpn .
This gives
(7.43)
The model shows that for each step dh, taken in lateral direction, more o f the circumference w i l l obtain an
elliptic shape and fewer remains circular. This is due to a supposed increase o f length c in lateral direction which
leads to an increase o f angle r j . The elliptical shape however becomes more circular unti l the entire pile regains
Fig. 7.9 Parabolic shape in lateral pile direction
its original circular shape at the end o f the damage (see Fig. 7.8).
The distorted area on the top o f the pile t ip w i l l have a parabolic shape in lateral direction (see Fig. 7.9). This is
the resuh o f the fact that length 1 does not decrease linear over the lateral distorted length h.
G. Kramer 40
Chapter 7
7.4 Numerical model for behaviour model I
A numerical model has been made in which the entire pile is discretised. How this has been done is shown in
f o l l o w m g subparagraphs. The programming language Turbo Pascal has been used. The programme is given in
Appendix 8, page 4 e.a.. The purpose o f the programme is to determine which parts o f a pile show plastic
behaviour and which parts do not during loading o f the pile t ip.
7.4.1 Discretisation of a distorted pile
Discretisation means nothing more than the division o f a length into some parts. In radial dhection this can be
done in some angle (j) (rad). In lateral length, the pile w i l l be divided in parts dh (see Fig. 7.10). Values for R„e„
can be given to each o f this pieces.
dl
Fig. 7.10 Discretised part ofthe pile
7.4.2 Determination ofthe strain in a pile part
The ini t ia l ly undistorted pile parts all carry the same information as they all have the same radius and no strain
yet occurs in any part o f the pile. The pile can thus be divided in such a way that the distorted pile can be
compared wi th the undistorted pile. I f the distorted pile is looked at, it can be seen that all parts have a different
radius. This means that, taken a same angle (f) for each part, the length dl becomes different for each deformed
pile part. I f the strain in the material at a distance z from the center line is needed to be known, length dl for both
the undistorted and distorted pile part has to be the same. The angle (j) for the undistorted pile part has to be
chosen in such a way that length dl is the same as the length dl o f the distorted part. The strain e o f a point at
distance z f rom the center can be determined i f the new and the old radius are known. The derivation o f the
strain at a pomt z f rom the center line w i l l be started wi th . To determine the strain e, one has to know the
original and the new length o f t h e pile part (see Fig. 7.11 and Fig. 7.12).
Fig. 7.11 Old dimensions of pile part Fig. 7.12 New dimensions of pile part
G. Kramer 41
Chapter 7
Eq. 7.44 gives dl ,
rf/, = rf/„(l + — ) (7.44) pile
Eq. 7.45 dl |* gives
rf/, = rf/„(l + — ) r
(7.45)
The strain e is given by
e = dh
(7.46)
Substituting Eq. 7.44 and Eq. 7.45 in Eq. 7.46 give the strain as a function o f the length z, the new radius and the
old radius
( 1 + — ) - )
e =
1+- new pile
(7.47)
pile
7.4.3 Behaviour of pile part under pressure
stress (N/mm ) I
Loaded materials have three ways o f behaviour. Their behaviour
depends on shain and the yield stress o f t h e material. I t can be either
elastic, elastic-plastic or fu l l y plastic. Fig. 7.13 shows a simplified
stress-strain curve.
Materials first behave elastic (see Fig. 7.14), then elastic-plastic (see
Fig. 7.15) and f inal ly full-plastic (see Fig. 7.16) i f load is inferred. A
maximum elastic strain ep can be found which varies for each materi
al.
strain (%)
Fig. 7.13 Simplified stress-strain curve
Fig. 7.14 Elastic material behaviour Fig. 7.15 Elastic-plastic material behaviour Fig. 7.16 Full-plastic material behaviour
G. Kramer 42
Chapter 7
Strain is tlius important for recognizing tlie behaviour o f a pile part. I f the strain does not exceed e\ the material
w i l l behave elastic.
Fig. 7.17 Point w' and w within pile wall
I f the material exceeds stram e', h w i l l behave plastic. Within the wal l thickness o f the pile, a clear point w can
be found at which elastic behaviour ends and plastic behaviour continues (see Fig. 7.17). The equation for point
w* is:
E
1
new pile
(7.48)
A point t at a distance smaller than t ' w i l l behave elastic as a point at a larger distance than t* w i l l behave plastic.
I f the calculated point t* exceeds half the wa l l thickness, the material w i l l behave f u l l y elastic. For every point o f
the pile circumference point t* can now be determined. In this way the parts o f the pile circumference that
behave elastic, the parts that behave elastic-plastic and the parts that behave full-plastic, can be determined.
7.4.4 Calculation of plastic work and elastic energy
7.4.4.1 Plastic worlt
With the value o f t* known for every pile part o f the circumference, the plastic work per unit area wi th in this part
can be determined. The plastic work is given by
W
P. = 2 | a^*(e -eOrfz [NIm] (7.49)
W '
Substitutmg Eq. 7.47 in Eq. 7.49 gives
P „ = 2 [ a *(z ( J - - - L ) - ^ ) d , (7 50)
^«e» ''pile E
G. Kramer 43
The solution o f this integral is given by
Chapter 7
(7.51)
This can be written as
pile Ewt 2 r r ., E new pile
(7.52)
which is the same as
P» = " v ( — - — ) ( ^ ' - w - 2—(w -w •) ''new ''pile ^
(7.53)
The total o f plastic work can be found by summation o f the plastic work over the discretised pile parts.
7.4.4.2 Elastic energy
W i t h the value o f t ' known for every pile part o f the circumference, the elastic energy wi th in this part can be determined. The elastic energy is given by
£^ = 2( ƒ (oe)rfz + fiae')dz ) (7.54)
in which the first integral gives the elastic part and the second integral the elastic-plastic part o f t h e solution.
Wi th O = E*e for the elastic part and e = o^E for the plastic part this gives
E^ =2( ƒ iEe^)dz + ƒ {^)dz ) (7.55)
Substitufion o f Eq. 7.47 in Eq. 7.55 gives
£ = 2( r & ' ( - L - _ L ) V , . p ^ , ) J r ., J E
new pile
(7.56)
The solution o f this integral is given by
-) + 2 — ( w - w ) [ ] new pile m'
(7.57)
G. Kramer 44
Chapter 7
7.5 External work
External work is caused by the load. It consists o f an elastic and a plastic part and has to be in balance wi th the
total o f internal work. This gives Eq. 7.58
K - P . ^ E. [ ^ ] (7.58) m
in which
+ Kp (7.59) m
External work can be found as the area below the load-displacement curve (see Fig. 7.18). The figure is a resuh
o f measurements during an experiment. It can be written as
= ^Fda [Nm] (7.60)
Load (N)
Elastical part
Displacement (mm)
Instead o f solving this integral one can discretise the area in parts da. Each part w i l l have a medium value for the
load F. To know the enthe extemal work one only has to count the discretised surfaces. This process can be
done w i t h the aid o f 'Excel ' , a spreadsheet programme. The total plastic work and elastic energy can be
calculated and hereafter compared wi th the theoretical outcome. I f the values match, an emphical database can
be made in which combinations o f a distorted pile shape wi th a load needed to cause the pile damage, can be
found. In this way, h should be possible to predict the distorted shape o f the pile by knowing the pile material
and the load applied to the pile.
G. Kramer 45
Chapter 8
8 Comparison of experimental and theoretical results of pile-loading system
This chapter gives a review o f the tests done wi th the pile t ip deformer (see Fig. 4.10) which is used to make
elliptic/oval initial damage. Chapter 7 deah wi th the development o f a model that could represent the shape o f
the init ial damaged pile t ip durmg loadmg. Input for the model is given by several measured lengths during the
pile loadmg. Experiments were done to determme elastic and plastic energy wi th in a pile during loading and to
see the effect o f various shapes on the shape o f the mitial distortion. It was hied to show the validity o f the
model by comparing the plastic work as calculated wi th the plastic work as obtained f rom the experiments.
M u c h time was spent w i th the set up o f the test equipment and the avoidance o f hysteresis to obtain valuable
values fo r the elastic energy and plastic work wi th in the pile. Besides this, a program had to be written which
could calculate theoretical values for the elastic energy and plastic work.
The way m which hysterisis wi th in the equipment was dealt wi th , w i l l be discussed in Par. 8.1. The influence
various loading shapes had on the shape o f t h e pile tip during loading w i l l be discussed in Par. 8.2. Par. 8.3
shows the obtamed test resuh for two performed tests series. Par 8.4 shows the output o f the computer program
in which plastic work and elastic energy are calculated wi th in a pile during the loadmg process. Both resuhs w i l l
be compared m Par. 8.5. Conclusions are given in Par. 8.6.
8.1 How to determine and deal with hysterisis
Hysteresis wi th in test equipment has to be avoided as it dishirbs the test results. Many things can cause
hysteresis. Loadmg equipment always shows some hysteresis. Unfortunately, little can be done about that. I f the
various parts o f the test set are not sufficiently f ixed to each other, hystersis occurs because o f movement
between the parts. A better connection among all parts can reduce this part o f hysteresis. Friction between the
pile tip and the die can be seen as hysteresis as wel l . When load on the pile tip is decreased, the load-
displacement path is enormously disturbed as a sudden fall-back o f the load occurs. As was writ ten in Par. 7.5, a
load-displacement curve is needed to determine plastic work and/or elastic energy. Fig. 8.1 shows the load-
displacement curve obtained before attempts were made to reduce the hysteresis. Fig. 8.2 shows the load-
displacement curve when f r ic t ion between the pile tip and the loading shape was reduced. Fig. 8.3 and Fig. 8.4
show the obtained load-displacement curves when displacement between the various parts o f the test set was
reduced.
Ruull o rWIU (lliloitlon l o l 'GKl l ' RemUt orlnllUI dl.lartkn EUlp.t'
ooo 0.S0 l.oo I.JO xm 2.50 Ï.0O I . H 1.11 l-H i . I I l . H 1.» I.M
DbplmBnllnin) Dll ,U»Btlt IBB)
Fig. 8.3 Load-displacement curve with almost no hysterseis Fig. 8.4 Load-displacement curve with almost no hysteresis
left left
G. Kramer 46
Chapter 8
Putting a ball bearing between the rod and the load cell reduced fr ic t ion between the pile tip and the die (see Fig.
8.5). The ball bearing made small horizontal displacement o f the die possible. The die now can fo l low the
relative small horizontal pile tip displacement (see Fig. 8.6). The horizontal displacement remams small
compared w i t h the vertical displacement because the pile deforms simuhaneously. Remaining hysteresis has to
be subtracted from the plastic work.
Fig. 8.5 Hinge between load cell and die Fig. 8.6 Horizontal and vertical displacement of pile tip
8.2 Influence of various stamps on shape of pile tip during loading
The diameter o f the die seems to have influence on the shape o f the inhial distortion in the pile tip in two ways.
Obtaming plastic pile tip deformation during loading when diameters were used which were only a bit smaller
than the pile diameter seemed very d i f f i cuh . Deformation seemed to occur more easily when dies wi th larger
diameters were used. The shape o f the damaged pile tip during loading seemed to depend on the diameter o f the
die as wel l . When small diameters were used, the pile only obtained a surface o f contact the size o f which
depended on the amount o f load. When large diameters or a plain plates were used, the surface o f contact
coUapsed according to the collapse theory o f Prof Vreedenburgh (see Appendix 3).
Various curvatures can as wel l be found along the guiding system's sleeve cone. This cone is used to guide the
pile in the pile sleeve. The maximum effective cone diameter has a value o f about twice the pile diameter. This
shows that curvatures up to 60 mm could be given to the dies. The maximum diameter used, had a value o f 42
m m . When this diameter was used on the scaled piles, not much load was needed to obtain quite large initial
distortions. Using even larger diameters would lead to even less required load and larger initial distortion. Fig.
8.7 gives the tendency obtained fo rm experiments for the load needed to obtain the same size o f inhial distortion
and the size o f this distortion for various ratios o f die diameters over pile diameters.
0 I 1
Pushing shape diameter
Pile diameter
Fig. 8.7 Tendency in required load and obtained initial distortion
G. Kramer 47
Chapter 8
8.3 Obtained test results
Several tests were done to obtain an idea about the shape a pile tip would obtain when it hhs the sleeve cap. A
program was written in Quick Basic (see Appendix 8, page 12). I t could measure the amount o f load m every
displacement step and that could write the data m a data f i l e . The first test was wi th a die diameter o f 33 mm,
only 3 m m larger than the pile diameter. Al though much load was placed on the pile tip, no deformation
occurred. The pile obtained a surface o f contact that was too small to lead to plastic deformation as the pile got
stuck between the two die sides (see Fig. 8.8).
Fig. 8.8 Pile tip getting stuck between two sides
Two test series w i l l be discussed to show the kind o f output that can be obtained f r o m the test results and the
way this result can be translation into something useful. A die diameter o f 42 m m was used for both test series.
8.3.1 Hysteresis and Young's modulus
The hysteresis and the Young's modulus o f the pile can both be determined wi th in one test. A small plug is
placed in the pile tip to impede pile tip deformation. Hysteresis is now considered the difference between the
upward and downward load-displacement curve. Fig. 8.9 and Fig. 8.10 show the curves for respectively 'test 1'
and 'test2'. Hysteresis was measured to be 4.18 % o f the area below the load-displacement curve for test 1 and
5.4 % for test 2. The Young's modulus o f both piles was calculated with the bending formula given by Eq. 8.1.
Decermln jlion of Young Mndulu! inil hyilcrtili for 'lesi I ' Ddcroiimtioii of Young Modulm mil hyrtereib for 'lesl 2'
in which w represents the displacement (mm); F represents the load on the pile tip (N) ;
1 represents the pile length from pile tip to clamp (mm); E represents the Young's modulus (N/mm') ;
I represents the moment o f inertia (mm'').
G. Kramer 48
Chapter 8
The moment o f mertia for hollow piles w i th small pile walls is given by
Chart 8.1 gives the various needed parameters for both used piles.
Parameter Test 1 Test 2
Load on pile tip (N) 239.12 225.63
Length 1 to clamp (mm) 31.4 31.9
Displacement w (mm) 5 5
Outer diameter (mm) 31.58 31.58
Inner diameter (mm) 30.98 30.98
Chart 8.1 Various needed parameters
The calculated Young's modulus for test 1 and test2are respectively 1.4'''10" N / m ' a n d 1.35"'10" N / m ' .
8.3.2 Load displacement curves of i n i t i a l dde fo rmat ion tests
Fig. 8.11 and Fig. 8.12 show the obtained load-displacement curves for respectively test 1 and test 2.
Load-displacement cunc (esl I Load-dlsplflcement cune 'lest 2'
Fig. 8.11 Load-displacementcurve 'test 1' Pig. g.12 Load displacement curve 'test 2'
Fig. 8.13 shows the division o f the area below the load-displacement curve in a plastic/elastic part. The value for
the plastic work is calculated by discretising the area in parts 'da' which each have a medium value for the load.
As still some hysteresis has to be compensated, 5% o f the plastic area w i l l be subtracted from the plastic work.
Elastic energy however cannot be obtained f rom the test results because the pile displacement is different from
the die displacement. This is caused by the deformation o f the pile during the loading process. The real pile
displacement w i l l be much smaller than 10 mm. Plastic deformation however can be measured as the area
between the loading and the unloading curve w i l l remain the same, even i f the real pile displacement is plotted
on the X-axis (see Fig. 8.14).
The calculated plastic work has a value o f 231.3 N m m in case o f test 1 and a value o f 109 N m m in case o f test 2.
G. Kramer 49
Chapter 8
Load(N)
Elastical part
da Displacement (mm)
Fig. 8.13 Division of area below curve in plastic and elastic part
Load.diiplacemenl path foTdiipl . of die Load-dijplaccment path for diipl. of pile Max. load on pile lip
DtiptaccmenI (mm)
Fig. 8.14 Conservation of plastic work area
8.4 Graphical display of calculated values from the numerical model
The maximum horizontal and vertical distance between points and the longitudinal deformed length were
measured durmg the loading test at various loading points. The values o f the various measured lengths for test 1
and test 2 can be found in appendix 9, page 1. These values were, together wi th the pile parameter values, used
as input for the computer program. Chart 8.2 gives the amount o f load on the pile tip for the points at which
deformed lengths were measured.
Test Name Load (N) Test Name Load(N)
Testl,Aml 44.2 Testl,Am6 236.7
Testl,Am2 84.6 Testl,Am7 272.2
Testl,Am3 120 Testl,Am8 312.7
Testl,Am4 160 Testl,Am9 344.6
Testl,Am5 197.4 Testl.AmlO 372.8
Chart 8.2 Load on pile tip
The calculated values for test 1 its elastic energy wi th in the cross-section at 0 m f r o m the pile tip can be found in
appendix 9, page 2. I t seemed that no plastic work was calculated as the strain wi th in the discretised pile parts
remamed below the elastic Ihnit. The values for the elastic energy remained low as wel l . The elastic enerev can
be plotted as a function o f the rotation angle ( j ) . Fig. 8.15 and Fig. 8.16 show the deformed pile cross-section at
some length f rom the pile tip wi th various magnitudes o f load were placed on the pile t ip. Fig. 8.17 and Fig. 8.18
show the curve o f the elastic energy as wel l as the way it increases when more load is placed on the pile for the
pile t ip and cross-sections at various lengths f rom the pile t ip. The rotation angle phi is zero at the top o f t h e pile
tip. This is the place where the die touches the pile t ip.
Fig. 8.15 Test 1 its deformed pile at pile tip Fig. 8.16 Test 1 its deformed pile at some distance from pile tip
G. Kramer 5Ö
Chapter 8
Distribution of elastic energy in cross-section Om from pile tip
0.025 1
Kotation angle phi (rad)
Fig. 8.17 Distribution of elastic energy in cross-section at pile tip
Distribution of elastic energy in cross-section at various distances from pile
tip
0 1 2 3 4 5 6 7
Rotation angle phi (rad)
Fig. 8.18 Distribution of elastic energy in cross-sections at various distances from pile tip
The results o f program 'ellipse' are as expected. The shape o f the deformed pile is calculated for every cross-
section o f the pile. Considering the distribution o f the elastic energy, it can be seen that most elastic energy
appears right below the pomt o f contact wi th the die. The point that has a new radius wi th the same value as the
original radius shows no elastic behaviour at all . A l l points o f the bottom ellipse, which describes the unloaded
side o f the pile, seem to have obtained the same amount o f deformation. This can be concluded as the elastic
energy remams ahnost constant.
N o plastic work is however calculated by the program as the elastic l i m h seems not to be exceeded. This is
conhary to the experimental results. The reason for this is given in Par. 8.6.
G. Kramer 51
Chapter 8
8.5 Deformed lengths as function of load
The measured deformed lengths can be plotted against the load on the pile tip. Fig. 8.19 and Fig. 8.20 give these
plots fo r respectively test 1 and test 2. The maximum horizontal and vertical distance between two pomts o f the
cross-section at the pile t ip are divided by the pile diameter to obtain a dimensionless number.
2a/D and d/D as a function of the load 28/0 and d/D as a function of llic load
Fig. 8.19 Maximum horizontal and vertical distance beUveen points of the cross-section at the pile tip of test 1
Fig. 8.20 Maximum horizontal and vertical distance between points of the cross-section at the pile tip of test 2
The same can be done for the longitudinal deformed length. Fig. 8.21 and 8.22 show the results for test 1 and
h/D as a function of the load h/D m a function of thc toad
Fig. 8.21 Measured longitudinal deformed length in test 1 for Fig. 8.22 Measured longitudinal deformed length in test 2 for various various loads placed on pile tip loads placed on pile tip test 2.
Linearhy is found for the way in which the maximum horizontal length between two points increases and the
maximum vertical length between two points decreases. The length o f the deformed zone seems to have a finite
value.
I f more tests were to be done, a data base can be made in which the shape o f the deformed pile during loading
and the permanent pile deformation in the unloaded situation can be stored as a funct ion o f the load on the pile
t ip. Unfortunately, not enough time was available to investigate the dimensions o f the permanent pile
deformation in the unloaded situation as a function o f the maximum load on the pile t ip. The shape o f t h e initial
distortion in an unloaded situation has to be known as load on the pile tip w i l l become zero when the pile slides
through the pile sleeve in the soil. Fig 8.23 shows the increase and decrease o f the load during the various steps
o f the pile installation.
G. Kramer 52
Chapter 8
A m o u n t o f load
Pile descends in water
Sleeve cone is hit
0
Pile slides over sleeve cone
Pile slides through pile sleeve
Pile is dr iven in soil
Installation Step
Fig. 8.23 Load on pile tip during various installation steps
8.6 Difference in calculated plastic work
The difference in the theoretical calculated plastic work and the experimental outcome might be explained i f the
geometry o f the deformation model is looked at. It was said before that model 1 o f chapter 7 was used to
describe the shape o f a pile during a loading test. This model was written into a program that could calculate the
plastic work and elastic energy wi th in a pile by knowing the strain in all discretised pile parts. I t now seems that
only elastic energy was measured. This means that the discretised pile parts obtained less than the maximum
elastic strain as calculated wi th the yield strength and the Young's modulus o f the pile.
I f model I I was used instead o f model I , plastic work would probably be measured. The geometry o f model I I
enables plastic hinges to occur in the two points in which the circular shape changes into the elliptic shape (see
Fig. 7.5). More plastic work w i l l be calculated as local bending is accounted for .
8.7 Conclusions
Up to now, a comparison between experimental resuhs and a theoretical model can hardly be made. To obtain a
better comparison, several points have to be adapted:
- model I I o f chapter 7 has to be used instead o f model 1 as it enables the occurrence o f 'plastic' hinges;
- a test set up has to be made in which hardly any hysteresis occurs. The reduction to 5% might not yet be
enough.
- more tests need to be done to change the yet describing model into a predicting model. I f enough data can be
collected, an idea about the size o f the initial distortion for various cases can be obtained.
G. Kramer 53
Chapter 9
9 Model on elastic pile-soil interaction behaviour during driving
A n elastic model is proposed for the interaction between soil and pile during penetration o f t h e pile. The model
can calculate the amount o f radial pile deformation wi th given values for certain parameters. I t then can be seen
i f the amount o f deformation is acceptable. Both soil and pile behaviour durmg penetration is looked at. Linear
springs are used to mdicate the behaviour o f both materials. When a pile wi th an initial damaged pile tip
penetrates the soil, pressure w i l l be build up as soh normally entering the pile is now pushed away (see Fig. 9.1).
The amount o f pressure that is build up can be calculated i f both the material stiffness and the displacement are
known. Eq. 9.1 shows how stress wi th in and displacement o f the material determine the stiffness K .
The pile strength depends on hs material properties, represented by the Young's modulus and the Poissons ratio
V and its dimensions (diameter and wall thickness). These factors can, combined, be put in a factor and seen
upon as a stiffness o f the pile. Both stresses in the soil and stresses in the pile can now be calculated and
springs
point
Fig. 9.1 Initial pile shape used in pile-soil interaction model
interpreted.
Par. 9.1 gives the assumed shape o f the init ial damage. In Par. 9.2, the way in which the stiffnesses for both pile
and soil are determined, is discussed. A n easy way o f calculating the Young's modulus o f soil is given in Par.
9.3. Par. 9.4 discusses the pile-soil interaction model and the use o f rigidhies wi th in the model. The possibility
o f determining a maximum penetration depth or maximum radial displacement is given in Par. 9.5. A n example
that uses pile parameters o f the brass model piles is given in Par. 9.6. Par. 9.7 gives a graphical output in which
the effect can be seen o f one changing parameter on another. How to bring plasticity in the model and the effect
o f this plasticity is discussed in Par. 9.8. Conclusions are f ina l ly given in Par. 9.9.
9.1 Shape o f initial damage
A pile w i t h an elliptical pile tip damage is chosen as initial pile shape. The ellipse consists o f t h e axes a and b
wi th a > b. The damage can be found over a longitudinal length 1 and is considered linearly decreasing over this
length. The maximum angle a describes the angle given by the arctangent o f the maximum damage at the pile
tip over the longitudinal length 1. In fo l lowing equations the maximum angle w i l l be called tana to s impl i fy the
equations. The radius o f the points on an ellipse are written in polar coordinates. This gives fo r the radius at a
depth z
Ka,„, = Kile - z*iana*cos2Q (9.2)
G. Kramer 54
Chapter 9
A t a depth I the radius is given by (see Fig. 9.1):
Koin, = K<ie - '*tana*co^20 (9.3)
For axes a and b Eq. 9.4 and Eq. 9.5 are found (see Fig. 9.2):
a = i?^,,^ + z*tana (9.4)
(9.5)
Fig. 9.2 Cartesian and polar coordinates
9.2 Determinat ion o f t h e rigidit ies o f pile and soils
To determine the various rigidities Ksoiii„, V^^^AmK and Kpüe o f respectively the soil wi th in the pile, the soil outside
the pile and the pile itself, equations had to be found by which the radial stresses and displacements wi th in the
pile are given. Equations which originate from the calculation o f stresses in tunnel linings can be o f use. I f the
effect o f gravitation is not counted wi th , an open-ended large diameter pile can be seen as a tunnel. The
complete solution for the ovalisation of tunnels is given by Verrui j t [3] . This solution can be used, as the first
step in the deformation process o f a pile is the ovalisation o f the pile.
Appendix 4 gives the equations for the displacement, sfrain, volume sfrain and stresses. Out o f theses equations,
the radial sfress (see Eq. 9.6) and the radial displacement (see Eq. 9.7) are used to determine the rigidities.
1 o ^ = {{m - \)e + 2e^^)n = W - A - 1^] ^0^26 r ' r
(9.6)
u = + — + — ] C052Ö r
(9.7)
Four constants, A , B , C and D have to be determined. This can be done only i f equations are found in which
boundary condhions for the situation can be prescribed.
G. Kramer 55
Chapter 9
The pile in soil is modeled as in Fig. 9.3.
Fig. 9.3 Model of a pile with soil in and outside of the pile
r is the radial distance to a point P.
R is the inner radius o f the pile,
t is the wal l thickness o f the pile.
s represents the radial location o f the soil inside the pile influenced by the boundary condition at r = R
h represents the radial dimensions o f the soil outside the pile influenced by the boundary condition at r = R+t
It can be seen that the boundary conditions vary for each o f the material. Soil wi th in the pile w i l l react
differently compared to the pile. The stiffness value w i l l thus be different too. Sme counts for the pile itself. The
mothod how stiffnesses fo r respectively soil wi thin the pile, soil outside the pile and the pile itself are derived, is
demonstrated m Par. 9.2.1 to 9.2.3.
9.2.1 Soil within the pile
Four boundary condhions are to be determined for the soil wi th in the pile, two for each boundary. The inner
radius R o f the pile gives the outer boundary. The pile's center gives the inner boundary. Ovalisation o f t h e pile
is assumed (see Fig. 9.4), this gives the first boundary condition. Shear stresses are considered negligable
between soil and in pile. This gives the second and third condition. The fourth condition is given by the
assumption that no displacement o f the soil occurs in the center o f the pile.
Summarising:
- r = R-s, u^ = 0 ;
- r = R-s, a „ = 0 ;
- r = R, a„ =p'^cos2e;
- r = R, o„ = 0 .
The computer program Maple V has been used in determining the
constants A , B, C and D wi th previous boundary condhions. The
calculations done by Maple V are shown in appendix 5.
Fig. 9.4 Ovalising pile tip with soil inside and outside ofthe pile
G. Kramer 56
Chapter 9
As was mentioned before, the * stiffness o f a material can be seen as the stress in a certain point divided by the
displacement o f that point. In a same way, the stiffness o f the soil wi thin the pile was determined. The radial
stress was divided by the radial displacement u^.
Two calculations were done, one for material wi th and one for material without a Poisson's ratio v. The
calculated stiffness for the soil w i thm the pile wi th a Poisson's ratio v is given by (see Appendix 5):
3 E
^ " ( - 3 . 2 v ) ( i . v ) : ^ ^^-^^
The calculated stiffness fo r the soil wi th in the pile having a Poisson's Ratio v o f 0.25 is given by:
E ., E ., SOU _ soil
Komn = 0 ' 9 6 f ^ = (9.9)
9.2.2 Soil outside the pile
The stiffness o f the soil outside the pile has been calculated in the same way as the soil wi th in the pile. In
determining the stiffness o f the soil outside the pile fo l lowing boundary condhions are given:
- r = R+t, u, =p*cos26;
- r = R+t, o„ = 0 ;
- r = R+h, u, = 0 ;
- r = R+h, a„ = 0 .
Constants A , B, C and D are again calculated wi th Maple V . Two calculations were done, one fo r material wi th
and one for material without a Poisson's ratio v. The calculated stiffness for the soil outside the pile wi th a
Poisson's Ratio v is given by (see Appendix 5):
K = 1 (-172981 + 118981V) ^ „ , 7
6 0 ( 1 + v)(4621 - 8642V + 3721v')
The stiffness as given in Eq. 9.12 had to be corrected as a negative stiffness was obtained f rom the calculations.
This stiffness is found for the case in which length h is given the magnitude o f 10 times the pile radius. I f
another length for h is taicen, this w i l l hardly lead to a change o f the values as given in Eq. 9.10. The calculated
stiffoess for the soil outside the pile wi th a Poisson's Ratio v o f 0.25 is given by:
= 0 . 6 0 ^ (9.11)
The value o f 0.6 is found i f distance approaches inf ini ty . I f h is given a value o f for instance 10 times the pile
radius, the value o f 0.6 becomes about 0.62 which is slightly higher.
G. Kramer 57
Chapter 9
9.2.3 Pile Stiffness K^„,
I f , in the complete solution for ovalisation, boundaries are chosen at the inner pile wa l l radius R and the outer
pile wa l l radius R+t, f o l l owmg boundary conditions are obtained:
- r = R: o„= p*cos2e;
- r = R: 0^=0;
- r = R+d: o „ = p * c o s 2 0 ;
- r = R+d: a „= 0.
Constants A , B , C and D are again calculated wi th Maple V. Two calculations were done, one fo r material wi th
and one for material without a Poisson's ratio v. The calculated pile stiffiiess w i th a Poisson's Ratio v is given
by (see Appendix 5):
= ? (9.12) Rr-1 + v (•1 + v\ d 4
The stiffiiess as given in Eq. 9.12 had to be corrected as a negative stiffness was obtained f rom the calculations.
The calculated pile stiffness that does not contain a Poisson's Ratio v is given by:
3 E^aJ Kile = (9.13)
8 R'
These calculated stiffnesses are valid in case the pile ovalises over its entire length. I f only a part o f the pile, a
r ing, ovalises during the process, the rectangular cross sections o f the ring do not distort during bending as wi th
an isolated ring. The quantity E / ( l - v ' ) should be used instead o f E itself (Timoshenko, Theory o f Elasticity,
Chapter I V , Buckling o f compressed rings and curved bars, page 207). Eq. 9.12 thus changes into Eq. 9.14.
Ep<,j'
8 { - i + v ) ( i + V) n - v'-)/?^ Kile - . . " \ . (9.14)
Eq. 9.13 remains the same as the value for the Poisson's ratio used in the determination is zero.
A l l the parameters o f the pile can be refound in the pile stiffness K . Chart 9.1 shows the parameters and their
influence on the stress AP in a pile part ds'''dh:
Young's modulus E A larger Young's modulus w i l l increase the stresses
AP in a pile part ds^'dh i f the displacement condhions
remain the same.
Wall thickness t A larger wall thickness w i l l increase the stresses AP
in a pile part ds'*'dh i f the displacement conditions
remain the same.
Radius o f the pile RpHj A larger pile radius w i l l decrease the stress AP in a
pile part ds*dh i f the displacement condifions remain
the same. The reason for this is a larger carrying
circumference o f the pile
Chart 9.1 Parameters of influence on the pile's behaviour during penetration
G. Kramer 58
Chapter 9
9.3 Calculation of the Young's modulus for soils
Some simple equations can be given in the determination o f the Young's modulus for soils. The stiffness
parameter can be writ ten as
(9.15)
m which:
- p'"'' in this equation has a constant value o f 100 kPa;
- p ' is the cell pressure or horizontal in-situ sttess;
- G"* and m are given in fo l lowing chart
Type o f sand G^'f [kPa] m
Very loose 5000 0.5
Very dense and clean 15000 0.5
Chart 9.2 G"' and m given for two types of sand
The initial stiffness parameter is about twice as large as G'". This gives
9.16)
The initial stiffness G and the Young's modulus are connected through Eq. 9.17
G soil 2(1 + v)
(9.17)
Substitution o f Eq. 9.16 in Eq. 9.17 and rewrit ing gives
^ 4G'M + v) (9.18)
I f , for instance, the cell pressure in the pressure vessel and the type o f sand are known, the Young's modulus can
be calculated.
G. Kramer 59
Chapter 9
9.4 Pile-soil interaction model
Durmg penetration o f a pile, three situations might occur to the inhially damaged pile shape.
1. the mit ial ly damaged pile shape keeps its shape (see Fig. 9.5);
2. the in i t ia l ly damaged pile shape deforms. The deformation enters the previously undamaged pile part over a
length h smaller than the penetration length d (see Fig. 9.6);
3. the inhial ly damaged pile shape deforms further. The deformation enters the previously undamaged pile part
over the same length same as the penehation length d (see Fig. 9.7).
Fig. 9.5 Initially damaged pile tip keeps its Fig. 9.6 Initial damage entering pile over shape during driving, h = d some length, h < d
Fig. 9.7 Initial damage entering pile over maximum length, h = 0
Which o f the three described situations occurs, depends on the parameters o f both soil and pile. I f the shength o f
the pile is greater than the strength o f the surrounding soil, the pile tip w i l l not undergo any further deformation.
I f a pile is lowered in for example water, h w i l l not deform. Length h is than equal to the penetration length d. I f
the pile is however driven through hard material, it w i l l deform at a maximum rate, resuhing h to become zero.
Fig. 9.8 Radius of undeformed pile tip after penetration of length d
Fig. 9.9 Radius of a deformed pile tip after penetration of length d
Before discussing the equations for the deformations o f soil and pile, it should be mentioned that the angle a is
seen as a constant during the entire penetration process. Various tests done in the first months o f the graduation
period have shown that the angle o f the init ial damage hardly changes during the penetration process.
I f the pile does not deform during penetration, the new radius o f a point at depth z is (see Fig. 9.8):
R...... = R^.,. - (z-cO*tana*coi26 point
(9.19)
I f the pile deforms during penetration, the new radius o f a point at depth z is given by (see Fig. 9.9)
^point = V " (z-/')*tana*co^20 (9.20)
G. Kramer 60
Chapter 9
The horizontal deformation length Upne is the difference between the undefonmed and deformed pile shape at any
depth z. This gives
^piie " id-h)*tatia*cos2Q (9.21)
The sprmg's compression or elongation is given by (see Fig. 9.9)
i V . = hnana*cos2Q spring
(9.22)
in which 0 < h < d.
9.4.1 Stresses in springs
Pile deformation causes an mcrease o f shess in the soil at those points where the soil (=spring) is pushed in and
a decrease o f stress in the soil at those points where the soil (=spring) obtains more space. Fig. 9.10 to Fig. 9.12
show the displacement o f a soil particle mside and outside the pile when a pile penetrates the soil.
VJ
Fig. 9.10 Horizontal particle displacement as a result of pile penetration
Fig. 9.11 Horizontal displaced particles on the inner and outer side of the pile wall
Fig. 9.12 Maximum displacement of the inside and outside particle
A n increase or decrease o f stress resuhing f rom pile deformation w i l l thus result in an increase or decrease o f the
initial stresses Qo or Po at depth z* (see Fig. 9.13A, 9.13B and 9.13C).
Soilprcssure
Fig. 9.13A Initial horizontal stresses at depth z*
Fig. 9.I3B Initial stresses on inner and outter pile wall side at depth z*
, Situation B
Fig. 9.13C Stress increase and decrease in the springs as a result of pile penetration and deformation
The absolute stress increase APpoi„, on the outer pile wal l is the same as the stress in the outer spring which is
given by
(9.23) Ap = K *V point soilout spring outside
G. Kramer 61
Chapter 9
The absolute sfress mcrease AQp<,i„, on the inner pile wal l is the same as the sfress in the inner sprmg which is
given by
^Qpolnl ~ ^soilin * ^spring inMe (9-24)
The total sfresses on the hiner and outer pile wal l are the combinations o f inhial sfresses and the sfress increase
and decrease as a resuh o f the pile deformation. Fig. 9.14A shows the resuhing sfresses on hiner and outer pile
wal l as a function o f the angle 6. Fig. 9.14B shows the sfress increase m a spring wi th a deformmg pile wal l .
p, ^p,
Q,
stress on outer pile wall Springs before pile deformation
1/4% 3/4-K 5/4n 7/4-n. £
Stress on Inner pile wall
1/4-K 3/4% 5/4% 7/4% 6
Fig. 9.14A Resulting stresses as a function of 9
Inside soil Pile Outside soil
Springs after pile deformation
Fig. 9.14B Stresses in soils and pile wall as a result of pile deformation
The stress increase AP w i t h m a certain pile area ds*dh is given by the product o f the pile stiffness Kpn, and the
deformation length U . This gives
point '^pile '-'point (9.25)
9.4.2 The equ i l i b r ium o f stress increment
Sfress increase at any point o f the pile wal l has to be the same as the sfress increases wi th in that point to keep the
same pile shape. This leads to the equation o f equilibrium as given in Eq. 9.26 in case o f a deformation directed
to the pile center (see Fig. 9.13 and Fig. 9.15, situation A ) and Eq. 9.27 in case o f a deformation directed away
from the pile center (see Fig. 9.13 and Fig. 9.15, situation B) .
K *F soilout spring
^pih ^pile ^soilin spring
(9.26)
(9.27)
Substituting o f Eq. 9.21 and 9.22 in Eq. 9.26 and Eq. 9.27 gives
Kiie*^d-h)H&na*cos2Q = K^^.j^^*h*tana*cos2Q (9.28)
G. Kramer 62
Chapter 9
and
K^.i^*(d-h)*tana*cos2d = K^^.i.^*h Hana*cos2Q (9.29)
Rewritmg o f Eq. 9.28 and 9.29 gives
soilout *h (9.30)
(9.31)
As equation 9.30 counts for those parts o f the pile that deform toward the pile center, so does equation 9.31 for
those parts o f the pile that deform from the pile center. Either the soil or the pile can be sfronger at a particular
depth z. The one thing that has to be done to find out which o f the two materials behaves stronger, is the
substitution o f the pile and the soil parameter values and the value o f the penefration length d. I f the calculated
stress wi thm the pile is smaller than the stresses on the pile, the pile w i l l collapse. I f the calculated sfress wi th in
the pile is larger than the sfress on the pile, the soil w i l l collapse instead o f the pile.
9.4.3 Combin ing o f t h e two soil rigidities i n the equ i l ib r ium equation
The stiffness ¥^^x\m and K^oUout can be combined into the factor K , „ j | . Fig. 9.15 shows the increment and decrement
o f stresses in the soil inside (A) and outside (B) the pile. These sfresses cause deformation o f the pile.
Deformation o f the pile leads to both a decrease o f sfress on the inner side o f the pile wal l and to an increase o f
sfress on the outer side o f the pile wal l when the pile wa l l deforms toward the pile center and opposite i f the pile
wa l l deforms away from the center. The decrease o f the stress on the inner pile wa l l increases the effect o f the
increase o f sfresses on the outer side o f the pile wal l .
A B
Fig. 9.15 Resulting stresses after increase and decrease of stress in soil within and outside of the pile
G. Kramer 63
Chapter 9
Substitution o f K,„iii„ and K,„ii„„, tlius gives, for the case in which v equals 0
K., = Komn ^ Ko.,0.. - - 0 . 6 ^ ^ = 1 . 6 ^ (9.32) % 7 c ^ p « e ^p/fe
Displacement o f the pile times hs stiffness has to be the same as displacement o f the soil times hs stiffness to
have an equilibrium o f stresses. This gives
Kne*Up,, = Ko^VsoU (9.33)
As example, the stiffiiess equation for the soil without a Poisson's ratio w i l l be used in combination wi th the
stiffness equation for the pile in which both the Poisson's ratio and the effect o f a partly undamaged pile on the
damaged part are not included. Substihiting Eq. 9.13 and Eq. 9.32 in Eq. 9.33 and rewrhing leads to Eq. 9.34.
This equation is the e q u i l i b r i u m equation between radial shesses m pile and soil
8 R
9.4.4 Factor 1.6 within the equilibrium equation
The factor 1.6 in the equation equilibrium is based on the idea o f a stress increase on the outer pile wal l resulting
f r o m a stress increase in the soil outside the pile in combination wi th a stress decrease on the inner pile wal l . The
mcremental gap between the inner pile wa l l and the soil wi th in the pile causes this stress decrease.
No influence o f the soil above the particle has yet been considered. I f enough soil is present above the particle
that finds hself confronted wi th a gap besides it, particles f rom above w i l l f i l l the gap between inner pile wa l l
and the particle. The decrease o f stresses on the inner pile wal l w i l l then be reduced and h might even occur that
no decrease whatever occurs. Reduction o f the stress decrease leads to a reduction o f the factor 1.6. In the
extreme situation in which no helping influence o f the soil wi th in the pile is to be expected, this factor w i l l be
reduced to 0.6. This is the K-value o f the soil outside the pile.
For situations m which the soil column wi th in the pile plugs, it is most probable that the model as proposed in
this chapter loses its value. Another model has to be made when the soil wi th in the pile prevents the pile f r om
deforming.
9.5 Determination of maximum deformation with a given penetration length
Knowing Eq. 9.34, h is possible to determine a maximum penetration length d i f a maximum radial pile t ip
deormation (d-h)tana is given or vice versa. Eq. 9.33 now has to be rewritten as a ratio o f h over d.
9.5.1 Ratio of h overd
The ratio o f h over d is determined in fo l lowing way. h/d can be written as
h ^ 1
\ ^ Koi (9.35)
G. Kramer 64
Chapter 9
Substituting Eq. 9.13 and Eq. 9.32 in Eq. 9.35 gives
h 1
' 1 . 1 . 6 . ^ . 1 ^ (^-^6)
3 E^„j\iu
Eq. 9.36 can be rewritten as a funct ion o f the D over t ratio. This gives
h
d J ^ 1.6 ^ , „ „ ^ ^ ^ „ . ^ 3 (9.37)
3 EpUe t
9.5.2 Check on position pile and soil parameters w i t h i n h/d-equation
The place o f the parameters wi th in Eq. 9.37 is checked to see i f the equation satisfies the ideas behind the model.
I t is known that h is zero for situations in which the deformation has entered the pile over a length d and that h
has the same value as d for situations in which no deformation o f the pile occurred (see Fig. 9.16).
Each o f the parameters w i l l be given the value o f zero or inf in i ty . This value w i l l be substituted in Eq. 9.37 to
see the result on the ratio h/d. A h/d-ratio o f 1 indicates that the pile
does not deform during penetration, a h/d-ratio o f 0 indicates that the
pile deforms maximally during penetration. Es„i| is started wi th .
Esoii = 0 (water) gives a h/d-ratio o f 1;
Esoii = °° (very hard rock) gives a h/d-ratio o f 0;
Epiie = 0 gives a h/d-ratio o f 0;
Epiie = °° gives a h/d-ratio o f 1;
t = 0 gives a h/d-ratio o f 0;
t = «> gives a h/d-ratio o f 1;
Dpiie = 0 gives a h/d-ratio o f 1;
Dpiie = °° gives a h/d-ratio o f 0.
Most o f previous condhions speak for themselves. The influence o f
Fig. 9.16 Various length ofh at a same penetration the pile D/t-ratio is more d i f f i c u h to understand. I t is, however,
length d obvious f rom tests that a pile wi th a smaller D/t-ratio deforms less
easy than a pile wi th a large D/t-ratio.
9.6 Example of calculated radial damage
A n example is given in which the penetration depth d is given and the radial displacement (d-h)tana is to be
calculated. The radial pile displacement is given by Eq. 9.15. Clean sand wi th a G'^^ o f 7500 kPa is taken as the
soil in which the pile is driven. A cell pressure o f 1.5 bar is placed on the soil sample in the pressure vessel. The
Young's modulus o f the sand is detennined wi th Eq. 9.18. A Poisson's ratio o f 0.25 is assumed f o r the sand. The
calculated value o f the Young's modulus o f the sand is 45489 kPa which is 4.54"' 10' Nm"^.
The Young's modulus o f t h e pile is 120000 MPa which is 1.2'* 10" N m ' ^ The pile diameter is 31 mm, its wal l
thickness 0.35 m m and tan a o f the inhial damage is 1 10'^. The penetration depth is 0.30 m.
G. Kramer 65
Chapter 9
Using Eq. 9.37, tlie calculated value for h is
h = 0.30* 5 = 0.00678m
1 + 1.6^4.54*10' 31.45 3 (9.38)
3 1.2*10" 0.35
The maximum radial displacement to the pile center is, according to Eq. 9.21
I f the angle a is doubled, the radial displacement w i l l double as wel l . I t can be seen that angle a has an
enormous influence on the radial displacement.
9.7 Graphical output
m Inner Diameter
penetration depth
Cell pressure
With the computer program Excel, graphics have been made in which the value o f 1] h/d, 2] h and 3] (d-h)tana
are shown for various values o f the D/t-ratio, the Young's modulus o f soil and the angle o f the init ial damage.
Fig. 9.18 to 9.20 show the values o f h/d, h and (d-h)tana for fo l lowing example:
G"' : I * 10' N/m^ p ''"' : 1 10' N/m^
0.5 Epiie 31mm t a n a
0.60 m D/t-ratio
variable, range 0 - 6 bar (kg/cm^)
1.2*10" N/m^
0.01
variable, 4 0 - 100
It can be seen in the figures that a larger D/t-ratio leads to a larger ultimate damage. The maximum damage is
not only larger, h also mhiates sooner. This can be seen f rom the gradient o f the D/t-curves. I t becomes steeper
as the D/t-ratio grows. A larger D/t-ratio thus resuhs in a less s t i f f pile.
G. Kramer 66
Chapter 9
The same figures are made for a shuation in which factor 1.6 is reduced to 0.6. Fig. 9.21 to Fig. 9.23 are the
result. The place o f the curves for the various D/t-ratios becomes different as a result o f the reduction o f factor
1.6.. Higher values for the Young's modulus o f soil are needed to obtain for example the same radial damage.
G. Kramer 67
Chapter 9
Value or hid at various combinations of (Dlt)'^3 ratio's and Youngs modulus Soil with constant angle alpha of initiat distortion
6.O0E-K)7
Youngi modului Soli (fVm'-l)
Fig. 9.21 Values of h/d for the equilibrium equation with factor 0.6 instead of 1.6
G. Kramer 68
Chapter 9
9.8 Plastic instead of elastic behaviour during penetration
I f material deforms too much, the maximum strain it can bear is exceeded. From that point, stresses remain
almost the same wi th increasing displacement (see Fig. 9.24 and 9.26). A constant shess w i l l lead to a smaller
material stiffness. For the soil wi th in and outside the pile only a small deformation is needed to obtain plastic
behaviour. Besides this, another thmg causes a reduction o f the Soils stiffness in longitudinal dhection f rom the
pile t ip. Soil entering the pile w i l l have a certam volume, which depends on the open area o f t h e pile t ip. As the
area o f a circle is more than the area o f an ovalised shape, not enough soil w i l l enter the pile to fill it completely.
The stiffness o f the soil wi th in the pile w i l l thus reduce significantly. The stiffness o f the soil at the pile tip
however remains the same as the total inner area is filled wi th soil.
G. Kramer 69
Chapter 9
The Strain needed to obtam plasticity m a pile is much larger. Knowmg this, one could wonder why the pile
collapses as the soil w i l l lose its stiffness easier than the pile. This question however can be answered quite
simply. Durmg penetration, the pile tip w i l l contmuously meet new soil layers. As these soil layers have not
faced any deformation prior to the pile's penefration, they w i l l behave elastic. The pile however contmuously
deforms durmg penefration. A t some pomt, the maxhnum sfram wi thm the pile is reached and part o f t h e pile tip
w i l l start to behave plastical.
From this point on, h w i l l become much easier to deform the pile as part o f t h e pile tip has a smaller stiffness.
Fig. 9.27 Step I in deformation process Fig. 9.28 Step II in deformation process Fig. 9.29 Step III in deformation process
I f ovalisation o f the pile occurs, four pomts, K, L , M and N are found which simultaneously become plastic as
maximum sfrain is reached m these points at first (see Fig. 9.27). Decreasing rigidities lead to a larger
displacement under the same loadmg condifions. Points K , L , M and N w i l l thus deform quicker than the points
next to them. This w i l l eventually lead to a peanut shape. Fig. 9.27 to Fig 9.29 show the process in its various
phases.
9.9 Conclusions
- I t can be concluded that the order o f magnifride o f the radial deformation found for the example pile m Par. 9.6 is reasonable.
- Thè calculated rigidhies for pile and soil probably keep their values i f shapes alike the ovalised shape are
considered (e.g., elliptic or half-elliptic shape). Other initial damage shapes can thus be compared using the
same theoredcal stiffness values for pile and soil.
- Deformation in longitudinal direction o f the pile is caused by a continuous deformation o f t h e pile t ip. The
pile parts above o f the pile tip ' f o l l o w ' the deformadon o f t he phe tip.
- The calculated pile tip deformations during penefration are probably lower than the ones that w i l l be
measured in the experiments. This is a result o f the absence o f plastic behaviour in the model. Plastic
behaviour reduces the pile stiffness. Easier deformadon w i l l be a resuh o f this.
G. Kramer 70
Chapter 10
10 Experiments on pile-soil interaction during driving
10.1 Introduction
Various experiments were done to investigate tlie pile-soil interaction process. The first test series were done to
obtam information about the parameters o f infiuence (see Chapter 5). Various shapes for the inhial pile tip
distortion were given after which the pile was driven m the soil. I t was concluded that the shape o f the mitial
distortion had a major influence on both the cell pressure at which plastic deformation o f the pile occurred and
the shape o f the final distortion. I f no mitial distortion was given to the pile tip, nothing happened during
drivmg. The given pile t ip distortions can be roughly placed in one o f the three fo l lowing groups;
11 the elliptic/oval shape o f the entire pile t ip;
2] the elliptical distortion at one side o f the pile;
3] the local inhial distortion at one side o f the pile.
These three shapes caused the final deformation to have respectively 1] a peanut shape, 2] a cashew nut or
peanut shape and 3] a cashew nut or slammed shape, (see chart 10.1)
Shape o f the mif ia l distortion Shape o f the final distortion
no mitial distortion no pile deformation
elliptic/oval shape peanut shape
elliptic distortion at one side peanut shape or cashew nut shape
local mhial distortion cashew nut shape or slammed pile tip
Chart 10.1 Initial and resulting final shape
The axial length over which deformation occurred after driving varied for all mentioned shapes. The slammed
shape deformation occurred only at the pile t ip. A peanut shape was found over a large pile length. The length o f
the cashew nut shape laid in between.
Using this mformation, more tests were done in which the magnitudes and dimensions o f all the known impor
tant parameters were registered. This chapter presents the results o f the performed test series. The test procedu
res are described in Par. 10.2. A review on the angle a is given in chapter 10.3. The results o f the test series are
presented in Par. 10.4. Graphical output o f t h e results can be found in Par. 10.5. Par. 10.6 describes the influence
of the parameters as shown in the tests. Finally conclusions are given in Par. 10.7.
10.2 Test procedures
The procedures used wi th in a test series have to be known prior to the test series to obtain relevant and useful
information. I t has to be known which parameters need to be changed during the experiments and which
parameters remain constant. A failure criterion has to be given as wel l .
Three parameters were to be changed in the test series. These were:
1] the D/t-rafio o f t h e model piles
2] the initial damage and its gradient at the pile tip
3] the pressure on the soil sample
The Young's modulus o f the pile w i l l remain constant as we l l as the soil sample type in which the pile is driven.
Two thmgs need to be mentioned to avoid questions. They consider the magnitude o f the D/t-ratio and the way
m which the cell pressure on the soil sample has been increased.
G. Kramer 71
Chapter 10
Scaled piles having D/t-ratio's higher than the D/t-ratio's o f real piles needed to be used for two reasons. I t
seemed impossible to obtain plastic deformation m piles havmg normal D/t-ratio's i f maximum cell pressure
was placed on the soil sample. The mmhnum possible D/t-ratio o f the model piles lies around 80.
I f lower D/t-ratio's are requhed, other piles material need to be used.
The cell pressure was increased f rom 0.5 bar to the maximum attainable pressure or the pressure at which the
pile obtamed plastic deformation wi th steps o f 0.25 bar. A maximum cell pressure o f 3.75 bar could be attained
on the soil sample.
As a crherion for pile failure, deformation had to be visible after driving o f t h e pile in the soil sample. I t seemed
very d i f f i cu l t to determme the exact cell pressure at which elastic deformation occurred. This is basically due to
the combination o f a relatively low Young's modulus and a high yield stress o f t h e brass material. Releasing the
cell pressure o f t h e soil sample instantaneously lead to loss o f the elastic deformation obtained during driving. I f
no deformation could be measured, the pile was considered not deformed. Only i f deformation could be
measured, a pile was considered deformed.
10.3 The angle a within the initial distortion
Although the size o f the mit ia l distortions varied in the experiments, a more important parameter wi thm the
mhial distortion seemed to cause the variety o f final pile tip shapes. This parameter is called angle a and seemed
to be o f major mfiuence to both fmal shape and cell pressure needed to deform a pile. Angle a has to be seen as
the gradient w i t h m the ini t ia l distortion and can be calculated i f both init ial radial distortion and axial length
over which this distortion occurs are known.
The axial deformed pile length depends on both angle a and the driving length o f t h e pile. A n increasing driving
length w i l l lead to more deformation. I f this driving length is considered constant, the amount o f radial deforma-
Pile 1 P i k 2 P i k 1
A n g k a , A n g k a ,
Fig. 10.1 Two pile walls with differetit angles a
Radial distortion I
Fig. 10.2 Radial and axial distortion after penetration over a length d
P i k I P i k 2
"1 l^-
Radifll distortion 1 Max. radial distortion 2
Fig. 10.3 Maximum radial deformation resulting in maximum axial deformation
t ion depends only on the angle a wi thin the initial distortion.
A small angle a enables the pile to deform over a longer pile length, as the inif ia l distortion slowly enlarges.
Radial distortion 1 which is caused by angle a, is thus smaller than radial distortion 2 caused by the larger angle
« 2 (see Fig. 10.1 and Fig. 10.2). Wi th a constant ratio between radial and axial deformadon, the pile tip o f pile 2
w i l l be closed earlier than the pile tip o f pile 1 (see Fig 10.3). The maximum axial deformed length w i l l be
smaller for pile 2 than for pile 1.
I f the angle a is taken too large, pile dr iving w i l l lead to a slammed pile t ip. The axial deformed length w i l l be,
in this case, smaller than the radial deformed length as can be seen in Fig 10.4.
G. Kramer 72
Chapter 10
10.4 Results of pile-soil interaction tests
A total o f eighteen piles were tested to determine how a pile deforms during driving. Piles wi th various D/t-
ratio's were used. Ini t ial distortions w i th various dimensions and gradients were given to these piles. The piles
were driven in the soil sample on which a certain pressure was placed. I f the pile remained undeformed, cell
pressure was increased and the pile was driven in the soil another time. By this the magnitude o f soil pressure
needed to deform the piles and the min imum init ial damage the pile tips needed to deform at a certain cell
pressure could be determined. The tests resulted in a variety o f deformed shapes (see Appendix 6).
Fig. 10.4 Slammed pile tip
In i t ia l distortions above some magnhude always seemed to enable deformation during driving. The piles o f Fig.
10.5 show that deformation w i l l occur around the initial distortion, wherever this distortion was positioned. Pile
GK13 deformed when 2.0 bar o f cell pressure was placed on the soil sample.
Fig. 10.5 Initial pile tip damages and their gradients. If large enough, they will lead to pile deformation
G. Kramer 73
Chapter 10
A n overview o f all the experiments w i l l be given in which fo l lowing point can be found:
- The name o f the test and the figure m which the test result can be found;
- D/t-ratio representmg the ratio o f outer pile diameter over wal l thickness;
- length a representing the maximum initial distorted radial length at the pile t ip to the center;
- length I representing in case o f the doorslag-, ellipse- and gk-series the tangential distorted length at the pile
tip and m case o f the final-series the radial distortion away from the center;
- length h representing the inhial distorted lateral length;
- tan a representmg the gradient within the inhial distortion;
- The cell pressure needed to give the pile plastic deformation.
Name test (Figure) D/t a 1 h tana = a/h Cell pressure at which plastic deformation occurred
Doorslag 1 (10.6) 157 0.3 3.7 6.25 0.048 1.25
Doorslag 2 (-) 114 0.125 7.85 15.5 0.0081 3.0
Doorslag 3 (10.6) 114 0.12 11.4 10.6 0.011 2.0
Doorslag 4 (10.6) 84.5 0.35 4.6 6.3 0.055 1.25
Doorslag 5 (10.6) 97 0.65 9 10 0.065 1.25
Doorslag 8 (10.6) 80 0.7 6.2 7.1 0.098 1.5
Ellipse 1 (-) 164 0.22 13 38 0.0058 ended by extemal cause
Ellipse 3 (-) 80 0.2 9.45 86 0.0023 none, max cell pressure 3.7 bar
G K l (10.7) 126 1.45 32.8 136 O.OIl 1.5
GK 7 (-) 92 0.12 32 105 0.0011 none, max cell pressure 3.5 bar
GK 10(10.7) 156 1.06 29.4 14.3 0.074 1.0
GK 12(10.7) 143 0.07 18 135 0.0005 none, max cell pressure 3.7 bar
FINAL 1 (10.8) 157 0.61 0.64 162 0.0038 none, max cell pressure 3.75 bar
FINAL 2 (10.8) 157 0.4 0.2 45 0.0090 3.0
FINAL 3 (-) 140 1.0 0.95 123 0.0081 none, max cell pressure 3.0 bar
FINAL 4 (-) 140 0.4 0.15 46 0.0087 elastic deformation at 1.5 bar
FINAL 5 (-) 157 2.35 1.4 228 0.0010 none, max cell pressure 2.5 bar
FINAL 6 (-) 140 1.5 1.3 62.5 0.024 2.0
Chart 10.2 Overview of all pile-soil interaction experiments and their parameter values
Plastic deformation instead o f elastic deformation had to be taken because, w i th the test equipment, visualizing
elastic deformation was hardly possible. When a pile is driven in the soil sample, it becomes very d i f f i cu l t to
look at the pile t ip. When the cell pressure is released f r o m the sample after the pile driving and the pile is taken
out o f the sample, all possible elastic deformation is gone and no deformation can be measured.
I f the sand wi th in the pile is sucked out and replaced wi th gypsum, elastic deformation can be measured. Many
piles w i l l then be needed as f i l l i n g a pile wi th Gypsum w i l l make it impossible to do more tests wi th the same
pile. A device could be developed which can measure the deformation in-situ. One could think o f a small sonar
survey device. Development o f such devices take however very much time. Cell pressures lower than the
pressures in chart 10.2 might then probably be enough to obtain the 'unmeasurable' elastic deformation.
G. Kramer 74
\ lU. 10(1 I l i l . ' l i i - l i iMi icd p i k - s 1)1 l l i c ' i l i i i i i s l , ! " ii-^l si-iiL-s
Chapter 10
Chapter 10
10.5 Graphical output for various parameter combinations
To determine which parameters have most influence on the process and to see i f pile behaviour can be predicted
wi th the chcumstances surrounding the pile known, various graphs have been made in which combinations o f
Values for cell pressure at which plastic deformation did ordid not occurs for
various combinations of D/t-ratio and Angle alpha within initial distortion
Fig. 10.10 Overview of all performed experiments
parameters are displayed. Fig. 10.10 shows the resuh o f all performed experiments.
I t can be clearly seen that piles having a larger angle a wi th in the initial distortion need less cell pressure to
obtain deformation during driving. I t seems more d i f f i c u h to determine the influence o f the D/t-ratio.
A distinction has to be made between the experiments in which the piles did not deform and the ones m which
the piles deformed. Fig. 10.11 shows the experiments in which no pile deformation occurred. Fig. 10.12 shows
the experiments in which deformation occurred. Chart 10.3 shows the experimental results ordered f rom a small
to large gradients.
G. Kramer 77
Chapter 10
Naine test D/t-ratio (-) Angle alpha (rad) Cell Pressure (bar) Deformation (y/n)
G K 12 143 0.0005 3.7 n
G K 7 92 0.001 3.5 n
E L L I P S E 3 80 0.002 3.7 n
FINAL 1 157 0.004 3.75 n
F I N A L S 157 0.008 3.5 n
DOORSLAG 2 114 0.008 3 y
FINAL 2 157 0.009 3 y
GK 1 126 0.010 1.5 y
DOORSLAG 3 114 0.011 2 y
FINAL 3 140 0.012 3 n
FINAL 6 140 0.045 2.0 y
DOORSLAG 1 157 0.048 1.25 y
DOORSLAG 4 84.5 0.055 1.25 y
DOORSLAG 5 97 0.065 1.25 y
G K 10 156 0.075 1 y
DOORSLAG 8 80 0.098 1.5 y
Chart 10.3 Test results ordened in increasing angle alpha
Chart 10.3 clearly shows that almost all test wi th an angle alpha larger than approximately 0.01 rad obtained
plastic deformation. Piles having a smaller angle alpha obtained no plastic deformation whatever.
Maximum cell pressure placed on pile, no deformation yet occurred
Fig. 10.11 Experiments in which no plastic deformation occurred whatsoever
G. Kramer 78
Chapter 10
Cell pressure at which plastic deformation occurred
Fig 10.12 Experiments in which plastic deformation occurred when some amount of cell pressure was placed on the pile
10.6 Importance and clear influence of a parameter value on test result
Two parameters seem to have influence on the process and on the amount o f cell pressure needed to obtam
plastic deformation in a pile. These parameters are the gradient or angle a wi th in the init ial distortion and the
D/t-ratio o f the pile. Not enough tests have been done to obtain the exact boundary at which deformation occurs.
I t is investigated i f some regularity can be discovered in the test results. Fig. 10.10 shows very clearly that the
D/t ratio's have much less effect than the angle wi th in the initial distortion. While a smaller angle a leads to a
higher cell pressure needed to obtain plastic deformation, such effect can hardly be found for a changing D/t-
ratio. Fig. 10.13 and Fig. 10.14, in which respectively lines w i t h approximately the same angle a and lines wi th
approximately the same D/t-ratio are plotted as a function o f respectively the D/t-ratio and the cell pressure in
the first case and the angle a and the cell pressure in the second case, underline these conclusions.
Fig. 10.13 Lines with approximately the same angle a
G. Kramer 79
Chapter 10
Lines with the same D/t-ratio plotted as function of angle alpha and cell pressure
<
0»
U
0.02 0.04 0.06
Angle alpha (rad)
0.08 0.1
• D/t = 80
- D / t = 84.5
D/t = 92
- D / t = 97
X D/t = 114
— 0 _ -D/ t = 126
+ D/t = 140
- D/t = 157
-D/ t = 164
Fig. 10.14 Point having the same D/t-ratio
Fig. 10.15 Angle a plotted against the cell pressure at which plastic deformation occurred
G. Kramer 80
Chapter 10
No regularity at al l can be found in Fig. 10.13. I t looks as i f the D/t ratio does not matter at all although it was
expected that piles wi th a higher D/t-ratio wou ld behave less s t i f f I f Fig. 10.14 is looked at, regularity can only
be found in the Ime wi th a D/t-ratio o f 157. I f however the effect o f the D/t-ratio is regarded as a higher order
effect in the deformation process, all points can be combined to one series. This leads to Fig. 10.15. A tendency
toward lower cell pressures needed when larger angle a's are given to the initial distortion is found. Fig. 10.16
gives the s implif ied curve o f failure based on Fig. 10.15.
10.7 Conclusions
It is very d i f f i cu l t to draw conclusions from the test results obtained at this moment. Many tests were done
wi th in the first months o f the graduation period. These were meant to determine the influence o f the various
parameters. Data about the size o f the dimensions or the amount o f cell pressure needed to obtain plastic
deformation is not available from these tests. Six o f the seventeen tests performed resulted in no deformation at
all. The size o f the init ial damage or the angle a seemed not large enough to visualize plastic deformation.
What is lef t are the results o f 10 tests in which plastic pile deformation occurred when a certain amount o f cell
pressure was placed on the soil sample. A certain tendency can be found from these tests. I t seems that the angle
a o f the ini t ia l distortion is the main parameter o f influence on the process. A certain mmimum angle was
needed to start the deformation process. I f the angle a was increased, less cell pressure was needed to obtain
plastic deformation wi th in the pile.
The size o f the inhial distortion must have hs influence on the process as wel l . When piles were driven m the
soil sample for the second time wi th the same cell pressure applied to the soil sample, more deformation was
obtained. This is reasonable as the total amount o f sfress on a pile w i l l increase i f the inhial distorted area is
increased.
Not much can be said about the influence o f the D/t-ratio on the process as the test results do not give enough
feed back. I t is expected that the cell pressure needed to obtain plastic deformation w i l l decrease i f piles having a
same inhia l distortion and angle a but wi th an increasing D/t-ratio are driven in the soil sample. Sample piles
wi th D/t-ratio's varying f rom 80 to 157 were used. The effect o f an increasing D/t-ratio on the deformation
process could however not be proved as too few tests were done.
X
0.0 0.01 0,02 0.03 0.04 0.05 0.06 0,07 0,08 0.09 0,10
Angle a (rad)
Fig, 10,16 Regression curve through the points of Fig. 10.15
G. Kramer 81
Chapter 11
11 Comparison of pile-soil interaction model and data obtained from experiments
11.1 Introduction
Test results obtained in the various performed experiments have to be compared wi th the proposed theoretical
model to show this model can be o f use for the prediction o f pile deformation during driving. As elastic
deformation could not be measured after the pile drivmg, only an indication o f the cell pressure at which the pile
deformed can be given. The theoretical model is only o f use m situations in which the pile behaves elastic. A
way had to be found m which experhnents and theory could be verified and compared wi th each other.
11.2 Proposed comparison method
Plastic pile behaviour occurs i f radial deformation becomes too large. The radial pile deformation can be
calculated wi th Eq. 11.1 i f the influence o f the Poisson's ratio in both soil and pile is disregarded.
u = d*(l - i )*tana
3 £ ., t pile
I f the Poisson's ratios are taken in account (Eq. 9.8 and Eq. 9.10) as wel l as the influence o f only part o f the pile
ovalismg (Eq. 9.14), Eq. 11.2 has to be used.
u = d*(\- —)*tana 1 (-172981 + 118981V .,) E
1+-
_^ soil \ soil
(-3 - 2 v , J ( l ^ v . J ^ ( 1 ^ v^,,)(4621 - 8642v^„,, . l l l W ^ ) ^ ( „ 2 )
3 ^ul
piU'^ p,le' ^pile' pile
Elastic pile behaviour w i l l , m theory, occur i f the radial shain remains less than the maximum elastic strain. No
deformation w i l l then be visible when the pile is taken out o f the soil sample after the dr iving test. Test
parameters were placed m Eq. 11.1 and Eq. 11.2 to determine i f the theory corresponds wi th the experimental
results. Par. 11.3 w i l l deal wi th the comparison o f the registered and calculated pile behaviour.
11.3 Comparison of theoretical values and experimental results
Before the theoretical values can be compared wi th the experimental results, some assumptions have to be made.
The cell pressure has to be rewritten into some Young's modulus o f the soil sample. Par. 9.3 describes the way
in which this is done. G,^f is given a value o f 10000 kPa. This represents dense and clean sand. As value for the
Poisson's ratio o f the soil, 0.25 is taken. The Yie ld strength o f the pile is given a value o f 5.5*10* N/m^. The
Young's modulus o f the pile is given a value o f 1.2* 10" N / m l The Poisson's ratio o f the pile is given a value o f
0.35. I f the penetration length o f a pile is unknown, 25 cm is assumed. This is a value in between the measured
penehation lengths. Chart 11.1 gives an overview o f the assumed values.
Paraineter Assumed value Parameter Assumed value
1.0*10'N/m^ Young's modulus pile 1.2*10" N/m'
Poisson's ratio soil 0.25 Poisson's ratio pile 0.35
Yield strength pile 5.5*10'N/m^ Driving length (if unknown) 0.25 m
Chart 11.1 Assumed parameter values
G. Kramer 82
Chapter 11
Appendix 7, page 4 gives tiie calculations o f the radial deformation for Eq. 11.1. I f , e.g., a radial displacement o f
less than a millimeter is found, it can be assumed that no permanent deformation increase could be measured
after driving. The pile w i l l then be seen as undeformed and a label 'elastic' is given to the theoretical outcome. I f
a very high radial deformation value is calculated, the label 'plastic' is given to the theoretical outcome result as
the radial displacement at which plasticity occurs w i l l probably be exceeded. Fig. 11.1 and Fig. 11.2 visualize
the radial deformation as calculated for various cases in a 2D and 3d-graph. As it is impossible to put f ive
different parameters w i t h m one figure, the name given to the experhnent is used to indicate the value o f the D/t-
ratio, the maxhnum cell pressure placed on the soil sample and the angle a wi th in the inhial damage. Values for
these three parameters can be found in chapter 10, chart 10.2.
Fig. 11.1 3D-review of calculated maximum radial deformation within piles
Maximum theoretical radial deformation of the piles during driving for various experiments using the test
parameter as input
Fig. 11.2 2D-review of calculated maximum radial deformation within piles
G. Kramer 83
Chapter 11
The resuhs o f the calculations are given m Chart 11.2 as wel l as the experimental results. The last two columns
o f the chart are used to show i f the theoretical outcome is the same as the experimental outcome. I f h does, an
' y ' is written. I f i t does not, a ' n ' is written. I f it is not clear i f the calculated deformation would lead to elastic or
plastic behaviour, test result w i l l be regarded as giving a boundary point.
Naine test Maximum cell pressure on soil sample
Deformed in test (y/n)
Theoretical value for the radial deformation (mm)
Plastic/elastic behaviour according to Eq. 11.1
Same result in test and theory (Eq. 11.5)
Doorslag 1 1.25 y 11.99 Plastic Ok
Doorslag 2 3 y 2.02 Plastic Ok
Doorslag 3 2 y 2.74 Plastic Ok
Doorslag 4 1.25 y 13.66 Plastic Ok
Doorslag 5 1.25 y 16.18 Plastic Ok
Doorslag 8 1.5 y 24.32 Plastic Ok
Ellipse 1 1.5 Test was not fmished due to extemal cause, calculated radial deformation 1.45
Ellipse 3 3.7 n 0.46 Elastic Ok
G K 1 1.5 y 2.53 Plastic Ok
G K 7 3.5 n 0.19 Elastic Ok
GK 10 1 y 11.77 Plastic Ok
GK 12 3.7 n 0.11 Elastic Ok
Final 1 3.75 n 0.65 Elastic Ok
Final 2 3 y 1.89 Plastic/Elastic Boundary point
Final 3 3 n 1.70 Plastic/Elastic Boundary point
Final 4 1.5 y 1.91 Plastic Ok
Final 5 3.5 n 0.29 Elastic Ok
Final 6 2 y 5.99 Plastic Ok
Chart 11.2 Comparision between experimental and theoretical outcome
I t can be concluded that theory and practice lead, for most experiments, to the same results. I f plasticity occurred
in an experiment, the calculated radial deformation seems large enough to show plastic deformation behaviour.
A boundary value for the theoretical radial deformation between 1.70 mm and 1.89 mm is found above which
plastic deformation always seems to occur. I f radial deformation remains lower than this value, no plastic
behaviour w i l l be found wi th in the pile after the driving test. I f the shape o f the f ina l deformation wi th in the
piles is looked at, other values than the calculated ones w i l l be measured. The cause o f this can be found in the
plastic behaviour as plastic behaviour leads to a reduction o f the capacity to counteract deformation. Higher
deformation values w i l l be the resuh o f this change in behaviour.
To make the influence o f the various used parameters better visible. Par. 11.4 w i l l visualize the influence o f the
various parameters on the deformation process.
G. Kramer 84
Chapter 11
11.4 Influence ofthe parameters on the process
The influence a parameter has on the process o f deformation can be found i f the effect o f a parameter value
change on the process can be determined. The dr ivmg length needed to obtam for instance plastic deformation
behaviour depends on a variety o f parameter values. I f only one o f these parameter values is changed, the effect
o f this change can be visualized. The place a parameter has wi th in the formula now is o f great importance. It
was already concluded that the angle a wi th in the init ial damage seemed to have much more influence on the
process than the D/t-ratio. The D/t-ratio, the angle a and the cell pressure w i l l be changed w i t h the other
parameters remammg constant. The performed calculations can be found in Appendix 7, page 5, 6 and 7. Chart
11.3 shows the parameter values, both the varied and the constant.
Parameter Constant/Variable Value Parameter Constant/Variable Value
Cell pressure variable/constant variable 0 -4 bar constant 3.0 bar
Young's modulus soil
constant 5.54E+08 N/m' 2
Poisson's ratio soil constant 0.25 Young's modulus pile
constant 1.20E+11 N/m' 2
Poisson's ratio pile constant 0.35 Outer diameter constant 3.1 cm
Gref constant 7.50E+06N/m'^2 Tan alpha variable/constant variable 0 - 0.02 constant 0.0075
Penetration depth variable 0 - 45 cm D/t-ratio variable/constant variable 50-135 constant 80
Chart 11.3 Used parameter values
Fig. 11.3 shows that a change o f the D/t-ratio w i l l have very little to hardly any effect on the process. The
theoretical radial deformation is divided by the pile radius to obtain the dimensionless relative radial
deformation. The maximum radial deformation seems to remain constant for the various values o f t h e D/t-ratio
at certain driving lengths and mainly dependant o f the driving length.
G. Kramer 85
Chapter 11
Fig. 11.4 shows the plotted 3D-graph in which the relative radial deformation depends on a varymg angle a and
a varymg driving length. I t can be seen that an increase o f the angle a by 100% leads to an mcrease o f the
relative radial deformation o f 100%. The parameter seems to have a major influence on the deformation process.
As it is very d i f f i cu l t to measure the right angle a wi th in a pile, a large error o f measurement can be expected. I t
is thus o f utmost importance to f i nd a way in which the angle a can be measured wi th a very small error o f
measurement.
Fig. 11.4 Relative radial deformation as a function of a varying angle a and driving length
Fig. 11.5 shows the mfluence o f the cell pressure on the deformation process. N o cell pressure leads, o f course,
to no relative radial deformation. I t seems that the influence o f a change in cell pressure has not much influence
on the relative radial deformation.
G. Kramer 86
Chapter 11
Fig. 11.3 to Fig. 11.5 show the mfluence o f one changing parameter on the deformation process. I t is as wel l
possible to show the mfluence o f three changing parameters on the process. Points can then be plotted
representing a certam relative radial deformation. Fig. 11.6 shows such a graph in which points are plotted
which represent a relative radial deformation between 10% and 1 1 % . The range and the unit o f the variable
parameters is given in chart 11.4. The values are considered for a dr iving length o f 25 cm.
Parameter Range Unhs
Cell pressure 0 - 2 0 bar
D/t-ratio 5 0 - 1 1 0 -
Angle a 0 - 0 . 0 1 rad
Chart 11.4 Range of variable parameters
I t can be seen that only very small angle a's are needed to make deformation o f the pile possible. I f higher D/t-
ratio's are considered, h seems that the effect o f angle a on the process is much higher than the effect o f the D/t-
ratio. The same conclusion could be drawn f rom the experimental series. I t can as we l l be seen that i f an angle a
within the initial damage is given to two identical piles having the same D/t-ratio, the pile wi th the larger angle
needs less cell pressure to deform.
I f the cell pressure is regarded at which the deformation process starts, something sfrange is found. The pile-soil
interaction model shows that a pile w i l l deform instantaneously i f the pile is driven into the soil. Very small cell
pressures are enough to cause little deformation to the pile. As can be seen in Fig. 10.16, a min imum cell
pressure o f about 1 bar seemed needed to obtain deformation. Par. 11.5 w i l l try to give an answer on this
difference m behaviour.
10% relative radial derormation catised by the inlluence of 3 parameters at a driving length of 25 cm
Fig. 11.6 Points representing a 10% relative radial deformation as calculated for various combinations ofthe D/t-ratio, cell pressure and angle a within the initial damage
G. Kramer 87
Chapter 11
11.5 Difference in required initial cell pressure
As the pile penetrates the soil, various soil layers wi th increasing stiffness w i l l be passed. Experiments suggested
a min imum cell pressure on the soil sample was needed to obtain pile deformation. Two things might happen i f
the pile penetrates the soil:
- the soil is pushed away easily and no pressure is build up against the pile wal l ;
- the soil reacts s t i f f enough for pressure to be build up against the wal l .
I n the second case, pressure w i l l , i f enough is present, lead to pile deformation. The process o f pile penetration
can thus be divided in two steps; a track in which soil is pushed away and a track in which the soil has enough
rigidity to cause damage to the pile tip (see Fig. 11.7).
Fig. 11.7 The two steps in pile penetration
The process can as we l l be considered in a second way. In case o f very small mhial damages, soil w i l l only be
pushed away over a small distance. I f .soil stiffness is not large enough to build up the pressure needed to deform
the pile, h w i l l only be pushed away. I f soil stiffness is large enough, enough pressure w i l l be bui ld up against
the wal l to make h deform.
11.6 Conclusions
It can be concluded that the calculated radial deformations o f the theoretical model match quite wel l wi th the
experimental plastic or elastic behaviour which occurred in the piles. The model is however a simple one that
uses for example only the maximum angle a wi th in the init ial damage instead o f the entire distorted shape.
Because o f this simplicity, the effect a parameter has on the deformation can be incorrect. The effects o f both the
cell pressure and the D/t-ratio seem to be too low while the effect o f the angle a dominates everything. The
driving length is important as plastic behaviour w i l l only occur i f the pile tip is penetrated in the soil sample over
enough length.
A minimum cell pressure is required to obtain deformation. I f cell pressures remain below this min imum value,
no deformation w i l l occur as soil surrounding the pile tip is pushed away.
G. Kramer 88
Conclusions & Recommendations
12 Conclusions & Recommendations
This chapter presents the fma l conclusions o f this study on the collapse mechanism o f open-ended large
diameter piles during dr ivmg. As conclusions have already been given at the end o f most chapters, some
conclusions presented m this chapter w i l l be a repethion o f these.
Recommendations for both groups are given at the end o f this chapter.
12.1 Conclusions
Conclusions on Shell's model for the deformation behaviour of a pile during driving.
- The model as proposed by Shell is correct. The model is however nothing else than a energy balance. To the
opinion o f the author some parameters o f mfluence on the deformation process have to be added to obtain a
better model.
- I f the in i t ia l phase o f the deformation process is looked at, the elastic deformation zone has to be taken
mstead o f the plastic zone.
Conclusions on the parameters of influence on the deformation behaviour of a pile during driving.
- Many parameters seem to have mfluence on the deformation process o f a pile during driving. It is very
d i f f i c u h to f i nd the exact mfluence o f each parameters as they probably influence each other;
- Penetration o f a pile having an inhial damaged pile tip causes stress wi th in the soil. I f these stresses become
too large, the pile cannot bear them any more and w i l l start to deform.
- The size o f the fma l deformation after dr ivmg depends on the boundary conditions like the dr iving depth and
the gradient wi th in the init ial damage.
- Combinations o f boundary conditions can be found which w i l l always lead to deformation o f the pile during
drivmg.
Conclusions on the deformation behaviour of a pile during contact with the guiding system
- The presented model, used for the indication o f inhial damage, indicates that inhial damage could have been
created during contact between the pile t ip and the sleeve cap.
- A certain influence can be expected f r o m the shape o f the object that is h h by the pile t ip. The shape o f the
ini t ia l damage wi th in a pile can vary both in size as in shape as the boundary conditions change for each
pile lowered. A large range o f initial damages can be expected to occur wi th in the piles.
Conclusions on the proposed model for the pile shape as a result of a certain loading condition
- Model I does not seem to calculate sufficient plastic work. A geometrical model that enables hinges to occur
w h h i n the shape has to be used instead. Model 11 as presented in chapter 7, Par 7.3 might represent the right
model.
Conclusions on the comparison of experimental and theoretical results of pile-loading system
Up to now, a comparison between experimental results and a theoretical model is d i f f i cu l t to make. To obtain
a better comparison, several points have to be adapted:
- model I I o f chapter 7 has to be used instead o f model I as h enables the occurrence o f 'plasfic ' hinges;
- a test set up has to be made in which hardly any hysteresis occurs. A reduction to 5% o f the surface below
the load-displacement curve might not yet be enough.
- more tests need to be done to change the 'observing' model into a 'predicting' model. I f enough data can be
collected, an idea about the size o f the inhial damage in reality can be obtained.
Conclusions on the model on elastic pile-soil interaction behaviour during driving
- I t can be concluded that the order o f magnitude o f the radial deformation found for the example pile in
Par. 9.6 is reasonable.
- Deformation in longitudinal direction o f the pile is caused by a continuous deformation o f the pile tip. The
pile parts above o f the pile tip ' f o l l o w ' the deformation o f the pile t ip.
G. Kramer 89
Conclusions & Recommendations
- The calculated pile t ip deformations during penehation are probably lower than the ones that w i l l be
measured in the experhnents. This is a result o f the absence o f plastic behaviour in the model. Plastic
behaviour reduces the pile stifness. Easier deformation w i l l be a resuh o f this.
Conclusions on the experiments on pile-soil interact ion d u r i n g d r i v i n g
- I t seems that the angle a wi thm the inhial damage is the main parameter o f influence on the process. A
certain min imum angle is needed to start the deformation process. I f the angle a is mcreased, less cell
pressure is needed to obtain plastic deformation wi th in the pile.
- When piles were driven m the soil sample for the second time wi th the same cell pressure applied to the soil
sample, more deformation was obtained. This is logical as the total amount o f stress on a pile w i l l increase i f
the init ial distorted area is increased.
- Not much can be said about the mfluence o f the D/t-ratio on the process as the test results do not give enough
feed back. I t is expected that the cell pressure needed to obtain plastic deformation w i l l decrease i f piles
having a same inhial damage and angle a but an increasing D/t-ratio are driven in the soil sample. No t much
influence o f the D/t-ratio might be caused by the use pile D/t-ratio's m the range o f 80 to 160. The influence
might be higher i f piles wi th lower D/t-ratio's are used.
Conclusions on the comparison o f pile-soil interact ion model and data obtained f r o m experiments
- I t can be concluded that the theoretical model shows quite wel l though quathitatively i f plastic or elastic
behaviour might occur m a pile. The model is however a simple one that uses for example only the
maximum angle a wi th in the inhial damage instead o f the entire distorted shape. Because o f this sunplicity,
the effect a parameter has on the deformation can be incorrect.
- The effects o f both the cell pressure and the D/t-ratio seem to be too low while the effect o f the angle a
dommates everything.
- The dr iv ing length is important as plastic behaviour w i l l only occur i f the pile t ip is penehated in the soil
sample over enough length.
- A min imum cell pressure seems to be required to obtain deformation. I f cell pressures remain below this
mmimum value, no deformation w i l l occur as soil surrounding the pile tip is pushed away.
12.2 Recommendations
12.2.1 Recommendations on the experimental par t o f t h e graduat ion projec t
Brass piles
Several recommendations are given for the equipment and materials to be used.
- Although brass piles seem able to show the collapse mechanism, using steel piles would be better. A l l the
differences that might exist between the two materials and which might have influence on the process w i l l
then disappear. The combination o f a relative high yield stress and a relative low Young's modulus leads to
high values for the maximum elastic strain. A material has to be used that has a lower maximum elastic strain
to observe permanent pile deformation easier
The pile t ip deformer
- I f more tests are to be done on the occurrence o f an initial damage wi th in a pile, a test set up has to be bu ih in
which even less hysteresis occurs than was the case in the used set up. This point has a very high priori ty.
- Pushing shapes having a larger diameter, need to be used to obtain pile tip damage more easy.
The pressure vessel
- A larger pressure vessel has to be build fo r several reasons:
More dr iv ing length is required to enable the growth o f very small inhial pile tip damages during
driving. I t seemed that quite some driving length was needed to obtain plastic instead o f solely elastic
pile behaviour;
A larger soil sample w i l l decrease the influence o f the side and bottom boundaries;
G. Kramer 90
Conclusions & Recommendations
I f more cell pressure can be placed on the soil sample, stiffer soil behaviour can be obtained. Less
driving length is then requhed to obtain visible deformation.
A larger dr iving hammer is requhed i f higher cell pressures are placed on the soil sample. The driving
hammer used in this research project seemed able to drive piles in the soil. The amount o f blows
however increased very much i f higher cell pressure were put on the soil sample. The time needed to
do a test thus mcreased very much as well.Pile soil-interaction tests
- More tests need to be done to obtain a clearer view on the parameters o f influence and the way m which
combinations o f theses influence the deformation process. A test system has to be made that prevents
informat ion gaps f r o m occurrmg. I f too many parameters are changed in the tests, a clear test series can only
be made at great expense.
12.2.2 Recommendations on the theoretical par t o f t h e graduat ion project
I n i t i a l pile t ip damage
- I t could be useful to write model I I in a software programme. B y this, the loading history on a pile can be
simulated. Existmg deformation theories provide enough tools to calculate the new pile shape when
maximum load is applied to and after that removed f rom the pile. The exact pile shape before entermg the
soil can then be described.
Pile-soil interact ion
- The proposed model o f chapter 9 seems able to show whether plastic deformation w i l l occur under certain boundary condhions or not. The influence o f some parameters seems however incorrect. More attention needs to be given to this problem;
- No attention has been given to the plugging effects o f the soil wi th in the pile. This effect however has much
influence on the behaviour o f the soil wi th in the pile. It might even prevent a pile from deforming.
12.2.3 Recommendations on the construction o f an o i l p l a t f o r m w i t h the same foundat ion type
As ini t ia l pile damage might be caused during lowering o f the pile, the consfruction has to be adapted.
Experiments have shown that no deformation occurred during driving i f no init ial damage was given to the pile
t ip. Preventing inhial damage to occur in a pile tip is thus the most important subject o f any foundation
construction to be developped in fiittire. I f a same guiding system w i l l be used, three measurements can be taken.
1 The pile lowering velocity has to be kept as low as possible when the pile enters the sleeve cone. Possible
distttrbance o f t h e lowering velocity as caused by e.g., waves has to be prevented as much as possible.
2 The second measurement considers the shape o f the cone. I f a longer cone is used having a more vertical
wal l , less impact is to be expected during lowering o f t h e pile.
3 I f a smaller D/t-ratio o f the pile tip is taken, the pile can be subjected to larger impact energies without deforming.
G. Kramer 91
References
References
[I] H . G . B . Allersma, july 1995
'Simulation o f buckling o f open-ended cylinder piles during dr iv ing '
D e l f t University ofTechnology, Faculty o f C i v i l Engmeering,
Department o f Hydraulic and Geotechnical Engineering, Section o f Geomechanics
[2] A. V a n Haaren, Leidschendam, August 1994
'Pile pluggmg during static loading'
D e l f t University ofTechnology, Faculty o f C i v i l Engineermg,
Offshore Technology, Geotechnical Department
© Fugro Engineers B .V. August 1994
[3] A. Verruij t , april 1996
'Stresses in Tuimel Linings '
D e l f t University o f Technology, Faculty o f C i v i l Engineering,
Deparhnent o f Hydraulic and Geotechnical Engineering, Section o f Geomechanics
[4] Scope o f w o r k provided by Shell
Study on Collapse o f Foundation Piles
Contract no. EP/MC/95092
[5] J . G . Potyondy
Skin friction between various soils and construction materials,
Geotechnique V o l 11, No. 2, Pg. 339-353
[6] S. Timoshenko
'Bucklmg o f Bars Compressed beyond Proportional L i m h '
Theory o f Elastic Stability, Pg. 156-165
[7] S. Timoshenko
'Buckl ing o f compressed rings and curved bars'
Theory o f Elastic Stability, Pg. 204-225
[9] M . F . Randolph, E . G . Leong, A . M . Hyden and J . D . Murff , 1992
'Soi l Plug Response in Open-Ended Pipe Piles'
Joumal o f Geotechnical Engineering, May 1992, V o l . 118, No. 5, Pg. 743-759
[10] M . F . Randolph, E . G . Leong and G . T . Houlsby, 1991
'One-Dimensional Analysis o f Soil Plugs in Pipe Piles'
Géo techn ique V o l . 4 1 , No. 4, Pg. 587-598
[ I I ] Brucy, F . , Meunier, J . And Nauroy, J - F , 1991
'Behaviour o f Pile Plug in Sandy Soils During and Af te r D r i v i n g '
OTC 6514, 23rd Offshore Technology Conference in Houston, Texas
[12] K a r l Terzaghi, M . L G . E . , H o n . M . A S G E
'Evaluation o f coefficients o f subgrade reaction'
Geotechnique. V o l 5, No . 4, pp. 297-326
[13] J .P . Den Hartog
'Sterkteleer'
Uitgeverij Het Spectrum, Ufrecht/Antwerpen, 1967, page 1 3 4 - 1 4 1
G. Kramer 92
Appendices of the thesis report about InYcstigation of the Collapse Mechanism of Open Ended Piles during Installation
Table of contents
Appendix 1 Researcli on the Parameters o f Influence on the deformation
o f open-ended large diameter piles during driving
Appendix 2 Shell Research data on primary piles
Appendix 3 Theories behmd the test series on init ial distortion
Appendix 4 Complete solution for ovalisation o f a tunnel
Appendix 5 Calculation o f Rigidity w i th the use o f MapleV
Appendix 6 Various obtained pile shapes after driving tests
Appendix 7 Comparison o f theoretical calculations and experhnental resuhs
Calculations for the mfluence o f a varying parameter
Appendix 8 Computer programmes written for various experiments and data processing
Appendix 9 Test results inhial distortion tests
