three-dimensional numerical investigation of …
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Construction Technology and Management Thesis
2020
THREE-DIMENSIONAL NUMERICAL
INVESTIGATION OF NEGATIVE SKIN
FRICTION ON PILE GROUP FOR
VERTICAL LOADING
AMARE, DESALEGN
http://hdl.handle.net/123456789/11621
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BAHIR DAR UNIVERSITY
BAHIR DAR INSTITUTE OF TECHNOLOGY
SCHOOL OF RESEARCH AND POSTGRADUATE STUDIES
FACULTY OF CIVIL AND WATER RESOURCE ENGINEERING
THREE-DIMENSIONAL NUMERICAL INVESTIGATION OF NEGATIVE SKIN
FRICTION ON PILE GROUP FOR VERTICAL LOADING
DESALEGN AMARE FETENE
Bahir Dar, Ethiopia
June 25, 2020
DECLARATION
I, the undersigned, declare that the thesis comprises my own work. In compliance
with internationally accepted practices, I have acknowledged and refereed all
materials used in this work. I understand that non-adherence to the principles of
academic honesty and integrity, misrepresentation/ fabrication of any
idea/data/fact/source will constitute sufficient ground for disciplinary action by the
University and can also evoke penal action from the sources which have not been
properly cited or acknowledged.
Name of the student Desalegn Amare Signature _____________
Date of submission: ________________
This thesis has been submitted for examination with my approval as a university
advisor:
Name: _Siraj Mulugeta (PhD)
Advisor’s Signature :
i
ABSTRACT
3D ABAQUS model has been conducted to investigate the effect of negative skin friction
on piles installed through soft clay .Coulomb frictional model built in ABAQUS can be
selected to depict the interaction at the pile-soil interface condition which has frictional
coefficient . NSF is a common problem if a pile is designed in a highly compressible soil.
A grid configuration of 3 x 3, 4 x 4 and 5 x 5 piles was considered for this research. The
effects of pile tip, pile shaft friction, pile socket length, and magnitude of applied load and
load variation on the pile were studied. The pile cap selection was done by considering
formation of constant pile cap settlement and uniform distribution of loads throughout the
pile cap length. In the case of a short pile, the negative skin friction may cover the most
entire length, and accordingly, the down-drag force is transmitted to the pile’s tip in the form of penetration to the underlying strata, whereas for a long pile, the down-drag force
is mainly taken by the compression of the pile’s material and little or none is transmitted to the pile’s tip. The maximum mobilized negative shaft resistance developed at the entire
depth of the pile and this value changed to zero at the neutral point. At the working load
level, the drag force may be large enough to reduce the pile capacity or to overstress the
pile’s material, causing fractures or perhaps structural failure of the pile, or possibly
pulling out the pile from the cap when L/D become small. For similar axial load
application into the model with and without pile cap, the negative skin friction distribution
made visible difference.
Key words: Negative skin friction, Neutral plane, Axial load
ii
ACKNOWLEDGEMENTS
First, my sincere gratitude and appreciation goes to my advisor Dr.Siraj Mulugeta. His
unlimited help and advice has helped me in accomplishing this thesis. I would also like to
extend my thank to my Colleague Seto Melese. He has assisted me in introducing
ABAQUS numerical modeling software which has helped me a lot in doing this thesis.
Last but not least, I would like to thank all those whom I received encouragement and
support throughout the course of this thesis.
iii
CONTENTS
ABSTRACT .............................................................................................................. i
ACKNOWLEDGEMENTS .................................................................................... ii
LIST OF FIGURE .................................................................................................. vi
LIST OF TABLE .................................................................................................. viii
LIST Of SYMBOLS ............................................................................................... ix
1.INTRODUCTION 1
1.1 Background .................................................................................................... 1
1.2 Problem Statement ............................................................................................ 3
1.3 Objective of the study ........................................................................................ 3
1.3.1General objective .......................................................................................................... 3
1.3.2 Specific objective ........................................................................................................ 3
1.4 Scope of the study .............................................................................................. 3
1.5 Significance of the study ................................................................................... 4
2. LITERATURE REVIEW 5
2.1 General ............................................................................................................... 5
2.20 Negative skin friction on the pile groups ....................................................... 6
2.3 Pile Group Behaviour and Effeciency ............................................................. 7
2.4 Loads in pile groups ........................................................................................ 12
2.4.1 Axial Load Behavior of pile ...................................................................................... 12
2.5 Factors Influencing Pile Group Behavior ..................................................... 13
2.6 Loading Condition ........................................................................................... 14
2.7 Properties of Pile Cap ..................................................................................... 15
2.8 Properties of Pile .............................................................................................. 15
2.9 The Embedded Pile Concept .......................................................................... 16
2.10 Contact Behaviors of Pile -Soil Interface .................................................... 17
2.11 Parametric Study ........................................................................................... 17
2.12 Methods to Estimate the Load Capacity of Piles ........................................ 18
2.12.1 Friction Capacity: β Method .................................................................................... 19
2.11 End-Bearing Capacity: -Method .............................................................................. 20
iv
β.1β.β Method for Group Pile .......................................................................................... 21
2.13 Boundary Conditions .................................................................................... 22
2.14 Location of the Neutral Plane ....................................................................... 23
2.15 Physical Properties of Typical Sand Soil ..................................................... 24
β.16 Poisson’s Ratio ........................................................................................................... 25
2.17 Angle of Internal Friction ............................................................................. 25
2.18 Unit Weight of the Soil .................................................................................. 26
2.19 Computation of the Soil Settlement ............................................................. 27
3. METHODOLOGY 29
3.1Finite Element Method ..................................................................................... 29
3.3 Finite Element Modeling ................................................................................. 29
3.4 Pile –Soil- Pile Interaction .............................................................................. 30
3.5 Material Model ................................................................................................ 31
3.6 3D Finite Element Modeling Technique of Piles and Pile Cap ................... 31
3.7 Basic Assumptions Used in 3D Numerical Modeling ................................. 33
3.8 Theoretical Estimation of Vertical Load Capacity of Piles ....................... 34
3.8.1 Friction capacity: Method ...................................................................................... 34
3.9 Estimation of Pile Group Efficiency .............................................................. 37
3.10 Analytical Estimation of Drag-Loads .......................................................... 40
3.11 Model Discretization ................................................................................................. 40
3.12 Pile Configuration ......................................................................................... 41
3.13 Pile Cap Sensitivity Analysis ........................................................................ 43
3.14 Numerical Model Verification ...................................................................... 45
4. CHAPTER FOUR 47
4.1 Parametric Analysis ........................................................................................ 47
4.2 General .......................................................................................................................... 47
4.3 The Distribution of Load in a Pile and its Neutral Plane ............................ 47
4.4 Self-Weight Stress Field .................................................................................. 48
4.5 Normal Pressure and Friction Interface ....................................................... 49
4.6 Effect of Variable Load on the Pile Group ................................................... 49
v
4.6.1 Pile and Soil Settlement in Different Pressure Loads ................................................ 49
4.6.2 Drag -Load Distribution for Different Pressure Loads ............................ 50
4.6.3 Neutral Plane Determination Due to Load Variation ............................... 51
4.6.4 Negative Skin Friction Determination ........................................................ 53
4.8 Effect of Pile Cap on The Pile Group ............................................................ 55
4.8.1 Neutral Plane Determination ..................................................................................... 55
4.8.2 Negative Skin Friction Determination ....................................................................... 56
4.9 Numerical Analysis of Pile Group With variable Pile Lengh and Diametres57
4.9.1 Pile Group ..................................................................................................... 57
4.9.2 Pile Group Settlement .................................................................................. 57
4.9.3 Ultimate Pile Group Capacity ..................................................................... 58
4.10 Axial Load Distribution For Different Pile diameter................................ 60
4.11 Effect of Pile Diametre to NSF ..................................................................... 61
4.13 Effect of Pile Length and Diamatre on the Neutral Plane ......................... 64
4.14 Cause of Minimum l/d Ratio to Excessive Pile Settlement ....................... 67
4.15 Effect of group Pile Spacing on NSF ........................................................... 68
4.16 Effect of Pile Length on NSF (5D)................................................................ 71
4.16.2 Effect of Pile Length in Negative Skin Friction (4D ) ............................. 74
4.16.3 Effect of Pile Length on NSF (3D ) ........................................................... 77
5. CONCLUSIONS AND RECOMMENDATION 81
5.1 CONCLUSION ................................................................................................ 81
5.2 RECOMENDATION .................................................................................. 83
REFERENCES 84
vi
LIST OF FIGURE
Figure 2. 1 Single pile vs. pile group load-settlement behavior of individual piles ............. 8
Figure 2. 2 Group efficiency according to Converse-Labarre (after Garg, 1979) ............. 11
Figure β. γ Feld’s method for estimating the group capacity of friction piles ................... 12
Figure 2. 4 Column loads ................................................................................................... 13
Figure 2. 5 Block-Failures model for closed-spaced piles, Reese, Wang et al. (2000) ...... 15
Figure β. 6 Piles’ side friction (skin friction) and end bearing, Sam Helwany, (β007) ..... 21
Figure 2. 7 Pile group With Pile Cap, Helwany, (2007) .................................................... 22
Figure 2. 8 KELVIN element type with node (ABAQUS, 2010) ...................................... 22
Figure 2. 9 Illustration, of NSF mechanism Gwee Boon Hong, (2013)............................ 24
Figure 2. 10 Influence factor for settlement, after Poulos, (1989) ..................................... 28
Figure 3. 1 3D mesh generations and calculation model with given pressure ................... 41
Figure 3. 2 Pile group layout and cross sectional view ..................................................... 42
Figure 3. 3 Pile group configuration with different pile spacing ...................................... 42
Figure 3. 4 Pile cap settlement with different thickness .................................................... 43
Figure 3. 5 The Pile Settlement with Different Thickness ................................................ 45
Figure 3. 6 Model verification ........................................................................................... 46
Figure 4. 1 Positive and Negative Shaft Resistance .......................................................... 48
Figure 4. 2 Self-weight stress fields for elastic analysis method ....................................... 48
Figure 4. 3 Normal pressure .............................................................................................. 49
Figure 4. 4 Drag load along the pile group with normalized depth .................................... 51
Figure 4. 5 Location of Neutral Plane for different axial load ........................................... 52
Figure 4. 6 Neutral plane location for 200 kPa ................................................................ 53
Figure 4. 7 Skin Friction Distribution with Different Axial Load .................................... 54
Figure 4. 8 Skin friction distribution for different pressure loads ..................................... 54
Figure 4. 9 Location of neutral Plane (S.L = 75 kPa) ........................................................ 55
Figure 4. 10 Negative Skin Frictions with and without Pile Cap ....................................... 56
Figure 4. 11 The pile group settlement with different pile diameter and spacing .............. 58
Figure 4. 12 Group Pile Settlement and its maximum capacity of the pile group ............. 58
Figure 4. 13 Determination of Pile Capacity for 3D Pile Spacing ..................................... 59
Figure 4. 14 Pile group settlements at failure stage with minimum l/d ratio .................... 60
Figure 4. 15 axial load distribution for different pile diameter for 5D pile spacing .......... 60
Figure 4. 16 axial load distribution for different pile diameter ......................................... 61
Figure 4. 17 NSF distribution with respect to pile diameter and its l/d ratio .................... 62
Figure 4. 18 Distribution of NSF with different pile diameter (3D). ................................ 63
Figure 4. 19 Location of neutral plane for 5D pile spacing (S = 5D) ................................ 65
Figure 4. 20 Location of neutral plane with different pile length and diameters ............... 66
Figure 4. 21 Location of neutral plane for 3D Pile Spacing............................................... 67
Figure 4. 22 The Failure Stage for 4D and 3D Pile and Soil settlement ........................... 68
Figure 4. 23 Skin friction distribution through pile length of 20 m ................................... 69
Figure 4. 24 Skin friction distributions through pile length of a = 15 m and b = 10 m ..... 70
Figure 4. β5 Skin frictions on pile’s shaft with (a) 5D-20 m and (b) 5D-15 m.................. 71
Figure 4. β6 Skin frictions on pile’s shaft with 10 m pile length (S = 5D) ....................... 74
vii
Figure 4. β7 Skin frictions on pile’s shaft with (a) 4D-20 m (b) 4D- 15 m ....................... 76
Figure 4. 28 Skin frictions on pile’s shaft with 10 m pile length (S= 4D) ........................ 77
Figure 4. β9 Skin frictions on pile’s shaft (a) β0 m and (b) 15 m with (γD) ..................... 79
Figure 4. 30 Skin frictions on piles shaft with 10 m pile length (3D) ................................ 80
viii
LIST OF TABLE
Table 2. 1 ultimate capacity (After Feld, 1943) ................................................................. 12
Table 2. 2 typical elastic moduli of sand soils after USACE table D-3 ............................. 24
Table β. γ Typical Poisson’s ratio of soils after Bowles, 1996 .......................................... 25
Table 2. 4 typical angle of internal friction for sand soils after Meyerhof, 1956 ............... 25
Table 2. 5 typical angle of internal friction for sand soils after Peck, 1974 ....................... 26
Table 2. 6 typical unit weight values of granular soils after Bowles, 1996 ....................... 26
Table 3. 1 Reynolds guideline chart of pile cap thickness with pile dia. ........................... 31
Table 3. 2 Material properties used in the analysis ........................................................... 31
Table 3. 3 Types of model which is performed in this research ........................................ 32
Table 3. 4 pile settlement with different pile cap thickness .............................................. 44
Table 4. 1 Pile and soil settlement with neutral plane for constant pile length (20m) ....... 50
Table 4. 2 Pile and soil settlement for different pile length. ............................................. 63
Table 4. 3 Pile settlements and neutral plane with different pile diameter ........................ 64
Table 4. 4 Maximum Negative and positive skin friction .................................................. 73
ix
LIST Of SYMBOLS
NSF = Negative Skin friction
NP = Neutral Plane
Es = Young’s modulus
Gs = group efficiency factor
Sg = group settlement
Se = settlement of single pile
FE = finite element
=efficiency of the pile group
S = center to center pile spacing
D = pile diameter
QB =ultimate capacity of the block of pile
Qa = allowable capacity of single pile
Qg(u) = ultimate load bearing capacity of the group pile
Qs (u) = ultimate load bearing capacity of the single pile
P = axial column load
W = weight of the pile cap
Qb = end bearing capacity
Qf = friction capacity
fs = friction stress
Ko =lateral earth pressure coefficient
Nq and Nc = bearing capacity coefficient
Lg =group length
Bg = group width
Ag = area of the group
P (g) = perimeter of the group
1
1. INTRODUCTION
1.1 Background
Negative skin friction (NSF) is one of the most common problems encountered in piling
engineering, and occurs when a pile is installed through a layer of soft consolidating clay.
Such consolidation may occur due to placement of a fill or construction of a building. As
the consolidation progresses, the adjacent surrounding soil settles to a larger extent
relative to the pile and induces a “drag load” towards the direction of gravity. This
downward drag load on the pile is termed as NSF. Research on group efficiency of pile
subjected to vertical and lateral loading in weak soil has been a challenge for geotechnical
engineers for the last 50 years. The majority of these researches deal with the group
behavior. Piles are normally designed to achieve axial loading capacity through the
development of positive shaft skin resistance and end-bearing resistance. The positive
shaft skin resistance will be developed under the condition that the pile settles more than
adjacent soil. However, in areas of deep compressible soil, the soil adjacent to a pile is
likely to settle more than the pile, and the relative settlement between pile and soil will
change the direction of skin friction on the pile, that is, negative skin friction (NSF) occurs
Liu, Gao et al. (2012). Terzaghi, Peck et al. (1996) presented that the concept of negative
skin friction was first researched on the problem of differential settlement for the building
adopted pile foundation. With the development of the national economy, more and more
high-rise buildings appear and the usage of pile foundation is getting frequent. In
particular, pile foundation becomes the main foundation form in super-tall buildings in
soft soil areas (Xia, Hu et al. (2013). He also recommended that skin friction around piles
and resistance at pile tips are two parts that consist of the support of pile foundation.
Because the soil surrounding the pile settles is more than the pile, negative skin friction
(NSF) appears. It can cause the increase of the compressive force, the decrease of effective
pile capacity, the enlargement of pile displacement and can even influence the usage of the
building and the safety of the structure. Lee and Ng (2004) developed a numerical model
for pile groups under NSF using FEM, and pointed out that the effect of soil slip at the
pile-soil interface was a key factor affecting pile groups behavior. Shen and Teh (2002)
built a theoretical calculation model based on its variation using potential energy principle,
and calculated results were compared with field measured values. Lee, Bolton et al. (2002)
studied on drag-load, down-drag and the efficiency of pile groups under NSF by using
FEM ABAQUS, and pointed that surface load, the friction coefficient of pile-soil
interface, the arrangement of pile groups and the spacing of piles are the major factors that
affect the results . Jeong, Lee et al. (2004) on this study included that the drag-load
influenced by the slip of pile-soil interface, pile head load etc. Comodromos and Bareka
(2005) studied on drag-load and the location of neutral plane on single pile in layered soil
and included that the results influenced by the sequence of applying pile head load and
2
surface load using FLAC3D software. The constrains of pile cap make the difference of
the displacement of each pile small, and then causes the development of NSF of each pile
related, coordinated. Yang, Jiang et al. (2013) conclude that the pile side friction is related
to the section displacement of pile, the pile load and the soil characteristic. He also
suggested under the vertical load, the friction of filling soil brings to play step by step and
reaches the ultimate state and then the side friction of clay.
Lee and Ng (2004) recommended that the relative settlement between the piles and the
consolidating soil may result in a large down-drag force, which is time dependent, for a
pile group, the down-drag force on an individual pile is smaller than on an isolated single
pile due to interaction effects. Thach, Liu et al. (2013) reported vertical soil settlement is
larger than that of pile, drag-load (the additional compressive force) and down-drag (the
excessive pile settlement) of pile caused by negative skin friction (NSF) occurred. NSF is
one of the common problems in the designing and construction of pile foundations in soft
ground. In general, negative skin friction on pile is caused by surcharge load or
consolidating soil. There are several parameters affecting the pile group behavior such that
soil properties (Bowles 1997, Tomlinson and Woodward 2006, Rollins et al. 2005,
Yenginar and Tan 2015, Fellenius 2015), pile installation methods (Yenginar 2014,
Zarrabi and Eslami 2015), pile geometry (Lv et all. 2012), groundwater level and
saturation degree of soil (Olgun et all. 2015) are the major factor of NSF.
Huang, Zheng et al. (2015) when piles are constructed in consolidating ground, negative
skin friction (NSF) is induced as a result of the downward movement of the soil relative to
the pile. He also reported that group effect coefficient and neutral plane depth increase
with the increase of pile spacing because of the less interaction of piles. These studies
were very helpful in understanding the NSF behaviors of pile embedded in a consolidating
soil, while few literatures focused on mathematical model analysis of negative skin
friction of pile embedded in a consolidating soil. NSF on pile shaft was increased with the
increase of consolidation time and tended to be stabilized at last. Model tests and
numerical simulation results have demonstrated that the drag-load and down-drag on
individual piles in a group was smaller than that on an isolated single pile. This study was
very helpful in understanding the behaviors of pile group under drag-load. It was evident
from the literature as cited above that most of the available studies were limited to
empirical methods or mathematical model, while a few were on numerical models or
theoretical methods. Hence, need to develop numerical models to predict the negative skin
friction with considering pile configuration, pile-soil interface element, and pile length
variation with constant axial load. This research also investigates load variation and pile
group configuration on NSF. Such analysis will be presented in this study.
3
1.2 Problem Statement
Most of the time engineers don’t take account NSF on pile design and try to change the
pond area into mass filling. To change the design criteria and manage such problems,
understand the principle of negative skin friction is so crucial. But as some scholars stated
that the determination of the load-bearing capacity of group piles is extremely complicated
and has not yet been fully resolved by the cause of many factors. Due to this reason the
parameters which are studied in this research has been minimized. In the present study the
behavior of pile group in sand and clay layer upon the variation of pile spacing, length,
pile diameter and distribution of loads are examined.
1.3 Objective of the study
1.3.1General objective
Numerical investigation of negative skin friction of pile group for vertical loading
1.3.2 Specific objective
(a) To review the pertinent literature on the topic of pile group behavior, this subjected to
axial loading
(b) To carry out a parameter study on a pile subjected to NSF in order to study the
influence of selected design factors on negative skin friction.
(c) Analyze the negative skin friction with respect to different pile length
(d) To investigate negative skin friction with respect to different pile diameter
(e) Investigate the effect of pile settlement on the pile group with different loading
condition.
1.4 Scope of the study
Pile groups are mostly used in practical engineering, though single pile with large
diameter is rarely used. Large amount of model tests and engineering measurements show
the working properties of pile groups are quite different from single pile. The working
properties of pile groups are influenced by the joint action.
NSF only focuses on pile groups with capped and uncapped under axial loading
The groundwater table is on the ground surface.
4
Only 3D, 4D and 5D pile group configuration are examined
Number of piles are 3 x 3, 4 x 4 and 5 x 5
20 m ,15 m and 10 m pile length are used
The pile cap dimension was 8 m x 8 m x 1.5 m
The soil model dimension was 86 m x 86 m x 36 m
1.5 Significance of the study
This numerical study on the behavior of loaded piles in a multi-layered soil medium is
advantageous to validate theoretical investigation with numerical investigation for pile
foundations subject to negative skin friction. To appropriately predict the factors affecting
the efficiency of pile groups exposed for axial loads and determines the contribution of
pile cap in group efficiency and enables as to select appropriate type of constitutive
models used for numerical analysis. This study also gives semi analytical approach for
negative skin friction piles and investigates the effect of negative skin friction on the
efficiency of the pile group. Determine the appropriate surcharge load with respect to the
pile length and given pile spacing. This study has concerned about the effect of NSF on
pile group and gives the information to the pile designer.
5
2. LITERATURE REVIEW
2.1 General
Negative skin friction is a soil resistance acting downwards along the pile shaft as a result
of a down-drag and inducing compression in the pile. The evaluation of negative skin
friction (NSF), which occurs when the soil next to a pile settles more than the pile, is a
common problem in the design and construction of pile foundations in soft ground.
Various causes have been reported, which are related mainly to the increase in effective
vertical stress in soil (e.g. Phamvan, 1989; little, 1994; Lee et al., 1998). The development
of additional compressive force (drag-load) in a pile and excessive pile settlement (down-
drag) could cause difficulty in construction and maintenance of the structure supported.
Fellenius (1984) suggests that the problem of negative skin friction is settlement not
bearing capacity, i.e., the magnitude of the drag-load is no direct relevance to the
geotechnical capacity of the pile. Lee (1993) stated that piles are embedded in a
consolidating soil, negative skin friction develops due to the interaction between the piles
and the settling soil. Hanna and Sharif (2006) suggested that negative skin friction is
developed on the pile’s shaft shortly after applying the surcharge load, and continues to
exist until the completion of the consolidation of the surrounding soil.Kong, Yang et al.
(2008) states that NSF may occur by downward vertical soil stress near the pile transferred
to the pile shaft when the soil next to a pile settles more than the pile under surface load or
groundwater lowering conditions. The pile is usually modeled as a beam loaded at the free
(for rotation) pile head by the given either axial or lateral load. In most of the real cases,
piles are composed into pile-groups with a common capping beam or slab in order to
strengthen their stiffness and load resistance. Karolina Gorska et al. (2017), Poulos (1971)
method assumes that the soil is elastic and it accounts for the influence of one pile on
other piles in the group through the use of influence factors based on linear elastic theory.
A pile cap that remains in contact with the ground provides additional lateral restraint to
the group. However, settlement or scour of the soil around the piles may reduce or
eliminate the cap-soil contact and thereby reduce the lateral restraint provided by the cap.
For this reason, the resistance of the cap to lateral loads is usually neglected Phillip S. K.
et al (2013). The distributions of drag-load were influenced by load sequence of pile head
load and surface load significantly, Qing, Gang-qiang et al. (2008) .The behavior of pile
groups, however, is more complex and has not been adequately examined or understood.
While many model tests were carried out in loose and dense sands Singh and Prakash
(1973), the few field test available, particularly with regard to bored pile groups, are either
not well documented Liu et al. (1985) or deal with special conditions such as under-
reamed pile groups Garg (1979).
6
2.20 Negative skin friction on the pile groups
Negative skin friction is an unusual pile-soil interaction phenomenon that happens in
driving piles into the soil has filled in, upon or at the end stage of the accomplishment of
piling procedure Hussein Y., (2018). The magnitude of the movement necessary for
negative skin friction to develop has been reported in a few papers. Walker (1973)
reported that a 35 mm settlement of the ground surface due to a 3 meters high surcharge
placed around single piles was sufficient to develop negative skin friction down to a depth
of 18 meter. Comodromos and Bareka (2005) stated that the effect of negative skin
friction was quantified from the analysis of the particular soil profile and that the use of
these quantitative data would be unwise in soil profiles and pile group configurations.
Drag load is induced on the pile as an additional load due to negative skin friction
conventionally develops on the pile surface, which needs to be considered in pile design
Noor, Hanna & Mashhour, (2013). Bjerin (1977) found that negative skin friction was
fully mobilized to a depth of about 25 meter after a relative displacement of about 5 mm
as measured at a short distance away from the pile (about 0.12 meter). He also suggested
that at 5m, the relative displacement was about 8 mm. Bozozuk (1981) found that a
reversal of direction of shear forces down to a depth of 20 meter occurred when loading a
pile and generating a relative movement of about 5 mm at the pile head. Bjerrum,
Johannessen et al. (1969) reported negative skin friction developing along piles at a site
where the settlement under a recent fill amounted to 2 meter, he also reported that about
the same magnitude of negative skin fraction developed on the same type of piles driven
under an adjacent, 70 year old fill of the same height in the same type of soil, which did
not experience any new settlement after the pile installation. He also showed that negative
skin friction is proportional to the effective overburden stress in the soil surrounding the
pile. Zeevaert (1972) presented a method of calculating the negative skin friction based on
the reduction of the effective overburden stress caused by the soil "hanging" on the pile.
The constant of proportionality is called beta-coefficient, , and it is a function of the earth
pressure coefficient in the soil Ks, times the soil friction, tan ϕ', times the ratio of the wall
friction M = tan δ'/tan ϕ'. (Bozozuk, 1972).
M.J. Tomlinson suggested that Calculation of the magnitude of the negative skin friction
is a complex problem which depends on the following factors.
7
a) The relative movement between the fill and the pile shaft.
b) The relative movement between any underlying compressible soil and the pile
c) The elastic compression of the pile under the working load.
d) The rate of consolidation of the compressible layers.
2.3 Pile Group Behaviour and Effeciency
Piles are usually constructed in groups and tied together by a concrete cap at the ground
surface. Piles in closely spaced groups behave differently than single isolated piles
because of pile-soil-pile interactions that take place in the group. Tuan (2016) suggested
that determination of the load-bearing capacity of group piles is extremely complicated
and has not yet been fully resolved. The loads applied by a structure are quite large and
usually cannot be supported by a single pile, so a number of piles are placed together to
form a pile group, with a substantial reinforced concrete pile cap placed on top to transfer
and distribute the loadings from the structure to the piles G. E. Barnes ,(1995). He also
suggested that Piles are grouped together usually on a square grid pattern with the
structural load transferred to and shared between the piles by a thick reinforced concrete
pile cap. The analysis of a pile group is three dimensional. Consequently current methods
of analysis of pile groups subjected to combined axial loads, lateral loads and turning
moments are either wholly based on linear elastic soil behavior Poulos (2006) ,or combine
nonlinear single pile response with linear elastic forms of interaction O'Neil et al. (1977).
If piles are far apart in terms of multiples of pile diameter, pile–soil–pile interaction will
not occur. As the piles become closer to each other, the stress in the soil from the
distribution of axial load or lateral load to the soil will affect nearby piles. The simple way
to consider the influence of the effect of the stresses in the soil is to think of the efficiency
of closely spaced piles becoming less than unity, Reese, Isenhower et al. (2006).
The main effects which influence the behavior of pile groups are, according to Rudolf
(2005):
The stiffness of the raft and/or the superstructure
The pile type
The installation procedure
The size of the pile group
The ratio of pile spacing to pile length
The soil type.
8
The settlements of a pile group in working load conditions are in general bigger than the
vertical displacements of a single pile with equivalent load (Fig. 2.1a). The group effect is
related to increased settlements of a pile, if this pile is affected by the displacement field
of a neighboring pile Randolph (2003). At high load levels, pile groups show in general a
stiffer response than single piles, which comes from the fact that the stress state in the soil
increases. But as stated by Kempfert and Rudolf (2005), pile groups in the allowable load
range experience generally higher displacements than single piles. Within a pile group, the
behaviors of the individual piles also differ significantly. Fig.2-1b illustrates the load-
settlement behavior of the center, edge and corner pile of a 9-pile group. The load carried
by the piles varies depending on the stiffness of the superstructure. If the raft and/or the
superstructure are relatively stiff, more loads are initially transferred to the corner piles.
(a) (b)
Figure 2. 1 Single pile vs. pile group load-settlement behavior of individual piles
A typical quantity to describe the group effect is the group efficiency factor Gs, which is
defined as the ratio of the average group settlement (Sg) divided by the settlement of a
single pile (Se) at the same load level. � = ��� ………………………… (2.1)
To evaluate the load-settlement behavior of pile groups, a number of approaches are
available in the literature. There are empirical methods as presented by Skempton (1953)
or Hettler (1986) and other approaches that use equivalent piers or equivalent rafts (e.g.
Randolph 1994). The size and the position of the equivalent raft depend on the load
transfer mechanism of the pile (end-bearing or friction pile), while the equivalent pier
needs an equivalent diameter and homogenized stiffness. Analytical methods to calculate
9
settlements of pile groups can be divided into a group that does not take pile-pile
interaction into account and another group that accounts for pile interactions by means of
interaction factors. Detailed information related to the first group is given in Rudolf
(2005) and an overview of the possibilities of the latter group is presented by, Poulos
(2006). All approaches mentioned have deficiencies either to the geometrical definition of
the pile group or to a realistic representation of the soil. In the author's opinion, pile
groups are a typical example of boundary value problems where numerical analyses - and
especially 3D modeling - are essential. Various authors showed the potential of different
numerical methods; e.g.El-Mossallamy, Hefny et al. (2013), who used a coupled finite
element and boundary element method; Comodromos and Bareka (2005) who conducted
the finite difference method to analysis axially-loaded pile groups; or Chow (2007), who
applied a combination of finite layer and FE technique to study pile group effects. Of
course, the finite element technique is also increasingly utilized to calculate the
performance of such foundation. Several efficiency formulas have been proposed to relate
the behavior of a pile group to that of the individual piles in the group. These formulas are
mostly based on relating the group efficiency to the spacing between the piles and always
yield g values of less than unity, regardless of the pile/ soil conditions. A major apparent
shortcoming in most of the available efficiency formulas is that they do not account for the
characteristics of the soil in contact with the pile group.
The most acceptable formulas for pile groups in clay are briefly summarized as follows:
1. The converse-Labarre (Bolin 1941) method. Formula is one of the most widely used
formulae for evaluating pile group behavior. According to this formula, the efficiency of
the group is equal to: � = − − + − ……………… (2.2)
Where η = Efficiency of the pile group, m = Number of rows, n = Number of columns = − � …………........... (2.3)
s = Center to center spacing of piles, d = diameter of piles
10
2. Feld (1943) method. Feld proposed a rule of thumb to determine the efficiency of a pile
group. In his method, the capacity of a pile group is defined as the summation of the
capacities of the individual piles in the group multiplied by a factor ranging between 0.72
and 0.94 according to the number of piles. Feld also suggested a method by which the load
capacity of the individual piles in the group embedded in sand could be obtained.
According to this method, the capacity of the pile is reduced by 1/16 by each adjacent
diagonal or row pile.
3. Whitaker (1957) method. Whitaker developed design charts for determining the
efficiency of a pile group based on the results of the experimental models. These charts are
adopted in the design manuals of the U.S. Army Corps of Engineers and the U.S. Navy.
4. Poulos and Davis (1980) method. The pile group efficiency is defined as
� = + ( ∗ ∗� )� ………………… (2.4)
Where QB and Qa = the ultimate load capacities of the block of piles (equivalent large
pile), and that of a single pile, respectively.
Pham AnhTuan (2016) Suggested that the most widely recognized standard for
quantifying group interaction effects in the group efficiency factor, η, which is defined in
Equation (1) as the average capacity per pile in a group dived by the capacity of a single
pile. � = �� �∑ �� = �� �(�� � ) ………………. (2.5)
Where ηg = group efficiency; = ultimate load-bearing capacity of the group pile; = ultimate load-bearing capacity of the single pile; n = the number of piles in the
group.
11
Figure 2. 2 Group efficiency according to Converse-Labarre (after Garg, 1979)
5. Los angles group action, 1944 equation can be expressed as: � = − �� [ − + − + √ − ] …………………… (2.6)
6. Seiler and Keeney also expressed the pile group efficiency as: � = { − [ �� − ] [ + −+ − ]} + .+ ..……………… (2.7)
Where s = Center to center spacing of piles in ft.
The above equations were developed under the geometric condition of the pile group
number of piles, center to center spacing of the piles in the group. Furthermore, they did
not consider the other important parameters, such as length of the pile, soil property and
load distribution between the piles. The technique is well explained if one examines
Figure 3, which shows the plan of a group pile. Different loads will be assigned to
different piles within the group based on their position. With this in mind table 2-1
presents the load distribution and the reduction factor of each pile within the group.
12
Table 2.1 ultimate capacity (After Feld, 1943)
Hence � = �� ���� = . QuQu = %
Figure 2. 3 Feld’s method for estimating the group capacity of friction piles
2.4 Loads in pile groups
2.4.1 Axial Load Behavior of pile
David M. Potts (2001) suggested that one of the important issues when analyzing a pile
subject to vertical loading is the modeling of the interface between the pile and the soil
adjacent to the pile shaft. Yasser Khodair et al (2013) the applied axial load did not
significantly affect neither the induced bending moment nor lateral displacement in the
pile. A compressive load applied to the head (top) of the pile is transferred to the
surrounding soil by a combination of skin friction along the embedded length and end
bearing at the tip (bottom) of the pile. For relatively short piles, only the end bearing effect
is significant. For relatively long piles in soil (excluding tip bearing piles on rock), the
predominant load transfer is due to skin friction and axial tension load is resisted only by
skin friction Reed L. Mosher (2000). When the load is applied at the centroid of the group
it is assumed to be distributed uniformly to all piles by the pile cap, which is taken to be
rigid, this gives the load per pile T.J. Macginley (1990) . Pile foundations carrying vertical
(axial) loads are necessary to support large structures when the grounds (geotechnical
conditions) are not strong and stiff enough to support the structure Karolina Gorska et al.
(2017). Fa = (P+W)/N Where P is the axial load from the column, W is the weight of the
13
pile cap and N is the number of piles figure 2-4; but as it compared from the weight of
other structure the weight of the pile cap is very small in this paper it is ignored. For this
study axial load is take in consideration.
Figure 2. 4 Column load
2.5 Factors Influencing Pile Group Behavior
Driven piles: Driven piles are normally placed in groups with spacing’s less than 6B where B is the width or diameter of an individual pile. The pile group is often joined at the
ground surface by a concrete slab such as a pile cap, Figure 2-8a. If pile spacing within the
optimum range, the load capacity of groups of driven piles in cohesion less soils can often
be greater than the sum of the capacities of isolated piles, because driving can compact
sands and can increase skin friction and end-bearing resistance .
Batter: Battered piles are used in groups of at least two or Pile Groups more piles to
increase capacity and loading resistance. The angle of inclination should rarely exceed 20
degrees from the vertical for normal construction and should never exceed 26½ degrees.
Battered piles should be avoided where significant negative skin friction and down-drag
forces may occur. Batter piles should be avoided where the structure’s foundation must respond with ductility to unusually large loads or where large seismic loads can be
transferred to the structure through the foundation.
Fixity: The fixity of the pile head into the pile cap influences the loading capacity of the
pile group. Fixing the pile rather than pinning into the pile cap usually increases the lateral
stiffness of the group, and the moment. A group of fixed piles can therefore support about
twice the lateral load at identical deflections as the pinned group. A fixed connection
between the pile and cap is also able to transfer significant bending moment through the
connection. The minimum vertical embedment distance of the top of the pile into the cap
required for achieving a fixed connection is 2D where D is the pile diameter or width.
Stiffness of pile cap: Xia, Hu et al. (2013) in practical engineering, pile cap is neither
completely flexible nor completely rigid. The stiffness of the pile cap will influence the
distribution of structural loads to the individual piles .The thickness of the pile cap must
be at least four times the width of an individual pile to cause a significant influence on the
14
stiffness of the foundation (Fleming et al. 1985). A rigid cap can usually be assumed for
gravity type hydraulic a rigid cap can usually be assumed for gravity type hydraulic.
Soil modulus: The elastic soil modulus Es and the lateral modulus of subgrade reaction
Els relate lateral, axial, and rotational resistance of the pile-soil medium to displacements.
The modulus of submerged sands should be reduced by the ratio of the submerged unit
weight divided by the soil unit weight. The modulus of elasticity or Young’s modulus of a soil is an elastic soil parameter most commonly used in the estimation of settlement from
static loads. Young’s modulus, Es, may be estimated from empirical correlations,
laboratory test results and field tests. Typical values of elastic moduli for sand soil are
presented in table 2.3.
2.6 Loading Condition
Suggested that the pile groups in stiff or even hard clays with a relative length L/D<25
and normalized spacing S/D higher than 3.0 a settlement of the order of 10% of the pile
diameter (D) is sufficient to reach the bearing capacity of the group, while for higher
values of the ratio L/D and closer pile dispositions increased settlement level is required.
In this study, the pile geometry is symmetric, if it can be symmetry the full load was
applied to the pile in the FEM analysis in the form of pressure load on the pile cap. Most
pile foundations consist not of a single pile, but of a group of piles for supporting
superstructures. The problem is complicated by the presence of the pile cap in two ways.
1. The cap is perfectly rigid and the axial loading is symmetrical, all of the piles will settle
the same amount. However, if the cap is flexible, the settlement of the piles will be
different.
2. If the cap rests on the ground surface, some of the axial load will be sustained by
bearing pressure on the cap. Many authors have treated the problem of the distribution of
the axial load to the piles and to the cap. However, conservatively, the assumption can be
made that there can be settlement of the soil beneath the cap and that the entire load is
taken by the piles. The position of each pile in the group is less important than that of piles
under lateral loading. A number of investigators, such as Poulos and Davis (1980) and
Focht Jr and Koch (1973) have used the theory of elasticity to develop interaction. The
concept of block failure (i.e., simultaneous failure of the piles and of the mass of soil
within the pile group) is commonly used to calculate the ultimate capacity of a closed-
spaced pile group. As shown in figure 2.5.
15
Figure 2.5 Block-Failures model for closed-spaced piles, Reese, Wang et al. (2000)
2.7 Properties of Pile Cap
A pile cap is a thick concrete mat that rests on concrete or timber piles that has been
driven in to soft or unstable ground to provide a suitable foundation. El-Garhy et al.
(2009) presents the results of experimental study on model piles to show the effect of pile
cap elevation below the ground surface and pile spacing on lateral resistance of single pile
and pile groups driven in sand. U. K. Nath et al (2013), a pile cap is mostly reinforced
concrete slab or block to resist the given load which comes from super structure and
interconnects a group of piles. It should normally be rigid so as to distribute the forces
equally on the piles of a group. In general it is designed like a footing on soil but with the
difference that instead of uniform reaction from the soil, the reactions in this case are
concentrated either point loads or distributed. In practical there is no completely rigid and
completely flexible pile cap. Pile caps are modeled as a plate element and can be used to
simulate the influences of pile.
2.8 Properties of Pile
Concrete circular section pile with linear elastic properties was used in this study. The pile
was simulated utilizing 8-noded brick elements. Concrete piles may be divided into two
basic categories: Precast piles and cast-in-situ piles. For this study pre-cast concrete piles
can be used. It can be prepared by using ordinary reinforcement, and they can be square or
octagonal in cross section. Reinforcement is provided to enable the pile to resist the
bending moment developed during pickup and transportation, the vertical load, and the
bending moment caused by a lateral load. For this study the load type was axial. So the
16
bending moment is not my concern. The piles are cast to desired lengths and cured before
being transported to the work sites, Das (2010). Rabbany, Islam et al. (2018) pile spacing
depends on different factors. Geotechnical engineers make their decision as per field
condition and different lab test and analysis (Which is not covered in this study). The
center to center distance of pile is related to different factors such as type of pile (Friction
pile, end bearing pile etc.), type of soil (Less compressive soil, high compressive soil etc.).
The small change in pile spacing initiates a significant change in pile cap design which is
directly related to economy & safety. In usual practice piles are spaced 2.5 times the
diameter for the end bearing piles or 3.0 times the diameter for friction pile. The usual
length of concrete pile is 10 m to 15 m and its respective load is . 2.9 The Embedded Pile Concept
Habil. P (2012) Numerical methods are increasingly utilized to calculate the performance
of deep foundations, for this calculation a two-dimensional representation of pile groups is
usually not sufficient and 3D modeling is required. This naturally leads to very large
models if a high number of piles are discretized with volume elements, thus problems that
are difficult to analyze. An attractive method to reduce the complexity of such models is
the use of a so called embedded pile formulation, where piles are not explicitly modeled
with continuum finite elements but replaced by a special “formulation” that can take into
account the behavior of a pile penetrating a finite element in any orientation. The benefit
of this concept is that piles are not discretized by means of volume elements and thus do
not affect the finite element mesh. H.K. Engin (2009) conclude that the embedded pile
model consisting of beam elements with non-linear skin and tip interfaces is developed in
finite element model to describe the pile-soil interaction in an efficient manner. The
interaction between the pile and the surrounding soil at the pile shaft is described by
means of embedded interface elements. At the pile tip, the soil resistance against
compression is represented by means of embedded non-linear spring elements. There is no
need for mesh refinement around piles as 3D mesh is not distorted by introducing these
elements which make embedded piles very efficient and time saving especially when a
large group of piles is modeled. Embedded piles are available in both finite element codes
PLAXIS 3D and ABAQUS. The studies presented in this thesis are mainly conducted by
ABAQUS.
17
2.10 Contact Behaviors of Pile -Soil Interface
Zhan (2012) suggested the contact behaviors at the pile-soil surface include load transfer
mechanisms both in the normal and tangent direction. The normal force is transferred only
when pile and soil are contact tightly; otherwise, it becomes zero. This kind of normal
contact behavior can be modeled by “hard” contact option provided by ABAQUS. The
tangent behavior can range from rough contact with no relative sliding between soil and
pile occurs to frictionless sliding conditions with no friction develops along the shaft of
the pile. For contact between these two ideal cases, Coulomb frictional model built in
ABAQUS can be selected to depict the interaction at the pile-soil interface condition
prescribed frictional coefficient . The two ideal contact conditions can also be realized
through prescribed a higher or zero frictional coefficients. The shear resistance of interface
is always dependent on the frictional coefficient and normal stress if no limit shear
resistance is defined. Trochanis, Bielak et al. (1991) the soil-pile interface modeling is
very important due to its influence on the pile response under lateral loading .In the soil-
pile interaction, the surrounding soil and the pile elements are assumed deformable. The
surface of pile elements and soil elements have contact, which the surface of pile elements
are selected as “Master surface” and the surfaces of soil elements are defined as “Slave
surface” . In ABAQUS these surfaces are called the contact pair.
2.11 Parametric Study
The behavior of a pile in a group is influenced by the presence of loadings on neighboring
piles when piles are closely spaced. This is referred to as group effect. A major parameter
influencing the group effect is the spacing between piles. Experiments by Koerner and
Mukhopadhyay (1972) and Ito and Matsui (1976) clearly show this influence through the
use of small scale experiments: at center to center spacing larger than 5 diameters there is
a small group effect while below 2.5 diameters there is a definitely large group effect.
Based on the above literature review, a series of numerical analyses on pile groups were
performed for layered soil conditions, center to center spacing in this paper were 3D, 4D
and 5D. The cases of pile groups with pile cap are analyzed. The other parameter which is
taken in to consideration for this study was length of the pile .The pile length which is
used for this study were 20 m,15 m,10 m, and 5 m. It is assumed that the external load is
only applied to the ground surface of the soil as a distributed load (i.e. rigid pile cap). The
18
piles are square for simplicity. The water table is assumed constant at the bottom ground
surface and a drained analysis was performed. The ultimate down-drag forces result from
the long term behavior of the soil and are calculated on the basis of effective stress
parameters. The soil properties chosen to represent soft clay, loose sand and bearing sand
were selected accordingly. The drained Poisson’s ratio of the soil is taken to be 0.3 in all
cases. Table 2-8 and 2-9 shows the material properties of concrete and soil respectively.
2.12 Methods to Estimate the Load Capacity of Piles
Pile load carrying capacity depends on various factors, including
(1) Pile characteristics such as pile length, cross section, and shape
(2) Soil configuration and short- and long-term soil properties
(3) Pile installation method, but its installation effect is ignored for this study
Obviously in Geotechnical engineering, there are two basic methods to estimate the load
capacity of piles which are α and methods. - Method: The α-method is used to calculate the load capacity of piles in cohesive soils.
This method is based on the un-drained shear strength of cohesive soils; thus, it is well
suited for short-term pile load capacity calculations. The ultimate load capacity of a pile is
the sum of its friction capacity, , and end-bearing capacity, . The friction capacity of
pile in this method which is interface shear stress , between the pile surface and the
surrounding soil determines the value of skin friction. This value is the product of α and
cu (un-drained shear strength of soil). = (2.8)
Where α is a factor that can be obtained from one of several semi-empirical equations
available in the literature (e.g., API, 1984; Semple and Ridgen, 1984; Fleming et al., 1985)
but this method is used for only short term analysis so it is not take into consideration for
this work.
−Method: This method can be used for both cohesive and cohesion less soils. The
method is based on effective stress analysis and is suited for short- and long-term analyses
of pile load capacity Helwany (2007). He also suggested that four main measures must be
19
considered for a successful finite element analysis of soils considering their long-term
(drained) behavior.
(1) The initial conditions of the soil strata (initial geostatic stresses, initial pore water
pressures, and initial void ratios) must be estimated carefully and implemented in the
analysis. The initial conditions will determine the initial stiffness and strength of the
soil strata;
(2) The boundary conditions must be defined carefully as being pervious or impervious;
(3) The long-term strength parameters of the soil must be used in an appropriate soil
model
(4) Loads must be applied very slowly to avoid the generation of excess pore water
pressure throughout the analysis.
Drained and un-drained analyses differ only in the way we apply the load: Very slow
loading allows the generated excess pore water pressure to dissipate and the long-term
strength parameters to be mobilized, whereas fast loading does not allow enough time for
the pore water pressure to dissipate, thus invoking the short-term strength of the soil. This
means that there is no need to input the short term strength parameters because the
constitutive model will react to fast loading in an “un-drained” manner, Sam Helwany,
(2007). For this study drained analysis and slow loading (long term) analysis is used.
2.12.1 Friction Capacity: β Method
This method consider the pile embedded in thick homogenous soil which is fully saturated
.The average lateral effective stress exerted on the pile by the surrounding soil is �ℎ′.This
stress is taken as the lateral effective stress at the mid-point of the pile. The friction stress
between the pile and the surrounding soil can be calculated by multiplying the friction
factor µ, between the pile and the soil with the value ℎ′ . Thus = µ�ℎ′ but �ℎ′ = � ′ where � ’ is the vertical effective stress at the pile
midpoint and is the lateral earth pressure coefficient at rest so the friction stress = µ � ′ (2.9)
The skin friction force between the pile surface and soil is calculated as follows = = µ � ′ × � × ℎ (2.10)
20
= � ′ × � × ℎ = µ
The lateral earth pressure coefficient at rest is given by = − � �′ . where
is over consolidated ratio, for normally consolidated clay soil = . In clays, the
value of can be estimated from above equation µ = tan ϕ Burland (1973) .For sands,
McClelland (1974) suggested values of ranging from 0.15 to 0.γ5. Meyerhof (1976)
suggested values of = . , . , and 1.2 for ϕ'= β8◦, γ5◦, and γ7◦, respectively.
2.11 End-Bearing Capacity: -Method
Using Terzaghi’s bearing capacity equation, the bearing capacity at the base of the pile
can be calculated: = � ′ + ′ (2.11)
Where (� ′ ) is the vertical effective stress at the base of the pile, is the cohesion of
the soil under the base of the pile, and and are bearing capacity coefficients.
The corresponding load capacity is = = [ � ′ + ′ ] (2.12)
Where, is equal to the cross-sectional area of the base of the pile.
Janbu (1976) presented equations to estimate and for various soils: = ( �′ + √ + tan � ) exp � �′ (2.13) = − �′ (2.14)
Where η is an angle defining the shape of the shear surface around the tip of a pile as
shown in figure 2-7 .The angle η ranges from π/γ for soft clays to 0.58π for dense sands.
The ultimate load capacity of a pile is the sum of its friction capacity and end-bearing
capacity: = + (2.15)
21
Figure 2. 6 Piles’ side friction and end bearing, Sam Helwany, (2007)
2.1β.β Method for Group Pile
Piles are generally used in groups. The arrangements, such as rectangular and circular, are
possible. The spacing, s, between two piles center to center should be greater than 2D,
where D is the pile diameter. A concrete cap is generally used to connect the heads of the
piles in a pile group. Loads are applied to the cap that transfers them to the piles. There are
two possible mechanism of failure in pile group.
1. Single-pile failure mechanism: In this mechanism each single pile in the group
fails individually, and the failure of all piles occurs simultaneously. In this case the
pile group capacity, � , is equal to , where n is the number of
piles in the group and is the load capacity of a single pile. For a single
pile can be calculated using the α-method and/or the -method but for this study
method is take into consideration.
2. Block failure mechanism: In this mechanism the pile group, along with the soil
between the piles, fails as a monolith (big block) that has the dimensions × × defined in figure 2-7. The group load capacity for this failure mechanism
can be calculated using the α-method and/or the -method applied to a “mammoth”
pile having the dimensions of the failing block. By using method, calculation of
block failure is as follows: = ∑�=�= � ′ � � � � � ℎ �] + [ � ′ + ′ ] (2.16)
22
Where ( block is the pile group capacity with block failure, n is the number of piles,
perimeter and area of the group is as follows :
= + (2.17) = × . (2.18)
Figure 2.7 Pile group With Pile Cap, Helwany, (2007)
2.13 Boundary Conditions
The boundary conditions differ according to the type of loading. In static analyzing the
bottom of the model which demonstrates the top of the bedrock layer was fixed in all
directions. However the top face of the model was free to move in all directions in both
static and dynamic analyzing. The symmetry surfaces were free to move on the surface of
the symmetry plane, but fixed against the normal displacement to the plane. In order to
illustrate a horizontally infinite soil medium during static and dynamic analysis, the
elements along the sides of the model were simulated as Kelvin elements (spring and
dashpot), and they were free to move in vertical direction as shown in the figure 2-9.
(a) eight-nodded element (b) two-nodded Element (c) Five nodded element
Figure 2. 8 KELVIN element type with node (ABAQUS, 2010)
23
2.14 Location of the Neutral Plane
Neutral Point: The point where the shear stress along the pile changes over from negative
skin friction into positive shaft resistance is called the neutral point, Saha (2015) . He also
suggested that about neutral plane is the depth where the shear stress along the pile
changes over from negative skin friction into positive shaft resistance. According to
Fellenius and Siegel (2008) the neutral plane is the plane where there is no relative
movement between the pile and the soil. He also indicated that the greater the pile toe
resistance, the deeper the neutral plane, and the larger the drag-load. The neutral plane is
the location where NSF transits into PSF and is also the point where the drag-load, PN is
at its maximum since it signifies the plane of force equilibrium, Gwee Boon Hong (2013)
figure 2.9 .The neutral plane, where the pile settles the same amount as surrounding soil, it
is also an important parameter in estimating the drag-load in a pile Liu, Gao et al. (2012)
.The neutral plane is located where the negative skin friction changes over to positive shaft
resistance (the point of equilibrium). Its location is determined by the requirement that the
sum of the applied dead load plus the drag-load is in equilibrium with the sum of the
positive shaft resistance and the toe resistance of the pile. Fellenius (1984) also reported
that the influence of upper load on neutral point position. The settlement of a pile due to
skin friction eventually leads to equilibrium where the upper soil layers exert a downward
force while the lower layers exert an upward force on the pile. The location of the
transition between negative shear and positive shear is referred to as the neutral plane. A
ratio of the depth of the neutral plane to the pile length in compressible strata, LNP/L, is
suggested to be taken approximately as 0.75 if no test data is available NAVFAC (1986).
This value is not conservative for an end-bearing pile, where the neutral plane is expected
to be close to the toe of the pile. NAVFAC (1986) also suggests calculating the depth of
neutral plane by trial and error procedure by comparing the settlement of soil to that of
pile. Endo et al. (1969) demonstrated clearly that for piles subjected to NSF, there exists a
point where the NSF transits into PSF and at this point, the soil and pile displacement
equalizes. In the case of Indraratna, Balasubramaniam et al. (1992) the final NP was found
to be at the bottom of the soft consolidating clay as beyond this depth, relatively stiff clay
was present. Shen (2008) suggested that although ZNP would generally shift upward upon
application of load at pile head, the extent of this shift is very much dependent on other
24
factors such as the end-bearing condition and should therefore be treated with caution in
design.
Figure 2. 9 Illustration, of NSF mechanism Gwee Boon Hong, (2013)
2.15 Physical Properties of Typical Sand Soil
Several manuals and studies have been published regarding the physical properties of
typical sands. Empirical correlations or values for the necessary material characteristics
were employed in the present study. The sand soil is modeled as elasto-plastic material
and the interacting concrete as perfectly elastic material. The young’s modulus and
poison’s ratio define a given perfectly elastic material. Whereas, if one uses the Mohr-
Coulomb plastic constitutive model, then cohesion and angle of internal friction will
define the plastic behavior of a given material like soil and rocks. In the present study, the
Mohr-coulomb constitutive model was employed. In the subsequent sections, each
parameter that defines elastic and plastic behavior of soils is reviewed.
Table2. 2 typical elastic moduli of sand soils after USACE table D-3
Soil ,
Loose sand
Dense sand
9,500-23,750
23,750-95,000
25
β.16 Poisson’s Ratio
Poisson's ratio, named after Siméon Poisson, is the negative ratio of transverse to axial
strain. When a material is compressed in one direction, it usually tends to expand in the
other two directions perpendicular to the direction of compression. This phenomenon is
called the poisons effect.
Table 2. 3 Typical Poisson’s ratio of soils after Bowles, 1996
soil Poisson’s ratio
Most clay soils 0.4 to 0.5
Saturated clay soils 0.45 to 0.5
Cohesion-less ,medium and dense 0.2 to 0.35
Cohesion-less ,loose to medium 0.3 to 0.4
2.17 Angle of Internal Friction
Angle of internal friction for a given soil is the angle on the graph (Mohr's Circle) of the
shear stress and normal effective stresses at which shear failure occurs or it is the
maximum angle of obliquity at which sliding of unstable soil mass over a stable soil mass
will occur. One of the empirical correlations of angle of internal frictions with SPT
numbers for sands has been given. The relation is summarized (table 2-4)
Table 2. 4 typical angle of internal friction for sand soils after Meyerhof, 1956
SPT penetration ,
N value (blows/foot) Density of sand ϕ (degrees)
<4
4-10
10-30
30-50
>50
Very loose
Lose
Medium
Dense
Very dense
<30
30-35
35-40
40-45
>45
26
Another correlation of SPT numbers with the angle of internal friction was given in the
table 2.5.
Table 2. 5 typical angle of internal friction for sand soils after Peck, 1974
SPT penetration ,
N value (blows/foot)
Density of sand
ϕ (degrees)
<4
4-10
10-30
30-50
>50
Very loose
Lose
Medium
Dense
Very dense
<30
30-35
35-40
40-45
>45
2.18 Unit Weight of the Soil
Unit weight of a soil mass is the ratio of the total weight of soil to the total volume of soil.
Empirical values for , of granular soils based on the standard penetration number are
given in table 2-6.
Table 2. 6 typical unit weight values of granular soils after Bowles, 1996
SPT penetration ,N value / /
0-4 70-100 11-16
4-10 90-115 14-18
10-30 110-130 17-20
30-50 110-140 17-22
>50 130-150 20-24
27
2.19 Computation of the Soil Settlement
The pile settlement can be calculated if the load carried by skin friction and the load
transferred to the base at the working load can be reliably estimated. The head settlement
is then given by the sum of elastic shortening of the shaft and compression of the soil
beneath the base as follows: = ��+ � �� � + . � . ( − )�� ………… (16)
Where S = settlement of the pile, Eb = deformation modulus of the soil, Qs and Qb loads
on the pile shaft and base respectively, L = shaft length, Ep = elastic modulus of pile
material, D = the pile diameter, = Poisson’s ratio, � = is influence factor related to the
ratio of L/R, if L/D > 5 � is taken as 0.5, M.J.Tmlinson (2004).
The settlement of the single pile is governed largely by the following dimensionless
parameters:
The length to diameter ratio
The pile stiffness factor K, the ratio of the young’ modulus of the equivalent solid
pile sections, Ep, to the young’ modulus of the soil, Es.
The Eb/Es, the ratio of the young’ modulus of the bearing stratum at the pile tip to
the young’s modulus of the soil. Settlement of a single pile floating in a
homogenous sand soil layer using the concepts of theory of elasticity was
computed from the equation provided by Poulos, 1989). = / ∗ �
Where P is the load applied at the top of the pile, L is the length of the pile (solid cross-
section), D is the diameter of the pile, Es is the modulus of elasticity of the soil at the tip of
the pile, Ep is the modulus of elasticity of the pile, Ip is the influence factor for settlement,
K is pile stiffness factor and is given by: = /
The influence factor for settlement is a function of stiffness factor and L/d ratio. The
diagram below is used to get the influence factor for settlement.
28
Figure 2. 10 Influence factor for settlement, after Poulos, (1989)
29
3. METHODOLOGY
3.1Finite Element Method
According to Poulos and Davis (1980) FEM offers the most powerful analytical approach
for pile design as both the non-linear behavior of soil and the complete history of pile can
be modeled. However, one should recognize that FEM is a complex tool which requires
the user to have a good understanding of the specific engineering problem to be solved.
On the other hand, the problem domain should also be kept as small as possible so as to
minimize computation time.
ABAQUS is one type of finite element method which is powerful engineering simulation
programs. It is the finite element method that can solve problems ranging from relatively
simple linear analyses to the most challenging nonlinear simulations. ABAQUS contains
an extensive library of elements that can model virtually any geometry. Designed as a
general-purpose simulation tool, it can be used to study more than just structural
(stress/displacement) problems. Problems with multiple components are modeled by
associating the geometry defining each component with the appropriate material models
and specifying component interactions. In a nonlinear analysis it automatically chooses
appropriate load increments and convergence tolerances and continually adjusts them
during the analysis to ensure that an accurate solution is obtained efficiently (ABAQUS
user manuals 6.13.).
3.3 Finite Element Modeling
For the investigation of the behavior of vertical piles under vertical loading conditions a
three-dimensional (3D) numerical model was used. The finite element software ABAQUS
2011 was applied. The finite element soil models used in this study were the linear elastic
(LE) and Mohr Coulomb (MC) model. The Mohr–Coulomb model was selected in this
research due to its wide use in practice and a limited number of input parameters. A non-
associated elastic-perfectly plastic model with Mohr–Coulomb failure criterion is used for
soils. It has five input parameters, i.e., elastic modulus (E) and Poisson’s ratio (v) for soil
elasticity, friction angle (φ) and cohesion (c) for soil plasticity and dilatancy angle (ψ). An
isotropic elastic model is used for modeling of pile and pile cap. The analysis was
calculated in analytical and numerical method. For this analysis: First, the self-weight of
30
the pile and soil is applied using the ‘‘gravity’’ option. Since the initial ground stress is
important in geotechnical engineering problems, the ‘‘geostatic’’ command is invoked to
make sure that equilibrium is satisfied within the layered soil and the pile. Second, a
uniform surcharge is applied on the pile cap in the form of pressure load and no drainage
is allowed in this step. As indicated above the excess pore water pressure assumed
completely dissipated and used drained (long term) condition. Solid reinforced concrete
piles and pile caps were used for this study by using isotropic elastic concrete model.
Circular section pile with linear elastic properties was used in this study. The piles were
embedded through consolidating clay soil and loose sand with the length of 19.5 m. The
pile cap was direct contact with the ground surface. One of the most important issues in
geotechnical numerical modeling is the simulation of the soil’s stress-strain-behavior.
3.4 Pile –Soil- Pile Interaction
Zhan, Wang et al. (2012) suggested the contact behaviors at the pile-soil surface include
load transfer mechanisms both in the normal and tangent direction. The normal force is
transferred only when pile and soil are contact tightly; otherwise, it becomes zero. This
kind of normal contact behavior can be modeled by “hard” contact option provided by
ABAQUS. The tangent behavior can range from rough contact with no relative sliding
between soil and pile due to frictionless sliding conditions with no friction develops along
the shaft of the pile. For contact between these two ideal cases, coulomb frictional model
built in ABAQUS can be selected to depict the interaction at the pile-soil interface
condition which has frictional coefficient . In this study the modeling is take in to
consideration penalty contact type which has frictional coefficient value of 0.385. In an
ABAQUS/Standard simulation possible contact is defined by assigning the surface names
to a contact interaction (contact pair approach) or by invoking an automatically-defined
all-inclusive element-based surface as the contact domain (general contact approach). The
soil (more flexible surface) is slave surface, pile and pile cap (the more rigid surface) is
the Master surface. The small-sliding formulation (available only for contact pairs) is
appropriate if the relative motion of the two surfaces is less than a small proportion of the
characteristic length of an element face.
31
Table 3. 1 Reynolds guideline chart of pile cap thickness with pile dia. Pile dia. (mm) 300 350 400 450 500 550 600 750
Thickness (mm) 700 800 900 1000 1100 1200 1400 1800
3.5 Material Model
Sheng L. (2018) suggested that soil is unacceptable to reach plastic stage under the design
load for the pile foundation. He also stated that getting the plastic range, the pile fails and
excessive deformation may happen. For this research, elastic model can be adopted for the
pile when dealing with design load. Considering past engineering practices, Mohr-
Coulomb Model has been chosen for this study. Parameters of pile and soil can be seen in
table 3.2
Table 3. 2 Material properties used in the analysis
Soil
, Ф(de
gree)
Cohesion
Poisons
ratio ,
Unit weight
ɣ /
Soft clay 5000 20 10 0.3 18 0.65
Loose sand 12000 30 0.01 0.3 18 0.6
Medium sand 50000 35 0 0.3 20 0.5
Concrete � --- 0.25 25 ---
3.6 3D Finite Element Modeling Technique of Piles and Pile Cap
A pile cap is an important structural element in pile foundation designed to transfer loads
from a column to a group of piles. In the present study the reinforcement square pile cap is
considered to be elasto-plastic with elastic modulus Ec. The diameter of the steel bar in
this study is selected ф mm .The center-to-center distances between the piles were kept
equal to 3D, 4D and 5D. Iskander, Hanna et al. (2001) stated that the pile cap should
extend for distance of 100 to 150 mm outside the outer face of the pile in the group. The
clear overhang of the pile cap beyond the external face of pile was assumed as 3/8-times
the side dimension of the pile .The pile cap should overhang the outer piles by at least 150
32
mm but should not be excessive, generally not more than the pile diameter. Elastic
concrete material was used to simulate the pile and pile cap materials. Table 2-8 shows
material properties of the piles and pile cap. Weight of the pile cap was ignored as it is
small to the ranges of loads that the pile group was subjected. The boundary conditions of
x, y, and z plane was as follows: The boundary condition of the bottom plane was fixed
(ECASTRE U1= U2 =U3 = UR1 = UR2 = UR3 = 0). The displacement /rotation in the y
direction become zero, the displacement of x direction become free to move. Similarly
when the displacement /rotation of x become zero, the displacement of y was free. In
general this model was free from strain –stress boundary influence. The shape and plan
dimensions of the pile cap depend on the number of piles in the group and the spacing
between each pile. Concrete strength grade of pile cap and pile is C-25. The concrete
cover for reinforced pile cap was 300 mm, the parametric values for the elastic behavior of
the soil is shown in the table 2-8.The material of pile was simulated by using elastic
constitute model with young’s modulus E equal to 30 � and poison’s ratio 0.β5. For
bearing sand soil young’s modulus is 50 MPa and poison’s ratio 0.γ. Its internal frictional
angle ϕ is 350 and dilatancy angle is taken as 0.1. A small cohesion 1 and 3 were set
for bearing and loose sand respectively to avoid divergence in analysis. For soft clay soil
in drained condition, the value of the elastic modulus and poison’s is 5 MPa and 0.3
respectively. For dense sand, dilation parameter was used with a value of 100. The model
has three different layered soils which are soft clay, loose sand and bearing sand which
have 15.25 m, 15.25, and 5.5 m respectively.
33
Table 3. 3 Types of model which were performed in this research
Pile spacing Pile length (m) Load (kN) Model type
3D
20 4,350 1
15 4,350 2
10 4,350 3
4D
20 7,733 1
15 7,733 2
10 7,733 3
5D
20 12,083 1
15 12,083 2
10 12,083 3
3.7 Basic Assumptions Used in 3D Numerical Modeling
a) The piling has its own effect to the stress –strain behavior of the soil stratum but
for this analysis the effect was ignored.
b) The piles are installed through soft clay and loose sand with the pile tip located at
the interface between loose sand and bearing sand layer.
c) The consolidation analysis requires more calculation time and memory space, only
drained analyses have been conducted
d) All analyses were carried out with a groundwater table equal to the ground surface.
e) The excess pore water pressure assumed completely dissipated and used drained
(long term) condition
f) An isotropic elastic model is used for modeling of pile and pile cap
g) Uniform surcharge loading is applied on the pile cap in the form of pressure load
and no drainage is allowed in this step
h) Solid reinforced concrete piles and pile caps were used for this study by using
isotropic elastic concrete model
i) The piles were embedded through consolidating clay and loose sand soil with the
length of 19.5m
j) The pile cap was direct contact with the ground surface.
k) An elasto-plastic material law with Mohr-Coulomb failure criterion was used to
describe the behavior of clay and sand soil.
34
l) The pile diameters of the pile for this study were 800, 600 and 300mm.
m) The pile length which is used for this research were 20 m,15 m and 10 m
n) The dimension of the soil layer which is used for this research 86 m x 86 m x 36 m
3.8 Theoretical Estimation of Vertical Load Capacity of Piles
The design philosophy for resisting vertical load is accomplished by calculating the
ultimate pile capacity Qu to determine the load to cause bearing failure, then using factor
of safety (FS) to estimate the allowable pile capacity that can limit the settlement to
permissible level, U.S Army Corps of Engineers, (2004). It is necessary to divide the
calculated ultimate resistance of the pile (or the ultimate resistance derived from load
testing) by a safety factor to obtain the design working load on the pile, M. J. Tomlinson,
(2004). As indicated above from literature review, method is selected for this paper.
3.8.1 Friction capacity: Method
This method considers the pile embedded in thick homogenous soil which is fully
saturated.
stress is taken as the lateral effective stress at the mid-point of the pile. The friction stress
fs between the pile and the surrounding soil can be calculated by multiplying the friction
factor µ, between the pile and the soil with the value h’. Thus = µ�ℎ′ �ℎ′ =� ′ where σv’ is the vertical effective stress at the pile mid-point and ko is the lateral
earth pressure coefficient at rest so the friction stress is equal to: = µ � ′………… (4.1)
The skin friction force between the pile surface and soil is calculated as follows
= = µ � ′ × � × ℎ ……….. (4.β) = µ ……… (19)
= − � �′ . …………. (4.γ)
OCR is over consolidation ratio, for normally consolidating clay soil OCR is 1 Eq. 4.3 = tan / ∗ = .
From the given Eq. (19) the value of isμ = . ∗ . = . .
The value of which was calculated above is almost similar to the value that suggested by
Liu, Gao et al. (2012) which was 0.2. For sands, McClelland (1974) suggested values of
ranging from 0.15 to 0.35. Meyerhof (1976) suggested values of = 0.44, 0.75, and 1.β
35
for ϕ'= β8◦, γ5◦, and γ7◦, respectively. The calculated value 0.182 is in the range of
McClelland (1974). The additional literature which was provided the different value is:
Vesic (1977) assumed that the drag-load is proportional to the effective vertical stress and
proposed that the value to be adopted for compressible strata of clay and silt to be in the
range of 0.15 to 0.30. The value varies depending on the type of soil: from 0.2 to 0.25
for clay, from 0.25 to 0.35 for silt, and from 0.35 to 0.50 for sand. Canadian foundation
engineering design manual (2006), suggests the application of value in the range of 0.2–
0.3. The calculated value is almost similar with literatures which provided above. So the
selected value of is equal to 0.2.
The friction capacity of the piles at the middle point is calculated as follows Eq. 4.1 = ′ ′ = −� � = ′� = − . ��/ ∗ . = = ∗ . = .
The skin friction force between the pile surface and soil is calculated as follows eq.4.2 = . ∗ ∗ ∗ . = . ∗ ∗ . ∗ . = .
End bearing capacity calculation by using method
Using Terzaghi, Peck et al. (1996) bearing capacity equation, the bearing capacity at the
base of the pile can be calculated Eq. (9). The end bearing capacity is calculated as
follows:
= = [ ′ + ′ ] ……… (4.4)
Jambu (1976) presented equation to estimate and for various soils Eq. (2.10).
Where; is an angle defining the shape of the shear surface around the pile tip. The value
is ranges from /3 for soft clays to 0.58 for dense sands .The base of the pile tip was at
the dense sand so the value is equal to 0.58.
= . = . = ( + √ + tan ) exp ∗ . = . …….. (4.5)
36
= − = . − = . …………….. (4.6) For this thesis the value of is 0.1 kPa
The pile is symmetrical throughout the given model; the area of the base is similar to the
area of the pile head which was . = = ∗ . = . ………….. (4.7)
The vertical effective stress at the base of the pile
′ = ℎ = − . / ∗ . = . = . ∗ . + . ∗ . ∗ . = .
To calculate the ultimate capacity of the pile, the self-weight of the pile should be
subtracted from the summation of shaft resistance and the end-bearing resistance; = + − � ……….. (4.8) � = ′ ……….. (4.9)
Where W is the weight of pile, is the cross-sectional area of pile base, ’ = vertical
effective stress eq.4.9: � = ∗ / − . / ∗ . = = . + . − = .
The pile spacing and the number of piles were 3D, 4D, 5D and 5x5, 4x4, 3x3,
respectively. The factor of safety was 2. Then calculate the working load by dividing the
ultimate pile capacity ( ) by factor of safety.
Working load for single pile is eq.4.8
The allowable pile group capacity is: = ��� = . �� = . …………… (4.10)
For 9 piles groups (3 x 3) = . ∗ = . kN
For 16 piles groups (4 x 4)
37
= . ∗ = .
For 25 pile groups (5 x 5) = . ∗ = , .
The maximum allowable load which was used for this study in a given software package
was 4348.8 kN (3 x 3) pile group, 7732.8 kN (4 x 4) pile group and 12,082.5 kN (5 x 5)
pile group.
3.9 Estimation of Pile Group Efficiency
Piles are generally used in groups. The arrangements, such as rectangular and circular, are
possible. The pile spacing, s, between two piles center to center should be greater than 2D,
where D is the pile diameter. A concrete cap is generally used to connect the heads of the
piles in a pile group. Loads are applied to the cap that transfers them to the piles.
Feld (1943) proposed a rule of thumb to determine the efficiency of a pile group. In his
method, the capacity of a pile group is defined as the summation of the capacities of the
individual piles in the group multiplied by a factor ranging between 0.72 and 0.94
according to the number of piles.
The converse –Laborre Bolin (1941) formula is one of the most widely used formulas for
evaluating pile group behavior. According to this formula the efficiency of the pile group
is equal to = − − + −
Where = Efficiency of the pile group, m = Number of rows, n = Number of columns
α = tan -1(d/s), s = center to center spacing.
As shown in the figure bellow the configuration of the piles were 3x3 and the total
numbers of piles in the group were nine. Two basic scenarios were taken into
consideration about pile center to center spacing; the pile spacing was 3D and 2.5D.
For a given spacing of 3D, 4D and 5D and a pile diameter of 0.6 m, the spacing is 1.8, 2.4
and 3 m respectively. = tan− .. = . eq. (2.3)
38
As shown in the pile location the number or rows and the number of columns are equal: = = By substituting the value, the total efficiency of the group is as:
= − . − + −∗ = . %
For 4D pile spacing by using Laborre -Bolin formula the pile group efficiency is
calculated as:
= − − + −
= tan− .. = .
= − . − + −∗ = . %
In similar formulae and calculation for 3D pile spacing the pile group efficiency was 80
%. Efficiency also increases. 5D, 4D and 3D pile spacing have a group efficiency of
72.7%, 76.6 % and 80% respectively. For this pile spacing the value of spacing to
diameter ratio (s/d) was greater than 2. This value indicate that when the number of pile
and spacing increase, the pile group efficiency also increase. For these three different piles
spacing the efficiency was less than unity. Generally, higher efficiencies occur with an
increase in the number of piles in the group.
Several efficiency formulas have been proposed to relate the behavior of a pile group to
that of the individual piles in the group. These formulas are mostly based on relating the
group efficiency to the spacing between the piles and always yield -g values of less than
unity, regardless of the pile/ soil conditions and it also depends on spacing to diameter
ratio(s/d) where “s” is the pile spacing and “d” is the pile diameter. A major apparent
shortcoming in most of the available efficiency formulas is that they do not account for the
characteristics of the soil in contact with the pile group. The most acceptable formulas for
pile groups in clay are briefly summarized in literature review.
Feld proposed a rule of thumb to determine the efficiency of a pile group. In his method,
the capacity of a pile group is defined as the summation of the capacities of the individual
39
piles in the group multiplied by a factor ranging between 0.72 and 0.94 according to the
number of piles.
The pile group efficiency is calculated by using Poulos and Davis (1980) method: The pile
group efficiency is defined:
� = + ( ∗ ∗� )� ………….. (4.11)
Where is the ultimate load capacities of the block of piles (equivalent large pile), is
a single pile capacity, m is number of rows, n is number of columns.
= . = eq. (4.10)
= + ∗ ∗ . = + ( .. ) = . The pile group efficiency for the given pile is 99.8 %
For 4 x 4 pile groups efficiency is calculated as follows by using eq. (4.13)
= + ∗ ∗ .. = + ( .. ) = . The pile group efficiency for the given pile is 99.7 %
For 5 x 5 pile group the pile group efficiency is calculated as follows:
= + ∗ ∗ .. = + ( .. ) = .
The pile group efficiency for the given pile is 99.3%
The group efficiency value which is calculated by using Poulos and Davis formulae is
greater than the value which is calculated by using Laborre –Bolin formulae. I conclude
that the efficiency of the pile group which is calculated by using Poulos and Davis
formulae is better than Laborre –Bolin formulae. Poulos consider the block capacity of the
pile and single pile capacity beyond to Laborr-Bolin.
40
3.10 Analytical Estimation of Drag-Loads
The method will be suggested for design, since it is based on the effective stress theory
and coincides more with engineering circumstances. Fellenius (2006) summarized the
drag load of several history cases and gave the average value along the whole pile length
for each case. In present study, the values are calculated at the middle of effective stress
or unit weight and compare the results from the other literature and field measurement
values. The constant value can be applied from the ground surface to the neutral plane to
calculate the drag-load, though the decrease of value is noticed in the areas close to the
neutral plane Liu, Gao et al. (2012) . Based on his study, a simple design procedure is
proposed for estimating the drag-load in a single pile as follows:
a) Select an appropriate value based on soil and pile conditionsμ 0.β suggested for
an uncoated pile and 0.09 for a bitumen-coated pile.
b) Identify the neutral plane based on the soil modulus ratio between the bearing layer
and the consolidating layer. A conservative value of 0.8 can be selected if no soil
modulus available.
c) Calculate the drag-load at the neutral plane level = ∫ ∗ ∗ ′ ���� where
C is the perimeter of the pile, ’ is the average vertical effective stress in the soil
along the pile to the neutral plane.
d) Modify the drag-load by multiplying a factor due to surcharge.
e) Modify the drag-load by multiplying a factor due to relative pile/soil stiffness. = . , = ∗ . = ∗ . =
Where LNp is the Neutral plane, this value is not conservative its value may change
according to the value of soil stiffness.
3.11 Model Discretization Numerical analyses have been conducted examining pile groups in 3D conditions. A
relatively fine mesh is used near the pile–soil interface, and it becomes coarser further
from the pile Lee, Bolton et al. (2002). Wriggers and Nackenhorst (2006) stated that the
surface to surface scheme was used for discretization of the continuum for contact in the
model such that the pile, pile cap and soil surface were considered the master and slave
surface respectively. The contact constraint was fulfilled by using the penalty approach.
41
To avoid excess penetrations of the slave node into the master surface, the slave surface
should be densely meshed. The value of the friction coefficient for a penalty parameter
was 0.385 which was chosen for pile-soil interaction from a depth of 0-19.5 m.
Geotechnical and other discipline software ABAQUS is used to create a model of pile
group with pile cap. In the 3D analyses 3 x 3, 4 x 4 and 5 x 5 pile groups have been
considered with a typical minimum and maximum pile spacing, S, of 3D, 4D and 5D
(where D is the pile diameter). An elastic model is used for the pile and a non-associated
Mohr– Coulomb model for the clay and sand. The finite element meshing of 3×3 pile
group with cap is shown in figure 3.1. The model was developed using solid elements,
entitled C3D20R in ABAQUS/CAE, meaning brick elements with quadratic
approximation with 20 nodes and reduced integration. A preliminary mesh for both the
full and symmetric model was generated. Soil and pile are modeled by node brick
elements.
Figure 3. 1 3D mesh generations and calculation model with given pressure
3.12 Pile Configuration
As indicated above from the given methodology, the model had different pile spacing
with fixed dimension of pile cap. Proper arrangement of pile with in the given spacing was
take in to consideration. The number of piles was changing according to pile spacing. As
shown in the figure 3.2 for 5D pile spacing the center, side and corner pile configuration
was written according to the given pile number and spacing . Also as shown in the figure
3.3 the 3D pile spacing the center, side and corner pile was written in the form of plane
dimension with the numbers piles as the given configuration.
42
(a) 3 x 3 and 600 mm dia. Model (b) 3 x 3 and 800 mm dia
Figure 3. 2 Pile group layout and cross sectional view
Model Parametric study also states pile group having different number of piles. The
number of piles located in c-ø soil is conducted by varying parameters like pile length (l)
and spacing (s) of piles and thickness (t) of pile cap. Cross sectional view and plan of pile
group are shown in Figures 3.3 a,b, respectively. Material properties are listed in table 2.8.
(a) 4 x 4 plan geometry (b) 5 x 5 plan geometry
Figure 3. 3 Pile group configuration with different pile spacing
43
3.13 Pile Cap Sensitivity Analysis
A pile cap is a thick concrete mat that rests on concrete or timber piles that has been
driven in to soft or unstable ground to provide a suitable foundation. El-Garhy et al. Nath
and Hazarika (2013) , a pile cap is mostly reinforced concrete slab or block to resist the
given load which comes from super structure and interconnects a group of piles. It should
normally be rigid so as to distribute the forces equally on the pile group .But in reality no
completely rigid and completely flexible pile cap. To determine the cap rigidity and
capacity of load transfer which comes from supper structure has taken in to consideration
the pile group settlement and cap settlement itself. The piles settle equal amount when the
cap become relatively rigid. To chick up its rigidity and load transfer capacity has taken
three different types of model which dimension were 8 m x 8 m x 0.8 m, 8 m x 8 m x 1 m
and 8 m x 8 m x 1.5 m. The Settlement of the pile cap was varying according to its given
dimension. As shown in the figure 3.4 the cap settlements vary with respect to the cap
thickness. For 8 m x 8 m x 0.8 m, the maximum settlements were at the center of the pile
cap. For 8 m x 8m x 1 m the cap settlement distribution was show less variation with
respect to 0.8 m cap thickness but high variation from the pile cap of 1.5 m.
Figure 3. 4 Pile cap settlement with different thickness
0 1 2 3 4 5 6 7 8-80
-78
-76
-74
-72
-70
-68
-66
-64
-62
-60
Pile Cap Length (m)
Pile
Ca
p s
ett
lem
en
t (m
m)
t = 1.5 m
t = 1 m
t = 0.8 m
settlement at the center of cap
44
Table 3. 4 pile settlement with different pile cap thickness
For t = 0.8 m For t = 1m For t = 1.5 m
Corner Side Center Corner Side Center Corner Side Center
-8.8 -9.3 -9.8 -9.0 -9.0 -9.1 -7.5 -7.6 -7.7
-8.7 -9.1 -9.7 -8.9 -8.9 -9.1 -7.5 -7.5 -7.6
-8.6 -9.1 -9.7 -8.8 -8.9 -9.0 -7.4 -7.4 -7.6
-8.5 -9 -9.6 -8.7 -8.8 -9.0 -7.3 -7.4 -7.6
-8.5 -8.9 -9.5 -8.7 -8.8 -9.0 -7.2 -7.3 -7.5
-8.4 -8.9 -9.5 -8.6 -8.7 -8.9 -7.2 -7.3 -7.5
-8.4 -8.8 -9.4 -8.6 -8.7 -8.9 -7.2 -7.2 -7.4
-8.4 -8.8 -9.4 -8.6 -8.6 -8.8 -7.1 -7.2 -7.4
-8.3 -8.8 -9.3 -8.5 -8.6 -8.8 -7.1 -7.2 -7.3
-8.3 -8.8 -9.3 -8.5 -8.6 -8.8 -7.0 -7.1 -7.3
-8.3 -8.8 -9.4 -8.4 -8.6 -8.8 -7.0 -7.1 -7.3
As stated from figure 3.4 the cap settlement distribution of 1.5 m thickness was slightly
uniform throughout the pile cap thickness and has minimum deferential settlement from
one edge to the other edge of pile cap. Generally when the thickness was 1.5 m, the
settlement of the cap curve changed to straight line compare to the other thickness. The
pile cap selection was done by considering constant pile cap settlement distribution
throughout pile cap length. This value stated that proper load transfer mechanism from
pile cap to the pile. The minimum settlement to thickness ration of the cap was stated .The
settlement ratio are 4.3 % , 6.6 %, and 8.1 % for 1.5 m ,1 m and 0.8 m respectively. The
minimum settlement ratio was occurred from the cap dimension of 8 m x 8 m x 1.5 m so
this pile cap dimension was taken for this model. Figure 3.5 states that the pile settlement
throughout the pile cap length was almost similar when the pile thickness is equal to 1.5
m.
45
Figure 3. 5 The Pile Settlement with Different Thickness
3.14 Numerical Model Verification
In order to verify the feasibility of 3D FEM model for NSF problems, FEM model which
is developed from known case Indraratna, Balasubramaniam et al. (1992) and the model
results are compared with the field measurements. Group pile model was calculated with
assuming the elastic modulus of pile Ep was 30 GPa and Poisson’s ratio υ was 0.β5, other
parameters were chose the same to table 2.8. Through the comparison between the
numerical model of this paper and the numerical model built on literature to prove that the
study on the NSF of pile foundation is correctness through this paper’s numerical model.
Figure 4.6 showed that when surface load (S.L.) equal to 25 kPa, the skin friction
distributions along pile depth were in good agreement between the results obtained by this
paper and the results obtained by literature Hanna and Sharif (2006) and after Indraratna,
Balasubramaniam et al. (1992) Furthermore, it can be noted that the predicted normalized
neutral plane depth (LNP/L) is 0.75, whereas the average numerical result of this paper
0.74 (see table 4.3). It should be mentioned here that this agreement is testimony to the
validity of the numerical model under all possible loading conditions since skin friction
incorporate the settlements, effective stresses, and the axial loads acting on the pile. As
shown in the figure 3.6, the validity of present study from two known scholar in-situ test
model shows good agreement.
0 5 10 15 20-10
-9.5
-9
-8.5
-8
-7.5
-7
-6.5
Pile Depth (m)
Pile
Set
tlem
ent (
mm
)
t = 1 m ( Corner Pile)
t = 0.8 m (Side Pile)
t = 0.8 m ( Center Pile)
t = 1 m (Side Pile )
t = 1 m (Center Pile)
t = 0.8 m ( corner PIle)
t = 1.5 m (Corner Pile )
t = 1.5 m (Side Pile)
t = 1.5 ( Center Pile)
46
Figure 3. 6. Model verification
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-40 -30 -20 -10 0 10 20 30 40 50
Z/L
Skin Friction (kPa)
Adel M.Hanna et.al 2006
Present Model
Indraratna et.al1992
47
4. CHAPTER FOUR
4.1 Parametric Analysis
4.2 General
Parametric study is mainly carried out to investigate the variation of solutions to the
problem at hand on the variation of different input parameters. The sensitivity of the
solutions was studied. Parameters such as diameter of piles, spacing of piles, pile length
and length to diameter ratios were altered and the solutions were investigated. The
solutions were mainly ultimate bearing capacities, skin and tip resistances at the ultimate
load and pile group settlements .A grid configuration of square pile group 3x 3, 4 x 4 and
5 x 5 were considered throughout this chapter. Hence, the number of piles is 9, 16 and 25
with respect to its configuration.
4.3 The Distribution of Load in a Pile and its Neutral Plane
There must always be equilibrium between the sum of the dead load applied to the pile
head and the drag-load, and the sum of the positive shaft resistance and the toe resistance.
The depth where the shear stress along the pile changes over from negative skin friction
into positive shaft resistance is called the neutral plane Fellenius and Siegel (2008) . He
also suggested that this plane is where there is no relative displacement between the pile
and the soil. The location along the pile at which the sustained forces (i.e., drag load plus
sustained) structure load are in equilibrium with the combination of (positive direction
shaft resistance) below the neutral plane and toe resistance. This is the location where the
maximum compressive load occurs in the pile. It is also the location at which there is zero
relative movement between the pile and soil.
Fig.4.1 illustrates the distribution of load in a pile subjected to a service load, Qd, and
where the shear stress along the pile induced by a relative displacement is a function of the
effective overburden stress. For reasons of simplicity, the shear stress along the pile is
assumed to be independent of the direction of the displacement, i.e., the negative skin
friction, qn, is equal to the unit positive shaft resistance, rs. Assume, also, that a toe
resistance, Rt, is available. The drag-load Qn is the sum of the negative skin friction along
the pile, and the total shaft resistance Rs, is the sum of the unit shaft resistance. These
conditions are used to determine the location of the neutral plane.
48
Figure 4. 1 Positive and Negative Shaft Resistance
4.4 Self-Weight Stress Field
The weight of pile and soil was calculated by using the same value of density 2 x 103
kg/m3 for bearing sand soil ,1.8 x103 kg/m3 for loose sand, and 1.8 x 103 kg/m3 for soft
clay soil in order to obtain a balance state of self-weight stress easily. The self-weight
stress field can be established through two methods. One is using the “geostatic” option provided by ABAQUS, which need to specify the coefficient of lateral earth pressure ko.
In the study, ko was set as (v/1-v), and is Poisson’s ratio of soil. The lateral earth
pressure coefficient ko is equal to 0.538 for loose sand and 0.428 for bearing sand soils
separately. The other is to change the soil into elastic material and set the material of pile
as soil. Then the weight of pile and soil were obtained through elastic analysis and the
stresses in centroid of each element were output. The initial self-weight stress field for the
next analysis step of bearing capacity of pile was established by inputting the centroid
stresses. The self-weight stress field for pile cap and pile is calculated by using ABAQUS
software package (fig. 4.2).
Figure 4. 2 Self-weight stress fields for elastic analysis method
NP
49
4.5 Normal Pressure and Friction Interface
The modeling of normal pressure in pile-soil contact surface is important for this kind of
problem because the shear resistance interface is dependent on it. It can be seen that there
is only a little bit difference between them, which perhaps was arisen by the adjusting of
contact of pile and soil. One can deduce that the shear resistance in the interface will be
fully mobilized, and this is confirmed by the friction and normal pressure along the shaft
of pile (see fig.4.3).
Figure 4. 3 Normal pressure
4.6 Effect of Variable Load on the Pile Group
4.6.1 Pile and Soil Settlement in Different Pressure Loads
Saha (2015) suggested that down-drag is the downward movement on a deep foundation
unit due to negative skin friction and expressed in term of settlement. When soil moves
downward relative to the pile, it creates a drag force on and within the pile. The downward
soil movement creates the potential for downward pile movement. This downward pile
movement is referred to as down-drag. As shown in the table 4.2, the pile settlement was
almost similar for one given load. According to the given load, the pile settlement was
different from one surcharge load to the other. As shown in table. 4-1 the maximum pile
head settlement was developed at the center pile which is 4.9 mm after pile load 50 kPa
was applied. When the surrounding load was applied and increased to 75 kPa, the pile
50
head settlement increases and reaches 8.9 mm. When the pressure load increased to 100 to
200 kPa, the pile head settlement increased to 13.1 mm to 34.4 mm respectively (see table
4.1). The axial force of pile indicates that the neutral plane varies from 0.6L to 0.8L (table
4.1) and drag-load varies from 265 kN to 1170 kN (fig. 4.4). Due to the great stiffness of
pile-end soil in this model, the maximum neutral plane is reached 80% of pile length for
200 kPa surcharge load. This result indicated that the maximum negative skin (shaft)
resistance developed due to maximum surcharge load and excessive soil settlement. The
increment of soil settlement is larger than that of pile when the surrounding loads
increases, which cause neutral plane moves down to the pile tip.
Table 4. 1 Pile and soil settlement with neutral plane for constant pile length (20m)
Pressure
Load
Pile head Settlement
(mm)
Max. Soil surface
Settlement (mm)
Neutral plane to
Length Ratio / Corner Side Center
50 4.8 4.9 4.9 50.2 0.6
75 8.7 8.8 8.9 75.8 0.6
100 13 13 13.1 140.2 0.56
200 34 34 34.4 1308 0.8
4.6.2 Drag -Load Distribution for Different Pressure Loads
For relatively small surcharge load of 50 kPa , the drag-load attained the value of 265 kN
(8.2 % of the ultimate capacity of the pile). The drag-load becomes maximum value of
1170 kN (9.14 % of ultimate capacity of the Pile) when a surcharge load of 200 kPa .This
indicates that a non-linear relation between the surface loads and resulting drag load. The
decreasing trend after the maximum value of the drag load is due to the change of the
shear-stress direction (the neutral line or plane) in the pile skin. Negative skin friction
developed along the pile shaft till the drag load completely overcome (see figure 4.4).
When the axial pressure load was 50 kPa and 75 kPa, the drag-load around the pile tip was
negative. This implies that the axial load was relatively small and the drag force
dominated the allowable load of the pile.
51
Figure 4. 4 Drag load along the pile group with normalized depth
4.6.3 Neutral Plane Determination Due to Load Variation
Fellenius and Siegel (2008) stated that the movement at the pile toe must be equal to or
exceed the movement required to mobilize the ultimate toe resistance of the pile. Beneath
to the neutral plane, there would be the usual positive skin friction as the pile settles more
than the adjacent soil below this elevation C.F. Leung (2009). In most soils, this required
movement is about 1 % to 2 % of the pile toe diameter of driven piles and about 5 % to 10
% of the toe diameter for bored piles. Fig 4-5 stated that the pressure load which is applied
to the piles were 50 kPa, 75 kPa, and 100 kPa. The corresponding maximum pile head
settlement was 4.9, 8.9 and 13.1 mm respectively. This pile settlement increment is the
result of axial load increment and down-drag. When the axial load is increase, the pile
settlement also increases in the case of down drag from the surrounding soil. The down
drag increment is the cause of the neutral plane variation but the neutral plane variation is
insignificant for these two axial loads. When the load was 50 kPa, the neutral plane was
12 m. This value stated that the point of equilibrium developed at 60% of the pile length.
This value also shows that the negative shaft resistance covers 60 % from total pile length.
When the axial load was 75 kPa, the neutral plane was also 12 m. Bellow the neutral plane
the pile settlement is greater than the soil settlement which was the result of the soil
settlement at neutral plane plus the elastic shortening of the pile (fig 4.5a). Generally the
load increment was the cause of the change of the negative and positive shaft resistance of
the pile due to load transfer mechanism from soil to pile and pile to soil. Therefore, the
0
0.2
0.4
0.6
0.8
1
-400 -200 0 200 400 600 800 1000 1200
Z/L
Drag-Load (kN)
S.L = 75 kPa
S. L = 100 kPa
S.L = 50 kPa
S. L = 200 kPa
52
soil settlement transfers load to the pile. Below the neutral plane, the settlement of the soil
is less than the settlement of the pile and load is transferred from the pile to the soil.
Accordingly, pile settlement equals soil settlement at the neutral plane. Therefore, pile
settlement is controlled by the soil compressibility below the neutral plane and the
magnitude of the load application. At an elevation where the pile and soil settlements are
the same, there would be no load transfer at this elevation.
(a) (b)
Figure 4. 5 Location of Neutral Plane for different axial load
As previously stated, the neutral plane is the depth at which the sum of the un-factored
permanent load plus the negative shaft resistance is equal to the positive shaft resistance
plus the toe resistance. The neutral plane is not only the result of the relative movement of
single pile in the group but also the result of corner, side and center pile. Pile cap
sensitivity analysis is used for this purpose. When the axial load was 200 kPa, the
settlement of corner, side and center pile was 34, 34 and 34.4 mm respectively (see
fig.4.6). Similarly when the axial load was 200 kPa the neutral plane was 16 m. This value
also shows that negative shaft resistance covers 80% of the pile length. The settlement of
corner, side and center pile are almost similar in the given pressure load. This similar pile
group settlement shows the pile cap rigidity as stated at pile cap sensitivity analysis. At
lower portion of neutral plane, load transfer from pile to soil and above the neutral plane is
vice versa. The settlement of the pile is equal to the settlement of the soil at the elevation
of the neutral plane plus the elastic compression of the pile due to the dead load and the
drag-load in combination.
0
0.2
0.4
0.6
0.8
1
-60-50-40-30-20-1001020
Z/L
Settlement (mm)
Neutral PLane
Pile Toe Penetration
Pile Settlement= soil settlement at neutral plane + Elastic pile shortening
Soil Settlement
Pile Head Settlement
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-160-140-120-100-80-60-40-20020
Z/L
Settlement (mm)
Soil settlement (50 kPa)
Pile Settlement (50 kPa)
Soil Settlement (75 kPa)
Pile Settlement (75 kPa)
Soil Settlement (100 kPa)
Pile Settlement (100 kPa)
NP
53
Figure 4. 6 Neutral plane location for 200 kPa
4.6.4 Negative Skin Friction Determination
Fig. 4.7 (a, b) presents that when the upper loads P are different, the distribution
patterns of NSF of piles in the pile group are different. The maximum negative skin
friction was developed in the center pile. As shown from this figure the minimum
negative skin friction also develops in the center pile. The pressure load of 50 kPa
results the minimum positive shaft resistance at the ratio of Z/L from 0.2 to 0.9. Fig
4.7 (b) presents the pressure load of 75 kPa results minimum positive shaft
resistance at the ratio of Z/L from 0.4 to 0.8. When the ratio of Z/L was equal to 0.9
and extends to pile tip, the positive shaft resistance of center pile was larger than
side and corner pile. But the value of negative and positive skin friction in the
center, side and corner piles was depending on the value of Z/L ration. The first
maximum value of negative skin friction was developed in the center pile .The
second maximum negative skin friction developed in the side pile and the least
value was developed in the side pile. The maximum axial load made visible
difference between side, corner and center of NSF.
0
0.2
0.4
0.6
0.8
1
-1000-5000500
Z/L
Settlement (mm)
Pile Settlment
Soil Settlement
Neutral Plane
54
(a) (b)
Figure 4. 7 Skin Friction Distribution with Different Axial Load
When the upper load is small, the value of positive skin friction on lower part of each pile
is small (fig. 4.8). With the increase of upper load; the value of positive skin friction
improves. Fig. 4.8 a, b also shows that the upper load is small, the NSF on upper part of
each pile generally coincides each other. With the increase of upper load, the coincidence
disappears, and NSF of the upper part of each pile was different.
(a) (b)
Figure 4. 8 Skin friction distribution for different pressure loads
In general the negative skin/shaft resistance covers 3/5 of the total pile length when the
axial load of 50, 75 and 100 kPa. This shows that the equilibrium point found at Z/L was
equal to 0.6. When the axial load was 200 kPa the amount of negative shaft resistance
covered 80 % of the total length of the pile. As stated above from literature review, the
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-100 -50 0 50 100 150
Z/L
Skin Friction (kPa)
Corner Pile
Side Pile
Center Pile
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-100 -50 0 50 100 150 200 250
Z/L
Skin Friction (kPa)
Corner Pile
Side Pile
Center Pile
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-300 -200 -100 0 100 200 300
Z/L
Skin Friction(kPa)
Corner Pile
Side Pile
Center Pile
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-600 -400 -200 0 200 400 600 800 1000 1200
Z/L
Negative Skin Friction (kPa)
Corner Pile
Side Pile
Center Pile
100 kPa
200 kPa
P = 50 kPa P = 75 kPa
55
neutral plane is equal to 0.75 L where L is the total pile length. So the load of 200 kPa was
greater than the given limit as compared to given literature with respect to numerical value
of maximum amount of drag-load and excessive downward soil movement.
4.8 Effect of Pile Cap on The Pile Group
4.8.1 Neutral Plane Determination
Figure 4.9 presents the same pressure load of 75 kPa and the neutral plane was different
with this load. For the capped model the amount of neutral plane was approximately 11 m
and for uncapped model the value of neutral plane moves downward which was equal to
13.2 m. As shown in the figure 4.9 (a, b) The pile settlements of corner ,side and center
pile were almost similar for capped model but for uncapped model the settlement of
corner ,side and center pile had little different among them . Generally the pile settlement
has no significant difference which the model with pile caps. The pile cap is used to
balance the load which comes from the supper structure and used to form similar pile
settlement. As shown in the figure 4.9 (a, b) for similar pressure load which was 75 kPa,
the soil surface settlements was different. When the load was 75 kPa and the model has no
pile cap, the amount of surface settlement was 185 mm. In the same load, the model with
pile cap, the amount of soil surface settlement was 123.7 mm. The pile cap has significant
effect in pile and soil settlement. The pile group with pile cap can partly constrain the
displacement of piles at different positions, though the effect of constraint is smaller than
that of pile group with if the model has no pile cap.
(a) (b)
Figure 4. 9 Location of neutral Plane (S.L = 75 kPa)
0
0.2
0.4
0.6
0.8
1
-140-120-100-80-60-40-2002040
Settlement (mm)
Z/L
Side Pile
Center Pile
Corner Pile
Soil Settlement
NSF
NP
PSR
0
0.2
0.4
0.6
0.8
1
-200-150-100-500
Setllement (mm)
Z/L
Pile Settlement
Soil Setllemetnt
NP
Uncapped Model Capped Model
56
4.8.2 Negative Skin Friction Determination
The negative skin friction distribution along the pile length with and without pile cap for
the load applied of 50 kPa was stated at the figure 4-10a. For the model without pile cap,
negative skin friction was developed from pile head at which Z/L is equal to 0.6 of the
total pile depth. As shown from figure 4.10a, the negative skin friction distribution from
the model without pile cap, there was big difference among corner, side and center pile
above the neutral plane. For the formation of this difference among side, corner and center
pile negative skin friction was the absence of pile cap. The maximum negative skin
friction was developed at the side pile. From this figure, the model with pile cap the
negative skin friction distribution coincide each other. The amount of negative skin
friction distribution among side, corner and center pile was almost the same.
(a) (b)
Figure 4. 10 Negative Skin Frictions with and without Pile Cap
The negative skin friction distribution along the pile length with and without pile cap for
the load applied of 75 kPa was stated at the figure 4-10b. For the model without pile cap,
negative skin friction was developed from pile head to at which Z/L is equal to 0.7 of the
total depth. As result of the model without pile cap, negative skin friction distribution
among the corner, side, and center pile forms visible difference. From figure 4.8 the
negative skin friction from 0.1% of the total piles length to 0.7 %, has similar distributions
for caped model. When the applied axial load increases from 50 kPa to 75 kPa the drag
load distribution made big difference at which the model was absence of pile cap (see
fig.4.10 a,b). In general for similar axial load application into the model, the negative skin
friction distribution made visible difference.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-200 -150 -100 -50 0 50 100 150 200 250 300
Z/L
Skin Friction (kPa)
Corner pile with cap
Side pile with cap
Center Pile with cap
Cornet pile without cap
Side pile without cap
Center pile without cap
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-400 -300 -200 -100 0 100 200 300 400 500
Z/L
Skin Feiction (kPa)
Corne pile without cap
Side pile without cap
Center pile without cap
corner pile with cap
side pile with cap
Center pile with cap
P = 50 kPa P = 75 kPa
57
4.9 Numerical Analysis of Pile Group With variable Pile Lengh and Diametres
4.9.1 Pile Group
Barnes (2016) Stated that the loads applied by a structure are quite large and usually
cannot be supported by a single pile, so a number of piles are placed together to form a
pile group, with a substantial reinforced concrete pile cap placed on top to transfer and
distribute the loadings from the structure to the piles. Piles are always arranged in a group
of three or more. Moreover, these groups of piles are tied together by a structure known as
pile cap. The pile cap is attached to the heads of each pile and makes them act together as
pile foundation. If two piles are driven close together, soil stresses caused by the piles
tend to overlap, and the bearing capacity of the pile group consisting of two piles which
was less than the sum of the individual capacities. As many Scholars stated that piles
should be spaced relatively far apart and this consideration is offset, however, the unduly
large pile caps that would be required for the wider spacing. As stated from pile cap
sensitivity analysis, the pile group configuration by using the given spacing and cap
dimension should be taken in consideration. Pile group capacities and settlements are
discussed thoroughly within the scope of this study. Parameters that affect the behavior of
piles in group like diameter, pile length and spacing of piles and material behavior were
taken in to consideration. The numerical results are listed in the table 4.3.
4.9.2 Pile Group Settlement
Comodromos, Papadopoulou et al. (2009) suggested that the pile groups in stiff or even
hard clays with a relative length L/D<25 and normalized spacing S/D higher than 3.0 a
settlement of the order of 10% of the pile diameter (D) is sufficient to reach the bearing
capacity of the group, while for higher values of the ratio L/D and closer pile dispositions
increased settlement level is required. The settlement of the group is major criterion that
can specify the working load in addition to the shear failure criterion. The settlement of
piles in the group was investigated at the heads and tips of each pile in the group
independently. The effect of spacing, load variation, and length of piles was investigated
to assess the group behavior in this regard. The pile cap was rigid and it didn’t allow differential settlements at the pile heads. But, the settlements at the bottom were different
at each pile due to the ends were free to either elongate or shorten depending on the extent
of stress overlap by the soil-pile-soil interaction. Group settlement is considered as the
settlement of the group as a whole monitored just at the point of application of the load or
just at the center of the pile cap. Table 4.3 summarizes the group settlements of each pile
spacing and pile length at the ultimate loads.
58
(a) (b)
Figure 4. 11 The pile group settlement with different pile diameter and spacing
4.9.3 Ultimate Pile Group Capacity
Figure 4.12a presents 3D, 4D and 5D pile spacing and the pile diameter was 6000 mm
.For this pile spacing and pile diameter, the result of pile head and pile toe penetration has
not visible difference. This means the value of the pile settlement at the head is almost
similar to the pile settlement at the pile toe .The pile settlement at the pile head and the
settlement at the pile toe makes visible difference when the pile diameter is small(d =
300mm) see fig.4.12b . The pile diameter has significant effect on pile settlement.
(a) (b)
Figure 4. 12 Group Pile Settlement and its maximum capacity of the pile group
As shown in the fig. 4-14a the maximum pile tip settlement is equal to 98.8.mm. From this
figure the ultimate capacity of the pile group is equal to 7074 kN at the pile length of 10
m. Figure 4.14b states that the pile tip settlement and the amount of axial load at the pile
tip. At l/d ratio 67 (300mm dia.), maximum axial load was developed as compared to l/d
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-15-14-13-12-11-10-9-8-7-6-5
Z/L
Pile Settlement (mm)
5D pile spacing
4D pile spacing
3D pile spacing
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-40-35-30-25-20-15-10-50
Z/L
Pile Settlement (mm)
3D pile spacing
4D pile spacing
5D pile spacing
0 500 1000 1500 2000 2500
-25
-20
-15
-10
-5
0
Axial Load (kN) for S = 5D
Pile
Tip
S
ett
lem
en
t (m
m)
L =20 m, L/D = 33
L= 15 m , L/D =25
L =10 m , L= 17
0 1000 2000 3000 4000 5000 6000
-50
-45
-40
-35
-30
-25
-20
-15
-10
-5
0
Axial Load (kN) for S = 4D
Pile
Tip
Se
tt.(
mm
)
L= 20 m ,L/D = 33
L= 15 m , L/D = 25
L =10 m , L/D = 17
S = 4D
S = 5D
59
ratio is equal to 25(800 mm dia.). The minimum pile settlement was developed at the
small value of L/D ratio this value indicated that axial load at the pile tip also minimum.
In general the pile diameter has its own effect for the pile -soil relative settlement. For
similar pile spacing and surcharge load with different l/d ratio the soil –pile relative
settlement made visible difference
Figure 4-13 (a) presents the ultimate capacity of the pile group is equal to 2467 kN for 5D
pile spacing. The axial load distribution through the pile length covers 56.8 % from the
total pile length when the pile length become 10m (L/D = 17). The axial load distribution
through the pile length covers 58.6 % from the total pile length with the pile length of 10
m (L/D =17). For 3D pile spacing and 3 x 3 pile group, the theoretical ultimate capacity of
the pile group was 12080.5 kN. The pile length of 20 m and 15 m can carry the load which
comes from supper structure (applied axial load) but the pile group developed excessive
pile settlement at the minimum pile length of 10 m. The load distribution and the load
carrying capacity are also depending on the pile length and its settlement.
(a) (b)
Figure 4. 13 Determination of Pile Capacity for 3D Pile Spacing
The pile settles the same amount as surrounding soil at the neutral plane. A ratio of the
depth of the neutral plane to the pile length in compressible strata, LNP/L, is suggested to
be taken approximately as 0.75 if no test data is available NAVFAC (1986). This is the
location where the maximum compressive load occurs in the pile .It is also the location at
which there is zero relative movement between the pile and the soil, Fellenius and Siegel
(2008).The neutral plane is the location where there is no relative displacement between
the pile and the soil. Consequently, whatever the settlement in the soil is as to magnitude
and distribution, the settlement of the pile head is equal to the settlement of the neutral
plane plus the compression of the pile caused by the applied dead load plus the drag-load
(fig 4.1). For similar l/d ratio the pile settlement was vary according to axial load
distribution. If the pile spacing was minimum, the axial load distribution into the pile toe
0 1000 2000 3000 4000 5000 6000 7000 8000
-100
-90
-80
-70
-60
-50
-40
-30
-20
-10
0
Axial Load (kN) for S = 3D
Pile
Tip
Se
ttle
me
nt
(cm
)
Ultimate capacity of pile = 7074 kNpile group settlement at failure = 98.8 cm s = 3D, L =10 m ,L/D =17
0.0
500.0
1000.0
1500.0
2000.0
2500.0
3000.0
1 6 11 16
Axia
l L
oad
(kN
)
Pile Tip Settlement (mm)
3D-300mm dia. 3D- 800 mm dia.
l/d = 67
l/d = 25 l/d = 17
60
become bigger and bigger at minimum l/d ratio in the case of load transfer from soil to
pile around pile toe.
Figure 4. 14 Pile group settlements at failure stage with minimum l/d ratio
4.10 Axial Load Distribution For Different Pile Diameter
Fig. 4.15 illustrates the axial load distribution through entire length of the pile with 5D
pile spacing. Constant pile length and 600 mm pile diameter developed maximum axial
load the side pile. The minimum pile diameter (300 mm) developed maximum axial load
at side pile. The maximum axial load developed at the side pile was different with
different pile diameter. Fig. 4.15b states that the maximum l/d ratio results maximum axial
load at the point of Z/L ratio of 0.1 Due to prior over coming of drag-load ,the axial load
distribution at maximum l/d ratio was low bellow the middle point of the pile length. In
general the pile diameter has its own effect on axial load distribution throughout the pile
depth.
(a) (b)
Figure 4. 15 axial load distribution for different pile diameter for 5D pile spacing
S = 4D
S =3D
S = 5DL/D = 17
Axial Load
Settlement
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-200 0 200 400 600 800 1000 1200
Z/L
Axial Load (kN)
Corner pile
Side pile
Center pile
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 1000 2000 3000 4000 5000 6000
Z/L
Axial Load (kN)
Corner Pile
Side Pile
Center pile
600 mm diameter
800 mm diameter
61
Fig. 4.16 illustrates the axial load distribution through entire length of the pile with 800
mm diameter pile with 5D pile spacing and 300 mm pile diameter with 3D pile spacing.
As shown from the fig.4.16a the pile diameter was 800 mm and constant pile length the
maximum axial load was developed at the side pile. When the pile diameter was 300 mm
and constant pile length, the maximum axial load developed at corner pile. The maximum
axial load developed at the side pile from different pile diameter but the value is not the
same. As shown fig. 4.16b illustrates that the maximum l/d ratio results maximum axial
load at the point of Z/L ratio of 0.1 at the corner pile. The maximum axial load developed
at the small diameter and minimum pile spacing and the pile spacing. Due to prior over
coming of drag-load the axial load distribution at maximum l/d ratio the axial load
becoming low bellow the middle point of the pile length.
(a) 5D- 800 mm dia. (b) 3D -300mm and 800 mm dia.
Figure 4. 16 axial load distribution for different pile diameter
4.11 Effect of Pile Diametre to NSF
Figure 4.17 a, b Presents NSF development in different pile diameter and spacing with
constant pile length, the maximum and minimum negative and positive shaft resistance
was developed at l/d ratio 25, 33 and 67(4D and 5D). The maximum negative skin friction
was developed at the result of pile length to diameter ratio of 67. Decreasing l/d ratio from
67 to 33 and 25, the negative skin friction was minimum (see fig.4.17a). Fig.4.17b
presents length to diameter ratio of 67and the maximum negative skin friction was
developed. If l/d ratio decreases from 67 to 33 and 25, this decreasing value shows that the
minimum negative skin friction (see fig.4.17b). The maximum negative skin friction was
developed at the point which l/d ratio was minimum (l/d =25) .But similar l/d ratio and
different pile spacing have developed different value of negative skin friction. For the
same pile diameter which was 300 mm and different pile spacing of 5D and 4D, the
negative skin friction which was developed for the given spacing and diameter has big
difference. But for similar pile spacing which was 4D and different value of diameters
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-150 -100 -50 0 50 100 150 200 250
Z/L
Axial Load (kN)
Corner Pile
Side Pile
Center Pile
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-1000 0 1000 2000 3000 4000 5000 6000 7000 8000
Z/L
Axial Load (kN)
Corner pile ( d =300 mm)
Side Pile ( d = 300 mm)
Center Pile ( d= 300 mm)
Corner Pile ( d = 800 mm)
Side Pile ( d = 800 mm)
Center Pile ( d = 800 mm)
62
which was 300 mm and 800 mm, the negative skin friction developed at the dia. of 800
mm was greater than the negative skin friction developed at 300mm (see fig. 4.17b).
(a) (b)
Figure 4. 17 NSF distribution with respect to pile diameter and its l/d ratio
Figure 4.18 Presents NSF developments in constant pile spacing and different pile
diameter, the maximum and minimum negative and positive shaft resistance was
developed at l/d ratio of 25, 33 and 67. The result of pile length to diameter ratio of 25 was
developed maximum negative skin friction. The minimum negative skin friction was
developed as compared to negative skin friction which was indicated in fig.4.18b .The
cause of the formation of different negative skin friction for constant pile length and
diameter was pile spacing and pile numbers. The maximum negative skin friction was
developed at the point which l/d ratio was minimum (l/d =25) with 3D pile spacing. In
similar pile spacing and different value of diameters which was 300 mm, 600 mm and 800
mm, the negative skin friction developed at the dia. of 800 mm was greater than the
negative skin friction developed at 300mm (see fig. 4.18). In general the pile spacing, pile
number and diameters have its own effect for the development of NSF.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-150 -100 -50 0 50 100 150 200
Z/L
Maximum Negative Skin Friction
l/d = 33
l/d = 25
l/d = 67
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-600 -500 -400 -300 -200 -100 0 100 200 300 400
Z/L
Skin Friction (kPa)
l/d = 33 ( dia. = 600 mm)
l/d = 25 ( dia. = 800 mm)
l/d = 67 (dia. = 300 mm)
63
Figure 4. 18 Distribution of NSF with different pile diameter (3D).
Table 4.2 shows the model types with their respective variable quantities used in the
analyses of pile group and its numerical results. Table 4.2 shows the model which contains
constant diameter and different value of pile length. Table 4.3 also shows the models
which have different pile diameters of 800, 600 and 300 mm with constant pile length
with respect to numerical value of pile settlement and neutral plane.
Table 4. 2 Pile and soil settlement for different pile length.
Pile
spacing
Pile
Length
(m)
Pile group
Settlement
(mm)
Max.
Soil
surface
Settl.(m
m)
Neutral
Plane
(m)
LNP/L
L/D
5D
20 7.7 63.8 12.5 0.625 33
15 15.1 63.8 8.5 0.56 25
10 22.2 63.8 7.65 0.765 17
4D
20 12.4 237.5 14.5 0.725 33
15 25.8 237.5 12 0.80 25
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-800 -600 -400 -200 0 200 400 600
Z/L
Skin Friction (kN)
l/d = 33 (600 mm dia.)
l/d = 25 (800 mm dia.)
l/d = 67 (300 mm dia)
64
10 47.7 237.5 None - 17
3D
20 14.4 404.4 15 0.75 33
15 37.2 660.2 14 0.93 25
10 98.8 1126 None - 17
Table 4. 3 Pile settlements and neutral plane with different pile diameter
Pile
Spacing
Pile diameter
(mm)
Max. Pile
Settlement
(mm)
Neutral Plane
(m)
L/D
5D
300 24.1 9.0 67
600 7.7 12.5 33
800 8.3 13.0 25
4D
300 29.1 15.0 67
600 12.4 14.5 33
800 23.1 12.8 25
3D
300 35.7 15.5 67
600 14.4 15.0 33
800 20.6 14.0 25
4.13 Effect of Pile Length and Diamatre on the Neutral Plane
As stated in the pile cap analysis, the rigidity of the pile cap has own significant role for
the determination of the pile settlement. In real situation no complete flexible and
complete rigid pile caps. But if the pile was relatively rigid, the corner, side and center pile
developed almost the same settlement.
Fig. 4-19a shows that under the condition of 5D pile spacing and 20 m, 15 m and 10 m
pile length. The displacements of pile on the top of corner, side and center pile for 20 m
pile length are 7.5 mm, 7.6 mm and 7.7 mm. The pile settlement at the pile head is almost
similar to the pile settlement at the pile toe (see fig 4.19a). The settlement of pile on the
top of corner, side and center pile for 15 m pile length are 15 mm, 15.1 mm and 15.2 mm
respectively. The displacements of pile on the top of corner pile side pile and center pile
for 10 m pile length are 22.0 mm, 22.2 mm and 22.4 mm respectively. Fig. 4.19a presents
65
the minimum pile length was developed maximum settlement with a constant pile spacing
and pressure load. The pile settlement increment shows large pile tip mobilization and the
neutral plane approach to the pile tip. The pile settlement increment also shows the pile
approaches to failure. This maximum pile and soil settlement hove no neutral point
(equilibrium point) and the soil bearing capacity is very low. When the pile length was 20
m for constant pile spacing 5D, the neutral plane was 12.5m. For 15 m pile length, the
neutral plane was 8.25. In similar fashion when the pile length was 10 m, the neutral plane
was 7.25 m. The same pile length and different pile spacing have significance effect on
pile settlement with minimum l/d ratio. So the length and spacing is significant factor for
negative skin friction of pile groups.
Fig.4.19b presents similar pile length and different value of l/d ratio. The neutral plane
was 9m for 300mm diameter pile with maximum l/d ratio. In similar manner l/d ratio was
minimum for 800mm pile diameter and the neutral plane was 12 m. Under this condition
when the pile diameter was 300 mm and 800 mm with the same pile spacing of 5D, the
maximum pile settlements were 24.1 mm and 8.3 mm. In general the maximum value of
l/d ratio has maximum pile settlement and minimum value of neutral plane. As the result
of minimum value of l/d ratio the neutral plane moves down as compared to maximum
value of l/d ratio.
(a) With different pile length (b) with different value of pile diameters
Figure 4. 19 Location of neutral plane for 5D pile spacing (S = 5D)
Fig. 4-20a shows that under the condition when the pile spacing is 4D and the pile length
are 20m, 15 m and 10 m. The displacements of 20 m pile on the top of corner, side and
center pile are 12.4 mm, 12.4 mm and 12.8 mm respectively. The settlement of pile on the
top of corner, side and center pile for 15 m pile length are 25.0 mm, 25.5 mm and 25.8
mm respectively. The settlement of pile head in the corner side and center pile for 10 m
pile length are 47.0 mm, 47.4 mm and 47.7 mm. respectively. As stated above for the
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-60-40-20020
Z/L
Settlement (mm)
Soil Settlement
Pile Settlement (20 m)
Pile Settlement (15 m)
Pile Settlement (10 m)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-70-60-50-40-30-20-10010
Z/L
Settlement (mm)
Soil Settlement
Pile Settlement (dia.= 600mm)
Pile settlement (dia. = 300 mm)
Pile Settlement (dia. = 800 mm)
NP
NP
66
same pile length and spacing from the given pile head settlement, the settlement of corner,
side and center pile for each pile length was nearly the same. This may be explained by
the fact that in the case of a short pile, the negative skin friction may cover the entire
length, and accordingly, the down-drag force was transmitted to the pile’s tip in the form of penetration to the underlying strata, whereas for a long pile, the down-drag force is
mainly taken by the compression of the pile’s material and little or none is transmitted to the pile’s tip.
Fig 4.20a stated that for 4D pile spacing which was short pile length 10 m , the negative
skin friction may cover the entire length, and accordingly, the down-drag force was
transmitted to the pile’s tip in the form of penetration to the underlying strata as a result no neutral plane .
Fig. 4-20b shows that under the condition of 4D pile spacing with constant pile length of
20 m ,the pile head settlement was differ from the pile toe settlement when l/d ratio was
25 and 67. The maximum pile settlement for the pile diameter of 300 mm and 600 mm
was 29.1 and 23.1 mm respectively.
(a) Different Pile Lengths (b) Different Pile Diameters.
Figure 4. 20 Location of neutral plane with different pile length and diameters
Fig. 4-21a presents that under the condition of 3D pile spacing with the pile length of
20m, 15 m and 10 m. The pile head displacements in the corner pile, side pile and center
pile for 20 m pile length are 14.1 mm, 14.1 mm and 14.3 mm respectively .The pile head
settlement in the corner, side and center pile for 15 m pile length are 36.2 mm, 36.6 mm
and 37.1 mm respectively. The pile head displacements in the corner pile, side pile and
center pile for 10 m pile length are 119 mm, 119.3 mm and 119.9 mm respectively. The
negative skin friction covers the entire length of the pile for short pile length. The absence
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-250-200-150-100-500
Z/L
Settlemet (mm)
Soil Settlement (20 m)
Pile Settlement (20 m)
Soil Settlement(15 m)
Pile Settlement (15 m)
Soil Settlement (10 m)
Pile Settlement (10 m)
NP
NP
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-250-200-150-100-50050
Z/L
Settlement (mm)
Soil Settlement
Pile Settlement (dia. = 600 mm)
Pile Settlement (dia. = 300 mm)
Pile Settlement (dia. = 800mm)
NP
NP
67
of neutral plane stated that the amount of drag load excessively increase up to the pile tip
and greater than pile positive shaft resistance.
Fig. 4-21b shows that under the condition of 3D pile spacing with constant pile length and
different pile diameters. The maximum pile settlements for 300 mm and 800 mm pile
diameter were 35.7 mm and 20. 6 mm respectively. Maximum value of l/d ratio was the
cause of the formation of excessive soil settlement and maximum drag-load.
(a) With different pile length (b) With different pile diameter
Figure 4. 21 Location of neutral plane for 3D Pile Spacing
4.14 Cause of Minimum l/d Ratio to Excessive Pile Settlement
Saha (2015) suggested that down-drag is the downward movement on a deep foundation
unit due to negative skin friction and expressed in term of settlement. When soil moves
downward relative to the pile, it creates a drag force on and within, the pile. The
downward soil movement creates the potential for downward pile movement. It is visible
that when the upper load was the same for one given pile spacing and length. Under the
constraint of pile cap, the displacement was almost the same among corner pile, side pile
and center pile. With the decreasing of pile length, the displacement of each pile in the pile
group was almost the same, but increase proportionally. That indicates the displacement of
corner pile was the same that of side pile and the displacement of side pile was nearly
similar with center pile.
As shown in the fig.4.22 the pile length was 10 m and the surrounding soil settlement and
pile settlement doesn’t coincide each other in the case of excessive load transfer from soil
to pile. As stated by many scholars, the neutral plane is the location at which there is zero
relative movement between the pile and the soil. Figure 4-22 illustrates when the pile
length was 10 m for both 4D and 3D pile spacing, there was no neutral plane by the cause
of excessively increase pile and soil settlement without coincides each other. Bellow the
neutral plane the pile settlement was greater than the soil settlement and the load transfer
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-1200-1000-800-600-400-2000200
Z/L
Setttlement (mm)
Soil Settlement (20 m)
Pile Settlement (20 )
Soil Settlement (15 m)
Pile Settlement (15 m)
Soil Settlement (10 m)
Pile Settlement (10 m)
NP
NP
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-450-400-350-300-250-200-150-100-50050100
Z/L
Settlement (mm)
Soil Settlement
pile Settlement (dia. = 600mm)
Pile Settlement (dia. = 300mm)
Pile Settlement (dia. = 800 mm)
NP
68
mechanism was from pile to soil. The absence of neutral plane stated that the amount of
drag load excessively increase up to the pile tip and the dominance of drag-loads over
positive shaft resistance and the applied surcharge load moves towards the pile settlement.
Figure 4. 22 The Failure Stage for 4D and 3D Pile and Soil settlement
4.15 Effect of group Pile Spacing on NSF
The position of pile has significant influence on the pile groups under NSF, and the group
effect coefficient which increases sequentially in order of corner, side and center pile. The
results show that group effect coefficient and neutral plane depth increase with the
increase of pile spacing because of the less interaction of piles. Furthermore, group effect
coefficient and neutral plane depth increase with the increase of surrounding load.
Figure 4.23 illustrates that for the pile spacing of 3D, 4D, and 5D, the pile group have
different negative skin friction. When the pile spacing increase from 3D to 4D then 5D,
the negative skin friction was decrease due to less interaction effect between pile groups
with a constant pile length of 20 m. The pile spacing 5D, 4D and 3D have different
number of piles 3 x 3, 4 x 4 and 5 x 5 respectively. The maximum negative skin friction
obtained from 3D pile spacing with 20 m pile length at the center pile was 188 kPa (See
fig.4-23). The negative skin friction distribution/ pile soil mobilization mostly developed
at the pile head. Decreasing pile spacing was the cause of soil mobilization and the
development of negative shaft resistance. So pile group spacing was one governing factor
of negative shaft resistance development. For constant pile length and different value of
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-1200-1000-800-600-400-2000
Z/L
Settlement (mm)
4D-Soil Settlement
4D- Pile Settlement
3D- Soil Settlement
3D- Pile Settlement
69
spacing to diameter ratio (s/d), as a result the pile group with minimum value of s/d ratio
develops maximum negative shaft resistance. The absence of neutral plane stated that the
amount of drag load excessively increase up to the pile tip and the dominance of drag-
loads over positive shaft resistance and the applied surcharge load moves towards the pile
settlement.
Figure 4. 23 Skin friction distribution through pile length of 20 m
The maximum negative skin friction develops at the center pile and 3D pile spacing. In
similar fashion for constant pile length and different value of spacing to diameter ratio
(s/d), the minimum value of s/d ratio develops maximum negative shaft resistance. This
value stated that the minimum value of s/d ratio aggravates the interaction between pile-
soil –pile interaction and was the cause of maximum drag- load. The amount of negative
and positive skin friction in 3D- pile spacing for 15 m pile length was 156.7 and 175.5 kPa
respectively. The negative shaft resistance covers 89.3% of positive shaft resistance. As
the result, the neutral plane approaches to the pile tip and the drag down movement goes
to down-ward. In 5D pile spacing, the amount of negative and positive skin friction was
54 kPa and 175.5 kPa respectively. This value shows that the negative skin friction was
30.7 % of the positive shaft resistance. This was good proportion of negative and positive
skin friction. The amount of negative and positive skin friction in 4D- pile spacing and 15
m pile length was 49.6 and 27 kPa respectively. As a result the neutral plane approaches to
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-250 -200 -150 -100 -50 0 50 100 150 200 Z
/L
Maximum Skin friction (kPa)
5D-20 m ,Center Pile
4D-20 m, Corner Pile
3D- 20 m ,Center Pile
70
the pile tip and the drag down movement increased alarmingly over positive shaft
resistance.
(a) (b)
Figure 4. 24 Skin friction distributions through pile length of
The maximum negative skin friction has developed at the center pile with 3D pile spacing
(fig 4-24b).This value shows that the spacing to diameter ratio (s/d) has significant effect
for the development negative skin friction. Rather than the spacing difference l/d ratio has
its own effect to the development of down-drag load and down ward movement of the
soil. The result of decreasing of pile length (l/d) ratio was the major cause of the formation
of maximum negative skin friction in 3D pile spacing and minimum pile length. Figure (4-
24 b) states that all maximum negative skin friction developed at the center pile with the
same pile length. In general pile spacing has significant effect for the formation of
negative skin friction with respect to pile length. Mostly maximum negative skin friction
develops in the center pile and minimum s/d and L/D.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-250 -200 -150 -100 -50 0 50 100 150 200
Z/L
Maximum Skin friction (kPa)
5D-15 m , Side pile
4D- 15 m ,Corner pile
3D- 15 m ,Center pile
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-150 -100 -50 0 50 100 150
Z/L
Maximum Negative Skin Friction (kPa)
5D- Center Pile
4D-Center Pile
3D-Center Pile
10 m pile length
15 m pile length
71
4.16 Effect of Pile Length on NSF (5D)
A ratio of the depth of the neutral plane to the pile length in compressible strata, LNP/L, is
suggested to be taken approximately as 0.75 if no test data is available NAVFAC (1986).
Figure 4.25 presents NSF is developed on the pile’s shaft after applying the surcharge load, and continues to exist until the completion of the consolidation of the surrounding
soil. Under surcharge loading, negative skin friction is induced on the top of the pile and
extends progressively to the mid part of the pile, until it reaches a maximum value at an
intermediate depth and finally decreases. As some intermediate depth above the neutral
plane, the maximum negative skin friction developed bellows the neutral plane around the
pile tip. Increasing the ratio LNP/L was significant in decreasing the pile length from 20 m
to 10 m for similar pile spacing of 5D (table 4.2). The negative skin friction distribution in
corner, side and center pile was different in 3x3 pile configuration. The maximum
negative skin friction of corner, side and center pile was developed at Z/L is equal to 0.1.
The amount of negative skin friction for 5D pile spacing with the pile length of 20 m, the
corner, side and center pile was 22.9, 7 and 29.5 kPa respectively. The maximum negative
skin friction was 29.5 kPa which was developed at the center pile but the minimum
negative skin friction was developed in the side pile. The negative skin friction
distribution through the entire length of the pile was different among corner, side and
corner pile. The maximum positive and negative skin friction also develops in the side pile
(figure 4.25 a). The minimum and maximum negative skin friction was varying according
to the given pile length. Figure 4.25 (a) presents the pile length was 20 m and the positive
skin friction distribution through the entire length of the center pile at the ratio of Z/L
from 0.3 to 0.9 was very small.
(a) (b)
Figure 4. 25 Skin frictions on pile’s shaft with the same spacing and variable pile length
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-40 -20 0 20 40 60 80 100
Z/
L
Skin Friction (kPa)
Corner Pile
Side Pile
Center Pile
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-100 -50 0 50 100 150 200
Z/L
Skin Friction (kPa)
Corner Pile
Side Pile
center Pile
S= 5D, L = 20 m S = 5D, L=15 m
72
Figure 4.25 presents the maximum negative skin friction of corner, side and center pile
was developed around Z/L ratio was 0.15 when the pile length was 15 m. The amount of
negative skin friction for 5D pile spacing with the pile length of 15 m for corner, side and
center pile was 52.5, 53.8 and 53.8 kPa respectively. As stated above the maximum
negative skin friction is 53.8 kPa which is found at the side and center pile but the
minimum negative skin friction was in the corner pile. But the negative skin friction
between corner, side and center pile has insignificant difference. The negative skin friction
distribution from the pile head to maximum negative value in the corner, side and center
pile was coincides each other. Figure 4.25 (b) presents the pile length was 15 m and the
positive skin friction distribution through the entire length of the center pile at the ratio of
Z/L from 0.55 to 65 was very small. But the negative skin friction distribution among
corner, side and center pile have nearly similar up to the maximum negative skin friction
point. Consequently, soil settled more than the pile resulting in negative skin friction
(NSF) along the upper portion of the pile (0 ≤ Z/L ≤ 0.65 and 0<=Z/L<= 0.42) at fig
4.25(a, b) respectively. This suggests that this portion of the pile is subjected to drag-load
by the surrounding soil. To maintain vertical equilibrium of the pile, the soil surrounding
the lower part of the pile (Z/L>0.65 and Z/L > 0.42) is resisted its settlement by
mobilizing positive skin friction (PSF) at the pile-soil interface and end-bearing resistance
at the toe of the pile.
73
Table 4. 4 Maximum Negative and positive skin friction
Pile Spacing Pile Length (m) Maximum Negative
Skin Friction (kPa)
Maximum Positive
Skin friction ( )
5D
20 m 30.5 95.8
15 m 53.9 175.5
10 m 46.9 187.5
4D
20 m 47.3 21.5
15 m 49.6 27
10 m 56.3 none
3D
20 m 188.5 50.3
15 m 156.7 175.5
10 m 80.5 none
The amount of negative skin friction for 5D pile spacing with the pile length of 10 m for
corner, side and center pile was 45.2, 46.6 and 46.9 kPa respectively. As stated above the
maximum negative skin friction is 46.9 kPa which is found at the center pile but the
minimum negative skin friction was in the corner pile. The negative skin friction
distribution from the pile head to maximum negative value in the corner, side and center
pile was coincides each other.
Figure 4.26 also stated that in the case of a short pile, the negative skin friction may cover
the entire length, and the down-drag force was transmitted to the pile’s tip in the form of
penetration to the underlying strata, whereas for a long pile, the down-drag force was
mainly taken by the compression of the pile’s material and little or none is transmitted to
the pile’s tip. Consequently, soil settled more than the pile resulting in negative skin
friction (NSF) along the upper portion of the pile (0 ≤ Z/L ≤ 0.45 for corner and side pile
but as stated above the minimum negative skin friction distribution developed up to the
ratio of Z/L was equal to 0.8. This suggests that this portion of the pile was subjected to
drag-load by the surrounding soil.
74
Figure 4. 26 Skin frictions on pile’s shaft with short pile length
4.16.2 Effect of Pile Length in Negative Skin Friction (4D )
Negative skin friction is induced from the top of the pile and extends progressively
downward until the maximum negative shaft resistance was achieved. As some
intermediate depth above the neutral plane the maximum negative skin friction developed
and decrease up to neutral plane. With 20 m pile length and 4D pile spacing, the minimum
positive skin friction was developed bellow the neutral plane around the pile tip. From the
pile top to some depth of the pile which is called neutral plane, the negative skin friction
decreases to a zero value. For 4D pile spacing and 20 m pile length, the neutral plane
value was 14.5 m (tab.4.3). This value shows that the negative shaft resistance covers
72.5 % of the total pile length (Lnp/L= 0.725). With respect to the given depth and pile
spacing and compare to the other pile spacing which is 5D, the positive skin friction
developed bellow neutral plane is going to minimum when L/D ratio become small and
small. The negative skin friction distribution in corner, side and center pile was different
in 4 x 4 pile configuration. As shown in the figure 4.26(a, b) the pile spacing was 4D and
pile length 20 m, and 15 m respectively. The maximum negative skin friction of corner,
side and center pile was developed around Z/L ratio is equal to 0.1 for 20 m pile length
with similar pile spacing (see fig. 4-27a). As shown in the fig. 4-27 (b) the maximum
negative skin for corner pile, side and center pile was developed around the ratio of Z/L is
equal to 0.15. The amount of negative skin friction for 4D pile spacing with the pile length
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-150 -100 -50 0 50 100 150 200
Z/L
Skin Friction (kPa)
Corner Pile
Side Pile
Center Pile
S = 5D, L =10 m
75
of 20 m for corner, side and center pile was 47.3 kPa, 39.8 kPa and 5.1 kPa respectively
(fig 4.27a). The amount of negative skin friction for 4D pile spacing with pile length of 20
m for corner, side and center pile was 49.7 kPa, 44.7 kPa and 7 kPa respectively
(fig.4.27b). The maximum negative skin friction is 47.3 kPa which is developed at the
corner pile but the minimum negative skin friction was in the center pile. The negative
skin friction which was stated at figure 4.27a and 4.27b the point of application of the
maximum and minimum negative skin friction or shaft resistance was shift when the pile
spacing changed from 5D to 4D for similar pile length. But at the pile tip, the maximum
positive and minimum positive shaft resistance was developed at the side pile and corner
pile. For 4D pile spacing with 20 m pile length, the minimum and maximum negative
shaft resistance developed at center and corner pile respectively. For this pile spacing and
length, the minimum and maximum positive shaft resistance developed at center and side
pile. Figure 4.27 (a, b) presents the minimum and maximum negative skin friction was
varying according to the given pile length and pile spacing with pile soil interacting or pile
configuration. The pile length was 15m and the positive skin friction distribution through
the entire length of the center pile at the ratio of Z/L from 0.7 to 0.8 was very small.
The negative skin friction (NSF) mobilization was formed above these indicated points
due to stress release and soil movement as mentioned towards the pile movement. This
implies that this portion of the pile is “dragged” down by the surrounding soil. To
maintain vertical equilibrium of the pile, the soil surrounding the upper part of the pile
resists from settling, by mobilizing PSF at the soil–pile interface. Figure 4.27 (a) the
neutral plane, where the zero shaft resistance is mobilized, is located at a depth of Z/Lp =
0.75 (above formation level). Figure 4.24(b) presents neutral plane, where the zero shaft
resistance was mobilized at a depth of Z/Lnp = 0.8 (above formation level).This location
was consistent with the depth where the maximum axial load was induced. To maintain
vertical equilibrium of the pile, the soil surrounding the lower part of the pile (Z/L>0.8 for
corner and side pile and Z/L > 0.75 for center pile is resisted its settlement by mobilizing
positive skin friction (PSF) at the pile-soil interface and end-bearing resistance at the toe
of the pile.
76
(a) (b)
Figure 4. 27 Skin frictions on pile’s shaft with different pile length
Fig. 4.28 presents the maximum negative and minimum positive shaft resistance of corner,
side and center pile. The maximum negative shaft resistance was developed at the ratio of
Z/L is equal to 0.2. The amount of negative shaft skin friction corner, side and center pile
was 56.3, 56.3 and 37.1 kPa respectively. Negative skin friction distribution coincides
each other from the ratio of Z/L is equal 0.6 at the negative side to 0.8 from the positive
side. The minimum positive shaft resistance was developed from the point Z/L is equal to
0.8 below the neutral plane. For this pile length the positive shaft resistance which was
developed at the point of Z/L is equal to 0.8 was influenced by drag down (drag-load).
The ratio of LNP/L is increasing when the pile length decrease from 20 m to 10 m for
similar pile spacing (table 4.2). The excessive pile settlement was the major cause of the
development of minimum positive skin friction. This excessive settlement causes the
parallel increment of pile and soil settlement and there was no equilibrium point between
pile and soil. This drag-load domination change the value of positive resistance to
negative resistance again fig. (4.28). When the pile length decrease to 10 m, the negative
shaft skin friction distribution cover 90 % of the total amount of skin friction. The rate of
increase of the ratio LNP/L due to decrease of the ratio L/D is significantly increase the
negative shaft resistance (table 4.2).
Figure 4.28 also stated that in the case of a short pile, the negative skin friction may cover
the most entire length, and accordingly, the down-drag force was transmitted to the pile’s
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-60 -50 -40 -30 -20 -10 0 10 20 30
Z/L
Skin Friction (kPa)
Corner Pile
side Pile
center Pile
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-60 -50 -40 -30 -20 -10 0 10 20 30
Z/L
Skin Friction (kPa)
Corner Pile
side Pile
Center Pile
S= 4D, L = 20 m S = 4D, L = 15 m
77
tip in the form of penetration to the underlying strata, whereas for a long pile, the down-
drag force is mainly taken by the compression of the pile’s material and little or none is
transmitted to the pile’s tip. At 10 m pile length, the pile was pulling out from the cap.
Figure 4. 28 Skin frictions on pile’s shaft with 10 m pile length (S= 4D)
4.16.3 Effect of Pile Length on NSF (3D )
Figure 4.28 presents negative skin friction is developed from the top of the pile and
extends progressively downward, until it reaches a maximum value at an intermediate
depth. The maximum negative skin friction developed and starting to minimum at some
intermediate depth above the neutral plane. Bellows the neutral plane around the pile tip
the minimum positive skin friction was developed for 20 m pile length for given pile
spacing. The negative skin friction decreases to a zero value at the neutral plane. For 3D
pile spacing and 20 m pile length, the neutral plane value was 15 m. But with respect to
the given depth and pile spacing as compared to the other pile spacing which are 5D and
4D, minimum positive skin friction developed bellow neutral plane. Figure 4.28 illustrate
that, the excessive pile settlement which was developed when pile length and pile spacing
was 10m and 3D respectively. When the pile length and pile spacing changed from 20 m
to 10, the drag-down movement of the surrounding soil with respect to pile was
increasing. When the pile length become 10 m for 4D and 3D pile spacing rather than 5D,
the drag load was excessively increase with maximum pile settlement. This excessive drag
down movement of soil with respect to pile causes the parallel increment of pile and soil
settlement. Due to this parallel increment of pile and soil settlement, there was the absence
of equilibrium point between pile and soil. Due to this reason negative skin friction
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-80 -60 -40 -20 0 20 40 60 80
Z/L
Skin Friction (kPa)
Corner Pile
Side Pile
Center Pile
78
distribution in corner, side and center pile was different in 5 x 5 pile configuration with 3D
pile spacing. The maximum negative shaft resistance was developed at the center pile.
This maximum shaft resistance developed around the ratio of Z/L is equal to 0.1 for 20 m
pile length. But when the pile length become 15 m the maximum negative shaft resistance
was developed around Z/L ratio is equal to 0.2.This value indicate that when the negative
skin friction distribution moves down ward with pile length minimum pile length.
Figure.4.29 (a) presents the amount of negative skin friction for 3D pile spacing with the
pile length of 20 m for corner, side and center pile was 30.4 kPa, 22.7 kPa and 188.5 kPa
respectively. The maximum negative skin friction is 188.5 kPa which is found at the
center pile but the minimum negative skin friction was developed in the side pile. The
minimum positive skin friction distribution through the entire length of the center pile at
the ratio of Z/L from 0.3 to 0.7
Figure .4.29b presents the amount of negative skin friction for corner, side and center pile
were 52.9 kPa, 10.7 kPa and 156.7 kPa respectively. The maximum negative skin friction
is 156.7 kPa which was found at the center pile but the minimum negative skin friction
was in the side pile. Generally, the point of application of the maximum and minimum
negative skin friction or shaft resistance was shift when the pile spacing changed from 5D,
4D to 3D for similar pile length. For 3D pile spacing with 20 m pile length, the minimum
and maximum negative shaft resistance developed at side and center pile respectively. For
this pile spacing and length, the minimum and maximum positive shaft resistance
developed at side and center pile.
79
(a) (b)
Figure 4. 29 Skin frictions on pile’s shaft (a) 20 m and (b) 15 m with (3D)
Figure 4.30 presents the pile length of 10 m and the NSF for corner, side and center pile
was 77.2, 71.1 and 80.5 kPa respectively. The maximum negative shaft skin friction was
80.5 kPa which developed at the center pile but the minimum negative shaft skin friction
was in the side pile. The pile length which was 10 m and the positive shaft resistance
which was developed at the ratio of Z/L was equal to 0.6 but this was influenced by drag
down (drag-load) .When the pile length decrease to 10 m, the negative shaft friction
distribution cover 90 % of the total pile length. The rate of increasing the ratio of LNP/L
due to decrease of the ratio L/D was significantly increases the negative shaft resistance
(table 4.2). This figure also stated that in the case of a short pile, the negative skin friction
may cover the most entire length, and the down-drag force is transmitted to the pile’s tip
in the form of penetration to the underlying strata, whereas for a long pile, the down-drag
force is mainly taken by the compression of the pile’s material and little or none is
transmitted to the pile’s tip. Generally excessive pile settlement was developed and the
load transfer from pile to soil reaches at the pile tip. The pile starts to pull out from the cap
at this short pile.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-250 -200 -150 -100 -50 0 50 100 150 200 250
Z/L
Negative Skin Friction (kPa)
Corner Pile
Side Pile
Center Pile
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-250 -200 -150 -100 -50 0 50 100 150 200 250
Z/L
Negative Skin Friction ( kPa)
Corner Pile
Side Pile
Center Pile
80
Figure 4. 30 Skin frictions on piles shaft with 10 m pile length (3D)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-200 -150 -100 -50 0 50 100 150 200
Z/L
Skin Friction (kPa)
Corner Pile
Side Pile
Center Pile
81
5. CONCLUSIONS AND RECOMMENDATION
5.1 CONCLUSION
The major parameters highly influencing the negative shaft resistance are pile
length, pile diameter, number of piles and pile spacing.
For uncapped model, the negative skin friction distribution of side, corner and
center pile made visible difference above the neutral plane.
For capped model the negative skin friction distribution coincide each other and
the amount of negative skin friction distribution among side, corner and center pile
nearly same.
For similar axial load application into the capped and uncapped model the negative
skin friction distribution made visible difference
In the case of a short pile, the negative skin friction may cover the entire length,
and accordingly, the down-drag force is transmitted to the pile’s tip in the form of
penetration
In the case of a long pile, the down-drag force is mainly taken by the compression
of the pile’s material and little or none is transmitted to the pile’s tip. The normalized depths (Z/L) increase the mobilized negative shaft resistance
decrease up to the neutral point.
At the working load level with minimum l/d ratio, the drag force may be large
enough to reduce the pile capacity or to overstress the pile’s material, causing fractures or perhaps structural failure of the pile, or possibly pulling out the pile
from the cap
For different pile spacing and constant pile length the negative skin friction
distribution/ pile soil mobilization mostly developed around pile head but the point
of maximum NSF goes down to the pile tip when l/d ratio was minimum
For constant pile length and different value of spacing to diameter ratio (s/d), as a
result of minimum value of s/d ratio develops maximum negative shaft resistance.
At the minimum value of l/d ratio, the negative skin friction distribution cover 90
% of the total pile length and the minimum negative skin friction distribution
develop at the center pile.
The shorter pile socket length may result in a higher elevation of neutral plane thus
lower drag-loads and, induced pile settlement can be more severe as compared to a
pile with a longer socket length.
When the upper load is small, the NSF on upper part of each pile generally
coincides each other, with the increase of upper load, the coincidence disappears,
that is, the NSF of the upper part of each pile become different.
At constant pile diameter and different pile spacing which are 5D, 4D and 3D,
maximum negative skin friction was developed due to interaction effect.
82
At constant pile spacing and different value of pile diameter the maximum
negative skin friction developed at the point of minimum l/d ratio.
In general the pile spacing, number of piles and diameters have its own effect for
the development of negative shaft resistance (NSF).
83
5.2 RECOMENDATION
The following recommendations are given for future research:
1. Try to use laboratory experimental value and validation of the analyses outputs obtained
from ABAQUS on the distribution of load to pile group based on physical modeling but
there are so many constraint to get the laboratory result in our country.
2. Extending the present study to complex loading patterns like eccentric, lateral loadings
and dynamic loading cases.
3. Extending the present study to complex soil strata conditions.
4. Extending the present study to pile –soil-pile interaction.
84
REFERENCES
Burland, J. (1973). "Shaft friction of piles in clay--a simple fundamental approach."
Publication of: Ground Engineering/UK/ 6(3).
Comodromos, E. M. and S. V. Bareka (2005). "Evaluation of negative skin friction effects
in pile foundations using 3D nonlinear analysis." Computers and Geotechnics 32(3): 210-
221.
Comodromos, E. M. and S. V. Bareka (2009). "Response evaluation of axially loaded
fixed‐head pile groups in clayey soils." International Journal for Numerical and Analytical Methods in Geomechanics 33(17): 1839-1865.
Comodromos, E. M., et al. (2009). "Pile foundation analysis and design using
experimental data and 3-D numerical analysis." Computers and Geotechnics 36(5): 819-
836.
Das, B. M. (2010). "Principles of Foundation Engineering, SI Edition." Cengage Learning.
El-Mossallamy, Y. M., et al. (2013). "Numerical analysis of negative skin friction on piles
in soft clay." HBRC Journal 9(1): 68-76.
Fellenius, B. H. (1984). Negative skin friction and settlement of piles. Proceedings of the
Second International Seminar, Pile Foundations, Nanyang Technological Institute,
Singapore.
Fellenius, B. H. (2006). "Results from long-term measurement in piles of drag load and
downdrag." Canadian Geotechnical Journal 43(4): 409-430.
Fellenius, B. H. and T. C. Siegel (2008). "Pile drag load and downdrag in a liquefaction
event." Journal of geotechnical and geoenvironmental engineering 134(9): 1412-1416.
Hanna, A. M. and A. Sharif (2006). "Drag force on single piles in clay subjected to
surcharge loading." International Journal of Geomechanics 6(2): 89-96.
Helwany, S. (2007). Applied soil mechanics with ABAQUS applications, John Wiley &
Sons.
Huang, T., et al. (2015). "The group effect on negative skin friction on piles." Procedia
Engineering 116: 802-808.
Indraratna, B., et al. (1992). "Development of negative skin friction on driven piles in soft
Bangkok clay." Canadian Geotechnical Journal 29(3): 393-404.
Iskander, M. G., et al. (2001). "Driveability of FRP composite piling." Journal of
Geotechnical and Geoenvironmental Engineering 127(2): 169-176.
Jeong, S., et al. (2004). "Slip effect at the pile–soil interface on dragload." Computers and
Geotechnics 31(2): 115-126.
Kempfert, H. and M. Rudolf (2005). Effects of actions due to group effect on the
superstructure on pile groups. Proceedings of the International Conference on Soil
Mechanics and Geotechnical Engineering, AA BALKEMA PUBLISHERS.
Kong, G.-Q., et al. (2008). "Study of loading rate effects on characteristics of negative
skin friction for pile groups." Electronic Journal of Geotechnical Engineering 13(L): 1-12.
85
Lee, C. (1993). "Pile groups under negative skin friction." Journal of geotechnical
engineering 119(10): 1587-1600.
Lee, C., et al. (2002). "Numerical modelling of group effects on the distribution of
dragloads in pile foundations." Geotechnique 52(5): 325-335.
Lee, C. and C. W. Ng (2004). "Development of downdrag on piles and pile groups in
consolidating soil." Journal of geotechnical and geoenvironmental engineering 130(9):
905-914.
Liu, J., et al. (2012). "Finite element analyses of negative skin friction on a single pile."
Acta Geotechnica 7(3): 239-252.
Nath, U. and P. Hazarika (2013). "Lateral resistance of pile cap–an experimental
investigation." International Journal of Geotechnical Engineering 7(3): 266-272.
Poulos, H. (2006). Pile group settlement estimation—Research to practice. Foundation
Analysis and Design: Innovative Methods: 1-22.
Poulos, H. G. (1971). "Behavior of laterally loaded piles I. single piles." Journal of Soil
Mechanics & Foundations Div.
Poulos, H. G. and E. H. Davis (1980). Pile foundation analysis and design.
Qing, Y., et al. (2008). "Model test study of negative skin friction for single pile under
surface load." Rock and Soil Mechanics 29(10): 2805-2810.
Rabbany, A. G., et al. (2018). "Pile Cap Performances in Different Consequences."
Randolph, M. F. (2003). "Science and empiricism in pile foundation design."
Geotechnique 53(10): 847-875.
Reese, L. C., et al. (2006). Analysis and design of shallow and deep foundations, John
Wiley.
Saha, A. (2015). "The influence of negative skin friction on piles and pile groups &
settlement of existing structures." International Journal on Emerging Technologies 6(2):
53.
Shen, W. and C. Teh (2002). "Analysis of laterally loaded pile groups using a variational
approach." Geotechnique 52(3): 201-208.
Terzaghi, K., et al. (1996). Soil mechanics in engineering practice, John Wiley & Sons.
Thach, P.-N., et al. (2013). "Vibration analysis of pile-supported embankments under
high-speed train passage." Soil Dynamics and Earthquake Engineering 55: 92-99.
Trochanis, A. M., et al. (1991). "Three-dimensional nonlinear study of piles." Journal of
geotechnical engineering 117(3): 429-447.
Tuan, P. A. (2016). "A simplified formular for analysis group efficiency of piles in
granular soil." International Journal of Scientific & Engineering Research 7(7): 15-21.
Xia, L. N., et al. (2013). 3D Finite Element Analysis of Negative Skin Friction (NSF)
Behaviors in Pile Groups with Cap. Applied Mechanics and Materials, Trans Tech Publ.
86
Yang, H., et al. (2013). Vertical Loading Test on the Bearing Capacity of Large-Diameter
Filling-Piles in the Mudstone and Sandstone Foundation. Advanced Materials Research,
Trans Tech Publ.
Zhan, Y., et al. (2012). "Modeling vertical bearing capacity of pile foundation by using
ABAQUS." Electronic Journal of Geotechnical Engineering 17: 1855-1865.