MÓNG BÈ TRÊN NỀN CỌC

PILED RAFT FOUNDATIONS
Be studied by the group of students include: Junior;Thai Binh Duong, Ngoc
Phu Nguyen, Thanh Binh Trinh, Quoc Tuan Luu, Van Thao Nguyen
Be supported by PhD. Si Hung Nguyen

INDEX
ABSTRACT
1. INTRODUCTION 12
2. SYMBOL TABLE 23
3. DEFINITION
4. ADVANTAGES OF PILED RAFT FOUNDATIONS
5. BACKGROUND OF ANALYSIS
5.1 Interactions in piled raft foundation
5.2. Review of design methods for piled raft foundation
5.2.1. Simplified method – Randolph [6] method
5.2.2. Approximate method – plate on springs approach [1]
5.2.3. More sophisticated computer-based methods
5.2.3.1. Hain and Lee [3] method
5.2.3.2. Reul and Randolph [16] method
6. PROPOSED DESIGN METHOD:
6.1. Modelling of piled raft foundations
6.2. Pile–soil–pile interaction factor
6.3. Pile–soil–raft interaction factor
6.4. Analysis procedure using SAP 2000
7. CENTRIFUGE TESTING PROGRAM
7.1. Tested soil
7.2. Test program and models
7.3. Test procedures
8. RESULTS AND DISCUSSION
8.1. Single pile tests
8.2. Raft tests

8.3. Piled raft tests
8.4. Comparison of piled raft behaviour between centrifuge test, proposed
method and Plaxis 3D analysis
8.5. Comparison of bending moment between proposed method and Plaxis 3D
analysi
8.6. Comparison of individual piles behaviour between centrifuge test,
proposed method and Plaxis 3D analysis
9. APPLICATION OF PILED RAFT FOUNDATIONS
9.1 Ground Conditions and Geotechnical Model
9.2 Foundation Layout
9.3 Overall Stability
9.4 Predicted Performance Under Vertical Loading
9.4.1 Vertical loading
9.4.2 Horizontal loading
10. CONCLUSIONS
11.REFERENCES
ABSTRACT: Piled raft foundations are increasingly being recognised as an economical
and effective foundation system for tall buildings. The aim of this essay is to describe a
unite element analysis of deep foundations piled and mainly piled raft foundations and sets
out some principles of design for such foundations, including design for the geotechnical
ultimate limit state, the structural ultimate limit state and the serviceability limit state. The
advantages of using a piled raft will then be described with respect to two cases: a small
pile group subjected to lateral loading. Attention will be focussed on the improvement in
the foundation performance due to the raft being in contact with, and embedded within, the
soil.A basic parametric study is restly presented to determine the incluence of mesh
discretisation, of materials - loose or dense sand -, of dilatancy and interface elements.
Then the behavior of piled raft foundations is analysed in more details using partial
axisymmetric models of one pile-raft.
1. INTRODUCTION
In traditional foundation design, it is customary to consider first the use of shallow

foundation such as a raft (possibly after some ground-improvement methodology
performed). If it is not adequate, deep foundation such as a fully piled foundation is used
instead. In the last few decade, an alternative solution has been designed: piled raft
foundation. Unlike the conventional piled foundation design in which the piles are
designed to carry the majority of the load, the design of a piled raft foundation allows the
load to be shared between the raft and piles and it is necessary to take the complex soil-
struture interaction effects into account.
The concept of piled raft foundation was firstly proposed by Davis and Poulos in
1972 and is now used extensively in Europe, particularly for supporting the load of high
buildings or towers. The favorable application of piled raft occurs when the raft has
adequate loading capacities, but the settlement or differential settlement exceed allowable
values. In this case, the primary purpose of the pile is to act as settlement reducer.
2. SYMBOL TABLE
Numbe
r
Symbol Explanation Unit
1 C resistance property for SLS
2 D pile diameter m
3 e pile spacing m
4 E action effect
5 Es stiffness modulus
MN/m²
6 F Action
MN
7 Fk,i characteristic value of an action i
MN
8 Ftot,k sum of characteristic values of all actions
MN
9 H sum of horizontal actions
MN

10 i index for an action
-
11 j index for a pile
-
12 k index for characteristic value
-
13 n number of actions
-
14 m number of piles of a CPRF
-
15 qb base pressure of a pile
MN/m²
16 qs(z) skin friction of a pile
MN/m²
17 R resistance
MN
18 Rb,k(s) characteristic value of the base resistance of a pile as a

function of settlement
MN
19 Rtot,k (s) characteristic value of the total resistance of a CPRF as
a function of settlement
MN
20 R1,tot,k characteristic value of the total resistance of a CPRF for
ULS
MN
21 Rpile,k,j characteristic value of the resistance of the pile j of a
pile group
MN
22 Rraft,k characteristic value of the resistance of a

MN
23 Rs,k(s) characteristic value of the skin friction resistance of a
pile
MN
24 s settlement
m
25 spr settlement of a CPRF
m
26 ssf settlement of shallow foundation
m
27 s2 allowable settlement for SLS
m
28 Δs2 allowable differential settlement for
m
29 V sum of vertical actions
MN
30 x,y,z cartesian coordinates
m
31 αpr pile raft coefficient
-
32
γ

partial safety factor
-
33 σ(x,y) contact pressure
MN/m²
3. DEFINITION
The Combined Pile Raft Foundation (CPRF) is a geotechnical composite
construction that combines the bearing effect of both foundation elements raft and piles by

taking into account interactions between the foundation elements and the subsoil shown in
Figure 1.1.
The characteristic value of the total resistance R
tot
,k (s) of the CPRF depends on the
settlement s of the foundation and consists of the sum of the characteristic pile resistances
, ,
( )
m
pile k j
j
R s
∑
and the characteristic base resistance R
raft
,k (s). The characteristic base
resistance results from the integration of the settlement dependant contact pressure
( , , )s x y
σ
in the ground plan area A of the raft.
,
( ) ( , , )
raft k
R s s x y dxdy
σ
=
∫∫
The bearing behaviour of the CPRF is described by the pile craft coeficient
pr
α

which is defined by the ratio between the sum of the characteristic pile resistanses
, ,
( )
m
pile k j
j
R s
∑
and the characteristic value of the total resistance
,
( ) :
tot k
R s
, ,
, ( )
( )

m
pile k j
j
pr
tot k s
R s
R
α
=
∑
The pile raft coefficient varies between
0
pr

α
=
(spread foundation) and
1
pr
α
=

(pure pile foundation). Figure 1.2 shows a qualitative example of the dependence between
the pile raft coefficient
pr
α
and the settlement of a CPRF
pr
s
related to the settlement of a
spread foundation S
sf
with equal ground plan and equal loading.
The pile raft coefficient
pr
α
depends on the stress level and on the settlement of the
CPRF.
4. ADVANTAGES OF PILED RAFT FOUNDATIONS
- Piled raft foundations utilize piled support for control of settlements with piles
providing most of the stiffness at serviceability loads, and the raft element providing
additional capacity at ultimate loading.
- Consequently, it is generally possible to reduce the required number of piles when
the raft provides this additional capacity. In addition, the raft can provide redundancy to

the piles, for example, if there are one or more defective or weaker piles, or if some of the
piles encounter karstic conditions in the subsoil. Under such circumstances, the presence
of the raft allows some measure of re-distribution of the load from the affected piles to
those that are not affected, and thus reduces the potential influence of pile “weakness” on
the foundation performance.
- Another feature of piled rafts, and one that is rarely if ever allowed for, is that the
pressure applied from the raft on to the soil can increase the lateral stress between the
underlying piles and the soil, and thus can increase the ultimate load capacity of a pile as
compared to free-standing piles (Katzenbach et al., 1998).
- A geotechnical assessment for design of such a foundation system therefore needs
to consider not only the capacity of the pile elements and the raft elements, but their
combined capacity and interaction under serviceability loading.
- The most effective application of piled rafts occurs when the raft can provide
adequate load capacity, but the settlement and/or differential settlements of the raft alone
exceed the allowable values.
- Poulos (2001) has examined a number of idealized soil profiles, and found that the
following situations may be favourable:
• Soil profiles consisting of relatively stiff clays
• Soil profiles consisting of relatively dense sands.
In both circumstances, the raft can provide a significant proportion of the required
load capacity and stiffness, with the piles acting to “boost” the performance of the
foundation, rather than providing the major means of support.
Figure 2: Combined Pile Raft Foundations
5. BACKGROUND OF ANALYSIS
5.1 Interactions in piled raft foundation
The behaviour of a piled raft foundation is influenced by the interactions between
the piles, raft and soil, and consequently interaction factors have been widely adopted for
the prediction of the response of a piled raft. In reality, there are two basic interactions,
pile–soil–pile interaction and pile–soil–raft interaction, as shown in Figure 3. The pile–
soil–pile interaction is defined as the additional settlement of a pile caused by an adjacent

loaded pile, and the pile–soil–raft interaction is defined as superposing the displacement
fields of a raft caused by a pile supporting the raft. The pile–soil–pile interaction is an
important consideration in the analysis of pile groups and piled rafts, and the pile–soil–raft
interaction is necessary for analysing piled rafts. Several approaches for determination of
these two interaction factors are tabulated in Table 1.
Figure. 3. The interactions in a piled raft foundation system.
Table 1. Approaches for determining interaction factors.
Method Type of
interaction
Equation Comment
Poulos and
Davis [4]
Pile–pile
interaction
(α)
w
w
α
∆
=
– Considering the additional
settlement of a pile (ΔW)
caused by an adjacent pile
– The contribution of the
adjacent pile was not
presented clearly in the
equation
Poulos [9] Pile–pile
interaction
(α)

1
w
n
k j kj
j i
Q
ω α
=
∆ =
∑
– Considering the additional
settlement of a pile caused
by adjacent piles in the term
of axial loads of adjacent
piles Q
j
Randolph
[11]
ln
1
2
ln
r
p
rp
m
p
r
r
r

r
α
 
 ÷
 ÷
 
= −
 
 ÷
 ÷
 
r
m
= 2.5ρL(1 − υ
s
)
– Considering the additional
settlement of a circular rigid
raft caused by a pile
– Not considering the change
in soil stiffness along the pile
and the flexibility of the raft.
The parameter for
considering soil stiffness
is ρ which is the degree of
homogeneity of the soil
Randolph
[6]
Pile–raft
interaction

ln
1
ln
r
p
rp
m
p
r
r
r
r
α
 
 ÷
 ÷
 
= −
 
 ÷
 ÷
 
r
m
= 0.25 + Lζ[2.5ρ(1 − υ) − 0.25]
ζ = E
sl
/E
sb
ρ = E

sav
/E
sl
– Considering the additional
settlement of a circular rigid
raft caused by a pile
– Considering the soil
stiffness along the pile (E
sav
),
at pile tip (E
sb
) and pile head
(E
sl
)
– Not considering the
flexibility of the raft
Clancy and
Randolph
[2]
Pile–raft
interaction
( )
p
r
rp pr
p r
k
P

w
P k
α
= −
– The settlement of piled raft
and load transmitted for piles
and for raft are needed
– Can consider the flexibility
of the raft
Nomenclature:
Δw
k
= additional of pile k caused by other piles
ω
1
= displacement due to unit load of pile k and pile j
Q
j
= the load on pile j; α
kj
= interaction factor for pile k due to any other pile j within the
group
α
rp
= interaction factor between a pile and a raft;r
r
= the diameter of the raft
r
p
= the diameter of the pile

ρ = the degree of homogeneity of the soil
L = the length of the pile
υ
s
= Poisson ratio of soil
E
sl
= soil Young’s modulus at level of pile tip
E
sb
= soil Young’s modulus of bearing stratum below pile tip
E
sav
= average soil Young’s modulus along pile shaft
P
p
= total load carried by pile group in combined foundation
P
r
= total load carried by raft in combined foundation
k
p
= overall stiffness of pile group in isolation
k
r
= overall stiffness of raft in isolation
w
pr
= settlement of a piled raft foundation.
The approach of Poulos and Davis [4] for obtaining the pile–pile interaction factor

considers a pair of vertical piles spaced at (S) and embedded in a horizontally layered soil.
The formulation is based on the additional settlement of a pile under the interaction of the
other pile. Poulos [9] proposed another approach that can be used for calculating the
additional settlement of a pile caused by a pile group surrounding it by superposing
additional settlement caused by each pile. The difference between these two approaches is
that in the later method the additional settlement of a pile is a function of the forces of
other piles in the pile group.
In the approach developed by Clancy and Randolph [2], the interaction factor of a
pile to a raft (α
rp
) is calculated based on the additional settlement of a circular rigid raft
caused by its supporting pile. This formulation, however, does not consider the change in
soil stiffness along the pile, and therefore Randolph [6]proposed a modified version of his
earlier formulation by considering the stiffness of soil at the pile head and the pile tip and
along the pile shaft. Nevertheless, neither of Randolph’s approaches considers strength
characteristics of soil (e.g., friction angle, cohesion) or the flexibility of the raft.
The approach of Clancy and Randolph [2] is used to calculate α
rp
when the
settlement of the piled raft and the load transmitted to the piles and to the raft are known.
The advantage of this method is that it can determine the interaction of the pile group to
the raft. The difficulty of estimating the load transmitted to the pile group and the raft,
however, hinders practical use of this formulation.
5.2. Review of design methods for piled raft foundation
5.2.1. Simplified method – Randolph [6] method
This method is based on calculation of the total stiffness of the piled raft by means
of the stiffness of the pile group and the stiffness of an unpiled raft in isolation and the
interaction between one pile with the region of the raft surrounding the pile. Thus, the
settlement of the foundation and the ratio of transmitted load to the raft can be calculated.
This method can obtain the behaviour of the piled raft in the form of a tri-linear

load–settlement curve [ 10] ). Nevertheless, this method only considers the interaction
between the piles and the raft and not the interaction between piles in the pile group. The
application, however, is quiet easy for hand calculation, as the method is fairly
straightforward.
5.2.2. Approximate method – plate on springs approach [1]
This method is based on the elastic theory and interactions between the components
of the piled raft foundation. Poulos [1] modelled a piled raft in the form of a plate
supported by springs representing piles. This method is implemented via the program
GARP (Geotechnical Analysis of Raft with Piles) which allows consideration of the
layered soil profile to failure behaviour and the effect of piles reaching their ultimate
capacity. Four interactions were considered in this program, interaction between elements
of the raft, interaction between piles, influence of the raft on the piles, and influence of the
piles on the raft.
The remarkable advantage of this method is that it can obtain the distribution of the
stress inside the raft and can consider the ultimate capacity of piles. Nevertheless, the
behaviour of piles under the transmitted load depends on the soil model, with many
parameters required when using the GARP program. This can cause that the behaviour of
piles deviate from the real behaviour if the soil is not modelled reliably. Consequently, the
obtained settlement of the foundation will inevitably include some errors. Moreover, the
based on the elastic theory of the analysis is another limitation, and its complexity also
prohibits its application for design (it can be only applied by using the GARP program).
5.2.3. More sophisticated computer-based methods
5.2.3.1. Hain and Lee [3] method
Hain and Lee [3] analysed two components, soil and piles, to solve the problem of a
piled raft, where the soil elements and the pile elements were arranged compatibly with the
raft. In the model, the soil surface was meshed into a number of square or rectangular 4-
node finite elements. The nodes located at the piles are called pile nodes and the remaining
nodes are referred to as soil nodes. The pile–pile interaction and pile–soil interaction are
used to calculate the vertical settlement of each node. The total supporting soil–pile group
stiffness can then be obtained and the settlement and stress on the raft are estimated. This

analysis rigorously considers the interaction between soil and piles and solves many
problems such as flexibility of the raft, ultimate capacity of piles. Nevertheless, this
method also has several limitations. First, if the raft consists of a series of bending plates,
the number of soil nodes will be very high, and the calculation cost is consequently large.
Conversely, if the soil nodes are reduced, the number of bending plates is decreased,
and the calculation results, especially the internal stress of the raft, will be less accurate. In
addition, because the effect of the raft in the interactions is not considered and the pile
stiffness is only correlated with Young’s modulus of the pile (E
p
) and Young’s modulus of
the soil mass (E
s
) (K
p
= E
p
/E
s
), the accuracy of the results will be further worsened.
5.2.3.2. Reul and Randolph [16] method
This method bases totally on the finite element method. The authors used Abaqus
program to simulate piled rafts and proposed that modelling the soil and foundation by
finite elements can allow the most rigorous treatment of the soil–structure interaction. This
method has several remarkable advantages.
First, the soil can be modelled as a multiphase medium which consists of three
components solid phase (grains), liquid phase (pore water) and gaseous phase (pore air), so
the geotechnical characteristics of soil can be considered effectively.
Second, the nonlinear material behaviour of the soil can be taken in to account with
the elastoplastic cap model.
Third, the plastic behaviour of soil can be considered by the nonassociated flow

potential (G
s
) of the shear surface and the associated flow potential (G
c
) of the cap.
Fourth, the contact between structure and soil and the various types of applied load
can be simulated. Nevertheless, this method still has some problems. In modelling pile–
soil interaction, the interface element was not used so the method could not consider the
relative motion between the pile elements and soil elements. Moreover, the calculating
time for obtaining a solution is long and Abaqus program is not easy for practicing
engineers to use.
In general, the existing methods can be employed to solve the piled raft problem
fairly completely. However, there exist some limitations as mentioned above, especially
with application to engineering work, because they are quite complex (i.e., the
approximate methods and more rigorous computer-based methods). This paper hence
proposes an analysis method to solve several problems, including:
• Simplification for ease of application for practicing engineers.
• Solving piled raft problem without any sophisticated finite element model for soil
and helping practicing engineers control well the mechanism of piled rafts.
• Using a combination of the single pile and unpiled raft behaviours to estimate the
behaviour of the piled raft fairly exactly.
• Obtaining nonlinear behaviour of a piled raft foundation by using the nonlinear
behaviour of the single pile.
• Estimation of the settlement of the foundation and the distribution of the bending
moment in the raft with reasonable accuracy.
6. PROPOSED DESIGN METHOD
6.1. Modelling of piled raft foundations
In this study, the raft is modelled as a series of bending plates, each pile is modelled
as a pile spring at the pile’s position, and the relative raft–soil stiffness is modelled by
means of raft springs with the quantity and the position decided by the designer, as shown

in Figure. 2. However, in order to solve the stiffness of the pile springs, it is convenient to
assume that vertical forces are only transmitted from the raft to the head of a pile[3]. This
assumption involves neglecting the lateral pile head force and the lateral pile movement. In
general, the total vertical loads are considerably greater than the total lateral loads, so the
lateral movements of the raft are small. In the case of large lateral loads subjected to the
raft, the batter piles will be used and can be modelled as lateral pile springs. However, this
problem is not considered in the scope of this paper. Then, the vertical displacement of a
pile is given by:
( )
1
1J 1K
1, K
w (1)
n
pK pJ KJ pK
J J
P P
δ α δ
−
= ≠
= +
∑
where w
pK
is the vertical displacement of the pile K; δ
1J
, δ
1K
are the displacement due to the
unit load of the piles J and K, respectively, which can be derived from the load–settlement

curve of a single pile having the same size; P
pJ
is the load on pile J; α
KJ
is the pile–soil–pile
interaction factor of pile J on pile K; P
pK
is the load on pile K; and n is the number of piles.
Figure. 2 Model of piled raft foundation. (a) A piled raft foundation. (b) Modelling for
proposed design method.
The stiffness of pile spring K is given by:
(2)
w
pK
p pk
pK
P
K K
= =
where K
pK
is the stiffness of pile spring K
To solve the stiffness of raft springs, the lateral force and lateral movement are also
neglected. The vertical displacement of a raft spring is given by:
equation(3)
( )
1
1
w w (3)
n

rpM M M KM rM
K
Q
ρ β
=
= +
∑
where w
rpM
is the vertical displacement of the raft spring M in consideration of pile
interactions
w
rM
is the vertical displacement of the raft spring M without pile interactions;
- ρ
1M
is the displacement of the raft springM due to the unit load, which can be calculated
from elastic theory or derived from the load–settlement curve of an unpiled raft having the
same size as the raft of piled raft
Q
M
is the load on the raft spring M; and β
KM
is the pile–soil–raft interaction factor of
pile K for the raft spring M.
The stiffness of the raft spring M is given by:
(4)
w
M
r rM

rmM
Q
K K
= =
where K
rM
is the stiffness of the raft spring M
6.2. Pile–soil–pile interaction factor
The pile–soil–pile interaction factor, α, is used to calculate the additional settlement
of a pile caused by adjacent piles. In the case of two piles K and J, additional settlement
for pile K can be written as follows:
1
w (5)
K J J
Q KJ
ω α
∆ =
Then,
1
w
(6)
K
KJ
J J
Q
α
ω
∆
=
where α

KJ
is the interaction factor of pile J on pile K
Δw
k
is the additional settlement of pile K caused by pile J
ω
1J
is the settlement due to a unit load of pile J; Q
J
is the load on pile J
The interaction factor between pile K and pile J can be defined as follows:
additional displacement of pile K caused by unit load on by J

displacement of pile J due to unit load
(7)
KJ
α
=

In this paper, the finite element method (FEM) via Plaxis 3D Foundation program is
employed to obtain this factor. The input parameters are presented in Table 2. The soil
used is silica sand with two different relative densities, 70% and 40%. The parameters of
soil are chosen at the level of depth about two-third of the pile length from the pile head.
The characteristics of the tested soil taken from the drained triaxial tests are presented in
detail in the tested soil section. In the FEM, the soil is considered as a hardening model of
the case of hyperbolic relationship for standard drained triaxial test and the dilatancy of the
sand is also considered [15]). The piles are represented by embedded pile elements. The
embedded pile beam can be placed arbitrarily in a soil volume element, and at the position
of the beam element nodes virtual nodes are created in the soil volume element from the
element shape functions. Then, the special interface forms a connection between the beam

element nodes and these virtual nodes, and thus with all nodes of the soil volume element.
The interaction with soil at the pile skin and at the pile foot is described by means of
embedded interface elements. These interface elements are based on 3-node line element
with a pairs of nodes instead of single nodes. One node of each pair belongs to the beam
element, whereas the other (virtual) node is a point in the 15-node wedge element
belonging to soil element. The skin interaction is taken into account by the development of
skin traction and the foot interaction is considered by the development of the foot force.
Table 2. Plaxis 3D input parameters.
Parameter Input value
Soil material
L/d = 25 and D
r
= 70%
Dry density (γ
d
) 15.13 kN/m
3
Secant Young’s modulus (E
50
) 50 MPa
Friction angle (ϕ) 43°
Confinement pressure 150 kPa
Poisson’s ratio (υ) 0.25
L/d = 25 and D
r
= 40%
Dry density (γ
d
) 13.7 kN/m
3

Secant Young’s modulus (E
50
) 25 MPa
Friction angle (ϕ) 40°
Confinement pressure 150 kPa
Poisson’s ratio (υ) 0.25
L/d = 16.7 and D
r
= 70%
Dry density (γ
d
) 15.13 kN/m
3
Secant Young’s modulus (E
50
) 28.5 MPa
Friction angle (ϕ) 43°
Confinement pressure 100 kPa
Poisson’s ratio (υ) 0.25
Pile material
Young’s modulus (E) 2.82E+04 MPa
Density (γ) 15 kN/m
3
Poisson’s ratio (υ) 0.16
First, the model of a single pile subjected to load F was simulated to obtain the
settlement. The modelling of two separate piles subjected to the same load F with the
given spacing (S) was then performed to obtain the settlement of each pile. The additional
settlement was calculated by the difference in the settlements between the case of a single
pile and the case of two piles. Using Eq. (7), the pile–soil–pile interaction for the given
pile spacing can be obtained. In this paper, the number of pile spacing (up to S/d = 16) was

selected corresponding with the piled raft models of centrifuge tests. Thus, a large value of
pile spacing is not necessary for this study. The pile–soil–pile interaction curve was
constructed as shown in Figure. 3.
Figure. 3. Pile–soil–pile interaction factors for homogeneous soil layer.
(a) Comparison of interaction factors between FEM result obtained for Silica
sand D
r
= 70%, υ = 0.25 with the result of Poulos and Davis [4]K = 1000, υ = 0.5.
(b) Comparison of interaction factors between dense and loose sands in same L/D ratio.
(c) Comparison of interaction factors between two different L/D ratios in dense sand.
Figure 3a shows a comparison between the FEM results obtained for silica sand
(D
r
= 70% and υ = 0.25) and the results of Poulos and Davis [4] (overall stiffness K = 1000
and Poisson’s ratio υ = 0.5) in the case of a length–diameter ratio L/d = 25. General
agreement in the trend that the interaction factor decreases with increasing pile spacing
between the two results is observed. The difference in the values originates from the
different Poisson’s ratio, type of soil, and the analysis method, but is still acceptable.
Poulos and Davis [4]suggested the pile–soil–pile interaction curves for various types of
soil and pile lengths based on an elastic continuum analysis. These curves can also be used
to obtain the pile–soil–pile interaction factor in an alternative way if the FEM is
unavailable.
Figure 3b and c shows pile–soil–pile interaction factors, obtained by the finite
element method, as a function of the pile spacing to diameter ratio (S/d). When this ratio
increases, the interaction factor decreases. This means that when the distance (S) is small,
the additional settlement of a pile caused by the other pile is large but when (S) is large, the
additional settlement becomes small and the behaviour of a pile more closely approximates
the behaviour of a single pile. The interaction factors are also dependent on the density of
soil and the ratio between the pile length and the diameter of the pile (L/d). It simply
explains in prose the form of the interaction equation that the coefficient α depends on the

displacement of pile J due to unit load so when the relative density of soil decreases the
settlement due to unit load of pile J increases and thus it makes the value of α reduces. In
the case of increasing pile length, when the length of pile J increases the capacity of this
pile develops making the settlement due to unit load of this pile lessens and thus the value
of α increases. Figure. 3 presents a comparison of pile–pile interaction curves for two
states of silica sand, dense and loose states.
6.3. Pile–soil–raft interaction factor
The FEM was employed to construct the pile–soil–raft interaction curve. The soil
same with the soil used to determine the pile–soil–pile interaction was represented. For the
given pile spacing, to derive the pile soil raft interaction factor, β, it was necessary to
prepare two separate models. The first model was a piled raft (four piles with the given
pile spacing) and the second model was an unpiled raft having raft with the same size as
that considered in the piled raft model as shown in Figure. 4. The additional settlement
(ΔW) of the raft caused by piles was obtained. The applied load for the unpiled raft model
equals the transmitted load to the raft in the piled raft model. The additional settlement
equals the difference in the settlement values for the raft between the two models. The
additional settlement caused by a pile for the raft equals ΔW divided by the number of
piles. The pile–soil–raft interaction coefficient, β, is then determined as follows:
additional displacement of the raft caused by a pile
(8)
displacement of the unpiled raft
β
=
Figure. 4. Model scheme for obtaining pile–soil–raft interaction.
The pile–soil–raft interaction curves were constructed as shown in Figure. 5. Figure.
5a provides a comparison of pile–soil–raft interaction factors between the results obtained
by the FEM and by the equation from Randolph [6]. The curve constructed by Randolph’s
approach was calculated with a Young’s modulus of soil at the pile head E
sl
= 8.61 MPa,

Young’s modulus at the bearing stratum below the pile tip E
sb
= 74.75 MPa, the average
Young’s modulus along pile shaft E
sav
= 46.63 MPa, and Poisson’s ratio υ = 0.25 (these
parameters are derived from silica sand in a dense state as used for the study in this paper).
It can be seen that there is good agreement between the two set of results, both in general
trends and in numerical values. This indicates that the factor can also be determined by the
method of Randolph [6] in an alternative way if the FEM is unavailable.
Figure. 5. Pile–soil–raft interaction factors for a square raft in homogeneous soil.
(a) Comparison of interaction factors between FEM and Randolph [6] in dense sand.
(b) Comparison of interaction factors between dense and loose sands in same L/D ratio.
(c) Comparison of interaction factors between two different L/D ratios in dense sand.
Figure. 5b and c shows the pile–raft interaction factor, obtained from finite element
method, as a function of the ratio S/d. When the distance (S) increases, the interaction
factors decrease. The interaction curves tend to converge to a value of about 10% when the
distance (S) becomes large. In comparison, the interaction curve of L/d = 25 is higher than
that of L/d = 16.7. This illustrates that as the length of the pile and the soil stiffness
respectively increase, the interaction effect between the pile and one point of the raft
becomes accordingly higher. The reason is that the coefficient β depends on the
displacement of the unpiled raft (according to Eq.(8)). When the relative density of soil
increases the capacity of the unpiled raft develops so its settlement reduces, and thus the
value of β increases. In the case of increasing pile length, the interaction length of piles to
the raft increases raising the pile–soil–raft interaction up.
6.4. Analysis procedure using SAP 2000
The proposed method is used to estimate the settlement and bending moment
induced in the raft of two piled raft models which are performed in centrifuge tests. To
conduct this method in a civil engineering analysis package and instruct the practicing
engineer reproducing the method, the SAP 2000 structural commercial program, which is

being used by many civil design companies at present, is used. This program cannot
simulate any soil model but with the help of the proposed method, it can solve the piled
raft problem well.
The analysis requires the following input data: the single pile behaviour, the unpiled
raft behaviour, and the pile–soil–pile and pile–soil–raft interaction factors. The pile–soil–
pile interaction factor plays a role of connecting pile springs working as a pile group while
the pile–soil–raft interaction factor helps the plate models operate as a real raft in the piled
raft foundation. As final outputs, the settlement of the piled raft and the distribution of the
bending moment and shearing force of the raft can be obtained. Figure. 6 shows a flow
chart of the analysis procedure. When the assumed load transmitted to the piles in the piled
raft in the first calculation is larger than the piles’ capacity, the “load cut-off” procedure [3]
is applied, where the piles’ capacity is taken to calculate the settlement of pile springs. The
remaining load is transmitted to the raft to calculate the settlement of the raft springs.
Figure. 6. Schematic of flow chart for SAP 2000 analysis.
The analysis procedure using SAP 2000 is as follows:
1. Model the piled raft foundation with SAP 2000, where the raft is modelled by a
bending plate having the same size as the raft, piles are modelled by pile springs and
relative raft–soil stiffness is modelled by raft springs. The plate is meshed into a series of
small plates to solve the bending moment and stress of the raft.
2. Determine the pile–soil–pile interaction factors for each pile spring and pile–soil–
raft interaction factors for each raft spring based on the interaction curves.
3. From the total applied load, assume the load for piles and the load for the raft
(about 80% and 20% of the total applied load, respectively), and assume the axial force
transmitted for each pile spring and each raft spring (usually at the first calculation, assume
that all axial forces of all pile springs are equal and all the axial forces of all raft springs
are equal).
4. Calculate the vertical settlement for each pile spring by Eq. (1) and each raft
spring by Eq. (3). The displacements of the pile due to unit load in
Eq. (1) (δ
1J

and δ
1K
respectively) are derived from the load–settlement curve of a single
pile, and the displacement due to the unit load for the raft spring (ρ
1M
) is calculated from
the load–settlement curve of an unpiled raft or the solution of Boussinesq for shallow
foundations [17].
5. Calculate the stiffness of each pile spring by Eq. (2) and the stiffness of each raft
spring by Eq. (4).
6. Assign all the calculated stiffness for all springs of the piled raft model in SAP
2000. This step establishes the boundary conditions for the plate model.
7. Solve the system of equations to obtain the preliminary settlement of the piled raft
and axial forces transmitted for each spring.
8. Calculate the difference in the axial forces of pile springs with a tolerance of
about 5–7%. If the differential values are larger than 7%, repeat the calculation from step 4
to step 8 to estimate the stiffness of all springs and the settlement of the foundation a
second time. This iterative process is terminated when the differential axial forces of the
pile springs are in a range of 5–7%. This tolerance is based on experience so it may be
chosen at the designer discretion.
7. CENTRIFUGE TESTING PROGRAM
Centrifuge tests were performed using the 240 g ton geotechnical centrifuge
equipment at KAIST (Korea Advanced Institute of Science and Technology) in Korea. The
maximum capacity of the KAIST beam centrifuge, with a 5 m radius, is 2400 kg for up to
100 g of centrifugal acceleration and 1300 kg at 130 g of maximum centrifugal
acceleration. The detailed specifications of the centrifuge equipment can be found in Kim
et al. [14]. Figure. 7a shows the centrifuge equipment with the testing system developed in
this study. The tests were carried out at two centrifugal acceleration levels, 50 g and 60 g.
Two centrifugal accelerations were adopted for making a difference in the pile length
between two piled raft models.

Figure. 7.KOCED geotechnical centrifuge with testing system and test model set-up.
(a) KOCED geotechnical centrifuge with testing system.
(b) Test model set-up.
7.1. Tested soil
Silica sand, with particle mean diameter D
50
= 0.22 mm, a uniformity
coefficient C
U
= 1.96 and classified as SP type (according to the Unified Soil Classification
System), was used for all centrifuge tests. Triaxial drained tests were performed to obtain
characteristics of the tested soils, with relative densities, D
R
≈ 70% and D
R
≈ 40%. The test
results are presented in Table 3.
Table 3. Silica sand parameters.
Relative
density
Confinement
pressure (kPa)
Depth
(m)
E (MPa)ε > 0.2
%
Peak
friction
angle (ϕ)
Critical state

friction angle
(ϕ
cr
)
Dense state 50 3.4 8.61 43° 33.5°
D
r
= 70% 100 6.8 28.42
(γ
d
= 1.49 t/m
3
) 200 13.6 74.75
Loose state 50 3.8 8.47 40°
D
r
= 40% 100 7.6 13.33
(γ
d
= 1.37 t/m
3
) 200 15.2 36.84
A homogeneous dry soil model was prepared by means of pluvial deposition to
relative densities D
R
of 70% and 40% (dense state and loose state, respectively) using a
travelling sand spreader, which controls the fall height and travel speed of the deposition
curtain. The spreader was passed repeatedly over the circular strong model box (900 mm
in a diameter) until the thickness of the sand layer was approximately 400 mm
(corresponding with 20 m at 50 g and 24 m at 60 g in the prototype scale).

7.2. Test program and models
In order to verify the applicability of the proposed method, two cases of piled raft
model tests were evaluated in the centrifuge tests for comparison; the two piled rafts have
different numbers of piles as well as different pile length and pile spacing. The first case is
sixteen piles (15 m pile length and 0.6 m in diameter in prototype) and 4d pile spacing, and
the second case is nine piles (10 m pile length and 0.6 m in diameter in prototype) and 3d
pile spacing. The piled raft models were loaded by loading equipment fixed to the rigid
frame of the box. A load cell was installed in the equipment to measure the amount of total
applied load. The raft settlement was measured by two linear displacement transducers
(LVDT) fixed on a frame that was connected to the frame supporting loading equipment.
The tips of the core of LVDTs rested on the two opposite corners of the raft. The average
values of data measured by the two LVDTs were taken as the settlement of the foundation.
The test model set-up is shown in Figure. 7b. The target of these tests is obtaining the
load–settlement curves of the two piled raft models in model scale. Then, these curves are
converted to prototype scale using the laws of similitude as in Table 4 [18] ) to compare
with the load–settlement curves of the two piled raft calculated by the proposed method
and Plaxis 3D Foundation.
Table 4. Scaling factor for centrifuge modelling [18].
Parameter Scaling factor Parameter Scaling factor
Acceleratio
n
N Length 1/N
Stress 1 Strain 1
Mass 1/N
3
Force 1/N
2
Stiffness 1/N Time (diffusion) 1/N
2
The material and thickness of the pile model and the raft model are selected in

considering the equivalent stiffness between the model scale and the prototype scale. In the
case of the pile model, the equilibrium of axial strain is considered, and in the case of the
raft model the equilibrium of deflection is considered. The number of centrifuge tests
performed is 10. The test programme are summarised in Table 5. Two tests were
performed at 50 g on the single pile model (pile length 220 mm) and a piled raft model
having nine piles (pile length 200 mm and three piles were equipped with load cells to
measure transmitted axial forces). In the piled raft tests, the rafts need to be completely
contacted with the soil surface, whereas in the pile group tests the rafts (or the caps) do not
contact with the soil surface. In order to make the same penetrated pile length in both piled
raft tests and pile group tests, the pile length model of pile group tests is longer than the
one of piled raft tests about 20 mm (1.2 m at 60 g in the prototype scale). The models were
made of aluminium alloy (E = 7E+04 MPa). Details of all models are summarised in Table
6, where the prototype and model scale dimensions are reported.
Table 5: Test program. UR = unpiled raft; SP = isolated single pile; PG = pile group;
PR = piled raft.
Schem
e
Test No. of piles Pile
spacing
D
r
of soil (%) Acceleration N (g)
UR T1 – – 70 60
UR T2 – – 40 60
SP T3 1 – 70 60
SP T4 1 – 40 60
SP T5 1 – 70 50
PG T6 16 4D 70 60
PG T7 16 4D 40 60
PR T8 16 4D 70 60

PR T9 16 4D 40 60
PR T10 9 3D 70 50
Table 6: Dimensions of centrifuge models. D
m-in
= inner diameter of pile; D
m-out
= outer
diameter of pile; L = length of pile; B
r
= width of raft;t
r
= thickness of raft.
Sche
me
Model scale a/
g
Prototype scale
D
m-in
(
mm)
D
m-out
(
mm)
L
m
(m
m)
B

rm
(m
m)
t
rm
(m
m)
D
m-
in
(
m)
D
m-
out
(
m)
L
m
(
m)
B
rm
(
m)
t
rm
(
m)
UR – – – 150 15 6

0
– – – 9 1.22
UR – – – 150 15 6
0
– – – 9 1.22
SP 8 10 270 – – 6
0
0.2 0.6 16.2 – –
SP 8 10 270 – – 6
0
0.2 0.6 16.2 – –
SP 10 12 220 – – 5
0
0.3 0.6 11 – –
PG 8 10 270 – – 6
0
0.2 0.6 16.2 – –
PG 8 10 270 – – 6
0
0.2 0.6 16.2 – –
PR 8 10 250 150 15 6
0
0.2 0.6 15 9 1.22
PR 8 10 250 150 15 6
0
0.2 0.6 15 9 1.22
PR 10 12 200 180 18 5
0
0.3 0.6 10 9 1.22
7.3. Test procedures

All models are decided to install at 1 g because if models are installed at 50 g or
60 g the pile group capacity will be increased by 50
2
or 60
2
times. Thus, it is very difficult
to penetrate the models into the soil with the loading equipment ability used. The
following test procedures have been adopted:
At 1 g: a homogeneous soil model was prepared by pluvial deposition into the circular box.
The box was then placed into the centrifuge basket and the model was then installed to the
loading equipment and penetrated the soil.
Single pile tests: the embedded lengths are 250 mm for the pile models having 270 mm
length and 200 mm for the pile model having 220 mm length.
Piled group tests: the embedded length is 250 mm.
Unpiled raft tests: the unpiled raft model was placed on the surface of the soil.
Piled raft tests: the piled raft model was penetrated into the soil until the raft reached the
soil surface.
At 50 g or 60 g: After the soil surface settles down completely, the models were penetrated
to the soil about 2∼3 mm to ensure the embedded length of piles still equals to the length
of piles in the piled raft and/or for the raft perfectly contacted with the soil surface (2–
3 mm is the settlement of the soil surface during the increase of the centrifugal acceleration
from 1 g to 50 g or 60 g). The loading tests were then performed. For all tests, loading
equipment penetrated the models at a rate of 0.04 mm per second (rate of penetration) until
a relative displacement w/d
p
≈ 30% was reached, where w is the measured settlement.
8. RESULTS AND DISCUSSION
8.1. Single pile tests
Figure. 8 shows the load–settlement curves (P
sp

–w
sp
curves) of three single piles. It
is observed that there are three stages in behaviour when a pile is subjected to a load. In
the first stage, the w
sp
increases almost linearly when the P
sp
increases up to the critical
load point. In the second stage, the P
sp
–w
sp
response becomes more curved, because
the w
sp
increases more than the first stage when the load increases. This stage can be called
the critical stage of the pile. In the third stage, the path of the pile’s behaviour becomes
nearly linear again, but the w
sp
develops quickly although the P
sp
does not increase
substantially.
Figure. 8. Centrifuge single pile load tests’ result in prototype scale.
Figure. 8 also presents a comparison of the behaviour of a single pile among three
cases of centrifuge tests. The bearing capacity of a pile includes shaft resistance and end
bearing resistance. The end bearing depends on the strength of the soil below the pile tip
and the shaft resistance is mainly based on the length of a pile. In the cases of two single
pile tests having the same pile length L = 15 m in different soil densities, the pile in the

dense state shows stiffer behaviour than that in the loose state. Nevertheless, the single pile
of L = 15 m in loose sand is still stiffer than the single pile of L = 9 m in dense sand. This
indicates that when the pile length increases the stress state increases corresponding with
the increase of embedded depth. This helps to increase considerably the pile capacity.
The P
sp
–w
sp
curve of the single pile is an important input value in the proposed
method. The settlement of a pile due to the unit load (δ
1
) (in Eq. (1)) can be obtained by
normalising the settlement of the pile with the corresponding load. It is important to note
that, in the third stage, the piles reach their limit capacity and thew
sp
increases
considerably, and as a result the settlement of piles due to the unit load cannot be obtained
from this stage.
8.2. Raft tests
The test results are presented in Figure. 9. It can be seen that the load–settlement
behaviour of an unpiled raft is almost linear and the stiffness of the raft on loose sand is
much lower than that on dense sand.
Figure. 9. Centrifuge raft tests’ result in prototype scale.
To calculate the stiffness of the raft springs, the settlement due to the unit load (ρ
1
)
(in Eq. (7)) is needed and this value can be obtained from the load–settlement behaviour of
the unpiled raft. It is noticed that in the case of silica sand this behaviour is almost linear,
and thus the unpiled raft stiffness can be estimated via elastic theory as an alternative
approach.

8.3. Piled raft tests
The results in Figure. 10 show that in the case of this study the piled raft’s behaviour
has two stages, where the first stage is curved and the second stage is linear. In the first
stage, the piled raft’s behaviour is governed by the piles’ behaviour when they are still in
working ability. Under the application of external load, the piled raft settles down and this
settlement provides the main contribution to pile settlement. In this stage, the raft supports
a small amount of the total load (about 10–20% of total load; [10]) and reduces the
settlement of the piled raft relative to the case of the pile group. Nevertheless, when the
external load increases to a very large value the piled raft’s behaviour becomes linear (it is
assumed that at this time the piles reached their limit capacity). This indicates that in this
stage the piled raft’s behaviour is governed by the raft’s behaviour. Initially, the subjected
load is transmitted to the piles until reaching their critical capacity. The load is thereafter
transmitted to the raft, and the settlement of the piled raft at this time increases
corresponding with the increase of settlement of the unpiled raft.
Figure. 10.Piled raft centrifuge testing results.
(a) Piled raft with 16 piles (D = 0.6 m; L = 15 m) in dense sand.
(b) Piled raft with 16 piles (D = 0.6 m; L = 15 m) in loose sand.
Additionally, the results of the centrifuge test also illustrate that the settlement of the
piled raft is smaller than that of the unpiled raft due to the contribution of the piles.
Besides, in Figure. 10a, with dense sand state the difference in load–displacement (P–w)
response between the piled raft and the pile group is small when the total load is less than
50,000 kN. The P–w path of the piled raft just deviates from the one of the pile group
when the total load passes 50,000 kN and the difference becomes larger when the load
continues to increase. The reason is that the settlement of the piled raft in large applied
load is smaller than the pile group because of the contribution of the raft. However, Figure.
10b shows that in loose sand state the P–w path of the piled raft starts to deviate from the
one of the pile group when the load is just about 15,000 kN. The piled raft shows much
stiffer behaviour than the pile group when comparing with the dense sand state case. It can
be concluded that a piled raft can give an increased benefit over a pile group in the looser
sand.

8.4. Comparison of piled raft behaviour between centrifuge test, proposed
method and Plaxis 3D analysis
Two piled rafts are simulated by means of three-dimensional finite element via
Plaxis 3D Foundation program in the prototype scale to obtain the load–settlement curves.
The input parameters are presented in Table 2. In this analysis, the soil is modelled in dry
state using a hardening model of the case of hyperbolic relationship for standard drained
triaxial test and the dilatancy of the sand is also considered (similar with the simulation of
soil in determining the pile–soil–pile and pile–soil–raft interaction factors section). The
soil parameters are selected at the level of two-third of the pile length from the pile head.
The size of the soil block consists of 54 m length and 24 m height for the case of the piled