INTRODUCTION
In a piled raft foundation, the total load of the superstructure is partly carried out by piles through skin friction and the remaining load is taken by raft through contact with the soil. In conventional piled foundation it is assumed that the raft does not carry any load even if the raft is in contact with the ground. Also, in conventional piled foundation, as the contribution of raft is ignored, long piles should be used which extend up to the deep hard strata. On the other hand, if only raft has to carry the total load of the superstructure, very thick raft is needed which increases the cost of the foundation. Such raft foundation undergoes excessive settlement. In such a condition, piled raft foundation can be considered as the best solution in which shorter piles and raft with lesser thickness can be provided. Since 1970 many researchers has studied about different properties of piled raft foundation and its influence on reducing the maximum and differential settlements.
Hooper (1973) studied the behavior of piled raft foundation
supporting a tower block in London. The field measurements which took along
several years were accompanied with the results of a finite element analysis.
In the analysis it was assumed that the load is distributed uniformly on the
raft. Based on the field measurements the estimated proportions of load taken
by piles and the raft at the end of construction were 60 and 40%, respectively.
It was found that the longterm effect of consolidation increases the part of
load which carried by piles and decreases raft contact pressure. Potts
and Martins (1982) considered mobilization of shear stress along a rough
pile shaft in normally consolidated clay in terms of effective stresses acting
in the clay. Their predictions of the stress changes that occur in the soil
adjacent to the pile shaft were in a good agreement with some experimental results.
Frank (1991) discussed design of 4 buildings supported
on piled raft in Germany. The analysis shows that compared to a raft foundation,
piled raft system reduces the settlement about 50%. They have reported actual
measurements of pile head forces, contact pressure between raft and soil and
the settlements of piled raft foundation for some of these buildings.
Liu and Novak (1991) presented pilesoil static interaction
by the combination of finite and infinite elements. The pile and the near field
soil medium were modeled by finite elements, whereas the far field soil medium
was modeled by mapped infinite elements. Axially loaded single pile and single
pile with cap subjected to monotonic loading were investigated. Yamashita
et al. (1994) reported the behavior of a five story building on piled
raft foundation of size 24x23 m with 20 piles of length 16 m and diameter 0.75
m. The results of field observations during construction and analytical study
of the same building have been compared. Gandhi and Maharaj
(1996) investigated the load sharing between pile and raft based on threedimensional
linear finite element method. The effects of spacing, soil modulus and length
of pile on load sharing between pile and raft have been discussed. Poulos
(2001) studied about horizontal and inclined loading apply to pile raft
foundation. Maharaj (2003) presented the results based
on three dimensional nonlinear finite element analysis of piled raft foundation.
It was found that the ultimate load capacity of flexible raft improves with
increasing the soil modulus and length of pile. However, although increasing
the soil modulus reduced the overall settlement, it increased differential settlement.
Dynamic characteristic of piled raft foundation is also important and several
papers exist, which deals with the dynamic characteristics of a structure supported
by a piled raft foundation. Nakaia et al. (2004)
did studies about dynamic characteristics of piled raft foundations. Katzenbach
and Turek (2004) exhibited their research about effect of raft in piled
raft foundation. They used a centrifuge model test and its simulation analysis
was discussed, followed by a parameter survey based on the finite element analysis.
In the centrifuge models test, structures supported by a piled raft foundation
and by a pile foundation were considered. A parameter survey was performed from
the viewpoint of foundation types and types of connection between the raft and
the piles. It was found from this study that, although the effect of the pile
head connection on the behavior of a superstructure is fairly small, when it
compared to the type of foundation, it does affect the load bearing characteristics
of piles even when piles are not connected to the raft foundation. One of the
best ways to control the maximum and differential settlement of piled raft foundations
is to use piles with different lengths in this system. Tan
et al. (2005) researched about effect of using piled raft system
with different length of piles in very soft clay for a 5 story building. A monitoring
scheme on the structures was successfully implemented.
Based on study review, it is found that few studies are carried out on pile raft system with piles of different dimensions. The present research aims to analyze the piled raft foundation with piles of different dimensions by 3D finite element method. The soil has been modeled as DruckerPrager elastoplastic material. Based on finite element analysis loadsettlement curves have been produced for different condition.
CONSIDERATION OF FINITE ELEMENT MODEL
Simplified 3D finite element analyses are used to model the pile raft system
in this study. Plan of simplified 3D model is shown in Fig. 1
and the selected piled raft section is shown in Fig. 2. The
raft, pile and soil in the selected piled raft section have been defined by
solid 45 (brick 8 node) elements. The element types, used for this model, are
available in Table 1. As it can be seen, element Brick8nodeSolid45
has been used for pile, raft and soil, element Contact3Dsurface to surfaceConta174
has been used for contact and element Target 170 has been used for target in
the model. By using these elements all characteristics of the model can defined
in ANSYS software. An interface zone is introduced around piles to purpose approximately
the slip between the soil and pile. Considered soil depth in the analysis is
about 40 m and raft dimensions are 68x30 m.

Fig. 1: 
Simplified plan of 3D model of raft and connected piles 

Fig. 2: 
Section of simplified 3D model of raft and connected piles 
Table 1: 
Element types of materials used in modeling 

Source: Author’s computation 
Table 2: 
Material properties 

Source: Author’s computation 

Fig. 3: 
3D view of piled raft system with different pile diameters 

Fig. 4: 
3D view of different piled raft models and loading on them 
Concrete raft has 1.0 m thickness. In preliminarily model (piles with equal
diameter) the cast in place concrete piles with dimensions of (1x1x10 m) have
been considered. Then, in complimentary model, the square piles with 10 m lengths
and different dimensions (0.6, 0.6, 1, 1.4, 1.6 m) are constructed (Fig.
3). As shown in Fig. 4, different point loads has been
applied as concentrated loads on the respective nodes on the foundation.
Five different soils are used in two layers to achieve clear concepts of operation
in all conditions. The selected soil has been idealized by DruckerPrager elastoplastic
continuum.
Table 3: 
Model properties 

Source: Author’s computation 
The concrete cast in place piles and concrete raft are modeled with elastic
criteria. The properties of the material such as used model, internal friction
angle, Dilatancy, module of elasticity, Poisson’s ratio and cohesion of
the pile, raft and soils are shown in Table 2. These parameters
are in the range of moderate and prevalent values. The interface properties
zone is selected similar to the soil properties. Combinations of these 5 soil
types create 8 models with 2 layers. The models are used for 2 systems with
equal and unequal diameter piles. Definition of soil layers for different models
is shown in Table 3. Eight models have been analyzed which
their top and bottom layer of soil differ for each model. Authors have chosen
this layer in order to make comparison between different conditions.
In all proposed piledraft systems, 2 cases are compared:
• 
Pile raft with the same pile diameters (System 1) 
• 
Pile raft with piles of different diameters (System 2) 
RESULTS AND DISCUSSION
The results of three dimensional analysis of pile raft system with equal and unequal pile diameter, placed in different soils have presented and a comparison has been done between different models. The vertical settlement contours for one of the analyzed models is shown in Fig. 5. Different colors shows different amount of settlement and by taking distance from the pile raft system, the amount of settlements become lower. Figure 5 has been extracted from finite element analysis.

Fig. 5: 
Contours of vertical settlement for piledraft system with
piles of different diameter 
Table 4: 
Effect of using piles with different diameters on total and
differential settlements 

Source: Author’s Computation 
The general pattern of vertical settlement of foundation may be evaluated from
Fig. 5. The results of finite element analysis in selected
models, including the effect of using different pile diameters on total and
differential settlements are shown in Table 4. It can be seen
that using piles with different diameters lead to lower settlements than using
same diameter for all piles. It is because of creating more strength in places
that the structure is under higher loads and lower strength in places that the
structure sustains lower loads. On the other hand, the friction of piles in
different parts of foundation is various and causes the structure to undergo
lower differential settlement. Piles with larger diameters in places that sustain
higher loads cause to decrease the distance between piles and it leads to increasing
the axial stiffness of piles and subsequently increasing the load capacity of
foundation.
The settlements of pile raft system with equal and unequal pile diameters have
been obtained from analyses for each model and the amount of decreasing in total
and differential settlements have been compared (Fig. 6).

Fig. 6: 
Decrease amount in total vertical settlement when using pile
raft system with different pile diameters 
As it can be seen, maximum vertical settlement of each model (in percent) which
has extracted from finite element analysis has been presented. Analysis of model
1 which soft clay and dense gravel have been placed in top and bottom layer
respectively, shows that the maximum settlement reduces about 32% or 2.3 cm
comparing with equal diameter piles (13% or 0.8 cm). It can be said that whatever
the soil which the pile tip is placed on, be denser, more loads will be sustain
by pile tip than by fraction and it causes more loading capacity of foundation
and lower settlements too. Therefore, model 1, 6 and 2 which have denser soils
in bottom layer (the layer which pile tip is placed on it), have the higher
bearing capacity and model 5, 4 and 8 which have looser soils in bottom layer,
have lower bearing capacity in comparison with other models. This is clearly
shown in Fig. 6. However, if the lower soil be in saturate
condition, it is not economical to use this system.
Differential settlements of pile raft foundation with equal and unequal pile
diameters for each model are compared in Fig. 7. The amount
of decrease in differential settlements varies between 0.3 to 2.7 cm (66 and
96%). It is clearly understood that by using system 2 (pile raft system with
unequal pile diameters), in best conditions, in model 1 (top layer is soft clay
and bottom layer is very dense gravel) differential settlement decreases 96.4%
or 2.7 cm. This is shown in Fig. 8 along the length of raft
foundation and it can be seen that by taking distance from edge of raft foundation,
settlement decreases, which could be because of reduction in amount of stress
in soil. These results confirm the obtained results of Potts
and Martins (1982) which were in a good agreement with some experimental
results. Similar investigation on pile raft foundation with equal pile diameter
has been done by Maharaj (2003).

Fig. 7: 
Decrease amount in differential settlement when using pile
raft system with different pile diameters 

Fig. 8: 
Settlement along raft foundation length for model 1 
However, if the bottom layer be a soft soil, using piled raft system with different
pile diameters cannot be a good way to control the maximum and differential
settlement of raft system and structure. In this case, using other ways such
as piled raft system with piles of different lengths may be a good attitude
to control maximum and differential settlements. Tan et
al. (2005) researched about effect of using piled raft system with different
length of piles in very soft clay.
From previous discussion, it can be concluded that pile raft systems with different pile diameters show better performance in comparison of systems with equal diameters. It is because of the more proper design of pile raft system; in places where higher loads are applied to the system, thicker piles are placed which can control the settlement and increase the bearing capacity of the system. On the other hand, in places under higher loads, larger diameters of piles cause a decreasing in the space between piles and consequently increase the bearing capacity of pile raft system.
CONCLUSIONS
Due to obtained results the following conclusions may be drawn:
• 
Using pile raft with different pile diameters in all types
of soils, with unequal applied loads, has better operation than piled raft
system with similar piles. But its behavior is not the same in all soil
conditions. For example if the top layer is soft clay and the bottom layer
is very dense gravel the operation of this system is better than the others 
• 
Using piles with different diameters lead to lower total settlements than
using same diameter for all piles. It is because of creating more strength
in places that the structure is under higher loads and lower strength in
places that the structure sustains lower loads 
• 
In the best condition by using pile raft with different pile diameters,
the maximum and differential settlement decrease 2.3 cm or 31.9% and 2.7
cm or 96.4%, respectively; this is an appropriate way to control the settlements
of foundations 
• 
Using piled raft system with different pile diameters can be a good suggestion
to control the maximum and differential settlements of raft system and structure
if the bottom layer is a dense soil. Besides it has economic advantages 
• 
If the bottom layer be a soft soil, using piled raft system with different
pile diameters can’t be a good way to control the maximum and differential
settlement of raft system and structure. In this case, using other ways
such as piled raft system with piles of different lengths may be a good
attitude to control maximum and differential settlements 
ACKNOWLEDGMENT
The authors are very grateful to Dr. Mehrab Jesmani for his fruitful discussions about finite element modeling.
NOTATIONS
n° 
= 
Internal friction angle 
Ψ° 
= 
Dilatancy

E 
= 
Module of elasticity (MPa) 
υ 
= 
Poisson ratio 
C 
= 
Cohesion (kN m^{2}) 