Available via license: CC BY-NC-SA 4.0
Content may be subject to copyright.
VOLUME 7 NO. 2, OKTOBER 2011
39
FLOATING RAFT-PILE FOUNDATIONS ANALYSIS
USING NUMERICAL SIMULATION
Helmy Darjanto1
ABSTRACT
The numerical simulation of raft-pile foundations subjected to vertical load is presented in this
paper. For comparison study, numerical models of single raft and pile groups are completed. The
numerical models are adopting the elastic constitutive law for the materials. The stresses and
vertical displacement of the models are observed. The behaviour of the raft-pile foundation
compared to the pile-group is then investigated. The results using the same external load show that
the raft-pile foundation has smallest displacement compared to the others. In terms of stresses, the
raft shows contribution of the load transfer to the underneath soil as well as the piles. Moreover, the
behaviour of the raft-pile system appears to be a combination of the pile-group and the single raft.
In order to estimate the bearing capacity of the raft-pile system, it is suggested that the contribution
of the raft should be included in addition of the piles’.
Keywords: raft-pile foundation, soil-structure interaction, floating foundation
1. INTRODUCTION
The total load of the pile groups involving the contribution of the cap using the numerical
simulation has been purposed by (Valliappan, 1999). The pile groups including the effect of the
cap transfer the load were then defined as the Raft-pile foundations. In this study, the raft-pile
foundations are formed as a solid structure. Then the effects of each element forms the foundation
can not be figured out. However in the practice, the group foundation is made of number of single
piles which individually has a load capacity and a cap on the ground.
The proposed method for analyzing and designing the raft-pile system has been published (Davis,
1987). Indeed, the scheme for solving the problem is based on the analysis of the group of the piles
rather than the behaviour of the system. Moreover, the proposed formulas are inadequate to be
adopted for describing the behaviour of the system.
When a group of piles is made up of several individual piles, the load capacity of the group cap
may not be the same as the sum of the load capacity piles. The effect of grouping the piles arises
the different amount of the group capacity and the sum of the individual contributing piles in term
of efficiency of the pile group. Based on the studies in the past, number of references have
suggested the formulas to estimate the pile group efficiency (Das, 1990 and Boowles, 1988).
In practices, even the pile cap commonly poured directly on the ground and effect the load transfer
mechanism, the effect of the cap to transfer the load to the underneath soil was usually unobserved.
The contribution of the cap which plays the important roles to group the piles has not been studied
well. Here, the effect of the cap of the pile groups is observed using numeral simulation. The term
of raft-pile foundation is then adopted for describing the system of the foundation.
Floating Raft-Pile Foundation Analysis
Using Numerical Simulation
40 | JURNAL REKAYASA SIPIL
A suggestion for the use of the virtual block capacity has been madein the past (Boowles, 1988).
The analysis is based on the shear around the block plus the block bearing point instead of sum of
the capacity of the piles. Then (Das, 1990) recommended adopting the lower values between those
two amounts as the ultimate load of the group.
The effects of the piles and the cap in terms of stresses of soil underneath the foundation are
studied here. The state of the art of the group efficiency formula employed to outline the load
capacity is discussed. The formulas suggested by (Hakam, 2004) and (Hakam, 2005) for floating
raft pile system in soft clays is then reviewed.
2. LOAD CAPACITY OF RAFT-PILE SYSTEMS
Based on several tests of foundations in laboratory (Hakam, 2004) analyzed the efficiency of the
raft-pile foundation which is defined as ratio of the system compared to the sum of the individual
pile and the raft. The efficiency of the raft-pile system, Erp is written as:
capacities raft and pile individual of sum the capacity pile-raft the
rp
E=
Using the above equation, the efficiencies of the raft-pile system number of tests are found higher
than 100%.
Since the efficiency of the raft-pile system is greater than the sum of pile and raft capacities, it is
suggested that for practical purposes to use the sum value of the piles and the raft that for load
capacity purposes (Hakam, 2005). Afterward, for a raft-pile foundation floating in soft clay, the
total load capacity of the system can be estimated as;
QT = QR + Σ (QP + QS)
Where QR is the load capacity of the raft (in the pile group case, it is the cap), QP and QS are the
bearing capacity of the pile at the tip and the skin resistance respectively.
The resistance of square raft foundation is thereafter predicted using the ultimate load capacity in
the form;
QR = Ab Ft Cu Nc*
Where, Ab is the cross section area of the foundation at the base, the bearing capacity factor Nc* is
5,14 and the value of the type factor Ft is 0.45 which represents the value for the punch failure. For
strip foundations with length-width ratio equal or greater than one and a half, the ultimate load
capacity Qu must be reduced by the factor of 0,77.
The ultimate point bearing capacity of pile can be estimated using;
QP = AP Cu(p) Nc
Where Cu(p) is undrained cohesion soil strength at the pile tip, AP is the cross section area of the
pile tip and Nc is the bearing capacity factor, it is 9 for Meyerhof’s and 5,7 for Janbu’s one.
However, since the piles are considered as floating one, the tip resistance will not be significant to
contribute the pile capacity.
Helmy Darjanto
VOLUME 7 NO.2, FEBRUARI 2011 | 41
The skin resistance for pile with the perimeter, Θ, is the sum of the resistance every length section,
∆L, that is calculated using;
Q
S = Σ (CuΘ∆L)
3. NUMERICAL SIMULATIONS AND RESULTS
The numerical tool used in this simulation is the finite element method. The raft and the soil are
modeled using three dimensional solid elements while the piles are modeled as beam elements. The
vertical load set on the top of the raft is 20 ton/m2. The soil has the modulus of elasticity and
Poisson’s ratio of 20 kg/cm2 and 0.4 respectively. For the raft and the piles that are 200000 kg/cm2
and 0.2. The diameter of the piles is 10 cm, the length of 150 cm and spacing of five times of the
diameter. The raft is square in shape with the width of 100 cm. The sketch of the simulation model
and the boundaries are shown in the Figure 1. The results are presented in the form of stress
contours and displacements in the following sections.
In the terms of vertical stresses for raft, pile group and raft-pile are shown in Figure 2,3 and 4
respectively. The colours of the contours are indicating the stress ratio compared to the total
applied load of 20 t/m2 as follow: pink, red, brown, yellow, green and blue that are -0.5, -0.3, -0.25,
-0.15, -0.1 and -0.01. For shear stress contour (Figure 5 - 7), the same colours are indicating stress
values of -0.3, -0.1, -0.05, 0.0, +0.05, +0.1 and +0.3 respectively.
Area of interest
10 m
5.5 m
Figure 1. 3D Numerical Model
Floating Raft-Pile Foundation Analysis
Using Numerical Simulation
42 | JURNAL REKAYASA SIPIL
Figure 2. Vertical Stress of Raft Foundation
Figure 4. Vertical
Stress
o
fTheRaft
-
Pile
Figure 3. Vertical Stress of The Pile-Group
-blue
-green
-yellow
-brown
-red
-pink
Helmy Darjanto
VOLUME 7 NO.2, FEBRUARI 2011 | 43
The normal stress in the soil for the single raft concentrates right under the base of the raft. Then it
reduces gradually as it is away from the base (Figure 2). For the pile-group, the normal stress
concentrates just around the tip of the piles, and reduces as it is far from. While, along the pile, the
normal stress is not significant, it can be understood since in this area, the shear stress is dominant
(Figure 3 and 6). For the raft-pile system, the compression in the soil is concentrate in two areas,
right in the base of the raft and in the area around the piles’ tip. Meanwhile along the pile between
those area, the normal stress in reduces as it shown in the pile-group. It shows that the normal stress
behaviour of the soil is combination between the raft and the piles (Figure 4). In the other words,
the vertical load on the top of the raft-pile system is transferred in terms of normal stress to
underneath soil under the base of the raft as well as under the tip of the piles.
Figure 5,6 and 7 show the shear stresses for raft, pile group and raft-pile under the foundation,
respectively. The fart-pile foundation figure shows the deeper shear stress bulb compared to the
others. It means that the soil deal with the shear stress covers up bigger area and then it gives
greater value in term of load capacity.
Then, with the same vertical load applied on the top of the foundations, the maximum
displacements of the foundation are presented in the Table 1.
The maximum displacement of each type of model gives the sensibly large values for practice. The
reason is the vertical load on the top of foundation is large enough since the soil parameter
performing the soft soil. However, the displacement of raft-pile gives the smallest value compared
to the others. In the other word for the same displacement allowed, the raft-pile can restrain greater
load than the others.
In fact, it is unrealistic to expect reliable good bearing capacity on soft soils. So, it is reasonable to
take into account every element of the system that contributing to support external load. Then, the
load capacity of the raft-pile must include the part of piles as well as the raft. Using combination of
classic formulas, the procedures to estimate the load capacity as described in the beginning section
is very worthy to be adopted. Furthermore, if the conventional load capacity formulas are
considered, the efficiency of the raft-pile system must be defined as a ratio of the system compared
to the sum of the individual pile and the raft.
Table 1. Maximum Displacement of Foundations
Foundation type Displacement (cm) Ratio to pile-group
Raft 13.6 108 % (8% greater)
Pile-group 12.6 100 %
Raft-pile 11.7 93 % (7% less)
Floating Raft-Pile Foundation Analysis
Using Numerical Simulation
44 | JURNAL REKAYASA SIPIL
Figure 5. Shear Stress Under The Raft
Figure 6. Shear Stress For The Pile-Group
Figure 7. Shear Stress For The Raft-Pile
Helmy Darjanto
VOLUME 7 NO.2, FEBRUARI 2011 | 45
4. CONCLUTIONS
The contribution of raft transferring superstructure load to the soil is conventionally ignored.
However for raft-pile foundations on soft to very soft soils, ignoring the raft contribution to the
foundation-soil interaction is practically extravagant. In fact that the raft can give the contribution
up to 30 percent of the system support, the value is principally important. Since using classic
formula of the group efficiency with the maximum value is 100% rarely happen, the effect of the
raft to the foundation system can not be simply discarded. Based on the numerical simulation, the
raft contribution transferring the load to the underneath soil in raft-pile system can clearly be
shown in terms of stress diagrams. In terms of displacement, the raft pile showed smallest value
than the displacements of pile group and the single raft.
5. ACKNOWLEDGEMENT
A great thanks is offered to Zahratul Husni who has given important contribution in this
work.
REFERENCES
Bowles, J. E., (1988), “Foundation Analysis and Design, McGraw-Hill Book Company”,
Singapore.
Das, B. M., (1990), “Principles of Foundation Engineering”, PWS-KENT Publishing
Company, Boston.
Davis, E.H. and Poulos, H.G., (1972), “The Analysis of Pile-Raft Systems, Aust.
Geomechanics Journal”, Vol. G2, no.1, pp 21-27
Hakam, A., Darjanto, H and Soepriono, Dj., (2004), “Floating Raft-Pile in Soft Clay”,
Jurnal Teknik Sipil, Univ. Tarumanegara, No.3, Tahun ke-X, pp 249-262.
Hakam, A., Novrial, Pane, I F., (2005), “Load Capacity of Floating Raft-Pile”, Atrium,
Universitas Sumatera Utara, Vol. 02, No.1, pp 5-14.
Valliappan, S., Tandjiria, V. and Khalili, N. , (1999), “Design of Raft-pile Foundation
Using Combined Optimization and Finite Element Approach”, International Journal
for Numerical and Analytical Methods in Geomechanics, Vol. 23, pp 1043-1065.
Floating Raft-Pile Foundation Analysis
Using Numerical Simulation
46 | JURNAL REKAYASA SIPIL
