Analytical Approaches for Analysis of Piled-raft Systems

International Journal of Advanced Engineering Technology E-ISSN 0976-3945

IJAET/Vol.II/ Issue IV/October-December, 2011/431-434

Research Article

ANALYTICAL APPROACHES FOR ANALYSIS OF PILED-RAFT

SYSTEMS Tejendra G Tank

1, Dr. S. P. dave

2

Address for Correspondence 1Research Scholar,

2Associate Professor,

Applied Mechanics Department, L. D. College of Engineering, Gujarat Technological University, Ahmedabad,

Gujarat (India)

ABSTRACT

At places where clay deposit are of larger thickness, and if it possesses sufficient strength (qu>100 KN/m2), raft foundation can be

employed. If the foundation has a very poor strength (qu=0 to 25 KN/m2), purely pile foundation will prove to be a better option.

But if the clay deposit has an intermediate strength (qu=50 to 100 KN/m2), the only option available is piled-raft foundation

which is economical since the piles help in reducing settlements and the raft provides an ample bearing capacity as well as

resistance to differential settlements. Thus piled-raft is a good alternative at places where more total settlements are permissible

for the structure along with a considerable bearing capacity. This review paper aims with an objective to summarize the

analytical approaches for the analysis of combined piled-raft systems which is an emerging concept specifically when foundations

are to be designed for clay deposits.

KEYWORDS Piled-Raft foundation, approximation method, finite element analysis, non-linear analysis of piled-raft, Poulos-

Davies-Randolph method.

I. INTRODUCTION

From the literature available, there are no particular

design rules or specifications developed for piled-raft

foundation2. It the only alternative available in certain

unavoidable circumstances such as places where there

is need of optimum bearing capacity with permissible

settlements, and when differential settlements are also

to be looked forward2. Piled-raft can be adopted

without any hesitation as the piles give resistance to

settlements and raft has two important roles to play.

• To provide bearing capacity to the

foundation.

• To avoid differential settlements.

Providing adequate bearing capacity to the foundation

is the main function of raft, but it also helps to avoid

the hindrance caused to the adjacent structures due to

differential settlement of one structure and maintains

the stability of the structure too. The main advantage of

piled-raft foundation is that less length of pile is

required in comparison to a complete pile foundation.

Maximum and differential settlements are reduced and

hence there is a considerable improvement in

serviceability criteria. Bearing capacity of shallow

foundations is increased using the load sharing

mechanism between pile and raft. Due to less

settlement, distress caused to adjacent structures is

reduced. Thus piled-raft system proves to be

economically beneficial.

II. DIFFERENT APPROACHES AVAILABLE

FOR ANALYSIS

A. Approximation method

In this particular method the raft is treated as a plate,

piles are considered as springs and the underlying soil

as an elastic continuum3. Here the interaction effects

between the piles are ignored. In this method, many

researchers made several methods so that satisfactory

results can be obtained in approximate method too.

Randolph (1983) presented a method to compute the

interaction between single pile and a circular shaft.

Flexibility matrix method was then used here to

calculate the overall stiffness of piled-raft foundation

by combining the individual stiffness of single piled-

raft unit. Kitiyodom and Matsumoto (2003) presented

an approach in which the piles were modeled by elastic

beams and the interactions between structural members

were approximated by Mindlin’s solutions. The

foundations can be subjected to both axial and lateral

loads and embedded in non-homogeneous soil. This

approach incorporated both the vertical and lateral

resistance of the piles and the base of the raft in the

analysis.

B. Finite Element Analysis

The finite element method is one of the powerful

techniques for analysis of piled raft systems. In order

to reduce more rigorous computational efforts,

problems are simplified into an axisymmetric problem

or a plane-strain problem3. In the year 2001 Prakoso

and kulhawy analyzed piled raft foundations by using

linear elastic and non-linear plane strain finite element

models involving the analysis of three dimensional

piled-rafts as a two-dimensional strip piled raft. Here

six nodded triangular elements were used to model the

piled-raft and the soil. Here since the rows of piles

were simplified into strips, the row of pile in-plane has

to be simplified into a plane strain pile with an

equivalent pile young’s modulus E(eq) in terms of

number of piles in row considered as below

E(eq) = (np(row-i).Ap.Ep) / Lr.Dp

Where,

np(row-i) = Number of piles in row “I”

Ap = Area of pile cross section

Ep = Young’s modulus of pile

Lr = Length of raft

Dp = Pile diameter



Mandolini and Viggiani (1997) presented an analysis to

predict the settlement of piled raft foundations. The

method takes into account the soil-structure interaction

and non-linear behavior at the pile-soil interface. The

piles were analyzed by the boundary element method

and the behavior of a pile group embedded in an elastic

continuum was then analyzed based on the use of

interaction factors. The raft was analyzed by the use of

the finite element method and the interaction between

the piles, raft and soil was represented by a linear

elastic model.

C. Non Linear analysis of Piled-Raft3

The general load-settlement pattern of piled raft is as

shown in Figure – 1. When the piled raft is loaded

below Pe, the behavior of pile as well as raft is elastic.

When it is loaded between Pe and Pu, the interface

between the soil and the pile starts to slip. The load in

excess of Pe is carried by raft alone only when the pile

capacity is mobilized. As shown in graph, when the

load reaches Pu, both pile as well as raft reach their

ultimate bearing capacity and thereby they can no

longer take additional loads. Hence we can see the

non-linear behavior of the foundation. Now to

stimulate the slip occurring at the interface, the analysis

process is implemented through an incremental-

iterative process. The application of loads is done in

increments and the raft-soil and pile-soil interfaces are

computed for each increment. Such interface forces

obtained are than compared with the limiting contact

pressures acting on the raft. The calculation of limiting

forces is done from the shear strength of the soil, Su.

Thus the limiting loads along the pile shaft for any pile

element ‘x’ is,

LRx = ca.C.δz

The limiting base load at pile base is given by,

LB = Nc.Su.A

Where,

ca= (Su. α) = Pile-soil adhesion.

C= Pile circumference

δz= Length of pile element ‘x’

α = Adhesion factor (as function of Su)

Nc= Bearing capacity factor (generally it is taken as

9 for piles in clay)

A= Area of pile base

Su= Shear strength of soil

Figure – 1 Load-Settlement pattern of Piled-

raft

As far as non-linear analysis of piled raft is concerned,

the effect of L/d ratio on settlement is as shown in

figure – 2.

Figure – 2 Effect of pile length on settlement

The effect of L/d ratio on load carrying capacity of

piles is shown in figure – 3 below.

0

100

5 10 15 20 25 30 35 40 45 50

% of load on piles

L/d

Effect on Load carried by

piles

Figure – 3 Effect of pile length on load on piles

D. Poulos-Davis-Randolph Method

The Poulos-Davis and Randolph method is a powerful

tool as far as the load carrying between pile and raft is

to be found out. This method gives directly the amount

of total load carried by raft. The remaining load

thereby is carried by the piles. The load settlement

pattern shown in figure–1 applies to the PDR method

too. It is seen that within elastic limit, the stiffness of

foundation is of raft alone until it reaches plastic limit1.

To find the vertical bearing capacity of a piled raft

foundation using manual approaches, the ultimate load

capacity can generally be taken as the lesser of the

following two values:

• The sum of the ultimate capacities of the raft

plus all the piles

• The ultimate capacity of a block containing the

piles and the raft, plus capacity of the portion of

the raft outside the periphery of the piles5.

Using this approach, the stiffness of the piled raft

foundation can be estimated as follows4

2.

(1 2. )

(1 )

p r cp

r pcp

K KKpr

K K

αα

+ −=

− ( )i− − − −−

Where,

2Area of raft

(1 )

r

s

GKr

I µ=

−

Where,



1 0.5B

Gr BL

= − sµ = Poisson’s ratio of Soil = 0.25

I = Influence factor for Raft = 1.2

pK =Entire Method given by Randolph as

mentioned below.

0

0

. 0.

4 2 tanh( )

(1 )

4 tanh( )1

(1 )

p

s

pi t

s

vI L

Pt vI r

vI LG r S

vI r

η πρµ ξ ς

ηπλ µ ξ

+ −= + −

Where,

iG = Shear Modulus of stiff clay = 150.Cu

Where,

Cu = 100 + 7.2(z)

z = Depth of pile tip from ground

pL = Pile length

0r = Pile radius

*G

Giρ =

Where,

0*

2

iG GG

+=

0 (150)( ,G Cu= At ground level)

i

b

G

Gξ =

Where,

i bG G= (Since shear modulus of stiff clay is equal to shear

modulus of stiff clay below pile tip at base.)

p

i

E

Gλ = = Pile soil stiffness ratio.

Where,

pE = Modulus of elasticity of pile material

0

b

r

rη = = Ratio of under ream of under reamed

piles

Where,

or = Pile Radius

br = Under ream increase radius of pile

m

o

rIn

rζ =

= Measure of radius of influence of pile

Where,

[ ]0.25 (2.5 (1 ) 0.25) .m s pr Lξ ρ µ= + − −

0

2

pLvI

r ζλ =

o.5

Putting all above parameters and finding the value we

get,

t

t

PK

S=

Thus we get stiffness of single pile

If we want settlement of single pile tS , we get it as

ttP

SK

=

Now stiffness of pile group can be obtained by:

.n.p wK Kη=

Where,

wη = n-e

n = Number of piles

e = Efficiency exponent

If we want settlement of pile group ( )pgS , we get it as

upg

p

PS

K=

Also , cpα can be obtained from equation below:

0

1 lnc

cp

r

rαζ

− =

Now since we have values of ,p rK K and cpα , we

can calculate prK from equation - ( )i

Thus percentage of total load on foundation shared by

raft can be calculated as:

)

(1 )

(1 2

r cp

t cp

p kr

P kp kr

αα

− = + − Where,

rp = Total load on Piled-Raft

If , 0.45,r

t

p

p= than one can conclude that 45

percent of total load will be shared by raft and rest will be

taken by piles.

III. CONCLUSIONS

• The approximation method allows only

vertical interaction between the raft piles and

the soil. The results obtained by

approximation method vary greatly.

• In finite element method for elastic-plastic

modeling, simplifications are necessary to

make same compression for equivalent plain

strain pile and in-plane row of piles.

• As the length of pile increases to a ratio of L/d

= 30, the settlement decreases.

• As the pile length increases to the ratio of L/d

= 30, the load carried by piles increases.

• Beyond L/d > 30, the pile length has little

effect on the settlement and the load carrying

capacity of piles.

• In most cases of piled raft, the amount of total

load carried by pile varies from 55 to 65

percent and that by raft varies from 35 to 45

percent.



• As the soil stiffness increases, the percentage

load shared by raft also increases with

increase in spacing between piles in Piled-Raft

system.

• As the length of pile increases, percentage

load taken by raft reduces (for a constant

thickness of raft).

• Increase in pile length results in increased

stiffness of pile approximately in the same

proportion as that of increase in diameter.

• As the stiffness of Piled raft increases,

settlement of foundation reduces.

• As the thickness of raft increases the

settlement reduces due to flexible behavior of

raft, but later on with increase in thickness of

raft, the settlement increases because of rigid

behavior of raft.

REFERENCES

1. Lecture note # 9, University of Texas at Arlington,

Geotechnical Engineering Laboratory, page 3.

2. Carsten Ahner and Dmitri Sukhov , “Combined

piled-raft foundation (CBRF) – safety concept”,

Institute of Concrete and Building Materials,

University of Leipzig, 2000.Page 334.

3. Helen Sze Wai Chow, Report on “Analysis of

piled-raft foundation with piles of different lengths

and diameters”, University of Sydney, 2007, page

23, page 184.

4. Gandhi S R, Maharaj D K, “Design of pile group

and pile cap”, Seminar by Indian geotechnical

society, Madras. Page 4.

5. Poulos H G, “Methods of analysis of Piled-Raft

foundations”, Report by Coffey Geosciences Pvt.

Ltd. & The university of sydney, Australia, July

2001, Page 4. 6. Gandhi S R, Maharaj D K, “Behaviour of piled-raft under

uniform loading”, Paper presented at Indian Geotechnical Conference, Bangalore. December 1995 Vol – 1. Page

170.

Documents

Analytical Approaches for Analysis of Piled-raft Systems