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ANALYSIS OF PILED RAFT FOUNDATION
A DISSERTATION Submitted in partial fulfillment of the
requirements for the award of the degree of
MASTER OF TECHNOLOGY In
CIVIL ENGINEERING (With S:peciaiizationi in Geotechnical Engineering)
By ALOK KU MAR
DEPARTMENT OF CIVIL ENGINEERING INDIAN INSTITUTE OF TECHNOLOGY ROORKEE
ROORKEE - 247 667 (INDIA)i JUNE, 2006
CANDIDATE'S DECLARATION
I hereby declare that the work which is being presented in the dissertation entitled
"ANALYSIS OF PILED RAFT FOUNDATION" in partial fulfillment of the
requirements for the award of the degree of Master of Technology in Civil Engineering
with specialization in Geotechnical Engineering submitted in the Department of Civil
Engineering, Indian Institute of Technology Roorkee, is an authentic record of my own
work carried out for a period from August, 2005 to June, 2006 under the supervision of
Dr. G. Ramasamy, Professor, and Dr. Priti Maheshwari, Lecturer, Department of Civil
Engineering, Indian Institute of Technology Roorkee, Roorkee.
The matter embodied in this dissertation has not been submitted by me for the
award of any other degree.
Place: Roorkee
Date:24Iune, 2006 (ALOK KUMAR)
CERTIFICATE
This is to certify that the above statement made by the candidate is correct to the
best of our knowledge.
(Dr. G. RAMASAMY) Professor, Department of Civil Engineering Indian Institute of Technology, Roorkee Roorkee-247 667 Uttaranchal India
(Dr. PRITI MAHESHWARI) Lecturer,
Department of Civil Engineering Indian Institute of Technology, Roorkee
Roorkee-247 667 Uttaranchal
India
ACKNOWLEDGEMENT
I express my deep sense of gratitude and sincere thanks to Dr G. Ramasamy,
Professor, Dr. Priti Maheshwari, Lecturer, Civil Engineering Department, Indian
Institute of Technology Roorkee, Roorkee for their valuable guidance. This work is
simply the reflection of their thoughts, ideas, and concepts and above there efforts. I am
highly indebted to them for their kind and valuable suggestions and of course their
valuable time during the period of the work. The huge quantum of knowledge I had
gained during their inspiring guidance would be immensely beneficial for my future
endeavours.
I shall be failing in my duty if I do not record my gratitude to my parents, friends
and other well wishers, who form an important part of my life, for their vicarious support
and enthusiastic help, without which this work might not have been in its present form.
Place: Roorkee
DateAlune, 2006 (ALOK KUMAR)
ii
ABSTRACT
Piled raft foundations are adopted to reduce the total and differential settlements of
foundations. In the present study, analysis of piled raft foundation is done by "Plate on
Spring" approach in which the raft is represented by an elastic plate while the soil and
piles are modeled as bed of equivalent spring at nodal points and intersecting spring
respectively. Finite difference method is used for the analysis of the foundation system.
The stiffness of pile is estimated by procedure given by Hazarika and Ramasamy (2000).
For the estimation of soil stiffness a method by De-beer and Martens (1975) is employed
for sand. For clays the same is estimated using immediate settlement and e-log p curve.
Software for the analysis of raft using finite difference method, estimation of stiffness for
soil and pile and the structural design of raft and pile is developed in MATLAB. Using
this software a typical case study is analyzed and results are presented. Effect of
coefficient of subgrade reaction of soil and pile stiffness on the settlement and bending
moment of raft are studied. Present study show that increase in coefficient of subgrade
reaction by three to four times, reduces the settlement by 55% to75% and bending
moment by 9.55% to 20% respectively. Piles located at boundary corner are more susceptible to tilting of pile in comparison to interior nodes.
iii
CONTENTS
CHAPTER
1.
2.
TITLE PAGE No.
CANDIDATE'S DECLARATION ACKNOWLEDGEMENT ii
ABSTRACT iii
LIST OF TABLES vii
LIST OF FIGURES viii
INTRODUCTION
1.1 General 1
1.2 Objectives and outline of Present Work 1
1.3 Thesis organization 2
LITERATURE REVIEW 2.1 General 3
2.2 Methods of Analysis of Piled Raft Foundation 4
2.2.1 Strip on Spring Approach 4
2.2.2 Plate on Spring Approach 5
2.2.3 Boundary Element Methods 5
2.2.4 Three Dimensional Finite Element Analysis 7
2.2.5 Simplified Finite Element Analysis 7
2.2.6 Simplified Analysis Methods 7
2.2.6.1 Poulos-Davis-Randolph (PDR) method 7
2.2.6.2 Burland's approach 10
3. PROPOSED METHOD OF ANALYSIS OF PILED RAFT FOUNDATION
3.1 General 12
3.2 Analysis of Raft by Finite Difference Technique 13
3.2.1 Governing Differential Equations 13
3.2.2. Steps in Analysis of Raft Slab 15
3.2.3 Governing Differential Equations in Finite
Difference Form 16
3.2.4 Treatment of Column Loads 21 #
3.2.5 Treatment of Moment Loading 22
3.3 Procedure for Estimation of Individual Element Stiffness
of Piled Raft Foundation 22
3.3.1 Stiffness Estimation of Soil below the Raft 22
3.3.1.1 Settlement of cohesive soils 23
3.3.1.2 Settlement for cohesionless soil 25
[De Beer and Martens Method (1957)]
3.3.2 Estimation of Stiffness for the Individual Pile 27
3.3.2.1 Estimation of shaft resistance and tip resistance 27
3.3.2.2 Estimation off„,,„ and qmax. 28
4. STRUCTURAL DESIGN OF RAFT AND PILE FOUNDATION
4.1 General 32 4.2 Design of Raft as a Flat Slab 34
4.2.1 Strips of Flat Slab as Raft 34
4.2.2 Proportioning of Raft Slab 34 4.2.3 Reinforcement Detailing 39
4.2.4 Summary of Steps in Design of Raft Slab 40 4.3 Design of Piles 40
4.3.1 Steps in Design of Pile Foundation 41 5. SALIENT FEATURES OF THE PACKAGE
5.1 General 44 5.2 Features of Package 44
6. RESULTS AND DISCUSSION 6.1 General 46 6.2 Verification of the Problem 46
6.2.1 Raft Foundation 46
6.2.2 Piled Raft Foundation 49 6.3 Parametric Studies 59
6.3.1 Effect of Coefficient of Subgrade Reaction 59 6.3.1.1 Effect of coefficient of subgrde reaction on deflection 59 6.3.1.2 Effect of coefficient of subgrade reaction on
bending moment 61
6.3.2 Effect of Stiffness of Pile 66
6.3.2.1 Effect of stiffness of pile on deflection of nodes 66
6.3.2.2 Effect of stiffness of piles on bending moment 68
6.3.3 Effect of Tilting of Pile 73
CONCLUSION AND SCOPE FOR FURTHER WORK 76
REFERENCES 77
LIST OF TABLES
Table Title Page No. No.
3.1 Values of Influence Factor I (Schleicher,1926) 25
3.2 Values of Ks (Tomlinson, 1987) 28
3.3 Values of tan 8 (Tomlinson, 1987) 28
3.4 Values of Ko (Tomlinson, 1987) 28
4.1 Coefficient of R (Limit State Method) 38
6.1 Details of Problem of Raft Foundation (Teng, 1969) 48
6.2 Comparison of Deflection at various nodes 49
6.3 Details of Five-Storied Building at Urawa City (Japan) 52 [Yamashita et al. (1994)]
6.4 Details of Soil Profile (Yamashita et al. 1994) 52
6.5 Location and Load Coming on the Pile 53
6.6 Computation for Pile Stiffness 54
6.7 Computation for Raft Stiffness 55
6.8 Deflection at Different Nodal Points for Raft foundation 56
6.9 Deflection at Different Nodal Points for Piled Raft foundation 57 6.10 Salient Design output for Raft and Piled Raft Foundation 58 6.11 Effect of k on Deflection 60 6.12 Effect of k on Bending Moment in X direction 62 6.13 Effect of k on Bending Moment in Y direction 63 6.14 Salient Design output for Raft Foundation 64 6.15 Effect of Stiffness of Pile on Deflection 67 6.16 Effect of Stiffness of Pile on Bending Moment in X direction 69 6.17 Effect of Stiffness of Pile on Bending Moment in Y direction 70 6.18 Salient Design output for Piled Raft Foundation 71 6.19.a Settlement of Nodes Due To Tilting 74 6.19.b Percentage Increase in Settlement of Nodes Due To Tilting 75
vii
LIST OF FIGURES
Fig. No. TITLE Page No. 1.1 Raft and piled foundation 2 2.1 Plate on Spring Model of Piled Raft Foundation 5 2.2 Typical Pile Groups (a) Piled Raft (b) Free Standing Group 6 2.3 Simplified Representation of a Pile Raft Unit 8 2.4 Burland's Simplified Design Concept 10 3.1 Plates on Springs Model of Piled Raft Foundation 12 3.2 Raft Slab in Grid Form 15 3.3 Typical Location of Interior Nodes 16 3.4 Typical Location of Boundary Nodes 17 3.5 Typical Location of Boundary Corner Nodes 19 3.6 Treatment of Column Loads 21 3.7 Distribution of Load at Nodes 22 3.8 Layered Soil Profile Considered 23 3.9 e-log p Curve for Cohesive Soils 23 3.10 Pressure vs. Settlement Curve for Raft 26 3.11 Axially Loaded Piles 29 3.12 Loads vs. Settlement Curve for Pile at Pile Head 31 4.1 Common Types of Raft Foundations 33 4.2 Division of Flat Slab into Column Strips and Middle Strips 35 4.3 Critical Sections for Shear in Flat Slabs 37 61. Details of a Footing Problem of Supporting a Column (Teng, 1969) 47 6.2 Bending Moments along Center Line of Footing 48 6.3 Elevation of Building (Yamashita et al. 1994) 50 6.4 Foundation Plan of Five Stories Building Urawa City (Japan) 51
(Yamashita et al. 1994) 6.5 Load vs. Settlement Curve for pile 54 6.6 Pressure vs. Settlement Curve for Raft 55 6.7 Deflection vs. Nodal points along A-A for Raft and Piled
Raft Foundation 58 6.8.a Deflection vs. Nodal Points along Section A-A 61
viii
6.8.b Deflection vs. Nodal Points along Section B-B 61
6.9.a Bending Moment in X- Direction vs. Nodal Point along Section A-A 64
6.9.b Bending Moment in Y- Direction vs. Nodal Point along Section A-A 65
6.9.c Bending Moment in X- Direction vs. Nodal Point along Section B-B 65
6.9.d Bending Moment in Y- Direction vs. Nodal Point along Section B-B 65
6.10.a Deflection vs. Nodal Points along Section A-A 68
6.10.b Deflection vs. Nodal Points along Section B-B 68
6.11.a Bending Moment in X- Direction vs. Nodal Point along Section A-A 71
6.11.b Bending Moment in Y- Direction vs. Nodal Point along Section A-A 72
6.11.c Bending Moment in X- Direction vs. Nodal Point along Section B-B 72
6.11.d Bending Moment in Y- Direction vs. Nodal Point along Section B-B 72
ix
CHAPTER 1
INTRODUCTION
1.1 GENERAL
Raft foundation is a structure which supports an arrangement of number of
columns in a row(s) to transmit load to the soil by means of continuous slab. It has an
advantage of reducing differential settlement as the concrete slab resists differential
movements between the loading positions. They are often required on soft or loose soils
with low bearing capacity as they can spread the loads over a large area.
Pile foundation is used when surface soil is unsuitable for shallow foundation, and
a firm stratum is so deep that it can not be reached economically by shallow foundation.
A pile foundation is generally much more expensive than a shallow foundation. It should
be adopted only when a shallow foundation is not feasible.
To overcome this issue, concept of piled raft foundation was developed. A pile
raft foundation (Fig.1.1) is the concept in which the total load coming from the
superstructure is partly shared by the raft through its contact with soil and the remaining
load is shared by piles through skin friction. A piled raft foundation is economical as
compared to the pile foundation because piles in this case do not have to penetrate to the
full depth of the clay layer but it can be terminated at higher elevation. Piled raft
foundations have been used successfully in Germany and other place where thick clay
deposits exist over large depth [Franke (1991), Yamashita et al. (1994)].
1.2 OBJECTIVES AND OUTLINE OF PRESENT WORK
In piled raft foundation, piles are provided to control settlement rather than carry
the entire load. Settlement and load carried by the piles and raft depend on the stiffness of pile and soil.
The objective of this study is to analyze and design the piled raft foundation.
Estimation of the stiffness of the soil and the pile is come out and the effect of different
values of stiffness is studies to reach this objective.
For analysis purpose, the raft is represented by an elastic plate, while the soil and
the piles are modeled as bed of equivalent spring at nodal points and interesting spring
respectively. Software for the analysis of raft using finite difference method, estimation of
1
/X-N,
Raft Pit es
Clay Layer
(a) Raft foundation. (b)- Piled raft foundation
stiffness for soil and pile and the structural design of raft and pile is developed in
MATLAB.
Fig 1.1 Raft and piled foundation
1.3 THESIS ORGANIZATION
Present thesis comprises of seven chapters as given below.
Chapter 1 gives an overall view of the problem considered. Chapter 2 deals with
the method of analysis of the pile raft foundation and discusses some of the work that has
already been conducted by various research workers. Chapter 3 gives a brief introduction
of the proposed method for the analysis of piled raft foundation and estimation of
stiffness for various element of the foundation system considered. Chapter 4 deals with
the structural design of piles and raft foundation. Chapter 5 pertains the salient features of
the software developed for the analysis and design of foundation system while chapter 6
discusses and analyzes the results in detail. Finally in chapter 7 conclusion of the present
work is presented and scope for the future work is also mentioned.
2
CHAPTER 2
LITERATURE REVIEW
2.1 GENERAL
Pile raft foundations are composite geotechnical structures which are
characterized by their capability of sharing loads between their respective foundation
components, i.e. piles and raft. They are particularly suitable in supporting major
structures with concentrated loads in highly compressible ground. Pile raft foundations
are required when the soil is very weak, highly compressive over large depth and in the
presence of high water table. It is also use to resist horizontal forces in addition to vertical
concentrated load and to resist uplift pressure.
Davis and Poulos (1972) developed the concept of piled raft foundation, which was further described by many authors, including Burland et al. (1977), Cooke (1986),
Chow and Thevendran (1987), Randolph (1994), Ta and Small (1996), Kim et al. (2001), Poulos (2001) etc.
Mindlin (1936) analyzed the behaviour of piled raft system based on elastic
solutions. A boundary element procedure to predict the settlement of piles and piles
groups has been developed by Poulos and Davis (1968) and Poulos (1968). Approximate
solution for piled raft has been obtained by Davis and Poulos (1972) based on the interaction between the single piles with rigid circular pile cap. Raft flexibility has been
considered by Hain and Lee (1978) by combining the finite element method for the raft
with the interaction factor procedure for the pile group. The stress distribution along the
pile shaft and beneath the raft could not be obtained by these approximate methods.
To overcome this more rigorous study using three dimension finite element has
been presented by Ottaviani (1975), but the analysis was valid for maximum 15 numbers
of piles. Later a hybrid finite element —elastic continuum method was developed by Hain
and Lee (1978) considering 6 x 6 piled raft. Further Griffiths et al. (1991) developed a
hybrid finite element continuum—load transfer approach to specially minimize the amount
of computations and increase the number of piles (more than 200 piles) in the analysis.
The effect of pile-cap-soil interaction, load carried by the raft and the effect of the
additional pile support on absolute and differential settlement have further been discussed by Randolph and Reul (2003).
3
2.2 METHODS OF ANALYSIS OF PILED RAFT FOUNDATION
Various theories have been developed for the analysis and design of the piled raft
foundation system. Each theory has its own limitations and degree of accuracy. Some of
these have been summarized by Poulos et al. (2001). These methods are dealt with in the
following sections.
2.2.1. Strip on Spring Approach (GASP, Poulos (2001))
In this approach the section of the raft was represented by a strip and the
supporting piles by springs. Approximate allowance was made for all four components of
interaction (raft- raft elements, pile-pile, raft pile, pile raft), and the effects of the parts of
the raft outside the strip section being analyzed were taken into account by computing the
free—field soil settlement due to these parts. These settlements were then incorporated into
the analysis, and the strip section was analyzed to obtain the settlement and moments due
to the applied loading on the strip section and the soil settlement due to sections outside
the raft.
The method has been implemented via a computer program GASP (Geotechnical
Analysis of Strip with Piles) and the results were reasonable agreement with more
complete methods of analysis. However, consideration of torsional moments with in the
raft and consistency in the settlement at a point if spring in two directions through that point are analyzed was not possible in this method of analysis.
GASP can take into account of the soil non linearity in an approximate manner by
limiting the strip-soil contact pressure not to exceed the bearing capacity (in compression)
or the raft uplift capacity (in tensions). The pile loads are similarly limited not to exceed
the compressive and uplift capacity of piles. However, the ultimate pile load capacities
must be predetermined, and are usually assumed to be same as those for isolated piles. In
reality, the loading transmitted to the soil by the raft can have a beneficial effect on the
pile behaviour in the piled raft system. Thus, the assumptions involved in modeling piles
in GASP analysis have the tendency to be a conservative side.
In carrying out the nonlinear analysis in which the strip is to be analyzed in two
directions It has been found desirable to consider the nonlinearity only in one direction
(the longer direction) and in the other (shorter) direction the pile and raft behaviour to be
linear. This avoids unrealistic yielding of soil beneath the strip and hence unrealistic
settlement predictions.
4
Plate element of raft I Applied load
eZ)
_
r
r \
N.
Soil spring Pile spring
2.2.2 Plate on Spring Approach (GARP) In this analysis the raft was represented by an elastic plate, the soil by an elastic
continuum and the piles were modeled as interacting springs (Fig. 2.1). Either finite
element method or finite difference method could be employed for the analysis. This
analysis was implemented via program GARP (Geotechnical Analysis of Raft with Piles).
Allowance was made for layering of soil profile, the effects of piles reaching their
ultimate load carrying capacity (both in compression and tension), the development of
bearing capacity failure below the raft, and the presence of free-field soil settlements
acting on the foundation system.
Fig. 2.1 Plate on Spring Model of Piled Raft Foundation
2.2.3 Boundary Element Methods A boundary element analysis based on elastic theory was performed by Kuwabara
(1989) to analyze the behaviour of piled raft foundation subjected to vertical load.
The pile group comprised of N identical elastic piles of length L, diameter d, and
Young's modulus of elasticity Ep, and was divided into ns number of shaft elements and
nb basic elements. The piles were fixed to a rigid raft which was divided in to nc, number
of rectangular elements. The surrounding soil was assumed to be homogeneous, isotropic,
half space, having Young's modulus Es and Poisson's ratio vs . The pile group in which
the raft and the soil surface were not in contact was referred to as 'the free standing (pile)
5
group', and a pile group in which the raft directly touches the surface of soil is referred to
as 'the piled raft (foundation)'.
Rigid Raft
L Bo ÷_44-d
Rigid Raft
Is NI al
L
1 I
Bo
L
Fig. 2.2 Typical Pile Groups (a) Piled Raft (b) Free Standing Group
The vertical displacement of soil adjacent to piles and the raft due to the stress
{ a } distributed on the pile shaft, the base and the raft are express as:
5 _ d s — E[1,1[01 (2.1) s
where 5'5= Soil displacement vector,
= Vertical stress vector on pile/raft soil interface.
Is = Vertical displacement influence factor matrix.
Bo = Width of overhang area of raft from surface of outer piles.
The pile displacement was described as the sum of the pile tip displacement and
the compression of the pile between the point considered and the tip due to the vertical
stress on the pile. The displacement of the foundation and the adjacent soil were equal
when slip or local yield on the interface did not occur. The addition of a vertical
equilibrium equation for the total system allowed all stress on the interface and the
vertical displacement of the raft to be solved.
The characteristics of settlement and load transfer of pile groups were evaluated
with several parameters, e.g., numbers of piles, N, pile length to dial ratio, L/d, pile
spacing to diameter ratio, s/d, relative stiffness of pile to soil, K= (Ep/Es)Ra where Ra is
the ratio of area of pile section to area bounded by outer circumference, and soil Poisson's
ratio, vs .
The limitations of this theory are that the effect of pile-soil slips, non-
homogeneity of soil and end bearing or underreamed piles were not considered.
6
2.2.4 Three Dimensional Finite Element Analysis Randolph and Reul (2003) carried out a complete three-dimensional analysis of
piled raft foundation using finite element method (ABAQUS program). The soil and the
foundation were modeled using finite elements, which allowed the most rigorous
treatment of the soil-structure interactions. The soil and the piles were represented by first
order solid finite elements of hexahedron and triangular (wedge shape). For the modeling
of the raft, the first order shell elements of square and triangular shape with reduced
integration were used. The soil below the foundation level was modeled using finite
elements. The soil above the foundation level was considered through its weight. The
circular piles were replaced by square piles with the same shaft circumference.
For the modeling of contact zone between soil and raft, and between soil and the
large diameter bored piles, thin solid continuum elements were applied instead of special
interface elements. The contact between the structure and the soil was described as
perfectly rough. This means that no relative motion took place between the nodes of the
finite elements that represented the structure and those of the finite elements that
represented the uppermost layer of soil. The material behaviour in the contact area was
simulated by the material behaviour of soil.
2.2.5 Simplified Finite Element Analysis Desai et al. (1974) propped a method for the analysis of piled raft foundation system
treating it as a plain strain problem. This method focused on the reducing the average
settlement as well as differential settlement. The model involved the fundamental
simplification of condensing a finite size piled raft into a strip pile raft. In addition, this
model can be used to analyze a relatively large pile raft without excessive modeling and
computing time.
2.2.6 Simplified Analysis Methods
2.2.6.1 Poulos-Davis-Randolph (PDR) method Randolph (1994) suggested that for assessing vertical bearing of a pile raft foundation
using simple approaches, the ultimate load capacity can generally be taken as the lesser of
the following two values.
1. The sum of ultimate capacities of the raft plus all the piles.
2. The ultimate capacity of a block containing the piles and the raft, plus that of the
portion of the raft outside the periphery of the piles.
7
Bearing Strata
Depth
d=2r soil
L
Young's Modulus E
Eso Esau
Est Est
Fig.2.3 Simplified Representation of a Pile Raft Unit
Fig 2.3 shows the typical pile raft unit considered by Randolph (1994) The stiffness of the piled raft foundation was estimated as follows:
1 c p.= + kr (1— acp ))1(1— otcp 2kr Ik)
(2.2)
where kpr = Stiffness of pile raft
kp = Stiffness of the pile group.
kr —= Stiffness of the raft alone
ctep = Raft pile interaction factor.
The raft stiffness k r and the pile group stiffness was estimated using elastic theory.
In the later case, the single pile stiffness was computed from elastic theory. Which then
was multiplied by a group stiffness efficiency factor which was estimated approximately
from elastic solution.
The proportion of the total applied load carried by raft was:
prl pe =k,(1— acd1(1c,+kr(1-00)= ( 2.3)
where
Pr = Load carried by raft
Pt = Total applied load.
8
The raft —pile interaction factor a was estimated as follows.
otcp = 1— ln(rc / r0 )/c (2.4)
where r = Average radius of pile cap for each pile, (corresponding to an area equal to the
raft area divided by number of piles)
ro = Radius of pile.
= in( r p, I r o )
r = {0.25 + [2.4p(1 — v) — 0.25 )1} * L (2.5)
-=E„
1 E„
v = Poisson's ratio of soil L = Length of pile
Est = Soil young's modulus at level of pile tip.
Esb = Soil young's modulus of bearing stratum below pile tip
Esav= Average soil young's modulus along pile shaft. First, the stiffness of the pile raft was computed from equation Eq. (2.2) for the
number of piles considered. This stiffness would remain operative until the pile capacity was fully mobilized. Making the simplified assumption that the pile load mobilization
occurs simultaneously, the total applied load, p1, at which the pile capacity is reached,
was given by:
p, = p up 1(1— X ) (2.6)
where pup = Ultimate load capacity of the piles in the group
X = Proportion of load carried by piles
9
P.
g - =allowable settlement piles to carry load excess of 0,-P,)
Raft Pile shaft capacity ( ) Equivalent raft section
2.2.6.2 Burland's approach Burland (1995) has developed the simplified process of design, for the piles to act as
settlement reducers and to develop their full geometrical capacity at the design load.
External load settlement for raft
g S. Total settlement S
(a) Load settlement for raft
Reduced column load
Central Load Q
Q=Q-0.9P„,
(b) Typical section of pile raft
Fig 2.4 Burland's Simplified Design Concept
The steps involves were
1. Estimation of the total long term load-settlement relationship for the raft without piles.
(Fig. 2.4) The design load po gave a total settlement So. 2. Assessment of an acceptable design settlement Sa, which should include a margin of
safety.
3. pi was the load carried by raft corresponding to Sa. 4. The load excess po-pi was assumed to be carried by settlement-reducing pile. The shaft
resistance of this pile will be fully mobilized and therefore no factor of safety was
applied. However, Burland suggested that a "mobilization factor" of about 0.9 be applied
to the 'conservative best estimate' of ultimate shaft capacity, Psu.
10
5. If the pile were located below column which carry a load in excess of ps., the piled raft
may be analyzed as a raft on which reduced column load act. At such column, the reduced
load Qr was
Qr = Q - 0.9P. (2.7)
6. The bending moments in the raft was obtained by analyzing the piled raft as a raft
subjected to reduced load Qr
7. The process for estimating the settlement of the piled raft was not explicitly set out by
Burland, but it would appear reasonable to adopt the approximate approach of Randolph
(1994) in which Eq. 2.2 could be used to estimate Kpr.
where
Sp, = Settlement of pile raft.
Sr= Settlement of raft without piles subjected to the total applied loading.
Kr = Stiffness of raft.
Kpr = Stiffness of piled raft.
11
e
CHAPTER 3
PROPOSED METHOD OF ANALYSIS OF PILED RAFT FOUNDATION
3.1 GENERAL
In the proposed method, the raft is represented by an elastic plate, while the soil and piles
are modeled as bed of equivalent spring at nodal points, and interesting spring
respectively as shown in Fig. 3.1. Finite difference method is used for the analysis of
foundation system. In this method the raft is divided in to m x n no. of grids and for a
given load condition the deflection at each nodal point is calculated, for which the
stiffness of pile and soil is required. The stiffness of the pile is estimated by procedure
given by Hazarika and Ramasamy (2000). For the estimation of soil stiffness a method by
De-beer and Martens (1957) is employed for sands. For clays the same is estimated using immediate settlement and e-log p curve.
Plate element of raft I I Applied load
Soil spring Pile spring
Fig 3.1 Plates on Springs Model of Piled Raft Foundation
12
Thus, the major steps involved in the analysis are below.
1. Analysis of raft by finite difference technique.
2. Estimation of stiffness procedure for individual elements of piled raft foundation
system.
3. Structural design of piles and raft foundation.
4. Development of software package for stiffness estimation of individual elements of
pile raft foundation, and structural design of piled raft foundation
5. Execution of software packages with illustrative examples.
3.2 ANALYSIS OF RAFT BY FINITE DIFFERENCE TECHNIQUE
Finite difference method (FDM) is widely used since the input data is minimal
compared to any other discrete method. Although the computations to built the stiffness
array are little extensive but it has reasonable flexibility and viable options in case of
rectangular boundaries.
FDM is based on the assumption that the subgrade can be substituted by a bed of
uniformly distributed coil spring with a spring constant (coefficient of subgrade reaction) k8. A Vertically loaded raft resting on an elastic foundation can be analyzed with the
simplest assumption that the intensity of reaction q of the subgrade is proportional to the
deflection w' of the raft. The upward reaction of the soil at any point has intensity kswi, provided w1 is positive.
3.2.1 Governing Differential Equations
a) The governing differential equation for a raft acting as slab under load is given by
DV 4 w1 = q — ks w (3.1)
where, 04 a4 iax4 2a4 iax20y2 a4 itay 4
D = Ed 3 /12(1-v2) E = Young's modulus of concrete (kN/m3 ) D = Thickness of the raft (m)
v = Poisson's ratio of the raft
wi = Deflection of raft (m)
q (x,y) =Downward intensity of the load at any point (kN/m3)
13
ks = Coefficient of subgrade reaction (kN/m3) Over small regions, the deflection of raft slab w' may be negative, in these circumstances the raft locally rises above its undeflected portion and loses contact with the soil, in such regions the term kswl in Eq. 3.1 must be omitted.
b) In the computation of solution of Eq. 3.1 it is convenient to work in terms of w and k as defined below,
w Dwi and k 103
Equation (3.1) thus becomes
V 4 w= q— kw (3.2)
with the understanding that w now measures the actual deflection multiplied by D, and k is the ratio of actual coefficient of subgrade reaction (ks) of the soil to flexural rigidity of the raft (D).
c) A function M (x,y) is introduced such that
M(x, y) = —V2 w (3.3)
M (x,y) =Moments function;
v 2 a 2
ax e a 2 ay 2
From the Eqs. 3.2 and 3.3, the fourth order biharmonic Eq. 3.2 is replaced by the simultaneous pair of second order equations as follow:
V 2w = —M
V 2 M = —(q — kw)
The above equations are solved by finite difference approximation. } (3.4)
14
111,11.11111
11 .01111111111.11111
4-
3.2.2 Steps in Analysis of Raft Slab
X-axis
Fig 3.2 Raft Slab in Grid Form
* -- Boundary corner nodes
• - Fictious node
• - Interior nodes
— Boundary nodes
(a) The slab is divided in to number of grids (Fig. 3.2) which gives rise to (m x n) nodal
points. (b) The pair of governing differential Eq. (3.4) is to be satisfied at all nodal points
Therefore, these differential equations are written in finite difference form at all nodal points, which yields (2 x m x n) simultaneous equations.
(c) Solution of the (2 x m x n) equation give deflection at nodal points, which are used to
obtain moments and shears forces, which are required for the design purpose.
15
3.2.3 Governing Differential Equations in Finite Difference Form
(a) Interior nodes
1, j)
Fig. 3.3 Typical Location of Interior Nodes
Writing Eq. 3.4 in finite difference form (using central difference) at a typical interior
node (i,j) ,
— = w[i +1][j] — 2w[i][j] + w[i —1][j] w[i][j +1] — 2w[i][j] + w[i][ j —1]
h 2 h2
w[i — l][ j] + w[i + 1][ j] + w[i][ j —1] + w[i][ j + 1] — 4w[i][ j] + h 2 M [i][ j] = 0 (3.5)
Again from Eq. 3.4
V2M = —(q — kw)
Writing the above equation using central difference at typical node (i,j),
M[i + l][j] + M[i — 1][ j] + M[i][j + 1] + M[i][j — 1] — 4 M [i][ j] + h 2 grill j]
— h 2 kw [ j] = 0 (3.6)
The above equations are applied at all interior nodes.
16
(1,i+1) 1- . (1+1, j+1)
(i,
4-(i+1, j+1) (1, -1)
(b) Boundary nodes
Fig 3.4 Typical Location of Boundary Nodes
When the Eqs. 3.5 and 3.6 are written at any typical boundary node (i,j), they involve nodal point (i+1, j), which lies outside the raft boundary. Such points are called fictitious points (Fig. 3.4). By applying boundary conditions, the fictitious nodal deflections and moments per unit length and shear forces per unit length are solved.
For a straight boundary parallel to the y-axis, the bending moments, Mx=0
Here, a2w 2 w
x aX2 V aye (Timoshenko and Woinowsky, 1959)
w[i ±1][j] = 2w[i][./] -w[i-1][A-v(wEil[i-F1]-E 2wEil[f]) Substituting w[i+1][j] from Eq. 3.7 in Eq. 3.5, one can obtained,
wEilli + 11+ w[i][./ — 1] 2 w[i][./] h2 M NU] = (1 v ) 0
Further, at the boundary, net shear forces = 0 From the equations of shear and moments, one can have following equations.
aa 2 w,
= (1 — v) (Timoshenko and Woinowsky, 1959) xay
am a ,2
N = = — W x
ax ,
(3.7)
(3.8)
17
From the above equations, Eq. 3.8.2 modifies to
OM --= 1/ 0 3 W (1 ) ax aXay 2
The above equation when written in finite difference forms yields:
MU+ = [ 1][./ ] ± (1h2v) (w[i 1][./ ± 1]+ w[i '][ t —
— 2w[i+ l][j]— w[i — l][j + 1] — w[i— 1][j— 1] + 2w[i — MA)
Above equation further contains three unknown w values, w[i+1][j], w[i+1][j+1], w[i+1][j-1]. Which can be obtained from Eqs 3.7 and 3.8 as given below.
t, v) W[i+ 1][j] = 2 w[i][./ ] — w[i 1][f] (1— v " M[i][.i ]
w[i + l][j+ 1] = 2w[i][ j +1]- w[i -1]U +11+ (I-v hv) M M [j ] (3.11)
w[i — l][j + 1] = 2w[i][j —1] — l][ j — 1] + (1 — h v) 2 M[i][j]
Substituting the Eq. 3.11 in Eq. 3.10, one can obtained,
M[i+1][j]. M[i-1][j]+v(M[i][j +1]+ Mi][j l] —
2(1 +v)M M[j]) + 2(1 —v) (2 w[i + j]— w[i— l][j+ 1]) (3.12)
Substitutions of Eq. 3.12 in Eq. 3.6 give
(1 + v)(M [i][ j + 1] + M [i][ j + 2M [i — l][ j] + h 2 grill
(1h2
v) + 2 (2w[i— l][j] — w[i — l ][ j + — w[i— l][ j — 1]) — h2k-w[i][11= 0
(3.13) So, by applying the moment and shear boundary conditions at boundary nodes, the unknown deflection and moment (per unit length) values at fictitious nodal points are evaluated and the equations for boundary nodes corresponding to Eqs. 3.5 and 3.6 are replaced by Eqs. 3.8 and 3.13. Similar type of equation for all the boundary nodes except at the corner is established.
(3.9)
1]
(3.10)
h 2
18
0.1+0 (i-1 j+1) -+-
,
j-1)
(c) Boundary corner nodes
(i, .1-1)
Fig 3.5 Typical Location of Boundary Corner Nodes
Similar to Eqs. 3.8 and 3.10 one can have
w[i][j + 1] = 2w[i][j] — w[i][j —1] — v(w[i + 111 j] + w[i — 1][ j] — 2w[i][j]) (3.14)
M[i][j + 1] = M[i][j —1] + (1—v) (w[i +1][ j +1]+ w[i —1][j +1]— 2w[i][j +1] h2
w[i — 1][j — 1] w[i + 1][ j — 1] + 2w[i][j — 1]) (3.15)
Again from the Eq. 3.7 one can obtained,
w[i±1][./] 2w[i][i] — — [i] v(w[i] {./ ± 1] ± w[i][./ — 1] —
Substituting w[i+1][j] in Eq. 3.14 one can obtained,
w[i + 1][ j] = 2 w[i][ j] — w[i — 1][ j ] (3.16)
w[i][ j + 1] = 2 -w [i][ j] — w[i][ j — 1]
At the corner load (i,j) M[i][j]=0 (3.17)
Substituting in the Eq. 3.6 for M[i+1][j], M[i][j+1], and M[i][j] from Eqs. 3.10, 3.15 and 3.17 respectively and then for w[i+1][j], and w[i][j+1] from Eq 3.16; one can get the following equations,
19
(1—v) h2
4 [i — 1][j] + 4w[i][ j — 1] —8w[i][j]+ 2w[i+1][j+n-- 2w[i — 1][ j —1])
+2(111[i 1] [1] + M [ill j —11) + h 2 q[i][ j] h 2kw[i][j] = 0 (3.18)
Further, Twisting Moment (per unit length) =0 52w = 0 (Timoshenko and Woinowsky, 1959) axay
w[i + l][ j + 1] = w[i - j + 1] - w[i - 1][ j 1]+ w[i + l][ j - 1] (3.19)
From Eq. 3.11 one can obtained,
hv2
w[i + 111 j - 1] = 2w[i][ j - 1] - w[i - 1][ j - 1] +v M [i][ j - 1]
1 -
w[i - 1][ j + 1] 2 w[i - 1][ j] - w[i - 1][ j - 1] + v hv A 1 [i - 111 j] 1 -
Substituting w[i+1][j-1], w[i-1][j+1] in Eq. 3.19,
w[i + l][j+ 1] = 2(w[i— 1][j] + w[i][j-1])— 3w[i — 1][j-1])
v h 2 • (M [1 - ][j] + M[i][j -1]) (3.20)
Lastly the final expression is obtained when the fictitious nodal deflection w[i+1][0-1] is
substituted in Eq. 3.15
wu-lju]+wmu u[i -1]Ei - - [i] + (1+ v)h2 4(1—v) (Mi-1][1] +Mtn [j —1]
h2 8(1 - v)
(h 2q[i][ j] - h2 kw[i][ j]) = 0 (3.21)
Eqs. 3.17, and 3.21 are the modified forms of Eqs. 3.6, and 3.5 at a corner of the
slab.Thus, the pair of Eq. 3.4 can be written in finite difference form as illustrated above at all the (m x n) nodal points. These are then solved to obtain the nodal deflections.
2
20
2
h
4
3.2.4 Treatment of Column Loads
In the above equations "q" is the intensity of the downward load. The loads on the raft
come through column as concentrated loads. The concentrated load (P) is converted into
equivalent intensities (q) as follow;
a) Load at an interior node b) Load at a boundary node
4 4
h2q = P
c) Load at a boundary corner node
h
h2q = 2P
h2q = 4P
Fig. 3.6 Treatment of Column Loads
d) Load not at a nodal point
A column not located at a nodal point might be considered to transmit the load to the
adjoining nodes. Closer the load to a particular node, higher will be the share of load to that node. Accordingly, this is represented in the mathematical form as given below,
21
_ bxdxP Pi hxh
axdxP hxh
bxcxP hxh
_ axcxP hxh
P 2
P3
P 4
Fig. 3.7 Distribution of Load at Nodes
where
P = Column load
P1, P2, P3 and P4 are the load acting on the nodes;
3.2.5 Treatment of Moment Loading To represent the effect of column transmitting moment in addition to the axial load
Ramasamy and Karwa (1999) assumed that moment may be taken into account in the
analysis by treating the column load P as acting at an eccentricity from the location of
column, i.e., the axial load position may be shifted by ex=Mx/P in the x-direction and ey=My/P in the y-direction. The load then may be treated as discussed section 3.2.4 above as applicable.
3.3 PROCEDURE FOR ESTIMATION OF INDIVIDUAL ELEMENT STIFFNESS OF PILED RAFT FOUNDATION.
3.3.1 Stiffness Estimation of Soil below the Raft.
To estimate the stiffness of the soil below the raft, layered soil profile consisting of
cohesionless and cohesive soil layers, is considered (Fig. 3.8). The stiffness of the pile is
estimated by procedure given by Hazarika and Ramasamy (2000). For the estimation of
soil stiffness a method by De-beer and Martens (1957) is employed for sands. For clays the same is estimated using immediate settlement and e-log p curve.
22
H2 Cohesionless soil
Cohesive soil H3
Cohesive soil H4
Cohesionless soil
Raft L x B Super Structure
Loose Soil H
Fig 3.8 Layered Soil Profile Considered
3.3.1.1 Settlement of Cohesive soils
(a) Consolidation settlement (e-log p curve method)
From an oedometers test, a relationship between log p and e (p-
pressure, e-void ratio) as shown in Fig. 3.9, may be obtained.
Log I)
Fig 3.9 e-log p Curve for Cohesive Soils
23
Settlement of the soil below raft,
s = Ae
AH 1 e0 (3.22)
where AH = Thickness of the layer
eo =- Initial void ratio of soil corresponding to pressure po, (the effective overburden
pressure at the mid depth of layer considered )
De = Change in void ratio due to increase in effective vertical pressure Ap due to the
structural loading as shown in Fig 3.8
The settlement can also be estimated from the expression below
s = C log{ PO "P } 11- e0 Po
where Co=compression index and can be determined from the e-log p curve.
(3.23)
= A e
log p 2 — log pi
As per Terzaghi and Peck (1967), Co can also be obtained empirically from the following
expression in the case of low to medium sensitivity of clays.
for undisturbed soils Cc=0.009(WL-10)
for remoulded soils Co=0.007(WL-10) Ho = Thickness of the layers
eo = Initial void ratio of the soil Po = Initial overburden pressure
WL = Liquid limit of the soil
Ap= Average effective vertical pressure at the centre of loaded area on the soil layers due
to net foundation pressure at the base of the raft
(b) Immediate settlement (Schleicher, 1926)
The linear theory of elasticity is used to determine the elastic settlement of the
footing on saturated clay. Immediate settlement of cohesive soil under an uniformly
distributed flexible area can be calculated by (Schleicher 1926),
24
s i = ( 1 7E, )qBI (3.24)
where
Si = Immediate settlement
q = Uniformly distributed load
B = Characteristic length of the loaded area.
E s= Modulus of elasticity of the soil.
v = Poisson's ratio (0.5 for saturated soil)
I = Influence factor (obtained from table 3.1)
.Table 3.1 Values of Influence Factor I (Schleicher, 1926)
Shape
Flexible footing
Rigid footing Centre Corner Average
Circle 1.0 0.64 0.85 0.79
Square 1.12 0.56 0.95 0.82
Rectangle 1.36 0.68 1.20 1.06
L/B=1.5 1.53 0.77 1.31 1.20
L/B=2.0 1.78 0.89 1.52 1.42
L/B=5.0 2.10 1.05 1.83 1.70
L/B=10.0 2.52 1.26 2.25 2.10
L/B=100. 3.38 1.69 2.96 3.40
To count the effect of nonlinearity of the soil Eq. 3.24 can be modified as
Si = qB il-v 2 N i ta q uq E 1 a qu
where qt, = Ultimate bearing capacity of soil.
a = Constant taken as 2.
(3.25)
3.3.1.2 Settlement of Cohesionless Soil [De Beer and Martens Method (1957)]
The settlement (hence total settlement) of cohesionless soil can be obtained by a method
proposed by De-Beer and Martens (1957).
According to De-Beer and Martens (1957), the consolidation settlement is obtained by
following expression
25
sc = [—H In Po + AP}ix RF Po
(3.26)
Here C =1.5 Ckd
Po ckd = Static cone resistance
c = Constant of compressibility
RF = Rigidity factor
Po = Effective overburden pressure on a layer before applying the foundation loads.
In case of soil profile with varying static cone resistance value, the average Ckd
values are assigned to different layers, and then computation is done for each layer. The
sum of the settlement for all these layers will be the estimated value of settlement for the
raft. To count the effect of nonlinearity of the soil Eq. 3.26 can be modified as
,H po Ap }] x RF
x(cxqu—Ap ) sc = [—int aqu (3.27)
C Po
Now the settlement of all layers with in the significant depth (2b below the raft) is
calculated for the various loading pressure and a plot as shown in Fig. 3.10 may be
obtained.
From the pressure vs. settlement response curve of the raft, the maximum allowable settlement (Sa) for the raft may be chosen depending on the soil conditions and
the type of superstructure as per IS: 1904:1978. Corresponding to the settlement Sa, the pressure p can be obtained from the pressure settlement curve. Therefore
Pressure (kN/m2)
Sa=Allowable settlement
Fig 3.10 Pressure vs. Settlement Curve for Raft
Sett l
emen
t (m
m)
26
( )113 q qm ax
zt (3.30)
Stiffness of the soil below the raft= (A x p )/Sa in kN/m
where A= Area of the raft represented by a spring.
3.3.2 Estimation of Stiffness for Individual Pile To estimate the stiffness of pile for layered soil profile, load vs. settlement curves
are developed using load transfer method given by Hazarika and Ramasamy (2000). This
method requires the estimation of pile shaft resistance and pile tip resistance, as given
below;
3.3.2.1 Estimation of shaft resistance and tip resistance
(a) Shaft resistance
The unit shaft resistance f mobilized at any shaft movements 'z' is expressed by the
following non linear relationship (Vijayvergiya, 1969).
for z zs
.F (3.28) I = fm ax { 2 _ 1
zs zs I
and for z>z, f = fmax (3.29)
where
zs=Critical movements of the pile segments at which the maximum shaft resistance fnax is
mobilized
(b) Tip resistance
The tip resistance q for a particular tip movement z as a function of qm.„ is expressed by
the following given equation (Vijayvergiya, 1969).
Based on available literature, Hazarika and Ramasamy (2000) suggested the value of
critical pile movement parameters as.
zs = 5 mm to 7.5 mm for clay and sand.
zt .= 0.04B to 0.06B
B = Pile tip dimension
27
3.3.2.2 Estimation of fmax and qmax
(a) For cohesionless soil
f =K a- tan .5 (331) max s v
where lc, = Lateral earth pressure coefficient
6 = Angle of wall friction between the pile and soil
ay. = Vertical effective pressure at the pile location under consideration
ko = Earth pressure coefficient at rest
Also qmax = 6v Ng (3.32)
where cy,' = Effective overburden pressure at the pile tip
Nq = Bearing capacity factor
The values of Ks, S and Nq can be obtained from the Tables 3.2, 3.3, and 3.4 respectively
Table3.2 Values of Ks (Tomlinson, 1987)
Installation method ks/ko
Driven piles, Large displacement 1.00-2.00
Driven piles, Small displacement 0.75-1.25
Bored and cast insitu 0.7-1.00
Jetted piles 0.5-0.70
Table 3.3 Values of tans (Tomlinson, 1987)
Material tans
Concrete 0.45
Wood 0.40
Steel (smooth) 0.20
Steel (rough, rusted) 0.40
Steel (corrugate) 0.35
Table 3.4 Values of Ko (Tomlinson (1987)
Type of soil Ko
Loose 0.50
Medium dense 0.45
dense 0.3 5
28
(b) For cohesive soils
where a = Adhesion factor
where
fma. (3.33)
qmax =Cu N, (3.34)
I•1c = Bearing capacity factor, normally taken as 9
Cu = Untrained shear strength of soil at the pile tip, usually taken as the average value
over a distance of twice the diameter below the pile tip.
3.3.2.3 Following are the various steps involved in the method proposed by
(Hazarika and Ramasamy, 2000)
Pile Head Q=Applied Load
12 I S2
Pile Segment
N S3
y1,mid I Q1, Y1
L1,1.2 =Segment lenghts I
Q2. 2, y4mid Y1,'Y2
Q1,Q2, =Segment tip movement =Axial forces on segment
S1,S2 =Skin Resistance of Segment YT= Tip Movement QT=Tip Resistance
v 3,mid
Sn j_ I 1
yn,mid pile Tip I
Qt YT
Fig 3.11 Axially Loaded Piles 1. A pile of given length L is divided into number of segment say 'n'. Then a small tip movement Yt is assumed for the bottom segment. 2. The tip resistance (q) is calculated for the assumed tip displacement, from the Eq.3.30. Thus tip load is given by
Qt=q x area of pile tip 3. Mid point movement (Ye ) of the bottom segment is estimated. For the first trial, the
mid point movement is assumed to the equal to the tip movement (Ye).
Lni
29
4. Using the estimated midpoint movement, the shaft resistance is obtained for the
assumed displacement from the Eqs. 3.28 and 3.29
Shaft load (Sn) transferred by the segment is given by:
Sn=l x C x Ln
where C = Circumference of the pile
Ln = Length of pile segment 'n'
5. Now the elastic deformation in the bottom half of the segment is calculated as
= 817 (Q"ll +Q tip) Ln 2 AE 2
Assuming a linear variation of load distributation in a segment.
(3.35)
Q m id Sn
2 Q tip
where A and E are the cross section area and elastic modulus of pile material
respectively.
6 .Now mid point movement is computed for the bottom segment, as
Yn,mid = gY Yt
7. Using the computed mid point movement, the shaft load of segment is calculated as per
step 4.
8. Shaft load is compared with the previous value. 9. If the difference is not with in a specified limit, step 5 to 8 is to be repeated, until the
convergence is reached.
Then Qn= Qt+ Sn
Y" Yi Ai 7)Ln (3.36)
10. The steps 3 to 9 are to be repeated for the next segment above the bottom segment and
worked up to compute the load (Q) and the settlement (Y) at the pile head. 11. The procedure is to be repeated for different tip movement values and a set of load
settlement values are to be obtained. The same are to be plotted to give the load settlement curve.
From the load settlement response curve for the pile, the maximum allowable settlements (Sa) for the pile is chosen as per IS: 2911:1979. From the Fig. 3.15, P is the load corresponding to Sa
30
Load (1(N) P
S.--allowable settlement
Settl
emen
t (m
m)
Therefore, Stiffness of each pile spring= P/Sa in kN/m
Fig 3.12 Load vs. Settlement Curve for Pile at Pile Head
CHAPTER 4
STRUCTURAL DESIGN OF RAFT AND PILE FOUNDATION
4.1 GENERAL
If the loads transmitted by the column in a structure are so heavy or allowable
pressure are so small that individual footing would cover more than about one-half of the
area, it may be better to provide a continuous footing under all columns and walls. Such a
footing is called a raft or mat foundation. Raft foundation is also used to reduce the
settlement of structures located above highly compressible deposits.
A raft foundation usually consists of a concrete slab with constant thickness
throughout its plan area, though other forms such as slab thickened under columns, slab
with pedestals, waffle-stab (Fig. 4.1) etc, are also adopted but the two basic structural
forms are: (a) Flat Slab Raft and (b) Beam and Slab Raft. These are indeed the same
structural alternatives for floor systems in the superstructure. As no specific codal
provisions are available for foundations of these types, the provisions relating to the flat
slab are adopted. Since the load for the design of the floors in the superstructure acts
downwards, unlike the soil pressure on the raft which acts in the opposite direction, the
positive moment mentioned in the code must be understood as producing tension at that
top and the negative moment as producing tension at the bottom for the raft. So using the
results of the analysis as input, the structural design of the raft is carried out as applicable
for flat slabs as per provisions of IS: 456:2000.
A flat slab is a raft of uniform thickness supporting the columns without the aid of
beams. In fact, the isolated footings are essentially flat slabs. The slab is directly
subjected to the action of concentrated column loads, it is treated as structure critical in
the punching shear mode as the footing. If the column is small and the column load is
larger, a substantially thick slab will be necessary to resist the punching shear around the
column. This situation can be contained if an appropriate provision for the progressive
transfer of the column load to the slab, depending upon the need is adopted as shown in
Figs. 4.1b and 4.1c. The section resisting punching shear is located in all cases at a
distance of half of the effective depth from the face of the transferring element.
32
A 13 • •
• 11111•111
11111•• ■
41)
(01)
: : • : • : : 111 •
:E. :• • : ,. : : ••
13 C D
t
I-- r —
• : • • • • . •
•
ir• •••••;
Not :11: :a: • • • — 4.1
• •
• I 4 I
. . s
•
1 • • • • •
7. I • • 1... '... 4
•
...-.1._.a.___, •„„,. a ,,,„.
I • .1 II
r — —1 • r — - • • • • • • • •
I t • • • •• ; •
•— .......I 'I.— ...,.,; .: • a a a:
....a :---;■
:•• II •
• II I 1
. • I I
s I r • • • 11 • • • • . -.”- ... •
.•....
A
A- A B-B
13
a) Flat Slab
b) Slab Thickened Under Columns
c-c D-r)
c) Slab With Pedestals d) Waffle Slab
Figure 4.1 Common Types of Raft Foundations
33
4.2 DESIGN OF RAFT AS A FLAT SLAB
Flat slab means a reinforced concrete slab with or without drops, supported
generally without beams, by columns with or without flared column heads (Fig. 4.1).
4.2.1 Strips of Flat Slab as Raft
The behaviour of flat slabs and flat plates (raft) are identical to those to two-way slabs with beams. The bands of slabs in the two orthogonal directions along the column lines may be considered to act as beams. A probable width of slabs acting as beams along
the column lines have been shown in Fig. 4.2 Such bands of slabs are referred as column strips which pass through the columns and middle strips which occur in the middle of two adjacent columns.
The following definitions shall apply for flat slab (IS: 456:2000)
(a) Column strip: It is a design strip having a width of 0.25 12, but not greater than 0.25 1 on each side of the column center-line.
where,
Ir.—Span in the direction moments are being determined, measured c/c of supports;
12= Span transverse to 11 measured c/c of supports;
(b) Middle strip: It is a design strip bounded on each of its opposite sides by the column strip.
(c) Panel: Panel means that part of a raft bounded on each of its four sides by the centre line of a column or center-lines of adjacent spans.
4.2.2 Proportioning of Raft Slab
The thickness of the flat slab in the superstructure is normally governed by considerations of limiting deflections. However, since the column loads are much higher for flat slabs the thickness is generally governed on the basis of punching shear. At the analysis stage, the depth of raft is initially chosen as the maximum of the following:
(a) Serviceability requirements (Deflection criteria) (IS: 456: 2000)
The design of flat slab is made for serviceability requirements of deflection i.e., the vertical deflection limits may generally be assumed to be satisfied provided that the critical depth of raft (deck) is chosen as the maximum of the values obtained as below.
34
B . : !
- --- .,.. —_____ .. ; •
• . i
. . .
. , . 7 ni i ! l ' MI i • _' . , : i t ; ! :. , ! •
• UMIIIIIIII I : ! ..., , : :
: ,, • .
1111110111•111 . . . .
• . !
M S
ACS
1, 1°1 ATNiti
1
4 __M. .S_____1•1 B 14 S
Figure 4.2 Division of Flat Slab into Column Strips and Middle Strips
35
(i) L/20 where, L is the maximum effective span of simply supported raft;
L/26 where, L is the maximum effective span of continuous support; (or)
L/7 where, L is the maximum cantilever length beyond the end columns of raft.
ii) For spans above 10m, the values in (i) may be multiplied by 10/span in meters, except
for cantilever in which case deflection calculations should be made.
iii) To be more economical, depending on the area and the type of steel, the values in (i)
and (ii) may be modified. The above mentioned (i) and (ii) are on the conservative
side.
(b) Punching shear criteria
(i) Critical section: The critical section for shear shall be at a distance cicps from the periphery of the column, perpendicular to the plane of the slab, where der, is the effective depth of the critical section. The shape in the plan is geometrically similar to the support immediately below the slab (Fig. 4.3)
(ii) Calculation of shear stress: The nominal shear stress ( r„ ) in flat slabs shall be
vc (4.1)
where,
boa cps
Ve = The two way critical shear force due to design load ; calculated as the net load at the critical section assuming the soil pressure over the raft is uniform;
b0 = The periphery of the critical section;
deps = Effective depth based on punching shear;
r, (4.2)
where,
Cs= (0.5+13c) <1
13c= Shorter side of column/Longer side of the column
c= 0-25(fck )°5 (Limit State method);
36
1
d/ Fig 4.3(a)
• • •
• • •
• •
• •
•
d/2
Fig 4.3(b)
Free Edge
t/2
d/2
where,
7Ald/214— •
Fig 4.3(c) Fig 4.3(d)
c=> Critical Section
d 1--> Effective Depth of Raft Slab
Figure 4.3 Critical Sections for Shear in Flat Slabs
37
fek= Characteristic strength of concrete (N/mm2)
The maximum depth obtained by the above consideration is provided as input for the
computation of the flexural rigidity of the raft slab, D used in the FDM analysis.
(c) Depth based on moment consideration
After the FDM analysis, the values of bending moment and shear force at each nodal
point are known. Then, the depth from bending moment consideration is checked as given
below,
The effective depth required is calculated from the formula
debln = VBR (4.3)
where,
R= Resisting moment factor of a balanced section;
B = Unit width along the raft
M = Maximum bending moment per unit width
R factor is obtained from Table 4.1 based on codal provisions of IS: 456:2000. The values of R given in the Table are valid when units for M and B are in N-mm and mm
respectively.
Table 4.1 Coefficients of R (Limit State method)
Grade of steel R
Fe 250 0.149fck
Fe 415 0.138 fek
Fe 500 0.133 v fek
The net effective depth provided to the raft dell should be the maximum of deck, deps, debm.
If the depth assumed in the analysis is much different from the depth now found required,
then the analysis is revised taking an appropriate revised effective depth.
38
4.2.3 Reinforcement Detailing
a) Area of steel
The area of steel (Ast) for maximum bending moments is determined from the following
equation
M = 0.87 f y A st d ebm [1 A f y
Bd ebm f ck (4.4)
where,
Ast=Area of reinforcement;
fy = Characteristic strength of steel;
Minimum area of steel in each direction
= 0.15 %of the c/s area of the raft for Mild steel bars;
= 0.12% of the c/s area of the raft for High strength deformed bars;
If Ast obtained using the Equ. 4.4 is less than the minimum specified, then the
minimum steel as mentioned should be provided.
(b) Selection of bar diameter and cover (IS: 456:2000)
i) The diameter of the main bars shall not be less than 8mm for high strength deformed
bars and 10 mm for plain mild steel bars. The selected bar diameter, 41) should not be
more than 0.125 times the thickness of the raft.
ii) The clear cover of the reinforcement from its face excluding plaster and other
decorative finish may be 25 to 50 mm. Extra cover ranging from 15 to 60 mm depending
upon the severity of the environment is provided and in no case the total cover should
exceed 75mm. The end cover at the sides of slab must be equal to 2 1 or 25 mm
whichever is more.
(c) Spacing of reinforcement
Spacing actually means the center to center distance between bars. In actual construction
also the position of the rods is marked from center to centre, in the forms. However code
mentioned the clear spacing between bars. Hence,
Design spacing (c/c) = clear spacing + (1)
39
Minimum clear spacing shall be maximum of
1. (b, if all bars are of equal diameter;
2. Highest 021) if bars of unequal diameter;
3. Nominal maximum size of coarse aggregate + 5mm.
Maximum clear spacing is the smaller of
1. 3 dcff;
2. 300 mm
4.2.4 Summary of Steps in Design of Raft Slab
a) The raft is divided into column strips along the column line and middle strips adjoining
the column strips in both the directions as shown in Fig. 4.2. The bending moment and
shear force distributions along these strips as obtained from the FDM analysis are used as
input to design.
b) The effective depth is obtained as the maximum of that calculated from deflection
criteria (deck), punching shear criteria (dep) and maximum bending moment (dcbm) The
total thickness of the raft is obtained after providing suitable cover.
c) The reinforcement is provided in the above strips according to the maximum moment
obtained from the analysis, i.e., the maximum negative moment per meter width along the
column strip is obtained and placed at the bottom of the slab. Similarly the reinforcement
is provided at the top of the slab for the maximum positive bending moment in that strip.
Thus the reinforcement is provided for both positive and negative moments:
d) The exercise as above is done for the middle strips also. The area of steel provided is
checked for minimum area specifications.
e) A typical plan of the reinforcement is shown in Fig. 4.2.
4.3 DESIGN OF PILES.
The pile is a small diameter column, which is driven or cast into the ground by suitable
means. The piles may be subjected to vertical loads, horizontal loads or both. They are
very useful and economical in transferring load through poor soil or water to a suitable
bearing stratum by means of end bearing. Such piles are referred to as the end bearing
piles. A foundation supported on end bearing piles will provide an economical solution
provided the bearing stratum is about 3 meter below the base level of structure. When the
40
bearing stratum is too deep to obtain end bearing, friction piles can be used. These piles
resist load by developing skin friction between the piles and adjoining soil.
A pile formed in the ground through bored excavation is referred to as a bored
cast in-situ pile. If the soil is stiff enough to stand on its own then there is no need to
provide a steel casing while boring. Such piles are called uncased bored piles. In some
cases, the soil is too week to stand alone; in such cases, the bore hole is stabilized by
filling it with bentonite mud slurry or a steel casing which is withdrawn while laying the
concrete. Under certain conditions, the steel casing is driven and left in place after placing
the concrete. Such piles are called encased bored piles.
A pile can be designed as a structural member in accordance with clause 6.3.1 of
IS: 2911:1979 (Part 1/section 1, 2, 3 and 4). Load from the superstructure is transferred to
the piles through pile cap. The load then start getting distributed through skin friction and
bearing and finally reaches the toe. Thus, a pile should have adequate strength to sustain
the design load and satisfy the design criteria as a reinforce concrete column.
4.3.1 Steps in Design of Pile Foundation. (LS: 2911:1979)
Step 1. Pile is designed as a column. Column is designed as short or long column
depending on slenderness ratio.
Effective slenderness ratio: The ratio of effective column length to least lateral dimension
is referred to as effective slenderness ratio. A column is said to be short if the slenderness
ratio is less or equal to 12.A long column has a slenderness ratio greater than 12.
Step 2. Column is designed for minimum eccentricity. And minimum eccentricity is
given by
emin > I D
300 30
>20mm
(4.4)
whichever is more.
where 1= Unsupported length of column in mm
D = Lateral dimension of column in the direction under consideration in mm.
Step 3. The column is checked for Design load.
(a) Ultimate load capacity: The maximum load which a pile can carry before failure, i.e.,
when the soil fails by shear as evidence from the load settlement curve or the pile fails as
a structure member.
(b) Load carrying capacity of piled- Static formula (IS: 2911:1979, Part 1, Section
41
2, clause 6.3.2)
(i) For cohesive soil:
Qu =Ap Nc 1 c +En ac
where,
QL, = Ultimate bearing capacity of pile in cohesive soil. ( kN/m2)
N, = Bearing capacity factor, usually taken as 9
cp = Average cohesion of soil at pile toe (kN/m2)
cci = Adhesion factor for ith layer depending on the consistency of soil
ci = Average cohesion for ith layer (kN/m2)
Ap= Surface area of pile stem in the ith layer (m2)
E = Summation for layers 1 to n in which pile is installed and contributes to positive
skin friction
(ii) For Cohesionless soil:
Q,, = A p(11 2Dy' N + PD A q ) +En ..=1 K Pd , tan (5,4.,
where,
Ap = Cross section area of pile toe (m2)
B = Stem diameter of pile (m)
y' = Effective unit weight of the soil at pile toe (kN/m3)
N1 & Ny = Bearing capacity factors depending upon the angle of internal friction at
toe
D = Stem diameter in m
PD = Effective overburden pressure at pile toe (kN/m2)
Nc, Nq = Bearing capacity factor depends upon the value of 4:1
Ki = Coefficient of earth pressure applicable for ith layer
8i= Angle of wall friction between pile and soil for the ith layer
AS; = Surface area of pile stem in the ith layer (m2)
E = Summation for layers 1 to n in which pile is installed and contributes to Positive 1=1
skin friction
(c) Safe load: It is the load derived by applying a factor of safety on the ultimate load
capacity of the pile or as determine from load test.
42
The minimum factor of safety on static formula should be taken 2.5.
Design load <Safe load.
Step 4. Structural Design of Pile Foundation is done on the following basic
(i) For f: D f I 2 and Mkp" 3 , percentage of steel for longitudinal reinforcement is
calculated from the chart in SP: 16
where,
Mu = Factorial moment.
Pu = Factorial axial load
d' = Clear cover
D = diameter of pile
As per IS: 2911:1979 (Part-2), the minimum area of longitudinal reinforcement is 0.4% of
sectional area calculated on the basis of outside diameter.
Step 5. IS: 456:2000, clause26.5.3 states that
(i) Minimum diameter of longitudinal reinforcement should not be less than 12mm.
(ii) Spacing of longitudinal bars measured along the periphery of pile should not exceed
300mm.
(iii) Diameter of lateral tie should not less than one fourth of the diameter of longitudinal
bar and in no case less than 6mm.
(iv) Clear cover to all main reinforcement in pile shaft should not less than 50mm.
(v) The minimum diameter of the links should not less than 6mm and minimum spacing
should not be less than 150mm.
Step 6. At top piles are attached to pile cap. The function of pile cap is to distribute the
load coming to it equally to all piles beneath it. The thickness of pile cap such that it
provides necessary anchorage of column and pile reinforcement. Clear cover for main
reinforcement should not less than 60mm.Pile should project 50mm into the pile cap.
43
CHAPTER 5
SALIENT FEATURES OF THE PACKAGE
5.1 GENERAL
A computer package on the Analysis and Design of Piled Raft Foundations has
been developed in `MATLAB' with graphic features, which can be run in any PC system.
5.2 FEATURES OF PACKAGE
• The analysis of the raft is done by finite difference scheme.
• The raft can be divided in to any no. of grid.
• The raft is treated as a flat slab
• Stiffhess of soil and pile are calculated by considering nonlinear behaviour of soil.
Structural design of pile and raft is done by IS: 456:2000 and IS: 2911:1979.
• Option to choose various grades of steel and concrete and the corresponding data base
on permissible stresses, design coefficients, etc., are incorporated.
• Provision is made to enable the user revise design at various stages such as thickness of
raft, soil pockets below the raft, selection of material etc.
• The user is guided by appropriate knowledge base on coda] provisions and practices at
various stages of design.
The other important features of the package are:
(i) Run of Package
A computer package on Finite Difference Analysis and Design of Piled Raft Foundation
(FDADPR) has been developed in `MATLAB' with graphic features. The program is
divided into separate functions (subroutine) for each process such that each process can
be independently called at any time and run DOS Operating System.
(ii) Data input
User can feed input through Data files or through keyboard in an interactive mode. Data
file can be prepared by running the program on hard disk or through floppy drive.
44
(iii) Various Checks during Analysis
The package caries out various help boxes which guides user to input the data required
for analysis as necessitated by standard tables starting from checking the thickness the of
the raft, co efficient of subgrade reaction etc.
(iv) Various Checks during Design
The package carries out design checks as necessitated by code, during various stages of
design. Starting from checking thickness of raft for moments, check for area of steel,
shear stress etc., is carried-out.
(v) Data output
On completion of the analysis and design, the user can store data in output file on hard
disk or on a floppy.
45
CHAPTER 6
RESULTS AND DISCUSSION
6.1 GENERAL In the present study, analysis and design of piled raft foundation has been carried out. A
few numerical problems on foundations have been solved for verification and the results are presented to illustrate
1. Major features of the study;
2. Effect of soil and pile stiffness on design;
3. Effect of piled raft foundation in comparison to raft foundation;
The raft has been designed by treating it as a flat slab based on Limit state method
incorporating the IS code provisions. The pile is designed as bored pile based on IS:
2911:1979.
6.2 VERIFICATION OF THE PROBLEM
6.23 Raft Foundation
Fig.6.1 represents the problem of footing that was solved by Teng (1969), using
finite difference method. The footing is divided in to 8 x 8 no. of grids and a concentrated
load is acting on the node 41 as shown in figure 6.1. Table 6.1 represents details of the
footing and properties of soil considered for the problem.
The same problem is also solved using the present study and the results are
compared. The comparison is shown in Table 6.2. The maximum and minimum
settlements are 2.3866 mm and 1.3347 mm at node 41 and 72 respectively in the present
study. While maximum and minimum settlements were found to be 2.387 mm and 1.3347
mm respectively by Teng (1969). Fig. 6.2 shows the variation of moment at various
nodal points.
It is clear that the results from the present study show good agreement with
obtained by Teng (1969), verifying the present formulation.
46
81
71
72
61
62 63
51
52
53 54
41
42
43
44 45
19 27
10
18
9
410.384 m
X-axis 3.072 m
Y-axis
Fig 6.1 Details of a Footing Problem of Supporting a Column (Teng, 1969)
47
Table 6.1 Details of Problem of Raft Foundation (Teng, 1969)
1 Length of Footing (m) 3.072
2 Breadth of Footing (m) 3.072
3 Thickness of the Footing (m) 0.3072
4 Poisons Ratio 0.15
5 Ks (kN/m3) 26523
6 Young's Modulus(kN/m2) 20369641.11
7 No of Grids 64
8 Total No of Nodes 81
9 Force (kN) 444.98
Fig 6.2 Bending Moment along 1r Centre Line of Footing
48
Table 6.2 Comparison of Deflection at Various Nodes
Node No Deflection (mm)
Teng (1969) Present Study
41 2.387 2.3866
42 2.244 2.2431
43 2.032 2.0316
44 1.816 1.8153
45 1.616 1.6153
51 2.151 2.1498
52 1.971 2.1498
53 1.771 1.77
54 1.578 1.5772
61 1.830 1.8289
62 1.655 1.6542
63 1.476 1.4756
71 1.501 1.5004 72 1.335 1.3347
81 1.77 1.767
6.2.2 Piled Raft Foundation
Fig. 6.3 shows the elevation of a building which is located in Urawa City, a suburb of Tokyo, Japan (Yamashita et al., 1994). The building is a five storied reinforced concrete construction and its plan measures 24m x 23m. A raft of thickness 0.3m with 20
piles (one under each column) constitutes the foundation. Fig. 6.4 shows the foundation
plan and Tables 6.3 and 6.4 show details of five storied building and soil profile respectively. Table 6.5 show the location and load coming on piles. Load settlement
curves for piles (Fig. 6.5) and raft (Fig. 6.6) are developed using computer program in
"MATLAB" using the Tables 6.6 and 6.7 respectively. Stiffness of piles and soils are estimated using these load settlement curves.
49
0.3 m thick 24mx23m raft
Sand
Superstructure
Layer 1
Layer 2
• 5m
1m A
8.5 m
Clay
Clay Layer 3 Sand
Layer 4 Clay
Layer 5 Sand Layer 6
Sand Layer 7
Clay Layer 8
Sand Layer 9
• ♦2 m 1
1
2.5m
3.5m
1.5m
5m
2 m
9m
Fig. 6.3 Elevation of Building (Yamashita et al., 1994)
50
n a
a 1 I t 1 a
a I I I I a 1 a
—e r 1 r a T I I I I I I I I I I
a a a a a a a i a i
23 m
4 ... ---
......
------
L A
r — — — — r — ---
r
r 4
a
r 11'
r
I. .1
1
— J
—1,
.
1
je
-8
_
I
_ _ — I
I I
I . . . .
— —r—
.. I
I L — — .1 ------ 4 .
I I r TI I L . 1 .
•
111
L
I ------
I I . I I r I I .
•Ir
I
— — —
I ---r
I :.. — — J
I I r —I I I L. . ,
L
— — _
. . .
—
....
I
I I— — — 1 --- I I I r T
I 4 . . AI ------
8 — 4 ...ta•
r — — — —
---
. —
. .
-
_ ..•■■•
1 ------
L ------
— —
—
------
6m
I I I .....1..L.......11 .......1.........L. ....1.......1.......1.....1
I I I I 3
I I I
I I I
--
a .1 1 L
6m
6m
---
--- ---
24m B Fig 6.4 Foundation Plan of Five Stories Building Urawa City (Japan)
(Yamashita et al., 1994)
51
Table 6.3 Details of Five-Storied Building at Urawa City (Japan) (Yamashita et al., 1994)
1 Length of Footing (m) 24
2 Breadth of Footing (m) 23 3 Thickness of the Footing (m) 0.30
4 Poisons Ratio 0.15 5 Ks (kN/m3) 1000 6 Young's Modulus(kN/m2) 2.5x107 7 No of Grids 552 8 Total No of Nodes 600 9 Total No. of Piles 20
Table 6.4 Details of Soil Profile (Yamashita et al., 1994) Layer No.
Density (kN/m3)
Ci, (kN/m2)
a lc, Ckd
(kN/m2)
cD
1- Clay 18 60 0.5 - - - 2- Sand 19 - - 0.45 4000 30 3- Clay 18.5 60 0.5 - - - . 4- Sand 19.5 - - 0.35 6000 32 5- Clay 18.5 100 0.5 - - - 6- Sand 19 - - 0.35 5000 33 7- Sand 18.5 - - 0.4 5000 30 8- Clay 19 200 0.5 - - - 9- Sand 20 - - 0.4 40000 41.2
52
Table 6.5 Location and Load Coming on the Pile
Node No. X co-ordinate (m) Y co-ordinate (m) Force on pile (MN)
1 0 0 2.16
7 6 0 3.09
13 12 0 2.95
19 18 0 2.71
25 24 0 1.88
301 0 11 2.79
307 6 11 3.86
313 12 11 3.95
319 18 11 3.76 325 24 11 2.83 426 0 17 2.24 432 6 17 2.57 438 12 17 1.58 444 18 17 2.91 450 24 17 1.61 576 0 23 1.25 582 6 23 1.79 588 12 23 1.02 594 18 23 1.57 600 . 24 23 0.96
53
Table 6.6 Computation for Pile Stiffness
No. Pile tip
movement (mm)
Pile head
movement (mm)
Compression of
the pile (mm)
Pile head
resistance (1(N)
1 0 0 0 0
2 1 2.5832 1.5832 1761.2
3 2 3.9418 1.9418 2108.8
4 3 5.1659 2.1659 2108.8
5 4 6.3231 2.3231 2441.1
6 5 7.4434 2.4434 2537
7 10 12.869 2.8691 2875.6
8 20 23.405 3.4054 3302.1
9 30 33.782 3.7816 3601.3 10 40 44.081 4.081 3839.5 11 50 54.334 4.334 4040.7 12 60 65.576 4.555 4216.5 13 70 74.753 4.7527 4373.7 14 80 84.932 4.9324 4516.6 15 90 84.932 4.9324 4516.6 16 100 84.932 4.9324 4516.6
LOAD (kN)
0 1000 2000 3000 4000 5000
0 -• E 20 -
I- z 40 -1.0 2 60
80
U' 100 -
Fig 6.5 Load vs. Settlement Curve for Pile
54
Table 6.7 Computation for Raft Stiffness
Pressure (kN/m2) Settlement (mm) Pressure (kN/m2) Settlement (mm)
0 0 50 57.746
1 1.2744 60 68.547
2 2.541 70 79.288
3 3.8 80 90.029 4 5.0518 90 100.83 5 6.2966 100 111.73 10 12.423 125 139.84 20 24.266 150 169.94 30 35.691 200 241.95 40 46.82 300 630.2
Fig 6.6 Pressure vs. Settlement Curve for Raft For analysis purpose two cases are considered. (i) raft foundation and (ii) Piled
raft foundation. For each case initially coefficient of subgrade reaction of soil (k) and C is
assumed.
where
C = Stiffness of pile/ (coefficient of subgrade reaction of soil x area of pile)
For raft foundation C is taken as I
The settlements of different nodes are calculated by the developed software, and
using these values the stiffness of soil and the piles are estimated. These stiffness values
55
should matched with the assumed value and if it is not matched then for these new values
of stiffnesses, settlements are found. This procedure is continued till the convergence is
reached. Tables 6.8 and 6.9 show the settlement values for raft and piled raft foundation
for different trials respectively.
Table 6.8 Deflection at Different Nodal Points for Raft foundation
Node k=1000
(kN/m3)
Deflection
(mm)
k=855.36
(kN/m3)
Deflection
(mm)
k=862.79
(kN/m3)
Deflection
(mm)
k=862.44
(kN/m3)
Deflection
(mm)
Trial 1 Trial 2 Trial 3 Trial 4
1 102.61 112.93 112.33 112.36
7 91.27 100.88 100.32 100.35
13 89.402 98.532 98.003 98.029
19 81.26 89.818 89.32 89.345
25 88.613 97.374 96.865 96.89
301 67.205 74.244 73.83 73.851
307 46.126 51.722 51.391 51.407
313 46.542 51.831 51.519 51.534
319 46,954 52.824 52.477 52.494
325 71.747 79.453 79.001 79.023
426 54.122 62.235 61.756 61.78
432 41.36 47.842 47.457 47.476
438 36.372 42.331 41.978 41.995
444 44.616 51.366 50.966 50.986
450 62.491 71.264 70.748 70.773
576 59.111 66.711 66.258 66.28
582 44.451 50.234 49.888 49.905
588 31.852 36.617 36.33 36.344
594 38.075 43.378 43.058 43.074
600 48.6 55.626 55.205 55.226
56
Table 6.9 Deflection at Different Nodal Points for Piled Raft foundation
Node k=1000
(kN/m3)
Deflection
(mm)
C=450
k=807.64
(kN/m3)
Deflection
(rnm)
647.9
k=808.58
(kN/m3)
Deflection
(mm)
550.8
k=809.42
(kN/m3)
Deflection
(mm)
535.45
Trial 1 Trial 2 Trial 3 Last trial
1 22.754 23.1 23.51 23.99
7 22.976 23.46 23.856 23.319
13 22.325 22.769 23.157 23.612
19 20.247 20.67 21.02 21.43
25 19.728 20.015 20.37 20.784
301 19.51 19.985 20.303 20.676
307 16.566 17.23 17.482 17.779
313 16.806 17.419 17.674 17.974
319 16.431 17.104 17.359 17.658
325 20.141 20.635 20.969 21.361
426 11.04 11.445 11.666 11.926
432 12.318 12.893 13.104 13.352
438 9.5189 10.017 10.202 10.42
444 13.602 14.209 14.437 14.706
450 13.624 14.07 14.331 14.638
576 12.834 13.099 13.329 13.6
582 12.656 13.016 13.226 13.471
588 7.8479 8.1134 8.2559 8.4235
594 11.042 11.391 11.574 11.787
600 43.804 10.278 10.462 10.679
C = Stiffness of soil/ (co-efficient of subgrade reaction of soil x area of pile)
57
RAFT —A— PILED RAFT
100 80 -
5 60 -40 -20 - 0
0 5 10 NEE 20 25
30
This case history of piled raft problem (Fig.6.3 &6.4) was solved by Yamashita at al.
(1994). The measured settlement was reported to be 1 Ornm-23 mm .The same problem is
also solved in the present study, and the results (Table 6.9 and Fig. 6.7) show that the
settlement of piled raft generally varied from about 8.5 mm-24 mm, agreeing well with
the value obtained by Yamashita et al. (1994). Table 6.10 shows silent design output for
raft and piled raft foundation.
Fig 6.7 Deflection vs. Nodal points along A-A for Raft and Piled Raft Foundation
Table 6.10 Salient Design output for Raft and Piled Raft Foundation
S.No. Description Raft Foundation Piled Raft Foundation
1 Max +ve B.M (kNm/m) in X-dir 193.09 50.91
Area of steel required (mm2) 2971.1 783.36
2 Max -ye B.M (kNm/m) in X-dir 390.91 136
Area of steel required (mm2) 6015 2092.36
3 Max +ve B.M (kNm/m) in Y-dir 290.4 71.48
Area of steel required (mm2)) 4468.4 1099.7
4 Max -ye B.M (kNm/m) in Y-dir 497.5 181 Area of steel required (mm2) 7655.1 2785.1
5 Max. Vertical deflection (mm) 112.36 23.99
6 MM. vertical deflection (mm) 10.87 4.11
7 Max. differential settlement 1 in 206.42 1 in 1050
58
Table 6.11 Effect of k on Deflection
Node Deflection (mm)
k (1(N/m3)x103 1 2 3 4
1 102.61 67.545 53.04 44.721
7 91.27 58.686 45.386 37.868
13 89.402 58.007 44.927 37.453
19 81.26 52.208 40.313 33.582
25 88.613 58.678 46.17 38.957
301 67.205 44.351 35.243 30.043
307 46.126 28.632 22.076 18.488
313 46.542 29.7 23.144 19.461
319 46.954 28.637 21.856 18.191
325 71.747 46.661 36.746 31.147
426 54.122 29.198 20.62 16.32
432 41.36 21.87 15.407 12.26
438 36.372 18.35 12.303 9.3496
444 44.616 24.163 17.267 13.86
450 62.491 35.133 25.446 20.475
576 59.111 36.456 28.445 24.102
582 44.451 27.637 21.783 18.588
588 31.852 18.486 14.068 11.731
594 38.075 23.223 18.309 15.679
600 48.6 28.492 21.841 18.368
60
Differential Settlement In present case, the maximum settlement for piled raft and raft foundation are 23.99 mm
and 112.36 mm (Table 6.10) respectively at node no.1, and the minimum settlements are 4.11 mm and 10.178 mm (Table 6.10) respectively at node no. 171. Hence in the case of raft foundation maximum differential settlement is (112.36-10.178)/(20.88 x 103) i.e.,
about 1 in 206.42. Whereas in the case of piled raft foundation, the maximum differential settlement is (23.994-4.1162)/(20.88 x 103) i.e., about 1 in 1050. Hence by using the piled
raft foundation the maximum differential settlement (Table 6.10) is reduces by 1 in 206.42 to 1 in 1050. Fig. 6.7 compares the settlement profile along section A-A for raft and piled raft foundation.
6.3 PARAMETRIC STUDIES 6.3.1 Effect of coefficient of subgrade reaction
To study the effect of variation of co-efficient of subgrade reaction, a range of different probable values of k are chosen and the problem given in Table 6.3 is solved.
6.3.1.1 Effect of coefficient of subgrde reaction on deflection
Table 6.11 shows the deflection of nodes with different values of k. The deflection of nodes 1 and 438 are 102.61 mm and 36.372 mm respectively for k =103 kN/m3. With increase in the value of k by 4 times, the deflection at node 1 and 438 decrease by 56.4 % and 74.29 % respectively.
Figures 6.8.a and 6.8.b show the deflection of nodes along the section A-A and B-B for different value of k. From the Figs. 6.8.a and 6.8.b deflection of typical nodes 301 and 13 are 66.369 mm and 91.27 mm respectively. While increasing the value of k by 4
times deflection are found to be 18.95 mm and 37.86 mm respectively, resulting in decrease in deflection by 71.4 % and 58.5 %.respectively.
The variation in k value by three to four times has resulted in 55 % to 75 % in maximum deflection.
59
80 70 •
O 60 • 50 •
W a s 40
30. FL4 20 •
10 •
DEFLECTION vs. NODAL POINTS
0
• 5
10
15
20
25 30
0
( -IF- k=1 k3 f k-3 • k=4 NODE
DEFLECTION vs. NODAL POINTS 100
80
0 60
40
i4 ▪ 20
5 10 15 20 25 30 -20
NODE k -1 -*-- k-2 k-3 k=4
Fig 6.8.a Deflection vs. Nodal Points along Section A-A
Fig 6.8.b Deflection vs. Nodal Points along Section B-B
6.3.1.2 Effect of co-efficient of subgrde reaction on bending moment
Tables 6.12 and 6.13 represent the bending moment in X and Y direction at the pile location From the Table 6.14 maximum positive and maximum negative bending
moment are 407.39 kN-m/m and 768.22 kN-mtm at node nos. 72 and 313 respectively for k=1000 IN/m3. With the increase the value of k by 4 times the corresponding values are
325.8 kN-m/m and 694.95 kN-m/m respectively. So, the percentage change in bending
moment are 20.025 % and 9.5 %.. Figs 6.9.a and 6.9.b show the bending moment in X
and Y direction along the section A-A, while Figs 6.9.c and 6.9.d show the bending moment in X and Y direction along section B-B
61
Table 6.12 Effect of k on Bending Moment in X direction
Node Moment in X Direction (k_N-m/m)
K (kN/m3)x103 1 2 3 4
1 0 0 0 0
7 -0.00798 -0.00798 -0.00797 -0.00795
13 -0.00786 -0.00774 -0.00765 -0.00758
19 -0.00677 -0.00684 -0.00686 -0.00686
25 0 0 0 0
301 0 0 0 0
307 -363.36 -365.59 -365.01 -363.61
313 -391 -386.41 -380.77 -375.89
319 -349.21 -352.47 -352.73 -351.97
325 0 0 0 0 426 0 0 0 0 432 -245.35 -248.6 -249.29 -248.94 438 -126.41 -130.62 -132.17 -133.11 444 -279.09 -282.04 -282.4 -281.74 450 0 0 0 0 576 0 0 0 0 582 -0.00494 -0.00495 -0.00492 -0.00487 588 -0.00198 -0.00213 -0.0022 -0.00224 594 -0.00429 -0.00434 -0.00433 -0.00429 600 0 0 0 0
62
Table 6.13 Effect of k on Bending Moment in Y direction
Node Moment in Y Direction (1cN-m/m)
K (kN/m3)x103 1 2 3 4
1 0 0 0 0
7 0 0 0 0
13 0 0 0 0
19 0 0 0 0
25 0 0 0 0
301 -0.0035 -0.00167 -0.00103 -0.00073
307 -468.4 -439.67 -419.24 -404.34
313 -492.54 -461.43 -439.48 -423.41
319 -452.28 -422.48 -402.71 -388.66
325 0.001941 0.003076 0.003457 0.003588
426 -0.00811 -0.00544 -0.00426 -0.00357
432 -218.51 -210.2 -210.27 -211.79
438 -123.41 -113.57 -113.15 -114.71
444 -273.3 -257.96 -254.14 -253.08
450 0.011001 0.008701 0.007394 0.006512
576 0 0 0 0
582 0 0 0 0
588 0 0 0 0
594 0 0 0 0
600 0 0 0 0
200 -
w 100
E 0"-- E z . -100 a 0 z -200 03
-300 -
I
10 15 25 30
NODE
K-1 -0- K=2 -k- K=3 --0-- K=4.
Table 6.14 Salient Design output for Raft Foundation
S1.No. Description k x103( kN/m3)
1 2 3 4
1 Max +ve B.M (kN-m/m) in X-dir. 192.5 188.5 184.38 180.35
Area of steel required (mm2)
at node 72
2962 2900.5 2837.1 2755.1
2 Max -ye B.M (kN-m/m) in X-dir. 391.02 386.41 380.72 375.89
Area of steel required (mm2)
at node 313
6016.7 5945.8 5858.2 5775.6
3 Max +ve B.M (kN-m/m) in Y-dir. 276.0 226.0 207.4 194.33
Area of steel required (mm2)
at node 72
4246.9 3477.5 3191.3 2990.2
4 Max -ye B.M (kN-m/m) in Y-dir. 492.5 461.4 439.46 423.21
Area of steel required (mm2)
at node 313
7578.2 7099.7 6762.1 6515.1
5 Max. Vertical deflection (mm) 102.61 67.45 53.04 44.72
6 Max positive Bending moment 407.39 360.43 340.66 325.8
Max negative Bending moment 768.27 737.22 712.7 694.95
Fig 6.9.a Bending Moment in X- Direction vs. Nodal Point along Section A-A
64
Fig 6.9.b Bending Moment in Y- Direction vs. Nodal Point along Section A-A
Fig 6.9.c Bending Moment in X- Direction vs. Nodal Point along Section B-B
Fig 6.9.d Bending Moment in Y- Direction vs. Nodal Point along Section B-B
65
6.3.2 Effect of Stiffness of Pile To study the effect of piled raft foundation with varying stiffness of pile, the
problem given in Table 6.3 is solved and results are presented in the following sections.
6.3.2.1 Effect of stiffness of pile on deflection of nodes
Table 6.15 shows the deflection of nodes with different values of stiffness of pile
keeping the value of k (103 kN/m3) constant. The deflection of typical node at 1 and 438
are 102.61 mm and 36.372 mm respectively for C=1.By increasing the C value by 150
times, the deflection at corresponding nodes are 48.093 mm and 19.726 mm. So,
percentage changes in these values are 53.18% and 47 % respectively for this particular
case. For C=600, the corresponding values are 18.011mm and 7.4757mm respectively.
Here percentage changes in these values are 82.44 % and 79.4 % respectively. That is
after particular values of C , the rate of change of settlement decreases.
Figs. 6.10a and 6.10b show the deflection of nodes along the section A-A and B-B
for different value of C.
The increase in C value by 600 times in this particular case resulted in 78 % to 83
% in maximum deflection.
66
Table 6.15 Effect of Stiffness of Pile on Deflection
Node k=1.0x103 (kN/m3)
Deflection (mm)
C=1 C=150 C=300 C= 600
1 102.61 48.039 30.884 18.011
7 91.27 46.13 30.64 18.39
13 89.402 45.147 29.867 17.826
19 81.26 40.818 27.039 16.192
25 88.613 41.551 26.752 15.627
301 67.205 37.125 25.54 15.798
307 46.126 29.201 21.128 , 13.629
313 46.542 29.624 21.434 13.83
319 46.954 29.288 21.044 13.481
325 71.747 38.872 26.5 1 16.256
426 54.122 24.648 15.347 , 8.585
432 41.36 23.55 1
16.187 9.9381
438 36.372 19.726 12.953 7.4757
444 44.616 25.684 17.785 11.013
450 62.491 29.434 18.697 10.691
576 59.111 26.995 17.366 10.19
582 44.451 24.217 16.6 10.233
588 31.852 16.124 10.569 6.239
594 38.075 20.978 14.449 8.9408
600 48.6 21.473 13.643 7.9278
C = stiffness of soil/ (co-efficient of subgrade reaction of soil x area of pile)
67
I
100 - E 80 - z O 60 -
40
u- 20 -
0 04.41"14-41”1"1-4ft ar as a
C=1 --s— C=150 C-300 C-600
0 5 10 15 20 25 30 NODE
Fig 6.10.a Deflection vs. Nodal Points along Section A-A
Fig 6.10.b Deflection vs. Nodal Points along Section B-B
6.3.2.2 Effect of stiffness of piles on bending moment
Tables 6.16 and 6.17 represent the bending moment values in X and Y direction at
the location of pile. From the Table 6.18 maximum positive and maximum negative
bending moment are 407.39 kN-m/m and 768.27 kN-m/m at nodes 72 and 313
respectively for C=1. With the increase in the value of C by 600 times, the corresponding
values are 89.24 lth-m/m and 240.4 kN-m/rn respectively. So, percentage changes in the
bending moment are 78.09 % and 68.7%. Figs 6.11.a and 6.11.b show the bending
moment in X and Y direction along the section A-A, while Figs 6.11.c and 6.11.d show
the bending moment in X and Y direction along section B-B
68
Table 6.16 Effect of Stiffness of Pile on Bending Moment in X direction
Node k=1.0x103 (kN/rn3)
Deflection (mm)
C=1 C=150 C=300 C= 600
1 0 0 0 0
7 -0.00798 -0.00292 -0.00141 -0.0018
13 -0.00786 -0.00264 -0.00133 -0.00157
19 -0.00677 -0.00244 -0.0012 -0.0015
25 0 0 0 0
301 0 0 0 0
307 -363.36 -177.48 -245.71 -116.45
313 -391 -182.49 -247.42 -119.42
319 -349.21 -166.56 -236.72 -108.21
325 0 0 0 0
426 0 0 0 0
432 -245.35 -105.7 -174.03 -66.948
438 -126.41 -11.651 -74.622 4.1311
444 -279.09 -124.89 -196.17 -80.412
450 0 0 0 0
576 0 0 0 0
582 -0.00494 -0.00214 -0.00097 -0.00136
588 -0.00198 -0.00046 -0.00041 -0.00023
594 -0.00429 -0.00192 -0.00088 -0.00122
600 0 0 0 0
C = Stiffness of soil/ (co-efficient of subgrade reaction of soil x area of pile)
69
Table 6.17 Effect of Stiffness of Pile on Bending Moment in V direction
Node k-----1.0x103 (1cN/m3)
Deflection (mm)
C=1 C=150 C=300 C= 600
1 0 0 0 0
7 0 0 0 0
13 0 0 0 0
19 0 0 0 0
25 0 0 0 0
301 -0.0035 -0.00122 -0.00061 -0.00025
307 -468.4 -303.35 -222.45 -145.36
313 -492.54 -321.17 -237.13 -156.72
319 -452.28 -287.51 -208.74 -134.96
325 0.001941 0.000797 0.000489 0.000277 426 -0.00811 -0.00448 -0.00308 -0.00191 432 -218.51 -117 -77.264 -45.491 438 -123.41 -34.853 -7.1203 7.944 444 -273.3 -154.08 -105.53 -64.863 450 0.011001 0.005228 0.003342 0_001924 576 0 0 0 0 582 0 0 0 0 588 0 0 0 0 594 0 0 0 0 600 0 0 0 0
C = Stiffness of soil/ (co-efficient of subgrade reaction of soil x area of pile)
70
-•- C=1 -• C=150 -A- C=300 --A- C=600
5 10 15 0 25 30
NODE
200
100
0 E Fc -100
-200
-300
BE
ND
ING
MO
ME
NT
Table 6.18 Salient Design output for Piled Raft Foundation
S.No. Description k=1.0x1031cN/m3
C= 1 150 300 600
1 Max +ve B.M (1cNm/m) in X-dir 192.5 105.29 77.02 44.55
Area of steel required (nun2) . 2962 1620.1 1185.1 685.5
2 Max -ve B.M (cNrn/m) in X-dir 391.02 249.82 182.49 119.42
Area of steel required (mm2) 6016.7 3844 2808 1837.5
3 Max +ve B.M (cNin/m) in Y-dir 276.0 141.86 95.54 58.08
Area of steel required (mm2)) 4246.9 2182.8 1470.1 893.69
4 Max -ve B.M (IcNm/m) in Y-dir 492.5 321.7 237.13 156.72
Area of steel required (mm2) 7578.2 4950.1 3648.8 2411.5
5 Max. Vertical deflection (mm) 102.61 48.038 30.88 18.39
6 Max. positive Bending Moment (kNtn/m) 407.39 214.8 15.0.0 89.24
Max. positive Bending Moment (IcNm/m) 768.27 496.97 364.8 240.4
Fig 6.11.a Bending Moment in X- Direction vs. Nodal Point along Section AA
71
C=1 —E— C=150 —A— C=300 • C=600
NODE BEND
ING
MOM
ENT 50
0
-50 E Z -100 AL
-150
-200
5 30
BEND
I NG
MOM E
NT 100
0
• -100 E z
•
-200
-300
-400
C=1 C=150 —A-- C=300 —0— C=600
C=1 —II— C=150 --a— C=300 C=600
400 1--, Z W 200 2 0 1 0 2 --- CD 5 10 15 20 25 30 z _Ic -200 Y ct
-400 Lu 03
-600 NODE
Fig 6.11.b Bending Moment in Y- Direction vs. Nodal Point along Section AA
Fig 6.11.c Bending Moment in X- Direction vs. Nodal Point along Section B-B
Fig 6.11.d Bending Moment in Y- Direction vs. Nodal Point along Section B-B
72
6.3.3 Effect of Tilting of Pile As it is extremely difficult to drive the pile absolutely vertical and to place the
foundation exactly over its center line, a pile is not used singularly beneath a column or a
wall. If eccentric loading results, the connection between the pile and column may break
or the pile may fail structurally because of bending stress. In the problem (Fig. 6.3) single
pile is placed under a column.
To analyze the effect of tilting of pile, reduced stiffness of pile (about 50%) is
considered. Table 6.19.a represent the settlement of nodes due to tilting of pile while
Table 6.19.b represents the percent increase in settlement of nodes due to the pile tilting.
The settlements of node no. 1 (boundary corner node) with and without tilting
have been found as 38.678mm and 20.043 mm (Table 6.19.b). Hence the percentage
increase in the settlement due to tilting is 60.875 (Table 6.19.b). For boundary node 7 the
settlements are 37.169 mm and 24.37 mm for with and without tilting respectively and
percentage increase in settlement is 52.51% (Table 6.19.b). For interior node 313 the
settlements are 24.896 and 38.26 with and without tilting (Table 6.I9.b). So, percentage
increase in settlement is 38.26% (Table 6.19.b).
Hence due to tilting the percentage increase in nodes are 58% to 62% for
boundary corner load, 49% to 53% for boundary nodes and 38% to 53% for interior nodes
respectively. So, boundary corner nodes are more critical (Table 6.19.b).
73
Table 6.19.b Percentage increase in Settlement of Nodes Due To Tilting
Node no. Settlement (mm)
No tilting With Tilting % increase
1 20.043 38.678 60.87
7 24.37 37.169 52.51
25 20.83 33.509 60.83
313 180..6 24.896 38.26
325 21.403 32.267 50.75
432 13.379 18.66 39.47
438 10.44 14.46 38.50
444 14.736 20.551 39.46
576 13.629 21.723 59.38
600 10.703 17.055 59.34
74
Tab l
e 6.1
9. a S
e ttlem
ent o
f Nod
es D
ue T
o Ti
lting
T ilti
ng o
f pile
at (S
ettlem
ent i
n m
m)
0 VD 24
. 043 11--
M ,zzi: CV
.-i en oo 6 (-‘1
kr) 0 0 oti .--1
.-.1 d- Cr) -4 r \I 13
. 382
1
10. 40
9 kr) kr) \-0 4
rn ■r,
tr; .-■
ON (!) t-Z 1-t
r-- kr) 24. 0 4
5
24. 3
71
20. 8
29
18. 00
4 Cr) d-. ---. (--.1
(--- tN M -
ON en 0 ..
00 r-- 4 .-. 21
.723
10. 70
4
-1- d- 4
c) O 4 c--4 24
. 376
el 00 6 c-A
cn 00 .0) oci .-(
kr) (N Cr) -4 it--4
Cr's 0 Cr) rn .-•
(--1 Cr) 0 -4 .-■
1-.4 lin WI 4::::4 ir-.4
-cr \-0 . en v...-4
kr) .. Cr) 6 -,
00 cn -71-
ft0 kr/ CD 4 ri 24
.37 1
20. 8
43 e...1 00 kr)
00 Il 21.3 4
3 Cr) ON r-- Cr) -
. '. "1-.
cr., -71- •-. kri Il
,--. •--i ir) Cr) vl
(4.-.) 00 kr) 0 v4
(--4 -1- 24
. 034
24. 3
74
20. 8
36
r-
oci ......
v....4
-. csr
v:o ■ro '3:3
00 N..
cr; -,
.--I r--
-1 ...-,
L
cn v■I
,-4
cz6 v■I
kr) (NI en 24.0
47
00en 4 CA
ON 6 CI
C4 00 c---: ,''''' 32
.267 00
en M
\-0 en 6
-Tr VD 4
00 VD M
kr) d- 6
C.-) •-1 Cn
4■4 t--- C Cr.; (--A
.7r 00 CA 4 c-A
r-- t.....*- 6 (-.4
v:,
OS -.4. tN
,.-.., Cl -4 CA
kr)
13. 47
3
11. 43
4
14. 8 2
8 -,
Cr) .--, 10. 69
4 1
r-Ni
24.0
49 (N 00
4 (NI 33
. 509
(NI 00 r-: -,
t---- -1- 4-I (4,4 13
.382 v.-4 kr)
c) ..1
..-4 en 4 •--- 13
.628
10. 70
6
ir- M '7r -1- kr; CA
ON VD .--0 Ir- en
\-0 kr) 00 0 (-•1
(N '7r ch Ir--: •-. 21
.415
d- 00 Cr) Cr) 10
. 446 ql d- Ir----
d: 13.63
3 ZOL '0 I
.--t 00 It- ■D 00 M
00 Ct■ 0 kr; (N
r-- en oe 6 CV
00 t-- cr, ir-- •-■
VD 0 d: -4 C■1
kr) t-- Cr Cr) ,,
(N iLon d: c:, ‘'.', 14
.738
13.6 3
3 CNI 0 r--- 6
Nod
e No.
r-- kr) r■I ,'4 Cr) CN•1 Cr) en d- en -1- d- d- r--- kr) 0 VD
CHAPTER 7
CONCLUSIONS AND SCOPE FOR FURTHER WORK
Piled raft foundation is adopted to reduce the total and differential settlement of
foundations, and thus estimation of settlement profile of piled raft foundation forms an
important design exercise. So accordingly a method is proposed to obtain the settlement
profile of piled raft foundation. In this proposed method, the raft is represented by an
elastic plate, while the soil and piles are modeled as bed of equivalent spring at nodal
points, and intersecting spring respectively. Software is developed for the analysis of raft
using finite difference method, estimation of stiffness for soil and pile and the structural
design of raft and pile in MATLAB. A typical case history is analyzed and the estimated
settlements are compared with observed settlement values. This exercise showed that the
proposed method can used for the analysis of piled raft foundation.
To see the effect of various parameters on the behaviour of piled raft foundation
system, a typical problem of piled raft is solved and the results show that,
(i) A variation in modulus of subgrade reaction by three to four times is resulted
in 55% to 75% change in maximum deflection and corresponding change in
moments are 9.5 % to 20.25 %.
(ii) For the problem considered, the differential settlement can be reduced to 1 in
1050, in case of piled raft foundation system from 1 in 206.42 in case of raft
foundation.
(iii) The increase in C value by 600 times in the problem considered resulted in
78% to 83% change in maximum deflection and corresponding change in
moments are 68% to 78% respectively.
(iv) Piles located at boundary corner are more susceptible to tilting of pile in
comparison to interior nodes.
The analysis adopted in the present study is strictly applicable to vertical
loading. In highly seismic area, estimation of the behaviour of the piled raft during
earthquake becomes an important factor in the foundation design process. So, one can
extend this method for the analysis for lateral load. This work can also be extended for
studying the optimal pile arrangement for minimizing differential settlement in piled raft
foundation and analyze the behaviour of piled raft foundation.
76
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