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Raft 
Foundations 
Design and Analysis with a 
Practical Approach 
SHARAT CHANDRA CUPTA 
Advisor, Indian Buildings Congress, 
Former Chief Engineer 
Central Public Works Department 
PUBLISHING FOR ONE WORLD 
NEW AGE INTERNATIONAL (P) LIMITED, PUBLISHERS 
New Delhi - Bangalore Calcutta Chennai Guwahati Hyderabad 
Lukhnow Mumbai . Pune 
Copyright O 1997 New Age International (P) Limited, Publishers 
NEW AGE INTERNATIONAL (P) LIMITED, PUBLISHERS 
NEW DELHI 
BANGALORE 
CALCUTTA 
CHENNAI 
GUWAHATI 
HYDERABAD 
LUCKNOW 
MUMBAI 
PUNE 
: 4835124, Ansari Road, Daryaganj, New Delhi-110 002 
: 35, Annapoorna Complex, South End Road, 
Basavangudy, Bangalore-560 004 
: 4018, Ballygunge Circular Road, Calcutta-700 019 
: 20, IInd Main Road Kasthuribai Nagar, Adyar, 
Chennai-600 020 
: Pan Bazar, Rani Bari, Guwahati-781 001 
: 1-2-4 1219, Gaganmahal, Near A.V. College, Domalguda, 
Hyderabad-500 029 
: 18, Madan Mohan Malviya Marg, Lucknow-226 001 
: 1281A. Noorani Building, Block No. 3, First Floor. 
L.J. Road, Mahim, Mumbai-400 016. 
: 44, Prashant Housing Society, Lane No. 6, Paud Road, 
Kothrud, Pune-4 1 1029. 
This book cr any-part there of may not be 
reproduced in any form without the 
written permission of the publisher 
This book is not to be sold outside the 
country to which it is consigned by 
New Age International (P) Limited 
ISBN : 81-224-1078-2 
Published by H.S. Poplai for New Age International (P) Limited, 4835124, Ansari 
Road, Daryaganj, New Delhi- 110002. Typeset by EPTECH, and printed ai Ram 
Printograph, C-114, Okhla Industrial Area, Phase I, New Delhi-110020. 
Printed in India 
Production : M.I. Thomas 
CONTENTS 
Preface 
i 
t 
I 1. INTRODUCTION 
2. NEED OF RAFT FOUNDATION 
3. TYPES OF RAFT FOUNDATION 
4. SURVEY OF AVAILABLE LITERATURE 
I 1 Foundation Engineering by Peck, Hansen and Thornburn 
I 4.2 Foundation Design and Practice by Elwyn. E.S. Seelye 1 4.3 Foundation Design by Teng 4.4 Foundation of Structures by Dunham 
i 4.5 Indian Standard Code of Practice for Design and Construction of Raft 
Foundation - IS 2950-1965 
Raft Foundation - The Soil Line Method of Design by A.L.L. Baker 
Indian Standard Code of Practice for Design and Construction of Raft Foundation 
1.S : 2950 (Part-I) 1973 
Foundation Engineering Handbook Edited by' Hans F. Winterkorn & Hsaiyang Fang 
Foundation Analysis and Design by Joseph. E. Bowels 
Building Code Requirements for Reinforced Concrete (ACI 31 8 - 77) 
Foundation Design and Construction by M.J. Tomlinson 
Design of Combined Footings and Mats ACI Committee 336 
Pile Foundation Analysis and Design by H.G.Poulos and E.H. Davis 1980 
Reinforced Concrete Designers Handbook by Charles E. Reynolds and 
James C. Steedman - 9th Edition 1981 
IS 2950 (Part I) 1981 -Code for Design and Construction of Raft Foundation Part I 
~ e s i ~ n 
Eleventh International Conference of Soil Mechanics and Foundation Engineering 
San Francisco, August 12 - 16,1985 
Foundation Design and Construction by M.J. Tomlinson, 5th Edition, 1986 
CONTENTS i 
Handbook of Concrete Engineering -Mark Fintel - 2nd Edition, 1986 
Reinforced Concrete Designer Handbook by Charles E. Reynolds and James 
Steedman, 10th Edition, 1988 
Building Code Requirements in Reinforced Concrete - ACI - 3 18 - 1989 
Foundation Engineering Hand book by Hsai-Yang-Fang 2nd Edition, 1991 
Design of Combined Footings and Mats - ACI committee 336 2R - 88 
Published in ACI Manual 1993 
Foundation Analysis and Design by Bowles, 4th Edition, 1988 
Proceedings of Indian Geo-Technical Conference 1992, Calcutta, December, 1992 
Designs of Foundation Systems - Principles and Practices by Nainan P. Kwian, 1992 
13th International Conference on Soil Mechanics and Foundation Engineering, 
New Delhi, January, 1994 
Soil Structure Inter-action -The Real Behaviour of Structures, published by the 
Institution of Structural Engineers, U.K. The Institution of Civil Engineers, 
U.K. International Association for Bridge and Structural Engineering in March, 1989 
5. DESIGN APPROACH AND CONSIDERATIONS 
5.1 Rigid Approach 
5.2 Flexible Approach 
5.3 Parameters for Raft Design 
5.4 Pressure Distribution Under the Raft 
5.5 Rigidity Criteria 
5.5.1 Proposed by IS : 2950 (Part I) 1981 
5.5.2 ACI Committee, 336 
5.5.3 Hetenyi's Criteria 
5.6 Modulus of Sub-Grade Reaction 
5.6.1 Recommended by Bowles 
5.6.2 IS : 2950 Part I Indian Standard Code of Practice for Design and 
Construction of Raft Foundation 2950 - 1981 
5.6.3 I.S. 9214-1979 - Method of Determination of Modulus of Subgrade 
Reaction (k value) of Soils in Field 
5.6.4. IS 8009 - Part I - 1978. Code of Practice for Calculation of Settlements of 
Foundations - Part I - Shallow Foundations. Subjected to Sy_mmetrical 
Static Vertical Load. 
5.6.5 Recommendation by Alpan and Prof. Alarn Singh 
5.6.6 Summary 
6. STRUCTURAL DESIGNERS DILEMMA 
7. STUDIES CARRIED OUT ON EFFECT OF VARIOUS PARAMETERS ON DESIGN OF RAFT 38 
7.1 Study 1 40 
7.1.1 Examples Selected 41 
7.1.2 Raft Size 41 
CONTENTS 
5 7.1.3 Soil Investigation 
! 7.1.4 Load Considered in Study 
7.1.5 Analysis 
: 7.1.6 ' Discussions of Results 
7.1.7 Conclusions 
7.2 Study 2 -Effect of Horizontal Loads 
7.2.1 Example Selected 
7.2.2 Discussion of Results 
7.2.3 Conclusion 
7.3 Study 3: Comparison with Conventional Rigid Methods 
7.3.1 Details of Conventional Method: Combined Footing Approach 
7.3.2 Examples Selected 
7.3.3 Discussion of Results 
7.3.4 Inverted Floor Method 
7.3.5 Conclusions 
1 7.4 Study 4. Another Office Building 7.4.1 Example Details 7.4.2 Comparison of Results t 
t 
1 7.4.3 Discussions of Results 
! 7.4.4 Conclusions 
I 
8. STUDIES CARRIED OUT ON ANALYSIS AND DESIGN OF PILED RAFTS 
1 
t 
i 8.1 Design Procedures being Used 
! 8.2 Example Selected 
8.3 Soil Data 
8.4 Methods of Analysis Studied 
8.4.1 Conventional Rigid Method with Simplified Models 
8.4.1.1 Combined footing approach 
8.4.1.2 Continuous beam analogy :inverted floor 
8.4.1.3 Comparison of results 
8.4.2 Piled RafPAnalysis Based on Finite Element Approach 
8.5 Study of Parameters Influencing the Raft Behaviour 
: 8.5.1 Effect of Raft Stiffness on the Pile Loads and Raft Moments ; 8.5.2 Effect of Superstructure and Retaining Walls on Foundation Stiffness 
I 8.5.3 Effect of Earthquake Loads and Moments 
I 8.5.4 Effect of End Bearing and Friction Piles 
8.5.5 Summary of Results 
I 8.6 Discussions 
8.7 Conclusions 
9. JOINTS IN RAFl'S 
10. SUMMARY OF STUDIES 
11. FACTORS AFFECTING CHOICE OF MET,HOD OF ANALYSIS 
12. GUIDELINES 
APENDM - ILLUSTRATIVE EXAMPLES 
A.l Conventional Rigid Method - Combined footing approach 
A.2 Flexible Raft - Beam on elastic foundation 
A.3 Piled Raft-Plate on elastic foundation 
CONTENTS 
INTRODUCTION 
I 
i 
t 
In 1957, when the author was a student of Civil Engineering at the Indian Institute of Technology, Kharagpur, 
the first institute of national importance, one of his professors of Civil Engineering at his first lecture in the 
class said: 
"Civil Engineering is 50% common sense but common sense is that sense which is quite uncommon. " 
After 34 years of experience in Civil Engineering construction and design, the author only wonders how 
true the statement of his Professor was and how much more it is true in case of foundation engineering. 
1.1 Foundation engineering has been practised as an art, without help of science, since time immemorial upto 
1920 when it had achieved a considerable amount of refinement. It was in the earlier 1920s that a concerted ! effort was made to study and undentand the physical laks governing the behaviour of sub surface materials, \ i.e.. soil from which foundations derived their support and on whose behaviour its own behaviour depends. 
This is the time when studyof soil mechanics was started and it was in 1919 when Karl Terzaghi, popularly 
known as 'father of soil mechanics', made successful attempt to explain the phenomenon of settlement oti a 
scientific basis. Though study of soil mechanics has provided us with new techniques for selecting appropriate 
type of foundation and predicting the behaviour of completed structures, it has not been able to decrease the 
importance of the accumulated experience of the ages. Amount of uncertainty and degree of variation in the 
properties of soil and number of parameters on which performance of a foundation depends, make exact 
solution impractical, if not impossible. With so much of advancement in science and computer application, 
structural design is still defined as:I5 
a creation of a structural fonn to satisfy a number of requirements. It is a combination of art and science. 
As a rule, there is no direct procedure leading to the solution of a specific problem. An engineer uses all 
his resources of knowledge experience and imagination to produce a trial scheme. He then constructs a 
mathematical model of such a solution to assess its adequacy and ifnecessary, modifies the original concept 
in the light of analytical results. The process is repeated until the designer is satisfied with thefinalproduct, 
taking into account not only structural adequacy but also such non-quantifiable factors as aesthetics, ease 
of construction and performance. The design process is characterised by a complex interaction of 
parameters and the need to arrive at decisions based on incomplete data Intuitive decisions which have to 
be taken, appear to be diametrically opposite to the logical nature of ... ' 
2 RAFT FOUNDATIONS-DESIGN AND ANALYSIS 
Foundation design and analysis is, at a stage behind structural analysis and design for superstructure, and 
even now continues to be practised more as an art and will probably continue to be done so, for many years 
to come. 
1.2 Available textbooks, handbooks, various publications and papers give widely different approaches to 
design of raft foundations. A designer, when faced with a task of designing a raft foundation, finds himself in 
a precarious position where he has to balance the time available for design, the cost of design, the need of 
adequate safety and, above all, acceptance of the design by the client and the professional community in general 
and decide the method of design to be followed by him. Generally, it is not practical for any designer to go 
through the various approaches as available in engineering literature at a particular time, compare their merits 
and demerits and select the most suitable for his purpose. He, therefore, perforce selects a particular textbook 
and applies the same to his problem, quite often little realising that the theoretical problem dealt with in the 
textbook is widely different from his practical problem relating to an actual building. Resulting solution may 
not be as satisfactory as he feels. 
An effort has been made in the following chapters to explain the various approaches suggested in literature, 
give their comparative limitations, examine the implications of the so-called more sophisticated approaches 
and finally make recommendation for the method which can be followed by a designer till he accumulates 
enough experience so as to select his own method particularly applicable to his problem. Intention of this 
publication is not to hinder initiative of an individual in going deeper in any problem, but to give him a 
comparative idea of available approaches with sufficient number of references which he can study during the 
beginning of his profession and formulate his own opinion in due course but still continuing to design 
satisfactory raft foundations. 
This publication should, therefore, be studied in this background. 
NEED OF RAFT FOUNDATION. 
Raft or Mat foundation is a combined footing that covers the entire area beneath a structure and supports all 
walls and columns. This raft or mat normally rests directly on soil or rock, but can also be supported on piles 
as well. 
Raft foundation is generally suggested in the following situations: 
(a) Whenever building loads are so heavy or the allowable pressure on soil so small that individual 
footings would cover more than floor area. 
(b) Whenever soil contains compressible lenses or the soil is sufficiently erratic and it is difficult to 
define and assess the extent of each of the weak pockets or cavities and, thus, estimate the overall 
and differential settlement. 
(c) When structures and equipment to be supported are very sensitive to differential settlement. 
(d) Where structures naturally lend themselves for the use of raft foundation such as silos, chimneys, 
water towers, elc. 
(e) Floating foundation cases wherein soil is having very poor bearing capacity and the weight of the 
super-structure is proposed to be balanced by the weight of the soil removed. 
(f) Buildings where basements are to be provided or pits located below ground water table. 
(g) Buildings where individual foundation, if provided, will be subjected to large widely varying 
bending moments which may result in differential rotation and differential settlement of individual 
footings causing distress in the building. 
Let us now examine each of the above situations in greater detail. 
2.1 In case of soil having low bearing pressure, use of raft foundation gives three-fold advantage: 
(a) Ultimate bearing capacity increases with increasing width of the foundation bringing deeper soil 
layers in the effective zone. 
(b) Settlement decreases with increased depth. 
(c) Raft foundation equalises the differential settlement and bridges over the cavities. Every structure 
has a limiting differential settlement which it can undergo without damage. The amount of 
differential settlement between various parts of a structure supported on a mat foundation is much 
lower than that if the sarne.structure was supported on individual footings and had undergone the 
same amount of maximum settlement. With these considerations, maximum total settlement which 
RAFT FOUNDATIONS-DESIGN AND ANALYSIS 
can be allowed for a particular structure on mat foundation is more than what is permitted when the 
structure is resting on individual footings. This, therefore, allows a higher bearing capacity for such 
situations. 
It may, however, be noted that if in a case deeper layers of soil are of very poor quality, increase in width 
of the foundation may not always lead to higher bearing capacity. In situation where comparatively s h a l l y 
top layers of soil are underlain with deeper layers of much poorer soils, it may be advantageous to provide 
individual footings so that the zone of influence of the footings remains within the top stronger layer. In such 
a situation, provision of a mat foundation may be disadvantageous. 
2.2 Some designers work on the rule that if more than 50% of the area of the structure is occupied by individual 
footings, it is necessary to provide an overall raft. This is not true and quite often, the quantity of reinforcing 
steel and concrete required to avoid excessive deflection and cracking of a raft carrying unequal column loads, 
necessitating carry-over of stresses from one part of the raft to the other part, may be large and may make raft 
foundation uneconomical. In such situations, it may be more economical to excavate the entire site to a level 
formation, construct individual closed space footings (sometimes touching each other) and then backfill around 
them. In these cases, however, one must weigh form work costs against the extra footing material required by 
using mat foundation. It should be considered that it is possible to construct alternate footings by using spacer 
pads against already laid footings and thus save form work cost.Quite often, doubt exists about the structural behaviour of individual footings touching each other. This 
problem of interaction of footings has been studied by many researchers. It has been reported that the effect 
of adjacent footings may vary considerably with the angle of shearing resistance. For low values, they are 
negligible though for high values they appear to be significant, particularly if a footing is surrounded by other I 
footings on both sides. It is also stated that these effects are considerably reduced as length over breadth ratio I 
of the footings approaches unity. There are practically no such effects in the case of punching shear failure. 1 
For these and other reasons, it has been recommended that interference effects need not be considered in 
designs. Adesigner should, however, be aware of the possibility of their existence in some special circumstan- 
11 
ces . I 
2.3 Situations exist in practice w h p a soil stratum contains compressible lenses or the soils have a formation 
where individual layers of soil are neither parallel nor can be reasonably stratified into different layers of known 
properties to enable calculations of settlement to a reasonable accuracy. In such situations, individual footings, 
if provided, would undergo widely varying settlements resulting in large differential settlement which cannot 
I 
be tolerated by the structure. I 
2.4 Situations, as mentioned in (c) and (d) above, are explicit and do not require further explanation. These 
are special cases, and adoption of raft foundation is more or less necessary by the particular nature of the 
problem involved. 
2.5 In cases where soil is very soft and highly compressible and the buildings cannot be founded on such soils 
in normal circumstances, it may be possible to provide the building with a basement in such a manner that 
weight of the structure is equal to the weight of the soil removed and, thus, there being no change in the stresses 
in the soil beneath the basement and, therefore, little settlement. However, in practice it is rarely possible to 
balance the loading so that no additional pressure comes on the soil. However, in such cases still, it is only a 
part of the total load which comes on the bottom soil and, thus, it is possible to construct a building inducing 
a much larger load than the soil would have otherwise supported. The basement provided, gives additional 
space in the building for the owner and can be made use of. However while constructing such foundations, 
NEED OF RAFT FOUNDATION 5 
reconsolidation of the soil, which has swelled as a result of removal of over burden pressure in excavating for 
the sub-structure, should always be considered and necessary steps be taken to prevent detrimental effects. 
2.6 Basements located below ground water table should use a mat as their base to provide water tight 
c.onstruction. The alternative of having individual columns footings connected by thin slabs has not proved to 
be successful in most of the cases; presents difficulties in water proofing; causes concentration of stresses at 
the junction of the thin slabs and footings and also at the junction of basement walls and raft causing cracks 
to develop. This arrangement, therefore, should not be resorted to unless the economy is of such a magnitude 
as to outweigh all other considerations. 
Even in cases where sub-soil water level is low and basement does not extend below ground water table, 
long-term built up of surface water accumulating against basement walls and bottom should be allowed for. 
This is particularly so in case of impermeable soils (permeability co-efficient below 0.1 mm per second) or of 
large surface areas draining towards the building. i.e., areas on sloping ground near hillocks. The basement 
' walls should also normally be designed as self-supporting cantilever retaining walls even though they may 
eventually be strutted by floor construction. It is inconvenient and often impossible to provide temporary raking 
struts to support a basement retaining wall until such time as strutting given by ground floor or intermediate 
basement floor is completed. 
2.7 Situations also arise when isolated footings are subjected to very large eccentric loadings, and one is faced 
with the possibility of excessive footing rotation, excessive differential settlement or possibility of exceeding 
the allowable bearing capacity of the soil at some location. This can happen when the building consists of shear 
walls and columns, shear walls sharing most of the horizontal load subjecting its footings to larger settlements 
and rotation, decreasing the effectiveness of the shear walls and also creating difficulties by way of large 
differential settlements. Raft, if provided, will even out these deformations. 
Mats or rafts are supported on piles'in cases where sub-soil conditions warrant provision of piles, but one 
has to have the basement. In such situations, raft also helps in making the basement water tight. 
It would, therefore, be seen that it is not possible to lay down hard and fast rules defining situations wherein 
a raft foundation is required. The author, therefore, opines that every designer should learn all that he can 
within reason about the conditions at site, determine the types of foundations that are practical, compare their 
cost, suitability, ease of construction, safety and select a type which in his judgement would serve the purpose 
well. There can always be differences of opinion about the solution decided by him, but as already mentioned 
in chapter I , it cannot be helped because foundation design still continues to be practised more as an art than 
an exact science. Two artists seldom agree. 
TYPES OF RAFT FOUNDATION 
Raft can be classified into various types on the basis of criteria used for classification. 
3.1 Based on the method of their support, raft can be: 
(a) Raft supported on soil, 
(b) Raft supported on piles, and 
(c) Buoyancy raft. 
3.2 On the basis of structural system adopted for the structure of the raft, these can be classified as: 
(a) Plain slab rafts which are flat concrete slabs having a uniform thickness throughout. This can be 
with pedestals or without pedestals. 
(b) Beam and slab raft which can be designed with down stand beam or upstand beam systems. 
(c) Cellular raft or framed raft with foundation slab, walls, columns and one of the floor slabs acting 
together to give a very rigid structure. 
Raft of uniform depth is most popular due to its simplicity of design and construction. This type is most 
suitable where the column loads are moderate and the column spacing fairly small and uniform. Pedestals are 
utilised to distribute the load on a bigger area in case of heavy column loads. 
3.3 Slab and beam raft is used as a foundation for heavy buildings where stiffness is the principal requirement 
to avoid excessive distortion of the super structure as a-result of variation in the load distribution over the raft 
or the compressibility of the supporting soil. These rafts, however, have many obvious difficulties. If the beams 
are deep, ribs placed below the basement floor or raft, the bottom of the excavation becomes badly cut up with 
trenches, impairing the bearing value of the soil because of its disturbance. Water proofing in case of basements 
becomes more complicated arid involved. If the beams are projecting up, usefulness of the basement is 
destroyed unless the entire foundation is lowered and the gap filled up or an upper slab is provided supported 
on these inverted beams to form the ground floor of the structure. 
3.4 Buoyancy raft are necessarily to be provided with a basement so that the weight of the soil removed 
balances to a large extent, the imposed load. Cellular raft consisting of foundation slabs, walls, columns and 
ground floor slab can be designed, but it creates considerableamount of uncertainties, difficulty of construction 
and quite often even in such cases, raft is designed as a slab of uniform rhickncss. 
TYPES OF RAFT FOUNDATION 7 
Raft, as a slab of uniform thickness, has an additional advantage of providing better water-proofing treatment 
ease of reinforcement fabrication and laying of concrete. This type of raft is most commonly used. 
Various types of rafts are shown in Fig. 3.1 
RAFT SUPPORTED ON PILE R A F T SUPPORTED ON SOIL BUOYANCY RAFT 
------------- 
FLAT PLATE RAFT 
--------------------- -- ------- ------------- --------------- 
i 
' FLAT PLATE WITH PEDESTALS BEAM AND SLAB RAFT 
: ------------------------- ------------------ 
Fig. 3.1 Various types of rafts 
FRAMED RAFT 
----------- 
SURVEY OF AVAILABLE 
LITERATURE 
Testbooks and design manuals by various authors suggest varying approaches to analysis and design of raft 
foundation. Differences of opinion exist in the method of analysis proposed to be adopted while determining 
moments, shear forces for the design of raft. Once the bending moments and shear forces are known, structural 
design does not present any difficulty and there exists no difference of opinion in this respect except very minor 
difference relating to desired thickness of slab and the effectiveness of the shear reinforcement 
Methods suggested by different authors are summarised below. These have been arranged chronologically 
with reference to date of publication of the testbooktdesign handbook. 
4.1 Foundation Engineering b y Peck, Hansen and hornb burn^ 
Raft is usually regarded and designed as an inverted continuqus flat slab floor supported without any upward 
deflections at the columns and walls. The soil pressure acting against the slab is commonly assumed to be 
uniformly distributed and equal to the total of all column loads multiplied by appropriate load factors and 
divided by the area of the raft. The moment and shears in the slabs are determined by the use of appropriate 
coefficient listed in the specifications for the design of flat slab floors. On account of erratic variation in 
compressibility in almost every soil deposit, there are likely to be correspondingly erratic deviations of the soil 
pressure from the average value. Since the moment and the shears are determined on the basis of the average 
pressure, it is considered good practice to provide this slab with more than theoretical amount of reinforcement 
and to use the same percentage of steel at top and bottom. This method has been widely used, often with 
complete success. On the other hand, it has also sometimes led to structural failure not only of the slab but also 
of the super structure. Therefore, its limitations must be clearly understood. The analogy follows only if the 
differential settlement between columns will be small and if the pattern of the differential settlement will be 
erratic rather systematic. The method is valid when the columns are more or less equally loaded and equally 
spaced. If the downward loads on some areas are on the average much heavier than on others, differential 
settlements may lead to substantial re-distribution of moments in the slabs resulting in unconservative design. 
Rafts are sometimes designed as if they rested on a bed of closely and equally spaced elastic springs of 
equal stiffness. The contact pressure beneath any small area is then proportional to the deflection of the spring 
SURVEY OF AVAILABLE LITERATURE 9 
in that area and thus to the settlement. The constant of proportionality 'K' is called the modulus of sub-grade 
reaction. Although, the theory has been well developed but the value of 'K' for real soils is not constant and 
depends not only on the stress deformation characteristics of the soil but also in a complex manner on the shape 
and size of the loaded area and the magnitude and position of nearby loaded areas. Evaluation of 'K' for design 
is difficult and fraught with uncertainty. Whatever method may be adopted for design, there is no guarantee 
that the deflections of the raft will actually be unimportant. In case, the structure covers a fairly large area with 
possibilities of differential settlements, it is not enough to provide great strength in the slab. It is also necessary 
to provide sufficient stiffness. However, a stiff foundation is likely to be subjected to bending moments far in 
excess of those corresponding to the flat slabsubgrade modulus analysis. 
There appears to.be no further edition of this book after 1954. 
4.2 Foundation Design and Practice b y Elwyn. E.S. seelye9 
According to Seelye after determining the soil pressures at various points of raft, shear and moment diagrams 
can be constructed for bands assumed from centre of bay to centre of bay. However, 65% of the moment is 
assumed to be resjsted by half the width of the band. There has not been any further edition of this book after 
1956. 
4.3 Foundation Design b y en^' 
In the conventional method, it is assumed that the mat is infinitely rigid and that the bearing pressure against 
bottom of the mat follows the planner distribution. The mat is analysed as a whole in each of two perpendicular 
directions. Thus the total shear forces acting on any section cutting across the entire mat is equal to the 
arithmetic sum of all forces and reactions (bearing pressure) to the left orright of the section. The total bending 
moments acting on such section is equal to the sum of all moments to the left or right of this section. 
Although the total shear and moments can be determined by the principles of simple statics, the distribution 
along this section is a problem of highly indeterminate nature, the average moment not being indicative of the 
sign and the magnitude of the bending moments in the individual strip in either direction. In order to obtain 
some idea as to the upper limit of these values, each strip bounded on central line of the column bays, may be 
analysed as independent continuous or combined footings. If the column loads are used, the soil reaction under 
each strip is determined without reference to the planner distribution determination for the mat as a whole. 
This method, undoubtedly, gives very high stress because it ignores the two way action of the mat. Therefore, 
certain arbitrary reduction in values (15% to 33113%) is made. 
The author gives other method like Finite Difference Method also for the design of the raft. There has not 
been any further edition of this book after 1962. The book, however, has been reprinted in 1992. 
The recommendation in this book can be summarised in the following words: 
A great refinement of calculations is not always justified or practicable in case of raft.foundations because 
of the uncertainties of the action of soil and of short thick members that are arranged in complicated and 
multiple systems. It is reasonable to assume that the mat is so stiff and the load so constant that plastic soil will 
compress and adjust itself so that each column load will spread almost uniformly under the mat in the general 
vicinity of that particular column. For example, the total unit pressure under the rectangular area D, E, F, G 
shown in Fig. 4.1 may be assumed equal to 114th of the total loads on the columns at D, E, F and G divided 
by the area of D, E, F, G plus the weight of the mat per sq m. For the purpose of computing average pressure 
10 RAFT FOUNDATIONS-DESIGN AND ANALYSIS 
under the slabs, near the walls, the outer column loads are treated as though they were concentrated at the 
columns. For this method, however, the load on adjacent columns should not differ very much and the bays 
in either direction should be reasonably, equal in length, the larger spacing not exceeding 1.2 time, the smaller 
one and the columns should be arringed in reasonably straight rows. 
Fig. 4.1 Plan of assumed columnsstrips and distribution of loads 
One method of making a preliminary analysis of such a mat is on the basis of an assumed supporting system 
of columns strips that constitute a grid of beam along the column rows in each direction. The portion of the 
slabs in the central areas is taken up to be supported by this grid. The effective width of these strips or shallow 
beams has to be assumed and it is normal to take it slightly more than, what is determined by 45 degrees fiom 
the pedestal or column, to the lower reinforcement in themat. Technically the top reinforcement of a central 
panel may be less than of the bottom. However, it may be advisable to reinforce both sides equally because 
any yielding of end restraint will increase the, tension in the top of the mat above the computed value. Each 
column strip may be analysed by moment dishbution if the variation of loading or spans make this desirable, 
the entire thing being designed as an inverted floor. The effect of hydrostatic pressure has to be considered 
wherever it is present. There has been no further edition of this book after 1962. 
4.5 Indian Standard Code of Practice for Design and Construction of Raft Foundation - IS 2950-1965' 
There are two approaches for design-conventional method and the elastic method. In the conventional method, 
the foundation is considered infinitely rigid and pressure distribution independent of the deflection of the raft. 
Soil pressures are also assumed to be planner so that the centroid of the soil pressure coincides with the line 
of action of the resulting forces of all the loads acting on the foundation. The method is normally used in design 
because of its simplicity . A generous amount of reinforcement is provided to safeguard uncertainties caused 
I SURVEY OF AVAILABLE LITERATURE 11 I by differential settlement. The raft is anabjsed as a whole in each of the two perpendicular directions. Thus, total shear forces and total bending moments acting on any section cutting across the entire raft is equal to the 
arithmetic sum of all forces and reactions/moments to the left or right of the section. The actual reinforcement I provided shall be twice that worked out theoretically. 
Elastic method has two approaches. In one, the soil is replaced by an infinite number of isolated springs. I In the other, the soil is assumed as a continuous elastic medium obeying Hook's Law. These methods are 
applicable in case the foundation is comparatively flexible and the loads tend to concentrate over small areas. 
The actual reinforcement can be one-and-a-half times that required theoretically. The famous soil line method 
falls in this category. 
! As limitations to applicability of the methods, code mentions that the coda1 provisions: 
(1) do not apply to large and heavy industrial construction where special considerations of the base 
pressure distribution will be required. 
i (2) apply only to fairly uniform soil conditions and for fairly horizontal planes of separation of layer 
below. 
I (3) foundations in seismic area and/or to vibrating load shall be given special considerations. 
i This code has been revised in 1973. Kindly see para 4.7. 
I 4.6 RafL Foundation - The Soil Line Method of Design by A.L.L. ~ a k e q ! According to Mr. Baker, the design of raft as a reversed floor is dangerous. Engineers being aware of this, who. 
' therefore, normally adopt the second method in which earth pressure is assumed to be uniform throughout and 
moments are obtained at any section by statics. He, however, feels that in the second method also high values 
' 
of moments are obtained, which may or may not be present, and it is irrational or wasteful to provide for such 
moments without investigating the deflections and variation in soil pressure. Mr. Baker has, therefore, 
suggested the soil line method which takes into account the variations in soil pressure and its relation to 
deflection but in order to simplify the calculations, it is assumed that the earth pressure varies throughout a 
beam according to straight line law. 
There is no further edition of this book after 1969. 
4.7 Indian Standard Code of Practice for Design and Construction of Raft Foundation 
1.S : 2950 (Part-I) 1973~ 
In the revised version of the code, following methods of analysis have been proposed: 
(a) Assumption of linearly varying contact pressure 
(b) Perfectly rigid structures 
(c) Perfectly flexible structures 
(d) Structures stiffened along one axis 
(e) Structures stiffened along both the axis 
(f) General methods: 
(i) Based on modulus of subgrade reaction, and 
(ii) Based on modulus of compressibility (half space theory). 
Method (a) corresponds to the conventional method in the earlier version of the code and has similar 
limitations. In method (b), contact pressure distribution is to be calculated based on Boussineq's Equation for 
Elastic Isotropic half space and is applicable when deformations of raft under loads are small as compared to 
the mean settlement of the structure. 
12 RAFT FOUNDATIONS-DESIGN AND ANALYSIS 
Method (c) is applicable for structures which have relatively less stiffening members specially resting on 
very stiff foundation soil. In this case, the deflections of the raft are same as the settlements of the foundation 
soil under external load. 
Method (d) is something in between methods (b) and (c) . Here in the direction of the stiffened axis the 
contact pressure distribution is determined by Boussineq's Equation as in method (b). In perpendicular 
direction distribution is determined as given in (f). 
Method (e) is same as method (b). The two methods under (f) are elastic methods and are used when 
simplified methods from (a) to (e) are not applicable. Details given in the codedo not provide enough guidance 
to enable the analysis and design 10 be completed by the designer. Apart from the limitations applicable in 
earlier version of the code it is stated that: 
(i) Allowable settlement both total and differential shall satisfy the requirement of the super-structure 
(ii) The approximate values of permissible settlements as given in earlier code have been deleted. 
This code has further been revised. Please see para 4.15. 
4.8 Foundation Engineering Handbook Edited by Hans F. Witerkorn & Hsaiyang an^'' 
Dr. Joseph E. Bowles and Wayne C. Teng are authors of chapters on spread footings, combined and special 
footings and mat foundation respectively. Chapter on floating foundation has been written by Dr. H.Q. Golder. 
This book classifies the method of design of mat foundation according to assumptions used. The rigid 
method which is the conventional method assumes that: 
(a) Mat is extremely rigid as compared to the sub-soil and, therefore, the flexural deflection of the mat, 
does not alter the contact pressure. 
(b) The contact pressure or the pile reaction are distributed in a straight line or a plain surface such that 
the centroid of the contact pressure coincides with the line of action of the resultant force of all the 
loads acting on the mat. When mat foundation is supported on piles, piles are assumed to be perfectly 
elastic. Raft is considered to be rigid when the column spacing is less than 1.751h or when the mat 
is supporting a rigid super-structure. his same as defined by Heteny. The mat is analysed as a whole 
in each of the two perpehdicular directions. The mat is divided into perpendicular bands of width 
between centre lines of adjacent column rows. Each band is assumed to act as an independent beam 
subjected to common contact pressure and known column loads. 
The simplified elastic method assumes that the soil behaves like an infinite number of individual elastic 
springs each of which is not affected by others. This foundation model is also referred to as Winkler foundation. 
Analysis procedures have also been developed for the beams onthe simplified elastic foundation concept. 
The mat is considered as a plate and the effect of each column load is considered in area surrounding the load. 
Using the method of super-imposition, effect of all the column loads within the zone of influence is calculated. 
Among computer-oriented methods suggested is finite difference method, based on the assumption that the 
sub-grade can be substituted by a bed of uniformly distributed elastic springs with a spring constant equal to 
coefficient of sub-grade reaction. For this purpose, the mat is divided into square areas. The deflection at the 
nodal points of these areas is expressed by a differential equation in terms of deflection at the adjacent points 
to the right, left, top and bottom. These simultaneous equations are solved with an electronic computer and 
deflection at all the points are determined. Once deflections are known, the bending moment at any point in 
each direction is determined from theory of elasticity. 
The finite element method transforms the problem of plates on elastic foundation into a computer-oriented 
procedure of matrix structural analysis. The mat is idealised as a mesh of finite elements inter-connected only 
SURVEY OF AVAILABLE LITERATURE 13 
at the comers and the soil may be modeled as a set of isolated springs or as an elastic isotropic half space. The 
matrix structural analysis can be extended to include the influence of the super-structure as well, thus the 
interaction between the super-structure, the foundation and the soil is accounted for. 
It is further suggested that in a mat supported on hard rock, the column loads are transmitted to the rock on 
relatively small areas directly under the column. A greater economy may be achieved by designing the mat by 
elastic methods. On very soft soils, the contact pressure against the mat foundation approaches planer 
distribution and, therefore, it is commonly justified to design a mat on mud, soft clay, peat, organic soils or 
even medium clays by the conventional rigid method. A generous amount of reinforcement running in both 
directions at top and bottom is suggested regardless of method of design used in view of the likelihood that 
the stresses actually introduced would bedifferent from those calculated irrespective of the method used foi 
analysis. 
Second edition of this book is published in 1991. Please see para 4.21. 
4.9 Foundation Analysis and Design by Joseph. E. ~owe l s ' " 
The mat may be designed as rigid structures thereby soil pressure are computed as Q = V/A in the case where 
the resultant of the forces coincide with the centre of the mat area. If resultant has eccentricity with respect to 
geometric centre, soil pressure is calculated by the relation 
In case, however, if the eccentricity is very large, the resulting internal stresses may be seriously in error. 
Once the dimensions of the mat are established, soil pressures at various locations beneath the base may be 
computed. With the pressure distribution known, the mat is sub-divided into a series of continuous beams 
(strips) centred on the appropriate column lines as shown in Fig. 4.2. For the series of beams, shear and moment 
diagram may be established using either combined footinglanalysis or beam moment coefficient. The depth is 
selected to satisfy shear stresses and is usually constant but the steel reinforcement vary from strip to strip. 
The perpendicular direction is analysed similarly, to complete the design. 
Fig. 4.2 
1 4 RAFT FOUNDATIONS-DESIGN AND ANALYSIS 
When the soil bearing pressure is low say 0.5 ~i~s l f t2 (25 K N I ~ ~ ) or less and if the deformation of the mat 
surface can be tolerated, the mat may be designed as an inverted flat slab, using heavy beams from column to 
column. The portion between beams is designed as a conventional one or two way slabs. 
When footings are designed as flexible members, the computation takes some form of the solution of a 
beam on an elastic foundation. The experience has indicated that the solution obtained are generally reliable 
when the data are satisfactory. Possibly the reasons, as to why the methods have not been widely used in the 
past, are ease of making conventional solution, which have been generally satisfactory and usually not much 
different from elastic solution. Second reason is that the soil data are generally obtained using the standard 
penetration test for which no straight forward conversion to a value of modulus of sub-grade reaction exists. 
Various methods for elastic analysis like finite element and finite differences have also been explained in this 
book. 
New edition of this book is publisheg in 1988. Kindly see para 4.23 
4~10 Building Code Requirements for Reinforced Concrete (ACI 318 - 77)18 
Matters relating to design of footings are included in this code in Chapter 15. paragraph 15.10 relates to 
combined footings and mats. This paragraph reads as under: 
15.10.1 Footings supporting more than one column, pedestal, or wall (combined footings or mats) shall be 
proportioned to resist the factored loads and induced reactions, iir accordance with appropriated design 
requirements of this code. 
15.10.2 The Direct Design Method of Chapter 13 shall not be used for design of combined footings and mats. 
15.10.3 Distribution of soil pressure under combined footings and mats shall be consistent with propemees 
of the soil and the structure and with establishedprinciples ofsoil mechanics. 
It would be seen that this code does not provide for much guidance in design of raft foundation. 
This code has been revised several times. Final being in 1989. Please see Para 4.20. 
4.11 Foundation Design and Construction by M . J . ~ o m l i n s o n ' ~ 
Mr. Tomlinson states that it is wrong in principal to assume that araft acts as an inverted floor slab on unyielding 
supports and to design the slab on the assumption that its whole area is loaded to the maximum safe bearing 
pressure on the soil as this canlead to wasteful and sometimes dangsrous designs. Allowance must be made 
for deflection under the most favourable combination of dead and live load and variation in soil compressibility. 
Guidance is required from the soil mechanics engineer on the estimated total and differential settlement for 
dead and live load considered separately. Some flexibility is desirable to keep bending moments and shear 
stresses to a minimum, but the degree of flexibility must be related to the allowable distortion of the 
super-structure. Basement rafts carrying heavy building on weak soils are often founded on piles. The normal 
function of the piles is to transfer the loading to stronger and less compressible soil at greater depth or if 
economically possible, to transfer the load to bed rock or other relatively incompressible strata. The piles also 
have the effect of stiffening the raft and reducing or eliminating re-consolidation of ground heave, thereby 
reducing differential settlement or tilting. In such cases, considerable heave takes place with further upward 
movement caused by displacement due to pile driving. After completion of piling, the swelled soil should be 
trimmed off to the finished level. The basement walls should generally be designed as self-supportingcantilever 
retaining walls even though they may eventually be supported by the floor construction and additional stability 
against overturning given by super-structure loading on top of the wall. The basement floor slabs must be able 
SURVEY OF AVAILABLE LITERATURE 15 
to withstand pressure on the underside of the slab together with stresses caused by differential settlement, 
non-uniform column loads, reaction from the retaining walls. If the columns are provided with independent 
t bases with only a light slab between them, there would be likelihood of failure of the slab from the pressure 
of the underlying soil.g 
Fifth edition of this book has been out in 1986. Please see para 4.17. 
4.12 Design of Combined Footings and Mats ACI Committee 33614 
The committee observes that no authentic method has been devised that can evaluate all the factors involved 
in the problem and allow carrying out determination of contact pressures under combined footings and mats. 
Simplifying assumption must, therefore, be made based on the knowledge of the interaction of the various 
elements of the system. The following factors should be considered while examining any problem: 
(1) Soil type immediately below the footing 
(2) Soil type at the greater depth 
(3) Size of footing 
i (4) Shape of footing 
(5) Eccentricity of loading 
(6) Rigidity of footing 
(7) Rigidity of the super-structure 
(8) Modulus of sub-grade reaction 
The committee suggests procedure to be followed for design of footings under two columns: grid 
foundations and smp footings supporting more than two columns and mat foundation. Linear soil pressure 
distribution is suggested for footings which can be considered rigid to the extent that only very small relative 
deformations result from the loading. The rigidity may result from the spacing of the columns on the footing 
from the rigidity of the footing itself or the rigidity of the super-structure. Limitations which must be fulfilled 
to make this assumption valid have been discussed in the report. 
Distribution of soil pressure by means of sub-grade reaction has been suggested where sub-soils are of such 
character that the deformations are localised in the general vicinity of the loads and when the maximum contact 
pressure is smaller than about one and a half times the ultimate bearing capacity. In case of rigid footings, it 
a is suggested that uniform or linear distribution of soil pressure can be assumed and the design based on statics. 
Flexible footing procedure is divided into 2 parts i.e. uniform condition and general condition. Uniform 
conditions are considered to be those where the variation in adjacent column loads and spans is not greater 
than 20%. For cases where supporting columns are at random location with varying intensities of loads a 
1 detailed design procedure based on plate theories has been recommended. 
4.13 Pile Foundation Analysis and Design by H.G.Poulos and E.H. Davis 1 9 8 0 ~ ~ 
: In this book, Chapter 10 deals with piled raft systems. The author says that, "in design of foundation for a large 
building on a deep deposit of clay it may be found that a raft foundation would have an adequate factor of 
safety against ultimate bearing capacity failure but the settlement would be excessive; traditional practice 
would then be, to pile the foundation and to choose the number of piles to give an adequate factor of safety 
assuming the piles take all the load; however it is clearly illogical to design the piles on an ultimate load basis 
when they have only been introduced in order to reduce the settlement on other-wise satisfactory raft." 
According to the author, once the have been introduced solely for the purpose of reducing the settlement 
16 RAFT FOUNDATIONS-DESIGN AND ANALYSIS 
design question becomes not "how many piles are required to carry the weight of the structure" but "how many 
piles are required to reduce the settlement to an acceptance level". 
However, in Chapter 5, the settlement behaviour of a free standing pile is obtained from the elastic-based 
analysis. The pile is divided into number of elements and the expressions for vertical settlement of the pile and 
the soil at each element in terms of unknown stresses on the piles are obtained and solved, imposing the vertical 
displacement compatibility condition, to arrive at the settlement behaviour of the pile. As a further extension, 
the unit consisting of a single pile with an attached cap resting on the soil surface is considered. It is assumed 
that purely elastic condition prevails upto the load at which the pile would fail if no cap were present and 
thereafter any additional load is taken entirely by the cap. The book gives charts indicating interaction factor 
between the raft and the pile for various values of length of the piles, diameter of the pile, poisson ratio of soil, 
height of soil layer over the rigid stratum and the cap diameter.The method is further extended to group of 
piles upto about 40 numbers. Curves are drawn which are applicable only for rigid rafts or perfectly flexible 
rafts. The entire emphasis is to work out the ratio of the load carried out by the piles and the raft soil system. 
No details are given on &e method to determine the bending moment and shear forces in the raft. It is only 
mentioned that none of the simple methods are satisfactory and a proper analysis of plate on piles and 
continuum is desirable. 
4.14 Reinforced Concrete Designers Handbook by Charles E. Reynolds and James C. Steedman - 
9th Edition 1981" 
This book suggests the analysis of a raft foundation supporting a series of symmetrically arranged equal loads 
on the assumption of uniformly distributed pressure on the ground considering the structure as an inverted 
reinforced concrete floor acted upon by the load of earth pressure from bottom. It is further suggested that 
when the columns on the raft are not equally loaded or are not symmetrically arranged, the raft should be so 
designed that the centroid coincides with the centre of gravity of the loads. If this coincidence of centre of 
gravity is impracticable owing to the extent of the raft being limited on one or more sides, the plan of the raft 
should be made so that the eccentricity of the total loading is a minimum, though this may produce a raft which 
is not rectangular in plan. 
4.15 IS 2950 (Part I) 1981 - Code for Design and Construction of Raft Foundation Part I ~ e s i ~ n ~ 
In the second revision of the code, two methods of analysis have been suggested depending upon the 
assumption involved. Conventional method assuming planner distribution of contact pressure is applicable to 
foundations which are rigid relative to supporting soil and the compressible soil layer is relatively shallow. 
The rigidity of the foundation is determined with a relative stiffness factor K > 0.5 or columns spacing less 
than 1.75A. Methods of determining value of K and hare given in the code. Conventional method is applicable 
when either of the two conditions are satisfied. The value of K depends upon the flexural rigidity of the 
super-structure, modulus of the compressibility of the foundation soil, thickness of the raft, length of the section 
in the bending axis and length perpendicular to the section under investigation. Value of h depends upon 
modulus of sub-grade reaction for the footing of the width of the raft, modulus of elasticity of concrete and 
moment of inertia of the raft. In this method, the raft is analysed as a whole in each of the two perpendicular 
directions on the basis of statics. 
In case of flexible footings, simplified methods are applicable when variation in adjacent column load is 
not more than 20% of the higher value and the structure (combined action of the super-structure and raft) may 
be considered as flexible, ie., relative stiffness factor K is greater than 0.5. In this method, it is assumed that 
SURVEY OF AVAILABLE I-ITERATURE 17 
the sub-grade conslsts of an infinite array of individual elastic springs each of which is not affected by others. 
This method is more or less same as the famous soil line method. 
When conditions, as mentioned above, for flexible foundations are not satisfied , a method based on closed 
form of solution of elastic plate theory has been suggested. The distribution of deflection and contact pressure 
& on the raft due to a column load is determined by the plate theory. Since the effect of a column load on the 
' 
elastic foundation is damped outrapidly. It is possible to determine the total effect at a point of all column 
loads with~n the zone of influence by the method of super-imposition. The computation of the effect at any 
point is restricted to columns of two adjoining bays in all directions. i 
: The code also lays down that: 
(a) Size and shape of the foundation adopted affects the magnitude of subgrade modulus which should 
be taken into consideration. 
(b) Consideration must be given to the increased contact pressure developed along the edges of the raft 
on cohesive soils and the opposite effect on granular soils. 
(c) Expansion joint should be provided when the structure supported by the raft consists of several parts 
with varying heights and loads or there is a change in the direction of the raft. 
(d) This code does not explicitly provide any guidance as to how factors emphasised in (a) and (b) above 
should be allowed for. The second part of the code relating to construction aspect is still not printed. 
There has not been any further revision and this code was reaffirmed in 1987. 
4.16 Eleventh Intenationul Conference of Soil Mechanics a d Foundation Engineering San Francisco, 
August 12 - 16 ,1985~~ 
In the conference while two papers were presented on instrumentation of pile raft foundation and cap pile soil 
interaction, there was no recommendation or paper on design of raft foundation. 
4.17 Foundation Design and Construction by M.J. Tomiinson, 5th Edition, 1986" 
There is no significant change in this edition from what was recommended in 4th edition 
4.18 Handbook of Concrete Engineering - Mark Fintei - 2nd Edition, 1986% 
This book makes no recommendation about raft foundation. 
4.19 Reinforced Concrete Designer Handbook by Charles E. Reynolds and James Steedman, 
10th Edition, 1988~' 
There is no change in recommendations from what was done in the earlier edition published in 1981 
4.20 Building Code Requirements in Reinforced Concrete - ACI - 318 - 1989~' 
Building code requirements since their second edition in 1977 have gone in for further revision 1983, 1989 
and 1992. In the latest revision there is no change in the code requirements for design of combir.ed footings 
and mats, but in commentary a reference has been made to 'design procedure for combined footings and mat 
is per report prepared by ACI committee 336'and also to a paper 'simplified design of footings by' Kramrisch, 
Fritz and Rpgers Paul published in American Society of Civil Engineers Proceeding, V. 87, NOSM 5, October 
1961, p. 19. 
18 RAFT FOUNDKTIONS-DESIGN AND ANALYSIS 
4.21 Foundation Engineering Handbook by Hsai-Yang-Fang 2nd Edition, 1 9 9 1 ~ ~ 
This edition has omitted the chapter on mat foundation which was originally'included in first edition. 
4.22 Design of Combined Footings and Mats - ACI committee 336 2R - 88 Published in ACI 
Manual 1 ~ 3 ~ ~ 
1966 report mentioned in para 4.12 above was reaffirmed in 1980 but has been completely revised and 
elaborated in 1988. This report suggests that: 
(a) Maximum unfactored design contact pressure should not exceed the available soil pressure deter- 
mined by geotechnical engineer. Where wind or earthquake forces form a part of the load 
combination, the allowable soil pressure may be increased as allowed by the local code and in 
consultation with geo-technical engineer. 
(b) Combined footings and mats are sensitive to time dependent sub surface response. Many structural 
engineers analyse and design mat foundations by computer using the finite element method. Soil 
response can be estimated by modelling with coupled or uncoupled "Soil springs". The spring 
properties are usually calculated using a modulus of subgrade reaction, adjusted for footing size, 
tributary area to the node, effective depth, and change of modulus with depth. The use of uncoupled 
springs in the model is a simplified approximation. The time dependent characteristics of the soil 
response, consolidation settlement or partial consolidation settlement, often can significantly 
influence the subgrade reaction values. Thus, the use of a single constant modulus of subgrade 
reaction can lead to misleading results. 
(c) Caution should be exercised when using finite element analysis for soils. Without good empirical 
results, soil springs derived form values of subgrade reaction may only be a rough approximation 
of the actual response of soils. Some designers perform several finite element analyses with soil 
springs calculated from a range of subgrade moduli to obtain an adequate design. 
(d) The response of a footing is a complex interaction of the footing itself, the superstructure above, 
and the soil. That interaction may continue for a long time until final equilibrium is established 
between the superimpos&l loads and the supporting soil reactions. Moments, shears, and deflections 
can only be computed if these soil reactions can be determined. 
(e) No analytical method has been devised that can evaluate all of the various factors involved in the 
problem of soil-structure interaction and allow the accurate determination of the contact pressures 
and associated subgrade response. 
(f) For mat foundations modulus of subgrade reaction cannot be reliably estimated on the basis of field 
plate load tests because the scale effects are too severe. I 
(g) Mats may be designed and analysed as either rigid bodies or as flexible plates supported by elastic I 
foundation. A combination analysis is common in current practice. An exact theoretical design of \ 
mat as plate on an elastic foundation can be made. However a number of factors like, difficulty in 1 I projecting subgrade responses, variation in soil properties both horizontal and vertical, mat shape, 
* ; 
variety of superstructure loads and assumption in their development and effect of superstructure 
stiffness on mat rapidly reduce exactness to a combination of approximations. The design is further 
affected by excavation heave. 
(h) After propottioning the mat size, compute the minimum mat thickness based on punching shear at 
critical columns based on column load and shear perimeter. It is common practice not to use shear 
reinforcement so that mat depth is maximum. 
i SURVEY OF AVAILABLE LITERATURE 19 
(i) In case column spacing is less than 1.75 divided by h or the mat is very thick and variation of column 
loads and spacing is not over 2096, mat may be designed by treating it as a rigid body and considering 
I strips both ways. These strips are analysed as combined footings with multiple column loads and 
loaded with the soil pressure on the strip and column reactions equal to loads obtained from the 
superstructure analysis. Since a mat transfers load honzontally, any given strip may not satisfy 
vertical load summation. 
Q) In case the criteria is not met with an approximate analysis can be made using the method suggested 
by ACI Committee 336 in 1966. 
(k) Computer aided finite differences, finite grid or finite element methods can be used where computers 
are available. The report gives details of these 3 methods. In any of these 3 methods node pressure 
should not exceed the safe bearing pressure value recommended by the geotechnical engineer. 
(1) A mat analysis is only as good as the soil parameters. Since it is very difficult for the geotechnlcal 
engineer to provide accurate vdues of moGulus of subgrade reaction, the structural designer may 
do the parametric study, varying the value of K over range of one half the furnished value to 5 or 
10 times the furnished value. 
(m) The analysis and design of combined footings and mats is a soil-structure interaction effort in which 
there is no unique method to determine mat deflection. The determination of mat deflection extends 
far beyond the analysis of a beam or finite element model to the prediction of subgrade response. 
The predictionof subgrade response, though part of the structural analysis of the mat, is more elusive 
than designers wish to admit. Experience with extensive measurements of both foundation loadings 
and subgrade response are needed to develop a high degree of confidence in the method selected. 
A very close working relationship must exist between the geotechnical and structural engineers to 
properly analyse comb~ned footings and mats. 
4.23 Foundation Analysis and Design by Bowles, 4th Edition, 1 9 8 8 ~ ~ 
In this edition analysis of mat foundation has further been elaborated considerably. Among the design methods 
included are conventional or rigid methods as explained in earlier edition stating that this method is not 
recommended at present because of substantial amount of approximations and the wide availability of 
computer programmes which are relatively easy to use and mat being generally too expensive and important 
not to use most refined analytical method available. 
The approximate flexible procedure suggested by ACI Committee 436 (1966) has been retained and 
elaborated. Further details have been given for finite difference method, finite element method and finite grid 
method applicable with computer. 
4.24 Proceedings of Indian Geo-Technical Conference 1992, Calcutta, December, 1 9 9 2 ~ ~ 
This conference does not have papers relating to design and analysis of raft foundation. 
4.25 Designs of Foundation Systems - Principles and Prrictices by Nainan P. Kurian, 1 9 9 2 ~ ~ 
The book details conventional approach to raft design as a flat slab and beam and slab raft, following the Indian 
Standard Code of Practice, more on the inverted floor approach. The book only mentions that an integrated 
analysis of the beam and slab on the computer by the finite element method using package programmes such 
as SAP IV which will give exact results based on the actual behaviour of the system can be carried out. This 
book also mentions about the design of raft foundation by the Soil line method stating that this method has 
20 RAW FOilNDATlONSDESlGN AND ANALYSIS 1 
I 
rather become obsolete in the wake of possibility of using more refined flexible methods with the aid of 
computer. 
4.26 13th International Conference on Soil Mechanics and Foundation Engineering, New Delhi 
January, 1 9 9 4 ~ ~ I I 
A paper by M.F. Randolph was presented as a special lecture on design methods for Pile Groups and Piled i 
Rafts. 
The paper recalls that in majority of the cases where piles form part of the foundation for a building or other 
structures, the primary reason for inclusion of the piles is to reduce settlements. However, once the decision 
has been made that piles are required the traditional design approach has been to ensure that the total structural 
load can be carried out by the piles, with adequate factor of safety against bearing failure. However, there is 
elastic interaction'between the raft and soil below, between piles and piles as the performance of a pile within i 
a group is affected by the presence of other piles. The key question that arises in the design of pile rafts concerns 
I the relative proportion of load carried out by raft and the piles and the effect of additional pile support on , 
absolute and differential settlements. ,The paper suggests that this distribution of load between the raft and piles 1 
be taken into account. The paper also gives methods by which this proportion of load between the two 
components are carried out. I 
4.27 Soil Structure Inter-action - The Real Behaviour of Structures, published by the Institution of 
Structure Engineers, U.K. The Institution of Civil Engineers, U.K. International Association 
for Bridge and Structural Engineering in March, 1 9 ~ 9 ~ ~ 
The above institutions constituted a joint committee under Dr. Sam Thornborn which prepared this report. 
Pointing out that, 
(i) Red behaviour of structures in contact with ground involves an inter-active process beginning with 
the construction phase and ending with a state of balance after a period of adjustment of stresses 
and strains within the structure and within the ground influenced by the structure. 
(ii) Actual behaviour of the structure relates to the inherent spatial variations in the ground and it should 
be appreciated that these variations are not always readily identifiable by occasional and local 
boring, sampling and testing. 
The report deals with the question of soil structure interaction in 2 parts. Pari I relates to structures supported 
by ground and Part I1 for ground supported by structures. 
(a) Under structures supported by ground, the report points out that engineers could estimate the 
settlements for a perfectly flexible load or they could estimate the avenge settlement of a rigid load 
but in between these limits, the engineers could say nothing. 
(b) Analytical methods have been developing so rapidly over the last few years that it is now possible 
to obtain solution to many complex problems which a few years ago would have been quite out of 
reach. If used sensibly and with discernment, these powerful analytical methods can be of consid- 
erable assistance enabling a designer to gain a feel for the behaviour of soil structure system. 
However, if used blindly, such methods cause menace and can be extremely misleading. The key 
to successful use is to gain a clear understanding of the idealisations that are being made and to be 
aware of, how far they may be, from reality. 
(c) For a framed building founded on a raft, during excavation some heave of the soil will occur. The 
raft will then be constructed and will be influenced by the differential settlement there after. As the 
SURVEY OF AVAILABLE LITERATURE 
i 
structural load is applied short term settlements take place, the part of the structure in existence 
t distorts and the overall stiffness gradually increases. The cladding is then added and may substan- 
tially increase the stiffness of the building. Finally, the imposed load is applied. Not all the 
components of the buildings are subject to the same relative deflection. The relative deflections 
experienced by the raft will be the largest. Those experienced by the structural members will vary 
with location and elevation in the building. The likelihood of damage will diminish, the larger the 
proportion of medium and long-term settlements, the smaller the ratio of imposedldead loads and 
later the stage at which the finishes are applied. 
(d) The report has an appendix which has reviewed currently available techniques for the analysis of 
the total soil structure system. More readily available computer packages that utilise these techni- 
ques, have been listed in the appendix. 
(e) The manner in which and the limitations with which super-structure can be modelled have been 
singled out. For soil model, it is pointed out that commonly known approach of treating the soil as 
a set of liner unconnected springs cannot be recommended for the analysis of rafts and continuous 
footings although this model has the advantage of being easily included in standard computer 
programmes for structural analysis. It is a poor physical model. The results of analysis based on use 
of this model may be excessively sensitive to the pattern of applied load. 
(f) The half space continuum using elastic theory for both stresses and strains has severe limitations 
because it does not take into account, the soil layering or the variation of soil modulus with depth 
within a given layer. In an extension of this method where elastic theory is used for strains only and 
then stresses are calculated using the various deformation moduli of the soil is better approximation. 
In a further improvement of a layered coniinuum the exact stresses and strains in a layered soil mass 
are calculated. 
(g) Super structure stiffness has a marked influenceon the behaviour of the raft and should not be 
ignored although the quantitative assessment of all but the simplest of the wall system connected 
to the raft may prove difficult. However, often the raft is itself a major contributor to the overall 
stiffness of the building. Since the raft is in intimate contact with the supporting soil, the inter-active 
effects are perhaps most marked in consideration of its own behaviour. In the design of raft 
foundation, it is totally unrealistic to ignore deformation and rely on moment and shears obtained 
from the analysis of the conventional flat slab method. It is equally unrealistic to compute 
deformation without consideration of the structural stiffness and then to design on the basis of the 
corresponding stress resultants. Rational design approach must be based on the results of an 
interactive analysis. 
DESIGN APPROACH AND 
CONSIDERATIONS 
Summary of methods suggested by various authors discussed in Chapter 4 would indicate that basically two 
approaches have been suggested for analysing the behaviour of raft foundation: 
A. Rigid foundation approach 
B. Flexible foundation approach 
5.1 Rigid Approach 
In rigid foundation approach, it is presumed that raft is rigid enough to bridge over non-uniformities of soil 
structure. Pressure distribution is considered to be either uniform or varying linearly. Design of rigid raft 
follows convkntional methods where again following two approaches have been suggested: 
(a) Inverted floor system 
(b) Combined footing approach 
In rigid rafts, differential settlements are comparatively low but bending moment and shear forces to which 
raft is subjected are considerably high. 
5.2 Flexible Approach 
In flexible foundation approach, raft is considered to distribute load in the area immediately surrounding the 
column depending upon the soil characteristics. In this approach differential settlements are comparatively 
larger but bending moments and shear forces to which the raft is subjected are comparatively low. Analysis is 
suggested basically on two theories 
(a) Flexible plate supported on elastic foundation, i.e., Hetenyi's Theory 
(b) Foundation supported on bed of uniformly distributed elastic springs with a spring constant 
determined using coefficient of sub-grade reaction. Each spring is presumed to behave inde- 
pendently, i.e., Winklers's foundation 
Based on these two basic approaches, methods suggested include simplified methods subject to certain 
limitations which can be carried out by manual computation. Also now available are computer based methods 
DESIGN APPROACH AND CONSIDERATIONS 23 
like finite element and finite differences methods. Finite differences method is based on the second approach 
uf uniformly distributed elastic springs and can consider one value of sub-grade modulus for the entire area. 
Finite element method transforms the problem of plates on elastic foundation into a computer oriented method 
of matrix structural analysis. In this method, plate is idealised as a mesh of finite elements inter-connected 
only at the nodes (corners), and the soil may be modelled as a set of isolated springs or as an elastic isotropic 
half space. The matrix structural analysis can be extended to include the influence of the super-structure as 
well. Thus, the interaction between the super-structure, the foundation and the soil can be accounted for. It is 
possible to consider different values of sub-grade modulus in different areas of the raft foundation. 
In case of piled rafts against the usual assumption of entire load being carried by piles alone, emphasis is 
now being laid on sharing of load between raft supported on soil, i.e., raft soil system and raft pile system. 
Sufficiently accurate methods for practical distribution of these loads are not yet available. 
As a simplification of treating the entire raft as a plate, concept of beam on elastic foundation is also being 
used. For this purpose raft is considered to consist of beams in both the directions. Each of these beams is 
-, 
treated as supported on springs having spring constant calculated using modulus of subgrade reaction and 
carrying column loads. The beam is then analysed as a bean1 on elastic foundation. 
5.3 Parameters for Raft Design 
In all these methods, however, three basic parameters, i.e., rigidity of the raft, pressure distribution under the 
raft and value of sub-grade modulus become important in addition to whatever other info&ation'is received 
from soil investigation report. These three parameters and method of their determination are discussed in 
subsequent paragraphs. 
A problem which has to be solved while designing a raft foundation is to evaluate the actual contact pressure 
of the soil against the raft. This problem has occupied many researchers theoretically and a lesser number 
experimentally with no exact values being known. Contact pressure, settlement of foundation, soil charac- 
teristics and its behaviour are so much inter-related and their relationship so complex, that soil foundation - 
structure interaction is not clear even now. Considering all these aspects it can be said that the contact pressure 
distribution under the raft depends upon: 
(1) The nature of the soil below the raft, i.e., a single homogenous mass or a layered formation, 
thicknesses of various layers and their relative locations 
(2) Properties of the soil 
(3) The nature of the foundation, i.e., whether rigid, flexible or soft 
(4) Rigidity of the super-structure 
(5) The quantum of loads and their relative magnitude 
(6) Presence of adjoining foundation 
(7) Size of raft 
(8) Time at which pressure measurements are taken 
The total settlement under the raft foundation can be considered to be made up of three components, i.e., 
S = Sd+Sc+Ss 
where Sd is the immediate or distortion settlement, Sc the consolidation settlement and Ss is the secondary 
compression settlement. The immediate component is that portion of the settlement which occurs simul- 
24 RAFT FOUNDATIONS-DESIGN AND ANALYSIS 
taneously with the load application, primarily as aresultof distortion within the foundation soils. Thesettlement 
is generally not elastic although it is calculated using elastic theory. The remaining components result from 
the gradual expulsion of water from the void and corresponding compression of the soil skeleton. The 
distinction between the consolidation and secondary compression settlement is made on the basis of physical 
process which control the time rate of settlement. Consolidation settlements are largely due to primary 
consolidation in which the time rate of settlement is controlled by the rate at which water can be expelled horn 
the void spaces in the soil. The secondary compression settlement, the speed of settlement is controlled largely 
by the rate at which the soil skeleton itself yields and compresses. The time rate and the relative magnitude of 
the 3 components differ for different soil types. Water flows so readily through most clean granular soil that 
the expulsion of water from the pores for all practical purposes is instantaneous and thus foundation settles 
almost simultaneously with the application of load. In cohesive soil, it takes considerable time for water to 
escape and thus settlement in cohesive soils continue much longer. In fact, it has been reported that the pressure 
under a mat foundation on clay may vary from time to time. 
It is usual to assume that the soil below the foundation is an isotropic homogeneous material for its entire 
depth. But normally this is not the situation and we get different layers in varying thickness, having different 
properties below foundation. If the thickness of the upper most layer is large relative to the dimension of the 
loaded area, it would probably be sufficient if the soils were considered as a

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