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RESEARCH PAPERInternational Journal of Recent Trends in Engineering, Vol. 1, No. 6, May 2009

16

Response of Raft Foundation on Varying StratumKumar Venkatesh

1, N.K. Samadhiya

2, and A.D. Pandey

2

1

Department of Civil Engineering, MNNIT, Allahabad, IndiaEmail: [email protected] Department of Civil Engineering & Earthquake Engineering, IIT Roorkee, India

Email: {nksamfce, adpanfeq}@iitr.ernet.in

AbstractThe effect on raft foundation of a barrage due tovarying stratum has been examined using finite element

analysis. The raft foundation is completely resting on soil

media and surrounded by soil and rock media. Eight noded

brick elements have been used for three-dimensional

modeling and meshing of the rock, soil, cut-off, pier, beam

and abutment but raft foundation has been meshed using

plate element. The relevant amount of soil and rock around

and bottom of the raft foundation has been modeled tosimulate the in-situ conditions. The raft foundation of a

typical barrage has been analyzed using the representative

load cases. Analysis of the barrage raft foundation has been

carried out and the influence of soil properties has been

studied at the region of transverse sections, which exhibited

the response in terms of moments and deformation with

significant difference.

Index Termsraft foundation, finite element method,

barrage

I. INTRODUCTION

A barrage is a diversion headwork, which is employedto divert water into the canal from the river. In a barragethe crest is kept at low level and heading up of water is

affected by the gates. During the floods, the gates areraised to pass the high flood flow, with afflux. When the

flood recedes, the gates are lowered and the flow isobstructed, thus maintaining required pond level at theupstream of the barrage.

Barrages may be made of masonry, plain cementconcrete or reinforced concrete, depending on the natureof foundation encountered, availability of construction

material, dewatering problems, economy of construction,etc. In recent years, the hydraulic and structural engineersare seized upon in the important task of evolving safe andeconomic design of raft foundation. A number ofanalytical methods are available for design of raftfoundation, viz., conventional method [1], Bakers

method [2] , Hetenyis method [3] and numericalmethods [4,5]. Out of the above Hetenyi,s method isadopted for analysis and design of barrage raft foundationin India as recommended by IS 11130-1984 [6]. Thefinite element analysis of barrages has been carried out bySasidhar [7]. A comparative analysis of a barrage raft

floor has been carried by Venkatesh et al [8]. This paperis an attempt to examine the response of raft foundationusing three dimensional finite element analyses resting on

varying foundation media and effects on that due to

variation of elastic modulus of alluvial soils.

II. FINITEELEMENTMETHOD

The finite element method is a numerical procedure foranalyzing structures and continua. It is a powerful tool instructural analysis of simple to complicated geometries.In the recent years with the advent of compact and

powerful computers, the analyses performed by finiteelement method have become more acceptable. Three

dimensional finite element program has been employed inthe present study. The basic steps involved in the finiteelement method are as mentioned below.

i. Discretization of the continuum.ii. Calculation of the element stiffness matrices.

iii. Assembling the element stiffness matrices.iv. Calculation of the element load vectors.v. Assembling the element load vectors.

vi. Imposition of boundary conditions.vii. Imposition of external forces.

viii. Calculation of the displacement vectors.ix. Calculation of the strains and stress field.

A detailed discussion on the finite element method isbeyond the scope of this paper but well documented in

standard literatures [4,5].

III. IDEALIZATIONOFBAYS

Raft foundation of a typical barrage bays 3-4 resting

on varying foundation media has been considered foranalysis by finite element method under representativeloading condition.

The raft foundation of bays 3-4 is separated by

expansion joints from rest of the bays. The plan of bays

3-4 (Fig. 1) with three sections of the barrage raft floor intransverse direction (across the flow) i.e. upstreamsection (A-A), ogee section (B-B) and downstreamsection (C-C) at different distances from upstream edgehas been chosen for the comparison. The barrage raftfoundation with cut-off of bays 3-4 are completely restingon alluvial soil with single and double pier but suddenly

at the edge of bay 4 towards bay 5 there is discontinuityin soil media due to presence of hard rock as shown intypical transverse section of the bays 3-4 (Fig. 2). Thelongitudinal section with variation in the height of pierfrom upstream (25 m) to downstream (3.5 m) along withraft foundation and cut-offs are as shown in Fig. 3.

2009 ACADEMY PUBLISHER

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Figure 1. Plan of barrage bays 3-4

Figure 2. Transverse section of barrage bays 3-4

Figure 3. Longitudinal section along the pier, raft foundation and cut-off

of the barrage bay

IV. PHYSICAL MODELING AND ANALYSISEight noded isoparametric brick elements have been

used for the three-dimensional modeling of soil and rockmedia. The cut-off, pier, abutment wall and beam havebeen also modeled using eight noded isoparametric brickelements. The four noded three-dimensionalisoparametric shell elements have been used for barrage

raft floor modeling to simulate the behaviour of raftfoundation as plate bending element having six degreesof freedom per node capable of taking loads normal to theplane [9]. In this model the depth of the soil and rockmedia considered is 80m from the crest level. The extentof surrounding soil and rock up to 35m on both sides of

the transverse section of the raft and 50m on both inupstream and downstream side equivalent to the length ofthe raft floor along the flow has been considered.

Several iterations were made for refining the mesh of

the models from coarser to finer till the values ofmoments at the same section under study in the two

consecutive models converged under gravity load. Thematerial properties of various components of barrage areas given in Table1. The adopted model with finiteelement mesh consisting of the pier and beam structurewith the supporting raft foundation is shown in Fig. 4.The finite element mesh for the entire structure-raft-

foundation soil and rock system has been presented inFig. 5. The dark grey portion in the figure resembles the

rock portion. The total number of elements used for theadopted finite element model is 18744, which resulted in21204 nodes in the model.

The boundary condition imposed on the finite elementmodels consist of restraining the limiting boundary of thefoundation soil and rock in such manner that

displacement normal to the boundary surface arerestrained i.e. the base of the foundation media at the

depth of 80 m is restrained against vertical displacementand at the ends along and across the direction of flow,foundation media is restrained against the horizontaldisplacement.

Assumptions and Condition of Analysis

It has been assumed that within the entire soil and rockmedia, elastic modulus and Poissons ratio remain thesame. Instead of soil and rock mass only stiffness of the

soil and rock have been considered, as it has beenassumed that it has already been settled due to its own

weight. Analysis have been carried out with values ofmodulus of elasticity, Es of surrounding soil taken as25000 kN/m

2, 50000 kN/m

2, 100000 kN/m

2and 200000

kN/m2 for constant Poissons ratio 0.3, whereas themodulus of elasticity and Poissons ratio for rock stratumhas been considered constant through out the analysis as

1 x 107

kN/m2

and 0.25 respectively.

Methodology

Except properties of soil all the material properties

remained constant and possessed linear behavior. Finite

element analysis for each material properties of thesurrounding soil, for the model bays 3-4 have beencarried out, which involves determination of momentsand deformation of the raft foundation.

Rock

Expansion joint

Raft

Soil

Side Cut-off

SinglePier

Expansionjoint

DoublePier

DoublePier

Pier

Raft Foundation

Side Cut-off

Downstream Cut-offUpstream Cut-off 5 m

3.5 m

3 m7.5 m

3 m

25 m

14

13

49.526 m

49.5

26m

30.5 m

11 m11 m

2.2

5m

DoublePier

SinglePier

Upstream Section4.5 m

DoublePier

Bay 3Ogee Section

Downstream Section

13.8 m

24.6 m

Bay 4

A A

B B

C C

SOIL

SOIL

SOIL

ROCK

2.2

5m


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-3000

-2000

-1000

0

1000

2000

3000

0 5 10 15 20 25 30 3

Distance (m) from Bay3 to Bay4

Es = 25000 kPa

Es = 5000 0 kPa

Es= 1000 00 kPa

Es= 2000 00 kPa

-3000

-2000

-1000

0

1000

2000

3000

0 5 10 15 20 25 30 3

Distance (m) f rom Bay3 t o B ay4

Es = 25000 kPa

Es = 500 00 kPa

Es= 1000 00 kPa

Es= 200 000 kPa

Figure 4. 3D-finite element discretization of the pier and raft floor

with cut-off of the bays 3-4

Figure 5. 3D-Finite element discretization of the pier, raft,soil and rock system of bays 3-4

TABLEI.

MATERIALPROPERTIES OFBAYS3-4MODEL

COMPONENTS

Modulus of

Elasticity (E)

(kN/m2)

Unit

Weight ()

(kN/m3)

Poissons

Ratio

()

Pier/Abutment 2.5 x 107 25 0.15

Raft Floor 2.5 x 107 25 0.16

Cut-off 2.4 x 107 25 0.18

V. BEHAVIOUR OF RAFT FOUNDATION

The trend of moments and deformation profile atvarious sections of raft foundation is similar irrespectiveof the variation of modulus of elasticity of surroundingsoil. The results of the moments at upstream section (A-

A), ogee section (B-B) and downstream section (C-C)have been presented in Fig. 6 to Fig. 8 for flow conditionunder gravity, hydrostatic and uplift load. It may beobserved in the transverse sections that positive moments

have decreased due to increase in elastic modulus of soiland the abrupt changes in moments can be observedtowards the rock end.This behavior may be contributedto increased stiffness of the soil which is appreciablydepicted in upstream and downstream sections.

Figs. 9 to 11 show the deformations at upstreamsection (A-A), ogee section (B-B) and downstreamsection (C-C) for flow condition under gravity,hydrostatic and uplift load. It has been observed that withthe increase in the stiffness of foundation soil, the

differential settlement has reduced. In case ofdeformations it is clear that there is a significant changeat the same sections due to variation of modulus ofelasticity of surrounding soil and the magnitude ofdeformation at different sections are also changing. Itshows that the behaviour of the raft foundation resting on

soil media affected by the varying soil properties inpresence of rock media present at the edge of raft

foundation.

Figure 6. Moments 'Mz' at upstream section (A-A) for flow condition

considering gravity, hydrostatic and uplift load

Figure 7. Moments 'Mz' at ogee section (B-B) for flow condition


ROCK

SoilSoil

Moments(kNm)

Moments(kNm)

Distance (m) from Bay 3 to Bay 4


Raft

Side Cut-off

Upstream

Cut-off

Downstream Cut-off

Double pier

Single pier

Double pier


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-4000

-2000

0

2000

4000

6000

8000

0 5 10 15 20 25 30 3

Distance (m) from Bay3 t o B ay4

Es = 25000 kPa

Es = 50000 kPa

Es= 100000 kPa

Es= 200000 kPa

-70

-60

-50

-40

-30

-20

-10

0

0 5 10 15 20 25 30 3

Distance (m) fro m Bay3 to B ay4

Es = 25000 kPa

Es = 5000 0 kPa

Es= 100000 kPa

Es= 200000 kPa

-70

-60

-50

-40

-30

-20

-10

0

0 5 10 15 20 25 30 3

Distance (m) fr om Bay3 to Bay4

Es = 25000 kPa

Es = 5000 0 kPa

Es= 100000 kPa

Es= 200000 kPa

-70

-60

-50

-40

-30

-20

-10

0

0 5 10 15 20 25 30 3

Distance (m) from Bay3 to Bay4

Es = 25000 kPa

Es = 5000 0 kPa

Es= 100000 kPa

Es= 200000 kPa

Figure 8. Moments 'Mz' at downstream section (C-C) for flow conditionconsidering gravity, hydrostatic and uplift load

Figure 9. Deformation at upstream section (A-A) for f low condition


Figure 10. Deformation at ogee section (B-B) for flow condition


Figure 11. Deformation at downstream section (C-C) for flow condition


VI. CONCLUSIONSOn the basis of the study carried out, the following

conclusions may be drawn:

(i) The variation of elastic modulus of soil andpresence of rock media plays a significant roleand affects the moments and deformations ofraft foundation.

(ii) The trend of moments and deformations of theraft foundation are similar at individual sections,with variation in the modulus of elasticity of soil

media but a significant qualitative difference hasbeen observed in moments and deformations atindividual sections.

REFERENCES

[1] J.E. Bowles, Foundation Analysis and Design. McGrawHill, New York, 1982.

[2] A.L.L. Baker, Raft Foundations, the Soil Line Method of

Design. Concrete Publications Limited, London, 1948.[3] M. Hetenyi,Beams on Elastic Foundations. The University

of Michigan Press, USA,1964.[4] C.S. Desai and J.F. Abel, 2000, Introduction to the Finite

Element Method. CBS Publisher and Distributors, New

Delhi, 2000.[5] C.S. Krishnamoorthy, Finite Element Analysis, Theory and

Programming. Tata McGraw Hill Publishing CompanyLimited, New Delhi, 2002.

[6] IS: 11130, Criteria for Structural Design of Barrages and

Weirs. Bureau of Indian Standards, New Delhi, 1984.[7] T. Sasidhar, 3-D Finite Element Analysis of a Barrage. M.

Tech. Dissertation, Department of Earthquake Engineering,IIT Roorkee, 2002.

[8] K. Venkatesh, A.D. Pandey and N.K. Samadhiya,Comparative analysis of raft foundation for a barrage in

India Proc. International Conference on GeotechnicalEngineering, Sharjah UAE, pp.468-473, October 2005.

[9] G.J.W. King, An introduction to superstructure/ raft/soil

interaction,Int. symposium on soil-structure interaction,University of Roorkee, India, pp. 453-466, 1977.

Moments(kNm)

Deformation(mm)

Deformation(mm)

Deformation(mm)






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