Design of Mat Foundations

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Hemant Kumar BhaskarRoll No:-0610421

Types of FoundationsShallow Foundations versus Deep Foundations

Foundations

ShallowFoundations

DeepFoundations

SpreadFootings

MatFoundations

DrivenPiles

DrilledShafts

Auger CastPiles

6/26/2014 2CE-533 Advanced Foundation Engineering

Mat/Raft Foundation?A foundation system in which essentially the entire

building is placed on a large continuous footing.Usually large concrete slab supporting many columns.Commonly used as foundation for silos, chimneys, large

machinery.It is a flat concrete slab, heavily reinforced with steel,

which carries the downward loads of the individualcolumns or walls.

6/26/2014 CE-533 Advanced Foundation Engineering 4

Mat Foundation often considered to be usedwhen dealing with the following conditions:

The spread footings cover over 50% of the foundationarea because of large column loads.

The soil is soft with a low bearing capacity.

Hydrostatic uplift resistance is needed etc.

Mat/raft foundation6/26/2014 6CE-533 Advanced Foundation Engineering

Types of Mat Foundations

To Design Mat Foundation:1. Determine the capacity of the foundation2. Determine the settlement of foundation3. Determine the differential settlement4. Determine the stress distribution beneath the

foundation5. Design the structural component of the mat

foundation using the stress distribution obtain from 4.

Bearing capacity of the Foundation

Bearing Capacity Analysis follows the same approach asfor spread footings

Factor of Safety (Das, 2004):Under normal Dead loads = 3.0(Min)

Under extreme loads = 1.75-2.0(Min)

dsBNdsNdsNcq qqqzDcccult 5.0

2). Settlement of foundationThe settlement tends to be controlled via the

following:Use of a larger foundation to produce lower soil

contact pressures.Displaced volume of soil (flotation effect);

theoretically if the weight of excavation equals thecombined weight of the structure and mat, thesystem "floats" in the soil mass and no settlementoccurs.

Bridging effects attributable to a. Mat rigidity. b. Contribution of superstructure rigidity to the mat.

By IS Code – 2950 (Part-1)

Foundation type Expectedmaximumsettlement, mm

Expecteddifferentialsettlement, mm

Spread 25 20

Mat 50 20

Design of Mat Foundations

Differential Settlement of Mat Foundations (AmericanConcrete Institute Committee 336, 1988)

Width of raft

Moment of inertia ofstructure per unit lengthat right angles to B

Modulus of Elasticity of Soil

Modulus of Elasticity of Material used inStructure

Rigidity Factor,

Design of Mat Foundations

Differential Settlement of Mat Foundations (AmericanConcrete Institute Committee 336, 1988)

3ahIIEIE bFb

flexural rigidity of the Superstructure and Mat

flexural rigidity of the framed members at right angles to B

/12 flexural rigidity of shear walls

shear wall thickness

shear wall

height

flexural rigidity of the mat foundationFE I

If 0 .5 , th e n m a t c a n b e tre a te d a s r ig id i .e . ( / ) 0

If 0 .5 , th e n ( / ) 0 .1

If 0 , th e n ( / ) 0 .3 5 (s q u a re m a ts ) a n d ( / ) 0 .5 ( lo n g m a ts )

Structural Design of Mat Foundations Approximate Method Flexible Method Finite Difference Method Finite Element Method

AN APPROXIMATE METHOD: The mat is divided into strips loaded by a line of columns and resisted

by soil pressure. This strip is then analyzed as a combined footing. (This method can be

used where the mat is very rigid and the column pattern is fairlyuniform in both spacing and loads.)

This method is not recommended at present because of the substantialamount of approximations and the wide availability of computerprograms that are relatively easy to use.

FLEXIBLE METHOD:1. Compute the plate rigidity D2. Compute the radius of effective stiffness L (Note: the

approximate zone of any column influence is ~ 4L).3. Compute the radial and tangential moments, the shear,

and deflection.

FINITE DIFFERENCE METHODThe finite-difference method uses the fourth-order differential equation based on the theory ofplates and shells [Timoshenko and Woinowsky-Krieger (1959)]:

The finite-difference method has several advantages:

It has been widely used (and should be used as a check on alternativemethods where it is practical).

It is reliable if the mat can be modelled using a finite-difference grid. It is rapid since the input data are minimal compared with any other

discrete method, and the computations to build the stiffness array arenot so extensive as other methods. Usually only three to five lines ofinput data are needed compared with up to several hundred for theother methods.

There are also a number of disadvantages:

It is extremely difficult to model boundary conditions ofcolumn fixity.It is very difficult to model notches, holes, or re-entrant

corners.It is difficult to apply a concentrated moment (as from a

column) since the difference model uses moment/unit ofwidth.

FINITE ELEMENT METHOD:

In the finite-element analysis, element continuity is maintained throughuse of displacement functions. The displacement function is of the form

REINFORCEMENTDETAILSOF MAT FOUNDATION

MAT FOUNDATIONWITH REINFORCED BARS

DESIGN OF MAT FOUNDATION USING SOFTWARES: Many types of software are available to design mat foundation some are like

ABAQUS V6.8, STAAD FOUNDATION,RISA FOUNDATION, ANSYS, etc.

MODELLING OF MATFOUNDATION

UsingSTAAD Foundation 2006

Some Highlight points of IS-2950 Part-1 (DESIGN AND CONSTRUCTION OFRAFT FOUNDATIONS )

For satisfactory design and construction of a raftfoundation, the following information is necessary:Site PlanLoading ConditionsEnvironmental FactorsGeotechnical InformationLimiting Value of Angular distortion and differential settlementRigidity of foundation and Super structure

METHODS OF ANALYSIS Rigidity of Superstructure And Foundation

Width of raft

Moment of inertia ofstructure per unit lengthat right angles to B

Modulus of Elasticity of Soil

Modulus of Elasticity of Material used inStructure

Determination Of Critical Column SpacingEvaluation of the characteristics γ is made as follows:

Where,k = modulus of subgrade reaction in KN/m3

B = width of raft in cmEc = modulus of elasticity of concrete in MPaZ = moment of inertia of the raft in m4

Depth of Foundation : The depth of foundation shall generally be not less than 1 m.

Construction Practices Applicable to the Design of Mats.

Thickness T is determined from two-way shear (punchingshear); Typical mat thickness T: Stories B=45' B=90' B=120'

< 5 24" 31" 39"5 - 10 35" 47" 59”10 - 20 59" 78" 98"

Conclusions:The primary objective of this report is to discuss various methods of

design of mat foundation with structural reinforcement view has beendone starting from simple analysis to methods in research with rigorousanalysis.

The use of software's to design mat foundation had been introducedto track the current era of computers.

Bowles,J.E. (2000) Foundation Analysis and Design.

A.C.I.Committee 336, Suggested analysis and design procedures for combined footingsand mats, ACI Struct J (1988), pp. 304–324.

S.N. Shukla, A simplified method for design of mats on elastic foundations, ACI J (1984),pp. 469–475. View Record in Scopus | Cited By in Scopus (2)

O.C. Zienkiewicz, The finite element method (3rd ed.), McGraw-Hill, UK (1977).

G. Bézine, A new boundary element method for bending of plate on elastic foundations,Int J Solids Struct 24 (1988), pp. 557–565. Abstract | PDF (589 K) | View Record in Scopus| Cited By in Scopus (0)

REFERENCES:

Design of Mat Foundations

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