ENCE 4610 - Foundation Analysis and Design

7/25/2019 ENCE 4610 - Foundation Analysis and Design

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ENCE4610

Foundation

Analysis

and

DesignShallow Foundations:Overview

Terzaghis Method of Bearing Capacity

Estimation


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TypesofShallow

Foundations Shallow foundations are

usually placed within a depth

D beneath the groundsurface less than the minimumwidth B of the foundation

Shallow foundations consist of: Spread and continuous footings

Square, Rectangular orCircular Footings

Continuous footings

Ring Foundations

Strap Footings

Wall footings

Mats or Rafts

Thisimagecannotcurrently bedisplayed.


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FootingsA spread footing

distributes column orother loads from thestructure to the soil,where B < W < 10B

A continuous footingis a spread footingwhere W > 10B.

A wall footing is along load bearingfooting


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DimensionandRubbleStoneFootings

Before 1800, most

all footings wereunreinforcedmasonry, as shown

Dimension stonefootings

Rubble stone footings

Satisfactory forlighter structures,they were tooheavy for the larger

structures of the19th century



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SteelGrillageFootingsThisimagecannotcurrently bedisplayed.

Used first with the Montauk Block Building in Chicago

(1882). First foundation type specifically designed for flexure.


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TypicalConcreteFootingThisimagecannotcurrently bedisplayed.


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Thisi magecannotcurrently bedisplayed.

MethodsofConstructionof

ConcreteFootings

Formed footing

Once form is made, before concrete

is poured either anchor bolts ordowels are placed to enable

connection of the foundation with

the building.


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MatFoundations A mat is continuous in two

directions capable ofsupporting multiple columns,

wall or floor loads. It hasdimensions from 20 to 80 ft ormore for houses and hundredsof feet for large structuressuch as multi-story hospitals

and some warehouses Ribbed mats, consisting of

stiffening beams placedbelow a flat slab are useful inunstable soils such as

expansive, collapsible or softmaterials where differentialmovements can be significant(exceeding 0.5 inch).


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ConditionsforMat

Foundations Structural loadsrequire large area tospread the load

Soil is erratic andprone to differentialsettlements

Structural loads areerratic

Unevenly distributedlateral loads

Uplift loads are largerthan spread footingscan accommodate;

weight of the mat isa factor here

Mat foundations areeasier to waterproof


Example:Chase Tower,

Houston, TX

Matfoundation is 3

metres thick

and bottomed

at 19.2 mbelow street

level


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DistributionofBearing

Pressure Distribution of bearing pressure depends on

Eccentricity, if any, of applied load

Magnitude of the applied moment, if any Structural rigidity of the foundation

Stress-strain properties of the soil

Roughness of the bottom of the foundation

Spread footings are nearly rigid; effects offoundation/soil flexibility usually ignored

Mat foundations are more flexible; flexibility animportant factor


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BearingPressureDistribution

ConcentricLoadsThisimagecannotcurrently bedisplayed.

Flexiblefoundation

on clay

FlexibleFoundation

on Sand

Rigid

foundation

on clay

Rigid

Foundation

on Sand

Simplified

Distribution


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TermsUsedinShallow

Foundations Total Overburden

Pressureo Intensity of total overburden

pressure due to the weight ofboth soil and water, at thebase level of the foundation

Effective Overburden

Pressureo Effective overburden pressure

at the base of the foundation

wsatw DDq += 10

wsubw DDq += 10

Ultimate Bearing

Capacityo Maximum bearing capacity of

the soil at which shear failure

takes place

Net Bearing Capacityo Bearing capacity in excess of

the overburden pressure

Gross and Net

Allowable Bearing

Pressure

ounu

qqq =

Fqq ua =


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BearingCapacityFailure

General Shear Failureo Most common type of shear

failure; occurs in strong soilsand rocks

Local Shear Failureo Intermediate between

general and punching shearfailure

Punching Shear Failureo Occurs in very loose sands and

weak clays


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SoilConditionsandBearing

CapacityFailureThisimagecannotcurrently bedisplayed.

(after Vesi (1973)


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CommentsonShear

Failure Usually only necessary

to analyse general

shear failure Local and punchingshear failure canusually be anticipatedby settlement analysis

Failure in shallowfoundations isgenerally settlementfailure; bearing

capacity failure mustbe analysed, but inpractical terms isusually secondary tosettlement analysis



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DevelopmentofBearing

CapacityTheory Application of limit equilibrium methods first

done by Prandtl on the punching of thickmasses of metal

Prandtl's methods adapted by Terzaghi to

bearing capacity failure of shallowfoundations

Vesi and others (Meyerhof, Brinch Hansen,

etc.) improved on Terzaghi's original theoryand added other factors for a more complete

analysis


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AssumptionsforBearing

CapacityMethods Geometric assumption

Depth of foundation is lessthan or equal to its width

GeotechnicalAssumptions Soil beneath foundation is

homogeneous semi-infinite

mass* Mohr-Coulomb model for soil General shear failure mode is

the governing mode (but notthe only mode)

No soil consolidation occurs Soil above bottom of

foundation has no shearstrength; is only a surchargeload against the overturningload*

Foundation-SoilInterface

Assumptions Foundation is very rigidrelative to the soil

No sliding occursbetween foundation and

soil (rough foundation) Loading Assumptions

Applied load iscompressive andapplied vertically to the

centroid of thefoundation* No applied moments

present

* We will discuss workarounds to these assumptions


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LimitEquilibriumMethod

(CircularFailureSurface,CohesiveSoil)


022

0 =B

BbpBcBbB

Bbq=M ultA

Assume: No soil strength due to internal friction (cohesive soil,)shear strength above foundation base neglected

0

0

6.2822

p+cN=q

=Np+c=q

cult

c

ult

k


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Skempton BearingCapacity

(Undrained CohesiveSoils) Uses circular and other

slip surface forms

Only for undrained,uniform cohesive soils(non-uniform withmodification)

Equation for unit grossultimate capacity:

Bearing capacity factorfor rectangularfoundations:

0p+cN=q cult

( ) ( )

1001684 ScRc

N

L

BN

+=


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Thisi magecannotcurrently bedisplayed.

FailureGeometryforGeneral

BearingCapacity Methods


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TerzaghiEquationsand

FactorsThisimagecannotcurrently bedisplayed.


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TerzaghiBearingCapacityEquation

Eccentricity will be explained later


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TerzaghiBearingCapacityFactors

Te a hi Bea i


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TerzaghiBearing

CapacityFactorTable

E l f T hi


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ExampleofTerzaghis

MethodThisimagecannotcurrently bedisplayed.

Use Terzaghi's Method

Given

Square Foundation asShown

Grounwater table is 50'

below surfaceIgnore slab-on-gradeflooring

Find

Ultimate bearingcapacity and columnload to produce same

E l f T hi


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ExampleofTerzaghis

Method

Solve for qult

Obtain Bearing Capacity Factors

( )Square

BN'+Nq+Nc'=qqocult 0.41.3


E l f T hi


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ExampleofTerzaghis

Method

Compute ultimate capacity Pult = qult * A Pult = (15,780)(3.25

2)

Pult = 166.7 kips

Keep in mind that the design load supported bythe foundation includes the weight of the footing,

which is part of the dead load

( )( )( ) ( )( )( ) ( )( )( )( )

psf=q

++=q

++=q

BN'+N'+Nc'=q

ult

ult

ult

qzDcult

15,780

309954357246

19.73.251210.422.46212137.161501.3

0.41.3

Notes on Terzaghis


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NotesonTerzaghi s

Method Since soil cohesion can be difficult to quantify,

conservative values of c (cohesion) should be

used Frictional strength is more reliable and does

not need to be as conservative as cohesion

Terzaghi's method is simple and familiar tomany geotechnical engineers; however, itdoes not take into account many factors, nordoes it consider cases such as rectangular

foundations It is primarily presented for historical reasons

Other Variations of Terzaghis


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OtherVariationsofTerzaghis

MethodPresentedinTextbook Bearing Capacity for

Local Shear Failureo Equations for local shear

failure have differentcoefficients but same bearingcapacity factors

o

Unless otherwise stated,assume general shear failure(but see Vesi chart presentedearlier)

o Make sure you dont use these

for general shear failure andvice versa

Equations for special

cases of c = 0 or = 0

Formulation for

Rectangular

Foundationso Rectangular foundations not

part of original Terzaghi theoryof bearing capacity

o Equations given in the book anextrapolation

o Rectangular foundations (all

shallow foundations, really)better analyzed using

methods such as Vesi,Meyerhof, Brinch-Hansen, etc.)


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ENCE 4610 - Foundation Analysis and Design

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