(2nd Lect) Bearing Capacity of Shallow Foundation

7/24/2019 (2nd Lect) Bearing Capacity of Shallow Foundation

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Course Contents for Advanced Foundation

Engineering

Before the Mid-Term ExaminationShallow Foundations

1.Basics of Bearing Caacit! Anal!sis for Shallow

Foundations "#ased on shear strength arameters$%.Secial Cases of Shallow Foundation &esigni.Foundation under inclined loading

ii.Eccentricall! loaded foundations

iii.Bearing caacit! of la!ered soilsiv.Closel! saced foundations

v.Bearing caacit! of foundations on sloe

vi.'lift caacit! of foundations

vii.&esign of Mat foundations

1


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(. &esign and Anal!sis of Shallow Foundations with

S)T *+, values. Settlement Anal!sis of Shallow Foundations

After the Mid-Term Examination

&ee Foundationsi.&esign of dee foundations under vertical loading

"including iles in grou$

ii.&esign of dee foundations under lateral loading

2


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Foundation- &esign Considerations

Factors to #e taen into consideration whendetermining the t!e of the #uilding foundations/

Function of the structure 0oads from the structure Bearing caacit! of foundation material Total and differential settlement of foundation 'lift forces acting on the foundation

Costs


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Soil Bearing Caacit!

The soil #earing caacit! needs to #edetermined. This can #e done #!/

0ocal or State Building Codes 'niform Building Code "'BC$ Soil testinganal!sis

Site insection and simle soil testing Soil #orings taen at roosed foundation

locations


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5

Bearing Capacity Theory

Bearing Caacit!


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Soil Bearing )ressure

Sread Footings

Calculated Soil Bearing 20oad "ounds$

Area of Footing "s3.ft$

Comare to Allowa#le SoilBearing Caacit!

Diminishing Soil Pressure

W

W

W=footing

widthCritical zonefor

compaction

Soilpressure cutby at this

levelSoilpressure cut

by 2! atthis level


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"

Bearing Capacity Failure

a$4eneral Shear FailureMost common t!e ofshear failure5 occurs in

strong soils and rocs

#$ 0ocal Shear Failure6ntermediate #etweengeneral and unchingshear failure

c$ )unching Shear Failure7ccurs in ver! loose

sands wea cla!s


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B.C. Failures

(Vesic, 1963 and 1973)

Deep

foundations

Sand

Circular foundations


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#

Bearing Capacity Failure

General shear failure

Local shear failure

Punching shearfailure


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1$

Comments on Shear Failure

'suall! onl! necessar! to anal!8e general shearfailure.

0ocal and unching shear failure can usuall! #eanticiated #! settlement anal!sis.

Failure in shallow foundations is generall!settlement failure5 #earing caacit! failure must #eanal!8ed9 #ut in ractical terms is usuall! secondar!to settlement anal!sis.


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11

Development of Bearing

Capacity Theory Alication of limit e3uili#rium methods first done #!

)randtl on the unching of thic masses

of metal.

)randtl:s methods adated #! Ter8aghi to #earing caacit!failure of shallow foundations.

;esicand others imroved on Ter8aghi:s original

theor! and added other factors for a more comlete anal!sis


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Bearing Capacity Theory

LIMIT EQUILIBRIUM

1. &efine the shae of a failure surface

%. Evaluate stresses vs. strengths along this surface


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1!

Assumptions for Terzaghi's Method

&eth of foundation is less than or e3ual to its width +o sliding occurs #etween foundation and soil

"rough foundation$ Soil #eneath foundation is homogeneous semi

infinite mass Mohr-Coulom# model for soil 4eneral shear failure mode is the governing

mode "#ut not the onl! mode$


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1%

Assumptions for Terzaghi's Method

+o soil consolidation occurs

Foundation is ver! rigid relative to the soil

Soil a#ove #ottom of foundation has no shear

strength5 is onl! a surcharge load against the

overturning load

Alied load is comressive and alied verticall! tothe centroid of the foundation

+o alied moments resent


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Terzagi!s Bearing Ca"acit# Teor#


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Ter8aghi develoed the theor! for continuous foundations

"simlest9 %& ro#lem$.

BNNNcq qzDcult:


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Nc= cohesion factor

Nq= surcharge factor

N= self wt factor



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Terzaghi Bearing Capacity

Factors

=>.< == whenNc

$%

= whenN

Nq

c


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*earing Capacity &actors


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2$

The eneral Bearing Capacity

!"uation#


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21

$otes on Terzaghi's Method

Since soil cohesion can #e difficult to 3uantif!9conservative values of c "cohesion$ should #e used.

Frictional strength is more relia#le and does not need to#e as conservative as cohesion.

Ter8aghi:s method is simle and familiar to man!

geotechnical engineers5 however9 it does not tae intoaccount man! factors9 nor does it consider cases such asrectangular foundations.


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& B +o sliding #etween footing and soil

soil/ a homogeneous semi-infinite mass

general shear failure

footing is ver! rigid comared to soil


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2!


!"uation#


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2%


!"uation#


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%esicFormula Shape Factors

+=

c

q

cN

N

L

Bs 1

+= tan1L

Bsq

=L

Bs .=1


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%esicFormula Depth Factors

= B

Dk 1tan

%$sin1"tan%1 += kdq

1=d

kdc -.=1+=


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Allo&ale Bearing Capacity

F

qq ulta=

(## Allo&ale Bearing Capacity

F(# Factor of safety

aq


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Factor of Safety

&eends on/

T!e of soil

0evel of 'ncertaint! in Soil Strength

6mortance of structure and conse3uences

of failure

0ielihood of design load occurrence


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+inimum &actor of Safety


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Selection of Soil Strength

)arameters'se Saturated Strength )arameters

'se 'ndrained Strength in cla!s "Su$

'se &rained Strength in sands9

6ntermediate soils that where artiall! drained

conditions exist9 engineers have var!ing

oinions5 'ndrained Strength can #e used #ut

it will #e conservative@

andc


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!1

Groundwater Effects


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!2

round&ater !ffects

Shallow groundwater affects shear strength in two wa!s/

educes aarent cohesion that taes lace when soils

are not saturated5 ma! necessitate reducing the cohesionmeasured in the la#orator!

)ore water ressure increases5 reduces #oth effective stress

and shear strength in the soil "same ro#lem as is exeriencedwith unsuorted sloes$

d t !ff t


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!!

round&ater !ffects

d l l f


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Groundwater level efects

$


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%round&ater le'el effects

Case 6

w =:

G d l l f


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=

BDD

w11:

Case 66

G d t l l f t


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Case 666

=:


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!,

FOOTINGS WITH ECCENTRIC

OR INCINE! O"!INGS

EccentricityInc#ination


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!#

Footings with 7ne a! Eccentricit! 6n most instances9 foundations are su#ected to moments in addition to the vertical load

as shown #elow. 6n such cases the distri#ution of ressure #! the foundation uon the

soil is not uniform.


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%$


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%1


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%2

Footings with one wa!eccentricit!

+ote that in these e3uations9 when the eccentricit! e#ecomes B?9qminis 8ero.

For e D B?9 qminwill #e negative9 which means that tension willdevelo.

Because soils can sustain ver! little tension9 there will #e asearation #etween the footing and the soil under it. Also note that the eccentricit! tends to decrease the load #earing

caacit! of a foundation. 6n such cases9 lacing foundation column off-center9 as shown in

Figure is ro#a#l! advantageous. &oing so in effect9 roduces a centrall! loaded foundation with a

uniforml! distri#uted ressure.


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%!

F77T6+4S 6T 7ne a!Eccentricit!


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%%

Footing &ith T&o)&ay !ccentricities

Consider a footing su#ect to a vertical ultimate load ultand a moment Mas shown inFigures a and #. For this case9 the comonents of the moment M a#out the x and ! axisare Mxand M!resectivel!. This condition is e3uivalent to a load laced

eccentricall! on the footing with x 2 eBand ! 2 e0as shown in Figure d.


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%5

Footing &ith T&o)&ay !ccentricities


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The Bearing Capacity of *ayered Soils

6n la!ered soil rofiles9 the unit weight of the soil9 the angle of friction andthe cohesion are not constant throughout the deth. The ultimate surfacefailure ma! extend through two or more of the soil la!ers.

Consider the case when the stronger soil is underlain #! a weaer soil. 6f9 the thicness of the la!er of soil #elow the footing9 is relativel! largethen the failure surface will #e comletel! located in the to soil la!er9which is the uer limit for the ultimate #earing caacit!.

6f the thicness is small comared to the foundation width B9 a unchingshear failure will occur at the to soil stratum9 followed #! a general shearfailure in the #ottom soil la!er.

6f is relativel! dee9 then the shear failure will occur onl! on the to soilla!er.

Documents

(2nd Lect) Bearing Capacity of Shallow Foundation