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BEARING CAPACITY OF SOIL

Dr. S. K. Prasad

Professor of Civil Engineering

S. J. College of Engineering, Mysore

7.0 Syllabus

1. Definition of ultimate, net and safe bearing capacities, Allowable bearing pressure

2. Terzaghis and Brinch Hansens bearing capacit e!uations " Assumptions and

#imitations

$. Bearing capacit of footings sub%ected to eccentric loading

&. 'ffect of ground water table on bearing capacit

(. )late load test, *tandard )enetration Test, +one )enetration Test- Hours

7.1 Definii!ns

Bearing capacit is the power of foundation soil to hold the forces from the

superstructure without undergoing shear failure or e/cessi0e settlement.

oundation soil is that portion of ground which is sub%ected to additional

stresses when foundation and superstructure are constructed on the ground. The

following are a few important terminologies related to bearing capacit of soil.

Super Structure

Foundation

Foundation Soil

Ground Level

ig. .1 3 4ain components of a structure including soil


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7.1.1 "li#ae Bea$in% Ca&a'iy ()f* 3 5t is the ma/imum pressure that a

foundation soil can withstand without undergoing shear failure.

7.1.+ Ne uli#ae Bea$in% Ca&a'iy ()n* ,5t is the ma/imum e/tra pressure

in addition to initial o0erburden pressure that a foundation soil can withstand

without undergoing shear failure.

!n6 !f7 !o

Here, !orepresents the o0erburden pressure at foundation le0el and is e!ual to

8D for le0el ground without surcharge where 8 is the unit weight of soil and D

is the depth to foundation bottom from 9round #e0el.

7.1.- Safe Bea$in% Ca&a'iy ()s* ,5t is the safe e/tra load the foundation soil is

sub%ected to in addition to initial o0erburden pressure.

on

s qFqq +=

Here. represents the factor of safet.

7.1. All!/able Bea$in% P$essu$e ()a* , 5t is the ma/imum pressure the

foundation soil is sub%ected to considering both shear failure and settlement.

7.1. F!unai!nis that part of the structure which is in direct contact with

soil. oundation transfers the forces and moments from the super structure to

the soil below such that the stresses in soil are within permissible limits and it

pro0ides stabilit against sliding and o0erturning to the super structure. 5t is a

transition between the super structure and foundation soil. The %ob of a

geotechnical engineer is to ensure that both foundation and soil below are safe


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against failure and do not e/perience e/cessi0e settlement. ooting and

foundation are snonmous.

7.+ 2!es !f s3ea$ failu$e

Depending on the stiffness of foundation soil and depth of foundation, the

following are the modes of shear failure e/perienced b the foundation soil.

1. 9eneral shear failure :ef ig. .1a

2. #ocal shear failure :ef ig. .1b

$. )unching shear failure :ef ig. .1c

*hear failure in foundation soil ) " ; cur0e in different foundation soils

ig. . 1 3 ooting on ground that e/periences a 9eneral shear failure, b #ocal shear

failure and c )unching shear failure

.2.1 9eneral *hear ailureThis tpe of failure is seen in dense and stiff soil. The following are some

characteristics of general shear failure.

1. +ontinuous, well defined and distinct failure surface de0elops between the

edge of footing and ground surface.

2. Dense or stiff soil that undergoes low compressibilit e/periences this

failure.$. +ontinuous bulging of shear mass ad%acent to footing is 0isible.


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&. ailure is accompanied b tilting of footing.

(. ailure is sudden and catastrophic with pronounced pea< in ) " ; cur0e.

=. The length of disturbance beond the edge of footing is large.

. *tate of plastic e!uilibrium is reached initiall at the footing edge and

spreads graduall downwards and outwards.

-. 9eneral shear failure is accompanied b low strain >(? in a soil with

considerable @ @$=o and large $C ha0ing high relati0e densit

5D C?.

.2.2 #ocal *hear ailure

This tpe of failure is seen in relati0el loose and soft soil. The following are

some characteristics of general shear failure.

1. A significant compression of soil below the footing and partial de0elopment

of plastic e!uilibrium is obser0ed.

2. ailure is not sudden and there is no tilting of footing.

$. ailure surface does not reach the ground surface and slight bulging of soil

around the footing is obser0ed.

&. ailure surface is not well defined.

(. ailure is characterized b considerable settlement.

=. ell defined pea< is absent in ) " ; cur0e.

. #ocal shear failure is accompanied b large strain 1C to 2C? in a soil

with considerabl low @ @>2-

o

and low > ( ha0ing low relati0edensit 5D 2C?.

.2.$ )unching *hear ailure

This tpe of failure is seen in loose and soft soil and at deeper ele0ations. The

following are some characteristics of general shear failure.

1. This tpe of failure occurs in a soil of 0er high compressibilit.

2. ailure pattern is not obser0ed.


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$. Bulging of soil around the footing is absent.

&. ailure is characterized b 0er large settlement.

(. +ontinuous settlement with no increase in ) is obser0ed in ) " ; cur0e.

ig. .2 presents the conditions for different failure modes in sand soil carring

circular footing based on the contributions from Eesic 1F=$ G 1F$

ig. .2 3 4odes of failure at different :elati0e densities G depths of

foundations

7.+. Disin'i!n be/een Gene$al S3ea$ 4 L!'al !$ Pun'3in% S3ea$

Failu$es

The basic distinctions between general shear failure and punching shear failure

are presented in Table .1.

Table .1 3 Distinction between 9eneral *hear G #ocal *hear ailures

Gene$al S3ea$ Failu$e L!'al5Pun'3in% S3ea$ Failu$e

ccurs in denseIstiff soil

@$=o, $C, 5DC?, +u1CC 2-o, >(, 5D>2C?, +u>(C (? :esults in large strain 2C?

ailure pattern well defined G clear ailure pattern not well definedell defined pea< in )7; cur0e o pea< in )7; cur0e


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Bulging formed in the neighbourhood of

footing at the surface

o Bulging obser0ed in the

neighbourhood of footing

'/tent of horizontal spread of

disturbance at the surface large

'/tent of horizontal spread of

disturbance at the surface 0er smallbser0ed in shallow foundations bser0ed in deep foundations

ailure is sudden G catastrophic ailure is gradual

#ess settlement, but tilting failure

obser0ed

+onsiderable settlement of footing

obser0ed

7.- Te$6a%3is bea$in% Ca&a'iy T3e!$y

Terzaghi 1F&$ was the first to propose a comprehensi0e theor for e0aluating

the safe bearing capacit of shallow foundation with rough base.

.$.1 Assumptions

1. *oil is homogeneous and 5sotropic.

2. The shear strength of soil is represented b 4ohr +oulombs +riteria.

$. The footing is of strip footing tpe with rough base. 5t is essentiall a two

dimensional plane strain problem.

&. 'lastic zone has straight boundaries inclined at an angle e!ual to @ to the

horizontal.

(. ailure zone is not e/tended abo0e, beond the base of the footing. *hear

resistance of soil abo0e the base of footing is neglected.

=. 4ethod of superposition is 0alid.

. )assi0e pressure force has three components ))+produced b cohesion, ))!

produced b surcharge and ))Jproduced b weight of shear zone.

-. 'ffect of water table is neglected.

F. ooting carries concentric and 0ertical loads.

1C.ooting and ground are horizontal.

11.#imit e!uilibrium is reached simultaneousl at all points. +omplete shear

failure is mobilized at all points at the same time.


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12.The properties of foundation soil do not change during the shear failure

.$.2 #imitations

1. The theor is applicable to shallow foundations

2. As the soil compresses, @ increases which is not considered. Hence full

plastic zone ma not de0elop at the assumed @.

$. All points need not e/perience limit e!uilibrium condition at different loads.

&. 4ethod of superstition is not acceptable in plastic conditions as the ground is

near failure zone.

ig. .$ 3 Terzaghis concept of ooting with fi0e distinct failure zones infoundation soil

.$.$ +oncept

A strip footing of width B graduall compresses the foundation soil underneath

due to the 0ertical load from superstructure. #et !fbe the final load at which the

foundation soil e/periences failure due to the mobilization of plastic

e!uilibrium. The foundation soil fails along the composite failure surface and


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the region is di0ided in to fi0e zones, Kone 1 which is elastic, two numbers of

Kone 2 which are the zones of radial shear and two zones of Kone $ which are

the zones of linear shear. +onsidering horizontal force e!uilibrium and

incorporating empirical relation, the e!uation for ultimate bearing capacit is

obtained as follows.

Lltimate bearing capacit, BNDNcNq qcf (.C++=

5f the ground is sub%ected to additional surcharge load !, then

BNNqDcNq qcf (.C, +++=

et ultimate bearing capacit, DBNDNcNq qcn ++= (.C

BNNDcNq qcn (.C1, ++=

*afe bearing capacit, [ ] DF

BNNDcNq qcs +++=1

(.C1,

Here, 6 actor of safet usuall $

c 6 cohesion

J 6 unit weight of soil

D 6 Depth of foundation

! 6 *urcharge at the ground le0el

B 6 idth of foundation

c, !, J6 Bearing +apacit factors

Table .2 3 Bearing capacit factors for different

Nc Nq Ng N'c N'q N'g

0 5.7 1.0 0.0 5.7 1.0 0.0

5 7.3 1.6 0.5 6.7 1.4 0.2

10 9.6 2.7 1.2 8.0 1.9 0.5

15 12.9 4.4 2.5 9.7 2.7 0.9

20 17.7 7.4 5.0 11.8 3.9 1.7

25 25.1 12.7 9.7 14.8 5.6 3.2

30 37.2 22.5 19.7 19.0 8.3 5.7


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34 52.6 36.5 35.0 23.7 11.7 9.0

35 57.8 41.4 42.4 25.2 12.6 10.1

40 95.7 81.3 100.4 34.9 20.5 18.8

45 172.3 173.3 297.5 51.2 35.1 37.7

48 258.3 287.9 780.1 66.8 50.5 60.4

50 347.6 415.1 1153.2 81.3 65.6 87.1

ig. .& 3 Terzaghis Bearing +apacit actors for different

7. Effe' !f s3a&e !f F!unai!n

The shape of footing influences the bearing capacit. Terzaghi and other

contributors ha0e suggested the correction to the bearing capacit e!uation for

shapes other than strip footing based on their e/perimental findings. The

following are the corrections for circular, s!uare and rectangular footings.


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.&.1 +ircular footing

BNDNcNq qcf $.C$.1 ++=

.&.2 *!uare footing

BNDNcNq qcf &.C$.1 ++=

.&.$ :ectangular footing

BNL

BDNcN

L

Bq qcf (.C2.C1,$.C1, +++=

.&.& *ummar of *hape factors

Table .2 gi0es the summar of shape factors suggested for strip, s!uare,

circular and rectangular footings. B and # represent the width and length

respecti0el of rectangular footing such that B > #.

Table .$ 3 *hape factors for different shapes of footing

S3a&e s' s) s8*trip 1 1 1

*!uare 1.$ 1 C.-

:ound 1.$ 1 C.=

:ectangle $.C1,L

B+ 1 2.C1,

L

B

7. L!'al s3ea$ failu$e

The e!uation for bearing capacit e/plained abo0e is applicable for soil

e/periencing general shear failure. 5f a soil is relati0el loose and soft, it fails in

local shear failure. *uch a failure is accounted in bearing capacit e!uation b

reducing the magnitudes of strength parameters c and as follows.

tan$

2tan 1 =

cc$

21=

Table .$ summarizes the bearing capacit factors to be used under different

situations. 5f is less than $=o and more than 2-o, it is not sure whether the


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failure is of general or local shear tpe. 5n such situations, linear interpolation

can be made and the region is called mi/ed zone.

Table .& 3 Bearing capacit factors in zones of local, mi/ed and general shear

conditions.

L!'al S3ea$ Failu$e 2i9e :!ne Gene$al S3ea$ Failu$e

@ > 2-o 2-o> > $= o @ $=o

c1, !

1, J1 c

m, !m, J

m c, !, J

7.; Effe' !f


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DD

ZW2B

InfluenceofR

W2

B

ig. .( 3 'ffect of water table on bearing capacit

Lltimate bearing capacit with the effect of water table is gi0en b,

21 (.C wwqcf BNDNcNq ++=

Here,

+=D

! w

w

1

1 12

1

where K1is the depth of water table from ground le0el.

1. C.(>:w1>1

2. hen water table is at the ground le0el Kw16 C, :w16 C.(

$. hen water table is at the base of foundation Kw16 D, :w16 1

&. At an other intermediate le0el, :w1lies between C.( and 1

Here,

+=B

!

w

w

2

2 12

1

where K2is the depth of water table from foundation le0el.

1. C.(>:w2>1

2. hen water table is at the base of foundation Kw26 C, :w26 C.(

$. hen water table is at a depth B and beond from the base of foundation

Kw26 B, :w26 1

&. At an other intermediate le0el, :w2lies between C.( and 1


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7.7 Effe' !f e''en$i' f!unai!n base

Resultant

of

superstructure

pressure

D D

B

Concentric

D D

e

Eccentric

ig. .= 3 'ffect of eccentric footing on bearing capacit

The bearing capacit e!uation is de0eloped with the idealization that the load on

the foundation is concentric. Howe0er, the forces on the foundation ma be

eccentric or foundation ma be sub%ected to additional moment. 5n such

situations, the width of foundation B shall be considered as follows.

eBB 21

=

5f the loads are eccentric in both the directions, then

BeBB 21 = G LeLL 2

1=

urther, area of foundation to be considered for safe load carried b foundation

is not the actual area, but the effecti0e area as follows.

111 "LB# =

5n the calculation of bearing capacit, width to be considered is B1where B1>

#1. Hence the effect of pro0ision of eccentric footing is to reduce the bearing

capacit and load carring capacit of footing.

7.= Fa'!$ !f Safey


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5t is the factor of ignorance about the soil under consideration. 5t depends on

man factors such as,

1. Tpe of soil

2. 4ethod of e/ploration

$. #e0el of Lncertaint in *oil *trength

&. 5mportance of structure and conse!uences of failure

(. #i


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7.> Densiy !f s!il , 5n geotechnical engineering, one deals with se0eral

densities such as dr densit, bul< densit, saturated densit and submerged

densit. There will alwas be a doubt in the students mind as to which densit

to use in a particular case. 5n case of Bearing capacit problems, the following

methodolog ma be adopted.

1. Alwas use dr densit as it does not change with season and it is

alwas smaller than bul< or saturated densit.

2. 5f onl one densit is specified in the problem, assume it as dr

densit and use.

$. 5f the water table correction is to be applied, use saturated densit in

stead of dr densit. n portions abo0e the water table, use dr

densit.

&. 5f water table is some where in between, use e!ui0alent densit as

follows. 5n the case shown in ig. a, Je!should be used for the second

term and Jsatfor the third term. 5n the case shown in ig. b, Jd should

be used for second term and Je!for the third term..


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21

2211

DD

DDeq

+

+=

D1

D2

B

D

B

a ater table abo0e base bater table below base

ig. . 3 '0aluation of e!ui0alent densit

7.10 , Fa'!$s influen'in% Bea$in% Ca&a'iy

Bearing capacit of soil depends on man factors. The following are some

important ones.

1. Tpe of soil

2. Lnit weight of soil

$. *urcharge load

&. Depth of foundation

(. 4ode of failure

=. *ize of footing

. *hape of footing

-. Depth of water table

F. 'ccentricit in footing load

1C.5nclination of footing load

11.5nclination of ground12.5nclination of base of foundation

7.11 B$in'3 ?ansens Bea$in% Ca&a'iy e)uai!n

As mentioned in pre0ious section, bearing capacit depends on man factors

and Terzaghis bearing capacit e!uation doers not ta


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comprehensi0e e!uation for the determination bearing capacit called

9eneralised Bearing +apacit e!uation considering the almost all the factors

mentioned abo0e. The e!uation for ultimate bearing capacit is as follows from

the comprehensi0e theor.

idsBNidsqNidscNq qqqqccccf (.C++=

Here, the bearing capacit factors are gi0en b the following e/pressions which

depend on .

tan1,(.1

2

&(,tan,

cot1,

2tan

=

+=

==

q

q

qc

NN

eN

NN

'!uations are a0ailable for shape factors sc, s!, sJ, depth factors dc, d!, dJ and

load inclination factors ic, i!, iJ. The effects of these factors is to reduce the

bearing capacit.

7.11 Dee$#inai!n !f Bea$in% Ca&a'iy f$!# fiel ess

ield Tests are performed in the field. Mou ha0e understood the ad0antages of

field tests o0er laborator tests for obtaining the desired propert of soil. The

biggest ad0antages are that there is no need to e/tract soil sample and the

conditions during testing are identical to the actual situation.

4a%or ad0antages of field tests are

*ampling not re!uired

*oil disturbance minimum

4a%or disad0antages of field tests are

#abourious

Time consuming

Hea0 e!uipment to be carried to field

*hort duration beha0ior


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.11.1 )late #oad Test

FoundationSoil

Sand Bags

Platform for

loading

Foundation Leel

!esting Plate

Dial "auge

ig. .- 3 tpical set up for )late #oad test assembl

1. 5t is a field test for the determination of bearing capacit and settlement

characteristics of ground in field at the foundation le0el.

2. The test in0ol0es preparing a test pit up to the desired foundation le0el.$. A rigid steel plate, round or s!uare in shape, $CC mm to (C mm in size,

2( mm thic< acts as model footing.

&. Dial gauges, at least 2, of re!uired accurac C.CC2 mm are placed on

plate on plate at corners to measure the 0ertical deflection.

(. #oading is pro0ided either as gra0it loading or as reaction loading. or

smaller loads gra0it loading is acceptable where sand bags appl theload.

=. 5n reaction loading, a reaction truss or beam is anchored to the ground. A

hdraulic %ac< applies the reaction load.

. At e0er applied load, the plate settles graduall. The dial gauge readings

are recorded after the settlement reduces to least count of gauge C.CC2

mm G a0erage settlement of 2 or more gauges is recorded.


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-. #oad Es settlement graph is plotted as shown. #oad ) is plotted on the

horizontal scale and settlement ; is plotted on the 0ertical scale.

F. :ed cur0e indicates the general shear failure G the blue one indicates the

local or punching shear failure.

1C.The ma/imum load at which the shear failure occurs gi0es the ultimate

bearing capacit of soil.

:eference can be made to 5* 1--- 7 1F-2.

The ad0antages of )late #oad Test are

1. 5t pro0ides the allowable bearing pressure at the location considering both

shear failure and settlement.

2. Being a field test, there is no re!uirement of e/tracting soil samples.

$. The loading techni!ues and other arrangements for field testing are

identical to the actual conditions in the field.

&. 5t is a fast method of estimating AB) and ) " ; beha0iour of ground.

The disad0antages of )late #oad Test are

1. The test results reflect the beha0iour of soil below the plate for a

distance of N2Bp, not that of actual footing which is generall 0er large.

2. 5t is essentiall a short duration test. Hence, it does not reflect the long

term consolidation settlement of clae soil.

$. *ize effect is pronounced in granular soil. +orrection for size effect is

essential in such soils.&. 5t is a cumbersome procedure to carr e!uipment, appl huge load and

carr out testing for se0eral das in the tough field en0ironment.

.11.2 *tandard )enetration Test


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Bore #ole

Split Spoon Sampler

!ripod

$% &g #ammer

'%(mm

ig. .- 3 tpical set up for *tandard )enetration test assembl

1. :eference can be made to 5* 21$1 " 1F-1 for details on *tandard

)enetration Test.

2. 5t is a field test to estimate the penetration resistance of soil.

$. 5t consists of a split spoon sampler (C.- mm D, $( mm 5D, min =CC

mm long and =$.(


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1. :elati0el !uic< G simple to perform

2. '!uipment G e/pertise for test is widel a0ailable

$. )ro0ides representati0e soil sample

&. )ro0ides useful inde/ for relati0e strength G compressibilit of soil

(. Able to penetrate dense G stiff laers

=. :esults reflect soil densit, fabric, stress strain beha0ior

. umerous case histories a0ailable

Disad0antages of *tandard )enetration Test are

1. :e!uires the preparation of bore hole.

2. Dnamic effort is related to mostl static performance

$. *)T is abused, standards regarding energ are not uniform

&. 5f hard stone is encountered, difficult to obtain reliable result.

(. Test procedure is tedious and re!uires hea0 e!uipment.

=. ot possible to obtain properties continuousl with depth.

.11.$ +one )enetration Test


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ig. .F 3 tpical set up for *tatic +one )enetration test assembl

1. :eference can be made to 5* &F=- )$ " 1F- for details on *tandard

)enetration Test.

2. +one )enetration Test can either be *tatic +one )enetration Test or

Dnamic +one )enetration Test.

$. +ontinuous record of penetration resistance with depth is achie0ed.

&. +onsists of a cone $= mm dia 1CCC mm2 and =Co0erte/ angle.

(. +one is carried at the lower end of steel rod that passes through steel tube

of $= mm dia.=. 'ither the cone, or the tube or both can be forced in to the soil b %ac


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2. 5f a small roc< piece is encountered, resistance shown is erratic G

incorrect.

$. 5n0ol0es handling hea0 e!uipment.

7.1+ P$esu#&i@e Safe Bea$in% Ca&a'iy

5t is the bearing capacit that can be presumed in the absence of data based on

0isual identification at the site. ational Building +ode of 5ndia 1F-$ lists the

0alues of presumpti0e *B+ in


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( Eer soft cla which can be penetrated se0eral centimeters with

the thumb

(C

= Blac< cotton soil or other shrin


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2. hat will be the net ultimate bearing capacit of sand ha0ing 6 $=oand Jd

6 1F


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D 6 1.( m

J 6 1F


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a. ater table is & m below 9round #e0el

:16 :26 1

J 6 1=.-


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c6 $.2

!6 22.(

J6 1F.

) 6 -CC


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capacit factor from the following table, calculate the safe bearing capacit

using Terzaghis theor. Lse factor of safet of $. Sul 2CC-

c ! J

1(o

12.F &.& 2.(2Co 1. .C (.C

2(o 2(.1 12. F.

As 6 2-o, the ground e/periences local shear failure

+ 6 2I$O1C 6 =.=


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c6 =1.$(

!6 &-.F$

J6 &.C$

6 $

:16 1

:26 C.(

[ ] DF

BNNDcNB

P

#

Pq

$$qcs

+++===

1&.C1,$.1 212

C(=.$1&.= 2$

=+ BB

B 6 C.2 m

7.1- E9e$'ise &$!ble#s

1. +alculate the ultimate bearing capacit of 2 m wide s!uare footing resting on

the ground surface of sand deposit with the following properties unit weight

1-.=


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The footings are placed at a depth of 1.( m from ground surface. Assume factor

of safet of 1.( and use Terzaghis bearing capacit e!uations

c ! J

$( (.- &1.& &2.&&C F(. -1.$ 1CC.&

&. Design a s!uare footing to carr a load of 1(CC


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ote 3 As > 2- o, the mode of failure is local shear failure. Hence correction

for bearing capacit factors and c are necessar

F. A circular footing is proposed on a cohesi0e ground with c 6 -


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7.1 Aii!nal uesi!ns

1 #ist the ad0antages and disad0antages of plate load test

2 Distinguish between *tandard )enetration Test and *tatic cone

penetration test

$ Distinguish between *tatic cone penetration test and dnamic cone

penetration test

& Distinguish between *tandard )enetration Test and dnamic cone

penetration test

( Distinguish general shear failure from local shear failure

= #ist the assumptions of Terzaghis bearing capacit theor

4ention the limitations of Terzaghis bearing capacit theor

- '/plain the effect of shape of footing on bearing capacit

F How does ground water table influence bearing capacitR '/plain

1C 'ccentricall placed footings perform better than concentricall placed

footings. 5s the statement true or false R Sustif our answer.

11 '/plain the effect of eccentricit of footing on its load carring capacit.

Describe the influence of one wa and two wa eccentricities.

12 hat is the influence of size of footing on cohesi0e soils R

1$ How do ou consider local shear effect in bearing capacit e!uation R

1& hat are the ad0antages of Brinch Hansens Theor o0er Terzaghistheor of bearing capacit R

1( Distinguish *afe Bearing +apacit from Allowable Bearing )ressure

1= Distinguish *afe Bearing +apacit from Lltimate Bearing +apacit

1 Briefl e/plain Terzaghis bearing capacit theor

1- Briefl e/plain Brinch Hansens bearing capacit theor

1F A granular soil possesses 6 $Co. '/plain the procedure adopted to

e0aluate *afe Bearing +apacit.


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2C How do ou determine *afe Bearing +apacit at a site R '/plain.

21 '/plain which unit weight of soil should be used in bearing capacit

determination. Sustif our answer.

22 A footing is designed to carr a specific load of superstructure. 5t is

decided to redesign the same to carr double the load. hat actions

would ou ta


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7.1 Refe$en'es

%. Bowles, J. E. &%'(() *Fo+ndaion #nalysis and Design-, Mc raw /ill

P+0licaions, New 1or2.

3. Craig, . F. &%'45) *Soil Mec6anics-, 5rdEdiion, Englis6 Lang+age

Boo2 Sociey 7 8an nosrand ein6old Co. Ld., London.

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