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DESIGN OF RETAINING WALLDESIGN OF RETAINING WALLAND FOUNDATIONSAND FOUNDATIONSDesign of simple column square footing

Design of simple column rectangular footingDesign of com ine! footing

Design of pile foun!ationDesign of retaining "all

JAYARAM D K

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FOUNDATIONFOUNDATION T#e foun!ation of a structure is t#epart of t#e structure "#ic# transferst#e loa! to t#e soil on "#ic# it rests$

T#e groun! surface in contact "it#t#e lo"er surface of t#e foun!ationis calle! t#e ase of t#e foun!ation

T#e groun! on "#ic# t#e foun!ationrest is calle! t#e su gra!e orfoun!ation soil$

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GL

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T*pes of Foun!ations T*pes of Foun!ations

Shallow FoundationsIf t#e !ept# of t#e foun!ation is

equal to or less t#an its "i!t# t#efoun!ation is classi+e! as s#allo"foun!ation

,i- Wall Footing

,ii-&olumn or Isolate! Footing,iii-&om ine! Footing,i)-.at Footing

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Deep foundationIf t#e !ept# of t#e foun!ation is greater t#an

its "i!t# it is calle! as !eep foun!ation$,i-Well foun!ation,ii-'ile foun!ation

Bearing Capacity of soil:A ilit* of t#e soil to resists t#e loa! "it# out

failure$

Causes of failure of foundations:,i- Unequal settlement of su soil,ii-S#in/age of soil elo" t#e foun!ation !ue

to "it#!ra"al of moisture

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Safe %earing capacit* of t#e !i0erentSafe %earing capacit* of t#e !i0erentsoilssoils

Types of Soil Safe BearingCapacity of soil( KN/m !

1$2ar! Dr* &la*

3$San! an! cla*mi4e!5$Firm cla*6$Fine con+ne! "et

san!7$Fine !r* san!8$&oarse san!9$Soft roc/:$2ar! roc/ ,mi4ture

57<

3

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Formula for +n!ing t#e !ept#Formula for +n!ing t#e !ept#of t#e foun!ation(of t#e foun!ation(

2

D- depth of the foundation in mp- Safe bearing capacity of the soilr-Specific weight of the soil

-Angle of repose

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esign 1:esign 1: Find the area and the depth ofFind the area and the depth offoundation required for a column carrying anfoundation required for a column carrying anaxial load of 1250 KN. he safe !earingaxial load of 1250 KN. he safe !earingcapacity of the soil is 120 KN"m2 . hecapacity of the soil is 120 KN"m2 . hedensity of the soil is 1# KN"m$ and has andensity of the soil is 1# KN"m$ and has anangle of repose of $0 degree.angle of repose of $0 degree.

Solution:"oad on the column # $ %& KN'ppro imate weight of foundation #

$ % KN( ta)e $& * of total weight!Total load # load on the column +

appro imate weight of the column,

# $ %& + $ % # $-.% KN

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'rea of the foundation # total load / safe'rea of the foundation # total load / safeearingearing

capacity of soilcapacity of soil= 1597>13<= 11$68 m3

'ro)i!e a foun!ation area of 13 m3Determination of depth of the

foundation:

.inimum !ept# of

3t#e foun!ation = ,p>?-@,1 sinB->,1Csin B-= ,131:- @,1 sin5,1Csin5

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!RAM"D S#R$%#$R" S&'()*+ !''#)*+

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(A,, !''#)*+

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)S',A#"D !''#)*+ 'R %',$M* !''#)*+

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%'M )*"D !''#)*+

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S#RA. !''#)*+

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%'*#)*$'$S !''#)*+

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RA!# !''#)*+

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(",, !''#)*+

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.)," !''#)*+

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Design of column footing:Design 2 : A square column 500mm X 500mmcarries an axial load of 1500 KN . Design thesquare footing for the column. The safe

bearing ca acit! of the column is ""5 KN#m".$se %"0 and &e '15 steel.

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Design of the foundation:Load on the column = 1500 KNApproximate eight of the footing at 10 ! of

the column load = 150 KN"otal load = 1#50 KN$afe %earing capacit& of the soil = 225 KN'm2Area of foundation = 1#50'225 = ()*** m2

+, + = ()*** m

% dth f f d ti

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%readth of foundation % & '().$$$* & 2.)1 say 2.)5 m

+o the area of the foundation is 2.)5 , 2.)5 m

Net up-ard pressure & load on the column " area ofthe footing

& 1500000"(2.)5 , 2.)5*

& 1 #$/).11 N"m2.

Depth of the foundation &inimum depth of the foundation

& (p"r* (1 sin3*"(14sin 3* 2

& (225"1#* (1 sin$0*"(14sin$0* 2

& 1./ m

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Determination of the depth of the

concrete sla% %elo the footing)-ritical section for %ending moment is =.2(50/500 '2 = 1125 mm = 1)125 m

aximum %ending moment = = 1 3*4()11 x 2)(5 , 1)125 x. 1)125'2

= *451(0 Nm

actored moment u = 1)5 ,

= 1)5 , *451(0 = 51((55 Nm)

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"o find the depth of the sla% in thefoundation)

u= 0)1*3 fc6 %d2

51((55000 = 0)1*3 , 20 , 500 . idth ofcolumn , d 2

d= #1* mm

D= #1* 7 12'2 7#0 = # 1 mm

.12/ dia of %ar 8 #0 0 clear co9er forfooting

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"he depth of sla% of the foundation isincreased %& *0 !D= # 1 , . 0)* , # 1 = 00 mm

d= 00 0 .12'2 / #0 =322 mm)

Determination of quantit& of steel

required:Ast = t , % x d

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Determination of area of mainreinforcement(

/ Ast= 'ercentage of steel !/ 'ercentage of steel =

2

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actored moment u = 1)5 ,

= 1)5 , *451(0 = 51((55 Nmc6 = 20 N'mm2And

e =415 N'mm2

b=500 mmAnd

d=822mmSubstitute all the values in the above formulawe getPt= 0.4 !

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Ast ( )t X b x d( *0.'+#100, x 500 x -"" ( 1 /" mm "

*o of bar 0#otal area1 area of one bar 0 3421 546 71789 2Assume 1" mm dia bars so ro ide 1- barsof 1" mm diameter.

2ere the column is square so ro ide thesame reinforcement on both the directions.

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R")*!'R%"M"*# D"#A),S '! %',$M* A*D !''#)*+:

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2) A rectangular column footing #00 mm, 400 mm carries an axial load of 300KN ) Design a rectangular footing tosupport the column ) "he safe %earingcapacit& of the soil is 200 KN'm2 ) ;se

20 concrete and e415 steel)Load on the column = 300000N

"#S$G% &' (#)*A%G+LA( '&&*$%G

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A roximate 3eight of the foundation ta4e 10 ofthe 3eight of the column ( -0000N

Total load ( --0000N

6afe bearing ca acit! of the soil is gi en as "00 KN#m"

( "00000N#m"

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Area of the foundation = "otal load '$afe %earing capacit& of the soil)= 330000'200000 = 4)40 m2"o find the length and %readth of thefoundation1 in case of square footing its easybecause by taking square root we get allthe values 1

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Area ( '.'78 ( '.'7( '.' #8

9quating the ro ections on both sidesbe!ond the footing

* 7;0.', ( *8;0.'.'#8?;0.', ( *8;0.

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6ol ing the abo e equation 3e get 8 ( "."

m

6ub this is 7 alue 3e get

7( '.'#8 ( '.'# "." ( " m

No3 find the ro ections on both the axis

( 0.- m

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Net u 3ard ressure ( column load # Area of thefooting

( -00000#'.'(1-1-"0 N#m"

Determination of reinforcement in section xx axis

and @@ axis.

7ending moment %!! ( 1-1-"0 X "."X 0.- X

*0.-#",. ( 1"-000 Nm

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&actored %oment %u! ( 1"-000 X 1.5( 1 "000 Nm

Determine the de th%u! ( 0.1/- &c4 bd "

1 "000 ( 0.1/- x "0 x

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&actored %oment %ux ( 11

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ro9iding 10 mm dia %ars at a clearco9er of (0 mm

D = * 3 7 .10'2 7 (0 = 4(* mm"he o9erall depth ma& increased %& *0!= 4(* 7 .0)* ,4(*

= #14) mm

D=#20 mm)

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*a,e -u and find Longer dire/tionsteel &actored %oment %u! ( 1"-000 X 1.5

( 1 "000 Nm

Determination of quantit! of steel required:

Ast ( )t X b x d6ub b(

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Problems Solutions/ A s;uare footing is to be constructed ona deep deposit of sand at a depth of 63m to carry a design load of 4 elduring rainy season6 Design the plandimension of footing gi>en ? sat 0 2 6@

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[ ] D F

R BN R N DcN B P

A P

q W W qc s γ γ γ γ ++−+===1

'.0,1*/.1 "1"

/" "'.5/"+".1'"/00 B B +=∴

0 62 m

/(hat will be the net ultimate bearing

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/(hat will be the net ultimate bearingcapacity of sand ha>ing 0 4Bϕ o and?

d 0 3 el6 Assume ! 0 26=6 $se#er aghiEs e;uations6 5Aug 2 48

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ϕ N c N q NB

/5 o 5+.- '1.' '".'

'0 o 5.+ -1./ 100.'

y linear interpolation * c 0 B=64@ *; 0 7364@ *? 0 =7 ato

BNNDN 501*Strip !ooting

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γ γ γ BN N DcN q qcn 5.0,1* +−+=

γ γ γ BN N DcN q qcn '.0,1*/.1 +−+=

; n 0 2 7@644

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/ A s;uare footing 26= m C 26= m is built on ahomogeneous bed of sand of density 3 ing an angle of shearing resistance of 4B o6 #he

depth of foundation is 6= m below the groundsurface6 %alculate the safe load that can be appliedon the footing with a factor of safety of 46 #a

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[ ] D F

R BN R N DcN B A

q W W qc s γ γ γ γ +++ .0,1/.1 "1"

Safe load . 0 ;sG G 0 42@=67

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p g yel46(ater table is 26= m below +round ,e>el76(ater table is at +round ,e>el6

$sing #er aghiEs e;uation ta

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[ ] D F

R BN R N DcN q W W qc s γ γ γ γ ++−+==1

5.0,1*'00 "1

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*o of bar 0#otal area1 area of one bar 0 7B671 546 71789 2

Assume 2 mm dia bar6.ro>ide 2 mm dia bars of numbers6

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Determination of area of mainreinforcement(

/ Ast= 'ercentage of steel !/ 'ercentage of steel =

2

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*o of bar 0#otal area1 area of one bar

0 3@ 1 546 71789 2 Assume 2 mm dia bar 6

.ro>ide 2 mm dia bars of 3 numbers6

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)ombined footing

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henever two or more /olumns in a straight lineare /arried on a single s3read footing it is /alleda /ombined footing. $solated footings for ea/h/olumn are generall the e/onomi/al.

)ombined footings are 3rovided onl when it isabsolutel ne/essar as

. hen two /olumns are /lose together /ausingoverla3 of ad6a/ent isolated footings2. here soil bearing /a3a/it is low /ausingoverla3 of ad6a/ent isolated footings

7.Pro1imit of building line or e1isting building orsewer ad6a/ent to a building /olumn

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=4

26 Slab and beam type

46 Strap type

#ypes of combined footing

6 Slab type

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B=

Design Steps/ "ocate the point of application of the

columnloads on the footing,

/ 2roportion the footing such that theresultant of loads passes through thecenter of footing,

/ Compute the area of footing suchthat the allowa le soil pressure is note ceeded,

/ Calculate the shear forces andending moments at the salientpoints and hence draw SFD and B3D,

/ Fi the depth of footing from thema imum ending moment,

/ Calculate the trans4erse endin

Design of com ined footing 0

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BB

g gSla and Beam type

$, Two interior columns ' and Bcarry .&& )N and $&&& )N loadsrespecti4ely, Column ' is -%&mm -%& mm and column B is

5&& mm 6 5&& mm in section,The centre to centre spacingetween columns is 5,7 m, The

soil on which the footing rests iscapa le of pro4iding resistanceof $-& )N/m , Design acom ined footing y pro4iding a

central eam 8oining the two

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BF

Solution( Dataf c/ = 37 Nlmm 3Hf *= 37< N>mm 3Hf = l5< /N>m 3 ,S%&-H&olumn A = 57< mm 4 57< mmH

&olumn % = 6

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B@

Pro3ortioning of base si e

(or

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F

%

F

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. efinitionsearing capacity is the power of foundation

soil to hold the forces from the superstructurewithout undergoing shear failure or e9cessi>esettlement6 !oundation soil is that portion ofground which is sub ected to additionalstresses when foundation and superstructureare constructed on the ground6 #he followingare a few important terminologies related to

bearing capacity of soil6

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+ltimate :earing )a3a/it 9D f < : )t is the

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ma9imum pressure that a foundation soilcan withstand without undergoing shearfailure6%et ultimate :earing )a3a/it 9D n< E )t is

the ma9imum e9tra pressure 5in addition toinitial o>erburden pressure8 that afoundation soil can withstand without

undergoing shear failure6

;Eo represents the o>erburden pressure at

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foundation le>el and is e;ual to D for le>elground without surcharge where is the unitweight of soil and D is the depth to foundationbottom from +round ,e>el6

Safe :earing )a3a/it 9D s < E )t is the safee9tra load the foundation soil is sub ected to inaddition to initial o>erburden pressure6

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2.2 -odes of shear failured h ff f f d l d

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Depending on the stiffness of foundation soil anddepth of foundation the following are the modes of

shear failure e9perienced by the foundation soil6/+eneral shear failure/,ocal shear failure/.unching shear failure

General Shear 'ailure

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*his t 3e of failure is seen in dense and stiffsoil. *he following are some /hara/teristi/sof general shear failure./)ontinuous well defined and distin/tfailure surfa/e develo3s between the edge

of footing and ground surfa/e./"ense or stiff soil that undergoes low/om3ressibilit e13erien/es this failure./)ontinuous bulging of shear massad6a/ent to footing is visible./ 'ailure is a//om3anied b tilting of footing.

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.unching Shear !ailure

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#his type of failure is seen in loose andsoft soil and at deeper ele>ations6 #hefollowing are some characteristics ofgeneral shear failure6/#his type of failure occurs in a soil of >eryhigh compressibility6

/!ailure pattern is not obser>ed6

/ ulging of soil around the footing isabsent6!ailure is characteri ed by >ery large

settlement eneral $hear ailure Local' unching $hear

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ailure

Cccurs in dense#stiff soil Cccurs in loose#soft soilesults in small strain *E5 , esults in large strain

*F"0 ,

&ailure attern 3ell defined

G clear

&ailure attern not 3ell

defined

7ulging formed in theneighbourhood of footing at

the surface

No 7ulging obser ed in theneighbourhood of footing

9xtent of horiHontal s read of 9xtent of horiHontal s read

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disturbance at the surface

large

of disturbance at the

surface er! small

Cbser ed in shallo3

foundations

Cbser ed in dee

foundations

&ailure is sudden G

catastro hic

&ailure is gradual

2.7 *er aghi@s bearing )a3a/it *heor#er aghi 5 3748 was the first to propose a comprehensi>e

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#er aghi 5 3748 was the first to propose a comprehensi>etheory for e>aluating the safe bearing capacity of shallowfoundation with rough base6

Assum3tions/Soil is homogeneous and $sotro3i/./*he shear strength of soil is re3resentedb -ohr )oulombs )riteria./*he footing is of stri3 footing t 3e withrough base. $t is essentiall a twodimensional 3lane strain 3roblem./#lasti/ one has straight boundariesin/lined at an angle eDual to F to thehori ontal.

,imitations

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/#he theory is applicable to shallowfoundations/ As the soil compresses L increaseswhich is not considered6 &ence fully

plastic one may not de>elop at theassumed L6/ All points need not e9perience limit

e;uilibrium condition at different loads6/Method of superstition is notacceptable in plastic conditions as the

ground is near failure one6

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#ffe/t of sha3e of 'oundation

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#he shape of footing influences thebearing capacity6 #er aghi and othercontributors ha>e suggested the correctionto the bearing capacity e;uation forshapes other than strip footing based ontheir e9perimental findings6 #he followingare the corrections for circular s;uare and

rectangular footings6

%ircular footing

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γ γ γ BN DN cN q qc f /.0/.1 ++=

S;uare footing

γ γ γ BN DN cN q

qc f '.0/.1 ++=

Rectangular footing

γ γ γ BN L B

DN cN L B

q qc f 5.0,".01*,/.01* −+++=

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@@

,earning 'utcomes:/ After this class students will be able to do the After this class students will be able to do the

complete design and detailing of different types ofcomplete design and detailing of different types of

retaining walls6retaining walls6

D"S)+* A*D D"#A),)*+'! R"#A)*)*+ (A,,S

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@3

+ra>ity retaining wall

+,

+,2

Retaining walls are usually

built to hold bac< soil mass6&owe>er retaining walls canalso be constructed foraesthetic landscapingpurposes6

R"#A)*)*+ (A,,

A%KS'),

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3

atter

Drainage &ole

#oe

%antile>er Retaining wall

with shear

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3

'#otos of Retaining"alls

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32

&lassi+cation ofRetaining "alls

/ Gra)it* "all .asonr* or 'lain

concrete/ &antile)er retaining "all R&&

,In)erte! T an! L-/ &ounterfort retaining "all R&&

/ %uttress "all R&&

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34

%ounterfort

+ra>ity R(#-Shaped R(

,-Shaped R(

ac

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37

Eart# 'ressure ,'-

/ Eart# pressure is t#e pressuree4erte! * t#e retaining materialon t#e retaining "all$ T#is pressureten!s to !eJect t#e "all out"ar!$

/ Types of earth pressure (

/ Acti)e eart# pressure or eart#pressure ,' a - an!

/ 'assi)e eart# pressure ,' p-$

/ Acti)e eart# pressure ten!s to!eJect t#e "all a"a* from t#e

ac/+ll$

. a

+,

ariation of "arth pressure

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3=

Factors a0ecting eart#pressure/ Eart# pressure !epen!s on t*pe of

ac/+llH t#e #eig#t of "all an! t#esoil con!itions

Soil con!itions( T#e !i0erent soilcon!itions are

/ Dr* le)ele! ac/ +ll/ .oist le)ele! ac/+ll/ Su merge! le)ele! ac/+ll/ Le)ele! ac/+ll "it# uniform

surc#arge

/ %ac/+ll "it# sloping surface

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3B

'nalysis for dry ac)lls

Ma9imum pressure at any height p0< aγ h#otal pressure at any height from top

p a0 12N

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3F

/ W#ereH / a = &oeKcient of acti)e eart# pressure

/ = ,1 sin φ->,1Csin φ-=tan 3φ/ = 1>/ pHcoeKcient of passi)e eart#

pressure/ φ= Angle of internal friction or angle of

repose/ γ =Unit "eig# or !ensit* of ac/+ll

/ If φ= 5< °H /a =1>5 an! / p=5$ T#us / a is ; times / p

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3@

/ p a = / a γ 2 at t#e ottom an!is parallel to incline!

surface of ac/+ll

/ / a =

/ W#ere θ=Angle ofsurc#arge

∴ Total pressure at ottom=' a = / a γ 2 3>3

ac

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33

Sta ilit* requirements of RW

/;t should not o4erturn/ ;t should not slide

/ ;t should not su side H i$e .a4$pressure at t#e toe s#oul! note4cee! t#e safe earing capacit* oft#e soil un!er "or/ing con!ition

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ec/ against o)erturning

Factor of safet* againsto)erturning

= . R > . O ≥ 1$77 ,=1$6>

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ec/ against Sli!ing

/ FOS against sli!ing/ = Resisting force to

sli!ing>/ 2oriMontal force

causing/ sli!ing

/ = µ∑W>'a ≥ 1$77,=1$6>

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2

.a4imum pressure at t#e toe

.ressure below theRetaining (all

#

9

92

(

(2

( 4

( 7

b12b1Be

9b

&14

. a

Σ(

&h

. ma9. min6

R

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4

/ Let t#e resultant R !ue to ∑W an! ' a

/ lie at a !istance 4 from t#e toe$/ = ∑.> ∑WH/ ∑. = sum of all moments a out toe$

/Eccentricit* of t#e loa! = e = , >3 4- < >8

/ .inimum pressure at #eel=ero$

/ For Mero pressureH e= >8H resultant s#oul! cutt#e ase "it#in t#e mi!!le t#ir!$

/ .a4imum pressure at toe=/ < S%& of soil$

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7

Dept# of foun!ation

/ Ran/ine s formula(

/ D f =

/

/ =/

Df

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=

'reliminar* 'roportioning

,T s#ape! "all-/ Stem( Top "i!t# 316

/ Toe pro ection= ,1>5 1>6-%ase "i!t#

&

2

b0 67& to 6B&

tp0 5 14- 178b&1 P&1 7

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B

Design of &antile)er RW

/ StemH toe an! #eel acts as cantile)er sla s

/ Stem !esign( . u=psf ,/ a γ 2 5>8-

/ Determine t#e !ept# ! from . u = . uHlim =P ! 3

/ Design as alance! section or URS an!+n! steel

/ . u=,f c/ -

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F

&urtailment of ars

A st .ro>ided

A st12

A st

Dist6fromtop

h2

">ery

alternatebar cut

A st

A st12 h2

, dt

h /

h

%ross section %urtailment cur>e

"ffecti>e depth 5d8 is.roportional to h

ending moment isproportional to h 4

A st is I l to 5 M1d8 and isI l to h 2

""

"1

"

1

.. hh

A

A

ei st

st ≈

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@

Design of 2eel an! Toe1$ 2eel sla an! toe sla s#oul! also e !esigne!

as cantile)er$ For t#is sta ilit* anal*sis s#oul!

e performe! as e4plaine! an! !etermine t#ema4imum en!ing moments at t#e unction$3$ Determine t#e reinforcement$5$ Also c#ec/ for s#ear at t#e unction$

6$ 'ro)i!e enoug# !e)elopment lengt#$7$ 'ro)i!e t#e !istri ution steel

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3

Design a cantile>er retaining wall 5# type8 to retain earth for aheight of 7m6 #he bac

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Dept# of foun!ation

/ To +4 t#e #eig#t of retaining"all Q2

/ 2= # CD f

/ Dept# of foun!ation

/ / D f =

/ = 1$35m sa* 1$3m H/ T#erefore 2= 7$3m

&

2

b

Df

h h

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'roportioning of

"all/ T#ic/ness of ase sla =, 1>1< to 1>16 -2

/

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2

/ ' #= 4 1>5 4 1: 4 6$973

=89$8: /N/ . = ' # #>5 = 8/ = 1

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4

/ &urtail 7#3-3 = 71

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7

/ De)elopment lengt# ,Stemsteel-/ L! =69 Y ar =69 4 13 = 786

mm

/ Secon!ar* steel for stem atfront

/

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U B V 3

U 2 V @

U 2 V 3

U V 7

Drawing and detailing