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IRC i45-1972

RFCOMMENDATIONS FOR ESTIMATING

THE RESISTANCE OF SOIL BELOW

THE MAXIMUM SCOUR LEVEL

IN THE DESIGN OF WELLFOUNDATIONS

OFBRIDGES

THE INDIAN ROADS CONGRESS

1996

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RECOMMENDATIONS FOR ESTIMATING

THE RESiSTANCE OF SOIL BELOWTHE MAXIMUM SCOUR LEVEL

IN THE DESIGN OF WELL

FOUNDATiONS

OF

BRIDGES

Pub!( s h e d &v

THE INDIAN ROADS CONGRESS

Janinagar House, Shahjaban Road

New DeH,i-H

1996

Pri~cR

(1tus I~ackiig ~

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IIC:rn-an

FirstPub lishedRepdntedReprinted

Reprinted

Reprinted

October, 1972March, 1984July,1987

March, 1992As 1996Octobei~2000

(RIghts of?WblIntk#adV flasbtkn ON NUtS)

Printed at DeeKay Printers,N ewDcliii(500copies)

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RECOMMENDATIONSFOR ESTIMATING THE RESISTANCE

OF SOIL BELOW THE MAXIMUM SCOUR LEVEL INTH E DESIGN OF WELL FOUNDATIONS OF BRiE GEh

1. INtRODUCTION

ii. The draft recommendations fur est imating the resistanceof soil be low the maximum scour level in thedesign ofwell founda-tions ofbridges we~efinalised by a Subcommit tee consist ing of the

following personnel attheir meetingheld on the lst March 1971.

S h r i B . Balwarn R a o c i .wwenor

2. Shr i 5. Seetharaman M em ber-Secr e tary

Memkn

3, SM S . B . iSu 7 . Shr i N~S . Ramaswamy4. Dr. K. K. Katti 5. Dr. K, S. Sankaran

5 , Sttri S. M. Kaul 9. SM Shitala Sharan6. Dr. P. Ray Chowdhury 10. SM S. N. Sinha

I.!. Shri T . N. Subba Lw

This draft w as approved by the Bridges Committee in theirmeetingshe ld on th e 1 7 t h Novembe r , 1 9 7 1 an d 14th April, 1972. It

was later approved by the Executive Committeein their meeting heldon the 26th and 27th April, 1 9 7 2 and by the Council in their 78thmeet ing he ld in Nainital on th e 10th July, 1 9 7 2 .

1 . 2 . T h e recommendat ions given in th is Standard I~avebeenlormuiated on the basis of th e observed behav iou r of mode ls ofwellfoundations and also th e wo:k done by many workers in this he ld .The basic a~surnptionsare ghen in Appendices.

1 . 3 . These studies have indicated that

(i) shar ing o F th e momen t be tween s ides and b a se is conti-nuously changing with th e increase in delhrmation of th esoil and

(ii) the weciranics ofsharingul ih e moment be tween the s idesand th e base is ent i re ly different for th e initial s t a ge s ofloading o t a w e l l a s compared to its eltirnate failun~

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1 . 4 . Elastic theory method iives the soil pressures at the sideand the base underde sign loads, bu t to determ ine th e actual factor ofsafety against failure, it will b e necessary to calculate th e ultimatesoil resistance, 1 h e re fore , th e design of well foundations shal l b e

checked by boththese methods.

2 . S C O P E

2.1. The procedure given is appl icable to th e design of wdlfoundations of br idges rest ing on non-cohesive soil like sand andsurrounded by th e same soil be low maximum scour level. Theprovisions of t h e s e re comme ndations will not apply ifth e depth of

embedment is less than 0.5 t ime s the width of foundation in th edirection oflateralforces .

3. PROCEDURE FO R CALCULATING THE SOIL R E S IS T A N C E

The resistance of the soil surrounding the well foundation shall

be checked:

(i) for calculation ofbase pressures by the elastic theory withthe use ofsubgrade moduli; and

(ii) by computing the ultimate soil resistancewith appropriatefactor ofsafety.

4 . Y w T h T I I O D OF CALCULATION

I . E!astic Theory (vide Annexure I)

Step 1: Determinethe values of W , H and M under combina-

tion ofnormal loads without wind and seismic loads assumingtheminimum grip length below maximum scour level as required underiRC 5l970

where

W total downward load acting at the base of well,including the selfweight ofwell.

* St md a SpLm ifi~0tot~ r n d CLdt otP t k tc~for RLMd 8t d g m s S c c r ~n

(i~nciatFeat utis of Deogn.

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H external horizontal fo:ce acting on the well at scour

level.

M :: total applied external moment about the base of

well , including those due to tilts and shifts.

Step 2: Compute l~and 1 v an d I

whe re

I - I a 4 - ml~( 1 i 2 ,.m~)

Is momen t of inertia of base about th . axis no rmu l todirection o h horizontal forces passing through itsCO.

lv = moment of inertia ofthe projected area in elevation

LD~of th e sotl m a s s offering resistancer

where

L = p ro jected width of the soil mass offering resistancemultiplied by appropriate value ofshape tactor.

Nose: The value of shape factor for circular wells shal l b etaken as 0.9. For square or rectangular wells where the resultanthorizontal force acts parallel to a principal axis, the shape factor

shall be unity andwhere the fotcesare inclined to the princtpab axis,

asuitable shape factor shall be based on experimental results.

= depth ofwell below scour level.

m = Ks/K: Ratio of horizontal to vertical coefficientof subgrade reaction at base, in the absence ofvalues for K

1 1 and K determined by field tests mshall generally be assumed as unity.

p = coefficient of friction between sides and th e soil=tan 8 , where 8 is the angle ofwall friction betweenwell andsoil.

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for rectangular well

d iamete r

for circular wellrD

Step 3 : Ensure the following

MH> .-. ( 1 4- rut)-- ~W

and H czM(l jup) + ~W

where

r D/2. l/mlv

coefficient offriction between the base and the soil.

It shall be taken as tan ~.

=

angle of internal friction ofsoil.

Step 4 : Che ck the elastic state

mM/I > y (Kp

if mM/f is > y (Kp K.~),findout the grip required by putting thelimiting value mM/I = y (Kp K4

where

= density of the soil (submerged density to be taken

when under wateror below water table).

K, & K,~ passive Le d actve pressure coefficientsto h e , c~.lcu-laced using Coultmbs theory, assuming8 ,.the angle

of wall friction between well and soil equal toj ~

but limited to a value of224.

Step 5 : Calcula:e

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where

~H~and ~ : : ; : r . maximumandminimum basep ressure respect ive ly .

A a re a of th e base ofwell,

B widthofthe base ofwell in the direction of forcesand mome nts .

P = Mfr

Step 6: Check r~(0, i .e . , no tension

j> allowable bearing capacity ofsoil,

Step 7: Ifan y of th e conditions in Steps 3 . 4and 6 or all do

not satisfy, redesign thewell accordingly.

Step S : Repeat the sante steps for combination with wind andwith seismic case separately.

U . . ULTZMATE kESlSTAfl~EMtTHOD (Ylde Annenirr2 )

Step 1: Check that W /A > oj2

W total downward load acting at the base of well,

including th e self weight of well, enhanced by asuitableload factorgiven vide Step6 .

A = areaof the b a s e ofwell.

= ultimate bearing capacity of the soil below the base

ofwell.

Step 2: Calculate the base resisting moment Mb at the plane

ofrotation by the following rormula:

M b = QWBtan 4 ~B = width in case of square and rectangular wells

parallel to direction of forces and diameter for

circulacwells,

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Q - a constant as given in Table I below for square orrectartguiaf base. A shape factor of 0.6 i s to bemultiplied for wells with circular base,

= angle of internal friction ofsoil.

T A B L E l

D /H 0 .5 1 .0 1 ,5 2.0 2 .5

Q 0 . 4 1 0.45 0.50 0.56 044

Note: The values of Q for intermediate D/.3 values in theabove range may be linearly interpolated.

M 5= 0.10 vD~(K, KA) L

where

y .= density of soil (submerged density to be taken for

soils under water or below water table)

L ~. projec:edwidth of the soil mass offeringresistance. Incase of circularwells. it sholl be 0,9diameterto account

for the shape~

D = depth of gripbelow maximum scour level,

K,, .K A passive and active pressure ectefficient to be calculatedusing Coulombs theory assuming 8 angle of wall

iriction between well and soil equal to 3 * but limitedto a value of 221,

Step 3 : Calculatethe resistingmoment due to frictionat frontand back faces (Mg) about the plane of rotation by followingformulae:

(i) For rectangular well

M,=0.l8y(K, X~)LtDsin)

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(ii) for circaI n r well

iS1~ oH 7IK KA) B~Vsin 3

step 4 Tie total resistancL moment M~about th e plane of

rotation shall be

M1 :: ~,7(M~+ M s +- M~1

Step 5 : CheckM~4: M

where

M .:: total applied external moment about the plane ofrotation, viz., located at O2D above the base, takingappropriate load factors as per combinations givenbelow

111) ,.. (I)

liD -fB~ l.4(Wc 4 Ep +WorS) ... (2)

lID + l.6L (3)

lID f B F i4(L + Wc~F Er) .. (4)

i.ID+B j 125(L+Wcj Ep+WorS) .,. (5)

where

D :,: dead load

L.: live load includingbraking, etc.

9 ~:~ buoyancy

Wc;~water current fo~c c

Ep = earthpressure

W wind lhrce

S sci~n~icforce

For horizontal force due to frictional resistance of

beanng d tie Todead and live loads, appropi iate factors shall be taken.

But effect ofdefocnaat ion due to temperature, shrinkage and creep

mq be neglected for normal structures,,

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Nose (ii) Moment due to shirt and alt ofwelts and piers anddirect loads, if any, shall also be considered ahout the plane or

rotation.

Step 6 : If the conditions in Steps i and 5 are not satisfied~redesign the well.

ELASTIC THEORY METHOD (Anne.vure t)

I INTRODUCTION

The following assuntpt ions are made in deriving the equations

based on elastic theory:

(i) Thesoil surrounding the well and below the base is perfectlyelastc!, homogensus and followr Hookes Law.

(ii) Underdesign working leads, the lateral. deflections are so

small that the urtit soil ~eact ion p iricre.a~es linearlywith increasinglateral deflection j as expressed by p Zr Kuz where Kn is the

caefhc~enLofho,rizont.:d ~uhgade reaction at the base,

(~hi)The coefficient of hothor,tal subgrade react ion increaseslinearlywith depthin . the case ofcohesioniesssoils.

(iv) The well is assumed .o he a rigid body su~ected to anerj,ter~a~unidirectional horizontal force. H and a moment Moat scour

level,,.

2. SYMBOLS

A area ofbase ofthe well.

a =m width of the base parallel to the direction of theexternalhorizontal force.

D ~ depth ofwell below scour level.

B

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II external horizontal force acting on the well at scour

level.

moment of inertia of the base about an axis passing

through C. .G.. and perpendicular to horizontalresultantforce.

moment of inertia about the horizontal axis passingthrough the CCI. . of the projectedarea in elevation o l

ID

the soil mass offering resistance

K coefficient of vertical suhgrade reaction at the base..

K1 coefficient of horizontal subgrade reaction at the hose.

KA., Kr active and passive pressure coefficients for cohesion~~

less soils as pei Coulomtds theory.

1. projected width ofthe soil mass offering resistance.

Note: .A shape factor of0,9may be applied for circular wells.

in =r , i.e., ratio of the horizontal to the vertical co-

efficient ofsuhgrade reactionsat the base.

hi total applied external moment atth e base= ~Mc. 4.H.D)

M0 =. moment ofthe external forces at scourlevel,

Mp :::r:::: moment of Paboutthe base.

M 5 resisting moment atthe base.

p ;rr horizontal :soil reaction.

p. Zr.: coeff icient offriction between the base and the soil.

p. .=.: coefficient .offriction between sides and the soil.

a density of soil. (submerged density to be ned win

under water)

angleofinternalfriction ofsoil.

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S a angle offriction between the sides of well and soiltaken equal to 3 ~ limited toa value of22r,

o := angular rotationof th e well as a rigid body.: : : horizontal soil reaction at depth y from scour level,

vertical soil reaction at distance X from C.O. of

base.

(T~= maximum and minimum base pressures.

~ P

distance from the axis passing the CO. of base atwhich the resultant vertical frictional force on. .~ide

actsnormal tothe direct ion of horizontal fb m c e : 13/2

in case of rectangular welis or, 0.318 diameter in

circular wells.

3. EQUATIONS FOR BASE PRESSURES

In the most general case,the centre ofrotation can beabove the

baseatC1, at the base C,or below the base atC a . It can be easily

visualised that the base movestowards thecentre F rotanon, if the

latter lies abovethe base sothat the horizontal frictional force at theha.se acts in the direction of H. lf the point of rotation lies belowthe base by a similar argument.:! it is seen that horizontal frictional

fo rc e . at base must be in the opposite sense to H. The maximum.frictional force which can developat the base is ~zW, At any parti-

cialar instant only a fraction ofit would be acting. 1 . .et it he denotedby flpW Where $ 3 is a factor always less than one.. ii is, therefore,clear that before movemem tak s place /3 must he between I and iresp.c.tively so that we can write that for point ofrotation at thebase $ 3 must b e . . . between. the lithits I to 1 In the p~.rticularcase

of heavy wells met within actual practice, the point ofrotation shalll:ie . a t o iu . rn : i : : i to ~ at the base. Let the ~rell rotate about a . point Cat a hor~i.ontaldistance X c from the centre of the well shown in

Fig.. I

P total horizontal soit reaction from the sides.

resisting moment .at the base.

l

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KeL D

LDPutting =

~,._2mKoh

(I)

Let M, be the moment ofP about base level

M, (D -~y) dy L

= m~eL (D y) dy

mKeLf y 2Dy~dy

4!, La mKoL (2)

Now consider the soil reaction acting at the base. Vertical

JeA*xtion at distanot ( IX 4 Xc)frwn centrc ofrotation (Xc ..~. I X ) o

K(Xc ~l

4.H12

M~_fvTydA.X...:Ko~(Xc~X)XdA

+1/2 +1/2

KOJXIJAiKOXc5XSJA

.1/2 -H/I

d A being a function o t I X

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As th e reference coordinates areat co. or ban

fxd A= 0 and l~fxtd A whence

KB

1 a (3)

1 or ciuilit~~will ~1 1 0

pP) P

or H - i -.. P (1 .+ fifl,)

H 1 flp\V

or P (4~

Taking moments about base

M.0 . j . . H. D = .M 1M, t

or Ni = ~ - F M, - 3 - ~ilP~D (5)

Substituting equations (1), (2) and (3)N. . . . K O

tu inK~l,.~3 /4d, . 2mK~l.~

K .( 3 ~ ,.: n~L (I -~

K (j NI/[t~ :, nt l~(I 2~/~)3

(6)

where I ... I n : in t (I I -

From equation (.4~

H . . t /3H~\~ M IP 2inK f t h/I) 2w

. 1 1 L f)

1) 1 wltcic r , --r 2 ml~

11 + P p W H - 3

fl~(W M -~H

t3

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p= r t7),~(w P 7)

Equation (7) is sLtisfied only i t ~ i whence we obtain

M7

> ~ZW~PP

or H > (1~zp)

~qil)+ p W

The vertical soil reaction is gwen by

7, Ke(X~+ IX )

W_~ilP=f5dA~Kef.(X~ + )QdA

= KofLdA+KofXdA

= KeX~.A

whence X~K e =.(W

K9X~4-Ko.X

= + K a. B f2

K a. 1 3 / 2

As Ku=

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e1 A 21

~H..J. ~L.! 9 ~ A 2) U

4. CONDITtONS OF STABILITY

fi) The maximum soil reaction from the sides cannot exceed

the mixim.um passive pressure at any depth, if the ~oil remains in an

elasticstate., This amounts tothe condition that at aay depth y

7(Kp K~)y or

ytK~-KA)y

orm !~(D.y)~Y(KpKA)

(at y =-. o L.H.S. is m aximum )

ormKo}y(Kp--KA)

orm~>y(KpKA)

(ii) The maximumcoil pressure a~ha. . , c O~ shall not exceed

.aliowable pressure on soil, similarly the mi n mumsoil pressure

shall not he less than 0, i.e., no tension,

ULTIMATE SOIL RESISTANCE METHOD (Anmxurc 2)

I. INfRODtJCTtON

Th.e elastic theory described in .lnnexure I approximatel>

determines the stresses in the so.il mass hut does not indicatethe safety

against ultimate failure of the 11w nl!at ion. For this it will be neces-sary toknow h.e modcoffail arc of well foundations.

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2 OBSERStD FAILURE OF TIlE WElL FOUNDATtONUNDER ULTIMAfl CM. NDtTtONS

The pattern of failure of the soil muss under the application of

r;hnsversLt II~rcesto largeand snia I I dept lis ofembedment is depleted

in F:Hc, 2 .

~ 1t~L ~.r...n ~:~ ,... ~ ~ 0S. . ,_ ~.d aFig 2

Thor s i I around he base in either case slides over a circular e\lindrftcal

path with centre of rot at ion soni~wheue above the base, The plastic

t~~owat the side follows I h~r tNt al concept as in the case of rigid

hulkhcitl at failure. Failure hay beer observed to occur at abcut 3~

rotat tonof the well in case ofno n-cohesive soils.

3 . QUANTUM OF RESISTANCE

Theobscrved variation of the total alt note icsislancc ofthe soul

noisy, i.e., both at the base and thu siles under sat yingdiicut loads isgiven in Fig. 3.

rhis study indicates that the total resistingmoment incleases with the

increase in the ratio of thedirect load to the nIt matebearangcapacityof the soil up to 0 5 to fl.7. After that it reduces. It is, therefore,necessary to ensure that the bearingporessure adopted has a factor ofsafety of twsa or more on ultimate bearing capacity of Ibe soil

cakutatc*l by any rational formula,

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hi

4 POINT OF R OTAUON A T FAILURE

(i Movementof the pohet ofrotation or the vertiod ails

~a)fleet ofgeom etry and horIzontalloadsThe geometry of the toundat ion, viz., the ratio of the width of

ftamndation toth e depth ofembedmen t in th e sofl and th e magni tudeof th e horizontal loads hae no ef fect in sFifting th e po~ntof rotationalong th e verticalaxis a s could be seen f rom Fig . 4 .

KV

~

Foundot~,nsof iftqr.nl w~JflnSt ~b2Ocyn

a *4~30CmWI

Position of th e centreofrotation a s a function ofrelative depthFig. 4

7

Fig 3

~1

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(h) Effect of direct loads

The point of rotation h a s a relatIon to th e ratio o~th e s u p e rimpostd vertical loadsto th e ultimate hear ingcapacity of th e s o i a s

s e e n from Fig 5~where

*0 P~ac tu a l v c r t c a l pnsuro ochn

1~ ult imata ~corQnc~cop~dtty

0*10 & oa cia p;ar

Fig. 5

Theactual variation is conf ined to a narrow range beti~en0.75and 0 8t ime s th e depth ofem b edment be low th e scour level. Takinginto account normally expected ver t ical loads on well foundations1

a f ixed value of 0 .2 t imes depth above th e b a se ofth e foundationhas beenadoptedforworking ou t th e soil re sistance.

(ii) Shift of th e point of rotation along th e horizontal axis

The point of rotat ion undergoes a change in th e horizontaldirection depending upon t h e g e o m e t r y of th e foundation and th eextent of defo~nationof th e foundation. Under ultimate conditions

the magni tude of horizootal shift of th e point a s function of D/Bratiois g iven in Fig. 6.

This shift in position of th e point of rotation in th e horizontaldirection will c a u s e variation in th e share of th e moments betweenthe s ides and th e base.

~5

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TRC : 45 1 9 7 2

02

0~4

03A

005

Found ations ofd ittrent widths

pAB-BoCm

4~~-4 ,~

t.0 t5 acs as s~

Position0fthe centreof rotation as a function ofrelative depth

Fig. 6

Note: For th e purpose of this analysis th e shi f t orth e pointof ro~ationalong th e hor izontal axis h a s b e e n ignored, in view ofo the r related indeterminate factors.

5. METHOD OF CALCULAT1ON

5,1. Base Resisting Momert (Mb)

The base resisting moment is the moment ofth e frictional forcesnobilised a long th e surface of rupture wh ich is assknd to becylindrical passing through th e corners of th e basefora square nIla s shown in Fig. 7.For circular wells, th e sur faee of rupture corres-ponds to that of a part of sphere with its centre a t th e point ofrotation and passing through th e pe r iphe ry of th e base.

if W is the total ve r t~calload au~mutedby appropriate load

factors given in su p pa ra 5.5 be low, th e lo*d pe r unit width willb e WfB, s~thichwill also be equal to the upnrd peusure as shownin Fig. 8.

(1) For a rec*a~*IarbaseCtnsider th e small aft of length td~ a t an angle of 4 from

theverticalanis..

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It ~holi7t11 idI c tp~neiu~R , d J. . ctps cL

Vertka 1~rcc~it th e clc~nent

Rd~cosJ.WBT)uc to t I i s ~crtka force the nornia I loice dc~dopedat the

ekment k 8 F~

where ~ R. d ~. coc ~ c~ ~L

= cos~d.L!~L

-~ ~

2WR 1 (I + COS 2cL)B j ~--~-.d~0

RWB~ (0+ Sm & COS 9~

B B /Bt+4ntDzsin8=~-, cosO=rn~~~,LanO=~2_-b;R==A~f~__.4_~_~~

W / ~ 4n~D~ I B 2nBD

F~ 2 \/ + ~ I. ~ nD +

Momentofresistanceof th e base about th e point of rotation

Mb=Fflcan#R (1)

(ii) For a circular base

Am ultiplicatio n factor of 0.6 is to be applied for the aboveexpression of Mb in order to acc~unt for the surface of rupture

being partof a sphere~

For both cases substituting the value n equa to 0 . 2D f~rthe point of rotation in formula (I) above, th e bas~resistance c~nbe siinpli~edan d expressed in tetrns ofB.

MD =Q W B tan ~

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where1 3 . wiil t h in the case of square and rectangular

wells parallel to th e direction of forces and

diameter for circular wells.Q a con~tant,which depends upon the shape ofwell as welt as th e DB ratio. Its values aregiven in Table 2 below fo r square or rectangular

wells. A shape factor of0.6 isto be multipliedfor wells with circularbase.

T A B L E 2

DB 0.5 1.0 t.5 2.0 2.5

- Q 0.41 0.45 050 0.56 044

Note The values ofQ for interrnedi;itc DR values in th e above

range may be linearly interpolated.

52. Side Resisting Moment (Mi)

The ultimate soil pressure distiihutIon at th e frunt and back

faces ofthe well f~u~dat~onis indicated inFig. 9 .

Fig. 9

22

///

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mc: 972

The point ofrotition is loctited at O,2D above th e )~ h esideresistancemoment will then b i S calculated as folk~~s

Let,7D(Kp K~j2-:::XrrBC; BF=Y

j ~ 3 ,DEF

O,2~ ~ 0,2D

x:Y x Y

D 5D1D

or ~r .. (I)From As AB C and CEF

D 2)

~ ~Equating (I) an d (2)

511DD--D1Y Y

or 6D1 = 2D:

where

= 1/3D ... (3)

Moment ofside resistance about O~is the algebraic moments of

As AB C and DEC

4D,X. 1D+1~, 2,X.~

XD + ~. D 15 1 35

13/135 XDt

= O.096D.X

Say = O.1DX

SubstItuting for X

Ms 0.1 yl) (K~ K.) per unit width of well;F O E a wtdthofL , Mi 0.1

1D (Kp K4,L

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5.3. ResistIng momentdue to McIleeenfront .5 beck faces (Mr)

Due to th e passive pressure of soil as shown in Fig. 9 , th e

fri:tional rorceson th e front and backraces of~tll will be acting inthe vertical direction and will also produce resisting moment Mr.For thepurposeofthis code, the effect of the active earth pressure

perpendicular to th e directions ofapplied forces is neglected. Theresisting moment Mf is calculated as follows:

The vertical pressure due to friction at an y level is sin S timesthepressureat that level whate 8 is the ang4e ofwallfriction,

Total friction force/unit width (A AOE + A BOD) sin SD1=D13

pressure at F -~ } yD (Kp.K*)

ArcaofAAOE 4. yD(K,K,~ q

~ ~ D (Kr IL)

Area ofA ROD yD (K, K4)

= 0 .1 yDiK,- IL)

Total friction ft~rce/uni~twidth

(K,IL) sinS

Moment abnutcentre ofrotation

(i) incaseof rectangularwells rot width L

Mf:J2?yDt (KpKA). ~sia8xL

(K,K,). B. sin8xi.

O.183v(KpK~OLB.D3 sinS

say 0.180 y(K,K,.) LBD sin 8

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(ii) In case ofcircular wells

B

LevLr arm =

Therefere M1= yD (Kp KA). ~ 1 .. sin S

Since 1 . (IS 13 in case ofcircular wcll

0.33 2 -= y(KpKA). BD s.n ~

0.105 y (Kp K~)B D sin 8

say 0.lly(KpK4,)BD sinS.5.4. Total resisting moment of soil

Total resisting moment of soil Mris given byMr= (M5 + M1 4- M r)

5.5. Factor of safety

A suitable safety factor has to be ensured takiMg into account the

probable variation of different loads and their combinations. Thevariation of strength characteristic of the soil sbowld also beaccounted for in calculating the resisting moment given by th e aboveexpression. Puttingi t mathematically

~ 11 (appliedload or moment)

A (soil resistingmoment~ 0)

whereload factor for a particular load

A= strength factor forthe resistance ofsoil.

The passive resistanceofthe soil depends on th e angle ofinternalfriction for variation of which a reduclion factor of 1.25 may be

applied. Further to take into account the special nature of risk offtilure of roundation, which is most imj~rtantpart of th e bridge,

another reduction factor of 1.15 may be applied. Hence the totalcoefficient applicable to th e R i gh t H a n d Side of th e abcve expres~

sion (1) will come to 0.7.

As regards the Left Hand Side of theexpression, the variation ofloads is described below:

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IRC: 451972

(i) Dead loS : The deadload bcing more or less a permanent

load, a factor 1.1 would be sufficient for the variations in densities of

materialsan d computationalerrors, etc.

(ii) Liveload: Consideringth eeffectofvariation in IRC loading met with in bridges, it is adequate to adopt a factor of 1.6 for

probable overloading with the combination of dead load only andl.4 with other combinations except with wind or seismic. Witheither wind or seismic due to reduced probability ofoccurrence of

maximum live load, a factor of 1.25 i s considered adequate.

(iii) Braking force, etc. : These longitudinal loads will cor-

respond to thecoefficien t adopted for liveload.

Notes:

(1) The forces due to characteristic imposed deformations

should be added, e.g., th e horizontal load due to frictional resistanceoIthe bearings may include the increase in dead an d live load.

(2) F or n orm a l structures imposed temperature deformationsof climatic origin and deformations due to creep an d shrinkage can

generally b e neglected for th e ultimate analysis. However, fo rstatically indeterminate structures, the forces due to above causesshould b e considered. Similarly, the forces due to settlement ofsupporthave also to be taken intoconsideration.

(iv) Watercurrent force: Due to possible error of20 per cent

in estimatingthe velocity, a factor of1.4 may be adopted.

(v) Buoyancy: The effect of buoyancy in reducing th edensityofsubm erged masses is more or less a constant and can be taken asunity.

(vi) Wind or seismic forces: When th e bridge is not covetedby live load, a factor of1.4 is considered adequate for wind or seismic

forces. Due to less probability ofcombination with maximum liveload,a reduced factor of 1.25 is adequate.

(vii) Earth presare on abutments: To account for increasedearth pressure resultingfrom either the density afsoil being higher or

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the angle of internal friction being lower than determined by tests rorvarious reasons, a factor of1 .4 is considered adequate for tomputa~

tion ofearth pressure.

Accordingly, the following combinations of load factors are

oltained:

LID (I)

i.ID+B+l,4(Wc +Ep +WorS) ...~.... (2)

l.1D+l.6L (3)

1.1D+B+l.4(L+Wc +E~) (4)

1.ID+B+l.25(L+W~+Ep +WorS) ........ (5)

where

D =dead load

L = live loadincludingbraking,etc.

B =buoyancy

Wc =water current force

Es =earth pressure

W =wind force

S =seismic force

(viii) Tilt and shift : In the computation ofapplicd momcnrs,effects ofmoments due to tilt and shift ofweDs, ifany, about tie

plane ofrotation shall also be considered.

6. In order to ensure th e factor ofsafety for ultimate resistanetaccordingto above concept, the total resistance niomcnt (Ma re dneed

by strength factor thou Id he not less than thi iota! applied manicat

(M) a bout th e point ui rotation for the appropriate conib flut ions aapplied loads enhanced by the taetors gi sen ahovc, i.e., tosay

0.7 (Mb f M3 -[ M1) ~ M