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Bottom of Form Table Cf $ontents =3= %T,C
G3D <+S%) CF *%(+ FCU <+S%) CF *%(+ $A* G3? $C$(US%CS M3= %T,C
A,,A)+'+T CF *%(+S % FCU6>?=72Bridge-Substructure-Anal&sis-
ABST,A$T The anal&sis and design of all the components of even the most simple bridget&pe can be a fairl& laborious and cumbersome ;ob especiall& "ith respect to the variouselements of the bridge substructure3 For bridges located on ma;or perennial rivers! resort"ill have to be made to deep foundations like "ells or pile foundations! the design of "hich involves length& computational eort3 The bridge engineer should be eLuipped"ith a hand& computational tool "ith the help of "hich he can Luickl& and reliabl&determine the suitabilit& of various la&outs and con@guration of the sub-structure before@naliQing the most optimum design of the substructure3 %n this thesis and attempt hasbeen made to develop a *3$3 based soft"are on EB3et platform for the anal&sis anddesign of substructure for bridges "ith simpl&supported spans3 The computerprogramme includes the anal&sis and of "all-t&pe and circular piers and includes theoption for the complete anal&sis and design of t"o-t&pes of deep foundations on the basisof the relevant %S $odes of *ractice8 Well foundations and pile foundations3 The pilefoundations can be anal&Qed and designed for both river and non-river bridge crossingsand the user is presented the option of t"o t&pes of piles for use in the foundations8under-reamed piles particularl& for non-river bridge foundations and bored cast-in-situcircular piles3 A note"orth& feature of the program is that lateral load anal&sis of bothfree and @edhead piles can be carried out b& the user in line "ith the recommendationsof the relevant %S $odes3 The user friendl& and interactive program assists the user in theselection of preliminar& dimensions of the "ell foundation! the safet& of "hich ischecked of the elastic state of the soil surrounding the "ell and at ultimate loads3Structural design of the critical "ell components like "ell curb! steining and "ell cap isincorporated in the soft"are3 The results for foundation design obtained from theprogram have been validated "ith long-hand calculations present in the Appendi3
$CT+TS $hapter o3 Title *g3 o3 $hapter-= %T,C$hapter-? W+(( FCU
D=?3G3M G3D3= Under-reamed *iles D>G3D3D Bored $ast-in-situ *iles ?7
G3D3? umbers! Spacing and Arrangement of *iles ?MG3D3G Safe Bearing $apacit& of *ile )roups ?G3D3MG3D36 (ateral load anal&sis of *iles G7G3D3 Structural M3D Functions (a&out of the Soft"are G>M3D3=Selection and %nput of *arameters used forAnal&sis and 3D Scope for Further Work =D>$hapter-N ,+F+,+$+S =?7A**+<% ASU**C,T%) (C) HA< $A($U(AT%CS FC, TH+%((UST,AT%E+ *,CB(+' C W+(( FCU
A**+<% BSU**C,T%) (C) HA< $A($U(AT%CS FC, TH+%((UST,AT%E+ *,CB(+' C *%(+ FCU
(%ST CF TAB(+S Table3o3Title *g3o3 D3= Ealue of constant for *ressure %ntensit& due to Water $urrent D3D *ermissible Stresses in $oncrete >?3= Silt factors for Sand& beds! %,$8 N-D777 N =M?3D Ealues of the constant K for sLuare or rectangular "ells D7G3=Bearing $apacit& Factor!??G3DEalue of coecient of horiQontal soil stress ??G3? Safe loads for under-reamed piles ?MG3GEalues of the constant k2m ? IG=G3M Ealues of the constant k2m D I G=A-= $alculation of 'aimum Shear forces bearings =G=A-D Stresses due to horiQontal shear force at bearings =G=A-? Summar& of Stresses due to various forces acting on the *ier =GDA-G ,esultant $ompressive Stresses at *oint OAP # OBP on *ier =G?A-M ,esultant Tensile Stresses at *oint OAP # OBP on *ier
=G?A-6 HoriQontal shear force at bearings # moments at the base of foundation =GNA- Seismic moment due of mass of bridge components # (ive load =GNB-= $alculation of 'aimum Shear forces at bearings =6NB-D Stresses due to horiQontal
shear force at bearings =6>B-? Summar& of Stresses due to various forces acting on the *ier =6>B-G ,esultant $ompressive Stresses at OAP # OBP on *ier =7B-M ,esultant Tensile Stresses at OAP # OBP on *ier =7B-6 'oment about longitudinal ais in pile cap from the critical section =NDB- $alculation of t"o-"a& shear force =NGB-N $alculation of one-"a& shear force at critical section along (-( ais of bridge=NM
(%ST CF F%)U,+S Fig3o3Title *g3 o3 D3= T&pical Shapes of *iers M?3= G36 *iled Foundation D>G3 (oad resisting mechanism in a pile ?=G3NBearing $apacit& Factor! for bored piles?DG3> Adhesion factor for cohesive soils ?GG3=7 T&pical arrangement of piles in a group ?6G3==
M6M3M Flo" $hart for calculation of soil resistance at ultimate loads MNM36 Flo" $hart for design of Well curb M>M3 Flo" $hart for design of Well steining 67
M3N Flo" $hart for design of Well $ap 6=M3> Flo" $hart for soil details 6?M3=7 Flo" $hart for calculating safe bearing $apacit& of bored cast-in-situ pile 6MM3==Flo" $hart for calculating safe bearing $apacit& of an under-reamed *ile66M3=D Flo" $hart for calculation of SB$ of group of bored cast-in-situ piles 6NM3=? Flo" $hart for calculation of SB$ of group of under-reamed piles 6>M3=G (ateral load capacit& of Under-reamed *ile 7M3=M (ateral load capacit& of Bored $ast-in-situ pile =M3=6 'oments in "ell-cap "h en full& clamped =6=A-=7 ,einforcement
=R
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$HA*T+, =
%T,C
length& and laborious task if thecalculations are attempted manuall&3 manuall&3 A design engineer "ould like to tr& various
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con@gurations! shapes and siQes of the principal components of a bridge before @naliQing themost optimum combination on the basis of safet&! economics and aesthetics of the elementsof the super-structure and the sub-structure3 At the same time! in spite of the best eortsduring sub-soil investigations! man& uncertainties al"a&s eist "ith respect to the sub-soilconditions "hich ma& be encoun tered at pier and foundation locations3 Unepected sub-soilconditions ma& reLuire a signi@cant redesign of the foundation or in etreme cases thefoundation t&pe ma& have to be changed from for eample an open-footing to a pile or a "ellfoundation3 For the above eventualities! it is desirable that a Luick! hand& and reliablecomputational reliablecomputational tool should be available to the design engineer for the anal&ses and design of bridge sub-structure in general and "ell and pile foundations in particular3%n this thesis an attempt has been made to develop *3$3 soft"are package in theEB3et platform platform for the anal&sis and design of sub-structures for concrete bridges "ithsimpl& supported spans3Anal&sis of the super-structure super-structure for loads transferred to the sub-structure is included inthe soft"are3 T"o %,$ loading categories8 $lass AA and $lass A are considered for super-structure super-structure anal&sis3 The option for single lane and t"o lanes of trac is included3 The user isprovided "ith the option of t"o t&pes of concrete piers8 "all-t&pe and hammer-head hammer-head t&pe"ith a circular shaft3 The anal&sis and design of both these t&pes of piers is included in thesoft"are3 %n the soft"are! the option is provided for t"o t&pes of deep foundations8 "ell andpiles3 Well Well foundations are essentiall& meant for river-bridge crossings "here as the optionfor pile foundations take care of pile anal&sis and design for both non-river and river bridgecrossings3 The anal&sis of the "ell foundation is carried out as per the relevant %,$ %,$ code forthe resultant aial! lateral loads and moments transferred tr ansferred from the super-structure for thefollo"ing t"o conditions8 =I The soil surrounding the "ell is in an elastic state DI Atultimate load conditions3 The program includes check on thickness of the bottom plug and theanal&sis and design of the critical components of a "ell viQ3 "ell curb! "ell steining and "ellcap3 *ractical considerations related to construction of "ells are eamined through a check onthe sinking eort developed in the "ell3 T"o T"o t&pes of
piles are available for design of pilefoundations8 =I Under-reamed Under-reamed piles and DI Bored cast-in-situ circular piles3 Under-reamedpiles Under-reamedpiles are essentiall& meant for nonriver bridge crossings and their design for vertical andlateral loads has been carried out as per recommendations of %S8 D>==3 The soft"are includesthe anal&sis and design of both free-head and @ed-head bored cast-in-situ circular piles incohesion less as "ell as cohesive soils3 A note"orth& feature of the soft"are is the lateralload anal&sis of the pile as per the relevant %S $ode3 The design of the pile foundation
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concludes "ith check on group behavior including settlement anal&sis and structural designof the pile and the pile cap3 =3D CBJ+$T%E+ CF TH+ TH+S%S
literature revie" on pile foundations # discusses the anal&sis# design steps of pile foundations3The features # limitations of the soft"are developed as the part of thesis "ork arebeing eplained in $hapter M3 The functioning of various modules of the soft"are areeplained in the form of Vo" chart! in the same chapter3The application of the proposed soft"are to the anal&sis # design of t&pical "ellfoundation and pile foundation is presented in $hapter 63The conclusions from the present stud& are discussed in $hapter 3,eferences form the last part of this thesis3
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$HA*T+, D
*%+,S # *%+, $A*S D3= %T,C
used in recent &ears3 Such pierslead to econom& in cost of superstructure as it reduces the span length of girders on eitherside of pier! but at the same time it "ill accumulate debris and Voating trees from the streamVo"3 T"o epansion ;oints formed on each pier "ill result in riding discomfort3
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aI Solid *ierbI $ellular T&pe *iercI Trestle ,3$3 *ier dI Hammer-head T&pe *iereI Framed T&pe *iersFig3 D3= T&pical Shapes of *iers
6R *age
'inimum top "idth of pier is kept 677 mm more than the out-to-out dimension of thebearing plates! measured along the longitudinal ais of the superstructure3 (ength of piershould not be less than =D77 mm in ecess of the out-to-out dimension of the bearing platesmeasured perpendicular to the ais of the superstructure3 The bottom "idth of pier is u suall&larger than the top "idth so as to restrict the net stresses "ithin the permissible values3 %t isnormall& sucient to provide a batter of = in DM on all sides for the portion of pier bet"eenthe bottom of the pier cap and the top of the "ell or pile cap! as the case ma& be3 D3? *,C$+
=3
(ive load8 This consists of (ive load of trac passing over the bridge3 +ect of eccentricloading due to live load should also be considered3 ?3
Buo&anc&8 Buo&anc& has the inVuence of reducing "eight3 %n masonr& or concrete structure! thebuo&anc& eect through pore pressure ma& be limited to =M percent of full buo&anc&on the submerged portion3 G3
Wind load8 Wind load is considered on the live load! superstructure and the part of thesubstructure above the base of pier or " ater level! "hichever is higher3 %t acts on thearea of the bridge in elevation and is thus al"a&s taken to be acting laterall& to thebridge onl&3 This force could be considered as per recommendations of %S8NM D 3 M3
HoriQontal forces due to "ater current8
HoriQontal force due to "ater current is considered on that part of substructure thatlies bet"een the "ater level and the base of pier3 The "ater current pressure is givenb& +Luation D3=! D3=I"here! 0 intensit& of pressure in k2m D due to "ater current! 0 a constant having dierent values for dierent shapes of piers3The values of this constant for dierent pier shapes are present in
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Table D3=E 0 velocit& of current in m2sec at the point "here pressure intensit&is being calculated3%t is assumed that the velocit& distribution in stream is such that E D ismaimum at the free surface of "ater! Qero at the deepest scour level and varieslinearl& in bet"een them3 Also the m aimum velocit& of Vo" is assumed to be eLualto times the velocit& of the current3Table D3=8 Ealue of constant for *ressure %ntensit& due to Water $urrent SHA*+ Ealues SLuare ended piers =3M7$ircular piers 7366*iers "ith semi-circular cut-"aters 7366*iers "ith triangular cut-"aters 73M to 73>Trestle t&pe piers =3DMFor calculating the pressure on the pier! the angle "hich the current makes"ith the ais of the pier should be taken into account3 )enerall&! the maimumvariation in the angle of
"ater current to the transverse ais of the bridge is taken asD7X3 Thus! the pressure along the ais of the pier and transverse to it is respectivel&given b&!D3DID3?I 63
$entrifugal forces8 $entrifugal forces are taken into account! "hen the bridge is located on a curve3 3
(ongitudinal forces8 (ongitudinal forces are caused due to tractive eort caused through acceleration of the driving "heels! braking eect due to application of brakes to the "heels #frictional resistance oered to the movement of free bearings due to change of temperature3 Braking eect is invariabl& greater than the tractive eort! and as aresult the tractive eort of vehicles is neglected3
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N3
Seismic forces8 Seismic force acts on all loads! "hich posses mass at their centre of gravit&3 gravit&3 Seismicforces acting in horiQontal direction! along longitudinal and transverse ais of thebridge are considered3 Forces acting in the vertical directions are comparativel& small!and are hence neglected3
ormal I $ase loading8 %t includes dead load! live load! buo&ant force! "ind load!forces due to "ater current! centrifugal forces! braking force2tractive force #horiQontal shear force at hinge bearings due to the eect of braking force! "ind load3 D3
Temperature Temperature TI $ase loading8 loading8 %t includes loads due to frictional restraint totemperature movement at bearings3 ?3
Seismic SI $ase loading8 %t includes seismic forces acting in horiQontal forcesacting in horiQontal direction3
$onsidering the probabilit& of earthLuake "ith other forces! it is generall& assumedthat earthLuake and "ind forces "ill not occur simultaneousl& and so onl& one can beconsidered at a time3 Taking Taking all the case loading into accounts! pier is anal&Qed for threedierent load combinations8 ormal I $ase! ormal and Temperature Temperature Y TI $ase $ase #ormal! Temperature Temperature and Seismic Seismic Y T Y SI $ase3(ongitudinal forces forces acting on the bridge like braking eort2tractive eort! frictionalresistance frictionalresistance at the bearings and seismic forces acting on live load and bridge superstructure "illproduce horiQontal shear force at the bearings3 The horiQontal shear force "ill be calculatedfor dierent load combinations as discussed above! and later is incorporated into theirrespective case of load combinations3Stresses developed into the pier due to dierent loads and forces are calculatedindividuall&! calculatedindividuall&! and the resultant maimum stress acting on the pier is "orked out for dierentload combinations3 The resultant maimum stress for each load combination should be "ithinthe permissible stress limits3 For brick masonr& in cement mortar! permissible compressivestress compressivestress is = '*a and permissible tensile stress is 73=7 '*a3 %n stone masonr&! compressivestress is limited to =3M '*a and tensile stress is limited to 73=7 '*a3 *ermissible stresses forconcrete are given in Table D= of %S8 GM6-D777 = ! for dierent grades of concrete3 Table D3=sho"s the permissible stresses for plain concrete used in bridge anal&sis and design3
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Table Table D3D8 *ermissible *ermissible Stresses Stresses in $oncrete )rade of $oncrete*ermissible $oncrete*ermissible Stresses in $oncrete in '*aIFor $ompression For Tension Tension ' =7 D3M -' =M G37 736' D7 M37 73N' DM 637 73>' ?7 N37 =37' ?M >37 =3=' G7 =737 =3D' GM ==37 =3?' M7 =D37 =3G%,$8 6-D777 6 allo"s the increase in permissible stresses of concrete for dierent loadcombinations3 For ormal and Temperature Y TI case i3e3 "hen the eect of temperatureis considered! permissible permissible stress can be increased b& =M percent3 Finall&! for ormal!Temperature and Seismic Y T Y SI case permissible stress can be eceeded b& M7Z3 %f themaimum stresses in piers for the "orst loading combination are more than the permissiblestress! it is reLuired to redesign the piers in order to bring maimum stresses "ithin thepermissible limit3 D3G $C$(US%CS The t&pes and the features features of piers and pier caps caps usuall& emplo&ed for bridgecrossings have been brieV& discussed together "ith anal&sis methodolog& and permissiblestresses for design3
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$HA*T+, ?W+(( FCU
?3D T.*+S CF W+(( FCU
== R *age
ver& large siQes! "ells "ith multiple dredge holes are used3 Wells of this t&pe have been usedfor the to"ers of the Ho"rah Bridge3
aI $ircular "ell bI
=D R *age
?3? +(+'+TS CF A W+(( FCU
"ell foundation is a t&pe of foundation "hich is generall& built in parts at thesurface and sunk to its @nal position! "here it forms the permanent foundation3 Fig3 ?3Dsho"s a t&pical section of a circular "ell foundation3Fig3 ?3D T&pical Section of Well Foundation aI
Well-cap8 %t is a ,$$ slab laid at the top of the "ell steining to transmit the loads and moments fromthe pier to the "ell or "ells belo"3 Shape of "ell cap is same as that of "ell "ith a possibleoverhand of =M7 mm all-around to accommodate length& piers3 %t is designed as a t"o-"a&slab "ith partial @edit& at supports3 The top of the "ell cap is usuall& kept at the bed level incase of rivers "ith seasonal Vo" or at about the lo" "ater level in case of perennial rivers3Thickness of "ell cap is usuall& bet"een =M77 mm to D777 mm3
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bI
Steining8
%t is the main bod& of the "ell "hich transfers load to the base of the foundation3 Steining isnormall& of reinforced concrete3 'inimum grade of concrete used in steining is 'D7 "ithcement content not less than ?=7 kg2m ? 3 To facilitate "ell sinking an o-set of M mm to =77mm is provided in "ell steining at its ;unction "ith the "ell curb3The thickness of "ell steining should not be less tan M77 mm nor less than that givenb& +L3 ?3=3?3=I
"here! t 0 minimum thickness of concrete steining! m!< 0 eternal diameter of circular "ell or dumb bell shaped "ell or smallerplan dimension of t"in < "ell! m!( 0 depth of "ell in m belo" (3W3(3 or top of "ell cap "hichever is greater! 0 a constant depending on the nature of subsoil and steining material takenas 73?7 for circular "ell and 737?> for t"in < "ell for concrete steiningin sand& strata and =7Z more than the corresponding value in the case of cla&e& soilI3 cI
Well curb8 %t is the "edge shaped ,$$ ring beam located at the lo"er portion of the "ell steiningprovided to facilitate sinking3 Well curb carries cutting edge for the "ell and is made up of reinforced concrete using controlled concrete of grade 'DM3 The cutting edge usuall& consistsof a mild steel eLual angle of side =M7 mm3 %n case blasting in anticipated! the outer face of the "ell curb should be protected "ith 6 mm thick steel plate and the inner face should have=7 mm thick plate up to the top of the curb and 6 mm plate further up to a height of ? mabove the top of the curb3 dI
Bottom plug8 After the "ell is sunk to the reLuired depth! the base of the "ell is plugged "ith concrete3This is called the bottom plug3 %t acts like an inverted dome supported b& the steining on allthe sides and transmits the load to the subsoil and acts as a raft against soil pressure frombelo"3 'inimum grade of concrete used in bottom plug is '=M3 Thickness of bottom plugshould not be less than the half of dredge-hole
diameter nor less than the value calculated in+L3 ?3D3! ?3DI"here! W 0 total bearing pressure at the base of "ell!
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f c 0 Veural strength of concrete in bottom plug!! and! 0 *oisson[s ratio for concrete! 73=N to 73D73
eI
Top plug8 The top plug is an unreinforced concrete plug! generall& provided "ith a thickness of about677 mm beneath the "ell cap to transmit the loads from the pier to the
steining3 'inimumgrade of concrete used in top plug is '=M3The space inside the "ell bet"een the bottom of the top plug and the top of bottomplug is usuall& @lled "ith clean sand! so that the stabilit& of the "ell against overturning isincreased3 While this practice is good in case of "ells resting on sand or rock! the desirabilit&of sand @lling for "ells resting on cla&e& strata is doubtful! as this increases the load on thefoundation and ma& lead to greater settlement3 %n the latter case! the sand @lling is done onl&for the part of "ell up to scour level! and remaining portion is left free3 fI
%ntermediate plug8 As discussed above! for "ells resting on cla&e& strata! it is not preferable to @ll the spaceinside the "ell completel& "ith sand3 %n such cases! sand @lling is not done or sand is @lledup to the scour level3 A concrete plug covering the @lling is usuall& provided! kno"n asintermediate plug3 Usuall&! thickness of intermediate plug is taken as M77 mm3 ?3G AA(.S%S A< <+S%) CF W+(( FCUMM-=>6 M recommend that the maimum scourdepth in a stream should be ascertained! "henever possible! b& actual soundings at or near thesite proposed for the bridge! during or immediatel& after a Vood before the scour holes havehad time to silt up appreciabl&3 %n case actual soundings are not possible! depth of scour instream can be ascertained using theoretical methods taking into account the velocit& of stream! characteristics of the river bed materials! and man& other factors3The %,$8 N-D777 N recommended formula for calculating the mean depth of scourbelo" High Flood (evel HF(I for natural channels Vo"ing over scourable bed is as follo"s8
! ?3?I "here! < b 0
=M R *age
0 ! K is the design discharge in the stream in m
? 2s
andis the linear "ater"a&! m! sf 0 Silt factor for a representative sample of the bed material obtained upto the level of the anticipated deepest scour! and!0 =36 ! d m is the median siQe of the bed sediments in mm3Table ?3= presents the %,$8 N-D777 N recommended values of silt factor for varioust&pes of sand& beds for read& reference and adoption3
Table ?3=8 Silt factors for Sand& beds! %,$8 N-D777 N The normal scour depth for natural streams in alluvial beds can also be calculated using (ace&[s formula given belo"8
! ?3GI
"here! d 0 ormal depth of scour belo" highest Vood level for regime conditions ina stable channel! m3K 0
2s and! f
0 (ace&[s silt factor for a representative sample of the bed material3 This can be determined from Table ?3=3The scour depth "ith maimum value! obtained from an& of the formulae as discussedabove "ill be considered as ! the mean scour depth for design of foundation3As per the recommendations of %,$8 N D777 N ! at the noses of piers! the maimumdepth of scour! d ma ! is taken as t"ice of mean scour depth! 3?3MI T&pe of bed material $oarse siltSilt2@ne sand'edium sand$oarse sandFine ba;ri and sandHeav& sand737G737N= to 73=MN73D?? to 73M7M73DM73>NN=3D> to D37773?M73M to 73673N to =3DM=3M=3MD37 to D3GD
=6 R *age
The "ell foundation shall be taken to such a depth that it is safe against scour3 Apartfrom this! the depth of the "ell foundation should also be sucient from considerations of bearing capacit&! settlement stabilit& and suitabilit& of strata at the founding level3 %nvariabl&!the "ell foundation in all cases shall be taken do"n to a depth "hich "ill provide sucientgrip3 The grip length belo" the anticipated maimum scour level shall not be less than =2? rd the maimum anticipated depth of scour belo" H3F3(3 ?3G3D (CA
(ive load?3
Buo&anc&G3
Wind loadM3
HoriQontal force due to "ater current63
$entrifugal forces3
(ongitudinal forcesN3
Seismic forces>3
HoriQontal shear forces at bearings due to longitudinal forces and seismic forces=73
Forces due to tilt and shift3The loads mentioned above are discussed in Section D3D of $hapter D3 These loads arecalculated "ith respect to the bridge superstructure and substructure and correspondingl&! thetotal vertical load! the total horiQontal forces acting along the longitudinal direction and thetransverse direction of bridge and the moments about the transverse and longitudinal ais of the bridge are obtained for the design of the "ell foundation3 'oments due to shift and tilt of "ells are also be included in the anal&sis of the "ell3 ?3G3?
STAB%(%T. AA(.S%S CF W+(( FCU
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stage "hich is assumed to prevail under vertical loading3 The %,$8 GM-=>D thereforespeci@es t"o checks! one for soil pressures under "orking loads and the other for the factorof safet& available "ith respect to ultimate strength of the surrounding the "ell3As per %,$8 GM-=>D
! the resistance of the soil surrounding the "ell is checked using8a3
+lastic theor&b3
*lastic theor& also called as Ultimate ,esistance 'ethodIThe follo"ing assumptions are made in computing soil pressure using elastic theor&8i3
The soil surrounding the "ell and belo" the base is perfectl& elastic! homogeneous and obe&s Hooke[s la" ii3
Under design loads! the lateral deVections are so small that the unit soil reaction \p[increases linearl& "ith increasing lateral deVections \Q[3 Hence p 0 H Q"here! H is the coecient of horiQontal subgrade reaction at the base3iii3
The coecient of horiQontal subgrade reaction increases linearl& "ith depths in thecase of cohesionless soils3iv3
The "ell is assumed to be a rigid bod&! sub;ected to an eternal unidirectional horiQontal force \H[ and moment \'[ at scour level3 As a conseLuence of the above assumptions! the pressure distribution is parabolic on the sidesof the "ell and linear at the base3The elastic theor& gives th e soil pressure in the sides and the base of the "ell underdesign loads3 Ho"ever! to determine the actual factor of safet& against failure it is necessar&to calculate the ultimate soil resistance "hich is done b& assuming plastic behaviour of thesoil at
ultimate loads3 For checking the ultimate load capacit& of the "ell foundation! theapplied loads are multiplied b& suitable load factors for various load combinations and theultimate resistance is reduced b& appropriate under-strength factors and the t"o are thencompared3A step-"ise description of these t"o methods of anal&sis of "ell foundations is givenbelo"8Both the above methods are applicable if the "ell foundation is resting onnon-cohesive soil like sand and is surrounded b& the same soil belo" the maimum scourlevel3The above methods should not be used for anal&sis if the depth of embedment of the "ellis less than 73M times the "idth of foundation in the direction of the principal lateral forces3
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=3
+(AST%$ TH+C,.ST+* =8 3 For sLuare or rectangular "ells"here the resultant horiQontal force acts parallel to the principal ais! theshape factor shall be unit& and "here the forces are inclined to theprincipal ais! a suitable shape factor based on eperimental results isused3< 0 depth of "ell belo" scour level!m 0
H 29 ,atio of horiQontal to vertical coecient of sub grade reaction atbase of "ell3 %n the absence of values for H and determined b& @eldtests m shall generall& be assumed to be unit&!0 coecient of friction bet"een the sides of the "ell and the soil0 ! "here ] is the angle of "all friction bet"een "ell and the soil!
^0 for a rectangular "ell!0 for a circular "ell3 ST+* ?8 +nsure the follo"ing8 ?3I
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?3NI "here! !0 coecient of friction bet"een the base of the and the soil3 %tshall be taken as0 angle of internal friction of soil3 ST+* G8 $heck the elastic state ?3>I
"here! 0 densit& of the soil submerged densit& to be taken "hen under "ater orbelo" "ater tableI 0 passive and active pressure coecients to b e calculated using $oulomb[stheor&! assuming \][! the angle of "all friction bet"een "ell and soil to be eLual to ! but limited to a value of 3 ?3=7I
?3==I
ST+* M8 $alculate ?3=DI "here! # 0 maimum and minimum base pressures! respectivel&!
A 0 area of the base of "ell! B 0 "idth of the base of "ell in the direction of forces and moments! * 0 '2r! ST+* 68 $heck i3e3 no tension! and!# allo"able bearing capacit& of soil3 ST+* 8 %f an& of the conditions in Step ? or Step G is not satis@ed! then the grip length of the "ell ma& be increased and all the calculations are revised3 %f the conditions in Step M arenot satis@ed then! either the grip length of the "ell or the diameter of the "ell is increased3 ST+* N8 The above steps are repeated for load combinations containing seismic and "indloads separatel&3
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D3
U(T%'AT+ ,+S%STA$+ '+THC
Y W or SI=3=< Y =36(=3=< Y B Y =3G( Y W $ Y+ * I=3=< Y B Y =3DM( Y W $ Y+ * Y W or SI"here! < 0 dead load( 0 live load including barking load and other forces related to live loadB 0 Buo&anc&W $ 0 "ater current force+ * 0 earth pressureW 0 "ind forceS 0 seismic forceA 0 area of the base of "ell0 ultimate bearing capacit& of soil belo" the base of "ell taking a factorof safet& of D3MI3 ST+* D8 $alculate the base resisting moment! ' b ! at the base of "ell using the follo"ingeLuation8' b 0 KWB! ?3=GI"here! B 0 "idth! in the case of sLuare and rectangular "ells measured parallel tothe direction of forces and diameter for circular "ellsK 0 a constant "hose values are given in Table ?3D belo" for "ells "ith asLuare or a rectangular base3 A value of 7367 is taken for circular "ells0 angle of internal friction of soil3Table ?3D Ealues of the constant K for sLuare or rectangular "ells <2B 73M =37 =3M D37 D3M K
73G= 73GM 73M7 73M6 736G
D= R
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The ultimate moment of resistance resistance of the "ell sides due due to the passive resistance of the soil! ! is calculated net3?3=MI"here! net3?3=MI"here! 0 densit& of soil submerged densit& to be taken for soils under "ater orbelo" the "ater tableI!( 0 pro;ected "idth of the soil mass oering resistance3 %n case of circular"ells! it shall be 73> times the "ell diameter 0 passive and active pressure coecients to be calculated using $oulomb[stheor&! assuming \][! the angle of "all friction bet"een the "ell and the surrounding soil to be eLual to but limited to a value of 3 ST+* ?8 The ultimate moment of resistance resistance of the "ell sides due due to friction! ! iscalculatediI iscalculatediI
For rectangular "ells!?3=6IiiI "ells!?3=6IiiI
For circular "ells!?3=I ST+* G8 The total ultimate moment of resistance of the "ell "ell is taken as ' t ' t 0 73' b Y' s Y' f
I ?3=NIWhere 73 is the strength reduction factor ST+* M8 $heck ' t '"here! ' 0 Total applied eternal moment about the plane of rotation of the "elltaking appropriate load factors as per combinations given vide step =3 ST+* 68 %f the conditions in Steps = and M are not satis@ed! the "ell shall be redesigned3 ?3G3G <+S%) CF W+(( $U,B When the "ell is dredged during the process of sinking! the curb cuts through the soilunder the action of the dead "eight of the steining including kentledge! if an& and hence hooptension is developed in the "ell curb3 The "ell curb has to be designed for the hoop tension3Total hoop tension ! ?3=>I "here! 0 running load of the "ell steining on the curb!d 0 mean diameter of "ell steining!0 angle of beveled edge of "ell curb "ith h oriQontal! and! _0 coecient of friction bet"een soil and concrete of curb3
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A minimum reinforcement of D kg2m ? is provided in the "ell curb 3 Ther einforcement is provided in the form of rings distributed along the perimeter of the "ellcurb! the rings being enclosed "ithin stirrups3 ?3G3M <+S%) CF W+(( ST+%%)8 Before designing the section of the steining! the stresses in the steining are calculatedat the level of maimum scour3 ?3D7I?3D=I" here! W 0
total vertical load acting up to the maimum scour depth!A 0 area of cross-section of "ell steining!' 0 ,esultant moment due to various loads as considered during anal&sisof "ell at maimum scour level5 0 Section modulus of "ell steining3The stresses should be "ithin the permissible limits3 *ermissible limit of stresses fordierent grades of concrete can be obtained from Table D3D3 %f the stresses eceed thepermissible limits! the thickness of the "ell steining has to be increased3A minimum thickness of the steining! t min ! given b& the follo"ing eLuation is reLuiredto avoid the ecessive kentledge during sinking of the "ell3Thickness! ?3DDI" here! d 0 eternal diameter of "ell!0 densit& of concrete! and! f
0 skin friction acting on the curved surface area of the "ell!0"here! 0
coecient of friction bet"een soil and concrete! A
0 coecient of active earth pressure0 submerged densit& of soil on the sides of steiningh 0 height of "ell3After performing the checks for stresses and thickness of steining! the reinforcementsin the steining are calculated3 The vertical reinforcements in the steining should not be lessthan 73=D percent of the gross sectional area of the actual thickness provided for the steining3The vertical reinforcement should be eLuall& distributed on both the faces of the steining3 The
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vertical reinforcement should be tied up "ith hoop steel not less than 737G percent of thevolume per unit length of the steining3 ?3G36 <+S%) CF BCTTC' *(U) The bottom plug has to be checked for minimum thickness given b& the follo"ingeLuations! F or circular "ellsI! ?3D?I For rectangular "ellsI!
?3DGI
"here! r 0 radius of "ell at the baseL 0 unit bearing pressure against the base of the "ell 0 Veural strength of concrete used in bottom plugb 0 short side of "ell ^ 0 short side2long side ratio of "ell3
?3G3 <+S%) CF W+(( $A* A "ell cap is needed to transfer the loads and moments from the pier to the "ell3 Theshape of the "all cap is normall& kept the same as of the "ell "ith a possible overhang of =M7 mm3 The top of the "ell cap is usuall& kept at about the lo" "ater level in case of perennial rivers3 The "ell cap is designed as a t"o-"a& reinforced concrete slab resting overthe top of "ell3 The support conditions are taken partiall& restrained3The design of the "ell cap is carried out b& assuming that the load from the pier actson an imaginar& circle having an area eLual to the area of dispersion of the loads transferredfrom the pier to the "ell cap3Since the "ell-cap is assumed to be partiall& restrained b& the steining! the moments inthe "ell-cap are calculated for circular patch loading and for U3<3(3 self-"eight of "ell capIfor the follo"ing t"o conditions8=I
Well cap freel& supported on steiningDI
Well cap full& clamped on steining $ondition =8 Well cap freel& supported on the steining Take! *oisson[s ratio of concrete! " 0 "eight of "ell cap per unit areaE 0 vertical load acting on the "ell-caph 0 eective diameter of "ell-cap! # are the
radial and the tangential moments in "ell-cap! respectivel&3
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%n the @rst instance! the moments in the "ell cap due to vertical loads transferred from thepier and the self "eight of the "ell cap are determined3iI
'oments beneath loaded area due to circular patch loading ?3DMI?3D6I d 0 diameter of eLuivalent circular patch loadingiiI 'oments beneath un loaded area due to circular patch loading?3DI?3DNIAt support! d 0 h9 0 =The radial and tangential moments in the "ell cap due to U3<3(3 are given b&
?3D>I?3?7I At centre! d 0 79 0 7At support! d 0 h9 0 = $ondition D8 Well cap full& clamped at support
iI
'oments beneath loaded area due to circular patch loading ?3?=I?3?DI d 0 diameter of eLuivalent circular patch loadingiiI 'oments beneath un loaded area due to circular patch loading ?3??I
?3?GI At support! d 0 h9 0 =The radial and tangential moments in the "ell cap due to U3<3(3 are given b&
?3?MI
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?3?6I
At centre! d 0 79 0 7At support! d 0 h9 0 =%f is the resultant moment per metre length of the pier! then maimum reactive moment atthe support 0Hence! the maimum moment at the centre of the "ell cap due to momentstransferred form pier 0The maimum moment at the edges of the "ell cap due to moments transferred frompier 0 3 The resultant moments for the design of the "ell-cap section at mid-span and atsupports can be found out as follo"s3' centre 0 'ean radial moment due to patch loads beneath the loaded areaIY 'ean radial moment due to U3<3(3 at the centre of "ell-capIY moment at the centre of "ell cap due to moments transferred from pierI' edge 0 'ean radial moment due to patch loads beneath unloaded areaIY 'ean radial moment due to U3<3(3 at the support of "ell-capIY moment at the edges of "ell cap due to moments transferred from pierIHence! the reinforcement at the centre of the "ell-cap is calculated for the moment ' centre and the reinforcement at the edges of "ell-cap is calculated for the moment ' edge 3 Half of themain tension reinforcement at the centre and at the support sections of the "ell cap isprovided on the compression face3 All reinforcement in the "ell-cap is provided as anorthotropic mesh3The "ell-cap is @nall& checked for punching shear as per %S8 GM6-D777 = 3 ?3M $C$(US%CS The role and the features of "ell foundations have been discussed in this chapter3 Thisstabilit& anal&sis of "ell foundations has been eplained and the design of variouscomponents has been brieV& revie"ed3
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$HA*T+, G
*%(+ FCU
The upper soil strata are too compressible or too "eak to support the heav& verticalreaction transmitted b& the superstructures and piers3 %n this instance! piles serve asetensions of piers to carr& the loads to deep! rigid stratum such as rock3 Such pilesare called as point or end bearing *iles3 %f a rigid stratum does not eist "ithinreasonable depth! the load must be graduall& transferred! mainl& b& the friction! alongthe pile shafts3 *iles transferring loads to soil b& skin friction through its lateralsurface area are called as Friction *iles3aI *oint Bearing *iles bI Friction *ilesFig3 G3= *iles $lassi@cation on the basis of load transfer mechanism
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bI
*iles are also freLuentl& reLuired because of relative inabilit& of other foundations totransmit inclined! horiQontal! or uplift forces and overturning moments3 As the name implies!uplift piles are used for resisting uplift forces on foundations3Fig3 G3D Uplift *ilescI
*ile foundations are often reLuired "hen scour around the foundations can causeerosion in spite of presence of strong! incompressible strata such as sand! gravel! etc3I atshallo" depths3 %n such cases! piles can be particularl& eective in b&passing scourable strataand transferring loads to in erodible soil3Fig3 G3? Use of piles in scourable bedsdI
%n areas "here epansive or collapsible soil etends to considerable depth belo" theground! pile foundations ma& be needed to ensure safet& against undesirable seasonalmovements of foundations3
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*age
Fig3 G3G *iles in epansive soils can control seasonal movements*iles can be classi@ed according to the materials of "hich the& are made of3 The mainmaterials used in makings piles are timber! reinforced concrete and steel3 ,einforced concretepiles are generall& used in pile foundations for bridges3 $oncrete piles are either precast orcast-in-situ3 *recast piles are installed into the ground b& drilling! "hile cast-in-situ piles arebored pile3 Under-reamed pile is a special t&pe of bored pile having one or more bulbs3 Withthe presence of under-ream! substantial bearing or anchorage is available3 These piles @ndapplication in "idel& var&ing situations in dierent t&pes of soils "here foundations arereLuired to be taken do"n to a certain depth3
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Fig3 G3M Free Standing *ile )roup Fig3 G36 *iled Foundation G3D <+S%) CF *%(+ FCU
%f pile foundations are to be used for river bridge crossings! then the maimum scourdepth for the stream has to be determined3 The calculation of maimum scour depth isdiscussed in Section ?3?3= of $hapter ?3 For river bridge crossings! the top of the pile cap isplaced at the level of (3W3(3! "hile for non-river bridge crossings! the pile cap is full& buriedinto the ground "ith its top placed at ground level3 (ater! the forces and moments acting atthe top of pile cap i3e3 at the base of pier are calculated! during the anal&sis of pier3 Aftercalculating the forces and moments at the base of pier! the aial loads in the piles due toapplied forces and moments are determined for an assumed siQe and con@guration of piles ina pile group3 The assumed pile properties are subseLuentl& checked for safet&3 G3D3= U<+,-,+A'+< *%(+S The diameter of under-reamed piles in bridge applications is generall& not taken lessthan ?77 mm3 The length of the pile is selected as per the nature of the soil strata3 Foreample! if a "eak la&er is underlain b& a strong stratum at a reasonable depth! the length of the pile is so chosen such that the penetration of the pile into the strong stratum bearingstratumI is a minimum of M times the pile diameter or "idth3 Cn the other hand! if the "eak la&er etends to a considerable depth! the length of pile is so chosen as to obtain adeLuate pilecapacit& through skin resistance3The design of under-reamed piles can be carried out "ith the aid of Table = of %S8D>==*art %%%I =>N7 G 3 Table = of %S8 D>==*art %%%I
=>N7 G "hich is reproduced in toto asTable G3? in this thesis is a useful guide for selecting important parameter "3r3t3 under-reamedpiles viQ3
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lateral load carr&ing capacit&3 Usuall& a suitable value is selected as the diameter of the pileshaft3 The diameter of the under-ream is taken as D3M times the diameter of pile shaft3 *ilescan have one or more than one un der-reams! but it is not advisable to have more than t"ounder-reams on one pile "ithout ensuring their feasibilit& in strata needing stabiliQation of boreholes b& drilling mud3 For piles up to ?77 mm diameter! the spacing bet"een consecutiveunder-reams should not eceed =3M times the diameter of the under-ream3 For piles of diameter greater than ?77 mm! spacing can be reduced to =3DM times the stem diameter3 Thetop-most under-ream should be at a minimum depth of D times the under-ream diameterbelo" the ground3 %n epansive soils! the top-most under-ream should not be less than =3M mbelo" ground level3 $learance bet"een the underside of pile cap embedded in the ground andthe top under-ream should be minimum =3M times the under-ream diameter3 $olumns ?I #GI of Table G3? provide minimum length for single and double under-reamed piles!respectivel&3After @ing the dimensions of the underreamed pile! the load bearing capacit& of asingle under-reamed pile is estimated3 The pile capacit& is compared "ith the maimum loadepected on the pile to ensure an adeLuate margin of safet&3 G3D3D BC,+< $AST-%-S%TU *%(+S The s
afe bearing capacit& of a pile can be determined from its ultimate bearingcapacit&! b& using a suitable factor of safet&3 The methods available to estimate the ultimatecapacit& of a single pile in compression can be grouped into the follo"ing categories8i3
Static-in-situ test3ii3
Static anal&sis!iii3
<&namic anal&sis!The static-in-situ test! popularl& kno"n as pile load test! is the onl& direct method fordetermining the allo"able load on piles3 %t is considered to be the most reliable of all theapproaches! primaril& due to the fact that it is an in-situ test performed on a pile of protot&pepile dimension3 *ile load test is a costl& test and is used to con@rm "hether the actual pileinstalled in the @led can take the load predicted b& static or d&namic anal&sis3 <&namicanal&sis is used for determining ultimate capacit& of driven piles3 Static anal&sis! "hich is based on \soil mechanics[ approach provides approimate estimates of pil e capacit&! asvalues of a number of parameters appearing in the static formulae are assigned empiricall&3For bored piles! static anal&sis is performed3 A brief description of static anal&sis of piles ispresented net3A pile "hen loaded! transfers the load through skin friction along the length of the
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pile and through point bearing at the tip of the pile3Thus! the ultimate capacit& of a pile ma& be obtained as!! G3=I"here!0 total skin frictional resistance!0 total point bearing resistance!0 unit skin frictional resistance!0 unit point resistance!0 lateral surface area of the pile! and!0 area of the pile tip3Fig3 G3 (oad resisting mechanism in a pileThe unit frictional resistance! and the unit point bearing resistance! ! depend onman& factors such as the t&pe of soil! method of installation and the pile material3 Cf these!the method of pile installation aects the pile capacit& signi@cantl&! and also makes theestimation of pile capacit& more comple3 %n order to clearl& identif&
the eect of pileinstallation and account for the same! it is convenient to discuss separatel& the case of piles incohesion-less soils and cohesive soils3
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*iles in $ohesion-less soil8 As suggested in +L3 G3=! the pile capacit& can be obtained as the sum of point bearingresistance and skin friction resistance3 *oint Bearing ,esistance8 The unit point bearing resistance in cohesion-less soil is given b&!! G3DI"here! 0 eective overburden stress at the level of the pile tip!B 0 diameter or "idth of pile!0 densit& of the soil!0 shape factor! 73G for sLuare or rectangular piles! and!73? forcircular piles! and!# 0 bearing capacit& factors3The second term in +L3 G3D! is usuall& neglected! particularl& in the case of long piles! as this constitutes an insigni@cant part of the total capacit&3 The @rst term in +L3G3D implies that the base resistance increases linearl& "ith depth3 The bearing capacit& factor!is a function of the angle of internal friction of soil! ! and its value can be obtained fromFig3 = of %S8 D>== *art =I =>> ? ! reproduced here as Fig3 G3N3 The bearing capacit& factor!can also be read o from TableG3=3Fig3 G3N Bearing $apacit& Factor! for bored piles3
Activit& =7I
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