DesignDESIGN OF CANTILEVER RETAINING WALLA)Data:-Height of Retaining wall =4.50mHeight of wall above G.L=4.50mHeight of wall below G.L=0.00mDry density of back fill material =1600Kg/CumWater content =0.23mDensity of back fill soil&material ( Submerged unit weight) =1968Kg/CumGrade of concrete =M25Grade of steel =Fe415Ground water Table level (Below G.L) =1.20mAngle of shearing resistance of back fill material&material at toe portion() (As per report) =32Angle of face of wall supporting earth with horizontal()(In degrees)87.5(in anti clock wise direction)Slope of back fill() =0Angle of wall friction () =16Surcharge over the back fill in terms of height of back fill =1.20mUndrained Cohesion ( c) =0Kg/sqmCharacteristic compressive strength =25N/sqmmTensile strength of steel =415N/sqmmUnit weight of concrete =2500Kg/CumB)Dimensions of the Cantilever wall(Assumed for preliminary design):-Thickness of stem at bottom =0.40mThickness of stem at top =0.20mThickness of base slab =0.40mBreadth of beam =0.45mDepth of beam =0.60mDia of Bored Cast-in situ straight pile assumed =0.50mDepth of pile =5.00mC/c spacing of piles in transverse direction =1.50mC/c spacing of piles in longitudinal direction =2.00mC)Design:-i)Earth pressure calculations:-Coefficient of active earth pressure by Coulomb's theory2Ka =Sin(+)sin sin(-)sin(+)sin(-)sin(+)From the above expression,Ka =0.3Hence,maximum pressure at the base of the wallPa =2656.80Kg/sqmThe pressure distribution along the height of the wall is as given below:-Pressure due toSurcharge load =708.48708.484.50m2656.80Total Active earth pressure force =9165.96Height from the bottom of the wall =1.76mThe active earth pressure acts on the wall as shown below:-Horizontal component of the earth pressure Ph =8692.77Kg/mVertical component of the earth pressure Pv =2906.98Kg/mii)Intial proportioning of the structure :-In view of the very poor bearing capacity of the soil,either gravity or cantilever retaining walls arenot economical.It is proposed to support the wall on base slab supported by longitudinal beams,which aresupported on piles.As per the clause 5.6.2 of IS 2911(1)-1,the minimum spacing between friction piles should not be less than3 times the diametre of the shaft,hence transverse spacing of 1.35m is adopted.Hence,total width of the pile cap =2.30mTwo rows of 450mm dia Bored cast-in-situ straight piles are proposed at spacing of2.00min longitudinaldirectionComputation of total vertical load on the pile :-i)Self weight of pile =2453.13kgii)Self weight of wall(2.00m length on two piles) =3375.00kgiii)Self weight of pile cap =2300.00kgiv)Self weight of beam =500.00kgv)Weight of earth on heel side =8413.20kgvi)Weight of earth on toe side =1003.68kg18045.01kgThe total lateral load due to earth pressure on the wall =17385.55KgDeduct lateral force to be resisted by the pile cap-cum-beam system =-2361.60Kg15023.95KgHence,the pile needs to be designed for safe vertical load carrying capacity of18.05tSimilarly,it needs to be designed for lateral load carrying capacity of7.51tii)Design of pile :-a)Safe vertical load carrying capacity:-To estimate the safe bearing capacity of pile, the ultimate bearing capacity of pile is calculated. Staticformulae are used in estimating ultimate bearing capacity of pile.As per Appendix A of IS 2911(1)-1Ultimate bearing capacity of a pile is given by,Qu = Qs + QpWhere Qs = Skin frictional resistance,Qp = End bearing resistanceIn the present case,the pile passes through the fine sand for a depth of 8.40m(As per soil testing report)Qs = fs x Asfs = K Pdi tanWhere,K = coefficient of earth pressure;Pdi = average effective overburden pressure in kgf/cm = angle of wall friction between pile and soil in degrees(To be taken equal to )As = surface area of pileEffective overburden preesure at top of the pile =960.00Kg/sqmEffective overburden preesure at the level of pile tip =5598.40Kg/sqm(Upto Water Table + After water table)Average effective overburden pressure along pile shaft Pdi =3279.20Kg/mHence Qs =4822.52kgQp = qp x Apqp = Pdi (Nq-1)Where,Pdi = Effective overburden pressure at tip of the pile in kgf/cmNq = Bearing capacity factor as per Fig.1 of IS 2911(1)-1Ap = End bearing area of pileNq =40Pdi =5598.4Kg/sqmAp =0.20sqmHence,Qp =43667.52kgUltimate bearing capacity of pile =48490.04kgApplying a factor of safety of 2, allowable safe bearing capacity =24.25tb)Lateral load carrying capacity:-Case1:- Pile considered as short fixed head pile embedded in cohesion less soilThe pile considered as short restrained(Fixed head) pile embedded in cohesionless soil.As per Broom'stheory,failure takes place when the load applied to the pile is equal to the ultimate lateral resistance of the soilPu = 1.5 L2 d KpWhere,L = Length of embeddmentd = Diametre of pileKp = Coefficient of passive earth pressureHence Pu =100000.00kgSafe lateral load carrying capacity =33.33t(Applying a factor of safety of 3)Case2:- Pile considered as short fixed head pile embedded in normally consolidated clayThe lateral load capacity of the pile is estimated as per the layer of soil situated at the ground level, as itwill have the major contribution in the lateral load capacity of pile.As the top most soil layer is normally consolidated clay,T = 5(EI/h)E = 5000fck =25000000I =0.00307m4For medium sand h =5260.00KN/cumT =1.71From Figure 2 of IS: 2911 (Part 1)-19793, depth of fixity Lf =2.500mAs the pile is short pile,the length of fixity is greater than the actual length,hence actual length is to beconsidered for design.Hence,lateral load capacity of fixed head pile is calculated as,Q = 12EIY/L3where, Y = limiting lateral deflection of pile head = 5 mm for bridge substructuresHence Q =294.72KN29.47tLoad carrying capacity is taken as average of the above two values31.40tc)Structural design of pile:-Now,the fixed end moment of the equivalent cantilever is given byMu = Q(Lf)/2 =9.39t-m=93.90KNmApplying a reduction factor of 0.82 as per IS 2911(PartI)-I,the moment =77.00KNmThe pile is to be designed for axial load Pu =270.75KNand moment of Mu =115.50KNmAssuming percentage of steel p =0.75p/fck =0.03Pu/fckD2 =0.043Mu/fckD3 =0.037d'/D =0.15Area of steel required =1471.88sqmmUsing 16mm dia HYSD bars,No.of bars required for each pile =7.3242436306Hence provide 8 Nos of 16mm dia bars for each pileProvide 8mm ties at 200mm c/cHence,the safe lateral load carrying capacity of pile is31.40tThe passive earth pressure on grade beam = Kph =3936.00Kg/sqmPassive earth pressure force for 2.0m length =2361.60Kg2.36tHence,the total lateral load carrying capacity of the structure is65.16tThe total lateral load due to active earth pressure =17385.55Kg17.39t< 65.16tHence safe.Centre to centre spacing between two rows of 500mm dia piles =1.50mHence,the over all width of the base slab =2.30mDesign of wall or stem:-Factored bending moment Mu =22960.26KgmEffective depth required d =Mu/0.138fckb =257.98mmOver all depth provided =400.00mmEffective depth provided(Assuming 40mm cover) d =352.00mmMu/bd2 =1.853From table 2 of SP 16,percentage of steel required =0.566Area of steel required =1992.32sqmmHence provide 16mm dia HYSD bars@ 100mm c/c spacingHence Ast provided =2009.60sqmmCurtail 1/3rd of the reinforcement from half of the heightCheck for shear:-Percentage of tension steel =0.57Maximum shear force on the member =86.93KNFactored Design shear force =130.39KNNominal shear stress tv =Vu/bd =0.37 N/sqmm 0.37Hence,no shear reinforcement is required.Provide temperature re inforcement @ 0.12%Area required =360.00sqmmProvide 1/3rd of above reinforcement on earthen side =120.00sqmmProvide 8mm dia @ 300mm c/c on earthen sideProvide 2/3rd of above reinforcement on other side =240.00sqmmProvide 8mm dia @ 200mm c/c on other sideProvide 10mm bars at 300mm c/c vertically on the outer face to support horizontal rodsDesign of base slab:-Thickness of base slab assumed =0.40mThe loading on the base slab can be approximated as shown below:-Wt.of wall =3375.00Kg/m33.75Earth pressure =8692.77Kg/mSelf weight =1000.00kg/m/mWt.of earth =8856kg/m/m1.76mRARB0.40.690.810.415306.83879454550.85Analysis is carried out assuming fixed supports to arrive at max.hogging moment,further supportsare assumed to be hinged to arrive at max.sagging moments.After analysis,RA =12.540kNRB =141.170kNThe bending moment diagram is as shown below:-100.12Knm100.12KnmMoment at A =8.64KnmMoment at B =36.24KnmFactored bending moment Mu =150.18KnmEffective depth required d =Mu/0.138fckb =208.64mmOver all depth provided =400.00mmEffective depth provided(Assuming 40mm cover) d =355.00mmMu/bd2 =1.192From table 2 of SP 16,percentage of steel required =0.353Area of steel required =1253.15sqmmHence provide 16mm dia HYSD bars@ 150mm c/c spacingHence Ast provided =1339.73sqmmCheck for shear:-Percentage of tension steel =0.38Maximum shear force on the member =141.17KNFactored Design shear force =211.76KNNominal shear stress tv =Vu/bd =0.60 N/sqmm 0.17Hence,no shear reinforcement is required.Provide same reinforcement at bottom also.Provide 10mm dia bars @150mm c/c at top&bottomas distribution reinforcement .Design of beam:-Breadth of the beam assumed =0.45mDepth of the beam assumed =0.60mUDL on beam :-Due to self weight of slab =1150.00Kg/mDue to weight of retained earth =8413.20Kg/m9563Kg/mTwisting moment on beam :-Due to earth pressure(Distributed to both beams) =7653.42Kgm2.00mAfter analysis,the bending moment diagram is31.90Knm15.90KnmFactored bending moment Mu =47.85KnmTorsional Moment 'T' in KN-m114.80KnmEquivalent bending moment Mt in KN-m157.57KnmDesign Moment Me1 in KN-m205.42KnmEffective depth required d =Mu/0.138fckb =363.75mmOver all depth provided =600.00mmEffective depth provided(Assuming 40mm cover) d =552.00mmMu/bd2 =1.498From table 2 of SP 16,percentage of steel required =0.449Area of steel required =1115.32sqmmHence provide 4 Nos of 20mm dia HYSD bars both at top&bottomProvide 2-12mm dia on each face as side face reinforcementHence Ast provided =1256.00sqmmPercentage of tension steel =0.51Maximum shear force on the member =46.40KNFactored shear force =69.60KNDesign shear force including equivalent shear due to torsion =477.78KNNominal shear stress tv =Vu/bd =1.92 N/sqmm