Sheet1DESIGN OF CANTILEVER RETAINING WALLData:-Height of Retaining wall(h) =3.20mHeight of wall above G.L=3.20mHeight of wall below G.L=0.00mDensity of back fill soil&material in toe portion(y) = 1800Kg/CumGrade of concrete =M25Grade of steel =Fe415Ground water Table level =Angle of shearing resistance of back fill material&material at toe portion(Q) = 30Angle of face of wall supporting earth with horizontal(a)(In degrees)87.36(in clock wise direction)Slope of back fill(b) =0Angle of wall friction (q) =15Undrained Cohesion ( c) =1600Kg/sqmSafe bearing capacity(SBC) =6500Kg/sqmSurcharge over the back fill(s) =0.60m(Assumed)Characteristic compressive strength =20N/sqmmTensile strength of steel =415N/sqmmUnit weight of RCC =2500Kg/CumUnit weight of PCC =2400Kg/Cum

Coefficient of active earth pressure by Coulomb's theory

Ka =Sin(a+Q)sina sin(a-q) sin(Q+q)sin(Q-b) sin(a+b)Sin(a+Q) =SIN[3.14*(85.58+30)/180] =0.902Sin(a-q) =SIN[3.14*(85.58-15)/180] =0.943Sina =SIN[3.14*(85.58)/180] =0.997Sin(Q+q) =SIN[3.14*(30+15)/180] =0.707Sin(Q-b) =SIN[3.14*(30-0)/180] =0.5Sin(a+b) =SIN[3.14*(85.58+0)/180] =0.997

From the above expression,

Ka =0.32

Dimensions of the Cantilever wall(Assumed for preliminary design):-

Thickness of base slab =0.30mWidth of the heel slab =2.00mThickness of stem at bottom =0.30mThickness of stem at top =0.15mLength of the toe =1.00m

3.20m

F G

C1.00m2.00m

Earth pressure at top including surcharge = Kays =345.6Kg/sqm

Earth pressure at bottom including surcharge = Kay(s+h) =2188.8Kg/sqm

Pressure distribution is as shown below:-

345.6

3.20m

2188.8345.6Area of the rectangular portion =1105.92Area of the triangular portion =3502.084608Taking moments of the areas about the toe of the wall

S.NoDescriptionAreaLever armMoment1Rectangular1105.921.61769.4722Triangular3502.081.06666666673735.552

4608.005505.024

Height from the bottom of the wall =1.19m

The active Earth pressure acts on the abutment as shown below:-

0.15

17.643.200m

1.19m

87.360.30m0.06Total earth pressure acting on the wall per 1m length P =4608.00Kg

Horizontal component of the earth pressure Ph =4391.55Kg

Vertical component of the earth pressure Pv =1395.70Kg

Eccentricity of vertical component of earth pressure = 0.09mTotal earth pressure = 4608.0Kg/mIt acts at a hieght of1.19mfrom the baseStability calculations:-Load(Kg)Lever arm about CMoment(Kg-m)Weight of the rectangular portion of stem =1200.00Kg1.081290.00

Weight of the rectangular portion of stem =600.00Kg1.20720.00

Wieght of base slab =2250.00Kg1.5003375.00

Wieght of soil on heel including surcharge = 12141.00Kg2.0024282.00Vertical component of earth pressure =1395.70Kg1.061479.4417586.70Kg31146.44

Note:-Weight of soil on the toe is neglected on the assumption that,it is scoured.Horizontal earth pressure force =4391.551.19m-5246.4325900.01

Lever arm x =M=1.47mVEccentricuty e = b/2-x =0.03m1.5 Hence,the structure is safe

Moment of overturning force,ie,Horizontal component of earth pressure about toe 'C' =5246.43Kgm

Moment of restoring forces about toe 'C' =31146.44Kgm

Factor of safety against overturning =5.94>2.0 Hence safe.Design of heel:-Length of heel =1.70mDownward load intensity due to self weight of base slab =2250.00Kg/m

Downward load intensity due to soil including surcharge =12141.00Kg/m

TOTAL14391.00Kg/m

The upward pressure distribution below the base slab is as given below:-

F G5510.50Kg/sqm

6213.97

1.00m0.30m1.70m

The upward pressure intensity at point 'F' is =5979.48Kg/sqm

The upward pressure intensity at point 'G' is =5909.13Kg/sqm

Total upward pressure force on heel portion due to soil reaction =9706.69Kg/m

The distance of centroid of upward soil reaction from 'G' is =0.84m

The distance of centroid of downward load intensity from 'G' is =0.85m

Resultant moment =4077.67Kg-m/m

Factored bending moment Mu =6116.51Kgm

Effective depth required d =Mu/0.138fckb =148.87mmOver all depth provided =300.00mmEffective depth provided(Assuming 50mm cover) d =242.00mmMu/bd2 =1.044From table 2 of SP 16,percentage of steel required =0.307Area of steel required =742.94sqmm

Hence provide 12mm dia HYSD bars@ 125mm c/c spacing

Hence Ast provided =904.32sqmmCheck for shear:-The critical section for beam shear is at distance of 'd' from the face of the support

Hence,the factored design shear force VFd =70.26KNat a distance 'd' from the face of the support

Nominal shear stress Tv =0.29N/sqmm0.29

Hence,the depth provided is safe from beam shear point of viewHence,no shear reinforcement is required.

Provide temperature re inforcement @ 0.15%

Area required =450.00sqmm

Taking 10mm dia HYSD bars,the spacing comes to 174.60mm

Hence provide 10mm dia bars @ 150mm c/c

Design of wall or stem:-

Factored bending moment Mu =7869.65Kgm

Effective depth required d =Mu/0.138fckb =168.86mm

Over all depth provided =300.00mm

Effective depth provided(Assuming 50mm cover) d =242.00mm

Mu/bd2 =1.344

From table 2 of SP 16,percentage of steel required =0.401

Area of steel required =970.42sqmmHence provide 12mm dia HYSD bars@ 100mm c/c spacing

Hence Ast provided =1130.40sqmmCheck for shear:-The critical section for beam shear is at distance of 'd' from the face of the support

Hence,the factored design shear force VFd =65.87KNat a distance 'd' from the face of the support

Nominal shear stress Tv =0.27N/sqmm0.27Hence,the depth provided is safe from beam shear point of viewHence,no shear reinforcement is required.

Provide temperature re inforcement @ 0.15%

Area required =337.50sqmm

Provide 1/3rd of above reinforcement on earthen side =112.50sqmm167.4666666667

Provide 8mm dia @ 200mm c/c on earthen side

Provide 2/3rd of above reinforcement on other side =225.00sqmm334.9333333333

Provide 8mm dia @ 150mm c/c on other side

Provide 10mm bars at 300mm c/c vertically on the outer face to support horizontal rods287.0857142857

Design of Toe:-Length of toe =1.00mDownward load intensity due to self weight =2250.00Kg/mDownward load intensity due to soil including surcharge =0.00Kg/m

TOTAL2250.00Kg/m

The upward pressure distribution below the base slab is as given below:-

F G5510.50Kg/sqm

6213.97

1.00m0.30m1.70m

The upward pressure intensity at point 'F' is =5979.48Kg/sqm

The upward pressure intensity at end of toe is =6213.97Kg/sqm

Total upward pressure force on heel portion due to soil reaction =6096.73Kg/m

The distance of centroid of upward soil reaction from 'F' is =0.50m

The distance of centroid of downward load intensity from 'G' is =0.50m

Resultant moment =1942.90Kg-m/mFactored bending moment Mu =2914.36KgmEffective depth required d =Mu/0.138fckb =102.76mmOver all depth provided =300.00mmEffective depth provided(Assuming 50mm cover) d =242.00mmMu/bd2 =0.498From table 2 of SP 16,percentage of steel required =0.142Min.percentage of steel as per IS 456 =0.15Area of steel required =363.00sqmmHence provide 12mm dia HYSD bars@ 150mm c/c spacing

Hence Ast provided =753.60sqmmCheck for shear:-The critical section for beam shear is at distance of 'd' from the face of the support

Hence,the factored design shear force VFd =57.70KNat a distance 'd' from the face of the support

Nominal shear stress Tv =0.24N/sqmm0.24Hence,no shear reinforcement is required.

Provide temperature re inforcement @ 0.15%

Area required =450.00sqmm

Taking 10mm dia HYSD bars,the spacing comes to 174.60mm

Hence,provide 10mm dia bars @ 150mm c/c

Sheet2

Sheet3