250223553-rcc-retaining-walls.xlsx

Design of RCC Retaining Wall Density of concrete Use Grade of concrete Steel grade Angle of repose of earth

= = = =

25 kN/m3 M 25 Fe 500 30 °

γ

=

20 kN/m3

Safe bearing capacity of foundation soil δ

= =

280 kN/m2 45 °

Fck

=

25 N/mm2

Fy

=

500 N/mm2

Density of back fill

= 32 mm = 40 mm = 32 + 40 / 2 = 52 mm

Dia of rod

Clear cover Consider rod dia Effiective cover Stem/Wall

Overall depth of wall " D " Effiective deprh " d "

= =

1200 mm 1148 mm

= =

900 mm 848 mm

Toe/Heel slab

Overall depth of slab " D " Effiective deprh " d "

451.113

0.3 45 ⁰

447.563

h1 7.321

3.55 m

w1 H 12.071 Stem

h 8.521

440.242

w2 0.3

Toe

0.9

1.2

2.4

439.942 Heel

h2 1.2

w3 0.9 w4

0.5

d

c 4.5

439.042

i. Stability Analysis Weight of wall

w1

= = =

0.3 x 7.621 x 1 x 25 53.03 kN 2.55 m

w2

= = =

0.5 x 0.9 x 7.621 x 1 x 25 114.32 kN 3m

w3

= = =

4.5 + 1.2 x 0.5 x 0.4 x 1 x 25 28.5 kN 2.25 m

w4

= = =

4.5 x 0.5 x 1 x 25 56.25 kN 2.25 m

Pa

= = = =

1/2 Ca γ H2

Leaverarm from point c Weight of wall Leaverarm from point c Weight of foundation Leaverarm from point c Weight of foundation Leaverarm from point c Preassure behind the wall Earth pressure coefficent

Ca H Pa

0.232 12.071 m 338.04 kN/m

Horizontal component

Ph

= =

Pa cos δ 292.75 kN

Vertical component

Pv

= =

Pa sin δ 239.03 kN

S.no 1 2 3 4 5 6

Loads

Magnitude of the load in kN

Distance fro c in m

Moment about c kN.m

w1 w2 w3 w4 Pv Moment of Ph Total

53.03 114.32 28.5 56.25 239.03 292.75 783.88

2.55 3 2.25 2.25

135.23 342.96 64.13 126.56

4.02

1176.86 1845.74

Resultant force on the wall meet the base at distance z from the heel end a z = 1845.74 / 783.88 = 2.35 m Eccentracity e = z - b/2 = 0.1 m But e < b/6 0.1 m < 0.75 m

i. Check for bearing pressure Pressure at the toe and at the heel are given by P

=

W/bl(1±6e/l)

Pmax

=

197.42 Kn/m2

Pmin

=

150.97 Kn/m2

15.097 t/m2 19.742 t/m2 ii. Factor of safety against overturning z Resisting moment about d

= =

2.35 m 1842.118 kN.m

Overturning moment about d

=

1176.86 kN.m

Factor of safety against overturning

= =

1842.118 1176.86 1.57

iii. Factor of safety against sliding Forces causing sliding Frictional force (µ W) µ = 0.55

= =

544.85 kN 299.67 kN

Factor of safety against sliding

=

299.67 292.75 1.02

= This is lessthan 1.5. Hence a Key shoild be provided

>

1.5 O.K

>

1 O.K

iv. Design of the stem/wall Bending moment for the stem per metre run M

Factroed B.M "M"

= = =

Ca γ h3/6 0.232 x 20 x 7.621 x 7.621 x 7.621 / 6 1026.89 kN.m

= 1.5 x 1026.89 = 1540.335 kN.m = 1540335000 = M 0.133 x Fck x b 1540335000 = 0.133 x 25 x 1000

Effective depth required " d² "

d² d

= 463258.647 = 680 mm

N.mm

Hence provide effective depth Main reinforcement Consider dia of bar

=

1148 mm

=

Ast Req

32 mm 1.5 x M = 0.87 x Fy x d ( 1 - 0.42 x 0.46)

Ast Req

1.5 x 1026.89 x 1000000 = 0.87 x 500 x 1148 x 0.8068 = 3823.12 mm²

For 32 mm dia bars "As" Spacing of bars " S " = 1000 As/Ast Req

803.84 mm² = 1000 x 803.84 / 3823.12 = 210.26 mm say 210 mm Provided steel reinforcement Ast Pro = 1000 As/S = 1000 x 803.84 / 210 = 3827.81 mm² HENCE SAFE Provided steel reinforcement 32 mm @210 mm c/c =

Distribution reinforcement Consider dia of bar Ast Req (As per clause 40.1 of IS 456-2000)

= 16 mm = 0.12 % BD = 0.0012 x 1000 x 1200 = 1440 mm²

Ast Req For 16 mm dia bars "As" = Spacing of bars " S " = 1000 As/Ast Req = Provided steel reinforcement

200.96 mm² 1000 x 200.96 / 1440 = 139.56 mm say = 1000 As/S = 1000 x 200.96 / 135 = 1488.59 mm²

Ast Pro

135 mm

HENCE SAFE Provided steel reinforcement 16 mm @135 mm c/c v. Design of the toe and Heel slab

0.9 m

1.2

2.4 m

Toe

c

d

b

i f e

160.96 Kn/m2

Heel

15.097 Kn/m2

j

197.42 Kn/m2

a h

g

112.34 Kn/m2

e 4.5 m Bending Moment Calculation of the toe slab

Loads

Magnitude of the load in kN

Distance fro c in m

Moment about c kN.m

1

Upward pressure cdif

144.86

0.45

65.19

2

Upward pressure efi

16.41

0.60

9.84

Deduct dead load 3 of the slab B.M for toe slab

17.00 178.27

0.45

7.65 82.68

S.no

Factroed B.M "M"

= 1.5 x 82.68 = 124.02 kN.m = 124020000 = M 0.133 x Fck x b 124020000 = 0.133 x 25 x 1000

Effective depth required " d² "

d² d Hence provide effective depth

= 37299.248 = 193 mm = 848 mm

Main reinforcement Consider dia of bar

=

N.mm

Ast Req

12 mm 1.5 x M = 0.87 x Fy x d ( 1 - 0.42 x 0.46)

Ast Req

1.5 x 82.68 x 1000000 = 0.87 x 500 x 848 x 0.8068 = 416.72 mm²

For 12 mm dia bars "As" Spacing of bars " S " = 1000 As/Ast Req

113.04 mm² = 1000 x 113.04 / 416.72 = 271.26 mm say 245 mm Provided steel reinforcement Ast Pro = 1000 As/S = 1000 x 113.04 / 245 = 461.39 mm² HENCE SAFE Provided steel reinforcement 12 mm @245 mm c/c =

Bending Moment Calculation of the heel slab

S.no

Loads

Magnitude of the load in kN

Distance fro c in m

Moment about c kN.m

1 2

Weight of backing Surcharge

457.26 85.20

1.2 1.6

548.71 136.32

3

Weight of heel slab

42.00

1.2

50.40

4

5

Total load

584.46

735.43

Deduct for upward pressure abjh

36.23

1.2

43.48

Deduct for upward pressure gih Total deduction

116.69 152.92

0.8

93.35 136.83

B.M for heel slab

Factroed B.M "M"

598.60

Hence provide effective depth

= 1.5 x 598.59936 = 897.89904 kN.m = 897899040 = M 0.133 x Fck x b 897899040 = 0.133 x 25 x 1000 = 270044.824 = 519 mm = 848 mm

Main reinforcement Consider dia of bar

=

Effective depth required " d² "

d² d

N.mm

Ast Req

25 mm 1.5 x M = 0.87 x Fy x d ( 1 - 0.42 x 0.46)

Ast Req

1.5 x 598.59936 x 1000000 = 0.87 x 500 x 848 x 0.8068 = 3017.01 mm²

For 25 mm dia bars "As" Spacing of bars " S " = 1000 As/Ast Req Provided steel reinforcement

490.625 mm² = 1000 x 490.625 / 3017.01 = 162.62 mm say 160 mm Ast Pro = 1000 As/S = 1000 x 490.625 / 160 = 3066.41 mm² HENCE SAFE =

Provided steel reinforcement 25 mm @160 mm c/c

Distribution reinforcement Consider dia of bar Ast Req (As per clause 40.1 of IS 456-2000)

= 12 mm = 0.12 % BD = 0.0012 x 1000 x 900 = 1080 mm²

Ast Req For 12 mm dia bars "As" = Spacing of bars " S " = 1000 As/Ast Req = Provided steel reinforcement

113.04 mm² 1000 x 113.04 / 1080 = 104.67 mm say = 1000 As/S = 1000 x 113.04 / 100 = 1130.4 mm²

Ast Pro

100 mm

HENCE SAFE Provided steel reinforcement 12 mm @100 mm c/c vi. Design of the key To provide a FOS of 1.5, the wall should be designed to remain in limiting equilibrium when the horizontal force on the wall is increased to 1.5 Ph 1.5 Ph Limiting friction force Unbalanced force

F

Safe horizontal soil pressure

1.5 x 292.75

= = = = = = =

439.125 kN 299.67 kN

439.125 - 299.67 139.455 kN 0.7 x SBC

0.7 x 280

=

196 Kn/m2

Let the height of the key 196 x y y Say

= = =

139.455 0.71 m 0.75 m

Maximum bending moment for the key M

Thickness of shear key proposed Dia of rod

Clear cover Consider rod dia Effiective cover

= = =

Wl / 2

139.455 x 0.75 / 2 52.3 Kn.m

=

300 mm

= 32 mm = 40 mm = 32 + 40 / 2 = 52 mm

Shear key

Overall width " D " Effiective deprh " d "

= =

300 mm 248 mm

Factroed B.M "M"

= 1.5 x 52.3 = 78.45 kN.m = 78450000 = M 0.133 x Fck x b 78450000 = 0.133 x 25 x 1000

Effective depth required " d² "

d² d Hence provide effective depth

= 23593.985 = 153 mm = 248 mm

Main reinforcement Consider dia of bar

=

N.mm

Ast Req

16 mm 1.5 x M = 0.87 x Fy x d ( 1 - 0.42 x 0.46)

Ast Req

1.5 x 52.3 x 1000000 = 0.87 x 500 x 248 x 0.8068 = 901.33 mm²

For 16 mm dia bars "As" Spacing of bars " S " = 1000 As/Ast Req

200.96 mm² = 1000 x 200.96 / 901.33 = 222.96 mm say 220 mm Provided steel reinforcement Ast Pro = 1000 As/S = 1000 x 200.96 / 220 = 913.45 mm² HENCE SAFE Provided steel reinforcement 16 mm @220 mm c/c Distribution reinforcement Consider dia of bar Ast Req (As per clause 40.1 of IS 456-2000)

= 10 mm = 0.12 % BD = 0.0012 x 1000 x 300 = 360 mm²

Ast Req For 10 mm dia bars "As" = Spacing of bars " S " = 1000 As/Ast Req = Provided steel reinforcement

=

Ast Pro

78.5 mm² 1000 x 78.5 / 360 = 218.06 mm say = 1000 As/S = 1000 x 78.5 / 215 = 365.12 mm²

HENCE SAFE Provided steel reinforcement 10 mm @215 mm c/c

215 mm

0

3

4 Toe 1

d

Density of concrete Use Grade of concrete Steel grade Angle of repose of earth Density of back fill

Safe bearing capacity of foundation so i. Stability Analysis Weight of wall Leaverarm from point c Weight of wall Leaverarm from point c Weight of foundation Leaverarm from point c

Weight of foundation Leaverarm from point c Earth surcharge weight Leaverarm from point c Earth pressure P1 due tosurcharge

Leaverarm from point c Earth pressure P2

Leaverarm from point c Let x be the distance from c of the poin

Eccentracity

ii. Factor of safety against overturnin Resultant of vertical forces from c lies

Resisting moment about d Overturning moment about d Factor of safety against overturning

iii. Factor of safety against sliding Forces causing sliding Frictional force Factor of safety against sliding

iv. Check for bearing pressure Pressure at the toe and at the heel are g

11.886 v. Design of stem Preassure behind the wall Earth pressure coefficent

Horizontal component of pressure

Bending moment at base of the vertica

Considering 1 m width of the vertical s

Using partial factor of 1.5 on the horizo

Effective depth required Depth of stem at base Assume dia of bar Clear cover Effective depth provided Area of tension steel is given by

Main Reinforcement Use 32

32

Provided steel reinforcement

Distribution Reinforcement Use 10

Check for shear

The shear strength of M The critical section for shear strength i

Factored shear force Nominal Shear stress

vi. Design of toe Dead load of foundation Overall depth Clear cover Assume dia of bar Effective depth

118.86

Using partial factor of 1.5 on

Effective depth required Effective depth provided

For 16 Spacing of bars " S " = 1000 As/Ast R Provided steel reinforcement

Check for shear The shear strength of M Factored shear force Nominal Shear stress

vii. Design of heel Dead load of foundation Earth surcharge load

Using partial factor of 1.5 on

Effective depth required Effective depth provided

For 32 Spacing of bars " S " = 1000 As/Ast R Provided steel reinforcement

Check for shear The shear strength of M Factored shear force Nominal Shear stress

0.3 10 °

w1 Stem w2 0.4 1.5

0.45

2.2 Heel

w3 0.6 w4

0.3 c 4.15

of concrete ade of concrete

= = = =

25 kN/m3 M 30 Fe 500 22 °

γ

=

20 kN/m3

aring capacity of foundation soil

= =

300 kN/m2 10 °

f repose of earth of back fill

δ

lity Analysis w1

= = =

0.3 x 3.4 x 1 x 25 25.5 kN 2.5 m

w2

= = =

0.5 x 0.15 x 3.4 x 1 x 25 6.375 kN 2.3 m

w3

= = =

4.15 + 0.45 x 0.5 x 0.3 x 1 x 25 17.25 kN 2.425 m

rm from point c

rm from point c

of foundation

rm from point c

of foundation

w4

rm from point c

urcharge weight

rm from point c ressure P1 due tosurcharge

rm from point c

= = =

4.15 x 0.3 x 1 x 25 31.125 kN 2.075 m

= = = = = = =

3.4 x 2.2 x 1 x 25 187 kN 1.1 m Ca γ h1 h2 0.488 x 20 x 4.15 x 4 162.02 kN 1.33 m 1/2 Ca γ h22

= = 0.5 x 0.488 x 20 x 4 x 4 = 78.08 kN rm from point c = 1.33 m e the distance from c of the point where the resultant force strikes the base x = 2.660 m e 6e base length

= = = =

or of safety against overturning nt of vertical forces from c lies at a distance =

x - b/2 0.585 m 6 x 0.585 4.15 0.85 m < Hence ok

g moment about d

= =

390.5281 267.25 1.46 m 718.9025 kN.m

ning moment about d

=

319.333 kN.m

of safety against overturning

= =

718.9025 319.333 2.25

tor of safety against sliding causing sliding (µ W) µ = 0.45

= =

80.25 kN 120.2625 kN

of safety against sliding

=

120.2625 80.25

1

=

ck for bearing pressure e at the toe and at the heel are given by P

=

1.5

W/bl(1±6e/l)

Pmax

=

118.86 Kn/m2

Pmin

=

9.93 Kn/m2

0.993 t/m2 t/m2

re behind the wall

ressure coefficent

ntal component of pressure

Pa Ca h Pa Ph

g moment at base of the vertical wall

= = = =

1/2 Ca γ h2

= =

Pa cos δ 55.55 kN/m

= =

Ph h/3

0.488 3.4 m 56.41 kN/m

62.96 kN.m/m

ering 1 m width of the vertical slab, its thickness is given by,

B.M = 0.138 Fck bd2 artial factor of 1.5 on the horizontal earth pressure 1.5 x 62.96 x 1000000 = 0.138 x 30 x 1000 d2

e depth required f stem at base

d2 d D ɸ

e depth provided tension steel is given by

d AtReq

Reinforcement mm dia steel at

= = = = = = = = = 160 mm c/c

22811.59 151 mm 450 mm 32 mm 25 mm 409 mm 0.36 fck b Xm 0.87 Fy 0.36 x 30 x 1000 x 0.48 x 409 0.87 x 500 4874 mm2/m

mm dia bar area

As AtPro

= = = = Say

803.84 mm2 1000 As/Ast Req 1000 x 803.84 / 4874 164.92 mm 160 mm

Provided steel reinforcement Ast Pro = =

1000 As/S 1000 x 803.84 / 160

= 5024 mm2/m HENCE SAFE

ution Reinforcement mm dia steel at At At 0.12 %

160 mm c/c = 0.785 x 10 x 10 / 160 / 409 x 100 = 0.12 % > 0.12 %

τc shear strength of M 30 = 0.54 N/mm2 ical section for shear strength is taken at a distance d from the bottom stem 1/2 Ca γ h2 cosδ Shear force V = h

Factored shear force

V Vu τv

l Shear stress

τc

ad of foundation D ɸ d

= = = = = =

= 0.16 N/mm2 τv > HENCE OK

= = = = = =

0.991 Critical Shear

509 1500

3.4 - 0.409 2.991 m 42.99 kN 1.5 x 42.99 64.485 kN Vu/bd

11.66 kN/m 600 mm 75 mm 32 mm 600 - 75 - 16 509 mm 2.459

509 450

2200

9.93 Kn/m2 Kn/m2 92.848

54.316

Vu Mu

= =

93.35 kN 105.84 kN.m

B.M = 0.138 Fck bd2 Using partial factor of 1.5 on the horizontal earth pressure 1.5 x 105.84 x 1000000 = 0.138 x 30 x 1000 d2 Effective depth required Effective depth provided Ast Req

d2 d d

= = = =

38347.83 196 mm 509 mm Mu 0.87 x Fy x d ( 1 - 0.42 x 0.46)

=

158.76 x 1000000 0.87 x 500 x 509 x 0.8068 888.73 mm² 200.96 mm² 1000 x 200.96 / 888.73 226.12 mm say 225 mm 1000 As/S 1000 x 200.96 / 225 893.16 mm²

Ast Req mm dia bars "As" of bars " S " = 1000 As/Ast Req

= = = = d steel reinforcement Ast Pro = = = HENCE SAFE Provided steel reinforcement 196 mm @225 mm c/c

shear strength of M 30 Factored shear force

τc

l Shear stress

τv

ad of foundation urcharge load

Vu

τc

= = = =

0.54 N/mm2 1.5 x 93.35 140.025 kN Vu/bd

= 0.28 N/mm2 τv > HENCE OK

= =

11.66 kN/m 187 kN/m

Vu Mu

= =

351.69 kN 410.14 kN.m

B.M = 0.138 Fck bd2 Using partial factor of 1.5 on the horizontal earth pressure 1.5 x 410.14 x 1000000 = 0.138 x 30 x 1000 d2 Effective depth required Effective depth provided Ast Req

d2 d d

= = = =

148601 385 mm 509 mm Mu 0.87 x Fy x d ( 1 - 0.42 x 0.46)

=

615.21 x 1000000 0.87 x 500 x 509 x 0.8068 3443.9 mm² 803.84 mm² 1000 x 803.84 / 3443.9 233.41 mm say 230 mm 1000 As/S 1000 x 803.84 / 230 3494.96 mm²

Ast Req mm dia bars "As" of bars " S " = 1000 As/Ast Req

= = = = d steel reinforcement Ast Pro = = = HENCE SAFE Provided steel reinforcement 385 mm @230 mm c/c

shear strength of M 30 Factored shear force

τc

l Shear stress

τv

Vu

τc

= = = =

0.54 N/mm2 1.5 x 351.69 527.535 kN Vu/bd

= τv > UNSAFE

1.04 N/mm2

cos 10 0.984808 cos 22 0.927184

0 0.991

118.86 92.848

1.5

79.488

1.95 2.459 4.15

67.676 54.316 9.93