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1.0 Design of Counterfort Retaining wall (Empty condition)on D/S)

265.80

264.257

265.8

7.91 10.54

6.37 7.92 10.54

11.11

257.89

255.2652.625

3.160

3.20254.69 0.575

A

2.9 0.61 3.16

6.670

1.1 Design Constants

For M20 grade of concrete and HYSD reinforcement

cbc = 7

m = 280/(3* cbc)

= 13.3

st = 230.00

K = 1/(1+( st/ m. cbc)

= 0.29

j = 1-(K/3)

= 0.90

R = 1/2* cbc*j*K

N/mm2

N/mm2

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= 0.91

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Height of wall = 11.110 m

Safe bearing capacity = 250

Unit weight of soil = 18

Unit weight of concrete = 25

Unit weight of PCC = 24

Coefficient of friction betwwen soil & concrete = 0.58

Surcharge load assumed = 10

1.2 Preliminary Dimensions of the wall components.

1) Base Width = 0.6*H

= 0.6*11.11

= 6.670 m

2)Toe Projection = b *

Where = 1-(p/2.2 r H)

= 1-(250/2.2*18*11.11)

= 0.432

= b *

= 6.67*0.432

= 2.9 m

3)Clear spacing of counterforts = 3.5*(H/r)^1/4

= 3.5*(11.11/18)^(1/4)

= 3.1 m

B)Thickness of counterfort = 0.375 m

C/C spacing of counterfort

S = 3.48 m

Since the projection of the toe slab is large, provide counterforts over toe slab in front.

4)Thickness of stem = 0.610 m

5)Thickness of base slab = 0.575 m

Effective depth(assuming 12 mm ) = 519 mm

KN/m2

KN/m3

KN/m3

KN/m3

KN/m2

1W1 W2 W3AB 1

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1.3 Check for Stability of wall

A) Check against overturning

B) Check against sliding

C)Check against max. pressure at toe

A) Check against overturning

Description Magnituude of load (KN) Lever arm(point D) Mom

1 Wt of Stem wall 0.61*10.54*25*3.48

559.358 3.21

2 Wt of base slab 0.575*6.67*25*3.48

333.66675 3.34

3 3.16*10.54*18*3.48

2086.31 5.09

4 Wt. of PCC over Toe 2.625*2.9*24*3.48

635.80 1.45

5 Wt. of counterfort 0.5*3.16*10.54*(25-18)*0.375

43.71 4.56

6 Surcharge 3.16*3.48*10

109.97 5.09

Total 3768.82 1

Horizontal earth pressure on the full height of the retaining wall tend to overturn the wall

PH =

= 0.5*18*11.11^2*0.624*3.48

= 2412.317 KN

where =

= horizontal seismic coefficient

=

= 1 (Table3)

Wt. of earth over heelslab

1/2**H2*Ca*S

(Considering Earthquake effect w.r.t IS:1893-1984 )

Ca=(1+/-v)cos2()/cos.cos2.cos(++)*[1/1+(sin(+).sin(-i-)/cos(-i).cos(++)^0.5]2

v 0.5*h

h

*I*0

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I = 1 (Table4)

= 0.040 (Table2)

= 1*1*0.04

= 0.040

= angle of internal friction of soil

= 30 degrees

=

=

= 0.5*0.04

= 0.020

= tan-1(0.04/1+/-0.02)

= 0.039

= 2.247 = angle which earth face of wall mak

= atan(0/10.54) degrees

= 0 degrees

= slope of earthfill

= 26.10 degrees

= angle of friction between wall & ear

= 10 degrees

Ca = 0.624

Acting at = H/3 from A

= 11.11/3

= 3.703 m

h

tan-1 (h/ 1+/- v)

v 0.5*h

(h/ 1+/- v)

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Passive pressure = 1/2*Cp*r*H^2*S

= 0.5*3.93*18*3.2^2*3.48

= 1260.42 KN

where = 0 degrees = 0 degreesCp = 3.930

Acting at = H/3

= 3.2/3

= 1.07 m

1) Moment due to PH = 2412.317*3.703

= 8933.62 KN-m

2)Moment due to passive pressure = 1260.417*1.07

= 1344.44 KN-m

Overturning Moment = 8933.62-1344.445

= 7589.17 KN-m

Factor of Safety =

= 15205.979/7589.171

= 2.004 Safe

B) Check against sliding

Total horizontal force tending to slide the wall

= 2412.317 KN

Total force opposing sliding = * W

= 0.58*3768.82

= 2185.913 KN

Factor of Safety = * W /PH

= 2185.91/2412.317

= 0.906 Safe

C)Check against max. pressure at toe

Cp=(1+/-)cos2(+)/cos.cos2.cos(+)*[1/1-(sin(+).sin(-i-)/cos(-i).cos(+)^0.5]2

MR/Mo

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Net moment or algebraic sum of moments about A

= MR-MO

= 15205.979-7589.171

= 7616.81 KN-m

Let x be the distance from toe(A) at which the resultant reaction acts

x =

= (15205.979-7589.171)/3768.816

= 2.02 m

Eccentricity (e) = (b/2)-e

= 6.67/2-2.02

= 1.31

= V/A(1+6*e/b)

= 354.29

= V/A(1-6*e/b)

= -29.55

The intensity of pressure at junction of stem with toe

= -29.55+(354.29--29.55)/6.67*(6.67-2.9

= 187.40

The intensity of pressure at junction of stem with heel

= -29.55+(354.29--29.55)/6.67*(6.67-2.9-0.61

= 152.30

1.4 Pressure Diagram

MR-M

O/ W

Pmax

at toe (A)

KN/m2

Pmin

at Heel

KN/m2

KN/m2

KN/m2

J

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0.61

0.575

2.9 3.2

-29.55

354.29

187.40 152.30

W1 W2W3 A B

BG

C

D

FF

E

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11.11

KN/m2

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(KN-m)

.74

.78

9.33

.90

.48

.74

5.98

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h vertical

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Density of soil= 15

angle repose= 30

Coefficent of active pressure= 0.333333

density of concrete 25

grade of steel = 500

grade of concrete= 30

design parameters

st= 130

cbc 10

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Kn/m2

degrees

Kn/m2

M Pa

M Pa