Design of Retaining Wall

DESIGN OF RETAINING WALL FOR RAMALINGESWARA NAGAR STPs Design of Retaining Wall – 7.50Mts. Height: Total height of retaining wall Base width Toe projection Width of Counter forts Thickness of stem Spacing between counter forts Height of earth filling on heel Sl. No 1. 2. 3.

Force W1=Wt of back fill W2 = Wt. of Stem Wt. of base Slab=W3

= = = = = = =

7.50m 4.50m 1.00m 0.50m 0.50m 3.00m 6.50m

Magnitude in KN 3.0 x 6.5 x 18 = 351.0 0.5 x 7.5 x 25 = 93.75 0.5 x 4.5 = 56.25

From toe x (m) 3.00 4.5 --- = 3.0 2 1.25 2.25 Total

M (KN-m) 1053 117.19 126.56 1296.75

Total Weight Stabilising moment

= 351 + 93.75 + 56.25 = 501.0 x N Ms = = 1297.0 KN-m 2 P = 1/2 x Ca x r x H M = P x H/3 M = 1/2 x 1/3 x 18 x 83/3 Overturning moment due to horizontal back fill earth pressure Mo = 1/3 x 18 x 73/6

=

343 KN-m

Total over turning moment Mo

=

343 KN-m

Factor of safety against overturning

= 0.9MS ------Mo

=

0.9 x 1297 -----------343

= 3.40 > 1.4 Hence O.K Sliding force

Resisting force

=

1 1 -- -- 18 x 72 = 2 3

= 0.5 (0.9 x 501) =

147 KN 225.45 KN

Factor of safety against sliding 225.45 -------- = 1.53 > 1.4 147

1

However, Shear Key is provided. Provide a raft beam with piles @ 3 m C/c of 450mm dia with 7-12 mm dia as main steel and 8mm stirrups @ 200 C/C and 5-12mm dia. at top & bottom with 8mm dia. stirrups @ 150mm C/c for raft beam. PRESSURE FROM SOIL: Total moment about ‘O’

= 1297 - 343 = 954 KN-m

Horizontal distance at which resultant intercepts base = 954 ---501

=

1.90

e = 2.25 - 1.90 = 0.35m P max

= 501 ---- (1 + 6 x 0.35) 4.5 4.5

= 163.30 KN/m2 < 175 KN/m2 ( consider piles of depth 3.60m with 450mm dia. ) P mm = 59.39 KN/m2, positive Hence O.K DESIGN OF STEM: Maximum horizontal pressure on stem

=

1 18 -- x -- x 6.52 3 2 126.75 KN/m2

= Maximum moment

M

M lim

=

126.75 x 32 x 1.50 12

=

142.59KN-m

=

0.138 f bd2

=

0.138 x 30 x 1000 x 4602

=

876 x 10 6 N-mn >M

Hence thickness of stem is sufficient 142.59 x 106

M --------

Bd 2 Pt Ast

=

------------------------

1000 x (460)2 = 0.67 = 0.20 % = 0.2 x 1000 x 460 -----------------------100 = 920.0 mm2/m (or) 9.20cm2/m 2

Provide 12mm dia bars at 120 mm c/c. Ast = 1005 mm2 Districbution steel

= 0.12 ----- x 460 x 1000 100 = 552 mm2

Provide 12 mm bars at 200 mm in both directions on the front side also to take care of + ve moment in the middle. CHECK FOR SHEAR: Maximum shear force at the face Of counterfort V

= 1.5 x 52.91

=

= 42.33 x (3-0.5) ------------------2 79.37KN

= 52.91 KN

Tv = 79.37 x 1000 ----------------- = 0.173 N/mm2 460 x 1000 Percentage reinforcement (Pt) Pt =

100 x 1005 --------------1000 x 460 Tc = 0.20 N/mm2

= 0.218

Tv < Tc Hence safe DESIGN OF TOE SLAB: Cantilever moment

= 163.30 x 1.02 ----------------- = 81.65 2 M = 1.5 x 81.65 = 122.48 KN-m – M Inn M 122.48 x 10 6 --- = ----------------Bd2 10 3 x (460) 2 Pt

=

0.58

= 0.170

Ast = 0.170 x 103 x 460 ------------------------- = 782 100 Provide 16 mm bars @ 200 mm c/c

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CHECK FOR SHEAR : Pressure at critical point

=

=

(163.30 - 59.39) 59.39 + -------------------- x (3.5 + 0.46) 4.5 150.83 KN/m2

Shear force pr metre width of toe V

=

1 -- (163.30 + 150.83) x (1.0 – 0.46) 2 = 84.82 KN

V

= 1.5 x 84.82 = 127.22

Tv

= 127.22 x 103 ----------------1000 x 460

=

0.28 N/mm

Ast

= 1000 ----- x ( ∏ x 162 /4) = 1004.8 mm 2 200

Pt

= 100 x 1004.8 ---------------- = 0.22 1000 x 460

Tc

= 0.35

Tv < Tc Hence D = 500 is safe DESIGN OF HEEL SLAB : Soil pressure at the junction with steam = 128.60 KN/m2 Load from back fill

= 117.00 KN/m2

Load from 500 mm thick slab (self weight) = 0.5 x 1 x 25 Downward Load

= 12.50 KN/m2

= 116.10 KN/m2

4

Maximum downward pressure intensity is at the edge P max

= 116.10 KN/m2

M

= 116.10 x 32 ------------------

= 87.08 KN-m

12 M

= 1.5 x 87.08

= 130.60 KN-m

M

130.60 x 106 = --------------1000 x (460)2

=

-----

bd2 Pt

=

0.17

Ast

=

0.2 x 1000 x 460 ---------------------100

0.61

= 920 mm2

Provide 16 mm dia bars @ 200 mm c/c Distribution steel of 12 mm diameter bars @ 200 mm is provided at right angle to main bars. DESIGN OF COUNTERFORT: For beam Action: Inclination of counterfort with horizontal (-)

7.5 = tan -1 ---3.0

= 68

Depth of counterfort ‘d’ for beam action at junction = 3.0 sin(-) = 2.79 m 1 18.x 6.53 = -- x ----------- x 3 3 2x3

Maximum moment on conterfort

= 823.90 KN-m M

=

1.5 x 823.90

= 1235.80 KN-m M --Bd2

=

1235.80 x 106 --------------- = 0.32 500 x (2790)2

Pt

=

0.11

5

Ast

=

0.20 x 500 x 2790 -----------------------100

= 2790 mm2 But minimum reinforcement required

= 085bd -------fy = 0.85 x 500 x 2790 --------------------415 = 2857 mm2

Provide 6 bars of 25 mm diameter Ast provider =

m x 252 6 x --------- = 2944.0 mm2 4

HORIZONTAL TIES : Consider bottom 1 m height of steem Maximum Pressure Total lateral pressure to be transferred From stem to slab Factored force Area of tensile steel required for it

= 42.33 KN/m2 = 42.33 (3-0.5) = 105.80 KN = 1.5 x 105.80 = 158.74 KN = 158.74 x 1000 -----------------0.87 x 415 = 440.0 mm2

Provide 12 mm dia bars at 150 mm c/c. VERTICAL STIRRUPS : Near end of heel downward force Factored force

= 116.10 KN/m2 = 1.5 x 116.10 = 174.15 KN/m2

Steel required to resist this tensile force

= 174.15 x 1000 -----------------0.87 x 415 = 482.0 mm2

Provide 12 mm dia bars at 150 mm c/c. Signed T.Moses Kumar, S.E-I & C.E-I/c

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