DESIGN OF RETAINING WALL FOR MITHI KHADI FOR SEISMIC CONDITION

1.0 DESIGN DATA

Assumed S.B.C :25 t/m²

Grade of concrete: M300

Tensile stresses in steel : 3657kg/cm²

Stresses in concrete: 133.00 kg/cm²

2.0 ACTIVE EARTH PRESSURE

phi = 30.000

delta = 20.000

alfa = 4.537

i = 0.000

For calculating the active earth pressure on substructures

Coulomb's theory will followed

Cos² (phi-alfa) Ka = ------------------------------------------------------------ _ _ | Sin(phi+del)xSin(phi-i) |² Cos²(alfa)xCos(alfa+del) [1+Sqr |------------------------ | |_ Cos(alf+del)xCos(alf-i) _|

Ka = 0.3313

3.0 Forces due to Active earth pressure

3.1 Horizontal force due to Active earth pressure

Horizontal Coefficent of active earth pressure

kah = 0.331

P1 = 0.331*2.000*0.5*4.960*4.960 = 8.15 t

is acting at h/3 = 1.653 m.

Moment due to Horizontal Active earth pressure M1 = 13.47 t.m

5.0 Forces due Earthpressure in seismic

5.1 Horizontal force due to Active earth pressure in seismic condition

Horizontal Coefficent of active earth pressure in seimsic

kahs = 0.057

P3 = 0.057*2.000*0.5*4.960*4.960 = 1.40 t

is acting at h/2 = 2.480 m.

Moment due to Horizontal Active earth pressure in seismic condition M3 = 3.48 t.m

5.2 Forces due to live load surcharge

P4 = 0.057 x 0.000 x 2.000 x 4.960 = 0.000

Moment at base due to live load surcharge in seismic condition M4 = 0.000 x 2/3 x 4.960 = 0.000 t.m. Total Moment about toe M = M1 + M2 + M3 + M4-M1v M = 16.95 t.m

6.0 LOADING AND MOMENT CALCULATION ABOUT X-X(With Seismic) -------------------------------------------------------------------- Loading Calculation Vert. Hori. L.arm B.M load load t t m t.m --------------------------------------------------------------------

Stem Wall 0.5x0.35x4.41x1.04x2.5 = 2.014 1.317 2.652 Wall 0.20x4.41x1.04x2.5 = 2.302 1.100 2.532

Base slab Toe 1.00x0.55x1.04x2.5 = 1.436 0.500 0.718 Toe 0.5x1.00x0.00x1.04x2.5 = 0.000 0.670 0.000 Mid. 0.55x0.55x1.04x2.5 = 0.790 1.275 1.007 Heel 1.80x0.55x1.04x2.5 = 2.584 2.450 6.331 Heel 0.5x1.80x0.00x1.04x2.5 = 0.000 2.150 0.000

Backfill & Surcharge Backfill 1.80x4.41x1.04x2.00= 16.575 2.450 40.608 Backfill0.5x0.35x4.41x1.04x2.00= 1.611 1.434 2.312 Surcharge 2.15x0.00x2.00 = 0.000 2.275 0.000

Earth pressure (1) Hori. comp. = 8.149 1.653 -13.474 (2) Vert. comp. = 0.000 1.550 0.000 (3) due to L.L. surcharge = 0.000 2.480 -0.000 (4) Hori. comp. in seismic = 1.402 2.480 -3.478 (5) due to L.L surcharge(seismic)= 0.000 3.307 -0.000 (6) due to stem intertia(seismic)= 0.127 2.020 -0.257 (7) due to stem intertia(seismic)= 0.146 2.755 -0.401

Seismic on Base Slab ********************* Toe 1.00x0.55x0.07x2.5 = 0.091 0.275 -0.025 Toe 0.5x1.00x0.00x0.07x2.5 = 0.000 0.550 -0.000 Mid. 0.55x0.55x0.07x2.5 = 0.050 0.275 -0.014 Heel 1.80x0.55x0.07x2.5 = 0.163 0.275 -0.045 Heel 0.5x1.80x0.00x0.07x2.5 = 0.000 0.550 -0.000 Uplift Pressure = 0.000 1.675 -0.000 -------------------------------------------------------------------- Total = 27.311 10.129 38.535 --------------------------------------------------------------------

C.G. of loading from face of the toe due to vertical load = 38.535 / 27.311

Distance x = 1.411 m

Eccentricity = b/2 - x = ( 3.350/2- 1.411) = 0.264 m

6.1 Base Properties

Area = 1 x 3.350 m² = 3.350 m²

Section modulus = (1* 3.350* 3.350)/6 = 1.870 m³

6.2 Pressure Calculations

Minimum pressure Pmin = P/A - M/Z = (27.31/ 3.35)-((27.31* 0.26)/ 1.87) t/m² = 4.30 t/m²

Maximum pressure Pmax = P/A + M/Z = (27.31/ 3.35)+((27.31* 0.26)/ 1.87) t/m² = 12.01 t/m²

6.3 Check for overturning

Factor of safety against overturning

Overturning Moment = 17.436 t.m

Stabilizing Moment = 55.971 t.m

Stabilizing Moment Factor of safety = ------------------- Overturning Moment

55.971 Factor of safety = ----------- 17.436

= 3.21

> 1.5 ( hence safe)

6.4 Check for sliding

Factor of safety against sliding

u = tan(30.00)

= 0.577

Sliding Force = 10.129 t

Vertical Force = 27.311 t

mu x Vertical Force Factor of safety = -------------------- Sliding Force

( 0.577 x 27.311) = ------------------- 10.129

= 1.56

> 1.2 ( hence safe)

7.0 DESIGN OF STEM

7.1 Design Constant

modular ratio m = 7.02

1 K = ----------------- rst 1 + ------- m x rcb

= 0.20

0.20 J = 1 - ------ 3 = 0.93

Q = 0.5 x133.00 x 0.93 x 0.20

= 12.61 kg/cm²

7.2 AT BASE OF STEM

Moment due to active earth pressure

0.331* 2.000* 4.410* 4.410*0.33* 4.410 M1 = -------------------------------------- 2

= 9.470 t.m

Moment due to live load surcharge Horizontal earth pressure due to live load surcharge P2 = 0.331 x 0.000 x 2.000 x 4.410000 = 0.000

Moment at base of stem due to live load surcharge M2 = 0.000 x 0.5 x 4.410 = 0.000 t.m. Moment due to active earth pressure in seismic condition

0.057* 2.000* 4.410* 4.410*0.5* 4.410 M3 = -------------------------------------- 2

= 2.444 t.m

Moment due to live load surcharge Horizontal earth pressure due to live load surcharge in seismic condition P4 = 0.057 x 0.000 x 2.000 x 4.410000 = 0.000

Moment at base of stem due to live load surcharge M4 = 0.000 x 0.66 x 4.410 = 0.000 t.m. Horizontal Seismic Force acting on Stem due to Inertia ------------------------------------------------------------------- Shape Vert. Hori. L.arm B.M load load t t m t.m -------------------------------------------------------------------- Tri. 0.5x0.35x4.41x0.07x2.5 = 0.127 1.470 0.187 Rect. 0.20x4.41x0.07x2.5 = 0.146 2.205 0.321

Total moment M = M1 + M2 + M3 + M4 + Moment due to inertia forces = 12.423 t.m.

(A) CHECK FOR DEPTH

M½ dreq = ----------- (Q x b)½

(12.423*100000)½ = ------------------------ (12.605*100)½

= 31.393 cm

< 55.00- 4.0 - 1.0 = 50.000, Hence O.K.

(B) REINFORCEMENT CALCULATION

M Area of steel required = ------------------ rst x J x d

12.423 x100000 = ---------------- 3657 x 0.93 x 50.00

= 7.288 cm²

0.12 x 55.00 x 100 Minimum area of steel reqd = --------------------- 100 = 6.60 cm²

Provide 16 dia 120 c/c ( 16.75 cm²)

Distribution Steel on each face = 6.60 x 0.5 cm²

= 3.30 cm²

Provide 10 dia 150 c/c ( 5.24 cm²)

(C) CHECK FOR SHEAR

Check for Shear As per IS 456

Maximum shear stress Tmax = 22.000 kg/cm²

Permissible shear stress

pt = 100 x Ast/(b x d)

= 0..3045%

As per table 23, of IS-456-2000

Tc = 0.25 N/mm² = 2.500 kg/cm²

Shear due to active earth pressure

P1 = 0.5 * Kah * r * h * h

= 0.5 * 0.331 * 2.000 * 4.410 * 4.410

= 6.442 t.

Shear due to live load surcharge

P2 = 0.000 t.

Total shear = P1 + P2

= 6.442 + 0.000

= 7.824 t.

v Actual Shear Stress = ----------- b x d

7.82 x 1000 = -------------- 100 x 50.00

= 1.56 kg/cm²

< 2.050 kg/cm²

Hence Shear reinforcement is not required

7.3 AT MID HEIGHT OF STEM

Moment due to active earth pressure

0.331* 2.000* 2.205* 2.205*0.33* 2.205 M1 = -------------------------------------- 2

= 1.184 t.m

Moment due to live load surcharge Horizontal earth pressure due to live load surcharge P2 = 0.331 x 0.000 x 2.000 x 2.205000 = 0.000

Moment at base of stem due to live load surcharge M2 = 0.000 x 0.5 x 2.205 = 0.000 t.m. Moment due to active earth pressure in seismic condition

0.057* 2.000* 2.205* 2.205*0.5* 2.205 M3 = -------------------------------------- 2

= 0.306 t.m

Moment due to live load surcharge Horizontal earth pressure due to live load surcharge in seismic condition P4 = 0.057 x 0.000 x 2.000 x 2.205000 = 0.000

Moment at base of stem due to live load surcharge M4 = 0.000 x 0.66 x 2.205 = 0.000 t.m. Horizontal Seismic Force acting on Stem due to Inertia -------------------------------------------------------------------- Shape Vert. Hori. L.arm B.M load load t t m t.m -------------------------------------------------------------------- Tri. 0.5x0.35x2.20x0.07x2.5 = 0.127 0.735 0.187 Rect. 0.20x2.20x0.07x2.5 = 0.146 1.102 0.321

Total moment M = M1 + M2 + M3 + M4 + Moment due to inertia forces = 1.997 t.m.

(A) CHECK FOR DEPTH

M½ dreq = ----------- (Q x b)½

( 1.997*100000)½ = ------------------------ (12.605*100)½

= 12.588 cm

< 37.50- 4.0 - 1.0 = 32.500, Hence O.K.

(B) REINFORCEMENT CALCULATION M Area of steel required = ------------------ rst x J x d

1.997 x100000 = ---------------- 3657 x 0.93 x 32.50

= 1.803 cm²

0.12 x 37.50 x 100 Minimum area of steel reqd = --------------------- 100 = 4.50 cm²

Provide 16 dia 240 c/c ( 8.38 cm²)

Distribution Steel on each face = 4.50 x 0.5 cm²

= 2.25 cm²

Provide 10 dia 150 c/c ( 5.24 cm²)

(C) CHECK FOR SHEAR

Check for Shear As per IRC-456-2000

Maximum shear stress Tmax = 22.000 kg/cm²

Permissible shear stress

pt = 100 x Ast/(b x d)

= 0.15%

As per table 23, of IS-456-2000

Tc = 0.200 N/mm² = 2.000 kg/cm²

Shear due to active earth pressure

P1 = 0.5 * Kah * r * h * h

= 0.5 * 0.331 * 2.000 * 2.205 * 2.205

= 1.611 t.

Shear due to live load surcharge

P2 = 0.000 t.

Total shear = P1 + P2

= 1.611 + 0.000

= 2.161 t.

v Actual Shear Stress = ----------- b x d

2.16 x 1000 = -------------- 100 x 32.50

= 0.66 kg/cm²

< 2.00 kg/cm²

Hence Shear reinforcement is not required

8.0 DESIGN OF HEEL

|-----------| |-----------| |-----------|8.44| /|\/|\/|\ | 4.30 + 1.44| \|/\|/\|/ | 1.44 + 9.21| \|/\|/\|/ | 9.21 t/m²| | | | |t/m² t/m² | | t/m²| || | | upward pressure self wt. of base slab backfill

4.30x1.80x 1.80 0.5x4.14x1.80x1.80 Moment at = ------------------- + -------------------------- face of stem 2 3

1.44x1.80x 1.80 0.5x0.00x1.80x1.80x1.80 = ------------------- - -------------------------- 2 3

9.21x1.80x 1.80 0.00x1.80x1.80x1.80 = ------------------- - -------------------------- 2 3

= 9.20 - 2.33 - 14.92

= -8.04 t.mt

(A) CHECK FOR DEPTH

M½ dreq = ----------- (Q x b)½

(8.04*100000)½ = --------------- (12.61*100)½

= 25.26 cm

< 55.00- 5.0 - 1.0 = 49.00 cm., Hence O.K

(B) REINFORCEMENT CALCULATION

M Area of steel required = -------------- rst x J x d

8.04 x100000 = ---------------- 3657 x 0.93 x 49.00

= 4.82 cm²

Provide 12 dia 180 c/c ( 6.28 cm²)

(C) CHECK FOR SHEAR

S.F at the face of stem

= 4.30 x 1.80 + 0.5 x 4.14 x 1.80

- 1.44 x 1.80 - 0.5 x 0.00 x 1.80

- 9.21 x 1.80 - 0.5 x 0.00 x 1.80

= 7.69 t

Check for Shear As per IS:456-2000

Maximum shear stress Tmax = 22.000 kg/cm²

Permissible shear stress

pt = 100 x Ast/(b x d)

= 0.098%

As per IS:456-2000

Tc = 0.200 N/mm² = 2.000 kg/cm²

v Actutal Shear Stress = --------- b x d

7.69 x 1000 = ------------- 100 x 49.00

= 1.57 kg/cm²

< 2.00 kg/cm²

Hence, Shear reinforcement is not required

0.12 x 0.55 x 100 x 100 Minimum area of steel reqd = ------------------------------ 100

= 6.60 cm²

Distribution Steel on each face = 6.60 x 0.5 cm²

= 3.30 cm²

Provide 10 dia 150 c/c ( 5.24 cm²)

9.0 DESIGN OF TOE

|-----------| |-----------| 12.01| /|\/|\/|\ | 9.71 + 1.44| \|/\|/\|/ | 1.44 t/m²| | | | |t/m² t/m²| | | | upward pressure self wt. of base slab

|--------------| 10.57| /|\/|\/|\/|\ | 8.27 t/m²| | | | | |t/m² | Net Pressure diagram

10.57x 1.00x 1.00 0.5x8.27x1.00x1.00 Moment at the = ----------------------- + --------------------- face of stem 3 3

= 3.52 + 1.38

= 4.90 t.mt

(A) CHECK FOR DEPTH

M½ dreq = ----------- (Q x b)½

(4.90*100000)½ = ----------------- (12.61*100)½

= 19.72 cm

< 55.00- 5.0 - 1.0 = 49.00 cm., Hence O.K.

(B) REINFORCEMENT CALCULATION

M Area of steel required = -------------- rst x J x d

4.90 x100000 = ---------------- 3657 x 0.93 x 49.00

= 2.93 cm²

Provide 12 dia 180 c/c ( 6.28 cm²)

(C) CHECK FOR SHEAR

S.F at effective depth from the face of stem

= 0.5 x 10.57 x 0.51 + 0.5 x 9.44 x 0.51

= 5.10 t

Check for Shear As per IS:456-2000

Maximum shear stress Tmax = 22.000 kg/cm²

Permissible shear stress

pt = 100 x Ast/(b x d)

= 0.114%

As per IS:456-2000

Tc = 0.200 N/mm² = 2.000 kg/cm²

v Actutal Shear Stress = --------- b x d

5.10 x 1000 = ------------- 100 x 49.00

= 1.04 kg/cm²

< 2.00 kg/cm²

Hence, Shear reinforcement is not required

0.12 x 0.55 x 100 x 100 Minimum area of steel reqd = ------------------------------ 100

= 6.60 cm² Distribution Steel on each face = 6.60 x 0.5 cm² = 3.30 cm² Provide 10 dia 150 c/c ( 5.24 cm²)