Retain Wall 1.5m High T Shape Wo Inclined Backfill Final 190313

8/12/2019 Retain Wall 1.5m High T Shape Wo Inclined Backfill Final 190313

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Shirish Patel and Associates

Consultants Private Limited

DELHI RAIL CORPORATION LTD.

JAIPUR METRO RAIL PROJECT

STAGE-1 (JP/EW/C2)

Table Of Content

Cl. Description Page

No. No.

1.0 Scope of the Report 1

2.0 Design Methodology 2

3.0 References 4

4.0 List of drawings 5

5.0 Assumption 6

6.0 Calculations 6.1) Wall W5 7

6.2) Wall W5A 11

6.3) Wall W5B 17

7.0 Substructure Analysis 7.1) Wall W5 23

7.2) Wall W5A 36

7.3) Wall W5B 39

8.0 Design of Footing 8.1) Wall W5 42

8.2) Wall W5A 45

8.3) Wall W5B 48

9.0 Design of Piercap 50

10.0 Summary 54

Appendix - A Dead Load Analysis 57

Appendix - B Live Load Analysis 59


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STAGE-1 (JP/EW/C2)

Figure 1

0.2

b-a =

1.50

2.50

2.20

0.200

B

0.70 78.7

0.70 1.00 12.28

0.30 0.30

0 A 0.750 0.3 0.750 14.85 14.85 1.49

1.8

Earth pressure diagram Surcharge

56 30 Pressure Dig

45.0 41

Normal case : GROSS PRESSURE DIAGRAM

75 12

49.0 38

W1

W2

W3W4W5

W6

W7

235520451.xls.ms_office DIAGRAM


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STAGE-1 (JP/EW/C2)

7.1) Earth Pressure co-efficient calcuation

7.1.1) Coulomb Earth pressure Theory :

Coefficient of active earth pressure :

( Refer equation 11-3 / Foundation analysis and design by Joseph E. Bowles )

a = 90 deg = 1.571 rad

f = 30 deg = 0.524 rad

d = 20 deg = 0.349 rad b

b = 0 deg = 0.000 rad

A= Sin2

( a + f ) = 0.750 d

B= Sin2

a = 1.000

C= Sin ( a - d ) = 0.940 a

D= Sin ( f + d ) = 0.766

E= Sin ( f - b ) = 0.500

F= Sin ( a + b ) = 1.000

Ka = A Ka = 0.297

B * C * (1+SQRT((D*E)/(C*F)))2

Coefficient of passive earth pressure :

( Refer equation 11-6 / Foundation analysis and design by Joseph E. Bowles )

a = 90 deg = 1.571 rad

f = 30 deg = 0.524 rad

d = 20 deg = 0.349 rad b

b = 0 deg = 0.000 rad

A= Sin

2

( a - f ) = 0.750 dB= Sin

2a = 1.000

C Si ( d ) 0 940


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STAGE-1 (JP/EW/C2)

7.1.2) Earth pressure co-efficient calculation under EQ condition as per IS 1893:1984

Coefficient of Active earth pressure : Refer IS 1893 - 1984 / Clause 8.1.1

a h = 0.072 a v = 0.036

f = 30 = 0.524 rads a = 0 = 0 rads

t = 0.00 = 0 rads d = 20 = 0.349 rads

a h using IS 1843:1984 Clause 3.4.2

b = 1.2 Table 3 IS 1893: 1984

I = 1.5 Table 4 IS 1893: 1984

a 0 = 0.04

a h = 0.04 x 1.2 x 1.5 = 0.072

l1 = tan-

a h = 0.069 = 3.976

1 + a v

l2 = tan-

a h = 0.075 4.271

1 - a v

( 1 + a v ) = 1.036 ( 1 - a v ) = 0.964

cos2

( f - l1 - a ) = 0.807

cos2

( f - l2 - a ) = 0.812 t

cos l1 = 0.998

cos l2 = 0.997 a

cos2

a = 1.000 d

cos ( d + a + l1 ) = 0.914

cos ( d + a + l2 ) = 0.912

sin ( f + d ) = 0.766

sin ( f - t - l1 ) = 0.439

sin ( f - t - l2 ) = 0.4341

cos ( a - t ) = 1.000

Ca = 0.918 x 0.387 = 0.356 Ca = 0.861 x 0.389 = 0.334

Ca = 0.356

Coefficient of Passive earth pressure : Refer IS 1893 - 1984 / Clause 8.1.2

a h = 0.072 a v = 0.036f = 30 = 0.524 rads a = 0 = 0 rads

t = 0 = 0 rads d = 20 = 0.349 rads

l1 = tan-

a h = 0.069 = 3.976

1 + a v

l2 = tan-

a h = 0.075 4.271

1 - a v

( 1 + a v ) = 1.036 ( 1 - a v ) = 0.964

cos2

( f l1 + ) = 0 807

For calculation of

For Zone III


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STAGE-1 (JP/EW/C2)

b) Net Horizontal pressure

Active earth pressure pressure = 21 = 21 kN

c) FOS against sliding 0.5 x 78 = 1.86 > 1.5

21 SAFE

d) Check for pressure :

P/A = ( 78 / 1.8 ) = 43.3 kN/m2

M/Z ( 78 x 0.09 x 6 ) / 1.8^2 = 13.0 kN/m2

Maximum pressure = P/A + M/Z = 56 kN/m2

Net max pressure= = 56.0 - 20 = 36 kN/m2

50

Minimum pressure = P/A - M/Z = 30 kN/m2

SAFE

7.1.3.5) Force on stem :

At Wall bottom (i.e. footing top level) :

h1 = 2.20 m

a) Earth pressure :

0.297 x 20 x 2.2 x 0.94 = 12.3 kN/m2

Total Earth pressure on stem

( 12.28 x 2.2 / 2 ) = 14 kN

Moment ( 14 x 2.2 * 0.42 ) = 13 kN-m

b) Surcharge force on stem :

1.49 x 0.94 x 2.2 = 3.1 kN

Moment ( 3.08 x 2.2 * 0.5 ) = 3 kN-m

Total SLS moment = ( 13+3 ) = 16 kN-m

Design Moment Mdu = ( 16 x 1.0 ) = 16 kN-m

Shear force = = ( 14+3.08 ) = 17 kN

Vu = 17.0 x 1.00 = 17 kN

7.5) Design toe slab :

Upward pressure on toe slab

= ( 45 + 56 ) / 2 x 0.75 38 kN

Moment due to upward pressure =

38 x 0.389 15 kN-m

Down ward force of soil= 0.70 x 20 x 0.750 10.50 kN/m

Self Weight = 0.75x0.3 x 25 5.60 kN/m

Total Downward Pressure = 16.1 kN/mMoment due to downward pressure =

16.1 x 0.750 2 6.0 kN-m


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STAGE-1 (JP/EW/C2)

Design Moment Mdu = ( 5.01 x 1 ) = 5.01 kN-m

Shear force = 38.6 - 27 = 12 kNVu = 12 x 1.0 = 12 kN


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STAGE-1 (JP/EW/C2)

7.1.4) Retaining wall design in siesmic case : (Ref. Fig -1 )

Design parameters :Grade of concrete = 35 N/mm

2

Height of wall above ground = 1.50 m

Depth of foundation below ground = 1.00 m

Total height of wall H = 2.5 m

Saturated Density of soil g = 20 kN/m3

Angle of internal friction = 30 Degree

Coeff. Of friction m = 0.5

Concrete density = 25 kN/m3

Horizontal Siesmic coeff. = 0.072

Vertical Siesmic coeff. = 0.036Coefficient of earth pressure Ka = 0.297

The wall is skew by an angle of 23 degree. Hence pressure on wall should be increase #REF!

Dynamic increament in Ka due to EQ, ' Ka1

0.356 - 0.297 = 0.059

Dyn increment Earth pressure at Base = Ka1 * g * H* Cos (+)

= 0.059 x 20 x 2.5 x 0.94 = 2.77 kN/m2

Dyn. Decrement in passive pressure at Base = Kp' * g * H

= -0.618 x 20 x 1 x 2/3 = -8.2 kN/m2

Surcharge pressure Ka*SL* Cos (+)

= 0.059 x 5 x 0.94 = 0.28 kN/m2

Summary of forces :

Load Load in kN L.A @ B Moment

(kN) (kN-m)

W1 2.2 x 0.2 x 25 x 0.072 0.8 1.400 1

W2 ( 0.1 x 2.2 ) / 2 x 25 x 0.072 0.2 1.033 0

W3 0.3 x 0.75x 25 x 0.072 0.4 0.150 0

W4 0.3 x 0.3 x 25 x 0.072 0.2 0.150 0

W5 0.3 x 0.75 x 25 x 0.072 0.4 0.150 0

W6 0.7 x 0.75 x 20 x 0.072 0.8 0.650 0W7 2.2 x 0.75 x 20 x 0.072 2.4 1.400 3

Total 5.0 5

Dynamic increment in Earth pressure :

P1 2.77 x 2.5 2.00 3.5 1.250 4

P2 0.28 x 2.50 0.7 1.650 1

Total 4.0 5

7.1.3.3) Load summary under ( Normal + EQ ) Load condition :

Total Vertical load = 78 = 78 kN

Total Stabilizing moment = 86 = 86 kN-m

Total horizontal Load = 21 + 5 + 4 = 30 kNTotal overturning moment 23 + 5 + 4 = 33 kN-m

Net stabilizing moment = 53 kN-m


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STAGE-1 (JP/EW/C2)

7.1.4.5) Force on stem under EQ condition :

a) At Wall bottom (i.e. Base slab top level) :

h1 = 2.20 ma) Earth pressure :

= 0.059 x 20 x 2.2 x 0.942 = 2.44 kN/m2

Total Earth pressure on stem

= ( 2.44 x 2.2 / 2 ) = 3 kN

Moment = ( 3 x 2.2 *0.46 ) 3.0 kN-m

Moment due to EP under Normal condition = 16 kN-m

b) Surcharge force on stem :

= 0.28 x 2.2 = 0.62 kN

Moment from 0.66h = ( 0.62 x 2.2 * 0.66 ) = 1 kNm

Moment due to SP under Normal condition = 3 kN-m

b) Earthquake force due to superstructure load, wall self wt & earthfill :

Load Load in kN Moment

(kN) (kN-m)

W1 2.2 x 0.2 x 25 x 0.072 0.8 1.100 1

W2 ( 0.1 x 2.2 ) / 2 x 25 x 0.072 0.2 0.733 0

W6 0.7 x 0.75 x 20 x 0.072 0.8 0.350 0

W7 2.2 x 0.75 x 20 x 0.072 2.4 1.100 3Total 4.0 4

Design moment :

Moment due to normal EP = 16 kN

Moment due to normal SP = 3 kN

Moment due to Dynamic increamental Earth pressur 3 kN

Moment due to Dynamic increamental SP 1 kN

Moment due to super str load 4 kN

Total SLS Moment 16+3+3+1+4 27 kN-m

Design Shear force =

Shear due to EP under normal load case = 14 kNShear due to SP under normal load case = 3 kN

Earth pressure due to EQ 3 kN

SP pressure due to EQ 1 kN

EQ Load due to super str load 4 kN

Total SLS Shear Force = 25 kN

8.5) Design toe slab :

Upward pressure on toe slab

= ( 75 + 49 ) / 2 x 0.75 ) 47 kNMoment due to upward pressure =

47 x 0.401 19 kN-m

L.A @ Wall

bottom


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STAGE-1 (JP/EW/C2)

11.0) Reinforcement calculation of Cantilever Retaining Wall for DL + EQ Load Case

The bending moment & shear forces as obtained from staad analysis is considered below to calculate reinforcement.

Grade of concrete = 30 Mpa n1 = 0.294Grade of steel = 500 Mpa j = 0.90

Modular ratio = 10 Q = 1.33

Permissible comp. flex. stress in concrete = 10.0 Mpa

Permissible tensile. stress in steel = 240 Mpa

11.1) Reinforcement calculation for Flexure :

Moment D clear d Mbal. Ast req. Ast req. Total Astmin Ast prov. Ast Total Remark.

Location cover (for flex.) (for torsion) Ast req. dia @ SpacingProv. Ast req.

(kn-m) (mm) (mm) (mm) (kn-m) (mm2) (mm2) (mm2) (mm2) (mm) (mm) (mm2) (mm2)

Stem Reinforcement 16 300 50 245 80 302 0 302 294 10 @ 150 524 302 safe

Base region @ 0.21

Toe Slab 9 300 75 220 64 189 0 189 264 10 @ 200 393 264 safe

0.18

Heel Slab 5.0 300 75 220 64 105 0 105 264 10 @ 200 393 264 safe

0.18

11.2 ) Shear Check

(mm) (mm) (mm) v(N/mm2)

Stem Reinf. 17 300 50 245 0.07 0.21 safe

Toe Slab 22 300 75 220 0.10 0.18 safe

Heel Slab 12 300 75 220 0.05 0.18 safe

Pt %

provide

d

Shear capacity of concrete

c (N/mm2) (IRC21-2000

Table 12B)

Remark

0.21

0.21

0.21

Location

Shear

Force

(kN)

Dclear

coverd

Shear

stress

235520451.xls.ms_office Design Nor by IRC


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STAGE-1 (JP/EW/C2)

11.0) Reinforcement calculation of Cantilever Retaining Wall for DL + EQ Load Case

The bending moment & shear forces as obtained from staad analysis is considered below to calculate reinforcement.

Grade of concrete = 30 Mpa n1 = 0.294Grade of steel = 500 Mpa j = 0.90

Modular ratio = 10 Q = 1.99

Permissible comp. flex. stress in concrete = 15.0 Mpa

Permissible tensile. stress in steel = 360 Mpa

11.1) Reinforcement calculation for Flexure :

Moment D clear d Mbal. Ast req. Ast req. Total Astmin Ast prov. Ast Total Remark.

Location cover (for flex.) (for torsion) Ast req. dia @ SpacingProv. Ast req.

(kn-m) (mm) (mm) (mm) (kn-m) (mm2) (mm2) (mm2) (mm2) (mm) (mm) (mm2) (mm2)

Stem Reinforcement 27 300 50 245 119 339 0 339 294 10 @ 150 524 339 safe

Base region @ 0.21

Toe Slab 13 300 75 220 96 181 0 181 264 10 @ 200 393 264 safe

0.18

Heel Slab 8.0 300 75 220 96 112 0 112 264 10 @ 200 393 264 safe

0.18

11.2 ) Shear Check

(mm) (mm) (mm) v(N/mm2)

Stem Reinf. 25 300 50 245 0.10 0.21 safe

Toe Slab 31 300 75 220 0.14 0.18 safe

Heel Slab -13 300 75 220 -0.06 0.18 safe

Location

Shear

Force

(kN)

Dclear

coverd

Shear

stress

0.21

0.21

0.21

Pt %

provide

d

Shear capacity of concrete

c (N/mm2) (IRC21-2000

Table 12B)

Remark

235520451.xls.ms_office Design EQ by IRC

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Retain Wall 1.5m High T Shape Wo Inclined Backfill Final 190313