Design Report Of Retaining Wall

DESIGN OF RETAINING WALL

CONTRACTOR

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FOR APPROVAL FOR APPROVAL FOR APPROVAL DESCRIPTION

31-08-2018 PRK 15-06-2018 RKM 23-03-2018 RKM DATE DESGND.

SWD SWD SWD CHKD.

SNC SNC SNC APPVD.

CONSULTANT CLIENT PROJECT TITLE DOC. NO

KEC INTERNATIONAL LTD. LAHMEYER INTERNATIONAL / NORCONSULT UPPER TAMAKOSHI HYDROELECTRIC POWER LTD NEW KHIMTI 220/132KV SUBSTATION DESIGN OF RETAINING WALL KEC/UTKHEP/17-2066/67/KHIMTI/C1/097 REV

2

PROJECT

220/132KV NEW KHIMTI SUBSTATION

TITLE

DESIGN OF RETAINING WALL

DOCUMENT NO KEC/UTKHEP/17-2066/67/KHIMTI/C1/097 DESIGNED CHECKED PRK SWD

DATE 31-08-2018 SHEET

Design of Retaining Wall (4.0 m height from FGL/NGL) Input Data: 2

Grade of Concrete

fck

=

Grade of Steel Coefficient of Friction, SBC of soil

fyk µ qa

= = = = =

500 0.55 200 250 228.815

=

278.815 KN/m²

(In case of seismic, allowable pressure shall be increased by 25%) Allowable gross capacity, qG,allow = qa + γsDf (=200+19.21x1.5) (In case of seismic, allowable pressure shall be increased by 25%) Allowable gross capacity, qG,allow = qa + γsDf (=250+19.21x1.5)

25 N/mm N/mm

2

KN/m² KN/m² KN/m²

φ i δ α

= = = =

Ka

=

1 - sin Φ 1 + sin Φ

Ka

=

0.35

Kp

=

2.88

Density of concrete

γc

=

25 KN/m³

Density of soil Design parameters and Levels: Lower side ground level

γs

=

19.21 KN/m³

Angle of repose Angle of sloping sand Angle of external friction between wall and earthfill, assume δ = (2/3 φ) Angle which earth face of the wall makes with the vertical =

Coefficient of active earth pressure (sloping backfill)

29 0.0 19.3 0

deg deg deg deg

Coefficient of passive earth pressure (at rest)

=

658.000 M 654.000 M 1.5 m

Depth of Foundation below FGL

FGL Df

=

Height of Wall above from FGL

h1

=

4.0 m

Tfooting

=

0.60 m

h0 H h2

= = =

4.90 m 5.50 m 0.90 m

Thickness of footing Height of wall Total height of wall Depth of top of footing below FGL

(upto top of footing only) (including thickness of footing)

Dimensions of Retaining Wall: Thickness of wall @ Top

Ttop

=

0.30 m

Tbottom

=

0.60 m

Tf

=

0.60 m

Length of toe

Ltoe

=

2.15 m

Length of heel

Lheel

=

4.00 m

=

6.75 m

Thickness of wall @ Bottom Thickness of footing

B = Ltoe + Tbottom + Lheel

Length of footing

W3 W1

h1

h0 H

α FGL/NGL W5

W4 h2

LHeel

LToe

B W2 B

Loading: (bottom of wall) (Pressure at Point B): Pressure due to inside sloping sand

Pe

=Ka x γs x h0

Pe

=0.35x19.21x4.9

=

32.66 KN/m²

Force acting on wall from inside soil

Pa

= 0.5 x Pe x h0

=

80.02 KN

Moment acting on wall at point B

MB

= Pa x h0/3

=

:. Calculation of Force and Moment

130.70 KN-m

Earth pressure coeifficients Active earth pressure co-efficient

Ka

=

0.35

Passive earth pressure co-efficient

Kp

=

2.88

=

0.510

for MCE

=

0.350

for DBE

=

(2/3)Ah

=

0.340

for MCE

0.233

for DBE

design horizontal seismic coefficient

Design vertical seismic coefficient

Active seismic pressure coefficient

Ah

Av

Casi λ λ1min λ2max

As per Technical Specification

(1±αv)cos2( φ-λ-α)/(cosλcos2αcos(δ+α+λ)) x [1/{1+{sin(φ+δ)x sin (φ-i-λ)/(cos(α-i)xcos(δ+α+λ))}0.5]2 (Refer IS:1893-1984-clause 8.1.1) = = = = =

tan-1αh/(1+-αv) 20.834 15.843 28.000 24.535

Degree

MCE

Degree Degree

DBE MCE

Degree

DBE

For simplifying the calculation of dynamic earth pressure coefficient, value of β can be taken = 0

i α Active seismic pressure coefficient

Casi

= = =

0 0 0.976

Caso

=

0.705

(Value of λ kept at max value to keep the formulae feasible)

Degree Degree MCE DBE

As per clause 8.1.1.2 of IS 1893, static active pressure due to earthquake is obtained by putting αh & αv and λ = 0 Static active seismic pressure coefficient

Passive seismic pressure coefficient

ki

Cpsi

=

0.31

(1±αv)cos2( φ-λ+α)/(cosλcos2αcos(δ-α+λ)) x [1/{1-{sin(φ+δ)x sin (φ+i-λ)/(cos(α-i)xcos(δ-α+λ))}0.5]2 (Refer IS:1893-1984-clause 8.1.2)

Cpsi

= = = = = =

tan-1αh/(1+-αv) 20.834 15.843 28.000 24.535 1.487

Cpso

=

2.268

λ λ1min λ2max Passive seismic pressure coefficient

Degree

MCE

Degree Degree

DBE MCE

Degree

DBE MCE

As per clause 8.1.2.2 of IS 1893, static passive pressure due to earthquake is obtained by putting αh & αv and λ = 0 Static passive seismic pressure coefficient

k0

Load Cases: 1. DL with pressure due to backfill soil 2. DL+ Pressure due to backfill + Seismic earth presure (MCE) 3. DL+ Pressure due to backfill + Seismic earth presure (DBE)

=

5.602 Load Combination: 1.5DL 1.0(DL+EL) for MCE 1.5(DL+EL) for DBE

DBE

Table-1: Load and moment calculation for load case1 Vertical Downward Weight

C.G. Seismic Force Point of Distance due to self application of Pi from Toe weight, Pi

Wi (kN/m)

Overturning moment due to Pi

Stablizing Moment

d (m)

αhWi (kN/m)

hi(m)

Moi=Pihi (kNm/m)

Mw = Wd (kN-m/m)

Remarks

W 1 = Ttop x h0 x γc

36.75

2.60

-

-

-

95.55

Wall weight (rectangular portion)

W 2 = B x Tf x γc

101.25

3.38

-

-

-

341.72

Toe & heel slab weight

376.52

4.75

-

-

1788.45

backfill weight (over heel)

18.38

2.35

-

-

43.18

Wall weight (triangular portion)

37.17

1.08

39.96

backfill weight (over toe)

W 3 = Lheelxh0x γs

W 4 = 0.5 x h0 x (Tbottom-Ttop) x γs W 5 = Ltoexh2x γs Total W i

570.06

-

-

-

-

-

2308.86

Overturning moment due to Pi

Stablizing Moment

Table-2: Load and moment calculation for load case1 (MCE) Vertical Downward Weight

C.G. Seismic Force Point of Distance due to self application of Pi from Toe weight, Pi

Wi (kN/m)

d (m)

αhWi (kN/m)

hi(m)

Moi=Pihi (kNm/m)

Mw = Wd (kN-m/m)

Remarks

W 1 = Ttop x h0 x γc

36.75

2.60

18.74

3.05

57.16

95.55

Wall weight (rectangular portion)

W 2 = B x Tf x γc

101.25

3.38

51.64

0.3

15.49

341.72

Toe & heel slab weight

376.52

4.75

1788.45

backfill weight (over heel)

18.38

2.35

43.18

Wall weight (triangular portion)

37.17

1.08

39.96

backfill weight (over toe)

W 3 = Lheelxh0x γs

W 4 = 0.5 x h0 x (Tbottom-Ttop) x γs W 5 = Ltoexh2x γs Total W i

570.06

9.37

2.23

79.75

20.93

93.59

2308.86

Overturning moment due to Pi

Stablizing Moment Mw = Wd (kN-m/m)

Table-3: Load and moment calculation for load case3 (DBE) Vertical Downward Weight

C.G. Seismic Force Point of Distance due to self application of Pi from Toe weight, Pi

Wi (kN/m)

d (m)

αhWi (kN/m)

hi(m)

Moi=Pihi (kNm/m)

Remarks

W 1 = Ttop x h0 x γc

36.75

2.60

12.86

3.05

39.23

95.55

Wall weight

W 2 = B x Tf x γc

101.25

3.38

35.44

0.3

10.63

341.72

Toe & heel slab weight

376.52

4.75

1788.45

backfill weight (over heel)

18.38

2.35

43.18

backfill weight (triangular portion)

37.17

1.08

39.96

backfill weight (over toe)

W 3 = Lheelxh0x γs

W 4 = 0.5 x h0 x (Tbottom-Ttop) x γs W 5 = Ltoexh2x γs Total W i

Overall depth of Wall, H

570.06

6.43

54.73 H

2.23

14.36

64.23

2308.86

=

5.500

m

H

P'av Pav β

Pah Ht/3

LOAD CASE 1 :

PRESSURE DUE TO BACKFILL

Active pressure due to backfill, PA = KaxγsxH

=

Active Force due to Backfill, Fa = PAxH/2

=

Active pressure due to surchage load of vehicle, PS = Kaxγsx1.2

=

8.00 kN/m2

Active Force due to Backfill, FS = PSx1.2

=

9.6 kN/m

Total horizontal force, Ph1 = (Fa+Pi+FS)

=

110.42 kN/m

Passive pressure due to backfill, PP = KpxγsxDf

=

83.05 kN/m2

Passive Force due to Backfill, Fp = PPxDf/2

=

62.29 kN/m

Overturning moment, Mo1

=

(= FaxH/3 + FSx(H-0.5*1.2))

Stability against overturning: Overturning moment for load case1

M01 Mp =

Stablizing moment due to passive pressure

FpxDf/3

Mw

Stablizing moment, Ms

36.66 kN/m2 100.82 kN/m

231.88 kN-m/m

=

231.88 kN-m/m

=

31.14375 kN-m/m

=

2340.00 kN-m/m

(FS) overturning = 0.9* Ms/Mo1

=

9.08

Stability against sliding: Sliding force, Ph1

=

110.42 kN

Resisting Force F = µ (Wi) + Fp

=

378.28 kN

(FS)Sliding

=

3.08

= = = = = =

4.05 1539.06 570.06 3.05 0.32 1.13

0.9*F/Ph1

Soil pressure at footing base Distance of vertical force from Toe Xw = Mw/Wi Stabilising Moment at heel, Mr = Wi ( B-Xw) Resultant vertical reaction = R = Wi Distance from heel Lr = (Mr + Mo1 - Mp)/R Eccentricity e = Lr - B/2 B/6

(Refer CL 214.1 of IRC 62014)

> 2.0, Hence OK

> 1.5, Hence OK

m m kN/m m m m

< B/6

Soil pressure at footing base Soil pressure at footing base:

:. ρmax,GROSS

=

ΣW B 108.48

:.

=

60.43

q

LOAD CASE 2 :

ρmin,GROSS

=

( 1± 6e/B)

KN/m²

KN/m² No tension at base

PRESSURE DUE TO BACKFILL+ SEISMIC (MCE) PRESSURE INCREMENT DUE TO BACKFILL AND SURCHARGE+SEISMIC (MCE) FORCE DUE TO SELFWEIGHT

Static Active pressure due to backfill, Psoil = KixγsxH

=

Force due to Backfill, Pa1 = PsoilxH/2

=

89.79 kN/m

Dynamic Active Seismic Force by backfill, Pa1si = CasixγsxHt2/2

=

283.58 kN/m

Dynamic force increment due to backfill, Pa2 =Pa1si - Pa1

=

193.79 kN/m

Dynamic pressure due to surchage load of vehicle, PS = Casixγsx1.2

=

Active Force due to Backfill, FS = PSx1.2

=

27 kN/m

=

390.33 kN/m

Static passive force, Pp1 = (1/2)xK0xγsxDf2

=

121.06 kN/m

Dynamic Passive Seismic Force by backfill, Pp1si = CpsixγsxDf2/2

=

32.14 kN/m

Dynamic force decrement due to backfill, Pp2 =Pp1-Pp1si

=

88.93 kN/m

Net horizontal passive force, Ph2 = Pp1si

=

32.14 kN/m

Total horizontal force, Ph1 = (Pa1+Pa2+Pi+Ps)

(89.79+193.79+79.75+27)

32.65 kN/m2

22.50 kN/m2

The dynamic increment shall be considered separately in addition to the static pressure and this will be considered to act at the mid-height of the wall as per the provision of the code IS 1893. The point of application of the dynamic decrement shall be assumed to be at an elevation 0.66H above the wall.

Overturning moment, M01

(= Pa1xH/3 + Pa2xH/2 + Moi + FSx(H-0.5*1.2))

Counter moment due to passive pressure, M02 Stability against overturning: Overturning moment Stablizing moment

=

(= Pp1xDf/3 + Pp2x(2/3)Df)

923.42 kN-m/m

=

149.46 kN-m/m

M01

=

923.42 kN-m/m

Mw + M02

=

2458.32 kN-m/m

(FS) overturning = 0.9* Ms/Mo1

=

2.40

Stability against sliding: Sliding force, Ph1

=

390.33 kN

Resisting Force F = µ ΣWi + Ph2

=

348.13 kN

(FS)Sliding

=

0.8

0.9*F/Ph1

> 1.5, Hence OK (for seismic case)

< 1.0, Not OK

Shear key need to be provided: Depth of shear key

ds

=

1.5

m

Total depth acting for passive pressure

dt

=

3

m

Passive Force due to Backfill, Fp = CpsixγsxDt2/2

=

128.54

Sliding force, Ph1

=

390.33 kN

Resisting Force F = µ (ΣWi) + Fp

=

444.53 kN

(FS)Sliding

=

1.02

= = = =

4.05 1539.06 570.06 4.06

0.9*F/Ph1

kN/m

> 1.0, Hence OK

Fp dt

ds

Shear Key

Soil pressure at footing base

Distance of vertical force from Toe Xw = Mw/Wi Stabilising Moment at heel, Mr = Wi ( B-Xw) Resultant vertical reaction = R = Wi Distance from heel Lr = (Mr + Mo1 - M02)/R Eccentricity e = Lr - B/2 B/6

= =

Soil pressure at footing base Soil pressure at footing base:

:. ρmax,GROSS

=

ΣW B 135.50

:.

=

33.41

KN/m²

q

=

ρmin,GROSS

( 1± 6e/B) KN/m²

Pressure on face of wall (Heel side) P1

=

93.91

KN/m²

Pressure on face of wall (Toe side) P2

=

102.98

KN/m²

Pmax,gross

P2

P1

No tension at base

Pmin,gross

m m kN/m m

0.68 m 1.13 m

< B/6

LOAD CASE 3 :

PRESSURE DUE TO BACKFILL+ SEISMIC (OBE) PRESSURE INCREMENT DUE TO BACKFILL AND SURCHARGE+SEISMIC (OBE) FORCE DUE TO SELFWEIGHT

Static Active pressure due to backfill, Psoil = KixγsxH

=

Force due to Backfill, Pa1 = PsoilxH/2

=

89.79 kN/m

Dynamic Active Seismic Force by backfill, Pa1si = CasoxγsxH /2

=

204.84 kN/m

Dynamic force increment due to backfill, Pa2 =Pa1si - Pa1

=

115.05 kN/m

Dynamic pressure due to surchage load of vehicle, PS = Casixγsx1.2

=

16.25 kN/m2

Active Force due to Backfill, FS = PSx1.2

=

19.5 kN/m

Total horizontal force, Ph1 = (Pa1+Pa2+Pi+Ps)

=

279.07 kN/m

2

2

32.65 kN/m2

=

121.06 kN/m

Dynamic Passive Seismic Force by backfill, Pp1si = Cps0xγsxDf /2

=

49.01 kN/m

Dynamic force decrement due to backfill, Pp2 =Pp1-Pp1si

=

72.05 kN/m

Net horizontal passive force, Ph2 = Pp1si

=

49.01 kN/m

Static passive pressure, Pp1 = (1/2)xK0xγsxDf

2

The dynamic increment shall be considered separately in addition to the static pressure and this will be considered to act at the mid-height of the wall as per the provision of the code IS 1893. The point of application of the dynamic decrement shall be assumed to be at an elevation 0.66H above the wall.

Overturning moment, Mo1

(= Pa1xH/3 + Pa2xH/2 + Moi + FSx(H-0.5*1.2))

Counter moment due to passive pressure, M02 Stability against overturning: Overturning moment for load case1 Stablizing moment

=

(= Pp1xDf/3 + Pp2x(2/3)Df)

640.78 kN-m/m

=

132.58 kN-m/m

M01

=

640.78 kN-m/m

Mw + M02

=

2441.44 kN-m/m

(FS) overturning = 0.9* Ms/Mo1

=

3.43

Stability against sliding: Sliding force, Ph1

=

279.07 kN

Resisting Force F = µ ΣWi + Ph2

=

365.01 kN

(FS)Sliding

=

1.18

0.9*F/Ph1

> 1.2, Hence OK

> 1.0, Hence OK

Shear key need to be provided: Depth of shear key

ds

=

1.5

m

Total depth acting for passive pressure

dt

=

3

m

Passive Force due to Backfill, Fp = Cps0xγsxDt2/2

=

196.06

Sliding force, Ph1

=

279.07 kN

Resisting Force F = µ (ΣWi) + Fp

=

512.05 kN

(FS)Sliding

=

1.65

= = = =

4.05 1539.06 570.06 3.59

0.9*F/Ph1

kN/m

> 1.0, Hence OK

Soil pressure at footing base

Distance of vertical force from Toe Xw = Mw/Wi Stabilising Moment at heel, Mr = Wi ( B-Xw) Resultant vertical reaction = R = Wi Distance from heel Lr = (Mr + Mo1 - M02)/R Eccentricity e = Lr - B/2 B/6

= =

Soil pressure at footing base Soil pressure at footing base:

:. ρmax,GROSS

=

ΣW B 100.97

:.

=

67.94

q

ρmin,GROSS

=

( 1± 6e/B)

KN/m²

KN/m² No tension at base

m m kN/m m

0.22 m 1.13 m

< B/6

Pressure on face of wall (Heel side) P1

=

87.51

KN/m²

Pressure on face of wall (Toe side) P2

=

90.45

KN/m²

Pmax,gross

P2

Pmin,gross

P1

Design of Toe slab The net pressure acting on toe slab shall be obtained by reducing net upward pressure of self weight of toe slab from gross pressure at base. γC x Tfooting

Self weight of toe slab, POT

=

Case 1: OBE Governing load combination is Net pressure acting on toe slab, Max. Pressure 1.5x100.97 - 1.5x15

=

W2

128.96 KN/m² W1

=

For trapezoidal area, moment shall be calculated as

113.18 KN/m²

 2W1  W2  L L  x xW1  W2 x  2  W1  W2  3

Mu =

Mu

285.89 KN-m

=

Case 2: MCE Governing load combination is Net pressure acting on toe slab, Max. Pressure 1.0x135.5 - 1.0x15

1.0 DL + 1.0 EL

Min. Pressure 1.0x102.98 - 1.0x15 Factored Moment,

L

1.5 DL + 1.5 EL

Min. Pressure 1.5x90.45 - 1.5x15

Factored Moment,

15 KN/m²

Mu

Calculation of Steel: Ast,Required Area of steel required in toe slab, Governing Factored Moment, Mu Effective Depth of Footing, d = D-(Clear Cover) - (0.5*Dia of Rebar) Clear Cover d' Dia of Rebar Φ :. d 2 Mu/(fckbd ) K=

=

120.50 KN/m²

=

87.98 KN/m²

=

253.45 KN-m

= =

Ast,Required

0.5xfck / fy x [1- sqrt{1 - (4.6 x K}] x b d 285.89 KN-m

= = = =

50 20 540 0.039

mm mm mm

=

1278.19

Sq.mm = =

Minimum area of steel required, As,min = 0.0012 b*d Area of steel required, As,req =

648.00 Sq.mm 1278 Sq.mm

Required spacing will be, SRequired = (π*Ø2/4)*1000/(As,req)

=

245.8 mm

Provide 20 Φ @ 140 mm c/c Area of steel provided, Ast,Provided = (Ø2*π/4)*1000/Sprovided

=

2244 Sq.mm

pt %

=

100*Ast/(b*d)

pt %

=

0.416

(where, b = 1000mm, unit width)

L

Shear Check The design shear force at d distance from face of wall (towards toe) Shear , V = W W 

 

Factored shear force, Vu Nominal shear stress, Design shear stress,

1

2

2

τv

= =

194.91 0.36

for pt %

=

0.416

τc

=

0.45

W2 W1

 x L  d   KNm/m N/mm2 N/mm2

OK

Design of Heel slab The net pressure acting on Heel slab shall be obtained by reducing net upward pressure of self weight of heel slab plus overburden pressure of soil from gross pressure at base. Self weight of Heel slab,

=

γC x Tfooting

=

15 KN/m²

Soil pressure on heel slab,

=

γs x (H-Tfooting)

= =

94.129 KN/m² 109.129 KN/m²

Net Downward Case 1: OBE Governing load combination is Net pressure acting on heel slab, Min. Pressure 1.5x109.129 - 1.5x87.51

1.5 DL + 1.5 EL

Max. Pressure 1.5x109.129 - 1.5x67.94

Factored Moment,

32.43 KN/m²

=

61.78 KN/m²

=

Mu

=

 2W1  W2 L x W1  W2 x 2  W1  W2

 L  x  3

415.99 KN-m

1.0 DL + 1.0 EL

Min. Pressure 1.0x109.129 - 1.0x33.41

Factored Moment,

=

Mu

Case 2: MCE Governing load combination is Net pressure acting on toe slab, Max. Pressure 1.0x109.129 - 1.0x93.91

W1 W2

Mu

Calculation of Steel: Ast,Required Area of steel required in toe slab, Governing Factored Moment, Mu Effective Depth of Footing, d = D-(Clear Cover)-(0.5*Dia of Rebar) Clear Cover d' Dia of Rebar Φ :. d Mu/(fckbd2) K=

=

15.22 KN/m²

=

75.72 KN/m²

=

444.42 KN-m

= =

Ast,Required

0.5xfck / fy x [1- sqrt{1 - (4.6 x K}] x b d 444.42 KN-m

= = = =

50 20 540 0.061

mm mm mm

=

2048.29

Sq.mm = =

Minimum area of steel required, As,min = 0.0012 b*d Area of steel required, As,req =

648.00 Sq.mm 2048 Sq.mm

Required spacing will be, SRequired = (π*Ø2/4)*1000/(As,req)

=

153.4 mm

Provide 20 Φ @ 140 mm c/c Area of steel provided, Ast,Provided = (Ø2*π/4)*1000/Sprovided

=

2244 Sq.mm

pt %

=

100*Ast/(b*d)

pt %

=

0.416

(where, b = 1000mm, unit width)

Shear Check The design shear force at d distance from face of wall (towards toe) Factored shear force, Vu = 163.0 τv Nominal shear stress, = 0.30 Design shear stress,

for pt %

=

0.416

τc

=

0.45

Design of Wall Calculation of Steel:

At bottom

4.90 m from top

KNm/m N/mm2 N/mm2

OK

Load Combination: for DBE for MCE

1.5DL 1.5(DL+EL) 1.0(DL+EL)

Case1:

Static Earth pressure, P1 = Ka x γs x h0

=

32.66 kN/m2

Factored Pressure 48.99 kN/m2

Case2: MCE

Dynamic Earth pressure, P2 = Casi x γs x h0

=

91.87 kN/m2

91.87 kN/m2

=

2

99.54 kN/m2

Case3: DBE

Dynamic Earth pressure, P3 = Cas0 x γs x h0

66.36 kN/m

So, case3 is governing [0.5xKixγsxh02x(h0/3) + 0.5x(Caso-Ki)xγsxho2x(h0/2)]

Moment acting at bottom of wall (At point B), factored moment, Mu

340.13 KN-m

=

(1.5x340.13)

=

510.195 KN-m

0.5xfck / fy x [1- sqrt{1 - (4.6 x K}] x b d

Ast,Required

=

Effective thickness of wall, d = Tf-(Clear Cover)-(0.5*Dia of Rebar) Clear Cover d' Dia of Rebar Φ :. d 2 Mu/(fckbd ) K=

= = = =

50 20 540 0.070

mm mm mm

Ast,Required

=

2383.45

Sq.mm

Area of steel required ,

Minimum area of vertical steel required, As,min = 0.0012 b*d

=

Area of steel required, As,req =

=

2383 Sq.mm

Required spacing will be, SRequired = (π*Ø /4)*1000/(As,req)

=

131.8 mm

Provide 20 Φ @ 125 mm c/c Area of steel provided, Ast,Provided = (Ø2*π/4)*1000/Sprovided

=

2513 Sq.mm

2

pt %

=

100*Ast/(b*d)

pt %

=

0.465

Curtailment of bar:

648.00 Sq.mm

(where, b = 1000mm, unit width)

Ast1/Ast2 = (h1/h2)2

Ast1 = 0.5Ast2

this gives

h1 =

Since, 50% of bar shall be Curtailed 0.7071*h2

[sqrt(1/2) = 0.7071]

= 3.46 m So, upto h1 height calculated as above 50% bar can be curtailed Minimum area of vertical steel required at outer face of wall, As,min = 0.0012 b*d Φ

=

12

Required spacing will be, SRequired = (π*Ø2/4)*1000/(As,req) Provide 12 Φ @ 125 mm c/c

=

Minimum area of horizontal steel required, As,min = 0.002 b*d Φ

=

16

Required spacing will be, SRequired = (π*Ø2/4)*1000/(As,req) Provide 16 Φ @ 125 mm c/c Shear Check At d distance from bottom 4.36 m from top The design shear force at h' distance from top of wall Shear , V = Load Factor = Factored shear force, Vu = τv Nominal shear stress, = Design shear stress,

648.00 Sq.mm

= mm

174.5 mm

1080.00 Sq.mm

= mm =

h' = 128.72 1.5 193.08 0.36

for pt %

=

0.465

τc

=

0.45

KNm/m Since DBE is governing KNm/m N/mm2 N/mm2

OK

186.2 mm

4.36

PROJECT

220/132KV NEW KHIMTI SUBSTATION

TITLE

DESIGN OF RETAINING WALL

DOCUMENT NO KEC/UTKHEP/17-2066/67/KHIMTI/C1/097 DESIGNED CHECKED PRK SWD

DATE 31-08-2018 SHEET

Design of Retaining Wall (3.0 m height from FGL/NGL) Input Data: 2

Grade of Concrete

fck

=

Grade of Steel Coefficient of Friction, SBC of soil

fyk µ qa

= = = = =

500 0.55 200 250 224.0125

=

274.0125 KN/m²

(In case of seismic, allowable pressure shall be increased by 25%) Allowable gross capacity, qG,allow = qa + γsDf (=200+19.21x1.25) (In case of seismic, allowable pressure shall be increased by 25%) Allowable gross capacity, qG,allow = qa + γsDf (=250+19.21x1.25)

25 N/mm N/mm

2

KN/m² KN/m² KN/m²

φ i δ α

= = = =

Ka

=

1 - sin Φ 1 + sin Φ

Ka

=

0.35

Kp

=

2.88

Density of concrete

γc

=

25 KN/m³

Density of soil Design parameters and Levels: Depth of Foundation below FGL

γs

=

19.21 KN/m³

Df

=

Height of Wall above from FGL

h1

=

3.0 m

Tfooting

=

0.45 m

h0 H h2

= = =

3.80 m 4.25 m 0.80 m

Angle of repose Angle of sloping sand Angle of external friction between wall and earthfill, assume δ = (2/3 φ) Angle which earth face of the wall makes with the vertical =

Coefficient of active earth pressure (sloping backfill)

29 0.0 19.3 0

deg deg deg deg

Coefficient of passive earth pressure (at rest)

Thickness of footing Height of wall Total height of wall Depth of top of footing below FGL

(upto top of footing only) (including thickness of footing)

Dimensions of Retaining Wall: Thickness of wall @ Top

1.25 m

Ttop

=

0.30 m

Tbottom

=

0.50 m

Tf

=

0.45 m

Length of toe

Ltoe

=

1.40 m

Length of heel

Lheel

=

3.10 m

=

5.00 m

Thickness of wall @ Bottom Thickness of footing

B = Ltoe + Tbottom + Lheel

Length of footing

W3 W1

h1

h0 H

α FGL/NGL W5

W4

h2

LHeel

LToe

B W2 B

Loading: (bottom of wall) (Pressure at Point B): Pressure due to inside sloping sand

Pe

=Ka x γs x h0

Pe

=0.35x19.21x3.8

=

25.33 KN/m²

Force acting on wall from inside soil

Pa

= 0.5 x Pe x h0

=

48.12 KN

Moment acting on wall at point B

MB

= Pa x h0/3

=

60.96 KN-m

:. Calculation of Force and Moment

Earth pressure coeifficients Active earth pressure co-efficient

Ka

=

0.35

Passive earth pressure co-efficient

Kp

=

2.88

=

0.510

for MCE

=

0.350

for DBE

=

(2/3)Ah

=

0.340

for MCE

0.233

for DBE

design horizontal seismic coefficient

Design vertical seismic coefficient

Active seismic pressure coefficient

Ah

Av

Casi λ λ1min λ2max

As per Technical Specification

(1±αv)cos2( φ-λ-α)/(cosλcos2αcos(δ+α+λ)) x [1/{1+{sin(φ+δ)x sin (φ-i-λ)/(cos(α-i)xcos(δ+α+λ))}0.5]2 (Refer IS:1893-1984-clause 8.1.1) = = = = =

tan-1αh/(1+-αv) 20.834 15.843 28.000 24.535

Degree

MCE

Degree Degree

DBE MCE

Degree

DBE

For simplifying the calculation of dynamic earth pressure coefficient, value of β can be taken = 0

i α Active seismic pressure coefficient

Casi

= = =

0 0 0.976

Caso

=

0.705

(Value of λ kept at max value to keep the formulae feasible)

Degree Degree MCE DBE

As per clause 8.1.1.2 of IS 1893, static active pressure due to earthquake is obtained by putting αh & αv and λ = 0 Static active seismic pressure coefficient

Passive seismic pressure coefficient

ki

Cpsi

=

0.31

(1±αv)cos2( φ-λ+α)/(cosλcos2αcos(δ-α+λ)) x [1/{1-{sin(φ+δ)x sin (φ+i-λ)/(cos(α-i)xcos(δ-α+λ))}0.5]2 (Refer IS:1893-1984-clause 8.1.2)

Cpsi

= = = = = =

tan-1αh/(1+-αv) 20.834 15.843 28.000 24.535 1.487

Cpso

=

2.268

λ λ1min λ2max Passive seismic pressure coefficient

Degree

MCE

Degree Degree

DBE MCE

Degree

DBE MCE

As per clause 8.1.2.2 of IS 1893, static passive pressure due to earthquake is obtained by putting αh & αv and λ = 0 Static passive seismic pressure coefficient

k0

Load Cases: 1. DL with pressure due to backfill soil 2. DL+ Pressure due to backfill + Seismic earth presure (MCE) 3. DL+ Pressure due to backfill + Seismic earth presure (DBE)

=

5.602 Load Combination: 1.5DL 1.0(DL+EL) for MCE 1.5(DL+EL) for DBE

DBE

Table-1: Load and moment calculation for load case1 Vertical Downward Weight

C.G. Seismic Force Point of Distance due to self application of Pi from Toe weight, Pi

Wi (kN/m)

Overturning moment due to Pi

Stablizing Moment

d (m)

αhWi (kN/m)

hi(m)

Moi=Pihi (kNm/m)

Mw = Wd (kN-m/m)

Remarks

W 1 = Ttop x h0 x γc

28.50

1.75

-

-

-

49.88

Wall weight (rectangular portion)

W 2 = B x Tf x γc

56.25

2.50

-

-

-

140.63

Toe & heel slab weight

226.29

3.45

-

-

780.71

backfill weight (over heel)

9.50

1.53

-

-

14.57

Wall weight (triangular portion)

21.52

0.70

15.06

backfill weight (over toe)

W 3 = Lheelxh0x γs

W 4 = 0.5 x h0 x (Tbottom-Ttop) x γs W 5 = Ltoexh2x γs Total W i

342.06

-

-

-

-

-

1000.84

Overturning moment due to Pi

Stablizing Moment

Table-2: Load and moment calculation for load case1 (MCE) Vertical Downward Weight

C.G. Seismic Force Point of Distance due to self application of Pi from Toe weight, Pi

Wi (kN/m)

d (m)

αhWi (kN/m)

hi(m)

Moi=Pihi (kNm/m)

Mw = Wd (kN-m/m)

Remarks

W 1 = Ttop x h0 x γc

28.50

1.75

14.54

2.35

34.16

49.88

Wall weight (rectangular portion)

W 2 = B x Tf x γc

56.25

2.50

28.69

0.225

6.45

140.63

Toe & heel slab weight

226.29

3.45

780.71

backfill weight (over heel)

9.50

1.53

14.57

Wall weight (triangular portion)

21.52

0.70

15.06

backfill weight (over toe)

W 3 = Lheelxh0x γs

W 4 = 0.5 x h0 x (Tbottom-Ttop) x γs W 5 = Ltoexh2x γs Total W i

342.06

4.85

1.72

48.07

8.32

48.93

1000.84

Overturning moment due to Pi

Stablizing Moment

hi(m)

Moi=Pihi (kNm/m)

Mw = Wd (kN-m/m)

Table-3: Load and moment calculation for load case3 (DBE) Vertical Downward Weight

C.G. Seismic Force Point of Distance due to self application of Pi from Toe weight, Pi

Wi (kN/m)

d (m)

αhWi (kN/m)

Remarks

W 1 = Ttop x h0 x γc

28.50

1.75

9.98

2.35

23.44

49.88

Wall weight

W 2 = B x Tf x γc

56.25

2.50

19.69

0.225

4.43

140.63

Toe & heel slab weight

226.29

3.45

780.71

backfill weight (over heel)

9.50

1.53

14.57

backfill weight (triangular portion)

21.52

0.70

15.06

backfill weight (over toe)

W 3 = Lheelxh0x γs

W 4 = 0.5 x h0 x (Tbottom-Ttop) x γs W 5 = Ltoexh2x γs Total W i

Overall depth of Wall, H

342.06

3.33

32.99 H

1.72

5.71

33.58

1000.84

=

4.250

m

H

P'av Pav β

Pah Ht/3

LOAD CASE 1 :

PRESSURE DUE TO BACKFILL

Active pressure due to backfill, PA = KaxγsxH

=

28.33 kN/m2

Active Force due to Backfill, Fa = PAxH/2

=

60.2 kN/m

Active pressure due to surchage load of vehicle, PS = Kaxγsx1.2

=

8.00 kN/m2

Active Force due to Backfill, FS = PSx1.2

=

9.6 kN/m

Total horizontal force, Ph1 = (Fa+Pi+FS)

=

69.80 kN/m

Passive pressure due to backfill, PP = KpxγsxDf

=

69.21 kN/m2

Passive Force due to Backfill, Fp = PPxDf/2

=

43.26 kN/m

Overturning moment, Mo1

=

(= FaxH/3 + FSx(H-0.5*1.2))

Stability against overturning: Overturning moment for load case1

M01 Mp =

Stablizing moment due to passive pressure

FpxDf/3

Mw

Stablizing moment, Ms

120.32 kN-m/m

=

120.32 kN-m/m

=

18.0234375 kN-m/m

=

1018.86 kN-m/m

(FS) overturning = 0.9* Ms/Mo1

=

Stability against sliding: Sliding force, Ph1

=

69.80 kN

Resisting Force F = µ (Wi) + Fp

=

232.86 kN

(FS)Sliding

=

3

= = = = = =

2.93 709.46 342.06 2.37 0.13 0.83

0.9*F/Ph1

Soil pressure at footing base Distance of vertical force from Toe Xw = Mw/Wi Stabilising Moment at heel, Mr = Wi ( B-Xw) Resultant vertical reaction = R = Wi Distance from heel Lr = (Mr + Mo1 - Mp)/R Eccentricity e = Lr - B/2 B/6

(Refer CL 214.1 of IRC 62014)

7.62

> 2.0, Hence OK

> 1.5, Hence OK

m m kN/m m m m

< B/6

Soil pressure at footing base Soil pressure at footing base:

:. ρmax,GROSS

=

ΣW B 79.08

:.

=

57.74

q

LOAD CASE 2 :

ρmin,GROSS

=

( 1± 6e/B)

KN/m²

KN/m² No tension at base

PRESSURE DUE TO BACKFILL+ SEISMIC (MCE) PRESSURE INCREMENT DUE TO BACKFILL AND SURCHARGE+SEISMIC (MCE) FORCE DUE TO SELFWEIGHT

Static Active pressure due to backfill, Psoil = KixγsxH

=

Force due to Backfill, Pa1 = PsoilxH/2

=

53.61 kN/m

Dynamic Active Seismic Force by backfill, Pa1si = CasixγsxHt2/2

=

169.33 kN/m

Dynamic force increment due to backfill, Pa2 =Pa1si - Pa1

=

115.72 kN/m

Dynamic pressure due to surchage load of vehicle, PS = Casixγsx1.2

=

Active Force due to Backfill, FS = PSx1.2

=

27 kN/m

=

244.40 kN/m

Static passive force, Pp1 = (1/2)xK0xγsxDf2

=

84.07 kN/m

Dynamic Passive Seismic Force by backfill, Pp1si = CpsixγsxDf2/2

=

22.32 kN/m

Dynamic force decrement due to backfill, Pp2 =Pp1-Pp1si

=

61.75 kN/m

Net horizontal passive force, Ph2 = Pp1si

=

22.32 kN/m

Total horizontal force, Ph1 = (Pa1+Pa2+Pi+Ps)

(53.61+115.72+48.07+27)

25.23 kN/m2

22.50 kN/m2

The dynamic increment shall be considered separately in addition to the static pressure and this will be considered to act at the mid-height of the wall as per the provision of the code IS 1893. The point of application of the dynamic decrement shall be assumed to be at an elevation 0.66H above the wall.

Overturning moment, M01

(= Pa1xH/3 + Pa2xH/2 + Moi + FSx(H-0.5*1.2))

Counter moment due to passive pressure, M02 Stability against overturning: M01 Overturning moment

=

(= Pp1xDf/3 + Pp2x(2/3)Df)

=

Mw + M02

Stablizing moment

469.33 kN-m/m 86.49 kN-m/m

=

469.33 kN-m/m

=

1087.33 kN-m/m

(FS) overturning = 0.9* Ms/Mo1

=

2.09

Stability against sliding: Sliding force, Ph1

=

244.40 kN

Resisting Force F = µ ΣWi + Ph2

=

211.92 kN

(FS)Sliding

=

0.78

0.9*F/Ph1

> 1.5, Hence OK (for seismic case)

< 1.0, Not OK

Shear key need to be provided: Depth of shear key

ds

=

1.25

m

Total depth acting for passive pressure

dt

=

2.5

m

Passive Force due to Backfill, Fp = CpsixγsxDt2/2

=

89.27

Sliding force, Ph1

=

244.40 kN

Resisting Force F = µ (ΣWi) + Fp

=

278.88 kN

(FS)Sliding

=

1.03

= = = =

2.93 709.46 342.06 3.19

0.9*F/Ph1

kN/m

> 1.0, Hence OK

Fp dt

ds

Shear Key

Soil pressure at footing base

Distance of vertical force from Toe Xw = Mw/Wi Stabilising Moment at heel, Mr = Wi ( B-Xw) Resultant vertical reaction = R = Wi Distance from heel Lr = (Mr + Mo1 - M02)/R Eccentricity e = Lr - B/2 B/6

= =

Soil pressure at footing base Soil pressure at footing base:

:. ρmax,GROSS

=

ΣW B 125.06

:.

=

11.77

KN/m²

Pressure on face of wall (Heel side) P1

=

82.01

KN/m²

Pressure on face of wall (Toe side) P2

=

93.34

KN/m²

q

Pmax,gross

=

ρmin,GROSS

P2

P1

( 1± 6e/B) KN/m² No tension at base

Pmin,gross

m m kN/m m

0.69 m 0.83 m

< B/6

LOAD CASE 3 :

PRESSURE DUE TO BACKFILL+ SEISMIC (OBE) PRESSURE INCREMENT DUE TO BACKFILL AND SURCHARGE+SEISMIC (OBE) FORCE DUE TO SELFWEIGHT

Static Active pressure due to backfill, Psoil = KixγsxH

=

Force due to Backfill, Pa1 = PsoilxH/2

=

53.61 kN/m

Dynamic Active Seismic Force by backfill, Pa1si = CasoxγsxH /2

=

122.31 kN/m

Dynamic force increment due to backfill, Pa2 =Pa1si - Pa1

=

68.7 kN/m

Dynamic pressure due to surchage load of vehicle, PS = Casixγsx1.2

=

16.25 kN/m2

Active Force due to Backfill, FS = PSx1.2

=

19.5 kN/m

Total horizontal force, Ph1 = (Pa1+Pa2+Pi+Ps)

=

174.80 kN/m

2

2

25.23 kN/m2

=

84.07 kN/m

Dynamic Passive Seismic Force by backfill, Pp1si = Cps0xγsxDf /2

=

34.04 kN/m

Dynamic force decrement due to backfill, Pp2 =Pp1-Pp1si

=

50.03 kN/m

Net horizontal passive force, Ph2 = Pp1si

=

34.04 kN/m

Static passive pressure, Pp1 = (1/2)xK0xγsxDf

2

The dynamic increment shall be considered separately in addition to the static pressure and this will be considered to act at the mid-height of the wall as per the provision of the code IS 1893. The point of application of the dynamic decrement shall be assumed to be at an elevation 0.66H above the wall.

Overturning moment, Mo1

(= Pa1xH/3 + Pa2xH/2 + Moi + FSx(H-0.5*1.2))

Counter moment due to passive pressure, M02 Stability against overturning: Overturning moment for load case1 Stablizing moment

=

(= Pp1xDf/3 + Pp2x(2/3)Df)

326.69 kN-m/m

=

76.72 kN-m/m

M01

=

326.69 kN-m/m

Mw + M02

=

1077.56 kN-m/m

(FS) overturning = 0.9* Ms/Mo1

=

2.97

Stability against sliding: Sliding force, Ph1

=

174.80 kN

Resisting Force F = µ ΣWi + Ph2

=

223.64 kN

(FS)Sliding

=

1.15

0.9*F/Ph1

> 1.2, Hence OK

> 1.0, Hence OK

Shear key need to be provided: Depth of shear key

ds

=

1.25

m

Total depth acting for passive pressure

dt

=

2.5

m

Passive Force due to Backfill, Fp = Cps0xγsxDt2/2

=

136.15

Sliding force, Ph1

=

174.80 kN

Resisting Force F = µ (ΣWi) + Fp

=

325.76 kN

(FS)Sliding

=

1.68

= = = =

2.93 709.45 342.06 2.80

0.9*F/Ph1

kN/m

> 1.0, Hence OK

Soil pressure at footing base

Distance of vertical force from Toe Xw = Mw/Wi Stabilising Moment at heel, Mr = Wi ( B-Xw) Resultant vertical reaction = R = Wi Distance from heel Lr = (Mr + Mo1 - M02)/R Eccentricity e = Lr - B/2 B/6

= =

Soil pressure at footing base Soil pressure at footing base:

:. ρmax,GROSS

=

ΣW B 93.04

:.

=

43.78

q

ρmin,GROSS

=

( 1± 6e/B)

KN/m²

KN/m² No tension at base

m m kN/m m

0.3 m 0.83 m

< B/6

Pressure on face of wall (Heel side) P1

=

74.32

KN/m²

Pressure on face of wall (Toe side) P2

=

79.25

KN/m²

Pmax,gross

P2

Pmin,gross

P1

Design of Toe slab The net pressure acting on toe slab shall be obtained by reducing net upward pressure of self weight of toe slab from gross pressure at base. γC x Tfooting

Self weight of toe slab, POT

=

Case 1: OBE Governing load combination is Net pressure acting on toe slab, Max. Pressure 1.5x93.04 - 1.5x11.25

L

1.5 DL + 1.5 EL =

=

For trapezoidal area, moment shall be calculated as

102.00 KN/m²

 2W1  W2  L L  x xW1  W2 x  2  W1  W2  3

Mu =

Mu

113.47 KN-m

=

Case 2: MCE Governing load combination is Net pressure acting on toe slab, Max. Pressure 1.0x125.06 - 1.0x11.25

1.0 DL + 1.0 EL =

113.81 KN/m²

Min. Pressure 1.0x93.34 - 1.0x11.25

=

82.09 KN/m²

Mu

=

101.17 KN-m

Factored Moment,

W2

122.69 KN/m² W1

Min. Pressure 1.5x79.25 - 1.5x11.25

Factored Moment,

11.25 KN/m²

Calculation of Steel: Ast,Required Area of steel required in toe slab, Governing Factored Moment, Mu Effective Depth of Footing, d = D-(Clear Cover) - (0.5*Dia of Rebar) Clear Cover d' Dia of Rebar Φ :. d 2 Mu/(fckbd ) K=

= =

Ast,Required

0.5xfck / fy x [1- sqrt{1 - (4.6 x K}] x b d 113.47 KN-m

= = = =

50 16 392 0.030

mm mm mm

=

690.09

Sq.mm = =

Minimum area of steel required, As,min = 0.0012 b*d Area of steel required, As,req =

470.40 Sq.mm 690 Sq.mm

Required spacing will be, SRequired = (π*Ø2/4)*1000/(As,req)

=

291.4 mm

Provide 16 Φ @ 125 mm c/c Area of steel provided, Ast,Provided = (Ø2*π/4)*1000/Sprovided

=

1608 Sq.mm

pt %

=

100*Ast/(b*d)

pt %

=

0.410

(where, b = 1000mm, unit width)

L

Shear Check The design shear force at d distance from face of wall (towards toe) Shear , V = W W 

 

Factored shear force, Vu Nominal shear stress, Design shear stress,

1

2

2

τv

= =

113.24 0.29

for pt %

=

0.410

τc

=

0.44

W2 W1

 x L  d   KNm/m N/mm2 N/mm2

OK

Design of Heel slab The net pressure acting on Heel slab shall be obtained by reducing net upward pressure of self weight of heel slab plus overburden pressure of soil from gross pressure at base. Self weight of Heel slab,

=

γC x Tfooting

=

11.25 KN/m²

Soil pressure on heel slab,

=

γs x (H-Tfooting)

= =

72.998 KN/m² 84.248 KN/m²

Net Downward Case 1: OBE Governing load combination is Net pressure acting on heel slab, Min. Pressure 1.5x84.248 - 1.5x74.32

1.5 DL + 1.5 EL

Max. Pressure 1.5x84.248 - 1.5x43.78

Factored Moment,

14.89 KN/m²

=

60.70 KN/m²

=

Mu

=

 2W1  W2 L xW1  W2 x 2  W1  W2

 L  x  3

218.3 KN-m

1.0 DL + 1.0 EL

Min. Pressure 1.0x84.248 - 1.0x11.77 Factored Moment,

=

Mu

Case 2: MCE Governing load combination is Net pressure acting on toe slab, Max. Pressure 1.0x84.248 - 1.0x82.01

W1 W2

Mu

Calculation of Steel: Ast,Required Area of steel required in toe slab, Governing Factored Moment, Mu Effective Depth of Footing, d = D-(Clear Cover)-(0.5*Dia of Rebar) Clear Cover d' Dia of Rebar Φ :. d Mu/(fckbd2) K=

=

2.24 KN/m²

=

72.48 KN/m²

=

235.76 KN-m

= =

Ast,Required

0.5xfck / fy x [1- sqrt{1 - (4.6 x K}] x b d 235.76 KN-m

= = = =

50 16 392 0.061

mm mm mm

=

1497.74

Sq.mm = =

Minimum area of steel required, As,min = 0.0012 b*d Area of steel required, As,req =

470.40 Sq.mm 1498 Sq.mm

Required spacing will be, SRequired = (π*Ø2/4)*1000/(As,req)

=

134.2 mm

Provide 16 Φ @ 125 mm c/c Area of steel provided, Ast,Provided = (Ø2*π/4)*1000/Sprovided

=

1608 Sq.mm

pt %

=

100*Ast/(b*d)

pt %

=

0.410

(where, b = 1000mm, unit width)

Shear Check The design shear force at d distance from face of wall (towards toe) Factored shear force, Vu = 102.4 τv Nominal shear stress, = 0.26 Design shear stress,

for pt %

=

0.410

τc

=

0.44

Design of Wall Calculation of Steel:

At bottom

3.80 m from top

KNm/m N/mm2 N/mm2

OK

Load Combination: for DBE for MCE

1.5DL 1.5(DL+EL) 1.0(DL+EL)

Case1:

Static Earth pressure, P1 = Ka x γs x h0

=

25.33 kN/m2

Factored Pressure 37.99 kN/m2

Case2: MCE

Dynamic Earth pressure, P2 = Casi x γs x h0

=

71.25 kN/m2

71.25 kN/m2

Case3: DBE

Dynamic Earth pressure, P3 = Cas0 x γs x h0

=

51.46 kN/m2

77.20 kN/m2

So, case3 is governing [0.5xKixγsxh02x(h0/3) + 0.5x(Caso-Ki)xγsxho2x(h0/2)]

Moment acting at bottom of wall (At point B), factored moment, Mu

158.64 KN-m

=

(1.5x158.64)

Ast,Required

=

0.5xfck / fy x [1- sqrt{1 - (4.6 x K}] x b d

Effective thickness of wall, d = Tf-(Clear Cover)-(0.5*Dia of Rebar) Clear Cover d' Dia of Rebar Φ :. d 2 Mu/(fckbd ) K=

= = = =

50 16 442 0.049

mm mm mm

Ast,Required

=

1316.70

Sq.mm

Area of steel required ,

=

237.96 KN-m

Minimum area of vertical steel required, As,min = 0.0012 b*d

=

Area of steel required, As,req =

=

1317 Sq.mm

Required spacing will be, SRequired = (π*Ø /4)*1000/(As,req)

=

152.7 mm

Provide 16 Φ @ 140 mm c/c Area of steel provided, Ast,Provided = (Ø2*π/4)*1000/Sprovided

=

1436 Sq.mm

2

pt %

=

100*Ast/(b*d)

pt %

=

0.325

(where, b = 1000mm, unit width)

Minimum area of vertical steel required at outer face of wall, As,min = 0.0012 b*d Φ

=

12

Required spacing will be, SRequired = (π*Ø2/4)*1000/(As,req) Provide 12 Φ @ 120 mm c/c

Φ

=

12

Required spacing will be, SRequired = (π*Ø2/4)*1000/(As,req) Provide 12 Φ @ 120 mm c/c Shear Check At d distance from bottom 3.36 m from top The design shear force at h' distance from top of wall Shear , V = Load Factor = Factored shear force, Vu = τv Nominal shear stress, =

530.40 Sq.mm

= mm =

Minimum area of horizontal steel required, As,min = 0.002 b*d

Design shear stress,

530.40 Sq.mm

213.2 mm

884.00 Sq.mm

= mm =

h' = 76.36 1.5 114.54 0.26

for pt %

=

0.325

τc

=

0.40

KNm/m Since DBE is governing KNm/m N/mm2 N/mm2

OK

127.9 mm

3.36

PROJECT

220/132KV NEW KHIMTI SUBSTATION

TITLE

DESIGN OF RETAINING WALL

DOCUMENT NO KEC/UTKHEP/17-2066/67/KHIMTI/C1/097 DESIGNED CHECKED PRK SWD

DATE 31-08-2018 SHEET

Design of Retaining Wall (2.0 m height from FGL/NGL) Input Data: 2

Grade of Concrete

fck

=

Grade of Steel Coefficient of Friction, SBC of soil

fyk µ qa

= = = = =

500 0.55 200 250 224.0125

=

274.0125 KN/m²

(In case of seismic, allowable pressure shall be increased by 25%) Allowable gross capacity, qG,allow = qa + γsDf (=200+19.21x1.25) (In case of seismic, allowable pressure shall be increased by 25%) Allowable gross capacity, qG,allow = qa + γsDf (=250+19.21x1.25)

25 N/mm N/mm

2

KN/m² KN/m² KN/m²

φ i δ α

= = = =

Ka

=

1 - sin Φ 1 + sin Φ

Ka

=

0.35

Kp

=

2.88

Density of concrete

γc

=

25 KN/m³

Density of soil Design parameters and Levels: Depth of Foundation below FGL

γs

=

19.21 KN/m³

Df

=

Height of Wall above from FGL

h1

=

2.0 m

Tfooting

=

0.30 m

h0 H h2

= = =

2.95 m 3.25 m 0.95 m

Angle of repose Angle of sloping sand Angle of external friction between wall and earthfill, assume δ = (2/3 φ) Angle which earth face of the wall makes with the vertical =

Coefficient of active earth pressure (sloping backfill)

29 0.0 19.3 0

deg deg deg deg

Coefficient of passive earth pressure (at rest)

Thickness of footing Height of wall Total height of wall Depth of top of footing below FGL

(upto top of footing only) (including thickness of footing)

Dimensions of Retaining Wall: Thickness of wall @ Top

1.25 m

Ttop

=

0.20 m

Tbottom

=

0.35 m

Tf

=

0.30 m

Length of toe

Ltoe

=

1.20 m

Length of heel

Lheel

=

2.45 m

=

4.00 m

Thickness of wall @ Bottom Thickness of footing

B = Ltoe + Tbottom + Lheel

Length of footing

W3 W1

h1

h0 H

α FGL/NGL W5

W4

h2

LHeel

LToe

B W2 B

Loading: (bottom of wall) (Pressure at Point B): Pressure due to inside sloping sand

Pe

=Ka x γs x h0

Pe

=0.35x19.21x2.95

=

19.66 KN/m²

Force acting on wall from inside soil

Pa

= 0.5 x Pe x h0

=

29.00 KN

Moment acting on wall at point B

MB

= Pa x h0/3

=

28.52 KN-m

:. Calculation of Force and Moment

Earth pressure coeifficients Active earth pressure co-efficient

Ka

=

0.35

Passive earth pressure co-efficient

Kp

=

2.88

=

0.510

for MCE

=

0.350

for DBE

=

(2/3)Ah

=

0.340

for MCE

0.233

for DBE

design horizontal seismic coefficient

Design vertical seismic coefficient

Active seismic pressure coefficient

Ah

Av

Casi λ λ1min λ2max

As per Technical Specification

(1±αv)cos2( φ-λ-α)/(cosλcos2αcos(δ+α+λ)) x [1/{1+{sin(φ+δ)x sin (φ-i-λ)/(cos(α-i)xcos(δ+α+λ))}0.5]2 (Refer IS:1893-1984-clause 8.1.1) = = = = =

tan-1αh/(1+-αv) 20.834 15.843 28.000 24.535

Degree

MCE

Degree Degree

DBE MCE

Degree

DBE

For simplifying the calculation of dynamic earth pressure coefficient, value of β can be taken = 0

i α Active seismic pressure coefficient

Casi

= = =

0 0 0.976

Caso

=

0.705

(Value of λ kept at max value to keep the formulae feasible)

Degree Degree MCE DBE

As per clause 8.1.1.2 of IS 1893, static active pressure due to earthquake is obtained by putting αh & αv and λ = 0 Static active seismic pressure coefficient

Passive seismic pressure coefficient

ki

Cpsi

=

0.31

(1±αv)cos2( φ-λ+α)/(cosλcos2αcos(δ-α+λ)) x [1/{1-{sin(φ+δ)x sin (φ+i-λ)/(cos(α-i)xcos(δ-α+λ))}0.5]2 (Refer IS:1893-1984-clause 8.1.2)

Cpsi

= = = = = =

tan-1αh/(1+-αv) 20.834 15.843 28.000 24.535 1.487

Cpso

=

2.268

λ λ1min λ2max Passive seismic pressure coefficient

Degree

MCE

Degree Degree

DBE MCE

Degree

DBE MCE

As per clause 8.1.2.2 of IS 1893, static passive pressure due to earthquake is obtained by putting αh & αv and λ = 0 Static passive seismic pressure coefficient

k0

Load Cases: 1. DL with pressure due to backfill soil 2. DL+ Pressure due to backfill + Seismic earth presure (MCE) 3. DL+ Pressure due to backfill + Seismic earth presure (DBE)

=

5.602 Load Combination: 1.5DL 1.0(DL+EL) for MCE 1.5(DL+EL) for DBE

DBE

Table-1: Load and moment calculation for load case1 Vertical Downward Weight

C.G. Seismic Force Point of Distance due to self application of Pi from Toe weight, Pi

Wi (kN/m)

Overturning moment due to Pi

Stablizing Moment

d (m)

αhWi (kN/m)

hi(m)

Moi=Pihi (kNm/m)

Mw = Wd (kN-m/m)

Remarks

W 1 = Ttop x h0 x γc

14.75

1.45

-

-

-

21.39

Wall weight (rectangular portion)

W 2 = B x Tf x γc

30.00

2.00

-

-

-

60.00

Toe & heel slab weight

138.84

2.78

-

-

385.28

backfill weight (over heel)

5.53

1.30

-

-

7.19

Wall weight (triangular portion)

21.90

0.60

13.14

backfill weight (over toe)

W 3 = Lheelxh0x γs

W 4 = 0.5 x h0 x (Tbottom-Ttop) x γs W 5 = Ltoexh2x γs Total W i

211.02

-

-

-

-

-

487.00

Overturning moment due to Pi

Stablizing Moment

Table-2: Load and moment calculation for load case1 (MCE) Vertical Downward Weight

C.G. Seismic Force Point of Distance due to self application of Pi from Toe weight, Pi

Wi (kN/m)

d (m)

αhWi (kN/m)

hi(m)

Moi=Pihi (kNm/m)

Mw = Wd (kN-m/m)

Remarks

W 1 = Ttop x h0 x γc

14.75

1.45

7.52

1.775

13.35

21.39

Wall weight (rectangular portion)

W 2 = B x Tf x γc

30.00

2.00

15.30

0.15

2.30

60.00

Toe & heel slab weight

138.84

2.78

385.28

backfill weight (over heel)

5.53

1.30

7.19

Wall weight (triangular portion)

21.90

0.60

13.14

backfill weight (over toe)

W 3 = Lheelxh0x γs

W 4 = 0.5 x h0 x (Tbottom-Ttop) x γs W 5 = Ltoexh2x γs Total W i

211.02

2.82

1.28

25.64

3.62

19.27

487.00

Overturning moment due to Pi

Stablizing Moment

Table-3: Load and moment calculation for load case3 (DBE) Vertical Downward Weight

C.G. Seismic Force Point of Distance due to self application of Pi from Toe weight, Pi

Wi (kN/m)

d (m)

αhWi (kN/m)

hi(m)

Moi=Pihi (kNm/m)

Mw = Wd (kN-m/m)

Remarks

W 1 = Ttop x h0 x γc

14.75

1.45

5.16

1.775

9.16

21.39

Wall weight

W 2 = B x Tf x γc

30.00

2.00

10.50

0.15

1.58

60.00

Toe & heel slab weight

138.84

2.78

385.28

backfill weight (over heel)

5.53

1.30

7.19

backfill weight (triangular portion)

21.90

0.60

13.14

backfill weight (over toe)

W 3 = Lheelxh0x γs

W 4 = 0.5 x h0 x (Tbottom-Ttop) x γs W 5 = Ltoexh2x γs Total W i

Overall depth of Wall, H

211.02

1.94

17.60 H

1.28

2.48

13.22

487.00

=

3.250

m

H

P'av Pav β

Pah Ht/3

LOAD CASE 1 :

PRESSURE DUE TO BACKFILL

Active pressure due to backfill, PA = KaxγsxH

=

21.66 kN/m2

Active Force due to Backfill, Fa = PAxH/2

=

35.2 kN/m

Active pressure due to surchage load of vehicle, PS = Kaxγsx1.2

=

8.00 kN/m2

Active Force due to Backfill, FS = PSx1.2

=

9.6 kN/m

Total horizontal force, Ph1 = (Fa+Pi+FS)

=

44.80 kN/m

Passive pressure due to backfill, PP = KpxγsxDf

=

69.21 kN/m2

Passive Force due to Backfill, Fp = PPxDf/2

=

43.26 kN/m

Overturning moment, Mo1

=

63.57 kN-m/m

(= FaxH/3 + FSx(H-0.5*1.2))

Stability against overturning: Overturning moment for load case1

M01 Mp =

Stablizing moment due to passive pressure

FpxDf/3

Mw

Stablizing moment, Ms

=

63.57 kN-m/m

=

18.0234375 kN-m/m

=

505.02 kN-m/m

(FS) overturning = 0.9* Ms/Mo1

=

Stability against sliding: Sliding force, Ph1

=

44.80 kN

Resisting Force F = µ (Wi) + Fp

=

160.23 kN

(FS)Sliding

=

3.22

= = = = = =

2.31 357.08 211.02 1.91 0.09 0.67

0.9*F/Ph1

Soil pressure at footing base Distance of vertical force from Toe Xw = Mw/Wi Stabilising Moment at heel, Mr = Wi ( B-Xw) Resultant vertical reaction = R = Wi Distance from heel Lr = (Mr + Mo1 - Mp)/R Eccentricity e = Lr - B/2 B/6

7.15

(Refer CL 214.1 of IRC 62014)

> 2.0, Hence OK

> 1.5, Hence OK

m m kN/m m m m

< B/6

Soil pressure at footing base Soil pressure at footing base:

:. ρmax,GROSS

=

ΣW B 59.88

:.

=

45.63

q

LOAD CASE 2 :

ρmin,GROSS

=

( 1± 6e/B)

KN/m²

KN/m² No tension at base

PRESSURE DUE TO BACKFILL+ SEISMIC (MCE) PRESSURE INCREMENT DUE TO BACKFILL AND SURCHARGE+SEISMIC (MCE) FORCE DUE TO SELFWEIGHT

Static Active pressure due to backfill, Psoil = KixγsxH

=

19.29 kN/m2

Force due to Backfill, Pa1 = PsoilxH/2

=

31.35 kN/m

Dynamic Active Seismic Force by backfill, Pa1si = CasixγsxHt2/2

=

99.02 kN/m

Dynamic force increment due to backfill, Pa2 =Pa1si - Pa1

=

67.67 kN/m

Dynamic pressure due to surchage load of vehicle, PS = Casixγsx1.2

=

22.50 kN/m2

Active Force due to Backfill, FS = PSx1.2

=

27 kN/m

=

151.66 kN/m

Static passive force, Pp1 = (1/2)xK0xγsxDf2

=

84.07 kN/m

Dynamic Passive Seismic Force by backfill, Pp1si = CpsixγsxDf2/2

=

22.32 kN/m

Dynamic force decrement due to backfill, Pp2 =Pp1-Pp1si

=

61.75 kN/m

Net horizontal passive force, Ph2 = Pp1si

=

22.32 kN/m

Total horizontal force, Ph1 = (Pa1+Pa2+Pi+Ps)

(31.35+67.67+25.64+27)

The dynamic increment shall be considered separately in addition to the static pressure and this will be considered to act at the mid-height of the wall as per the provision of the code IS 1893. The point of application of the dynamic decrement shall be assumed to be at an elevation 0.66H above the wall.

Overturning moment, M01

(= Pa1xH/3 + Pa2xH/2 + Moi + FSx(H-0.5*1.2))

Counter moment due to passive pressure, M02 Stability against overturning: M01 Overturning moment

=

(= Pp1xDf/3 + Pp2x(2/3)Df)

=

86.49 kN-m/m

Mw + M02

Stablizing moment

234.74 kN-m/m

=

234.74 kN-m/m

=

573.49 kN-m/m

(FS) overturning = 0.9* Ms/Mo1

=

2.20

Stability against sliding: Sliding force, Ph1

=

151.66 kN

Resisting Force F = µ ΣWi + Ph2

=

139.29 kN

(FS)Sliding

=

0.83

0.9*F/Ph1

> 1.5, Hence OK (for seismic case)

< 1.0, Not OK

Shear key need to be provided: Depth of shear key

ds

=

0.7

m

Total depth acting for passive pressure

dt

=

1.95

m

Passive Force due to Backfill, Fp = CpsixγsxDt2/2

=

54.31

kN/m

Sliding force, Ph1

=

151.66 kN

Resisting Force F = µ (ΣWi) + Fp

=

171.28 kN

(FS)Sliding

=

1.02

= = = =

2.31 357.08 211.02 2.39

0.9*F/Ph1

> 1.0, Hence OK

Fp

dt

ds

Shear Key

Soil pressure at footing base

Distance of vertical force from Toe Xw = Mw/Wi Stabilising Moment at heel, Mr = Wi ( B-Xw) Resultant vertical reaction = R = Wi Distance from heel Lr = (Mr + Mo1 - M02)/R Eccentricity e = Lr - B/2 B/6

= =

Soil pressure at footing base Soil pressure at footing base:

:. ρmax,GROSS

=

ΣW B 83.62

:.

=

21.89

KN/m²

Pressure on face of wall (Heel side) P1

=

59.70

KN/m²

Pressure on face of wall (Toe side) P2

=

65.10

KN/m²

q

Pmax,gross

=

ρmin,GROSS

P2

P1

( 1± 6e/B) KN/m² No tension at base

Pmin,gross

m m kN/m m

0.39 m 0.67 m

< B/6

LOAD CASE 3 :

PRESSURE DUE TO BACKFILL+ SEISMIC (OBE) PRESSURE INCREMENT DUE TO BACKFILL AND SURCHARGE+SEISMIC (OBE) FORCE DUE TO SELFWEIGHT

Static Active pressure due to backfill, Psoil = KixγsxH

=

19.29 kN/m2

Force due to Backfill, Pa1 = PsoilxH/2

=

31.35 kN/m

Dynamic Active Seismic Force by backfill, Pa1si = CasoxγsxH /2

=

71.52 kN/m

Dynamic force increment due to backfill, Pa2 =Pa1si - Pa1

=

40.17 kN/m

Dynamic pressure due to surchage load of vehicle, PS = Casixγsx1.2

=

16.25 kN/m2

Active Force due to Backfill, FS = PSx1.2

=

19.5 kN/m

Total horizontal force, Ph1 = (Pa1+Pa2+Pi+Ps)

=

108.62 kN/m

2

2

=

84.07 kN/m

Dynamic Passive Seismic Force by backfill, Pp1si = Cps0xγsxDf /2

=

34.04 kN/m

Dynamic force decrement due to backfill, Pp2 =Pp1-Pp1si

=

50.03 kN/m

Net horizontal passive force, Ph2 = Pp1si

=

34.04 kN/m

Static passive pressure, Pp1 = (1/2)xK0xγsxDf

2

The dynamic increment shall be considered separately in addition to the static pressure and this will be considered to act at the mid-height of the wall as per the provision of the code IS 1893. The point of application of the dynamic decrement shall be assumed to be at an elevation 0.66H above the wall.

Overturning moment, Mo1

(= Pa1xH/3 + Pa2xH/2 + Moi + FSx(H-0.5*1.2))

Counter moment due to passive pressure, M02 Stability against overturning: Overturning moment for load case1 Stablizing moment

=

(= Pp1xDf/3 + Pp2x(2/3)Df)

=

164.14 kN-m/m 76.72 kN-m/m

M01

=

164.14 kN-m/m

Mw + M02

=

563.72 kN-m/m

(FS) overturning = 0.9* Ms/Mo1

=

3.09

Stability against sliding: Sliding force, Ph1

=

108.62 kN

Resisting Force F = µ ΣWi + Ph2

=

151.01 kN

(FS)Sliding

=

1.25

0.9*F/Ph1

> 1.2, Hence OK

> 1.0, Hence OK

Shear key need to be provided: Depth of shear key

ds

=

0.7

m

Total depth acting for passive pressure

dt

=

1.95

m

Passive Force due to Backfill, Fp = Cps0xγsxDt2/2

=

82.83

kN/m

Sliding force, Ph1

=

108.62 kN

Resisting Force F = µ (ΣWi) + Fp

=

199.80 kN

(FS)Sliding

=

1.66

= = = =

2.31 357.08 211.02 2.11

0.9*F/Ph1

> 1.0, Hence OK

Soil pressure at footing base

Distance of vertical force from Toe Xw = Mw/Wi Stabilising Moment at heel, Mr = Wi ( B-Xw) Resultant vertical reaction = R = Wi Distance from heel Lr = (Mr + Mo1 - M02)/R Eccentricity e = Lr - B/2 B/6

= =

Soil pressure at footing base Soil pressure at footing base:

:. ρmax,GROSS

=

ΣW B 61.46

:.

=

44.05

q

ρmin,GROSS

=

( 1± 6e/B)

KN/m²

KN/m² No tension at base

m m kN/m m

0.11 m 0.67 m

< B/6

Pressure on face of wall (Heel side) P1

=

54.71

KN/m²

Pressure on face of wall (Toe side) P2

=

56.24

KN/m²

Pmax,gross

P2

Pmin,gross

P1

Design of Toe slab The net pressure acting on toe slab shall be obtained by reducing net upward pressure of self weight of toe slab from gross pressure at base. γC x Tfooting

Self weight of toe slab, POT

=

Case 1: OBE Governing load combination is Net pressure acting on toe slab, Max. Pressure 1.5x61.46 - 1.5x7.5

=

W2

80.94 KN/m² W1

=

For trapezoidal area, moment shall be calculated as

73.11 KN/m²

 2W1  W2 L xW1  W2 x  W W 2 2  1

Mu =

Mu

 L  x 3 

56.40 KN-m

=

Case 2: MCE Governing load combination is Net pressure acting on toe slab, Max. Pressure 1.0x83.62 - 1.0x7.5

1.0 DL + 1.0 EL

Min. Pressure 1.0x65.1 - 1.0x7.5 Factored Moment,

L

1.5 DL + 1.5 EL

Min. Pressure 1.5x56.24 - 1.5x7.5

Factored Moment,

7.5 KN/m²

Mu

Calculation of Steel: Ast,Required Area of steel required in toe slab, Governing Factored Moment, Mu Effective Depth of Footing, d = D-(Clear Cover) - (0.5*Dia of Rebar) Clear Cover d' Dia of Rebar Φ :. d Mu/(fckbd2) K=

=

76.12 KN/m²

=

57.60 KN/m²

=

50.36 KN-m

= =

Ast,Required

0.5xfck / fy x [1- sqrt{1 - (4.6 x K}] x b d 56.40 KN-m

= = = =

50 12 244 0.038

mm mm mm

=

557.05

Sq.mm = =

Minimum area of steel required, As,min = 0.0012 b*d Area of steel required, As,req =

292.80 Sq.mm 557 Sq.mm

Required spacing will be, SRequired = (π*Ø2/4)*1000/(As,req)

=

203.0 mm

Provide 12 Φ @ 115 mm c/c Area of steel provided, Ast,Provided = (Ø2*π/4)*1000/Sprovided

=

983 Sq.mm

pt %

=

100*Ast/(b*d)

pt %

=

0.403

(where, b = 1000mm, unit width)

L

Shear Check The design shear force at d distance from face of wall (towards toe) Shear , V = W W 

 

Factored shear force, Vu Nominal shear stress, Design shear stress,

1

2

2

τv

= =

73.64 0.30

for pt %

=

0.403

τc

=

0.41

W2 W1

 x L  d   KNm/m N/mm2 N/mm2

OK

Design of Heel slab The net pressure acting on Heel slab shall be obtained by reducing net upward pressure of self weight of heel slab plus overburden pressure of soil from gross pressure at base. Self weight of Heel slab,

=

γC x Tfooting

=

7.5 KN/m²

Soil pressure on heel slab,

=

γs x (H-Tfooting)

= =

56.6695 KN/m² 64.1695 KN/m²

Net Downward Case 1: OBE Governing load combination is Net pressure acting on heel slab, Min. Pressure 1.5x64.1695 - 1.5x54.71

1.5 DL + 1.5 EL

Max. Pressure 1.5x64.1695 - 1.5x44.05

Factored Moment,

14.19 KN/m²

=

30.18 KN/m²

=

Mu

=

 2W1  W2 L xW1  W2 x 2  W1  W2

 L  x  3

74.58 KN-m

1.0 DL + 1.0 EL

Min. Pressure 1.0x64.1695 - 1.0x21.89 Factored Moment,

=

Mu

Case 2: MCE Governing load combination is Net pressure acting on toe slab, Max. Pressure 1.0x64.1695 - 1.0x59.7

W1 W2

Mu

Calculation of Steel: Ast,Required Area of steel required in toe slab, Governing Factored Moment, Mu Effective Depth of Footing, d = D-(Clear Cover)-(0.5*Dia of Rebar) Clear Cover d' Dia of Rebar Φ :. d Mu/(fckbd2) K=

=

4.47 KN/m²

=

42.28 KN/m²

=

89.07 KN-m

= =

Ast,Required

0.5xfck / fy x [1- sqrt{1 - (4.6 x K}] x b d 89.07 KN-m

= = = =

50 12 244 0.060

mm mm mm

=

907.03

Sq.mm = =

Minimum area of steel required, As,min = 0.0012 b*d Area of steel required, As,req =

292.80 Sq.mm 907 Sq.mm

Required spacing will be, SRequired = (π*Ø2/4)*1000/(As,req)

=

124.7 mm

Provide 12 Φ @ 115 mm c/c Area of steel provided, Ast,Provided = (Ø2*π/4)*1000/Sprovided

=

983 Sq.mm

pt %

=

100*Ast/(b*d)

pt %

=

0.403

(where, b = 1000mm, unit width)

Shear Check The design shear force at d distance from face of wall (towards toe) Factored shear force, Vu = 51.6 τv Nominal shear stress, = 0.21 Design shear stress,

for pt %

=

0.403

τc

=

0.44

Design of Wall Calculation of Steel:

At bottom

2.95 m from top

KNm/m N/mm2 N/mm2

OK

Load Combination: for DBE for MCE

1.5DL 1.5(DL+EL) 1.0(DL+EL)

Case1:

Static Earth pressure, P1 = Ka x γs x h0

=

19.66 kN/m2

Factored Pressure 29.49 kN/m2

Case2: MCE

Dynamic Earth pressure, P2 = Casi x γs x h0

=

55.31 kN/m2

55.31 kN/m2

Case3: DBE

Dynamic Earth pressure, P3 = Cas0 x γs x h0

=

39.95 kN/m2

59.93 kN/m2

So, case3 is governing [0.5xKixγsxh02x(h0/3) + 0.5x(Caso-Ki)xγsxho2x(h0/2)]

Moment acting at bottom of wall (At point B), factored moment, Mu

74.22 KN-m

=

(1.5x74.22)

=

111.33 KN-m

0.5xfck / fy x [1- sqrt{1 - (4.6 x K}] x b d

Ast,Required

=

Effective thickness of wall, d = Tf-(Clear Cover)-(0.5*Dia of Rebar) Clear Cover d' Dia of Rebar Φ :. d 2 Mu/(fckbd ) K=

= = = =

50 12 294 0.052

mm mm mm

Ast,Required

=

929.75

Sq.mm

Area of steel required ,

Minimum area of vertical steel required, As,min = 0.0012 b*d

=

352.80 Sq.mm

Area of steel required, As,req =

=

930 Sq.mm

Required spacing will be, SRequired = (π*Ø /4)*1000/(As,req)

=

121.6 mm

Provide 12 Φ @ 115 mm c/c Area of steel provided, Ast,Provided = (Ø2*π/4)*1000/Sprovided

=

983 Sq.mm

2

pt %

=

100*Ast/(b*d)

pt %

=

0.335

(where, b = 1000mm, unit width)

Minimum area of vertical steel required at outer face of wall, As,min = 0.0012 b*d Φ

=

10

Required spacing will be, SRequired = (π*Ø2/4)*1000/(As,req) Provide 10 Φ @ 115 mm c/c

=

Minimum area of horizontal steel required, As,min = 0.002 b*d Φ

=

10

Required spacing will be, SRequired = (π*Ø2/4)*1000/(As,req) Provide 10 Φ @ 115 mm c/c Shear Check At d distance from bottom 2.66 m from top The design shear force at h' distance from top of wall Shear , V = Load Factor = Factored shear force, Vu = τv Nominal shear stress, = Design shear stress,

352.80 Sq.mm

= mm

222.6 mm

588.00 Sq.mm

= mm =

h' = 47.77 1.5 71.66 0.24

for pt %

=

0.335

τc

=

0.40

KNm/m Since DBE is governing KNm/m N/mm2 N/mm2

OK

133.6 mm

2.66

PROJECT

220/132KV NEW KHIMTI SUBSTATION

TITLE

DESIGN OF RETAINING WALL

DOCUMENT NO KEC/UTKHEP/17-2066/67/KHIMTI/C1/097 DESIGNED CHECKED PRK SWD

DATE 31-08-2018 SHEET

Design of Retaining Wall (1.0 m height from FGL/NGL) Input Data: 2

Grade of Concrete

fck

=

Grade of Steel Coefficient of Friction, SBC of soil

fyk µ qa

= = = = =

500 0.55 175 218.75 198.052

=

241.802 KN/m²

(In case of seismic, allowable pressure shall be increased by 25%) Allowable gross capacity, qG,allow = qa + γsDf (=175+19.21x1.2) (In case of seismic, allowable pressure shall be increased by 25%) Allowable gross capacity, qG,allow = qa + γsDf (=218.75+19.21x1.2)

25 N/mm N/mm

2

KN/m² KN/m² KN/m²

φ i δ α

= = = =

Ka

=

1 - sin Φ 1 + sin Φ

Ka

=

0.35

Kp

=

2.88

Density of concrete

γc

=

25 KN/m³

Density of soil Design parameters and Levels: Depth of Foundation below FGL

γs

=

19.21 KN/m³

Df

=

Height of Wall above from FGL

h1

=

1.0 m

Tfooting

=

0.30 m

h0 H h2

= = =

1.90 m 2.20 m 0.90 m

Angle of repose Angle of sloping sand Angle of external friction between wall and earthfill, assume δ = (2/3 φ) Angle which earth face of the wall makes with the vertical =

Coefficient of active earth pressure (sloping backfill)

29 0.0 19.3 0

deg deg deg deg

Coefficient of passive earth pressure (at rest)

Thickness of footing Height of wall Total height of wall Depth of top of footing below FGL

(upto top of footing only) (including thickness of footing)

Dimensions of Retaining Wall: Thickness of wall @ Top

1.2 m

Ttop

=

0.20 m

Tbottom

=

0.25 m

Tf

=

0.30 m

Length of toe

Ltoe

=

0.75 m

Length of heel

Lheel

=

1.80 m

=

2.80 m

Thickness of wall @ Bottom Thickness of footing

B = Ltoe + Tbottom + Lheel

Length of footing

W3 W1

h1

h0 H

α FGL/NGL W5

W4

h2

LHeel

LToe

B W2 B

Loading: (bottom of wall) (Pressure at Point B): Pressure due to inside sloping sand

Pe

=Ka x γs x h0

Pe

=0.35x19.21x1.9

=

12.66 KN/m²

Force acting on wall from inside soil

Pa

= 0.5 x Pe x h0

=

12.03 KN

Moment acting on wall at point B

MB

= Pa x h0/3

=

:. Calculation of Force and Moment

7.62 KN-m

Earth pressure coeifficients Active earth pressure co-efficient

Ka

=

0.35

Passive earth pressure co-efficient

Kp

=

2.88

=

0.510

for MCE

=

0.350

for DBE

=

(2/3)Ah

=

0.340

for MCE

0.233

for DBE

design horizontal seismic coefficient

Design vertical seismic coefficient

Active seismic pressure coefficient

Ah

Av

Casi λ λ1min λ2max

As per Technical Specification

(1±αv)cos2( φ-λ-α)/(cosλcos2αcos(δ+α+λ)) x [1/{1+{sin(φ+δ)x sin (φ-i-λ)/(cos(α-i)xcos(δ+α+λ))}0.5]2 (Refer IS:1893-1984-clause 8.1.1) = = = = =

tan-1αh/(1+-αv) 20.834 15.843 28.000 24.535

Degree

MCE

Degree Degree

DBE MCE

Degree

DBE

For simplifying the calculation of dynamic earth pressure coefficient, value of β can be taken = 0

i α Active seismic pressure coefficient

Casi

= = =

0 0 0.976

Caso

=

0.705

(Value of λ kept at max value to keep the formulae feasible)

Degree Degree MCE DBE

As per clause 8.1.1.2 of IS 1893, static active pressure due to earthquake is obtained by putting αh & αv and λ = 0 Static active seismic pressure coefficient

Passive seismic pressure coefficient

ki

Cpsi

=

0.31

(1±αv)cos2( φ-λ+α)/(cosλcos2αcos(δ-α+λ)) x [1/{1-{sin(φ+δ)x sin (φ+i-λ)/(cos(α-i)xcos(δ-α+λ))}0.5]2 (Refer IS:1893-1984-clause 8.1.2)

Cpsi

= = = = = =

tan-1αh/(1+-αv) 20.834 15.843 28.000 24.535 1.487

Cpso

=

2.268

λ λ1min λ2max Passive seismic pressure coefficient

Degree

MCE

Degree Degree

DBE MCE

Degree

DBE MCE

As per clause 8.1.2.2 of IS 1893, static passive pressure due to earthquake is obtained by putting αh & αv and λ = 0 Static passive seismic pressure coefficient

k0

Load Cases: 1. DL with pressure due to backfill soil 2. DL+ Pressure due to backfill + Seismic earth presure (MCE) 3. DL+ Pressure due to backfill + Seismic earth presure (DBE)

=

5.602 Load Combination: 1.5DL 1.0(DL+EL) for MCE 1.5(DL+EL) for DBE

DBE

Table-1: Load and moment calculation for load case1 Vertical Downward Weight

C.G. Seismic Force Point of Distance due to self application of Pi from Toe weight, Pi

Wi (kN/m)

Overturning moment due to Pi

Stablizing Moment

d (m)

αhWi (kN/m)

hi(m)

Moi=Pihi (kNm/m)

Mw = Wd (kN-m/m)

Remarks

W 1 = Ttop x h0 x γc

9.50

0.90

-

-

-

8.55

Wall weight (rectangular portion)

W 2 = B x Tf x γc

21.00

1.40

-

-

-

29.40

Toe & heel slab weight

65.70

1.90

-

-

124.83

backfill weight (over heel)

1.19

0.78

-

-

0.93

Wall weight (triangular portion)

12.97

0.38

4.86

backfill weight (over toe)

W 3 = Lheelxh0x γs

W 4 = 0.5 x h0 x (Tbottom-Ttop) x γs W 5 = Ltoexh2x γs Total W i

110.35

-

-

-

-

-

168.57

Overturning moment due to Pi

Stablizing Moment

Table-2: Load and moment calculation for load case1 (MCE) Vertical Downward Weight

C.G. Seismic Force Point of Distance due to self application of Pi from Toe weight, Pi

Wi (kN/m)

d (m)

αhWi (kN/m)

hi(m)

Moi=Pihi (kNm/m)

Mw = Wd (kN-m/m)

Remarks

W 1 = Ttop x h0 x γc

9.50

0.90

4.85

1.25

6.06

8.55

Wall weight (rectangular portion)

W 2 = B x Tf x γc

21.00

1.40

10.71

0.15

1.61

29.40

Toe & heel slab weight

65.70

1.90

124.83

backfill weight (over heel)

1.19

0.78

0.93

Wall weight (triangular portion)

12.97

0.38

4.86

backfill weight (over toe)

W 3 = Lheelxh0x γs

W 4 = 0.5 x h0 x (Tbottom-Ttop) x γs W 5 = Ltoexh2x γs Total W i

110.35

0.61

0.93

16.16

0.57

8.23

168.57

Overturning moment due to Pi

Stablizing Moment Mw = Wd (kN-m/m)

Table-3: Load and moment calculation for load case3 (DBE) Vertical Downward Weight

C.G. Seismic Force Point of Distance due to self application of Pi from Toe weight, Pi

Wi (kN/m)

d (m)

αhWi (kN/m)

hi(m)

Moi=Pihi (kNm/m)

Remarks

W 1 = Ttop x h0 x γc

9.50

0.90

3.33

1.25

4.16

8.55

Wall weight

W 2 = B x Tf x γc

21.00

1.40

7.35

0.15

1.10

29.40

Toe & heel slab weight

65.70

1.90

124.83

backfill weight (over heel)

1.19

0.78

0.93

backfill weight (triangular portion)

12.97

0.38

4.86

backfill weight (over toe)

W 3 = Lheelxh0x γs

W 4 = 0.5 x h0 x (Tbottom-Ttop) x γs W 5 = Ltoexh2x γs Total W i

Overall depth of Wall, H

110.35

0.42

11.09 H

0.93

0.39

5.65

168.57

=

2.200

m

H

P'av Pav β

Pah Ht/3

LOAD CASE 1 :

PRESSURE DUE TO BACKFILL

Active pressure due to backfill, PA = KaxγsxH

=

14.66 kN/m2

Active Force due to Backfill, Fa = PAxH/2

=

16.13 kN/m

Active pressure due to surchage load of vehicle, PS = Kaxγsx1.2

=

8.00 kN/m2

Active Force due to Backfill, FS = PSx1.2

=

9.6 kN/m

Total horizontal force, Ph1 = (Fa+Pi+FS)

=

25.73 kN/m

Passive pressure due to backfill, PP = KpxγsxDf

=

66.44 kN/m2

Passive Force due to Backfill, Fp = PPxDf/2

=

39.86 kN/m

Overturning moment, Mo1

=

27.19 kN-m/m

(= FaxH/3 + FSx(H-0.5*1.2))

Stability against overturning: Overturning moment for load case1

M01 Mp =

Stablizing moment due to passive pressure

FpxDf/3

Mw

Stablizing moment, Ms

=

27.19 kN-m/m

=

15.9456 kN-m/m

=

184.52 kN-m/m

(FS) overturning = 0.9* Ms/Mo1

=

Stability against sliding: Sliding force, Ph1

=

25.73 kN

Resisting Force F = µ (Wi) + Fp

=

101.03 kN

(FS)Sliding

=

3.53

= = = = = =

1.53 140.42 110.35 1.37 0.03 0.47

0.9*F/Ph1

Soil pressure at footing base Distance of vertical force from Toe Xw = Mw/Wi Stabilising Moment at heel, Mr = Wi ( B-Xw) Resultant vertical reaction = R = Wi Distance from heel Lr = (Mr + Mo1 - Mp)/R Eccentricity e = Lr - B/2 B/6

6.11

(Refer CL 214.1 of IRC 62014)

> 2.0, Hence OK

> 1.5, Hence OK

m m kN/m m m m

< B/6

Soil pressure at footing base Soil pressure at footing base:

:. ρmax,GROSS

=

ΣW B 41.95

:.

=

36.88

q

LOAD CASE 2 :

ρmin,GROSS

=

( 1± 6e/B)

KN/m²

KN/m² No tension at base

PRESSURE DUE TO BACKFILL+ SEISMIC (MCE) PRESSURE INCREMENT DUE TO BACKFILL AND SURCHARGE+SEISMIC (MCE) FORCE DUE TO SELFWEIGHT

Static Active pressure due to backfill, Psoil = KixγsxH

=

13.06 kN/m2

Force due to Backfill, Pa1 = PsoilxH/2

=

14.37 kN/m

Dynamic Active Seismic Force by backfill, Pa1si = CasixγsxHt2/2

=

45.37 kN/m

Dynamic force increment due to backfill, Pa2 =Pa1si - Pa1

=

Dynamic pressure due to surchage load of vehicle, PS = Casixγsx1.2

=

Active Force due to Backfill, FS = PSx1.2

=

27 kN/m

=

88.53 kN/m

Static passive force, Pp1 = (1/2)xK0xγsxDf2

=

77.48 kN/m

Dynamic Passive Seismic Force by backfill, Pp1si = CpsixγsxDf2/2

=

20.57 kN/m

Dynamic force decrement due to backfill, Pp2 =Pp1-Pp1si

=

56.91 kN/m

Net horizontal passive force, Ph2 = Pp1si

=

20.57 kN/m

Total horizontal force, Ph1 = (Pa1+Pa2+Pi+Ps)

(14.37+31+16.16+27)

31 kN/m 22.50 kN/m2

The dynamic increment shall be considered separately in addition to the static pressure and this will be considered to act at the mid-height of the wall as per the provision of the code IS 1893. The point of application of the dynamic decrement shall be assumed to be at an elevation 0.66H above the wall.

Overturning moment, M01

(= Pa1xH/3 + Pa2xH/2 + Moi + FSx(H-0.5*1.2))

Counter moment due to passive pressure, M02 Stability against overturning: M01 Overturning moment

=

(= Pp1xDf/3 + Pp2x(2/3)Df)

=

76.52 kN-m/m

Mw + M02

Stablizing moment

96.07 kN-m/m

=

96.07 kN-m/m

=

245.09 kN-m/m

(FS) overturning = 0.9* Ms/Mo1

=

Stability against sliding: Sliding force, Ph1

=

88.53 kN

Resisting Force F = µ ΣWi + Ph2

=

81.74 kN

(FS)Sliding

=

0.9*F/Ph1

2.30

> 1.5, Hence OK (for seismic case)

0.83

< 1.0, Not OK

Shear key need to be provided: Depth of shear key

ds

=

0.5

m

Total depth acting for passive pressure

dt

=

1.7

m

Passive Force due to Backfill, Fp = CpsixγsxDt2/2

=

41.28

Sliding force, Ph1

=

88.53 kN

Resisting Force F = µ (ΣWi) + Fp

=

102.45 kN

(FS)Sliding

=

1.04

= = = =

1.53 140.42 110.35 1.45

0.9*F/Ph1

kN/m

> 1.0, Hence OK

Fp dt

ds

Shear Key

Soil pressure at footing base

Distance of vertical force from Toe Xw = Mw/Wi Stabilising Moment at heel, Mr = Wi ( B-Xw) Resultant vertical reaction = R = Wi Distance from heel Lr = (Mr + Mo1 - M02)/R Eccentricity e = Lr - B/2 B/6

= =

Soil pressure at footing base Soil pressure at footing base:

:. ρmax,GROSS

=

ΣW B 43.63

:.

=

35.19

KN/m²

Pressure on face of wall (Heel side) P1

=

40.62

KN/m²

Pressure on face of wall (Toe side) P2

=

41.37

KN/m²

q

Pmax,gross

=

ρmin,GROSS

P2

P1

( 1± 6e/B) KN/m² No tension at base

Pmin,gross

m m kN/m m

0.05 m 0.47 m

< B/6

LOAD CASE 3 :

PRESSURE DUE TO BACKFILL+ SEISMIC (OBE) PRESSURE INCREMENT DUE TO BACKFILL AND SURCHARGE+SEISMIC (OBE) FORCE DUE TO SELFWEIGHT

Static Active pressure due to backfill, Psoil = KixγsxH

=

13.06 kN/m2

Force due to Backfill, Pa1 = PsoilxH/2

=

14.37 kN/m

Dynamic Active Seismic Force by backfill, Pa1si = CasoxγsxH /2

=

32.77 kN/m

Dynamic force increment due to backfill, Pa2 =Pa1si - Pa1

=

18.4 kN/m

Dynamic pressure due to surchage load of vehicle, PS = Casixγsx1.2

=

16.25 kN/m2

Active Force due to Backfill, FS = PSx1.2

=

19.5 kN/m

Total horizontal force, Ph1 = (Pa1+Pa2+Pi+Ps)

=

63.36 kN/m

2

2

=

77.48 kN/m

Dynamic Passive Seismic Force by backfill, Pp1si = Cps0xγsxDf /2

=

31.37 kN/m

Dynamic force decrement due to backfill, Pp2 =Pp1-Pp1si

=

46.11 kN/m

Net horizontal passive force, Ph2 = Pp1si

=

31.37 kN/m

Static passive pressure, Pp1 = (1/2)xK0xγsxDf

2

The dynamic increment shall be considered separately in addition to the static pressure and this will be considered to act at the mid-height of the wall as per the provision of the code IS 1893. The point of application of the dynamic decrement shall be assumed to be at an elevation 0.66H above the wall.

Overturning moment, Mo1

(= Pa1xH/3 + Pa2xH/2 + Moi + FSx(H-0.5*1.2))

Counter moment due to passive pressure, M02 Stability against overturning: Overturning moment for load case1 Stablizing moment

=

(= Pp1xDf/3 + Pp2x(2/3)Df)

=

67.62 kN-m/m 67.88 kN-m/m

M01

=

67.62 kN-m/m

Mw + M02

=

236.45 kN-m/m

(FS) overturning = 0.9* Ms/Mo1

=

Stability against sliding: Sliding force, Ph1

=

63.36 kN

Resisting Force F = µ ΣWi + Ph2

=

92.54 kN

(FS)Sliding

=

0.9*F/Ph1

3.15

> 1.2, Hence OK

1.31

> 1.0, Hence OK

Shear key need to be provided: Depth of shear key

ds

=

0.5

m

Total depth acting for passive pressure

dt

=

1.7

m

Passive Force due to Backfill, Fp = Cps0xγsxDt2/2

=

62.96

Sliding force, Ph1

=

63.36 kN

Resisting Force F = µ (ΣWi) + Fp

=

124.13 kN

(FS)Sliding

=

1.76

= = = =

1.53 140.42 110.35 1.27

0.9*F/Ph1

kN/m

> 1.0, Hence OK

Soil pressure at footing base

Distance of vertical force from Toe Xw = Mw/Wi Stabilising Moment at heel, Mr = Wi ( B-Xw) Resultant vertical reaction = R = Wi Distance from heel Lr = (Mr + Mo1 - M02)/R Eccentricity e = Lr - B/2 B/6

= =

Soil pressure at footing base Soil pressure at footing base:

:. ρmax,GROSS

=

ΣW B 50.39

:.

=

28.43

q

ρmin,GROSS

=

( 1± 6e/B)

KN/m²

KN/m² No tension at base

m m kN/m m

0.13 m 0.47 m

< B/6

Pressure on face of wall (Heel side) P1

=

42.55

KN/m²

Pressure on face of wall (Toe side) P2

=

44.51

KN/m²

Pmax,gross

P2

Pmin,gross

P1

Design of Toe slab The net pressure acting on toe slab shall be obtained by reducing net upward pressure of self weight of toe slab from gross pressure at base. γC x Tfooting

Self weight of toe slab, POT

=

Case 1: OBE Governing load combination is Net pressure acting on toe slab, Max. Pressure 1.5x50.39 - 1.5x7.5

=

W2

64.34 KN/m² W1

=

For trapezoidal area, moment shall be calculated as

55.52 KN/m²

 2W1  W2  L L  x xW1  W2 x  2  W1  W2  3

Mu =

Mu

17.27 KN-m

=

Case 2: MCE Governing load combination is Net pressure acting on toe slab, Max. Pressure 1.0x43.63 - 1.0x7.5

1.0 DL + 1.0 EL

Min. Pressure 1.0x41.37 - 1.0x7.5 Factored Moment,

L

1.5 DL + 1.5 EL

Min. Pressure 1.5x44.51 - 1.5x7.5

Factored Moment,

7.5 KN/m²

Mu

Calculation of Steel: Ast,Required Area of steel required in toe slab, Governing Factored Moment, Mu Effective Depth of Footing, d = D-(Clear Cover) - (0.5*Dia of Rebar) Clear Cover d' Dia of Rebar Φ :. d 2 Mu/(fckbd ) K=

=

36.13 KN/m²

=

33.87 KN/m²

=

9.95 KN-m

= =

Ast,Required

0.5xfck / fy x [1- sqrt{1 - (4.6 x K}] x b d 17.27 KN-m

= = = =

50 10 245 0.012

mm mm mm

=

164.31

Sq.mm = =

Minimum area of steel required, As,min = 0.0012 b*d Area of steel required, As,req =

294.00 Sq.mm 294 Sq.mm

Required spacing will be, SRequired = (π*Ø2/4)*1000/(As,req)

=

267.1 mm

Provide 10 Φ @ 150 mm c/c Area of steel provided, Ast,Provided = (Ø2*π/4)*1000/Sprovided

=

524 Sq.mm

pt %

=

100*Ast/(b*d)

pt %

=

0.214

(where, b = 1000mm, unit width)

L

Shear Check The design shear force at d distance from face of wall (towards toe) Shear , V = W W 

 

Factored shear force, Vu Nominal shear stress, Design shear stress,

1

2

2

τv

= =

30.26 0.12

for pt %

=

0.214

τc

=

0.33

W2 W1

 x L  d   KNm/m N/mm2 N/mm2

OK

Design of Heel slab The net pressure acting on Heel slab shall be obtained by reducing net upward pressure of self weight of heel slab plus overburden pressure of soil from gross pressure at base. Self weight of Heel slab,

=

γC x Tfooting

=

7.5 KN/m²

Soil pressure on heel slab,

=

γs x (H-Tfooting)

= =

36.499 KN/m² 43.999 KN/m²

Net Downward Case 1: OBE Governing load combination is Net pressure acting on heel slab, Min. Pressure 1.5x43.999 - 1.5x42.55

1.5 DL + 1.5 EL

Max. Pressure 1.5x43.999 - 1.5x28.43

Factored Moment,

2.17 KN/m²

=

23.35 KN/m²

=

Mu

=

 2W1  W2 L xW1  W2 x 2  W1  W2

 L  x  3

26.4 KN-m

1.0 DL + 1.0 EL

Min. Pressure 1.0x43.999 - 1.0x35.19 Factored Moment,

=

Mu

Case 2: MCE Governing load combination is Net pressure acting on toe slab, Max. Pressure 1.0x43.999 - 1.0x40.62

W1 W2

Mu

Calculation of Steel: Ast,Required Area of steel required in toe slab, Governing Factored Moment, Mu Effective Depth of Footing, d = D-(Clear Cover)-(0.5*Dia of Rebar) Clear Cover d' Dia of Rebar Φ :. d Mu/(fckbd2) K=

=

3.38 KN/m²

=

8.81 KN/m²

=

11.34 KN-m

= =

Ast,Required

0.5xfck / fy x [1- sqrt{1 - (4.6 x K}] x b d 26.40 KN-m

= = = =

50 10 245 0.018

mm mm mm

=

253.06

Sq.mm = =

Minimum area of steel required, As,min = 0.0012 b*d Area of steel required, As,req =

294.00 Sq.mm 294 Sq.mm

Required spacing will be, SRequired = (π*Ø2/4)*1000/(As,req)

=

267.1 mm

Provide 10 Φ @ 150 mm c/c Area of steel provided, Ast,Provided = (Ø2*π/4)*1000/Sprovided

=

524 Sq.mm

pt %

=

100*Ast/(b*d)

pt %

=

0.214

(where, b = 1000mm, unit width)

Shear Check The design shear force at d distance from face of wall (towards toe) Factored shear force, Vu = 19.8 τv Nominal shear stress, = 0.08 Design shear stress,

for pt %

=

0.214

τc

=

0.33

Design of Wall Calculation of Steel:

At bottom

1.90 m from top

KNm/m N/mm2 N/mm2

OK

Load Combination: for DBE for MCE

1.5DL 1.5(DL+EL) 1.0(DL+EL)

Case1:

Static Earth pressure, P1 = Ka x γs x h0

=

12.66 kN/m2

Factored Pressure 19.00 kN/m2

Case2: MCE

Dynamic Earth pressure, P2 = Casi x γs x h0

=

35.62 kN/m2

35.62 kN/m2

Case3: DBE

Dynamic Earth pressure, P3 = Cas0 x γs x h0

=

25.73 kN/m2

38.60 kN/m2

So, case3 is governing 2

2

[0.5xKixγsxh0 x(h0/3) + 0.5x(Caso-Ki)xγsxho x(h0/2)]

Moment acting at bottom of wall (At point B), factored moment, Mu

19.83 KN-m

=

(1.5x19.83)

=

29.745 KN-m

0.5xfck / fy x [1- sqrt{1 - (4.6 x K}] x b d

Ast,Required

=

Effective thickness of wall, d = Tf-(Clear Cover)-(0.5*Dia of Rebar) Clear Cover d' Dia of Rebar Φ :. d 2 Mu/(fckbd ) K=

= = = =

50 10 195 0.031

mm mm mm

Ast,Required

=

364.46

Sq.mm

Area of steel required ,

Minimum area of vertical steel required, As,min = 0.0012 b*d

=

234.00 Sq.mm

Area of steel required, As,req =

=

364 Sq.mm

Required spacing will be, SRequired = (π*Ø /4)*1000/(As,req)

=

215.5 mm

Provide 10 Φ @ 150 mm c/c Area of steel provided, Ast,Provided = (Ø2*π/4)*1000/Sprovided

=

524 Sq.mm

2

pt %

=

100*Ast/(b*d)

pt %

=

0.269

(where, b = 1000mm, unit width)

Minimum area of vertical steel required at outer face of wall, As,min = 0.0012 b*d Φ

=

10

Required spacing will be, SRequired = (π*Ø2/4)*1000/(As,req) Provide 10 Φ @ 150 mm c/c

=

Minimum area of horizontal steel required, As,min = 0.002 b*d Φ

=

10

Required spacing will be, SRequired = (π*Ø2/4)*1000/(As,req) Provide 10 Φ @ 150 mm c/c Shear Check At d distance from bottom 1.71 m from top The design shear force at h' distance from top of wall Shear , V = Load Factor = Factored shear force, Vu = τv Nominal shear stress, = Design shear stress,

234.00 Sq.mm

= mm

335.6 mm

390.00 Sq.mm

= mm =

h' = 19.68 1.5 29.52 0.15

for pt %

=

0.269

τc

=

0.37

KNm/m Since DBE is governing KNm/m N/mm2 N/mm2

OK

201.4 mm

1.71