DESIGN OF STONE MASONRY RETAINING WALL

A0.000 m1.000 m1.000 m

0.6 m1.600 m

70.632 KNdistance of Axle load from retaining wall top X 0.45 m

29 º

23.000

19.000

0.550

WALL TYPE : - W2 Y0.6 m

0.000 m

1.000 m 2.000 m 30/100

W = 56.488 KN

4.395 KNm

Road Formation Level0.667 m

1.000 0.400 0.6 0.600 m

X 1.600 m 1/5 0.320 hv, m 13.185

Binclined 1.632 m Active Soil pressure

Y

B Design parameters:-2.000 m

m= 0.225n= (assume multiple of 0.5) 4

m n Z = nH

0.225 0.250 0.500 4.657 2.3540.225 0.500 1.000 4.761 2.4070.225 0.750 1.500 4.869 2.4450.225 1.000 2.000 4.912

Geometry Data :-Height of Retaining wall from Top ground level to Top (h1) =Height of Retaining wall from Formation Road Level to Top ground level (h2) =Height of foundation from Formation Road Level (h3)or D =Top head of retaining wall (Bt) =Bottom width of retaining wall (Bb) = (For Initial section assume approx. ≈ 0.6H)

Surcharge load of Max. Vehicle axail load as per IRC6- 2000 [ Class A]= Load vehicle

Φ = angle betn resultant force and normal to failure plane/friction angle of soil

From

soi

l tes

t re

port

Unit weight of stone masonry wall (ϒs) = KN/m3

Unit weight of soil (ϒso) = KN/m3

Frictional coefficient μ =

bt=

h1=

A2

h2= H=h1+h2+h3= ka =(active earth pressure coefficient)

1/5

((A1 x X1) +(A2 x X2) + (A3 x X3) +(A4 x X4))/ ΣAn

Pa =1/2 x Pa x h4 =

A3 h4 = H/3 =h3=

A1 '

bb=

Pa=Kpa x ϒso x H = KN/m2

Total Height of retaining wall H = h1+h2+h3 =

σx =1.77Qpm2n2/(H2(m2+n2)3 for m>0.4 or

0.28Qpm2n2/(H2(0.16+n2)3 for m≤0.4

PH

7.207

0.400 m0.600 m0.064 m0.267 m0.700 m1.200 m1.067 m0.4001.2000.6000.256

2.456Weight of Stone masonry retaining wall (W) = 56.488 KN

0.667 m

0.347

distance of W from X = 0.790 m

7.207 KN

dist. of surcharge load from X=d = 0.59H for m ≤0.4 & 0.48H for m>0.4 1.180 m

13.185 KN/m

Overturning Moment 8.504 KNmResisting Moment 44.614 KNm

Overturning Moment 4.395 KNm

C Check against overturning:- For FOS = 1.5

44.614 KNm

12.899 KNm

3.459 OK

D Check againstg Sliding:- For FOS = 1.50.550

31.068 KN

Sum of Sliding Forces ( Surcharge Load + Active earth pressure) = 20.392 KN

Factor of safety against Sliding (FOS sliding) = 31.068 / 20.392 1.524 OK

ΣPH=

Base length of triange A1 =Base length of triange A3 =Base length of triange A4 =Distance of CG of A1 from X = X1

Distance of CG of A2 from X = X2

Distance of CG of A3 from X = X1

Distance of CG of A4 from X = X4

Cross section of Stone masonry retaining wall (A1) = m2

Cross section of Stone masonry retaining wall (A2) = m2

Cross section of Stone masonry retaining wall (A3) = m2

Cross section of Stone masonry retaining wall (A4) = m2

Cross section of Stone masonry retaining wall (ΣAn) = m2

height of line of action for lateral earth pressure (h4) =

Active earth pressure coeff. at base of wall (Kpa) =

Vehicle load surcharge Intensity PH=Σ(σz-1+σz)/2 x Z diff

Active earth pressure at base of wall Pa = Kpa x ϒso x H

Moment due to surcharge Load @ X = PH x dMoment due to selfweight of wall @ X = W x X

Moment due to active earth pressure @ X =1/2 x Pa x h4

Sum of resisting moment = ΣMres

Sum of Overturning moment = ΣMyy over

Factor of safety against Overturning (FOS overturning) =

Frictional coefficient μ = Resisting force against sliding (μW) =

1 2 3 4 5 6 7 8 9 10 11 12 13 14

4.500

4.550

4.600

4.650

4.700

4.750

4.800

4.850

4.900

4.950Surcharge load from vehicle

σx

( 1−Sinφ1+Sinφ )

A1X 1+A2X2+A3 X3+A4 X4

∑ An

DESIGN OF STONE MASONRY RETAINING WALL

A0.000 m1.500 m1.000 m

0.6 m1.800 m

70.632 KNdistance of Axle load from retaining wall top X 0.45 m

29 º

23.000

19.000

0.450

WALL TYPE : - W2 Y0.6 m

0.000 m

1.500 m 2.500 m 28/100

W = 76.452 KN

6.867 KNm

Road Formation Level0.833 m

1.000 0.500 0.6 0.700 m

X 1.800 m 1/5 0.360 hv, m 16.481

Binclined 1.836 m Active Soil pressure

Y

B Design parameters:-2.500 m

m= 0.180n= (assume multiple of 0.5) 5

m n Z = nH

0.180 0.200 0.500 3.002 1.5020.180 0.400 1.000 3.006 1.5220.180 0.600 1.500 3.081 1.5510.180 0.800 2.000 3.124 1.5670.180 1.000 2.500 3.144

Geometry Data :-Height of Retaining wall from Top ground level to Top (h1) =Height of Retaining wall from Formation Road Level to Top ground level (h2) =Height of foundation from Formation Road Level (h3)or D =Top head of retaining wall (Bt) =Bottom width of retaining wall (Bb) = (For Initial section assume approx. ≈ 0.6H)

Surcharge load of Max. Vehicle axail load as per IRC6- 2000 [ Class A]= Load vehicle

Φ = angle betn resultant force and normal to failure plane/friction angle of soil

From

soi

l tes

t re

port

Unit weight of stone masonry wall (ϒs) = KN/m3

Unit weight of soil (ϒso) = KN/m3

Frictional coefficient μ =

bt=

h1=

A2

h2= H=h1+h2+h3= ka =(active earth pressure coefficient)

1/5

((A1 x X1) +(A2 x X2) + (A3 x X3) +(A4 x X4))/ ΣAn

Pa =1/2 x Pa x h4 =

A3 h4 = H/3 =h3=

A1 '

bb=

Pa=Kpa x ϒso x H = KN/m2

Total Height of retaining wall H = h1+h2+h3 =

σx =1.77Qpm2n2/(H2(m2+n2)3 for m>0.4 or

0.28Qpm2n2/(H2(0.16+n2)3 for m≤0.4

PH

6.142

0.500 m0.700 m0.072 m0.333 m0.800 m1.333 m1.200 m0.6251.5000.8750.324

3.324Weight of Stone masonry retaining wall (W) = 76.452 KN

0.833 m

0.347

distance of W from X = 0.892 m

6.142 KN

dist. of surcharge load from X=d = 0.59H for m ≤0.4 & 0.48H for m>0.4 1.475 m

16.481 KN/m

Overturning Moment 9.060 KNmResisting Moment 68.167 KNm

Overturning Moment 6.867 KNm

C Check against overturning:- For FOS = 1.5

68.167 KNm

15.927 KNm

4.280 OK

D Check againstg Sliding:- For FOS = 1.50.450

34.403 KN

Sum of Sliding Forces ( Surcharge Load + Active earth pressure) = 22.623 KN

Factor of safety against Sliding (FOS sliding) = 34.403 / 22.623 1.521 OK

ΣPH=

Base length of triange A1 =Base length of triange A3 =Base length of triange A4 =Distance of CG of A1 from X = X1

Distance of CG of A2 from X = X2

Distance of CG of A3 from X = X1

Distance of CG of A4 from X = X4

Cross section of Stone masonry retaining wall (A1) = m2

Cross section of Stone masonry retaining wall (A2) = m2

Cross section of Stone masonry retaining wall (A3) = m2

Cross section of Stone masonry retaining wall (A4) = m2

Cross section of Stone masonry retaining wall (ΣAn) = m2

height of line of action for lateral earth pressure (h4) =

Active earth pressure coeff. at base of wall (Kpa) =

Vehicle load surcharge Intensity PH=Σ(σz-1+σz)/2 x Z diff

Active earth pressure at base of wall Pa = Kpa x ϒso x H

Moment due to surcharge Load @ X = PH x dMoment due to selfweight of wall @ X = W x X

Moment due to active earth pressure @ X =1/2 x Pa x h4

Sum of resisting moment = ΣMres

Sum of Overturning moment = ΣMyy over

Factor of safety against Overturning (FOS overturning) =

Frictional coefficient μ = Resisting force against sliding (μW) =

1 2 3 4 5 6 7 8 9 10 11 12 13 14

2.900

2.950

3.000

3.050

3.100

3.150

3.200Surcharge load from vehicle

σx

( 1−Sinφ1+Sinφ )

A1X 1+A2X2+A3 X3+A4 X4

∑ An

DESIGN OF STONE MASONRY RETAINING WALL

A0.000 m2.000 m1.000 m

0.6 m1.950 m

70.632 KNdistance of Axle load from retaining wall top X 0.45 m

29 º

23.000

19.000

0.450

WALL TYPE : - W2 Y0.6 m

0.000 m

2.000 m 3.000 m 25/100

W = 96.721 KN

9.889 KNm

Road Formation Level1.000 m

1.000 0.600 0.6 0.750 m

X 1.950 m 1/5 0.390 hv, m 19.778

Binclined 1.989 m Active Soil pressure

Y

B Design parameters:-3.000 m

m= 0.150n= (assume multiple of 0.5) 6

m n Z = nH

0.150 0.167 0.500 2.103 1.0440.150 0.333 1.000 2.072 1.0470.150 0.500 1.500 2.116 1.0670.150 0.667 2.000 2.152 1.0810.150 0.833 2.500 2.172 1.0890.150 1.000 3.000 2.183

Geometry Data :-Height of Retaining wall from Top ground level to Top (h1) =Height of Retaining wall from Formation Road Level to Top ground level (h2) =Height of foundation from Formation Road Level (h3)or D =Top head of retaining wall (Bt) =Bottom width of retaining wall (Bb) = (For Initial section assume approx. ≈ 0.6H)

Surcharge load of Max. Vehicle axail load as per IRC6- 2000 [ Class A]= Load vehicle

Φ = angle betn resultant force and normal to failure plane/friction angle of soil

From

soi

l tes

t re

port

Unit weight of stone masonry wall (ϒs) = KN/m3

Unit weight of soil (ϒso) = KN/m3

Frictional coefficient μ =

bt=

h1=

A2

h2= H=h1+h2+h3= ka =(active earth pressure coefficient)

1/5

((A1 x X1) +(A2 x X2) + (A3 x X3) +(A4 x X4))/ ΣAn

Pa =1/2 x Pa x h4 =

A3 h4 = H/3 =h3=

A1 '

bb=

Pa=Kpa x ϒso x H = KN/m2

Total Height of retaining wall H = h1+h2+h3 =

σx =1.77Qpm2n2/(H2(m2+n2)3 for m>0.4 or

0.28Qpm2n2/(H2(0.16+n2)3 for m≤0.4

PH

5.328

0.600 m0.750 m0.078 m0.400 m0.900 m1.450 m1.300 m0.9001.8001.1250.380

4.205Weight of Stone masonry retaining wall (W) = 96.721 KN

1.000 m

0.347

distance of W from X = 0.976 m

5.328 KN

dist. of surcharge load from X=d = 0.59H for m ≤0.4 & 0.48H for m>0.4 1.770 m

19.778 KN/m

Overturning Moment 9.430 KNmResisting Moment 94.428 KNm

Overturning Moment 9.889 KNm

C Check against overturning:- For FOS = 1.5

94.428 KNm

19.319 KNm

4.888 OK

D Check againstg Sliding:- For FOS = 1.50.450

43.524 KN

Sum of Sliding Forces ( Surcharge Load + Active earth pressure) = 25.105 KN

Factor of safety against Sliding (FOS sliding) = 43.524 / 25.105 1.734 OK

ΣPH=

Base length of triange A1 =Base length of triange A3 =Base length of triange A4 =Distance of CG of A1 from X = X1

Distance of CG of A2 from X = X2

Distance of CG of A3 from X = X1

Distance of CG of A4 from X = X4

Cross section of Stone masonry retaining wall (A1) = m2

Cross section of Stone masonry retaining wall (A2) = m2

Cross section of Stone masonry retaining wall (A3) = m2

Cross section of Stone masonry retaining wall (A4) = m2

Cross section of Stone masonry retaining wall (ΣAn) = m2

height of line of action for lateral earth pressure (h4) =

Active earth pressure coeff. at base of wall (Kpa) =

Vehicle load surcharge Intensity PH=Σ(σz-1+σz)/2 x Z diff

Active earth pressure at base of wall Pa = Kpa x ϒso x H

Moment due to surcharge Load @ X = PH x dMoment due to selfweight of wall @ X = W x X

Moment due to active earth pressure @ X =1/2 x Pa x h4

Sum of resisting moment = ΣMres

Sum of Overturning moment = ΣMyy over

Factor of safety against Overturning (FOS overturning) =

Frictional coefficient μ = Resisting force against sliding (μW) =

1 2 3 4 5 6 7 8 9 10 11 12 13 14

2.000

2.020

2.040

2.060

2.080

2.100

2.120

2.140

2.160

2.180

2.200Surcharge load from vehicle

σx

( 1−Sinφ1+Sinφ )

A1X 1+A2X2+A3 X3+A4 X4

∑ An

DESIGN OF STONE MASONRY RETAINING WALL

A0.000 m3.000 m1.000 m

0.6 m2.000 m

70.632 KNdistance of Axle load from retaining wall top X 0.45 m

29 º

23.000

19.000

0.450

WALL TYPE : - W2 Y0.6 m

0.000 m

3.000 m 4.000 m 15/100

W = 128.800 KN

17.580 KNm

Road Formation Level1.333 m

1.000 0.800 0.6 0.600 m

X 2.000 m 1/5 0.400 hv,m 26.370

2.04 m Active Soil pressure

Y

B Design parameters:-4.000 m

m= 0.113n= (assume multiple of 0.5) 8

m n Z = nH

0.113 0.125 0.500 1.200 0.5910.113 0.250 1.000 1.164 0.5840.113 0.375 1.500 1.171 0.5900.113 0.500 2.000 1.190 0.5990.113 0.625 2.500 1.206 0.6060.113 0.750 3.000 1.217 0.6100.113 0.875 3.500 1.224 0.6130.113 1.000 4.000 1.228

Geometry Data :-Height of Retaining wall from Top ground level to Top (h1) =Height of Retaining wall from Formation Road Level to Top ground level (h2) =Height of foundation from Formation Road Level (h3)or D =Top head of retaining wall (Bt) =Bottom width of retaining wall (Bb) = (For Initial section assume approx. ≈ 0.6H)

Surcharge load of Max. Vehicle axail load as per IRC6- 2000 [ Class A]= Load vehicle

Φ = angle betn resultant force and normal to failure plane/friction angle of soil

From

soi

l tes

t re

port

Unit weight of stone masonry wall (ϒs) = KN/m3

Unit weight of soil (ϒso) = KN/m3

Frictional coefficient μ =

bt=

h1=

A2

h2= H=h1+h2+h3= ka =(active earth pressure coefficient)

1/5

((A1 x X1) +(A2 x X2) + (A3 x X3) +(A4 x X4))/ ΣAn

Pa =1/2 x Pa x h4 =

A3 h4 = H/3 =h3=

A1 '

bb=

Pa=Kpa x ϒso x H = KN/m2

Binclined

Total Height of retaining wall H = h1+h2+h3 =

σx =1.77Qpm2n2/(H2(m2+n2)3 for m>0.4 or

0.28Qpm2n2/(H2(0.16+n2)3 for m≤0.4

PH

4.193

0.800 m0.600 m0.080 m0.533 m1.100 m1.600 m1.333 m1.6002.4001.2000.400

5.600Weight of Stone masonry retaining wall (W) = 128.800 KN

1.333 m

0.347

distance of W from X = 1.062 m

4.193 KN

dist. of surcharge load from X=d = 0.59H for m ≤0.4 & 0.48H for m>0.4 2.360 m

26.370 KN/m

Overturning Moment 9.896 KNmResisting Moment 136.773 KNm

Overturning Moment 17.580 KNm

C Check against overturning:- For FOS = 1.75

136.773 KNm

27.476 KNm

4.978 OK

D Check againstg Sliding:- For FOS = 1.750.450

57.960 KN

Sum of Sliding Forces ( Surcharge Load + Active earth pressure) = 30.563 KN

Factor of safety against Sliding (FOS sliding) = 57.960 / 30.563 1.896 OK

ΣPH=

Base length of triange A1 =Base length of triange A3 =Base length of triange A4 =Distance of CG of A1 from X = X1

Distance of CG of A2 from X = X2

Distance of CG of A3 from X = X1

Distance of CG of A4 from X = X4

Cross section of Stone masonry retaining wall (A1) = m2

Cross section of Stone masonry retaining wall (A2) = m2

Cross section of Stone masonry retaining wall (A3) = m2

Cross section of Stone masonry retaining wall (A4) = m2

Cross section of Stone masonry retaining wall (ΣAn) = m2

height of line of action for lateral earth pressure (h4) =

Active earth pressure coeff. at base of wall (Kpa) =

Vehicle load surcharge Intensity PH=Σ(σz-1+σz)/2 x Z diff

Active earth pressure at base of wall Pa = Kpa x ϒso x H

Moment due to surcharge Load @ X = PH x dMoment due to selfweight of wall @ X = W x X

Moment due to active earth pressure @ X =1/2 x Pa x h4

Sum of resisting moment = ΣMres

Sum of Overturning moment = ΣMyy over

Factor of safety against Overturning (FOS overturning) =

Frictional coefficient μ = Resisting force against sliding (μW) =

1 2 3 4 5 6 7 8 9 10 11 12 13 14

1.120

1.140

1.160

1.180

1.200

1.220

1.240Surcharge load from vehicle

σx

( 1−Sinφ1+Sinφ )

A1X 1+A2X2+A3 X3+A4 X4

∑ An

DESIGN OF STONE MASONRY RETAINING WALL

A0.000 m4.000 m1.000 m

0.6 m2.500 m

70.632 KNdistance of Axle load from retaining wall top X 0.45 m

29 º

23.000

19.000

0.450

WALL TYPE : - W2 Y0.6 m

0.000 m

4.000 m 5.000 m 18/100

W = 192.625 KN

27.469 KNm

Road Formation Level1.667 m

1.000 1.000 0.6 0.900 m

X 2.500 m 1/5 0.500 hv, m 32.963

2.55 m Active Soil pressure

Y

B Design parameters:-5.000 m

m= 0.090n= (assume multiple of 0.5) 10

m n Z = nH

0.090 0.100 0.500 0.775 0.3810.090 0.200 1.000 0.751 0.3740.090 0.300 1.500 0.744 0.3740.090 0.400 2.000 0.752 0.3780.090 0.500 2.500 0.762 0.3830.090 0.600 3.000 0.770 0.3870.090 0.700 3.500 0.777 0.3890.090 0.800 4.000 0.781 0.3910.090 0.900 4.500 0.784 0.3920.090 1.000 5.000 0.786

Geometry Data :-Height of Retaining wall from Top ground level to Top (h1) =Height of Retaining wall from Formation Road Level to Top ground level (h2) =Height of foundation from Formation Road Level (h3)or D =Top head of retaining wall (Bt) =Bottom width of retaining wall (Bb) = (For Initial section assume approx. ≈ 0.6H)

Surcharge load of Max. Vehicle axail load as per IRC6- 2000 [ Class A]= Load vehicle

Φ = angle betn resultant force and normal to failure plane/friction angle of soil

From

soi

l tes

t re

port

Unit weight of stone masonry wall (ϒs) = KN/m3

Unit weight of soil (ϒso) = KN/m3

Frictional coefficient μ =

bt=

h1=

A2

h2= H=h1+h2+h3= ka =(active earth pressure coefficient)

1/5

((A1 x X1) +(A2 x X2) + (A3 x X3) +(A4 x X4))/ ΣAn

Pa =1/2 x Pa x h4 =

A3 h4 = H/3 =h3=

A1 '

bb=

Pa=Kpa x ϒso x H = KN/m2

Binclined

Total Height of retaining wall H = h1+h2+h3 =

σx =1.77Qpm2n2/(H2(m2+n2)3 for m>0.4 or

0.28Qpm2n2/(H2(0.16+n2)3 for m≤0.4

PH

3.450

1.000 m0.900 m0.100 m0.667 m1.300 m1.900 m1.667 m2.5003.0002.2500.625

8.375Weight of Stone masonry retaining wall (W) = 192.625 KN

1.667 m

0.347

distance of W from X = 1.300 m

3.450 KN

dist. of surcharge load from X=d = 0.59H for m ≤0.4 & 0.48H for m>0.4 2.950 m

32.963 KN/m

Overturning Moment 10.178 KNmResisting Moment 250.317 KNm

Overturning Moment 27.469 KNm

C Check against overturning:- For FOS = 2.0

250.317 KNm

37.647 KNm

6.649 OK

D Check againstg Sliding:- For FOS = 2.00.450

86.681 KN

Sum of Sliding Forces ( Surcharge Load + Active earth pressure) = 36.413 KN

Factor of safety against Sliding (FOS sliding) = 86.681 / 36.413 2.381 OK

ΣPH=

Base length of triange A1 =Base length of triange A3 =Base length of triange A4 =Distance of CG of A1 from X = X1

Distance of CG of A2 from X = X2

Distance of CG of A3 from X = X1

Distance of CG of A4 from X = X4

Cross section of Stone masonry retaining wall (A1) = m2

Cross section of Stone masonry retaining wall (A2) = m2

Cross section of Stone masonry retaining wall (A3) = m2

Cross section of Stone masonry retaining wall (A4) = m2

Cross section of Stone masonry retaining wall (ΣAn) = m2

height of line of action for lateral earth pressure (h4) =

Active earth pressure coeff. at base of wall (Kpa) =

Vehicle load surcharge Intensity PH=Σ(σz-1+σz)/2 x Z diff

Active earth pressure at base of wall Pa = Kpa x ϒso x H

Moment due to surcharge Load @ X = PH x dMoment due to selfweight of wall @ X = W x X

Moment due to active earth pressure @ X =1/2 x Pa x h4

Sum of resisting moment = ΣMres

Sum of Overturning moment = ΣMyy over

Factor of safety against Overturning (FOS overturning) =

Frictional coefficient μ = Resisting force against sliding (μW) =

1 2 3 4 5 6 7 8 9 10 11 12 13 14

0.720

0.730

0.740

0.750

0.760

0.770

0.780

0.790Surcharge load from vehicle

σx

( 1−Sinφ1+Sinφ )

A1X 1+A2X2+A3 X3+A4 X4

∑ An

DESIGN OF STONE MASONRY RETAINING WALL

A0.000 m5.000 m1.000 m

0.6 m3.000 m

70.632 KNdistance of Axle load from retaining wall top X 0.45 m

30 º

23.000

20.000

0.450

WALL TYPE : - W2 Y0.6 m

0.000 m

5.000 m 6.000 m 20/100

W = 269.100 KN

40.000 KNm

Road Formation Level2.000 m

1.000 1.200 0.6 1.200 m

X 3.000 m 1/5 0.600 hv, m 40.000

3.059 m Active Soil pressure

Y

B Design parameters:-6.000 m

m= 0.075n= (assume multiple of 0.5) 12

m n Z = nH

0.075 0.083 0.500 0.541 0.2670.075 0.167 1.000 0.526 0.2610.075 0.250 1.500 0.517 0.2590.075 0.333 2.000 0.518 0.2600.075 0.417 2.500 0.523 0.2630.075 0.500 3.000 0.529 0.2660.075 0.583 3.500 0.534 0.2680.075 0.667 4.000 0.538 0.2700.075 0.750 4.500 0.541 0.2710.075 0.833 5.000 0.543 0.2720.075 0.917 5.500 0.545 0.2730.075 1.000 6.000 0.546

Geometry Data :-Height of Retaining wall from Top ground level to Top (h1) =Height of Retaining wall from Formation Road Level to Top ground level (h2) =Height of foundation from Formation Road Level (h3)or D =Top head of retaining wall (Bt) =Bottom width of retaining wall (Bb) = (For Initial section assume approx. ≈ 0.6H)

Surcharge load of Max. Vehicle axail load as per IRC6- 2000 [ Class A]= Load vehicle

Φ = angle betn resultant force and normal to failure plane/friction angle of soil

From

soi

l tes

t re

port

Unit weight of stone masonry wall (ϒs) = KN/m3

Unit weight of soil (ϒso) = KN/m3

Frictional coefficient μ =

bt=

h1=

A2

h2= H=h1+h2+h3= ka =(active earth pressure coefficient)

1/5

((A1 x X1) +(A2 x X2) + (A3 x X3) +(A4 x X4))/ ΣAn

Pa =1/2 x Pa x h4 =

A3 h4 = H/3 =h3=

A1 '

bb=

Pa=Kpa x ϒso x H = KN/m2

Binclined

Total Height of retaining wall H = h1+h2+h3 =

σx =1.77Qpm2n2/(H2(m2+n2)3 for m>0.4 or

0.28Qpm2n2/(H2(0.16+n2)3 for m≤0.4

PH

2.929

1.200 m1.200 m0.120 m0.800 m1.500 m2.200 m2.000 m3.6003.6003.6000.900

11.700Weight of Stone masonry retaining wall (W) = 269.100 KN

2.000 m

0.333

distance of W from X = 1.538 m

2.929 KN

dist. of surcharge load from X=d = 0.59H for m ≤0.4 & 0.48H for m>0.4 3.540 m

40.000 KN/m

Overturning Moment 10.368 KNmResisting Moment 414.000 KNm

Overturning Moment 40.000 KNm

C Check against overturning:- For FOS = 2.5

414.000 KNm

50.368 KNm

8.220 OK

D Check againstg Sliding:- For FOS = 2.50.450

121.095 KN

Sum of Sliding Forces ( Surcharge Load + Active earth pressure) = 42.929 KN

Factor of safety against Sliding (FOS sliding) = 121.095 / 42.929 2.821 OK

ΣPH=

Base length of triange A1 =Base length of triange A3 =Base length of triange A4 =Distance of CG of A1 from X = X1

Distance of CG of A2 from X = X2

Distance of CG of A3 from X = X1

Distance of CG of A4 from X = X4

Cross section of Stone masonry retaining wall (A1) = m2

Cross section of Stone masonry retaining wall (A2) = m2

Cross section of Stone masonry retaining wall (A3) = m2

Cross section of Stone masonry retaining wall (A4) = m2

Cross section of Stone masonry retaining wall (ΣAn) = m2

height of line of action for lateral earth pressure (h4) =

Active earth pressure coeff. at base of wall (Kpa) =

Vehicle load surcharge Intensity PH=Σ(σz-1+σz)/2 x Z diff

Active earth pressure at base of wall Pa = Kpa x ϒso x H

Moment due to surcharge Load @ X = PH x dMoment due to selfweight of wall @ X = W x X

Moment due to active earth pressure @ X =1/2 x Pa x h4

Sum of resisting moment = ΣMres

Sum of Overturning moment = ΣMyy over

Factor of safety against Overturning (FOS overturning) =

Frictional coefficient μ = Resisting force against sliding (μW) =

1 2 3 4 5 6 7 8 9 10 11 12 13 14

0.500

0.505

0.510

0.515

0.520

0.525

0.530

0.535

0.540

0.545

0.550Surcharge load from vehicle

σx

( 1−Sinφ1+Sinφ )

A1X 1+A2X2+A3 X3+A4 X4

∑ An

DESIGN OF STONE MASONRY RETAINING WALL

A0.000 m6.000 m1.000 m

0.6 m3.500 m

70.632 KNdistance of Axle load from retaining wall top X 0.45 m

30 º

23.000

20.000

0.450

WALL TYPE : - W2 Y0.6 m

0.000 m

6.000 m 7.000 m 21/100

W = 358.225 KN

54.444 KNm

Road Formation Level2.333 m

1.000 1.400 0.6 1.500 m

X 3.500 m 1/5 0.700 hv, m 46.667

3.569 m Active Soil pressure

Y

B Design parameters:-7.000 m

m= 0.064n= (assume multiple of 0.5) 14

m n Z = nH

0.064 0.071 0.500 0.399 0.1970.064 0.143 1.000 0.389 0.1930.064 0.214 1.500 0.382 0.1900.064 0.286 2.000 0.380 0.1900.064 0.357 2.500 0.381 0.1920.064 0.429 3.000 0.385 0.1930.064 0.500 3.500 0.389 0.1950.064 0.571 4.000 0.392 0.1970.064 0.643 4.500 0.395 0.1980.064 0.714 5.000 0.397 0.1990.064 0.786 5.500 0.398 0.1990.064 0.857 6.000 0.399 0.2000.064 0.929 6.500 0.400 0.2000.064 1.000 7.000 0.401

Geometry Data :-Height of Retaining wall from Top ground level to Top (h1) =Height of Retaining wall from Formation Road Level to Top ground level (h2) =Height of foundation from Formation Road Level (h3)or D =Top head of retaining wall (Bt) =Bottom width of retaining wall (Bb) = (For Initial section assume approx. ≈ 0.6H)

Surcharge load of Max. Vehicle axail load as per IRC6- 2000 [ Class A]= Load vehicle

Φ = angle betn resultant force and normal to failure plane/friction angle of soil

From

soi

l tes

t re

port

Unit weight of stone masonry wall (ϒs) = KN/m3

Unit weight of soil (ϒso) = KN/m3

Frictional coefficient μ =

bt=

h1=

A2

h2= H=h1+h2+h3= ka =(active earth pressure coefficient)

1/5

((A1 x X1) +(A2 x X2) + (A3 x X3) +(A4 x X4))/ ΣAn

Pa =1/2 x Pa x h4 =

A3 h4 = H/3 =h3=

A1 '

bb=

Pa=Kpa x ϒso x H = KN/m2

Binclined

Total Height of retaining wall H = h1+h2+h3 =

σx =1.77Qpm2n2/(H2(m2+n2)3 for m>0.4 or

0.28Qpm2n2/(H2(0.16+n2)3 for m≤0.4

PH

2.543

1.400 m1.500 m0.140 m0.933 m1.700 m2.500 m2.333 m4.9004.2005.2501.225

15.575Weight of Stone masonry retaining wall (W) = 358.225 KN

2.333 m

0.333

distance of W from X = 1.778 m

2.543 KN

dist. of surcharge load from X=d = 0.59H for m ≤0.4 & 0.48H for m>0.4 4.130 m

46.667 KN/m

Overturning Moment 10.504 KNmResisting Moment 637.023 KNm

Overturning Moment 54.444 KNm

C Check against overturning:- For FOS = 2.5

637.023 KNm

64.948 KNm

9.808 OK

D Check againstg Sliding:- For FOS = 2.50.450

161.201 KN

Sum of Sliding Forces ( Surcharge Load + Active earth pressure) = 49.210 KN

Factor of safety against Sliding (FOS sliding) = 161.201 / 49.210 3.276 OK

ΣPH=

Base length of triange A1 =Base length of triange A3 =Base length of triange A4 =Distance of CG of A1 from X = X1

Distance of CG of A2 from X = X2

Distance of CG of A3 from X = X1

Distance of CG of A4 from X = X4

Cross section of Stone masonry retaining wall (A1) = m2

Cross section of Stone masonry retaining wall (A2) = m2

Cross section of Stone masonry retaining wall (A3) = m2

Cross section of Stone masonry retaining wall (A4) = m2

Cross section of Stone masonry retaining wall (ΣAn) = m2

height of line of action for lateral earth pressure (h4) =

Active earth pressure coeff. at base of wall (Kpa) =

Vehicle load surcharge Intensity PH=Σ(σz-1+σz)/2 x Z diff

Active earth pressure at base of wall Pa = Kpa x ϒso x H

Moment due to surcharge Load @ X = PH x dMoment due to selfweight of wall @ X = W x X

Moment due to active earth pressure @ X =1/2 x Pa x h4

Sum of resisting moment = ΣMres

Sum of Overturning moment = ΣMyy over

Factor of safety against Overturning (FOS overturning) =

Frictional coefficient μ = Resisting force against sliding (μW) =

1 2 3 4 5 6 7 8 9 10 11 12 13 14

0.365

0.370

0.375

0.380

0.385

0.390

0.395

0.400

0.405Surcharge load from vehicle

σx

( 1−Sinφ1+Sinφ )

A1X 1+A2X2+A3 X3+A4 X4

∑ An

DESIGN OF STONE MASONRY RETAINING WALL

A0.000 m7.000 m1.000 m

0.6 m4.000 m

70.632 KNdistance of Axle load from retaining wall top X 0.45 m

30 º

23.000

20.000

0.450

WALL TYPE : - W2 Y0.6 m

0.000 m

7.000 m 8.000 m 22/100

W = 460.000 KN

71.111 KNm

Road Formation Level2.667 m

1.000 1.600 0.6 1.800 m

X 4.000 m 1/5 0.800 hv, m 53.333

4.079 m Active Soil pressure

Y

B Design parameters:-8.000 m

m= 0.056n= (assume multiple of 0.5) 16

m n Z = nH

0.056 0.063 0.500 0.306 0.1520.056 0.125 1.000 0.300 0.1480.056 0.188 1.500 0.294 0.1460.056 0.250 2.000 0.291 0.1460.056 0.313 2.500 0.291 0.1460.056 0.375 3.000 0.293 0.1470.056 0.438 3.500 0.295 0.1480.056 0.500 4.000 0.298 0.1490.056 0.563 4.500 0.300 0.1500.056 0.625 5.000 0.302 0.1510.056 0.688 5.500 0.303 0.1520.056 0.750 6.000 0.304 0.1520.056 0.813 6.500 0.305 0.1530.056 0.875 7.000 0.306 0.1530.056 0.938 7.500 0.307 0.1530.056 1.000 8.000 0.307

Geometry Data :-Height of Retaining wall from Top ground level to Top (h1) =Height of Retaining wall from Formation Road Level to Top ground level (h2) =Height of foundation from Formation Road Level (h3)or D =Top head of retaining wall (Bt) =Bottom width of retaining wall (Bb) = (For Initial section assume approx. ≈ 0.6H)

Surcharge load of Max. Vehicle axail load as per IRC6- 2000 [ Class A]= Load vehicle

Φ = angle betn resultant force and normal to failure plane/friction angle of soil

From

soi

l tes

t re

port

Unit weight of stone masonry wall (ϒs) = KN/m3

Unit weight of soil (ϒso) = KN/m3

Frictional coefficient μ =

bt=

h1=

A2

h2= H=h1+h2+h3= ka =(active earth pressure coefficient)

1/5

((A1 x X1) +(A2 x X2) + (A3 x X3) +(A4 x X4))/ ΣAn

Pa =1/2 x Pa x h4 =

A3 h4 = H/3 =h3=

A1 '

bb=

Pa=Kpa x ϒso x H = KN/m2

Binclined

Total Height of retaining wall H = h1+h2+h3 =

σx =1.77Qpm2n2/(H2(m2+n2)3 for m>0.4 or

0.28Qpm2n2/(H2(0.16+n2)3 for m≤0.4

PH

2.247

1.600 m1.800 m0.160 m1.067 m1.900 m2.800 m2.667 m6.4004.8007.2001.600

20.000Weight of Stone masonry retaining wall (W) = 460.000 KN

2.667 m

0.333

distance of W from X = 2.019 m

2.247 KN

dist. of surcharge load from X=d = 0.59H for m ≤0.4 & 0.48H for m>0.4 4.720 m

53.333 KN/m

Overturning Moment 10.607 KNmResisting Moment 928.587 KNm

Overturning Moment 71.111 KNm

C Check against overturning:- For FOS = 2.75

928.587 KNm

81.718 KNm

11.363 OK

D Check againstg Sliding:- For FOS = 2.750.450

207.000 KN

Sum of Sliding Forces ( Surcharge Load + Active earth pressure) = 55.580 KN

Factor of safety against Sliding (FOS sliding) = 207.000 / 55.580 3.724 OK

ΣPH=

Base length of triange A1 =Base length of triange A3 =Base length of triange A4 =Distance of CG of A1 from X = X1

Distance of CG of A2 from X = X2

Distance of CG of A3 from X = X1

Distance of CG of A4 from X = X4

Cross section of Stone masonry retaining wall (A1) = m2

Cross section of Stone masonry retaining wall (A2) = m2

Cross section of Stone masonry retaining wall (A3) = m2

Cross section of Stone masonry retaining wall (A4) = m2

Cross section of Stone masonry retaining wall (ΣAn) = m2

height of line of action for lateral earth pressure (h4) =

Active earth pressure coeff. at base of wall (Kpa) =

Vehicle load surcharge Intensity PH=Σ(σz-1+σz)/2 x Z diff

Active earth pressure at base of wall Pa = Kpa x ϒso x H

Moment due to surcharge Load @ X = PH x dMoment due to selfweight of wall @ X = W x X

Moment due to active earth pressure @ X =1/2 x Pa x h4

Sum of resisting moment = ΣMres

Sum of Overturning moment = ΣMyy over

Factor of safety against Overturning (FOS overturning) =

Frictional coefficient μ = Resisting force against sliding (μW) =

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

0.280

0.285

0.290

0.295

0.300

0.305

0.310

Surcharge load from vehicle

σx

( 1−Sinφ1+Sinφ )

A1X 1+A2X2+A3 X3+A4 X4

∑ An

DESIGN OF STONE MASONRY RETAINING WALL

A0.000 m8.000 m1.000 m

0.6 m4.500 m

70.632 KNdistance of Axle load from retaining wall top X 0.45 m

30 º

23.000

20.000

0.450

WALL TYPE : - W2 Y0.6 m

0.000 m

8.000 m 9.000 m 23/100

W = 574.425 KN

90.000 KNm

Road Formation Level3.000 m

1.000 1.800 0.6 2.100 m

X 4.500 m 1/5 0.900 hv, m 60.000

4.589 m Active Soil pressure

Y

B Design parameters:-9.000 m

m= 0.050n= (assume multiple of 0.5) 18

m n Z = nH

0.050 0.056 0.500 0.242 0.1200.050 0.111 1.000 0.238 0.1180.050 0.167 1.500 0.234 0.1160.050 0.222 2.000 0.231 0.1150.050 0.278 2.500 0.230 0.1150.050 0.333 3.000 0.230 0.1150.050 0.389 3.500 0.232 0.1160.050 0.444 4.000 0.233 0.1170.050 0.500 4.500 0.235 0.1180.050 0.556 5.000 0.237 0.1190.050 0.611 5.500 0.238 0.1190.050 0.667 6.000 0.239 0.1200.050 0.722 6.500 0.240 0.1200.050 0.778 7.000 0.241 0.1210.050 0.833 7.500 0.241 0.1210.050 0.889 8.000 0.242 0.1210.050 0.944 8.500 0.242 0.121

Geometry Data :-Height of Retaining wall from Top ground level to Top (h1) =Height of Retaining wall from Formation Road Level to Top ground level (h2) =Height of foundation from Formation Road Level (h3)or D =Top head of retaining wall (Bt) =Bottom width of retaining wall (Bb) = (For Initial section assume approx. ≈ 0.6H)

Surcharge load of Max. Vehicle axail load as per IRC6- 2000 [ Class A]= Load vehicle

Φ = angle betn resultant force and normal to failure plane/friction angle of soil

From

soi

l tes

t re

port

Unit weight of stone masonry wall (ϒs) = KN/m3

Unit weight of soil (ϒso) = KN/m3

Frictional coefficient μ =

bt=

h1=

A2

h2= H=h1+h2+h3= ka =(active earth pressure coefficient)

1/5

((A1 x X1) +(A2 x X2) + (A3 x X3) +(A4 x X4))/ ΣAn

Pa =1/2 x Pa x h4 =

A3 h4 = H/3 =h3=

A1 '

bb=

Pa=Kpa x ϒso x H = KN/m2

Binclined

Total Height of retaining wall H = h1+h2+h3 =

σx =1.77Qpm2n2/(H2(m2+n2)3 for m>0.4 or

0.28Qpm2n2/(H2(0.16+n2)3 for m≤0.4

PH

0.050 1.000 9.000 0.243

2.013

1.800 m2.100 m0.180 m1.200 m2.100 m3.100 m3.000 m8.1005.4009.4502.025

24.975Weight of Stone masonry retaining wall (W) = 574.425 KN

3.000 m

0.333

distance of W from X = 2.259 m

2.013 KN

dist. of surcharge load from X=d = 0.59H for m ≤0.4 & 0.48H for m>0.4 5.310 m

60.000 KN/m

Overturning Moment 10.687 KNmResisting Moment 1297.890 KNm

Overturning Moment 90.000 KNm

C Check against overturning:- For FOS = 2.75

1297.890 KNm

100.687 KNm

12.890 OK

D Check againstg Sliding:- For FOS = 2.750.450

258.491 KN

Sum of Sliding Forces ( Surcharge Load + Active earth pressure) = 62.013 KN

Factor of safety against Sliding (FOS sliding) = 258.491 / 62.013 4.168 OK

ΣPH=

Base length of triange A1 =Base length of triange A3 =Base length of triange A4 =Distance of CG of A1 from X = X1

Distance of CG of A2 from X = X2

Distance of CG of A3 from X = X1

Distance of CG of A4 from X = X4

Cross section of Stone masonry retaining wall (A1) = m2

Cross section of Stone masonry retaining wall (A2) = m2

Cross section of Stone masonry retaining wall (A3) = m2

Cross section of Stone masonry retaining wall (A4) = m2

Cross section of Stone masonry retaining wall (ΣAn) = m2

height of line of action for lateral earth pressure (h4) =

Active earth pressure coeff. at base of wall (Kpa) =

Vehicle load surcharge Intensity PH=Σ(σz-1+σz)/2 x Z diff

Active earth pressure at base of wall Pa = Kpa x ϒso x H

Moment due to surcharge Load @ X = PH x dMoment due to selfweight of wall @ X = W x X

Moment due to active earth pressure @ X =1/2 x Pa x h4

Sum of resisting moment = ΣMres

Sum of Overturning moment = ΣMyy over

Factor of safety against Overturning (FOS overturning) =

Frictional coefficient μ = Resisting force against sliding (μW) =

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

0.220

0.225

0.230

0.235

0.240

0.245

Surcharge load from vehicle

σx

( 1−Sinφ1+Sinφ )

A1X 1+A2X2+A3 X3+A4 X4

∑ An

H m Outward slope back slope2.000 0.600 1.600 1.632 0.320 1/5 3/102.500 0.600 1.800 1.836 0.360 1/5 7/253.000 0.600 1.950 1.989 0.390 1/5 1/4 4.000 0.600 2.000 2.040 0.400 1/5 3/205.000 0.600 2.500 2.550 0.500 1/5 9/506.000 0.600 3.000 3.059 0.600 1/5 1/5 7.000 0.600 3.500 3.569 0.700 1/5 3/148.000 0.600 4.000 4.079 0.800 1/5 9/409.000 0.600 4.500 4.589 0.900 1/5 7/30

H

1m

Typical diagram with Stone masonry wall geometry

Bt m Bb m Binclined m hv m

Bt

Bb

hvBinclined

Out

war

d slo

pe back slope

2.4563.3244.2055.6008.375

11.70015.57520.00024.975

Cross Section area m2