Stone masonry wall.xls

DESIGN OF STONE MASONRY RETAINING WALL A Geometry Data :Height of Retaining wall from Top ground level to Top (h1) =

0.000 m

Height of Retaining wall from Formation Road Level to Top ground level (h 2) =

1.000 m

Height of foundation from Formation Road Level (h3)or D =

1.000 m

Top head of retaining wall (Bt) =

0.6 m

Bottom width of retaining wall (Bb) = (For Initial section assume approx. ≈ 0.6H)

70.632 KN 0.45 m

vehicle

n

29 º

Φ = angle bet resultant force and normal to failure plane/friction angle of soil Unit weight of stone masonry wall (ϒs) =

3 23.000 KN/m

Unit weight of soil (ϒso) =

3 19.000 KN/m

Frictional coefficient μ =

WALL TYPE : -

From soil test report

Surcharge load of Max. Vehicle axail load as per IRC6- 2000 [ Class A]= Load distance of Axle load from retaining wall top X

1.600 m

0.550

Y

W2 bt=

0.6

m h1=

0.000 m

A2

2.000 m ka =(active earth pressure coefficient)

H=h1+h2+h3= 30/100

1.000 m 1/5

h2=

W=

56.488 KN

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

Pa =1/2 x Pa x h4 =

4.395

KNm

Road Formation Level A3 h3=

1.000

0.400 0.6 A1 ' X

h4 = H/3 =

0.600 bb= 1/5

1.600 m 0.320 hv, m

Pa=K p a x ϒso x H = 13.185 KN/m Active Soil pressure

1.632 m

Binclined

0.667 m

m

Y B Design parameters:Total Height of retaining wall H = h1+h2+h3 = m= n= (assume multiple of 0.5)

2.000 m 0.225 4

σx =1.77Qpm2n2/(H2(m2+n2)3 m

0.225 0.225 0.225 0.225

n

0.250 0.500 0.750 1.000

Z = nH

0.500 1.000 1.500 2.000

for m>0.4 or 0.28Qpm2n2/(H2(0.16+n2)3 for m≤0.4 4.657 4.761 4.869 4.912

P

H

2.354 2.407 2.445

2

ΣP =

7.207

H

Surcharge load from vehicle 1

2

3

4

5

6

7

8

9

10

11

12

13

14

4.950 4.900 4.850

σx

4.800 4.750 4.700 4.650 4.600 4.550 4.500

Base length of triange A1 =

0.400 m


0.600 m


0.064 m

Distance of CG of A1 from X = X1

0.267 m


0.700 m


1.200 m


1.067 m 2 0.400 m

Cross section of Stone masonry retaining wall (A1) =

2 1.200 m 2 0.600 m

Cross section of Stone masonry retaining wall (A2) = Cross section of Stone masonry retaining wall (A3) =

2 0.256 m 2 m 2.456

Cross section of Stone masonry retaining wall (A4) = Cross section of Stone masonry retaining wall (ΣAn) = Weight of Stone masonry retaining wall (W) = height of line of action for lateral earth pressure (h4) = Active earth pressure coeff. at base of wall (K p a ) =

distance of W from X =

 1    1 

Sin Sin

 

56.488 KN 0.667 m

  

0.347

A1 X1  A2 X 2  A3 X 3  A4 X 4  An

0.790 m

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

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

Active earth pressure at base of wall Pa = K pa x ϒso x H Moment due to surcharge Load @ X = PH x d

13.185 KN/m Overturning Moment

8.504 KNm

Resisting Moment

44.614 KNm

Overturning Moment

4.395 KNm

Moment due to selfweight of wall @ X = W x X Moment due to active earth pressure @ X =1/2 x Pa x h4

C Check against overturning:- For FOS = 1.5 Sum of resisting moment = ΣMres

44.614 KNm

Sum of Overturning moment = ΣMyy over

12.899 KNm

Factor of safety against Overturning (FOS overturning) =

3.459 OK

D Check againstg Sliding:- For FOS = 1.5 Frictional coefficient μ = Resisting force against sliding (μW) =

0.550 31.068 KN

Sum of Sliding Forces ( Surcharge Load + Active earth pressure) = Factor of safety against Sliding (FOS sliding) =

20.392 KN 31.068 /

20.392

1.524 OK


0.000 m


1.500 m


1.000 m


0.6 m


70.632 KN 0.45 m

vehicle

n

29 º


3 23.000 KN/m


3 19.000 KN/m


WALL TYPE : -



1.800 m

0.450

Y

W2 bt=

0.6

m h1=

0.000 m

A2


H=h1+h2+h3= 28/100

1.500 m 1/5

h2 =

W=

76.452 KN


Pa =1/2 x Pa x h4 =

6.867

KNm

Road Formation Level A3 h3 =

1.000

0.500 0.6 A1 ' X

h4 = H/3 =

0.700 bb= 1/5

1.800 m 0.360 hv, m


1.836 m

Binclined

0.833 m

m


2.500 m 0.180 5

σx =1.77Qpm2n2/(H2(m2+n2)3 m

0.180 0.180 0.180 0.180 0.180

n

0.200 0.400 0.600 0.800 1.000

Z = nH

0.500 1.000 1.500 2.000 2.500

for m>0.4 or 0.28Qpm2n2/(H2(0.16+n2)3 for m≤0.4 3.002 3.006 3.081 3.124 3.144

P

H

1.502 1.522 1.551 1.567

2

ΣP =

6.142

H


2

3

4

5

6

7

8

9

10

11

12

13

14

3.200 3.150

σx

3.100 3.050 3.000 2.950 2.900


0.500 m


0.700 m


0.072 m


0.333 m


0.800 m


1.333 m


1.200 m 2 0.625 m


2 1.500 m 2 0.875 m


2 0.324 m 2 m 3.324



 1    1 

Sin Sin

 

76.452 KN 0.833 m

  

0.347

A1 X1  A2 X 2  A3 X 3  A4 X 4  An

0.892 m


6.142 KN


1.475 m



9.060 KNm

Resisting Moment

68.167 KNm

Overturning Moment

6.867 KNm



68.167 KNm


15.927 KNm


4.280 OK


0.450 34.403 KN


22.623 KN 34.403 /

22.623

1.521 OK


0.000 m


2.000 m


1.000 m


0.6 m


70.632 KN 0.45 m

vehicle

n

29 º


3 23.000 KN/m


3 19.000 KN/m


WALL TYPE : -



1.950 m

0.450

Y

W2 bt= 0.6

m h1=

0.000 m

A2


H=h1+h2+h3= 25/100

2.000 m 1/5

h2=

W=

96.721 KN


Pa =1/2 x Pa x h4 =

9.889

KNm


1.000

0.600 0.6 A1 ' X

h4 = H/3 =

0.750 bb= 1/5

1.950 m 0.390 hv, m


1.989 m

Binclined

1.000 m

m


3.000 m 0.150 6

σx =1.77Qpm2n2/(H2(m2+n2)3 m

0.150 0.150 0.150 0.150 0.150 0.150

n

0.167 0.333 0.500 0.667 0.833 1.000

Z = nH

0.500 1.000 1.500 2.000 2.500 3.000

for m>0.4 or 0.28Qpm2n2/(H2(0.16+n2)3 for m≤0.4 2.103 2.072 2.116 2.152 2.172 2.183

P

H

1.044 1.047 1.067 1.081 1.089

2

ΣP =

5.328

H


2

3

4

5

6

7

8

9

10

11

12

13

14

σx

2.200 2.180 2.160 2.140 2.120 2.100 2.080 2.060 2.040 2.020 2.000


0.600 m


0.750 m


0.078 m


0.400 m


0.900 m


1.450 m


1.300 m 2 0.900 m


2 1.800 m 2 1.125 m


2 0.380 m 2 m 4.205



 1    1 

Sin Sin

 

96.721 KN 1.000 m

  

0.347

A1 X1  A2 X 2  A3 X 3  A4 X 4  An

0.976 m


5.328 KN


1.770 m



9.430 KNm

Resisting Moment

94.428 KNm

Overturning Moment

9.889 KNm



94.428 KNm


19.319 KNm


4.888 OK


0.450 43.524 KN


25.105 KN 43.524 /

25.105

1.734 OK


0.000 m


3.000 m


1.000 m


0.6 m


70.632 KN 0.45 m

vehicle

n

29 º


3 23.000 KN/m


3 19.000 KN/m


WALL TYPE : -



2.000 m

0.450

Y

W2 bt=

0.6

m h1=

0.000 m

A2


H=h1+h2+h3= 15/100

3.000 m 1/5

h2 =

W=

128.800 KN


Pa =1/2 x Pa x h4 =

17.580

KNm


1.000

0.800 A1 ' X

0.6

h4 = H/3 = 0.600

bb= 1/5

2.000 m 0.400 hv,m


2.04 m

Binclined

1.333 m

m


4.000 m 0.113 8

σx =1.77Qpm2n2/(H2(m2+n2)3 m

0.113 0.113 0.113 0.113 0.113 0.113 0.113 0.113

n

0.125 0.250 0.375 0.500 0.625 0.750 0.875 1.000

Z = nH

0.500 1.000 1.500 2.000 2.500 3.000 3.500 4.000

for m>0.4 or 0.28Qpm2n2/(H2(0.16+n2)3 for m≤0.4 1.200 1.164 1.171 1.190 1.206 1.217 1.224 1.228

P

H

0.591 0.584 0.590 0.599 0.606 0.610 0.613

2

ΣP =

4.193

H


2

3

4

5

6

7

8

9

10

11

12

13

14

1.240 1.220

σx

1.200 1.180 1.160 1.140 1.120


0.800 m


0.600 m


0.080 m


0.533 m


1.100 m


1.600 m


1.333 m 2 1.600 m


2 2.400 m 2 1.200 m


2 0.400 m 2 m 5.600



 1    1 

Sin Sin

 

128.800 KN 1.333 m

  

0.347

A1 X1  A2 X 2  A3 X 3  A4 X 4  An

1.062 m


4.193 KN


2.360 m



9.896 KNm

Resisting Moment

136.773 KNm

Overturning Moment

17.580 KNm



136.773 KNm


27.476 KNm


4.978 OK


0.450 57.960 KN


30.563 KN 57.960 /

30.563

1.896 OK


0.000 m


4.000 m


1.000 m


0.6 m


70.632 KN 0.45 m

vehicle

n

29 º


3 23.000 KN/m


3 19.000 KN/m


WALL TYPE : -



2.500 m

0.450

Y

W2 bt=

0.6

m h1=

0.000 m

A2


H=h1+h2+h3= 18/100

4.000 m 1/5

h2=

W=

192.625 KN


Pa =1/2 x Pa x h4 =

27.469

KNm


1.000

1.000 A1 ' X

0.6

h4 = H/3 = 0.900

bb= 1/5

2.500 m 0.500 hv, m


2.55 m

Binclined

1.667 m

m


5.000 m 0.090 10

σx =1.77Qpm2n2/(H2(m2+n2)3 m

0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090

n

0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000

Z = nH

0.500 1.000 1.500 2.000 2.500 3.000 3.500 4.000 4.500 5.000

for m>0.4 or 0.28Qpm2n2/(H2(0.16+n2)3 for m≤0.4 0.775 0.751 0.744 0.752 0.762 0.770 0.777 0.781 0.784 0.786

P

H

0.381 0.374 0.374 0.378 0.383 0.387 0.389 0.391 0.392

2

ΣP =

3.450

H


2

3

4

5

6

7

8

9

10

11

12

13

14

0.790 0.780

σx

0.770 0.760

0.750 0.740 0.730 0.720


1.000 m


0.900 m


0.100 m


0.667 m


1.300 m


1.900 m


1.667 m 2 2.500 m


2 3.000 m 2 2.250 m


2 0.625 m 2 m 8.375



 1    1 

Sin Sin

 

192.625 KN 1.667 m

  

0.347

A1 X1  A2 X 2  A3 X 3  A4 X 4  An

1.300 m


3.450 KN


2.950 m



10.178 KNm

Resisting Moment

250.317 KNm

Overturning Moment

27.469 KNm



250.317 KNm


37.647 KNm


6.649 OK


0.450 86.681 KN


36.413 KN 86.681 /

36.413

2.381 OK


0.000 m


5.000 m


1.000 m


0.6 m


70.632 KN 0.45 m

vehicle

n

30 º


3 23.000 KN/m


3 20.000 KN/m


WALL TYPE : -



3.000 m

0.450

Y

W2 bt=

0.6

m h1=

0.000 m

A2


H=h1+h2+h3= 20/100

5.000 m 1/5

h2=

W=

269.100 KN


Pa =1/2 x Pa x h4 =

40.000

KNm


1.000

1.200 A1 ' X

0.6

h4 = H/3 = 1.200

bb= 1/5

3.000 m 0.600 hv, m


3.059 m

Binclined

2.000 m

m


6.000 m 0.075 12

σx =1.77Qpm2n2/(H2(m2+n2)3 m

0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075

n

0.083 0.167 0.250 0.333 0.417 0.500 0.583 0.667 0.750 0.833 0.917 1.000

Z = nH

0.500 1.000 1.500 2.000 2.500 3.000 3.500 4.000 4.500 5.000 5.500 6.000

for m>0.4 or 0.28Qpm2n2/(H2(0.16+n2)3 for m≤0.4 0.541 0.526 0.517 0.518 0.523 0.529 0.534 0.538 0.541 0.543 0.545 0.546

P

H

0.267 0.261 0.259 0.260 0.263 0.266 0.268 0.270 0.271 0.272 0.273

2

ΣP =

2.929

H


2

3

4

5

6

7

8

9

10

11

12

13

14

σx

0.550 0.545 0.540 0.535 0.530 0.525 0.520 0.515 0.510 0.505 0.500


1.200 m


1.200 m


0.120 m


0.800 m


1.500 m


2.200 m


2.000 m 2 3.600 m


2 3.600 m 2 3.600 m


2 0.900 m 2 m 11.700



 1    1 

Sin Sin

 

269.100 KN 2.000 m

  

0.333

A1 X1  A2 X 2  A3 X 3  A4 X 4  An

1.538 m


2.929 KN


3.540 m



10.368 KNm

Resisting Moment

414.000 KNm

Overturning Moment

40.000 KNm



414.000 KNm


50.368 KNm


8.220 OK


0.450 121.095 KN


42.929 KN 121.095 /

42.929

2.821 OK


0.000 m


6.000 m


1.000 m


0.6 m


70.632 KN 0.45 m

vehicle

n

30 º


3 23.000 KN/m


3 20.000 KN/m


WALL TYPE : -



3.500 m

0.450

Y

W2 bt=

0.6

m h1=

0.000 m

A2


H=h1+h2+h3= 21/100

6.000 m 1/5

h2 =

W=

358.225 KN


Pa =1/2 x Pa x h4 =

54.444

KNm


1.000

1.400 A1 ' X

0.6

h4 = H/3 = 1.500

bb= 1/5

3.500 m 0.700 hv, m


3.569 m

Binclined

2.333 m

m


7.000 m 0.064 14

σx =1.77Qpm2n2/(H2(m2+n2)3 m

0.064 0.064 0.064 0.064 0.064 0.064 0.064 0.064 0.064 0.064 0.064 0.064 0.064 0.064

n

0.071 0.143 0.214 0.286 0.357 0.429 0.500 0.571 0.643 0.714 0.786 0.857 0.929 1.000

Z = nH

0.500 1.000 1.500 2.000 2.500 3.000 3.500 4.000 4.500 5.000 5.500 6.000 6.500 7.000

for m>0.4 or 0.28Qpm2n2/(H2(0.16+n2)3 for m≤0.4 0.399 0.389 0.382 0.380 0.381 0.385 0.389 0.392 0.395 0.397 0.398 0.399 0.400 0.401

P

H

0.197 0.193 0.190 0.190 0.192 0.193 0.195 0.197 0.198 0.199 0.199 0.200 0.200

2

ΣP =

2.543

H


2

3

4

5

6

7

8

9

10

11

12

13

14

0.405 0.400 0.395

σx

0.390 0.385 0.380 0.375

0.370 0.365


1.400 m


1.500 m


0.140 m


0.933 m


1.700 m


2.500 m


2.333 m 2 4.900 m


2 4.200 m 2 5.250 m


2 1.225 m 2 m 15.575



 1    1 

Sin Sin

 

358.225 KN 2.333 m

  

0.333

A1 X1  A2 X 2  A3 X 3  A4 X 4  An

1.778 m


2.543 KN


4.130 m



10.504 KNm

Resisting Moment

637.023 KNm

Overturning Moment

54.444 KNm



637.023 KNm


64.948 KNm


9.808 OK


0.450 161.201 KN


49.210 KN 161.201 /

49.210

3.276 OK


0.000 m


7.000 m


1.000 m


0.6 m


70.632 KN 0.45 m

vehicle

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

30 º

Unit weight of stone masonry wall (ϒs) =

3 23.000 KN/m


3 20.000 KN/m


WALL TYPE : -



4.000 m

0.450

Y

W2 bt=

0.6

m h1=

0.000 m

A2


H=h1+h2+h3= 23/100

7.000 m 1/5

h2=

W=

460.000 KN


Pa =1/2 x Pa x h4 =

71.111

KNm

Road Formation Level h4 = H/3 =

A3 h3=

1.000

1.600 A1 ' X

0.6

1.800

bb = 1/5

4.000 m 0.800 hv, m 4.079 m

Binclined

2.667 m

m

Pa=K p a x Active Soil pressure

2 ϒso x H = 53.333 KN/m


8.000 m 0.056 16

σx =1.77Qpm2n2/(H2(m2+n2)3 m

0.056 0.056 0.056 0.056 0.056 0.056 0.056 0.056 0.056 0.056 0.056 0.056 0.056 0.056 0.056 0.056

n

0.063 0.125 0.188 0.250 0.313 0.375 0.438 0.500 0.563 0.625 0.688 0.750 0.813 0.875 0.938 1.000

Z = nH

0.500 1.000 1.500 2.000 2.500 3.000 3.500 4.000 4.500 5.000 5.500 6.000 6.500 7.000 7.500 8.000

for m>0.4 or 0.28Qpm2n2/(H2(0.16+n2)3 for m≤0.4 0.306 0.300 0.294 0.291 0.291 0.293 0.295 0.298 0.300 0.302 0.303 0.304 0.305 0.306 0.307 0.307

P

H

0.152 0.148 0.146 0.146 0.146 0.147 0.148 0.149 0.150 0.151 0.152 0.152 0.153 0.153 0.153

ΣP =

2.247

H


2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

0.310 0.305 σx

0.300 0.295 0.290 0.285 0.280


1.600 m


1.800 m


0.160 m


1.067 m


1.900 m


2.800 m


2.667 m 2 6.400 m


2 4.800 m 2 m 7.200


2 1.600 m 2 20.000 m



 1    1 

Sin Sin

 

460.000 KN 2.667 m

  

0.333

A1 X1  A2 X 2  A3 X 3  A4 X 4  An

2.019 m


2.247 KN


Pa = K pa Moment due to surcharge Load @ X = PH x d Active earth pressure at base of wall

4.720 m

x ϒso x H


10.607 KNm

Resisting Moment

928.587 KNm

Overturning Moment

71.111 KNm



928.587 KNm


81.718 KNm


11.363 OK


0.450 207.000 KN


55.580 KN 207.000 /

55.580

3.724 OK


0.000 m

Height of Retaining wall from Formation Road Level to Top ground level (h2) =

8.000 m


1.000 m


0.6 m


70.632 KN 0.45 m

vehicle

n

30 º

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

3

Unit weight of stone masonry wall (ϒs) =

23.000 KN/m


20.000 KN/m

3


WALL TYPE : -



4.500 m

0.450

Y

W2 bt=

0.6

m h1=

0.000 m

A2


H=h1+h2+h3= 23/100

8.000 m 1/5

h2=

W=

574.425 KN


Pa =1/2 x Pa x h4 =

90.000

KNm

Road Formation Level h4 = H/3 =

A3 h3=

1.000

1.800 A1 ' X

0.6

2.100

bb=

4.500 m

1/5

0.900 hv, m 4.589 m

Binclined

3.000 m

m

Pa=K p a Active Soil pressure

2 x ϒso x H = 60.000 KN/m


9.000 m 0.050 18

σx =1.77Qpm2n2/(H2(m2+n2)3 m

0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050

n

0.056 0.111 0.167 0.222 0.278 0.333 0.389 0.444 0.500 0.556 0.611 0.667 0.722 0.778 0.833 0.889 0.944

Z = nH

0.500 1.000 1.500 2.000 2.500 3.000 3.500 4.000 4.500 5.000 5.500 6.000 6.500 7.000 7.500 8.000 8.500

for m>0.4 or 0.28Qpm2n2/(H2(0.16+n2)3 for m≤0.4 0.242 0.238 0.234 0.231 0.230 0.230 0.232 0.233 0.235 0.237 0.238 0.239 0.240 0.241 0.241 0.242 0.242

P

H

0.120 0.118 0.116 0.115 0.115 0.115 0.116 0.117 0.118 0.119 0.119 0.120 0.120 0.121 0.121 0.121 0.121

0.050

1.000

9.000

0.243

ΣP =

2.013

H


2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

0.245

σx

0.240 0.235 0.230 0.225 0.220


1.800 m


2.100 m


0.180 m


1.200 m


2.100 m


3.100 m


3.000 m 2 8.100 m


2 5.400 m 2 9.450 m


2 2.025 m 2 24.975 m

Cross section of Stone masonry retaining wall (A4) = Cross section of Stone masonry retaining wall (ΣAn) = Weight of Stone masonry retaining wall (W) = height of line of action for lateral earth pressure (h4) =

 1    1 

Active earth pressure coeff. at base of wall (K p a ) =


Sin Sin

 

574.425 KN 3.000 m

  

0.333

A1 X1  A2 X 2  A3 X 3  A4 X 4  An

2.259 m


2.013 KN


5.310 m



10.687 KNm

Resisting Moment

1297.890 KNm

Overturning Moment

90.000 KNm

Moment due to selfweight of wall @ X = W x X Moment due to active earth pressure @ X =1/2 x

Pa x h4


1297.890 KNm

Sum of Overturning moment = ΣMyy over Factor of safety against Overturning (FOS

100.687 KNm overturning)

=

12.890 OK


0.450 258.491 KN


62.013 KN 258.491 /

62.013

4.168 OK

Hm 2.000 2.500 3.000 4.000 5.000 6.000 7.000 8.000 9.000

Bt m 0.600 0.600 0.600 0.600 0.600 0.600 0.600 0.600 0.600

Bb m 1.600 1.800 1.950 2.000 2.500 3.000 3.500 4.000 4.500

Binclined m 1.632 1.836 1.989 2.040 2.550 3.059 3.569 4.079 4.589

hv m Outward slope back slope 0.320 1/5 3/10 0.360 1/5 7/25 0.390 1/5 1/4 0.400 1/5 3/20 0.500 1/5 9/50 0.600 1/5 1/5 0.700 1/5 3/14 0.800 1/5 9/40 0.900 1/5 7/30

H

Bt

1m

Bb hv

Typical diagram with Stone masonry wall geometry

Cross Section area m2 2.456 3.324 4.205 5.600 8.375 11.700 15.575 20.000 24.975

Stone masonry wall.xls

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