As Sing Ment

22 Unit Weight (γ) (KN/m3) = 18.5 8

15.075 15.075

54.693 1.923

1 31 13.314 266.285 928.325 1194.610 81.000 141.590 9.000 58.955

2 32 12.803 256.054 892.657 1148.711 80.000 137.613 10.000 73.866

3 35 11.425 228.504 796.613 1025.116 77.000 127.139 13.000 110.812 Pa

4 38 10.240 204.791 713.944 918.735 74.000 118.448 16.000 138.154

5 41 9.203 184.059 641.669 825.728 71.000 111.155 19.000 157.875 δo

6 44 8.284 165.685 577.613 743.298 68.000 104.978 22.000 171.371 yo

7 47 7.460 149.202 520.151 669.354 65.000 99.711 25.000 179.638 zo

8 50 6.713 134.256 468.045 602.301 62.000 95.196 28.000 183.384 zo

R

9 53 6.028 120.569 420.328 540.897 59.000 91.311 31.000 183.103 yo

10 56 5.396 107.921 376.237 484.158 56.000 87.962 34.000 179.125 (V-FW)

11 59 4.807 96.138 335.157 431.294 53.000 85.076 37.000 171.649 Fc

12 62 4.254 85.074 296.584 381.658 50.000 82.592 40.000 160.757 90-θo

13 65 3.730 74.609 260.104 334.713 47.000 80.463 43.000 146.427

14 68 3.232 64.644 225.363 290.008 44.000 78.651 46.000 128.537

15 71 2.755 55.092 192.064 247.156 41.000 77.126 49.000 106.855

16 74 2.294 45.879 159.945 205.824 38.000 75.863 52.000 81.030

17 75 2.144 42.872 149.460 192.332 37.000 75.496 53.000 71.421

Surcharge (q) (KN/m2) =

Cohesion (Cu) (KN/m2)=

Wall angle with horizontal (αo) =Height of Wall (H) (m) =Angle of Internal Friction (φo)=

Angle of Wall Friction (δo=tan-1(2/3tanφo))=

WaterThrust (Pw=0.5γwZ02)(KN/m2) =

Surcharge

Load (qb)

(KN/m)

Weight of

Wedge ((W=

(1/2(H2-

Z02)Cotθγ)

(KN/m)

CALCULATION OF ACTIVE THRUST FROM COULOMB METHOD

Angle for Active Thrust from horizontal xo=(90-α+δ)o =

Depth of Tension Crack (Z0) (m) =Wall Adhesion force (Fw= 0.75Cu(H-Z0)) (KN/m) =

Trial

Wedge

No.

Base

Angle

(θo)

Width of

Wedge

(b = h*tan(90-

θ)) (m)

Total

Vertical

Load, (V =

qb+W)

(KN/m)

Angle for

Reaction (R)

from

horizontal

yo=(90-θ+φ)o

Force due to

cohesion

(FC)=Cu(H-

Z0)/Sinθ

(KN/m)

Angle zo=(θ-

φ)o

Active

Thrust (Pa)

(KN/m)

Maximum of Minimum thrust obtained at θ = 50o

The Maximum Thrust = 183.384 (KN/m)

θ Vs. Pa Graph

y = -3E-08x6 + 1E-05x5 - 0.0017x4 + 0.1413x3 - 6.9826x2 + 196.92x - 2271.9 R² = 1

0.000

20.000

40.000

60.000

80.000

100.000

120.000

140.000

160.000

180.000

200.000

0 10 20 30 40 50 60 70 80

Val

ue

of

Act

ive

Th

rust

(P

a) (

KN

/m)

Value of Angle θ (degree)

θ Vs. Pa Graph

θ Vs. Pa Graph

Poly. (θ Vs. Pa Graph)

90

12

20

18.490

Pwθ

o


θ Vs. Pa Graph

Vs. Pa Graph

Vs. Pa Graph)

22 Unit Weight (γ) (KN/m3) = 18.5 8 90

15.075 15.075 12

72 0 20

1 13 34.652 693.036 2564.234 3257.270 35.000 426.760 55.000 3591.971

2 16 27.899 557.986 2064.549 2622.536 38.000 348.284 52.000 3298.839 A

3 19 23.234 464.674 1719.293 2183.967 41.000 294.869 49.000 3141.763

4 22 19.801 396.014 1465.251 1861.265 44.000 256.269 46.000 3075.530

5 23 18.847 376.936 1394.665 1771.601 45.000 245.693 45.000 3069.805

6 24 17.968 359.366 1329.654 1689.020 46.000 236.025 44.000 3071.563 zo x0

7 25 17.156 343.121 1269.548 1612.669 47.000 227.155 43.000 3080.614 zo

8 28 15.046 300.916 1113.390 1414.306 50.000 204.485 40.000 3151.561

9 31 13.314 266.285 985.253 1251.538 53.000 186.394 37.000 3293.694

10 34 11.860 237.210 877.676 1114.886 56.000 171.676 34.000 3524.625 R

11 35 11.425 228.504 845.464 1073.967 57.000 167.371 33.000 3626.930

12 36 11.011 220.221 814.818 1035.039 58.000 163.325 32.000 3745.019

13 37 10.616 212.327 785.611 997.938 59.000 159.517 31.000 3881.536

14 38 10.240 204.791 757.725 962.516 60.000 155.930 30.000 4039.869

15 39 9.879 197.584 731.059 928.643 61.000 152.546 29.000 4224.416

16 40 9.534 190.681 705.518 896.199 62.000 149.349 28.000 4440.969

17 41 9.203 184.059 681.018 865.077 63.000 146.328 27.000 4697.294

18 42 8.885 177.698 657.483 835.181 64.000 143.470 26.000 5004.028 yo

19 43 8.579 171.579 634.842 806.421 65.000 140.763 25.000 5376.130 B

Height of Wall (H) (m) = Wall angle with horizontal (αo) =

Angle of Wall Friction (δo=tan-1(2/3tanφo))= Angle for Active Thrust from horizontal xo=(90-α-δ)o = Cohesion (Cu) (KN/m2)=

CALCULATION OF PASSIVE THRUST FROM COULOMB METHOD

Wall Adhesion force (Fw= 0.75Cu(H-Z0)) (KN/m) = Depth of Tension Crack (Z0) (m) = Surcharge (q) (KN/m2) =

Trial

Wedge

No.

Base

Angle

(θo)

Width of

Wedge

(b = h*tan(90-

θ)) (m)

Surcharge

Load (qb)

(KN/m)

Weight of

Wedge ((W=

(1/2(H2-

Z02)Cotθγ)

(KN/m)

Total

Vertical

Load, (V =

qb+W)

(KN/m)

Angle for

Reaction (R)

from

horizontal

yo=(θ+φ)o

Force due to

cohesion

(FC)=Cu(H-

Z0)/Sinθ

(KN/m)

Angle

zo=(90-y)o

Active

Thrust (Pa)

(KN/m)

Angle of Internal Friction (φo)=

PpSinx/Tanz

Fc Cosθ

(PpCosx - FcCosθ - PpSinx/Tanz)

PpSinx

(V+Fw)+FcSinθ

θ Vs. Pp Graph

y = 2E-05x6 - 0.0034x5 + 0.22x4 - 7.7283x3 + 156.99x2 - 1797.7x + 12271 R² = 1

0.000

1000.000

2000.000

3000.000

4000.000

5000.000

6000.000

0 5 10 15 20 25 30 35 40 45 50

Val

ue

of

Pas

sive

Th

rust

(P

p)

(KN

/m)


θ Vs. Pp Graph

θ Vs. Pp Graph

Poly. (θ Vs. Pp Graph)

(V+Fw)+FcSinθ

Pp

D

(V+Fw)

C

θ0

Fc


PpSinx/Tanz

θ Vs. Pp Graph


20.281 20.281

50

1 31 8.321 416.070 384.865 800.935 2.000 88.000 29.438 200.000

2 35 7.275 363.752 336.471 700.223 5.500 84.500 69.410 200.000

3 38 6.516 325.806 301.371 627.177 8.500 81.500 94.698 200.000 Pa1 (90-x)o

4 41 5.854 292.712 270.759 563.471 11.500 78.500 113.671 200.000

5 44 5.269 263.445 243.687 507.132 14.500 75.500 127.625 200.000 xo

6 47 4.745 237.241 219.448 456.689 17.500 72.500 137.491 450.000 αo

7 50 4.270 213.520 197.506 411.026 20.500 69.500 143.946 800.000

8 53 3.837 191.832 177.444 369.276 23.500 66.500 147.481 1350.000

9 56 3.436 171.820 158.934 330.754 26.500 63.500 148.455 2280.000 R1

10 60 2.945 147.261 136.217 283.478 30.500 59.500 146.195 3500.000 V

11 63 2.603 130.142 120.381 250.523 33.500 56.500 142.036 4300.000

12 66 2.279 113.932 105.387 219.318 36.500 53.500 135.863 7850.000 yo

13 69 1.970 98.478 91.092 189.569 39.500 50.500 127.698 7850.000

14 72 1.673 83.649 77.375 161.024 42.500 47.500 117.512 7850.000

15 75 1.387 69.331 64.131 133.462 45.500 44.500 105.221 7850.000

16 78 1.108 55.424 51.267 106.691 48.500 41.500 90.684 7850.000

17 81 0.837 41.836 38.698 80.534 51.500 38.500 73.698 7850.000

17 84 0.570 28.484 26.348 54.832 54.500 35.500 53.984 7850.000

17 87 0.306 15.291 14.144 29.435 57.500 32.500 31.174 7850.000

Layer-I


Trial

Wedge

No.

Base

Angle

(θo)

Width of

Wedge

(b = h*tan(90-

θ)) (m)

Surcharge

Load (qb)

(KN/m)

Weight of

Wedge ((W=

(1/2H2Cotθγ)

(KN/m)

Total

Vertical

Load, (V =

qb+W)

(KN/m)

Angle for

Reaction (R)

from vertical

yo=(θ-φ)o


Angle of Internal Friction (φo)= Height of Wall (H1) (m) = Wall angle with horizontal (αo) =

Angle of Wall Friction (δo=tan-1(2/3tanφo))= Angle for Active Thrust from horizontal xo=(90-α+δ)o = Cohesion (Cu) (KN/m2)=

Angle αo=(90-

y)o

Active

Thrust (Pa)

(KN/m)

Active

Thrust (Pa)

(KN/m)

148.455 KN/m

θ Vs. Pa Graph

Pa1max =

y = -2E-08x6 + 6E-06x5 - 0.001x4 + 0.0897x3 - 4.7897x2 + 144.47x - 1763 R² = 1

0.000

20.000

40.000

60.000

80.000

100.000

120.000

140.000

160.000

0 10 20 30 40 50 60 70 80 90 100

Val

ue

of

Act

ive

Th

rust

(P

a) (

KN

/m)


θ Vs. Pa Graph

θ Vs. Pa Graph


38 Unit Weight (γ2) (KN/m3) = 20 7

27.513 27.513

50 64

29 Unit Weight (γ1) (KN/m3) = 18.5 5

20.281 90

50 20.281

64

Fa (90-x)o

xo

αo

10 65 2.332 116.577 107.834 224.411 36.000 54.000 137.030 3500.000

11 66 2.226 111.307 102.959 214.266 37.000 53.000 134.640 4300.000

12 67 2.122 106.119 98.160 204.279 38.000 52.000 132.030 7850.000 R2

13 68 2.020 101.007 93.431 194.438 39.000 51.000 129.197 7850.000 V

14 69 1.919 95.966 88.769 184.735 40.000 50.000 126.142 7850.000

15 70 1.820 90.993 84.168 175.161 41.000 49.000 122.861 7850.000 yo

16 71 1.722 86.082 79.626 165.708 42.000 48.000 119.353 7850.000

17 72 1.625 81.230 75.138 156.368 43.000 47.000 115.613 7850.000

17 73 1.529 76.433 70.700 147.133 44.000 46.000 111.637 7850.000

17 74 1.434 71.686 66.310 137.996 45.000 45.000 107.421 7850.000

18 75 1.340 66.987 61.963 128.951 46.000 44.000 102.959 7850.000


Layer-II

Angle of Internal Friction (φ2o)= Height of Wall (H2) (m) = Wall angle with horizontal (αo) =

Angle of Wall Friction (δ2o=tan-1(2/3tanφ2o))= Angle for Active Thrust from horizontal xo=(90-α+δ2)o = Cohesion (Cu) (KN/m2)=

Assumed Base Angle for Second layer (θ2) =

Angle of Internal Friction (φ1o)= Height of Wall (H1) (m) =

Total

Vertical

Load, (V =

qb+W)

(KN/m)

Angle for

Reaction (R)

from vertical

yo=(θ-φ1)o

Angle αo=(90-

y)o

Active

Thrust (Pa)

(KN/m)

Active

Thrust (Pa)

(KN/m)

Trial

Wedge

No.

Base

Angle in

Layer-I

(θo)

Width of

Wedge

(b = H1*tan(90-

θ)) (m)

Surcharge

Load (qb)

(KN/m)

Weight of

Wedge ((W=

(1/2H12Cotθγ)

(KN/m)


Angle of Wall Friction (δ1o=tan-1(2/3tanφ1o))=

Angle for Active Thrust from horizontal xo=(90-α+δ)o =



Fictitious Wall angle with horizontal (αo) =

Analysis in Layer -I for Trial Angle θ2 in Layer-II, the wedge line in Layer-II extended in Layer-I, form fictitious wall in layer-I from intersection of two layers and

refracted in layer-I towards vertical so that the angles in layer-I, i.e. θ21, θ22,θ23 etc are greater than θ2

Layer-I

Pa2

δ2

R3

φ1

(θ-φ2)

137.03 27.513

65

38 29

179.455 KN/m

Tan (θ-φ2) = (Pa2Cosδ2-FamaxSinφ1)/(V-Pa2 Sinδ2 +FamaxSinφ1)

Pa2=Vtan(θ-φ2)+Famax(Sinφ1+Tan (θ-φ2))/(Cosδ2+Tan (θ-φ2)) =

Angle of Wall Friction (δ2o=tan-1(2/3tanφ2o))=

Angle of Internal Friction (φ2o)=

Base Angle (θ) for Famax = Vertical Force (KN/m) with Surcharge for base angle corresponding to Famax found =

Angle of Internal Friction (φ1o)=

θ Vs. Fa Graph Calculation of Pa2 in Layer-II

Famax (KN/m) from θ Vs. Fa Graph found =

y = -6E-09x6 + 3E-06x5 - 0.0004x4 + 0.0449x3 - 2.7143x2 + 93.695x - 1251.1 R² = 1

0.000

20.000

40.000

60.000

80.000

100.000

120.000

140.000

160.000

64 66 68 70 72 74 76

Val

ue

of

Act

ive

Th

rust

(P

a) (

KN

/m)


θ Vs. Fa Graph

θ Vs. Fa Graph

FamaxSinφ1 FamaxSin

Pa2 Sinδ2

Pa2Cosδ2-FamaxSinφ1

62

10 50 4.195 209.775 194.042 403.817 21.000 69.000 144.726 3500.000

11 51 4.049 202.446 187.263 389.709 22.000 68.000 146.053 4300.000

12 52 3.906 195.321 180.672 375.994 23.000 67.000 147.078 7850.000

13 53 3.768 188.389 174.259 362.648 24.000 66.000 147.813 7850.000

14 54 3.633 181.636 168.013 349.649 25.000 65.000 148.270 7850.000

15 55 3.501 175.052 161.923 336.975 26.000 64.000 148.459 7850.000

16 56 3.373 168.627 155.980 324.607 27.000 63.000 148.388 7850.000

17 57 3.247 162.352 150.176 312.527 28.000 62.000 148.064 7850.000

17 58 3.124 156.217 144.501 300.718 29.000 61.000 147.496 7850.000 Fa (90-x)o

17 59 3.004 150.215 138.949 289.164 30.000 60.000 146.687 7850.000

18 60 2.887 144.338 133.512 277.850 31.000 59.000 145.644 7850.000 xo

19 61 2.772 138.577 128.184 266.761 32.000 58.000 144.371 7850.000 αo

20 62 2.659 132.927 122.958 255.885 33.000 57.000 142.871 7850.000

21 63 2.548 127.381 117.828 245.209 34.000 56.000 141.146 7850.000

22 64 2.439 121.933 112.788 234.721 35.000 55.000 139.198 7850.000 R2

23 65 2.332 116.577 107.834 224.411 36.000 54.000 137.030 7850.000 V

24 66 2.226 111.307 102.959 214.266 37.000 53.000 134.640 7850.000

25 67 2.122 106.119 98.160 204.279 38.000 52.000 132.030 7850.000 yo

26 68 2.020 101.007 93.431 194.438 39.000 51.000 129.197 7850.000

27 69 1.919 95.966 88.769 184.735 40.000 50.000 126.142 7850.000

28 70 1.820 90.993 84.168 175.161 41.000 49.000 122.861 7850.000

29 71 1.722 86.082 79.626 165.708 42.000 48.000 119.353 7850.000

30 72 1.625 81.230 75.138 156.368 43.000 47.000 115.613 7850.000

31 73 1.529 76.433 70.700 147.133 44.000 46.000 111.637 7850.000

32 74 1.434 71.686 66.310 137.996 45.000 45.000 107.421 7850.000

33 75 1.340 66.987 61.963 128.951 46.000 44.000 102.959 7850.000

34 76 1.247 62.332 57.657 119.989 47.000 43.000 98.245 7850.000

35 77 1.154 57.717 53.388 111.105 48.000 42.000 93.271 7850.000


Trial

Wedge

No.

Base

Angle in

Layer-I

(θo)

Width of

Wedge

(b = H1*tan(90-

θ)) (m)

Surcharge

Load (qb)

(KN/m)

Active

Thrust (Pa)

(KN/m)

Weight of

Wedge ((W=

(1/2H12Cotθγ)

(KN/m)

Total

Vertical

Load, (V =

qb+W)

(KN/m)

Angle for

Reaction (R)

from vertical

yo=(θ-φ1)o

Angle αo=(90-

y)o

Active

Thrust (Pa)

(KN/m)

Pa2

δ2

R3

φ1

(θ-φ2)

148.459 27.513

55

38 29

184.789 KN/m


Angle of Internal Friction (φ2o)= Angle of Internal Friction (φ1o)=



Famax (KN/m) from θ Vs. Fa Graph found = Angle of Wall Friction (δ2o=tan-1(2/3tanφ2o))=


y = -7E-09x6 + 3E-06x5 - 0.0005x4 + 0.0511x3 - 3.0166x2 + 101.56x - 1336.1 R² = 1

0.000

20.000

40.000

60.000

80.000

100.000

120.000

140.000

160.000

0 20 40 60 80 100

Val

ue

of

Act

ive

Th

rust

(P

a) (

KN

/m)


θ Vs. Fa Graph

θ Vs. Fa Graph


Pa2 Sinδ2


61

10 49 4.346 217.322 201.023 418.344 20.000 70.000 143.084 3500.000

11 50 4.195 209.775 194.042 403.817 21.000 69.000 144.726 4300.000

12 51 4.049 202.446 187.263 389.709 22.000 68.000 146.053 7850.000

13 52 3.906 195.321 180.672 375.994 23.000 67.000 147.078 7850.000

14 53 3.768 188.389 174.259 362.648 24.000 66.000 147.813 7850.000

15 54 3.633 181.636 168.013 349.649 25.000 65.000 148.270 7850.000

16 55 3.501 175.052 161.923 336.975 26.000 64.000 148.459 7850.000

17 56 3.373 168.627 155.980 324.607 27.000 63.000 148.388 7850.000

17 57 3.247 162.352 150.176 312.527 28.000 62.000 148.064 7850.000 Fa (90-x)o

17 58 3.124 156.217 144.501 300.718 29.000 61.000 147.496 7850.000

18 59 3.004 150.215 138.949 289.164 30.000 60.000 146.687 7850.000 xo

19 60 2.887 144.338 133.512 277.850 31.000 59.000 145.644 7850.000 αo

20 61 2.772 138.577 128.184 266.761 32.000 58.000 144.371 7850.000

21 62 2.659 132.927 122.958 255.885 33.000 57.000 142.871 7850.000

22 63 2.548 127.381 117.828 245.209 34.000 56.000 141.146 7850.000 R2

23 64 2.439 121.933 112.788 234.721 35.000 55.000 139.198 7850.000 V

24 65 2.332 116.577 107.834 224.411 36.000 54.000 137.030 7850.000

25 66 2.226 111.307 102.959 214.266 37.000 53.000 134.640 7850.000 yo

26 67 2.122 106.119 98.160 204.279 38.000 52.000 132.030 7850.000

27 68 2.020 101.007 93.431 194.438 39.000 51.000 129.197 7850.000

28 69 1.919 95.966 88.769 184.735 40.000 50.000 126.142 7850.000

29 70 1.820 90.993 84.168 175.161 41.000 49.000 122.861 7850.000

30 71 1.722 86.082 79.626 165.708 42.000 48.000 119.353 7850.000

31 72 1.625 81.230 75.138 156.368 43.000 47.000 115.613 7850.000

32 73 1.529 76.433 70.700 147.133 44.000 46.000 111.637 7850.000

33 74 1.434 71.686 66.310 137.996 45.000 45.000 107.421 7850.000

34 75 1.340 66.987 61.963 128.951 46.000 44.000 102.959 7850.000

35 76 1.247 62.332 57.657 119.989 47.000 43.000 98.245 7850.000


Trial

Wedge

No.

Base

Angle in

Layer-I

(θo)

Width of

Wedge

(b = H1*tan(90-

θ)) (m)

Surcharge

Load (qb)

(KN/m)

Weight of

Wedge ((W=

(1/2H12Cotθγ)

(KN/m)

Total

Vertical

Load, (V =

qb+W)

(KN/m)

Angle for

Reaction (R)

from vertical

yo=(θ-φ1)o

Angle αo=(90-

y)o

Active

Thrust (Pa)

(KN/m)

Active

Thrust (Pa)

(KN/m)

Pa2

δ2

R3

φ1

(θ-φ2)

148.459 27.513

49

38 29

168.457 KN/m







y = -8E-09x6 + 3E-06x5 - 0.0005x4 + 0.0533x3 - 3.1197x2 + 104.13x - 1362.7 R² = 1

0.000

20.000

40.000

60.000

80.000

100.000

120.000

140.000

160.000

0 10 20 30 40 50 60 70 80

Val

ue

of

Act

ive

Th

rust

(P

a) (

KN

/m)


θ Vs. Fa Graph

θ Vs. Fa Graph


Pa2 Sinδ2


60

10 48 4.502 225.101 208.218 433.319 19.000 71.000 141.110 3500.000

11 49 4.346 217.322 201.023 418.344 20.000 70.000 143.084 4300.000

12 50 4.195 209.775 194.042 403.817 21.000 69.000 144.726 7850.000

13 51 4.049 202.446 187.263 389.709 22.000 68.000 146.053 7850.000

14 52 3.906 195.321 180.672 375.994 23.000 67.000 147.078 7850.000

15 53 3.768 188.389 174.259 362.648 24.000 66.000 147.813 7850.000

16 54 3.633 181.636 168.013 349.649 25.000 65.000 148.270 7850.000

17 55 3.501 175.052 161.923 336.975 26.000 64.000 148.459 7850.000

17 56 3.373 168.627 155.980 324.607 27.000 63.000 148.388 7850.000 Fa (90-x)o

17 57 3.247 162.352 150.176 312.527 28.000 62.000 148.064 7850.000

18 58 3.124 156.217 144.501 300.718 29.000 61.000 147.496 7850.000 xo

19 59 3.004 150.215 138.949 289.164 30.000 60.000 146.687 7850.000 αo

20 60 2.887 144.338 133.512 277.850 31.000 59.000 145.644 7850.000

21 61 2.772 138.577 128.184 266.761 32.000 58.000 144.371 7850.000

22 62 2.659 132.927 122.958 255.885 33.000 57.000 142.871 7850.000 R2

23 63 2.548 127.381 117.828 245.209 34.000 56.000 141.146 7850.000 V

24 64 2.439 121.933 112.788 234.721 35.000 55.000 139.198 7850.000

25 65 2.332 116.577 107.834 224.411 36.000 54.000 137.030 7850.000 yo

26 66 2.226 111.307 102.959 214.266 37.000 53.000 134.640 7850.000

27 67 2.122 106.119 98.160 204.279 38.000 52.000 132.030 7850.000

28 68 2.020 101.007 93.431 194.438 39.000 51.000 129.197 7850.000

29 69 1.919 95.966 88.769 184.735 40.000 50.000 126.142 7850.000

30 70 1.820 90.993 84.168 175.161 41.000 49.000 122.861 7850.000

31 71 1.722 86.082 79.626 165.708 42.000 48.000 119.353 7850.000

32 72 1.625 81.230 75.138 156.368 43.000 47.000 115.613 7850.000

33 73 1.529 76.433 70.700 147.133 44.000 46.000 111.637 7850.000

34 74 1.434 71.686 66.310 137.996 45.000 45.000 107.421 7850.000

35 75 1.340 66.987 61.963 128.951 46.000 44.000 102.959 7850.000


Trial

Wedge

No.

Base

Angle in

Layer-I

(θo)

Width of

Wedge

(b = H1*tan(90-

θ)) (m)

Surcharge

Load (qb)

(KN/m)

Weight of

Wedge ((W=

(1/2H12Cotθγ)

(KN/m)

Total

Vertical

Load, (V =

qb+W)

(KN/m)

Angle for

Reaction (R)

from vertical

yo=(θ-φ1)o

Angle αo=(90-

y)o

Active

Thrust (Pa)

(KN/m)

Active

Thrust (Pa)

(KN/m)

Pa2

δ2

R3

φ1

(θ-φ2)

141.110 27.513

48

38 29

159.607 KN/m







y = -8E-09x6 + 3E-06x5 - 0.0006x4 + 0.0559x3 - 3.2403x2 + 107.08x - 1392.7 R² = 1

0.000

20.000

40.000

60.000

80.000

100.000

120.000

140.000

160.000

0 10 20 30 40 50 60 70 80

Val

ue

of

Act

ive

Th

rust

(P

a) (

KN

/m)


θ Vs. Fa Graph

θ Vs. Fa Graph


Pa2 Sinδ2


59

10 58 3.124 156.217 144.501 300.718 29.000 61.000 147.496 3500.000

11 59 3.004 150.215 138.949 289.164 30.000 60.000 146.687 4300.000

12 60 2.887 144.338 133.512 277.850 31.000 59.000 145.644 7850.000

13 61 2.772 138.577 128.184 266.761 32.000 58.000 144.371 7850.000

14 62 2.659 132.927 122.958 255.885 33.000 57.000 142.871 7850.000

15 63 2.548 127.381 117.828 245.209 34.000 56.000 141.146 7850.000

16 64 2.439 121.933 112.788 234.721 35.000 55.000 139.198 7850.000

17 65 2.332 116.577 107.834 224.411 36.000 54.000 137.030 7850.000

17 66 2.226 111.307 102.959 214.266 37.000 53.000 134.640 7850.000 Fa (90-x)o

17 67 2.122 106.119 98.160 204.279 38.000 52.000 132.030 7850.000

18 68 2.020 101.007 93.431 194.438 39.000 51.000 129.197 7850.000 xo

19 69 1.919 95.966 88.769 184.735 40.000 50.000 126.142 7850.000 αo

20 70 1.820 90.993 84.168 175.161 41.000 49.000 122.861 7850.000

21 71 1.722 86.082 79.626 165.708 42.000 48.000 119.353 7850.000

22 72 1.625 81.230 75.138 156.368 43.000 47.000 115.613 7850.000 R2

23 73 1.529 76.433 70.700 147.133 44.000 46.000 111.637 7850.000 V

24 74 1.434 71.686 66.310 137.996 45.000 45.000 107.421 7850.000

25 75 1.340 66.987 61.963 128.951 46.000 44.000 102.959 7850.000 yo

26 76 1.247 62.332 57.657 119.989 47.000 43.000 98.245 7850.000

27 77 1.154 57.717 53.388 111.105 48.000 42.000 93.271 7850.000

28 78 1.063 53.139 49.154 102.293 49.000 41.000 88.030 7850.000

29 79 0.972 48.595 44.950 93.546 50.000 40.000 82.513 7850.000

30 80 0.882 44.082 40.776 84.857 51.000 39.000 76.710 7850.000

31 81 0.792 39.596 36.626 76.223 52.000 38.000 70.611 7850.000

32 82 0.703 35.135 32.500 67.635 53.000 37.000 64.203 7850.000

33 83 0.614 30.696 28.394 59.090 54.000 36.000 57.473 7850.000

34 84 0.526 26.276 24.305 50.581 55.000 35.000 50.409 7850.000

35 85 0.437 21.872 20.232 42.104 56.000 34.000 42.993 7850.000


Trial

Wedge

No.

Base

Angle in

Layer-I

(θo)

Width of

Wedge

(b = H1*tan(90-

θ)) (m)

Surcharge

Load (qb)

(KN/m)

Weight of

Wedge ((W=

(1/2H12Cotθγ)

(KN/m)

Total

Vertical

Load, (V =

qb+W)

(KN/m)

Angle for

Reaction (R)

from vertical

yo=(θ-φ1)o

Angle αo=(90-

y)o

Active

Thrust (Pa)

(KN/m)

Active

Thrust (Pa)

(KN/m)

Pa2

δ2

R3

φ1

(θ-φ2)

147.496 27.513

58

38 29

187.584 KN/m







y = -7E-09x6 + 3E-06x5 - 0.0005x4 + 0.0499x3 - 2.971x2 + 100.69x - 1330.4 R² = 1

0.000

20.000

40.000

60.000

80.000

100.000

120.000

140.000

160.000

0 20 40 60 80 100

Val

ue

of

Act

ive

Th

rust

(P

a) (

KN

/m)


θ Vs. Fa Graph

θ Vs. Fa Graph


Pa2 Sinδ2


58

10 57 3.247 162.352 150.176 312.527 28.000 62.000 148.064 3500.000

11 58 3.124 156.217 144.501 300.718 29.000 61.000 147.496 4300.000

12 59 3.004 150.215 138.949 289.164 30.000 60.000 146.687 7850.000

13 60 2.887 144.338 133.512 277.850 31.000 59.000 145.644 7850.000

14 61 2.772 138.577 128.184 266.761 32.000 58.000 144.371 7850.000

15 62 2.659 132.927 122.958 255.885 33.000 57.000 142.871 7850.000

16 63 2.548 127.381 117.828 245.209 34.000 56.000 141.146 7850.000

17 64 2.439 121.933 112.788 234.721 35.000 55.000 139.198 7850.000

17 65 2.332 116.577 107.834 224.411 36.000 54.000 137.030 7850.000 Fa (90-x)o

17 66 2.226 111.307 102.959 214.266 37.000 53.000 134.640 7850.000

18 67 2.122 106.119 98.160 204.279 38.000 52.000 132.030 7850.000 xo

19 68 2.020 101.007 93.431 194.438 39.000 51.000 129.197 7850.000 αo

20 69 1.919 95.966 88.769 184.735 40.000 50.000 126.142 7850.000

21 70 1.820 90.993 84.168 175.161 41.000 49.000 122.861 7850.000

22 71 1.722 86.082 79.626 165.708 42.000 48.000 119.353 7850.000 R2

23 72 1.625 81.230 75.138 156.368 43.000 47.000 115.613 7850.000 V

24 73 1.529 76.433 70.700 147.133 44.000 46.000 111.637 7850.000

25 74 1.434 71.686 66.310 137.996 45.000 45.000 107.421 7850.000 yo

26 75 1.340 66.987 61.963 128.951 46.000 44.000 102.959 7850.000

27 76 1.247 62.332 57.657 119.989 47.000 43.000 98.245 7850.000

28 77 1.154 57.717 53.388 111.105 48.000 42.000 93.271 7850.000

29 78 1.063 53.139 49.154 102.293 49.000 41.000 88.030 7850.000

30 79 0.972 48.595 44.950 93.546 50.000 40.000 82.513 7850.000

31 80 0.882 44.082 40.776 84.857 51.000 39.000 76.710 7850.000

32 81 0.792 39.596 36.626 76.223 52.000 38.000 70.611 7850.000

33 82 0.703 35.135 32.500 67.635 53.000 37.000 64.203 7850.000

34 83 0.614 30.696 28.394 59.090 54.000 36.000 57.473 7850.000

35 84 0.526 26.276 24.305 50.581 55.000 35.000 50.409 7850.000


Trial

Wedge

No.

Base

Angle in

Layer-I

(θo)

Width of

Wedge

(b = H1*tan(90-

θ)) (m)

Surcharge

Load (qb)

(KN/m)

Weight of

Wedge ((W=

(1/2H12Cotθγ)

(KN/m)

Total

Vertical

Load, (V =

qb+W)

(KN/m)

Angle for

Reaction (R)

from vertical

yo=(θ-φ1)o

Angle αo=(90-

y)o

Active

Thrust (Pa)

(KN/m)

Active

Thrust (Pa)

(KN/m)

Pa2

δ2

R3

φ1

(θ-φ2)

148.064 27.513

57

38 29

187.111 KN/m







y = -7E-09x6 + 3E-06x5 - 0.0005x4 + 0.0482x3 - 2.879x2 + 98.125x - 1300.6 R² = 1

0.000

20.000

40.000

60.000

80.000

100.000

120.000

140.000

160.000

0 20 40 60 80 100

Val

ue

of

Act

ive

Th

rust

(P

a) (

KN

/m)


θ Vs. Fa Graph

θ Vs. Fa Graph


Pa2 Sinδ2


57

10 56 3.373 168.627 155.980 324.607 27.000 63.000 148.388 3500.000

11 57 3.247 162.352 150.176 312.527 28.000 62.000 148.064 4300.000

12 58 3.124 156.217 144.501 300.718 29.000 61.000 147.496 7850.000

13 59 3.004 150.215 138.949 289.164 30.000 60.000 146.687 7850.000

14 60 2.887 144.338 133.512 277.850 31.000 59.000 145.644 7850.000

15 61 2.772 138.577 128.184 266.761 32.000 58.000 144.371 7850.000

16 62 2.659 132.927 122.958 255.885 33.000 57.000 142.871 7850.000

17 63 2.548 127.381 117.828 245.209 34.000 56.000 141.146 7850.000

17 64 2.439 121.933 112.788 234.721 35.000 55.000 139.198 7850.000 Fa (90-x)o

17 65 2.332 116.577 107.834 224.411 36.000 54.000 137.030 7850.000

18 66 2.226 111.307 102.959 214.266 37.000 53.000 134.640 7850.000 xo

19 67 2.122 106.119 98.160 204.279 38.000 52.000 132.030 7850.000 αo

20 68 2.020 101.007 93.431 194.438 39.000 51.000 129.197 7850.000

21 69 1.919 95.966 88.769 184.735 40.000 50.000 126.142 7850.000

22 70 1.820 90.993 84.168 175.161 41.000 49.000 122.861 7850.000 R2

23 71 1.722 86.082 79.626 165.708 42.000 48.000 119.353 7850.000 V

24 72 1.625 81.230 75.138 156.368 43.000 47.000 115.613 7850.000

25 73 1.529 76.433 70.700 147.133 44.000 46.000 111.637 7850.000 yo

26 74 1.434 71.686 66.310 137.996 45.000 45.000 107.421 7850.000

27 75 1.340 66.987 61.963 128.951 46.000 44.000 102.959 7850.000

28 76 1.247 62.332 57.657 119.989 47.000 43.000 98.245 7850.000

29 77 1.154 57.717 53.388 111.105 48.000 42.000 93.271 7850.000

30 78 1.063 53.139 49.154 102.293 49.000 41.000 88.030 7850.000

31 79 0.972 48.595 44.950 93.546 50.000 40.000 82.513 7850.000

32 80 0.882 44.082 40.776 84.857 51.000 39.000 76.710 7850.000

33 81 0.792 39.596 36.626 76.223 52.000 38.000 70.611 7850.000

34 82 0.703 35.135 32.500 67.635 53.000 37.000 64.203 7850.000

35 83 0.614 30.696 28.394 59.090 54.000 36.000 57.473 7850.000


Trial

Wedge

No.

Base

Angle in

Layer-I

(θo)

Width of

Wedge

(b = H1*tan(90-

θ)) (m)

Surcharge

Load (qb)

(KN/m)

Weight of

Wedge ((W=

(1/2H12Cotθγ)

(KN/m)

Total

Vertical

Load, (V =

qb+W)

(KN/m)

Angle for

Reaction (R)

from vertical

yo=(θ-φ1)o

Angle αo=(90-

y)o

Active

Thrust (Pa)

(KN/m)

Active

Thrust (Pa)

(KN/m)

Pa2

δ2

R3

φ1

(θ-φ2)

148.388 27.513

56

38 29

186.186 KN/m







y = -6E-09x6 + 3E-06x5 - 0.0004x4 + 0.0449x3 - 2.7143x2 + 93.695x - 1251.1 R² = 1

0.000

20.000

40.000

60.000

80.000

100.000

120.000

140.000

160.000

64 66 68 70 72 74 76

Val

ue

of

Act

ive

Th

rust

(P

a) (

KN

/m)


θ Vs. Fa Graph

θ Vs. Fa Graph


Pa2 Sinδ2


56

10 55 3.501 175.052 161.923 336.975 26.000 64.000 148.459 3500.000

11 56 3.373 168.627 155.980 324.607 27.000 63.000 148.388 4300.000

12 57 3.247 162.352 150.176 312.527 28.000 62.000 148.064 7850.000

13 58 3.124 156.217 144.501 300.718 29.000 61.000 147.496 7850.000

14 59 3.004 150.215 138.949 289.164 30.000 60.000 146.687 7850.000

15 60 2.887 144.338 133.512 277.850 31.000 59.000 145.644 7850.000

16 61 2.772 138.577 128.184 266.761 32.000 58.000 144.371 7850.000

17 62 2.659 132.927 122.958 255.885 33.000 57.000 142.871 7850.000

17 63 2.548 127.381 117.828 245.209 34.000 56.000 141.146 7850.000 Fa (90-x)o

17 64 2.439 121.933 112.788 234.721 35.000 55.000 139.198 7850.000

18 65 2.332 116.577 107.834 224.411 36.000 54.000 137.030 7850.000 xo

19 66 2.226 111.307 102.959 214.266 37.000 53.000 134.640 7850.000 αo

20 67 2.122 106.119 98.160 204.279 38.000 52.000 132.030 7850.000

21 68 2.020 101.007 93.431 194.438 39.000 51.000 129.197 7850.000

22 69 1.919 95.966 88.769 184.735 40.000 50.000 126.142 7850.000 R2

23 70 1.820 90.993 84.168 175.161 41.000 49.000 122.861 7850.000 V

24 71 1.722 86.082 79.626 165.708 42.000 48.000 119.353 7850.000

25 72 1.625 81.230 75.138 156.368 43.000 47.000 115.613 7850.000 yo

26 73 1.529 76.433 70.700 147.133 44.000 46.000 111.637 7850.000

27 74 1.434 71.686 66.310 137.996 45.000 45.000 107.421 7850.000

28 75 1.340 66.987 61.963 128.951 46.000 44.000 102.959 7850.000

29 76 1.247 62.332 57.657 119.989 47.000 43.000 98.245 7850.000

30 77 1.154 57.717 53.388 111.105 48.000 42.000 93.271 7850.000

31 78 1.063 53.139 49.154 102.293 49.000 41.000 88.030 7850.000

32 79 0.972 48.595 44.950 93.546 50.000 40.000 82.513 7850.000

33 80 0.882 44.082 40.776 84.857 51.000 39.000 76.710 7850.000

34 81 0.792 39.596 36.626 76.223 52.000 38.000 70.611 7850.000

35 82 0.703 35.135 32.500 67.635 53.000 37.000 64.203 7850.000


Trial

Wedge

No.

Base

Angle in

Layer-I

(θo)

Width of

Wedge

(b = H1*tan(90-

θ)) (m)

Surcharge

Load (qb)

(KN/m)

Weight of

Wedge ((W=

(1/2H12Cotθγ)

(KN/m)

Total

Vertical

Load, (V =

qb+W)

(KN/m)

Angle for

Reaction (R)

from vertical

yo=(θ-φ1)o

Angle αo=(90-

y)o

Active

Thrust (Pa)

(KN/m)

Active

Thrust (Pa)

(KN/m)

Pa2

δ2

R3

φ1

(θ-φ2)

148.459 27.513

55

38 29

184.789 KN/m







y = -6E-09x6 + 3E-06x5 - 0.0004x4 + 0.0449x3 - 2.7143x2 + 93.695x - 1251.1 R² = 1

0.000

20.000

40.000

60.000

80.000

100.000

120.000

140.000

160.000

64 66 68 70 72 74 76

Val

ue

of

Act

ive

Th

rust

(P

a) (

KN

/m)


θ Vs. Fa Graph

θ Vs. Fa Graph


Pa2 Sinδ2


55

10 54 3.633 181.636 168.013 349.649 25.000 65.000 148.270 3500.000

11 55 3.501 175.052 161.923 336.975 26.000 64.000 148.459 4300.000

12 56 3.373 168.627 155.980 324.607 27.000 63.000 148.388 7850.000

13 57 3.247 162.352 150.176 312.527 28.000 62.000 148.064 7850.000

14 58 3.124 156.217 144.501 300.718 29.000 61.000 147.496 7850.000

15 59 3.004 150.215 138.949 289.164 30.000 60.000 146.687 7850.000

16 60 2.887 144.338 133.512 277.850 31.000 59.000 145.644 7850.000

17 61 2.772 138.577 128.184 266.761 32.000 58.000 144.371 7850.000

17 62 2.659 132.927 122.958 255.885 33.000 57.000 142.871 7850.000 Fa (90-x)o

17 63 2.548 127.381 117.828 245.209 34.000 56.000 141.146 7850.000

18 64 2.439 121.933 112.788 234.721 35.000 55.000 139.198 7850.000 xo

19 65 2.332 116.577 107.834 224.411 36.000 54.000 137.030 7850.000 αo

20 66 2.226 111.307 102.959 214.266 37.000 53.000 134.640 7850.000

21 67 2.122 106.119 98.160 204.279 38.000 52.000 132.030 7850.000

22 68 2.020 101.007 93.431 194.438 39.000 51.000 129.197 7850.000 R2

23 69 1.919 95.966 88.769 184.735 40.000 50.000 126.142 7850.000 V

24 70 1.820 90.993 84.168 175.161 41.000 49.000 122.861 7850.000

25 71 1.722 86.082 79.626 165.708 42.000 48.000 119.353 7850.000 yo

26 72 1.625 81.230 75.138 156.368 43.000 47.000 115.613 7850.000

27 73 1.529 76.433 70.700 147.133 44.000 46.000 111.637 7850.000

28 74 1.434 71.686 66.310 137.996 45.000 45.000 107.421 7850.000

29 75 1.340 66.987 61.963 128.951 46.000 44.000 102.959 7850.000

30 76 1.247 62.332 57.657 119.989 47.000 43.000 98.245 7850.000

31 77 1.154 57.717 53.388 111.105 48.000 42.000 93.271 7850.000

32 78 1.063 53.139 49.154 102.293 49.000 41.000 88.030 7850.000

33 79 0.972 48.595 44.950 93.546 50.000 40.000 82.513 7850.000

34 80 0.882 44.082 40.776 84.857 51.000 39.000 76.710 7850.000

35 81 0.792 39.596 36.626 76.223 52.000 38.000 70.611 7850.000


Trial

Wedge

No.

Base

Angle in

Layer-I

(θo)

Width of

Wedge

(b = H1*tan(90-

θ)) (m)

Surcharge

Load (qb)

(KN/m)

Weight of

Wedge ((W=

(1/2H12Cotθγ)

(KN/m)

Total

Vertical

Load, (V =

qb+W)

(KN/m)

Angle for

Reaction (R)

from vertical

yo=(θ-φ1)o

Angle αo=(90-

y)o

Active

Thrust (Pa)

(KN/m)

Active

Thrust (Pa)

(KN/m)

Pa2

δ2

R3

φ1

(θ-φ2)

148.270 27.513

54

38 29

182.898 KN/m







y = -6E-09x6 + 3E-06x5 - 0.0004x4 + 0.0449x3 - 2.7143x2 + 93.695x - 1251.1 R² = 1

0.000

20.000

40.000

60.000

80.000

100.000

120.000

140.000

160.000

64 66 68 70 72 74 76

Val

ue

of

Act

ive

Th

rust

(P

a) (

KN

/m)


θ Vs. Fa Graph

θ Vs. Fa Graph


Pa2 Sinδ2


54

10 53 3.768 188.389 174.259 362.648 24.000 66.000 147.813 3500.000

11 54 3.633 181.636 168.013 349.649 25.000 65.000 148.270 4300.000

12 55 3.501 175.052 161.923 336.975 26.000 64.000 148.459 7850.000

13 56 3.373 168.627 155.980 324.607 27.000 63.000 148.388 7850.000

14 57 3.247 162.352 150.176 312.527 28.000 62.000 148.064 7850.000

15 58 3.124 156.217 144.501 300.718 29.000 61.000 147.496 7850.000

16 59 3.004 150.215 138.949 289.164 30.000 60.000 146.687 7850.000

17 60 2.887 144.338 133.512 277.850 31.000 59.000 145.644 7850.000

17 61 2.772 138.577 128.184 266.761 32.000 58.000 144.371 7850.000 Fa (90-x)o

17 62 2.659 132.927 122.958 255.885 33.000 57.000 142.871 7850.000

18 63 2.548 127.381 117.828 245.209 34.000 56.000 141.146 7850.000 xo

19 64 2.439 121.933 112.788 234.721 35.000 55.000 139.198 7850.000 αo

20 65 2.332 116.577 107.834 224.411 36.000 54.000 137.030 7850.000

21 66 2.226 111.307 102.959 214.266 37.000 53.000 134.640 7850.000

22 67 2.122 106.119 98.160 204.279 38.000 52.000 132.030 7850.000 R2

23 68 2.020 101.007 93.431 194.438 39.000 51.000 129.197 7850.000 V

24 69 1.919 95.966 88.769 184.735 40.000 50.000 126.142 7850.000

25 70 1.820 90.993 84.168 175.161 41.000 49.000 122.861 7850.000 yo

26 71 1.722 86.082 79.626 165.708 42.000 48.000 119.353 7850.000

27 72 1.625 81.230 75.138 156.368 43.000 47.000 115.613 7850.000

28 73 1.529 76.433 70.700 147.133 44.000 46.000 111.637 7850.000

29 74 1.434 71.686 66.310 137.996 45.000 45.000 107.421 7850.000

30 75 1.340 66.987 61.963 128.951 46.000 44.000 102.959 7850.000

31 76 1.247 62.332 57.657 119.989 47.000 43.000 98.245 7850.000

32 77 1.154 57.717 53.388 111.105 48.000 42.000 93.271 7850.000

33 78 1.063 53.139 49.154 102.293 49.000 41.000 88.030 7850.000

34 79 0.972 48.595 44.950 93.546 50.000 40.000 82.513 7850.000

35 80 0.882 44.082 40.776 84.857 51.000 39.000 76.710 7850.000


Trial

Wedge

No.

Base

Angle in

Layer-I

(θo)

Width of

Wedge

(b = H1*tan(90-

θ)) (m)

Surcharge

Load (qb)

(KN/m)

Weight of

Wedge ((W=

(1/2H12Cotθγ)

(KN/m)

Total

Vertical

Load, (V =

qb+W)

(KN/m)

Angle for

Reaction (R)

from vertical

yo=(θ-φ1)o

Angle αo=(90-

y)o

Active

Thrust (Pa)

(KN/m)

Active

Thrust (Pa)

(KN/m)

Pa2

δ2

R3

φ1

(θ-φ2)

147.813 27.513

53

38 29

180.489 KN/m







y = -6E-09x6 + 3E-06x5 - 0.0004x4 + 0.0449x3 - 2.7143x2 + 93.695x - 1251.1 R² = 1

0.000

20.000

40.000

60.000

80.000

100.000

120.000

140.000

160.000

64 66 68 70 72 74 76

Val

ue

of

Act

ive

Th

rust

(P

a) (

KN

/m)


θ Vs. Fa Graph

θ Vs. Fa Graph


Pa2 Sinδ2


53

10 52 3.906 195.321 180.672 375.994 23.000 67.000 147.078 3500.000

11 53 3.768 188.389 174.259 362.648 24.000 66.000 147.813 4300.000

12 54 3.633 181.636 168.013 349.649 25.000 65.000 148.270 7850.000

13 55 3.501 175.052 161.923 336.975 26.000 64.000 148.459 7850.000

14 56 3.373 168.627 155.980 324.607 27.000 63.000 148.388 7850.000

15 57 3.247 162.352 150.176 312.527 28.000 62.000 148.064 7850.000

16 58 3.124 156.217 144.501 300.718 29.000 61.000 147.496 7850.000

17 59 3.004 150.215 138.949 289.164 30.000 60.000 146.687 7850.000

17 60 2.887 144.338 133.512 277.850 31.000 59.000 145.644 7850.000 Fa (90-x)o

17 61 2.772 138.577 128.184 266.761 32.000 58.000 144.371 7850.000

18 62 2.659 132.927 122.958 255.885 33.000 57.000 142.871 7850.000 xo

19 63 2.548 127.381 117.828 245.209 34.000 56.000 141.146 7850.000 αo

20 64 2.439 121.933 112.788 234.721 35.000 55.000 139.198 7850.000

21 65 2.332 116.577 107.834 224.411 36.000 54.000 137.030 7850.000

22 66 2.226 111.307 102.959 214.266 37.000 53.000 134.640 7850.000 R2

23 67 2.122 106.119 98.160 204.279 38.000 52.000 132.030 7850.000 V

24 68 2.020 101.007 93.431 194.438 39.000 51.000 129.197 7850.000

25 69 1.919 95.966 88.769 184.735 40.000 50.000 126.142 7850.000 yo

26 70 1.820 90.993 84.168 175.161 41.000 49.000 122.861 7850.000

27 71 1.722 86.082 79.626 165.708 42.000 48.000 119.353 7850.000

28 72 1.625 81.230 75.138 156.368 43.000 47.000 115.613 7850.000

29 73 1.529 76.433 70.700 147.133 44.000 46.000 111.637 7850.000

30 74 1.434 71.686 66.310 137.996 45.000 45.000 107.421 7850.000

31 75 1.340 66.987 61.963 128.951 46.000 44.000 102.959 7850.000

32 76 1.247 62.332 57.657 119.989 47.000 43.000 98.245 7850.000

33 77 1.154 57.717 53.388 111.105 48.000 42.000 93.271 7850.000

34 78 1.063 53.139 49.154 102.293 49.000 41.000 88.030 7850.000

35 79 0.972 48.595 44.950 93.546 50.000 40.000 82.513 7850.000


Trial

Wedge

No.

Base

Angle in

Layer-I

(θo)

Width of

Wedge

(b = H1*tan(90-

θ)) (m)

Surcharge

Load (qb)

(KN/m)

Weight of

Wedge ((W=

(1/2H12Cotθγ)

(KN/m)

Total

Vertical

Load, (V =

qb+W)

(KN/m)

Angle for

Reaction (R)

from vertical

yo=(θ-φ1)o

Angle αo=(90-

y)o

Active

Thrust (Pa)

(KN/m)

Active

Thrust (Pa)

(KN/m)

Pa2

δ2

R3

φ1

(θ-φ2)

147.078 27.513

52

38 29

177.535 KN/m







y = -6E-09x6 + 3E-06x5 - 0.0004x4 + 0.0449x3 - 2.7143x2 + 93.695x - 1251.1 R² = 1

0.000

20.000

40.000

60.000

80.000

100.000

120.000

140.000

160.000

64 66 68 70 72 74 76

Val

ue

of

Act

ive

Th

rust

(P

a) (

KN

/m)


θ Vs. Fa Graph

θ Vs. Fa Graph


Pa2 Sinδ2


52

10 51 4.049 202.446 187.263 389.709 22.000 68.000 146.053 3500.000

11 52 3.906 195.321 180.672 375.994 23.000 67.000 147.078 4300.000

12 53 3.768 188.389 174.259 362.648 24.000 66.000 147.813 7850.000

13 54 3.633 181.636 168.013 349.649 25.000 65.000 148.270 7850.000

14 55 3.501 175.052 161.923 336.975 26.000 64.000 148.459 7850.000

15 56 3.373 168.627 155.980 324.607 27.000 63.000 148.388 7850.000

16 57 3.247 162.352 150.176 312.527 28.000 62.000 148.064 7850.000

17 58 3.124 156.217 144.501 300.718 29.000 61.000 147.496 7850.000

17 59 3.004 150.215 138.949 289.164 30.000 60.000 146.687 7850.000 Fa (90-x)o

17 60 2.887 144.338 133.512 277.850 31.000 59.000 145.644 7850.000

18 61 2.772 138.577 128.184 266.761 32.000 58.000 144.371 7850.000 xo

19 62 2.659 132.927 122.958 255.885 33.000 57.000 142.871 7850.000 αo

20 63 2.548 127.381 117.828 245.209 34.000 56.000 141.146 7850.000

21 64 2.439 121.933 112.788 234.721 35.000 55.000 139.198 7850.000

22 65 2.332 116.577 107.834 224.411 36.000 54.000 137.030 7850.000 R2

23 66 2.226 111.307 102.959 214.266 37.000 53.000 134.640 7850.000 V

24 67 2.122 106.119 98.160 204.279 38.000 52.000 132.030 7850.000

25 68 2.020 101.007 93.431 194.438 39.000 51.000 129.197 7850.000 yo

26 69 1.919 95.966 88.769 184.735 40.000 50.000 126.142 7850.000

27 70 1.820 90.993 84.168 175.161 41.000 49.000 122.861 7850.000

28 71 1.722 86.082 79.626 165.708 42.000 48.000 119.353 7850.000

29 72 1.625 81.230 75.138 156.368 43.000 47.000 115.613 7850.000

30 73 1.529 76.433 70.700 147.133 44.000 46.000 111.637 7850.000

31 74 1.434 71.686 66.310 137.996 45.000 45.000 107.421 7850.000

32 75 1.340 66.987 61.963 128.951 46.000 44.000 102.959 7850.000

33 76 1.247 62.332 57.657 119.989 47.000 43.000 98.245 7850.000

34 77 1.154 57.717 53.388 111.105 48.000 42.000 93.271 7850.000

35 78 1.063 53.139 49.154 102.293 49.000 41.000 88.030 7850.000


Trial

Wedge

No.

Base

Angle in

Layer-I

(θo)

Width of

Wedge

(b = H1*tan(90-

θ)) (m)

Surcharge

Load (qb)

(KN/m)

Weight of

Wedge ((W=

(1/2H12Cotθγ)

(KN/m)

Total

Vertical

Load, (V =

qb+W)

(KN/m)

Angle for

Reaction (R)

from vertical

yo=(θ-φ1)o

Angle αo=(90-

y)o

Active

Thrust (Pa)

(KN/m)

Active

Thrust (Pa)

(KN/m)

Pa2

δ2

R3

φ1

(θ-φ2)

146.053 27.513

51

38 29

174.005 KN/m







y = -6E-09x6 + 3E-06x5 - 0.0004x4 + 0.0449x3 - 2.7143x2 + 93.695x - 1251.1 R² = 1

0.000

20.000

40.000

60.000

80.000

100.000

120.000

140.000

160.000

64 66 68 70 72 74 76

Val

ue

of

Act

ive

Th

rust

(P

a) (

KN

/m)


θ Vs. Fa Graph

θ Vs. Fa Graph


Pa2 Sinδ2


51

10 50 4.195 209.775 194.042 403.817 21.000 69.000 144.726 3500.000

11 51 4.049 202.446 187.263 389.709 22.000 68.000 146.053 4300.000

12 52 3.906 195.321 180.672 375.994 23.000 67.000 147.078 7850.000

13 53 3.768 188.389 174.259 362.648 24.000 66.000 147.813 7850.000

14 54 3.633 181.636 168.013 349.649 25.000 65.000 148.270 7850.000

15 55 3.501 175.052 161.923 336.975 26.000 64.000 148.459 7850.000

16 56 3.373 168.627 155.980 324.607 27.000 63.000 148.388 7850.000

17 57 3.247 162.352 150.176 312.527 28.000 62.000 148.064 7850.000

17 58 3.124 156.217 144.501 300.718 29.000 61.000 147.496 7850.000 Fa (90-x)o

17 59 3.004 150.215 138.949 289.164 30.000 60.000 146.687 7850.000

18 60 2.887 144.338 133.512 277.850 31.000 59.000 145.644 7850.000 xo

19 61 2.772 138.577 128.184 266.761 32.000 58.000 144.371 7850.000 αo

20 62 2.659 132.927 122.958 255.885 33.000 57.000 142.871 7850.000

21 63 2.548 127.381 117.828 245.209 34.000 56.000 141.146 7850.000

22 64 2.439 121.933 112.788 234.721 35.000 55.000 139.198 7850.000 R2

23 65 2.332 116.577 107.834 224.411 36.000 54.000 137.030 7850.000 V

24 66 2.226 111.307 102.959 214.266 37.000 53.000 134.640 7850.000

25 67 2.122 106.119 98.160 204.279 38.000 52.000 132.030 7850.000 yo

26 68 2.020 101.007 93.431 194.438 39.000 51.000 129.197 7850.000

27 69 1.919 95.966 88.769 184.735 40.000 50.000 126.142 7850.000

28 70 1.820 90.993 84.168 175.161 41.000 49.000 122.861 7850.000

29 71 1.722 86.082 79.626 165.708 42.000 48.000 119.353 7850.000

30 72 1.625 81.230 75.138 156.368 43.000 47.000 115.613 7850.000

31 73 1.529 76.433 70.700 147.133 44.000 46.000 111.637 7850.000

32 74 1.434 71.686 66.310 137.996 45.000 45.000 107.421 7850.000

33 75 1.340 66.987 61.963 128.951 46.000 44.000 102.959 7850.000

34 76 1.247 62.332 57.657 119.989 47.000 43.000 98.245 7850.000

35 77 1.154 57.717 53.388 111.105 48.000 42.000 93.271 7850.000


Trial

Wedge

No.

Base

Angle in

Layer-I

(θo)

Width of

Wedge

(b = H1*tan(90-

θ)) (m)

Surcharge

Load (qb)

(KN/m)

Weight of

Wedge ((W=

(1/2H12Cotθγ)

(KN/m)

Total

Vertical

Load, (V =

qb+W)

(KN/m)

Angle for

Reaction (R)

from vertical

yo=(θ-φ1)o

Angle αo=(90-

y)o

Active

Thrust (Pa)

(KN/m)

Active

Thrust (Pa)

(KN/m)

Pa2

δ2

R3

φ1

(θ-φ2)

144.726 27.513

50

38 29

169.866 KN/m







y = -6E-09x6 + 3E-06x5 - 0.0004x4 + 0.0449x3 - 2.7143x2 + 93.695x - 1251.1 R² = 1

0.000

20.000

40.000

60.000

80.000

100.000

120.000

140.000

160.000

64 66 68 70 72 74 76

Val

ue

of

Act

ive

Th

rust

(P

a) (

KN

/m)


θ Vs. Fa Graph

θ Vs. Fa Graph


Pa2 Sinδ2


50

10 49 4.346 217.322 201.023 418.344 20.000 70.000 143.084 3500.000

11 50 4.195 209.775 194.042 403.817 21.000 69.000 144.726 4300.000

12 51 4.049 202.446 187.263 389.709 22.000 68.000 146.053 7850.000

13 52 3.906 195.321 180.672 375.994 23.000 67.000 147.078 7850.000

14 53 3.768 188.389 174.259 362.648 24.000 66.000 147.813 7850.000

15 54 3.633 181.636 168.013 349.649 25.000 65.000 148.270 7850.000

16 55 3.501 175.052 161.923 336.975 26.000 64.000 148.459 7850.000

17 56 3.373 168.627 155.980 324.607 27.000 63.000 148.388 7850.000

17 57 3.247 162.352 150.176 312.527 28.000 62.000 148.064 7850.000 Fa (90-x)o

17 58 3.124 156.217 144.501 300.718 29.000 61.000 147.496 7850.000

18 59 3.004 150.215 138.949 289.164 30.000 60.000 146.687 7850.000 xo

19 60 2.887 144.338 133.512 277.850 31.000 59.000 145.644 7850.000 αo

20 61 2.772 138.577 128.184 266.761 32.000 58.000 144.371 7850.000

21 62 2.659 132.927 122.958 255.885 33.000 57.000 142.871 7850.000

22 63 2.548 127.381 117.828 245.209 34.000 56.000 141.146 7850.000 R2

23 64 2.439 121.933 112.788 234.721 35.000 55.000 139.198 7850.000 V

24 65 2.332 116.577 107.834 224.411 36.000 54.000 137.030 7850.000

25 66 2.226 111.307 102.959 214.266 37.000 53.000 134.640 7850.000 yo

26 67 2.122 106.119 98.160 204.279 38.000 52.000 132.030 7850.000

27 68 2.020 101.007 93.431 194.438 39.000 51.000 129.197 7850.000

28 69 1.919 95.966 88.769 184.735 40.000 50.000 126.142 7850.000

29 70 1.820 90.993 84.168 175.161 41.000 49.000 122.861 7850.000

30 71 1.722 86.082 79.626 165.708 42.000 48.000 119.353 7850.000

31 72 1.625 81.230 75.138 156.368 43.000 47.000 115.613 7850.000

32 73 1.529 76.433 70.700 147.133 44.000 46.000 111.637 7850.000

33 74 1.434 71.686 66.310 137.996 45.000 45.000 107.421 7850.000

34 75 1.340 66.987 61.963 128.951 46.000 44.000 102.959 7850.000

35 76 1.247 62.332 57.657 119.989 47.000 43.000 98.245 7850.000


Trial

Wedge

No.

Base

Angle in

Layer-I

(θo)

Width of

Wedge

(b = H1*tan(90-

θ)) (m)

Surcharge

Load (qb)

(KN/m)

Weight of

Wedge ((W=

(1/2H12Cotθγ)

(KN/m)

Total

Vertical

Load, (V =

qb+W)

(KN/m)

Angle for

Reaction (R)

from vertical

yo=(θ-φ1)o

Angle αo=(90-

y)o

Active

Thrust (Pa)

(KN/m)

Active

Thrust (Pa)

(KN/m)

Pa2

δ2

R3

φ1

(θ-φ2)

143.084 27.513

49

38 29

165.080 KN/m







y = -6E-09x6 + 3E-06x5 - 0.0004x4 + 0.0449x3 - 2.7143x2 + 93.695x - 1251.1 R² = 1

0.000

20.000

40.000

60.000

80.000

100.000

120.000

140.000

160.000

64 66 68 70 72 74 76

Val

ue

of

Act

ive

Th

rust

(P

a) (

KN

/m)


θ Vs. Fa Graph

θ Vs. Fa Graph


Pa2 Sinδ2


49

10 48 4.502 225.101 208.218 433.319 19.000 71.000 141.110 3500.000

11 49 4.346 217.322 201.023 418.344 20.000 70.000 143.084 4300.000

12 50 4.195 209.775 194.042 403.817 21.000 69.000 144.726 7850.000

13 51 4.049 202.446 187.263 389.709 22.000 68.000 146.053 7850.000

14 52 3.906 195.321 180.672 375.994 23.000 67.000 147.078 7850.000

15 53 3.768 188.389 174.259 362.648 24.000 66.000 147.813 7850.000

16 54 3.633 181.636 168.013 349.649 25.000 65.000 148.270 7850.000

17 55 3.501 175.052 161.923 336.975 26.000 64.000 148.459 7850.000

17 56 3.373 168.627 155.980 324.607 27.000 63.000 148.388 7850.000 Fa (90-x)o

17 57 3.247 162.352 150.176 312.527 28.000 62.000 148.064 7850.000

18 58 3.124 156.217 144.501 300.718 29.000 61.000 147.496 7850.000 xo

19 59 3.004 150.215 138.949 289.164 30.000 60.000 146.687 7850.000 αo

20 60 2.887 144.338 133.512 277.850 31.000 59.000 145.644 7850.000

21 61 2.772 138.577 128.184 266.761 32.000 58.000 144.371 7850.000

22 62 2.659 132.927 122.958 255.885 33.000 57.000 142.871 7850.000 R2

23 63 2.548 127.381 117.828 245.209 34.000 56.000 141.146 7850.000 V

24 64 2.439 121.933 112.788 234.721 35.000 55.000 139.198 7850.000

25 65 2.332 116.577 107.834 224.411 36.000 54.000 137.030 7850.000 yo

26 66 2.226 111.307 102.959 214.266 37.000 53.000 134.640 7850.000

27 67 2.122 106.119 98.160 204.279 38.000 52.000 132.030 7850.000

28 68 2.020 101.007 93.431 194.438 39.000 51.000 129.197 7850.000

29 69 1.919 95.966 88.769 184.735 40.000 50.000 126.142 7850.000

30 70 1.820 90.993 84.168 175.161 41.000 49.000 122.861 7850.000

31 71 1.722 86.082 79.626 165.708 42.000 48.000 119.353 7850.000

32 72 1.625 81.230 75.138 156.368 43.000 47.000 115.613 7850.000

33 73 1.529 76.433 70.700 147.133 44.000 46.000 111.637 7850.000

34 74 1.434 71.686 66.310 137.996 45.000 45.000 107.421 7850.000

35 75 1.340 66.987 61.963 128.951 46.000 44.000 102.959 7850.000


Trial

Wedge

No.

Base

Angle in

Layer-I

(θo)

Width of

Wedge

(b = H1*tan(90-

θ)) (m)

Surcharge

Load (qb)

(KN/m)

Weight of

Wedge ((W=

(1/2H12Cotθγ)

(KN/m)

Total

Vertical

Load, (V =

qb+W)

(KN/m)

Angle for

Reaction (R)

from vertical

yo=(θ-φ1)o

Angle αo=(90-

y)o

Active

Thrust (Pa)

(KN/m)

Active

Thrust (Pa)

(KN/m)

Pa2

δ2

R3

φ1

(θ-φ2)

141.110 27.513

48

38 29

159.607 KN/m







y = -6E-09x6 + 3E-06x5 - 0.0004x4 + 0.0449x3 - 2.7143x2 + 93.695x - 1251.1 R² = 1

0.000

20.000

40.000

60.000

80.000

100.000

120.000

140.000

160.000

64 66 68 70 72 74 76

Val

ue

of

Act

ive

Th

rust

(P

a) (

KN

/m)


θ Vs. Fa Graph

θ Vs. Fa Graph


Pa2 Sinδ2


90

0


θ Vs. Pa Graph

Vs. Pa Graph

Vs. Pa Graph)

90

0

0

Analysis in Layer -I for Trial Angle θ2 in Layer-II, the wedge line in Layer-II extended in Layer-I, form fictitious wall in layer-I from intersection of two layers and

refracted in layer-I towards vertical so that the angles in layer-I, i.e. θ21, θ22,θ23 etc are greater than θ2

V

Famax

224.411

Calculation of Pa2 in Layer-II

FamaxSinφ1

δ2

V

Famax

336.975


FamaxSinφ1

δ2

V

Famax

418.344


FamaxSinφ1

δ2

V

Famax

433.319


FamaxSinφ1

δ2

V

Famax

300.718


FamaxSinφ1

δ2

V

Famax

312.527


FamaxSinφ1

δ2

V

Famax

324.607


FamaxSinφ1

δ2

V

Famax

336.975


FamaxSinφ1

δ2

V

Famax

349.649


FamaxSinφ1

δ2

V

Famax

362.648


FamaxSinφ1

δ2

V

Famax

375.994


FamaxSinφ1

δ2

V

Famax

389.709


FamaxSinφ1

δ2

V

Famax

403.817


FamaxSinφ1

δ2

V

Famax

418.344


FamaxSinφ1

δ2

V

Famax

433.319


FamaxSinφ1

δ2

37 Unit Weight (γ) (KN/m3) = 19.5 8 90

26.674 63.326 12

1 45 5.657 14.368 40.638 0.000 792.438 792.438 7.924379

2 50 5.142 12.710 32.680 0.000 637.257 637.257 6.372568

3 55 4.589 11.474 26.325 0.000 513.330 513.330 5.133304

4 60 4.000 10.530 21.060 0.000 410.663 410.663 4.10663

5 63.5 3.570 9.999 17.846 0.000 347.994 347.994 3.479942

6 70 2.736 9.227 12.624 0.000 246.162 246.162 2.461615

7 75 2.071 8.782 9.092 0.000 177.298 177.298 1.772982

8 80 1.389 8.440 5.862 0.000 114.312 114.312 1.143124

1 15 7.727 149.518 577.694 0.000 11265.036 11265.036 11.26504

2 16 7.690 112.179 431.332 0.000 8410.970 8410.970 8.41097

3 18 7.608 74.862 284.791 0.000 5553.423 5553.423 5.553423

4 20 7.518 56.226 211.342 0.000 4121.160 4121.160 4.12116

5 22 7.417 45.063 167.128 0.000 3259.002 3259.002 3.259002

6 26.5 7.159 31.253 111.878 0.000 2181.627 2181.627 2.181627

7 30 6.928 25.323 87.721 0.000 1710.556 1710.556 1.710556

8 35 6.553 20.027 65.621 0.000 1279.604 1279.604 1.279604

9 40 6.128 16.668 51.074 0.000 995.941 995.941 0.995941

10 45 5.657 14.368 40.638 0.000 792.438 792.438 0.792438

Total

Vertical

Load, (V =

qb+W)

(KN/m)

Calculation of Passive Thrust (Pp)

Trial

Wedge No.

Base Angle

(θo)

z=Perpendic

ular Drawn

from A

=hCosθ

Failure Line

(m+n)

Area of

Wedge

Surcharge

Load (qb)

(KN/m)

Weight of

Wedge

((W=

0.5γxAxz)

(KN/m)

Total

Vertical

Load, (V =

qb+W)

(KN/m)

Force

Scale,

(1cm=100

KN/m)

Failure Line

(m+n)

Calculation of Active Thrust (Pa)

Force

Scale,

(1cm=100

KN/m)

Area of

Wedge

CALCULATION OF ACTIVE AND PASSIVE THRUST BY CULMANN METHOD

Angle of Internal Friction (φo)= Height of Wall (H) (m) = Wall angle with horizontal (αo) =

Angle of Wall Friction (δo=tan-1(2/3tanφo))= Slope angle with horizontal (βo) =Angle (αo-δo)

Trial

Wedge No.

Base Angle

(θo)

z=Perpendic

ular Drawn

from A

=hCosθ

Surcharge

Load (qb)

(KN/m)

Weight of

Wedge

((W=

0.5γxAxz)

(KN/m)

11 50 5.142 12.710 32.680 0.000 637.257 637.257 0.637257

12 55 4.589 11.474 26.325 0.000 513.330 513.330 0.51333

13 60 4.000 10.530 21.060 0.000 410.663 410.663 0.410663

14 65 3.381 9.798 16.564 0.000 322.990 322.990 0.32299

15 70 2.736 9.227 12.624 0.000 246.162 246.162 0.246162

16 75 2.071 8.782 9.092 0.000 177.298 177.298 0.177298

17 80 1.389 8.440 5.862 0.000 114.312 114.312 0.114312

34 Unit Weight (γ) (KN/m3) = 18.5

24.212

0

1 35 11.425 228.504 845.464 1073.967 89.000 0.000 1.000

2 38 10.240 204.791 757.725 962.516 86.000 0.000 4.000

3 41 9.203 184.059 681.018 865.077 83.000 0.000 7.000

4 44 8.284 165.685 613.034 778.719 80.000 0.000 10.000

5 47 7.460 149.202 552.049 701.251 77.000 0.000 13.000

6 50 6.713 134.256 496.747 631.003 74.000 0.000 16.000

7 53 6.028 120.569 446.104 566.673 71.000 0.000 19.000

8 56 5.396 107.921 399.309 507.230 68.000 0.000 22.000

9 59 4.807 96.138 355.709 451.847 65.000 0.000 25.000

10 62 4.254 85.074 314.772 399.845 62.000 0.000 28.000

11 65 3.730 74.609 276.054 350.663 59.000 0.000 31.000

12 68 3.232 64.644 239.184 303.828 56.000 0.000 34.000

13 71 2.755 55.092 203.842 258.934 53.000 0.000 37.000

14 74 2.294 45.879 169.753 215.633 50.000 0.000 40.000

15 77 1.847 36.939 136.674 173.613 47.000 0.000 43.000

16 80 1.411 28.212 104.386 132.598 44.000 0.000 46.000

17 83 0.982 19.646 72.688 92.334 41.000 0.000 49.000

17 86 0.559 11.188 41.397 52.585 38.000 0.000 52.000

17 89 0.140 2.793 10.333 13.126 35.000 0.000 55.000


Angle of Internal Friction (φo)= Height of Wall (H) (m) =

Angle of Wall Friction (δo=tan-1(2/3tanφo))= Angle for Active Thrust from horizontal xo=(90-α+δ)o =

θ Vs. Pa Graph

Wall Adhesion force (Fw= 0.75Cu(H-Z0)) (KN/m) = Depth of Tension Crack (Z0) (m) =

Trial

Wedge

No.

Base

Angle

(θo)

Width of

Wedge

(b = h*tan(90-

θ)) (m)

Surcharge

Load (qb)

(KN/m)

Weight of

Wedge ((W=

(1/2(H2-

Z02)Cotθγ)

(KN/m)

Total

Vertical

Load, (V =

qb+W)

(KN/m)

Angle for

Reaction (R)

from

horizontal

yo=(90-θ+φ)o

Force due to

cohesion

(FC)=Cu(H-

Z0)/Sinθ

(KN/m)

Angle zo=(θ-

φ)o

200.000

250.000

Val

ue

of

Act

ive

Th

rust

(P

a) (

KN

/m)

θ Vs. Pa Graph

Maximum of Minimum thrust obtained at θ = 59oThe Maximum Thrust = 190.977 (KN/m)

y = -2E-08x6 + 8E-06x5 - 0.0015x4 + 0.1442x3 - 8.1581x2 + 259.87x - 3427.1 R² = 1

0.000

50.000

100.000

150.000

0 10 20 30 40 50 60 70

Val

ue

of

Act

ive

Th

rust

(P

a) (

KN

/m)


8 90

24.212 0

0 20

0.000

20.394

71.548

110.369 Pa

139.492

160.817 δo

175.730 yo

185.257 zo

190.154 zoR

190.977 yoPw

188.127 (V-FW) θo

181.880 Fc

172.408 90-θo

159.794

144.040

125.068

102.721

76.757

46.839

12.516


Wall angle with horizontal (αo) =

Angle for Active Thrust from horizontal xo=(90-α+δ)o = Cohesion (Cu) (KN/m2)=

θ Vs. Pa Graph


Active

Thrust (Pa)

(KN/m)

WaterThrust (Pw=0.5γwZ02)(KN/m2) =

70 80 90 100

θ Vs. Pa Graph



24.212

0 0

1 6 76.115 1522.298 5632.504 7154.802 40.000 0.000 50.000 10571.5

2 7 65.155 1303.095 4821.453 6124.549 41.000 0.000 49.000 9583.7

3 8 56.923 1138.459 4212.299 5350.758 42.000 0.000 48.000 8876.5

4 9 50.510 1010.200 3737.741 4747.941 43.000 0.000 47.000 8360.2

5 10 45.370 907.405 3357.399 4264.804 44.000 0.000 46.000 7981.7

6 11 41.156 823.129 3045.576 3868.705 45.000 0.000 45.000 7707.9

7 12 37.637 752.741 2785.141 3537.882 46.000 0.000 44.000 7517.4

8 13 34.652 693.036 2564.234 3257.270 47.000 0.000 43.000 7396.7

9 14 32.086 641.725 2374.382 3016.107 48.000 0.000 42.000 7337.0

10 15 29.856 597.128 2209.374 2806.502 49.000 0.000 41.000 7333.4

11 16 27.899 557.986 2064.549 2622.536 50.000 0.000 40.000 7383.9

12 17 26.167 523.336 1936.345 2459.681 51.000 0.000 39.000 7489.1

13 18 24.621 492.429 1821.989 2314.418 52.000 0.000 38.000 7652.4

14 19 23.234 464.674 1719.293 2183.967 53.000 0.000 37.000 7880.1

15 22 19.801 396.014 1465.251 1861.265 56.000 0.000 34.000 9076.8

16 25 17.156 343.121 1269.548 1612.669 59.000 0.000 31.000 11695.4

17 26 16.402 328.049 1213.780 1541.828 60.000 0.000 30.000 13240.7

18 27 15.701 314.018 1161.865 1475.883 61.000 0.000 29.000 15465.3

19 28 15.046 300.916 1113.390 1414.306 62.000 0.000 28.000 18902.6

20 29 14.432 288.648 1067.996 1356.644 63.000 0.000 27.000 24852.4


Angle of Internal Friction (φo)= Height of Wall (H) (m) =

Angle of Wall Friction (δo=tan-1(2/3tanφo))= Angle for Active Thrust from horizontal xo=(90-α-δ)o =

Force due to

cohesion

(FC)=Cu(H-

Z0)/Sinθ

(KN/m)

Angle

zo=(90-y)o

Active

Thrust (Pa)

(KN/m)

θ Vs. Pp Graph

Wall Adhesion force (Fw= 0.75Cu(H-Z0)) (KN/m) = Depth of Tension Crack (Z0) (m) =

Trial

Wedge

No.

Base

Angle

(θo)

Width of

Wedge

(b = h*tan(90-

θ)) (m)

Surcharge

Load (qb)

(KN/m)

Weight of

Wedge ((W=

(1/2(H2-

Z02)Cotθγ)

(KN/m)

Total

Vertical

Load, (V =

qb+W)

(KN/m)

Angle for

Reaction (R)

from

horizontal

yo=(θ+φ)o

25000.0

30000.0

Val

ue

of

Pas

sive

Th

rust

(P

p)

(KN

/m)

θ Vs. Pp Graph

y = 0.0036x6 - 0.3454x5 + 13.338x4 - 266.96x3 + 2948x2 - 17419x + 51909 R² = 0.9995

0.0

5000.0

10000.0

15000.0

20000.0

0 5 10 15 20 25

Val

ue

of

Pas

sive

Th

rust

(P

p)

(KN

/m)


90

24.212 0

20

A

Pp

zo x0D

zo

R

(V+Fw)

C

yo θ0


Wall angle with horizontal (αo) =


θ Vs. Pp Graph


PpSinx/Tanz

Fc Cosθ

(PpCosx - FcCosθ - PpSinx/Tanz)

PpSinx

(V+Fw)+FcSinθ

30 35

θ Vs. Pp Graph

Poly. (θ Vs. Pp Graph)

r=ro.eθTanφ ro = 5 θ = 150 φ = 34

x

y 45-φ/2

yo

45-φ/2

H = 8 xo

α θ

θ1

ro β

r

r.Cosβ

A

r.Sinβ

1 5 27 0.454 0.891 2.408 4.725

2 10 22 0.375 0.927 2.107 5.215

3 15 17 0.292 0.956 1.744 5.705

4 20 12 0.208 0.978 1.316 6.189

5 25 7 0.122 0.993 0.818 6.661

6 30 2 0.035 0.999 0.248 7.114

7 35 -3 -0.052 0.999 -0.395 7.539

8 40 -8 -0.139 0.990 -1.114 7.929

9 45 -13 -0.225 0.974 -1.910 8.275

10 50 -18 -0.309 0.951 -2.783 8.567

11 55 -23 -0.391 0.921 -3.733 8.794

12 60 -28 -0.469 0.883 -4.757 8.947

13 65 -33 -0.545 0.839 -5.853 9.013

14 70 -38 -0.616 0.788 -7.018 8.982

15 75 -43 -0.682 0.731 -8.245 8.842

16 80 -48 -0.743 0.669 -9.529 8.580

17 85 -53 -0.799 0.602 -10.862 8.185

18 90 -58 -0.848 0.530 -12.233 7.644

19 95 -63 -0.891 0.454 -13.632 6.946

20 100 -68 -0.927 0.375 -15.045 6.079

21 105 -73 -0.956 0.292 -16.459 5.032

22 110 -78 -0.978 0.208 -17.855 3.795

23 115 -83 -0.993 0.122 -19.217 2.360

24 120 -88 -0.999 0.035 -20.522 0.717

25 125 -93 -0.999 -0.052 -21.750 -1.140

15.299

16.227

17.211

18.254

19.361

20.535

21.780

9.008

9.554

10.133

10.747

11.399

12.090

12.823

13.600

14.425

Sl No. θ1 β Sinβ Cosβ r.Sinβ r.Cosβr=ro.eθ1Tanφ

LOG-SPIRAL FORMATION

5.303

5.625

5.966

6.327

6.711

7.118

7.549

8.007

8.493

26 130 -98 -0.990 -0.139 -22.876 -3.215

27 135 -103 -0.974 -0.225 -23.873 -5.512

28 140 -108 -0.951 -0.309 -24.715 -8.030

29 145 -113 -0.921 -0.391 -25.371 -10.769

30 150 -118 -0.883 -0.469 -25.811 -13.724

31 155 -123 -0.839 -0.545 -26.003 -16.887

32 160 -128 -0.788 -0.616 -25.914 -20.246

33 165 -133 -0.731 -0.682 -25.509 -23.787

0.592423 7.725136

0.892962 8.215101

1.255803 8.705013

1.684464 9.189109

2.182135 9.660976

2.75159 10.11354

3.395107 10.53908

4.114379 10.92922

4.91042 11.27494

5.783471 11.56664

6.732895 11.79415

7.75708 11.94677

8.853335 12.01334

10.01778 11.98235

11.24527 11.84197

12.52924 11.58017

13.86168 11.18486

15.23298 10.64401

16.63189 9.945795

18.04542 9.078746

19.45881 8.031962

20.85541 6.795285

22.21673 5.359518

23.52238 3.716657

24.75004 1.860128

25.87557 -0.21495

26.87297 -2.51151

27.71453 -5.03024

28.37088 -7.7693

28.81118 -10.724

29.00326 -13.8867

28.91385 -17.2461

28.50884 -20.7874

34.879

23.100

24.501

25.986

27.562

29.233

31.005

32.885

-25

-20

-15

-10

-5

0

5

10

15

0 5 10 15

log plot

α = 58 xo(m)= 3 yo (m)= 3

x coor of pt.A,

x=xo+r.Sinβ

2.182

2.752

3.395

4.114

4.910

0.592

LOG-SPIRAL FORMATION

0.893

1.256

1.684

y coor of pt.A,

y=yo+r.Cosβ

22.217

23.522

11.245

12.529

13.862

15.233

16.632

5.783

6.733

7.757

8.853

10.018

7.725

8.215

8.705

9.189

9.661

10.114

10.539

10.929

11.275

11.567

11.794

11.947

24.750

18.045

19.459

20.855

10.644

9.946

9.079

8.032

6.795

12.013

11.982

11.842

11.580

11.185

5.360

3.717

1.860

28.811

29.003

28.914

28.509

25.876

26.873

27.715

28.371

-20.787

-5.030

-7.769

-10.724

-13.887

-17.246

-0.215

-2.512

15 20 25 30 35

log plot

log plot

As Sing Ment

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