as sing ment
TRANSCRIPT
![Page 1: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/1.jpg)
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)
![Page 2: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/2.jpg)
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)
![Page 3: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/3.jpg)
90
12
20
18.490
Pwθ
o
CALCULATION OF ACTIVE THRUST FROM COULOMB METHOD
![Page 4: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/4.jpg)
θ Vs. Pa Graph
Vs. Pa Graph
Vs. Pa Graph)
![Page 5: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/5.jpg)
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
![Page 6: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/6.jpg)
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)
Value of Angle θ (degree)
θ Vs. Pp Graph
θ Vs. Pp Graph
Poly. (θ Vs. Pp Graph)
(V+Fw)+FcSinθ
![Page 7: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/7.jpg)
Pp
D
(V+Fw)
C
θ0
Fc
CALCULATION OF PASSIVE THRUST FROM COULOMB METHOD
PpSinx/Tanz
![Page 8: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/8.jpg)
θ Vs. Pp Graph
![Page 9: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/9.jpg)
29 Unit Weight (γ) (KN/m3) = 18.5 5
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
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=
(1/2H2Cotθγ)
(KN/m)
Total
Vertical
Load, (V =
qb+W)
(KN/m)
Angle for
Reaction (R)
from vertical
yo=(θ-φ)o
CALCULATION OF ACTIVE THRUST FROM COULOMB METHOD
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)
![Page 10: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/10.jpg)
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)
Value of Angle θ (degree)
θ Vs. Pa Graph
θ Vs. Pa Graph
Poly. (θ Vs. Pa Graph)
![Page 11: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/11.jpg)
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
Surcharge (q) (KN/m2) =
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)
Assumed Base Angle for Second layer (θ2) =
Angle of Wall Friction (δ1o=tan-1(2/3tanφ1o))=
Angle for Active Thrust from horizontal xo=(90-α+δ)o =
Cohesion (Cu) (KN/m2)=
Surcharge (q) (KN/m2) =
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
![Page 12: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/12.jpg)
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)
Value of Angle θ (degree)
θ Vs. Fa Graph
θ Vs. Fa Graph
FamaxSinφ1 FamaxSin
Pa2 Sinδ2
Pa2Cosδ2-FamaxSinφ1
![Page 13: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/13.jpg)
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
Assumed Base Angle for Second layer (θ2) =
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)
![Page 14: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/14.jpg)
Pa2
δ2
R3
φ1
(θ-φ2)
148.459 27.513
55
38 29
184.789 KN/m
Base Angle (θ) for Famax = Vertical Force (KN/m) with Surcharge for base angle corresponding to Famax found =
Angle of Internal Friction (φ2o)= Angle of Internal Friction (φ1o)=
Tan (θ-φ2) = (Pa2Cosδ2-FamaxSinφ1)/(V-Pa2 Sinδ2 +FamaxSinφ1)
θ Vs. Fa Graph Calculation of Pa2 in Layer-II
Famax (KN/m) from θ Vs. Fa Graph found = Angle of Wall Friction (δ2o=tan-1(2/3tanφ2o))=
Pa2=Vtan(θ-φ2)+Famax(Sinφ1+Tan (θ-φ2))/(Cosδ2+Tan (θ-φ2)) =
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)
Value of Angle θ (degree)
θ Vs. Fa Graph
θ Vs. Fa Graph
FamaxSinφ1 FamaxSin
Pa2 Sinδ2
Pa2Cosδ2-FamaxSinφ1
![Page 15: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/15.jpg)
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
Assumed Base Angle for Second layer (θ2) =
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)
![Page 16: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/16.jpg)
Pa2
δ2
R3
φ1
(θ-φ2)
148.459 27.513
49
38 29
168.457 KN/m
Famax (KN/m) from θ Vs. Fa Graph found = Angle of Wall Friction (δ2o=tan-1(2/3tanφ2o))=
Base Angle (θ) for Famax = Vertical Force (KN/m) with Surcharge for base angle corresponding to Famax found =
Angle of Internal Friction (φ2o)= Angle of Internal Friction (φ1o)=
θ Vs. Fa Graph Calculation of Pa2 in Layer-II
Tan (θ-φ2) = (Pa2Cosδ2-FamaxSinφ1)/(V-Pa2 Sinδ2 +FamaxSinφ1)
Pa2=Vtan(θ-φ2)+Famax(Sinφ1+Tan (θ-φ2))/(Cosδ2+Tan (θ-φ2)) =
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)
Value of Angle θ (degree)
θ Vs. Fa Graph
θ Vs. Fa Graph
FamaxSinφ1 FamaxSin
Pa2 Sinδ2
Pa2Cosδ2-FamaxSinφ1
![Page 17: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/17.jpg)
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
Assumed Base Angle for Second layer (θ2) =
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)
![Page 18: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/18.jpg)
Pa2
δ2
R3
φ1
(θ-φ2)
141.110 27.513
48
38 29
159.607 KN/m
Famax (KN/m) from θ Vs. Fa Graph found = Angle of Wall Friction (δ2o=tan-1(2/3tanφ2o))=
Base Angle (θ) for Famax = Vertical Force (KN/m) with Surcharge for base angle corresponding to Famax found =
Angle of Internal Friction (φ2o)= Angle of Internal Friction (φ1o)=
θ Vs. Fa Graph Calculation of Pa2 in Layer-II
Tan (θ-φ2) = (Pa2Cosδ2-FamaxSinφ1)/(V-Pa2 Sinδ2 +FamaxSinφ1)
Pa2=Vtan(θ-φ2)+Famax(Sinφ1+Tan (θ-φ2))/(Cosδ2+Tan (θ-φ2)) =
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)
Value of Angle θ (degree)
θ Vs. Fa Graph
θ Vs. Fa Graph
FamaxSinφ1 FamaxSin
Pa2 Sinδ2
Pa2Cosδ2-FamaxSinφ1
![Page 19: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/19.jpg)
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
Assumed Base Angle for Second layer (θ2) =
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)
![Page 20: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/20.jpg)
Pa2
δ2
R3
φ1
(θ-φ2)
147.496 27.513
58
38 29
187.584 KN/m
Famax (KN/m) from θ Vs. Fa Graph found = Angle of Wall Friction (δ2o=tan-1(2/3tanφ2o))=
Base Angle (θ) for Famax = Vertical Force (KN/m) with Surcharge for base angle corresponding to Famax found =
Angle of Internal Friction (φ2o)= Angle of Internal Friction (φ1o)=
θ Vs. Fa Graph Calculation of Pa2 in Layer-II
Tan (θ-φ2) = (Pa2Cosδ2-FamaxSinφ1)/(V-Pa2 Sinδ2 +FamaxSinφ1)
Pa2=Vtan(θ-φ2)+Famax(Sinφ1+Tan (θ-φ2))/(Cosδ2+Tan (θ-φ2)) =
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)
Value of Angle θ (degree)
θ Vs. Fa Graph
θ Vs. Fa Graph
FamaxSinφ1 FamaxSin
Pa2 Sinδ2
Pa2Cosδ2-FamaxSinφ1
![Page 21: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/21.jpg)
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
Assumed Base Angle for Second layer (θ2) =
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)
![Page 22: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/22.jpg)
Pa2
δ2
R3
φ1
(θ-φ2)
148.064 27.513
57
38 29
187.111 KN/m
Famax (KN/m) from θ Vs. Fa Graph found = Angle of Wall Friction (δ2o=tan-1(2/3tanφ2o))=
Base Angle (θ) for Famax = Vertical Force (KN/m) with Surcharge for base angle corresponding to Famax found =
Angle of Internal Friction (φ2o)= Angle of Internal Friction (φ1o)=
θ Vs. Fa Graph Calculation of Pa2 in Layer-II
Tan (θ-φ2) = (Pa2Cosδ2-FamaxSinφ1)/(V-Pa2 Sinδ2 +FamaxSinφ1)
Pa2=Vtan(θ-φ2)+Famax(Sinφ1+Tan (θ-φ2))/(Cosδ2+Tan (θ-φ2)) =
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)
Value of Angle θ (degree)
θ Vs. Fa Graph
θ Vs. Fa Graph
FamaxSinφ1 FamaxSin
Pa2 Sinδ2
Pa2Cosδ2-FamaxSinφ1
![Page 23: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/23.jpg)
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
Assumed Base Angle for Second layer (θ2) =
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)
![Page 24: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/24.jpg)
Pa2
δ2
R3
φ1
(θ-φ2)
148.388 27.513
56
38 29
186.186 KN/m
Famax (KN/m) from θ Vs. Fa Graph found = Angle of Wall Friction (δ2o=tan-1(2/3tanφ2o))=
Base Angle (θ) for Famax = Vertical Force (KN/m) with Surcharge for base angle corresponding to Famax found =
Angle of Internal Friction (φ2o)= Angle of Internal Friction (φ1o)=
θ Vs. Fa Graph Calculation of Pa2 in Layer-II
Tan (θ-φ2) = (Pa2Cosδ2-FamaxSinφ1)/(V-Pa2 Sinδ2 +FamaxSinφ1)
Pa2=Vtan(θ-φ2)+Famax(Sinφ1+Tan (θ-φ2))/(Cosδ2+Tan (θ-φ2)) =
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)
Value of Angle θ (degree)
θ Vs. Fa Graph
θ Vs. Fa Graph
FamaxSinφ1 FamaxSin
Pa2 Sinδ2
Pa2Cosδ2-FamaxSinφ1
![Page 25: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/25.jpg)
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
Assumed Base Angle for Second layer (θ2) =
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)
![Page 26: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/26.jpg)
Pa2
δ2
R3
φ1
(θ-φ2)
148.459 27.513
55
38 29
184.789 KN/m
Famax (KN/m) from θ Vs. Fa Graph found = Angle of Wall Friction (δ2o=tan-1(2/3tanφ2o))=
Base Angle (θ) for Famax = Vertical Force (KN/m) with Surcharge for base angle corresponding to Famax found =
Angle of Internal Friction (φ2o)= Angle of Internal Friction (φ1o)=
θ Vs. Fa Graph Calculation of Pa2 in Layer-II
Tan (θ-φ2) = (Pa2Cosδ2-FamaxSinφ1)/(V-Pa2 Sinδ2 +FamaxSinφ1)
Pa2=Vtan(θ-φ2)+Famax(Sinφ1+Tan (θ-φ2))/(Cosδ2+Tan (θ-φ2)) =
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)
Value of Angle θ (degree)
θ Vs. Fa Graph
θ Vs. Fa Graph
FamaxSinφ1 FamaxSin
Pa2 Sinδ2
Pa2Cosδ2-FamaxSinφ1
![Page 27: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/27.jpg)
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
Assumed Base Angle for Second layer (θ2) =
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)
![Page 28: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/28.jpg)
Pa2
δ2
R3
φ1
(θ-φ2)
148.270 27.513
54
38 29
182.898 KN/m
Famax (KN/m) from θ Vs. Fa Graph found = Angle of Wall Friction (δ2o=tan-1(2/3tanφ2o))=
Base Angle (θ) for Famax = Vertical Force (KN/m) with Surcharge for base angle corresponding to Famax found =
Angle of Internal Friction (φ2o)= Angle of Internal Friction (φ1o)=
θ Vs. Fa Graph Calculation of Pa2 in Layer-II
Tan (θ-φ2) = (Pa2Cosδ2-FamaxSinφ1)/(V-Pa2 Sinδ2 +FamaxSinφ1)
Pa2=Vtan(θ-φ2)+Famax(Sinφ1+Tan (θ-φ2))/(Cosδ2+Tan (θ-φ2)) =
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)
Value of Angle θ (degree)
θ Vs. Fa Graph
θ Vs. Fa Graph
FamaxSinφ1 FamaxSin
Pa2 Sinδ2
Pa2Cosδ2-FamaxSinφ1
![Page 29: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/29.jpg)
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
Assumed Base Angle for Second layer (θ2) =
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)
![Page 30: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/30.jpg)
Pa2
δ2
R3
φ1
(θ-φ2)
147.813 27.513
53
38 29
180.489 KN/m
Famax (KN/m) from θ Vs. Fa Graph found = Angle of Wall Friction (δ2o=tan-1(2/3tanφ2o))=
Base Angle (θ) for Famax = Vertical Force (KN/m) with Surcharge for base angle corresponding to Famax found =
Angle of Internal Friction (φ2o)= Angle of Internal Friction (φ1o)=
θ Vs. Fa Graph Calculation of Pa2 in Layer-II
Tan (θ-φ2) = (Pa2Cosδ2-FamaxSinφ1)/(V-Pa2 Sinδ2 +FamaxSinφ1)
Pa2=Vtan(θ-φ2)+Famax(Sinφ1+Tan (θ-φ2))/(Cosδ2+Tan (θ-φ2)) =
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)
Value of Angle θ (degree)
θ Vs. Fa Graph
θ Vs. Fa Graph
FamaxSinφ1 FamaxSin
Pa2 Sinδ2
Pa2Cosδ2-FamaxSinφ1
![Page 31: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/31.jpg)
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
Assumed Base Angle for Second layer (θ2) =
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)
![Page 32: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/32.jpg)
Pa2
δ2
R3
φ1
(θ-φ2)
147.078 27.513
52
38 29
177.535 KN/m
Famax (KN/m) from θ Vs. Fa Graph found = Angle of Wall Friction (δ2o=tan-1(2/3tanφ2o))=
Base Angle (θ) for Famax = Vertical Force (KN/m) with Surcharge for base angle corresponding to Famax found =
Angle of Internal Friction (φ2o)= Angle of Internal Friction (φ1o)=
θ Vs. Fa Graph Calculation of Pa2 in Layer-II
Tan (θ-φ2) = (Pa2Cosδ2-FamaxSinφ1)/(V-Pa2 Sinδ2 +FamaxSinφ1)
Pa2=Vtan(θ-φ2)+Famax(Sinφ1+Tan (θ-φ2))/(Cosδ2+Tan (θ-φ2)) =
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)
Value of Angle θ (degree)
θ Vs. Fa Graph
θ Vs. Fa Graph
FamaxSinφ1 FamaxSin
Pa2 Sinδ2
Pa2Cosδ2-FamaxSinφ1
![Page 33: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/33.jpg)
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
Assumed Base Angle for Second layer (θ2) =
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)
![Page 34: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/34.jpg)
Pa2
δ2
R3
φ1
(θ-φ2)
146.053 27.513
51
38 29
174.005 KN/m
Famax (KN/m) from θ Vs. Fa Graph found = Angle of Wall Friction (δ2o=tan-1(2/3tanφ2o))=
Base Angle (θ) for Famax = Vertical Force (KN/m) with Surcharge for base angle corresponding to Famax found =
Angle of Internal Friction (φ2o)= Angle of Internal Friction (φ1o)=
θ Vs. Fa Graph Calculation of Pa2 in Layer-II
Tan (θ-φ2) = (Pa2Cosδ2-FamaxSinφ1)/(V-Pa2 Sinδ2 +FamaxSinφ1)
Pa2=Vtan(θ-φ2)+Famax(Sinφ1+Tan (θ-φ2))/(Cosδ2+Tan (θ-φ2)) =
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)
Value of Angle θ (degree)
θ Vs. Fa Graph
θ Vs. Fa Graph
FamaxSinφ1 FamaxSin
Pa2 Sinδ2
Pa2Cosδ2-FamaxSinφ1
![Page 35: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/35.jpg)
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
Assumed Base Angle for Second layer (θ2) =
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)
![Page 36: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/36.jpg)
Pa2
δ2
R3
φ1
(θ-φ2)
144.726 27.513
50
38 29
169.866 KN/m
Famax (KN/m) from θ Vs. Fa Graph found = Angle of Wall Friction (δ2o=tan-1(2/3tanφ2o))=
Base Angle (θ) for Famax = Vertical Force (KN/m) with Surcharge for base angle corresponding to Famax found =
Angle of Internal Friction (φ2o)= Angle of Internal Friction (φ1o)=
θ Vs. Fa Graph Calculation of Pa2 in Layer-II
Tan (θ-φ2) = (Pa2Cosδ2-FamaxSinφ1)/(V-Pa2 Sinδ2 +FamaxSinφ1)
Pa2=Vtan(θ-φ2)+Famax(Sinφ1+Tan (θ-φ2))/(Cosδ2+Tan (θ-φ2)) =
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)
Value of Angle θ (degree)
θ Vs. Fa Graph
θ Vs. Fa Graph
FamaxSinφ1 FamaxSin
Pa2 Sinδ2
Pa2Cosδ2-FamaxSinφ1
![Page 37: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/37.jpg)
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
Assumed Base Angle for Second layer (θ2) =
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)
![Page 38: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/38.jpg)
Pa2
δ2
R3
φ1
(θ-φ2)
143.084 27.513
49
38 29
165.080 KN/m
Famax (KN/m) from θ Vs. Fa Graph found = Angle of Wall Friction (δ2o=tan-1(2/3tanφ2o))=
Base Angle (θ) for Famax = Vertical Force (KN/m) with Surcharge for base angle corresponding to Famax found =
Angle of Internal Friction (φ2o)= Angle of Internal Friction (φ1o)=
θ Vs. Fa Graph Calculation of Pa2 in Layer-II
Tan (θ-φ2) = (Pa2Cosδ2-FamaxSinφ1)/(V-Pa2 Sinδ2 +FamaxSinφ1)
Pa2=Vtan(θ-φ2)+Famax(Sinφ1+Tan (θ-φ2))/(Cosδ2+Tan (θ-φ2)) =
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)
Value of Angle θ (degree)
θ Vs. Fa Graph
θ Vs. Fa Graph
FamaxSinφ1 FamaxSin
Pa2 Sinδ2
Pa2Cosδ2-FamaxSinφ1
![Page 39: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/39.jpg)
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
Assumed Base Angle for Second layer (θ2) =
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)
![Page 40: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/40.jpg)
Pa2
δ2
R3
φ1
(θ-φ2)
141.110 27.513
48
38 29
159.607 KN/m
Tan (θ-φ2) = (Pa2Cosδ2-FamaxSinφ1)/(V-Pa2 Sinδ2 +FamaxSinφ1)
Pa2=Vtan(θ-φ2)+Famax(Sinφ1+Tan (θ-φ2))/(Cosδ2+Tan (θ-φ2)) =
Famax (KN/m) from θ Vs. Fa Graph found = Angle of Wall Friction (δ2o=tan-1(2/3tanφ2o))=
Base Angle (θ) for Famax = Vertical Force (KN/m) with Surcharge for base angle corresponding to Famax found =
Angle of Internal Friction (φ2o)= Angle of Internal Friction (φ1o)=
θ Vs. Fa Graph Calculation of Pa2 in Layer-II
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)
Value of Angle θ (degree)
θ Vs. Fa Graph
θ Vs. Fa Graph
FamaxSinφ1 FamaxSin
Pa2 Sinδ2
Pa2Cosδ2-FamaxSinφ1
![Page 41: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/41.jpg)
90
0
CALCULATION OF ACTIVE THRUST FROM COULOMB METHOD
![Page 42: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/42.jpg)
θ Vs. Pa Graph
Vs. Pa Graph
Vs. Pa Graph)
![Page 43: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/43.jpg)
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
![Page 44: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/44.jpg)
V
Famax
224.411
Calculation of Pa2 in Layer-II
FamaxSinφ1
δ2
![Page 45: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/45.jpg)
![Page 46: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/46.jpg)
V
Famax
336.975
Calculation of Pa2 in Layer-II
FamaxSinφ1
δ2
![Page 47: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/47.jpg)
![Page 48: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/48.jpg)
V
Famax
418.344
Calculation of Pa2 in Layer-II
FamaxSinφ1
δ2
![Page 49: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/49.jpg)
![Page 50: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/50.jpg)
V
Famax
433.319
Calculation of Pa2 in Layer-II
FamaxSinφ1
δ2
![Page 51: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/51.jpg)
![Page 52: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/52.jpg)
V
Famax
300.718
Calculation of Pa2 in Layer-II
FamaxSinφ1
δ2
![Page 53: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/53.jpg)
![Page 54: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/54.jpg)
V
Famax
312.527
Calculation of Pa2 in Layer-II
FamaxSinφ1
δ2
![Page 55: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/55.jpg)
![Page 56: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/56.jpg)
V
Famax
324.607
Calculation of Pa2 in Layer-II
FamaxSinφ1
δ2
![Page 57: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/57.jpg)
![Page 58: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/58.jpg)
V
Famax
336.975
Calculation of Pa2 in Layer-II
FamaxSinφ1
δ2
![Page 59: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/59.jpg)
![Page 60: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/60.jpg)
V
Famax
349.649
Calculation of Pa2 in Layer-II
FamaxSinφ1
δ2
![Page 61: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/61.jpg)
![Page 62: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/62.jpg)
V
Famax
362.648
Calculation of Pa2 in Layer-II
FamaxSinφ1
δ2
![Page 63: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/63.jpg)
![Page 64: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/64.jpg)
V
Famax
375.994
Calculation of Pa2 in Layer-II
FamaxSinφ1
δ2
![Page 65: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/65.jpg)
![Page 66: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/66.jpg)
V
Famax
389.709
Calculation of Pa2 in Layer-II
FamaxSinφ1
δ2
![Page 67: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/67.jpg)
![Page 68: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/68.jpg)
V
Famax
403.817
Calculation of Pa2 in Layer-II
FamaxSinφ1
δ2
![Page 69: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/69.jpg)
![Page 70: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/70.jpg)
V
Famax
418.344
Calculation of Pa2 in Layer-II
FamaxSinφ1
δ2
![Page 71: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/71.jpg)
![Page 72: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/72.jpg)
V
Famax
433.319
Calculation of Pa2 in Layer-II
FamaxSinφ1
δ2
![Page 73: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/73.jpg)
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)
![Page 74: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/74.jpg)
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
![Page 75: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/75.jpg)
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
CALCULATION OF ACTIVE THRUST FROM COULOMB METHOD
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
![Page 76: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/76.jpg)
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)
Value of Angle θ (degree)
![Page 77: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/77.jpg)
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
CALCULATION OF ACTIVE THRUST FROM COULOMB METHOD
Wall angle with horizontal (αo) =
Angle for Active Thrust from horizontal xo=(90-α+δ)o = Cohesion (Cu) (KN/m2)=
θ Vs. Pa Graph
Surcharge (q) (KN/m2) =
Active
Thrust (Pa)
(KN/m)
WaterThrust (Pw=0.5γwZ02)(KN/m2) =
![Page 78: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/78.jpg)
70 80 90 100
θ Vs. Pa Graph
Poly. (θ Vs. Pa Graph)
![Page 79: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/79.jpg)
34 Unit Weight (γ) (KN/m3) = 18.5 8
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
CALCULATION OF PASSIVE THRUST FROM COULOMB METHOD
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
![Page 80: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/80.jpg)
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)
Value of Angle θ (degree)
![Page 81: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/81.jpg)
90
24.212 0
20
A
Pp
zo x0D
zo
R
(V+Fw)
C
yo θ0
CALCULATION OF PASSIVE THRUST FROM COULOMB METHOD
Wall angle with horizontal (αo) =
Cohesion (Cu) (KN/m2)=
θ Vs. Pp Graph
Surcharge (q) (KN/m2) =
PpSinx/Tanz
Fc Cosθ
(PpCosx - FcCosθ - PpSinx/Tanz)
PpSinx
(V+Fw)+FcSinθ
![Page 82: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/82.jpg)
30 35
θ Vs. Pp Graph
Poly. (θ Vs. Pp Graph)
![Page 83: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/83.jpg)
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
![Page 84: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/84.jpg)
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
![Page 85: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/85.jpg)
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
![Page 86: As Sing Ment](https://reader031.vdocuments.site/reader031/viewer/2022013117/577cc9ca1a28aba711a4a1cf/html5/thumbnails/86.jpg)
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