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Annexure-1
RESULTS OF STABILITY ANALYSIS OF THE OVER FLOW SECTION
A 1.68 0.61 Not Specified 7.00 INFINITY INFINITYB 0.65 1.13 0.00 7.00 1.87 3.26
C 0.82 0.62 -0.15 7.00 2.66 4.78
D (EQ-DN & d/s) 1.33 1.10
-1.30 7.00
15.06 18.07
D (EQ-DN & u/s) 2.05 0.37 15.06 18.07
D (EQ-UP & d/s) 1.30 0.84 13.59 16.30
D (EQ-UP & u/s) 2.03 0.11 13.59 16.30
E (EQ-DN & d/s) 0.16 1.78
-1.30 7.00
2.11 2.53
E (EQ-DN & u/s) 1.23 0.71 4.65 5.59
E (EQ-UP & d/s) 0.07 1.55 1.83 2.20
E (EQ-UP & u/s) 1.14 0.48 4.05 4.85
F 0.50 0.80 -0.30 7.00 4.24 4.46
G (EQ-DN & d/s) -0.13 1.75
-1.30 7.00
2.08 2.17
G (EQ-DN & u/s) 0.94 0.68 4.66 4.87
G (EQ-UP & d/s) -0.22 1.51 1.71 1.79
G (EQ-UP & u/s) 0.85 0.45 3.93 4.14
H (EQ-DN & d/s) 0.08 1.93
-1.88 7.00
2.33 2.33
H (EQ-DN & u/s) 1.60 0.41 7.69 7.69
H (EQ-UP & d/s) -0.31 1.85 1.83 1.83
H (EQ-UP & u/s) 1.21 0.33 6.30 6.30
All stresses are in N/mm2
LOAD CASE 1 s (heel) s (toe)Permissible Tensile stress
(N/mm2)Permissible Compressive stress
(N/mm2)
SLIDING FACTOR (With Partial factor of Safety)
SLIDING FACTOR (Without Partial factor of Safety)
ANNEXURE 1
Shrinagar Hydroelectric Project – Dam Stability Calculation
…………..HYDROELECTRIC PROJECT
STABILITY ANALYSIS OF THE OVER FLOW SECTION (As per code IS:6512-1984)
F = Factor of safety against sliding which should not be less than oneV = Vertical Reaction in kNH = Horizontal Reaction in kN
TanQ = Coefficient of internal friction of the materialC = Cohesion of material at the plane considered
= Partial factor of safety in respect of Friction
= Partial factor of safety in respect of Cohesion
H = 24,991 kNV = 64,770 kNM = 3,056,778 kN- m
Length Without tension = 90.23 US Corps FSF = 2.66 >1 (SAFE) 4.78
FOS (Sliding) = 2.59
Check for Stresses:-M
x = V3,056,778
= 64,770= 47.19 m
e = -2.08 mB/6 = 15.04 m B/6>e No Tension Develops At The Base
= V (1+ (6e/B))B
= 817
= 0.82
= 619
= 0.62
Flood Discharge Condition - Reservoir at Maximum flood pool elevation, all gates open, tail water at flood elevation, normal uplift and silt (if applicable)
Name of theForce
LeverArm(m)
V1 M1
Ww1
Ww2
Ww3
Ww4
V2 M2
WS1
WS2
V3 M3
V4 M4
Pw1
Pw2
H1 M5
PS1
PS2
H2 M6
Ff FC
Ff
FC
σmax/ σmin
σmax kN/m2
N/mm2
σmin kN/m2
N/mm2
F22
Smec Limited: Refer Fig C1
G22
Smec Limited: Refer Fig C1
ANNEXURE 1
Shrinagar Hydroelectric Project – Dam Stability Calculation
LOAD COMBINATION D
Notation
Magnitude of force (kN)Moments about heel (kNm)
Vertical Horizontal
Down (+) ve Towards U/s (-) ve Clockwise (+) ve
Up (-) ve Towards D/s (+) ve Anti-clockwise (-) ve
Weight of Section W 102,939 38.07 3,918,716
Vertical EQ Forces 6,588 38.07 376,197
Horizontal EQ Forces 9,882 33.37 494,604
Check Against Sliding :-V Tan (Q)
+CA
F =H
F = Factor of safety against sliding which should not be less than oneV = Vertical Reaction in kNH = Horizontal Reaction in kN
TanQ = Coefficient of internal friction of the materialC = Cohesion of material at the plane considered
= Partial factor of safety in respect of Friction
= Partial factor of safety in respect of Cohesion
a) EQ acting Downwards and D/S
H = 9,882 kN d/sV = 109,527 kN downwardsM = 4,789,516 kN- m
Length Without tension = 90.23 US Corps FSF = 15.06 >1 SAFE 18.07
FOS (Sliding) = 11.08
Net Positive Moment = 4,789,516 kN-mNet Negative Moment = 0 kN-mFOS (Overturning) = INFINITY
Check for Stresses:-M
x = V4,789,516
= 109,527= 43.73 m
e = 1.39 mB/6 = 15.04 m B/6>e No Tension Develops at the Base
σmax/ σmin = V (1+ (6e/B))B
σmax = 1,326
= 1.33
= 1,102
= 1.10
b) EQ acting Downwards and U/S
H = -9,882 kN u/sV = 109,527 kN downwardsM = 3,800,309 kN- m
Length Without tension = 90.23 US Corps FSF = 15.06 >1 SAFE 18.07
FOS (Sliding) = 11.08
Net Positive Moment = 4,294,913 kN-mNet Negative Moment = 494,604 kN-mFOS (Overturning) = 8.68
Check for Stresses:-
Load Combination A - (Dam completed but no water in reservoir and no tail water) combined with DBE
Name of theForce
LeverArm(m)
V1 M1
V2 M2
H1 M3
Ff FC
Ff
FC
kN/m2
N/mm2
σmin kN/m2
N/mm2
ANNEXURE 1
Shrinagar Hydroelectric Project – Dam Stability Calculation
Mx = V
3,800,309= 109,527= 34.70 m
e = 10.42 mB/6 = 15.04 m B/6>e No Tension Develops at the Base
= V (1+ (6e/B))B
= 2,055
= 2.05
= 373
= 0.37
c) EQ acting Upwards and D/S
H = 9,882 kN d/sV = 96,351 kN downwardsM = 4,037,123 kN- m
Length Without tension = 90.23 US Corps FSF = 13.59 >1 SAFE 16.30
FOS (Sliding) = 9.75
Net Positive Moment = 4,413,320 kN-mNet Negative Moment = 376,197 kN-mFOS (Overturning) = 11.73
Check for Stresses:-M
x = V4,037,123
= 96,351= 41.90 m
e = 3.21 mB/6 = 15.04 m B/6>e No Tension Develops at the Base
= V (1+ (6e/B))B
σmax = 1,296
= 1.30
σmin = 840
= 0.84
d) EQ acting Upwards and U/S
H = -9,882 kN u/sV = 96,351 kN downwardsM = 3,047,916 kN- m
Length Without tension = 90.23 US Corps FSF = 13.59 >1 SAFE 16.30
FOS (Sliding) = 9.75
Net Positive Moment = 3,918,716 kN-mNet Negative Moment = 870,800 kN-mFOS (Overturning) = 4.50
Check for Stresses:-M
x = V3,047,916
= 96,351= 31.63 m
e = 13.48 mB/6 = 15.04 m B/6>e No Tension Develops at the Base
= V (1+ (6e/B))B
σmax = 2,025
= 2.03
σmin = 111
= 0.11
σmax/ σmin
σmax kN/m2
N/mm2
σmin kN/m2
N/mm2
σmax/σmin
kN/m2
N/mm2
kN/m2
N/mm2
σmax/ σmin
kN/m2
N/mm2
kN/m2
N/mm2
ANNEXURE 1
Shrinagar Hydroelectric Project – Dam Stability Calculation
LOAD COMBINATION E
Notation
Magnitude of force (kN)Moments about heel (kNm)
Vertical HorizontalDown (+) ve Towards U/s (-) ve Clockwise (+) ve
Up (-) ve Towards D/s (+) ve Anti-clockwise (-) ve
Resultant Loads from Load Case B 80,250 42,918 3,948,131
Vertical EQ Forces 6,588 38.07 376,197
Horizontal EQ Forces 9,882 33.37 494,604
Horizontal Hydrodynamic Force 6,260 230,727
Vertical Hydrodynamic Force 794 6,648
Net Restoring Moment (+ve) 5,636,163 kN-m from Load Combination BNet Overturning Moment (-ve) -1,688,032 kN-m from Load Combination B
FOS (Overturning) 3
Check Against Sliding :-V Tan (Q)
+CA
F =H
F = Factor of safety against sliding which should not be less than oneV = Vertical Reaction in kNH = Horizontal Reaction in kN
TanQ = Coefficient of internal friction of the materialC = Cohesion of material at the plane considered
= Partial factor of safety in respect of Friction
= Partial factor of safety in respect of Cohesion
a) EQ acting Downwards and D/S
H = 59,059 kN d/sV = 87,632 kN downwardsM = 5,056,306 kN- m
Length Without tension = 90.23 US Corps FSF = 2.11 >1 (SAFE) 2.53
FOS (Sliding) = 1.48
Net Positive Moment = 6,744,338 kN-mNet Negative Moment = -1,688,032 kN-mFOS (Overturning) = 4.00
Check for Stresses:-M
x = V5,056,306
= 87,632= 57.70 m
e = -12.58 mB/6 = 15.04 m B/6>e No Tension Develops At The Base
= V (1+ (6e/B))B
= 1,784
= 1.78
= 158
= 0.16
b) EQ acting Downwards and U/S
H = 26,776 kN u/sV = 87,632 kN downwardsM = 3,605,645 kN- m
Length Without tension = 90.23 US Corps FSF = 4.65 >1 SAFE 5.59
FOS (Sliding) = 3.27
Net Positive Moment = 6,019,008 kN-mNet Negative Moment = -2,413,363 kN-m
Load Combination B - (Full reservoir elevation, normal dry weather, normal tail water, normal uplift; ice and silt (if applicable)) combined with DBE
Name of theForce
LeverArm(m)
V1 H1 M1
V2 M2
H2 M3
H3 M4
V3 M5
Ff FC
Ff
FC
σmax/σmin
σmax kN/m2
N/mm2
σmin kN/m2
N/mm2
ANNEXURE 1
Shrinagar Hydroelectric Project – Dam Stability Calculation
FOS (Overturning) = 2.49
Check for Stresses:-M
x = V3,605,645
= 87,632= 41.15 m
e = 3.97 mB/6 = 15.04 m B/6>e No Tension Develops at the Base
V (1+ (6e/B))
= B
= 1,228
= 1.23
= 715
= 0.71
c) EQ acting Upwards and D/S
H = 59,059 kN d/sV = 72,867 kN downwardsM = 4,290,617 kN- m
Length Without tension = 90.23 US Corps FSF = 1.83 >1 (SAFE) 2.20
FOS (Sliding) = 1.23
Net Positive Moment = 6,361,494 kN-mNet Negative Moment = -2,070,877 kN-mFOS (Overturning) = 3.07
Check for Stresses:-M
x = V4,290,617
= 72,867= 58.88 m
e = -13.77 mB/6 = 15.04 m B/6>e No Tension Develops At The Base
= V (1+ (6e/B))B
= 1,547
= 1.55
= 68
= 0.07
d) EQ acting Upwards and U/S
H = 26,776 kN u/sV = 72,867 kN downwardsM = 2,839,956 kN- m
Length Without tension = 90.23 US Corps FSF = 4.05 >1 SAFE 4.85
FOS (Sliding) = 2.72
Net Positive Moment = 5,636,163 kN-mNet Negative Moment = -2,796,207 kN-mFOS (Overturning) = 2.02
Check for Stresses:-M
x = V2,839,956
= 72,867= 38.97 m
e = 6.14 mB/6 = 15.04 m No Tension Develops at the Base
= V (1+ (6e/B))B
= 1,137
= 1.14
= 478
= 0.48
σmax/ σmin
σmax kN/m2
N/mm2
σmin kN/m2
N/mm2
σmax/ σmin
σmax kN/m2
N/mm2
σmin kN/m2
N/mm2
σmax/ σmin
σmax kN/m2
N/mm2
σmin kN/m2
N/mm2
ANNEXURE 1
Shrinagar Hydroelectric Project – Dam Stability Calculation
LOAD COMBINATION F
Notation
Magnitude of force (kN)Moments about heel (kNm)
Vertical HorizontalDown (+) ve Towards U/s (-) ve Clockwise (+) ve
Up (-) ve Towards D/s (+) ve Anti-clockwise (-) ve
Self Weight of Over Flow Section W 102,939 38.07 3,918,716
Weight of water in Over-Flow Section (U/S)
3,633 6.41 23,287
5,177 2.60 13,461
958 15.64 14,976
Weight of water in Over-Flow Section (D/S) 15,510 74.90 1,161,681
Resultant Water Weight Load 25,278 1,213,405
Weight of Silt in Over Flow Section (U/S) 4,990 4.61 23,001
Weight of Silt in Over Flow Section (D/S) 16 80.36 1,313
F = Factor of safety against sliding which should not be less than oneV = Vertical Reaction in kNH = Horizontal Reaction in kN
TanQ = Coefficient of internal friction of the materialC = Cohesion of material at the plane considered
= Partial factor of safety in respect of Friction
= Partial factor of safety in respect of Cohesion
H = 24,991 kNV = 58,919 kNM = 2,863,138 kN- m
Length Without tension = 90.23 US Corps FSF = 4.24 >1 (SAFE) 4.46
FOS (Sliding) = 2.36
Check for Stresses:-M
x = V2,863,138
= 58,919= 48.59 m
e = -3.48 mB/6 = 15.04 m B/6>e No Tension Develops At The Base
= V (1+ (6e/B))B
= 804
= 0.80
= 502
= 0.50
Load Combination C (Reservoir at Maximum flood pool elevation, all gates open, tail water at flood elevation, silt (if applicable)) combined with extreme uplift (Drains inoperative)
Name of theForce
LeverArm(m)
V1 M1
Ww1
Ww2
Ww3
Ww4
V2 M2
WS1
WS2
V3 M3
V4 M4
Pw1
Pw2
H1 M5
PS1
PS2
H2 M6
Ff FC
Ff
FC
σmax/ σmin
σmax kN/m2
N/mm2
σmin kN/m2
N/mm2
F22
Smec Limited: Refer Fig C1
G22
Smec Limited: Refer Fig C1
ANNEXURE 1
Shrinagar Hydroelectric Project – Dam Stability Calculation
LOAD COMBINATION G
Notation
Magnitude of force (kN)Moments about heel (kNm)
Vertical HorizontalDown (+) ve Towards U/s (-) ve Clockwise (+) ve
Up (-) ve Towards D/s (+) ve Anti-clockwise (-) ve
W 65,787 42,918 38.07 3,469,527
Vertical EQ Forces 6,588 38.07 376,197
Horizontal EQ Forces 9,882 33.37 494,604
Horizontal Hydrodynamic Force 6,260 230,727
Vertical Hydrodynamic Force 794 6,648
Net Restoring Moment (+ve) 5,636,163 kN-m
Net Overturning Moment (-ve) -2,166,636 kN-mFOS (Overturning) 3
Check Against Sliding :-V Tan (Q)
+CA
F =H
F = Factor of safety against sliding which should not be less than oneV = Vertical Reaction in kNH = Horizontal Reaction in kN
TanQ = Coefficient of internal friction of the materialC = Cohesion of material at the plane considered
= Partial factor of safety in respect of Friction
= Partial factor of safety in respect of Cohesion
a) EQ acting Downwards and D/S
H = 59,059 kN d/sV = 73,170 kN downwardsM = 4,577,702 kN- m
Length Without tension = 83.54 US Corps FSF = 2.08 >1 (SAFE) 2.17
FOS (Sliding) = 1.24
Net Positive Moment = 6,744,338 kN-mNet Negative Moment = -2,166,636 kN-mFOS (Overturning) = 3.11
Check for Stresses:-M
x = V4,577,702
= 73,170= 62.56 m
e = -17.45 mB/6 = 15.04 m B/6<e Tension Develops at The Base
= V (1+ (6e/B))B
= 1,752
= 1.75
= -130
= -0.13
b) EQ acting Downwards and U/S
H = 26,776 kN u/sV = 73,170 kN downwardsM = 3,127,041 kN- m
Length Without tension = 90.23 US Corps FSF = 4.66 >1 (SAFE) 4.87
FOS (Sliding) = 2.73
Net Positive Moment = 6,019,008 kN-mNet Negative Moment = -2,891,967 kN-mFOS (Overturning) = 2.08
Load Combination E (Load Combination B with DBE) - (Full reservoir elevation, normal dry weather, normal tail water, ice and silt (if applicable) combined with DBE), combined with extreme uplift (Drains Inoperative)
Name of theForce
LeverArm(m)
Resultant Loads from Load Case B (Drains Inoperative)
V1 H1 M1
V2 M2
H2 M3
H3 M4
V3 M5
Ff FC
Ff
FC
σmax/ σmin
σmax kN/m2
N/mm2
σmin kN/m2
N/mm2
ANNEXURE 1
Shrinagar Hydroelectric Project – Dam Stability Calculation
Check for Stresses:-M
x = V3,127,041
= 73,170= 42.74 m
e = 2.38 mB/6 = 15.04 m B/6>e No Tension Develops at the Base
= V (1+ (6e/B))B
= 939
= 0.94
= 683
= 0.68
c) EQ acting Upwards and D/S
H = 59,059 kN d/sV = 58,405 kN downwardsM = 3,812,013 kN- m
Length Without tension = 77.12 US Corps FSF = 1.71 >1 (SAFE) 1.79
FOS (Sliding) = 0.99
Net Positive Moment = 6,361,494 kN-mNet Negative Moment = -2,549,481 kN-mFOS (Overturning) = 2.50
Check for Stresses:-M
x = V3,812,013
= 58,405= 65.27 m
e = -20.15 mB/6 = 15.04 m B/6<e Tension Develops at The Base
= V (1+ (6e/B))B
= 1,515
= 1.51
= -220
= -0.22
d) EQ acting Upwards and U/S
H = 26,776 kN u/sV = 58,405 kN downwardsM = 2,361,352 kN- m
Length Without tension = 90.23 US Corps FSF = 3.93 >1 SAFE 4.14
FOS (Sliding) = 2.18
Net Positive Moment = 5,636,163 kN-mNet Negative Moment = -3,274,811 kN-mFOS (Overturning) = 1.72
Check for Stresses:-M
x = V2,361,352
= 58,405= 40.43 m
e = 4.68 mB/6 = 15.04 m No Tension Develops at the Base
= V (1+ (6e/B))B
= 849
= 0.85
= 446
= 0.45
σmax/ σmin
σmax kN/m2
N/mm2
σmin kN/m2
N/mm2
σmax/ σmin
σmax kN/m2
N/mm2
σmin kN/m2
N/mm2
σmax/ σmin
σmax kN/m2
N/mm2
σmin kN/m2
N/mm2
LOAD COMBINATION H
Notation
Magnitude of force (kN)Moments about heel (kNm)
Vertical HorizontalDown (+) ve Towards U/s (-) ve Clockwise (+) ve
Up (-) ve Towards D/s (+) ve Anti-clockwise (-) ve
Resultant Loads from Load Case B W 80,250 42,918 38.07 3,948,131
Vertical EQ Forces 9,361 38.07 356,342
Horizontal EQ Forces 14,041 33.37 702,749
Horizontal Hydrodynamic Force 8,894 327,824
Vertical Hydrodynamic Force 1,128 9,445
Net Restoring Moment (+ve) 5,636,163 kN-m
Net Overturning Moment (-ve) -1,688,032 kN-mFOS (Overturning) 3
Check Against Sliding :-V Tan (Q)
+CA
F =H
F = Factor of safety against sliding which should not be less than oneV = Vertical Reaction in kNH = Horizontal Reaction in kN
TanQ = Coefficient of internal friction of the materialC = Cohesion of material at the plane considered
= Partial factor of safety in respect of Friction
= Partial factor of safety in respect of Cohesion
a) EQ acting Downwards and D/S
H = 65,852 kN d/sV = 90,739 kN downwardsM = 5,344,492 kN- m
Length Without tension = 90.23 US Corps FSF = 2.33 >1 (SAFE) 2.33
FOS (Sliding) = 1.38
Net Positive Moment = 7,032,524 kN-mNet Negative Moment = -1,688,032 kN-mFOS (Overturning) = 4.17
Check for Stresses:-M
x = V5,344,492
= 90,739= 58.90 m
e = -13.78 mB/6 = 15.04 m B/6>e No Tension Develops At The Base
= V (1+ (6e/B))B
= 1,927
= 1.93
= 84
= 0.08
b) EQ acting Downwards and U/S
H = 19,983 kN u/sV = 90,739 kN downwardsM = 3,283,344 kN- m
Length Without tension = 90.23 US Corps FSF = 7.69 >1 SAFE 7.69
FOS (Sliding) = 4.54
Net Positive Moment = 6,001,951 kN-mNet Negative Moment = -2,718,606 kN-mFOS (Overturning) = 2.21
Check for Stresses:-M
x = V3,283,344
= 90,739= 36.18 m
e = 8.93 m
Load Combination B - (Full reservoir elevation, normal dry weather, normal tail water, normal uplift; ice and silt (if applicable) ) combined with MCE
Name of theForce
LeverArm(m)
V1 H1 M1
V2 M2
H2 M3
H3 M4
V3 M5
Ff FC
Ff
FC
σmax/ σmin
σmax kN/m2
N/mm2
σmin kN/m2
N/mm2
B/6 = 15.04 m B/6>e No Tension Develops at the Base
= V (1+ (6e/B))B
= 1,603
= 1.60
= 408
= 0.41
c) EQ acting Upwards and D/S
H = 65,852 kN d/sV = 69,761 kN downwardsM = 4,612,918 kN- m
Length Without tension = 75.28 US Corps FSF = 1.83 >1 (SAFE) 1.83
FOS (Sliding) = 1.06
Net Positive Moment = 6,666,737 kN-mNet Negative Moment = -2,053,820 kN-mFOS (Overturning) = 3.25
Check for Stresses:-M
x = V4,612,918
= 69,761= 66.12 m
e = -21.01 mB/6 = 15.04 m B/6<e Tension Develops at The Base
= V (1+ (6e/B))B
= 1,853
= 1.85
= -307
= -0.31
d) EQ acting Upwards and U/S
H = 19,983 kN u/sV = 69,761 kN downwardsM = 2,551,770 kN- m
Length Without tension = 90.23 US Corps FSF = 6.30 >1 SAFE 6.30
FOS (Sliding) = 3.49
Net Positive Moment = 5,636,163 kN-mNet Negative Moment = -3,084,393 kN-mFOS (Overturning) = 1.83
Check for Stresses:-M
x = V2,551,770
= 69,761= 36.58 m
e = 8.54 mB/6 = 15.04 m B/6>e No Tension Develops at the Base
= V (1+ (6e/B))B
= 1,212
= 1.21
= 334
= 0.33
σmax/ σmin
σmax kN/m2
N/mm2
σmin kN/m2
N/mm2
σmax/ σmin
σmax kN/m2
N/mm2
σmin kN/m2
N/mm2
σmax/ σmin
σmax kN/m2
N/mm2
σmin kN/m2
N/mm2
Calculation of Base Shear for Shrinagar
Top of the Dam 611 0.155Foundation Level 516Height of Dam 95
Area X Y KN/m Factor of A Horizontal EQ
Weight of Pier up to 6 204.811 24.831 608.06 1622 0.23 365Weight of Pier up to 5 180.796 29.331 601.496 1432 0.21 300Weight of Pier up to 5 217.51 32.927 596.493 1723 0.20 339Weight of Pier up to 5 491.816 37.098 589.25 3895 0.18 698Weight of Pier below 5 369.803 46.178 579.221 2929 0.15 453DL of Spillway Gate 15.4975 584.5 1206 0.17 202Dam Body- up to 567 530.651 31.036 573.3 12736 0.14 1786Dam Body- up to 557 503.841 36.44 561.976 12092 0.11 1361Dam Body- up to 547 545.851 35.691 551.977 13100 0.09 1153Dam Body- up to 537 607.193 37.314 541.856 14573 0.06 922Dam Body- up to 530 487.51 40.47 533.738 11700 0.04 508Dam Body- up to 524 458.816 42.9 526.959 11012 0.03 295Dam Body- up to 522 161.339 44.386 522.996 3872 0.02 66Dam Body- up to 516 510.808 46.143 519.082 12259 0.01 92