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)
Data to be inserted from drawings etc
Inputs that vary from block to block
Input Data
MWL = 609.80 mFRL = 605.50 mTop of Dam = 611.00 m
Crest Elevation = 584.50 mSilt level (u/s) = 584.50 mSilt Level (d/s) = 518.00 mGate Height = 22.50 m
Tail Water Level (normal) = 548.90 m
Tail Water Level (flood) = 586.90 mFoundation level for analysis = 516.00 m *RL of Start of U/s Slope = 581.45 mRL of Start of D/s Slope = 547.15 m
u/s slope = 0.15
u/s slope = 8.53
d/s slope = 0.9
Spillway slope = 0.9Lip Level = 575.00 m
Distance from heel to centre of gallery = 9.05 m
u/s Projection from Gate to Pier face = 5.645 mDepth of water at gate face under MWL conditions = 23.8 m
Depth of water at end of flip bucket under MWL conditions = 11.9 mExtra width at Heel = 3.0 mExtra height at Heel = 5.0 m
Seismic Coefficient for Dam (Acc. To EQ Deptt, IIT Roorkee Report) DBE MCE
= 0.160 0.23
= 0.11 0.15
Seismic Coefficient for Hydro Dynamic DBE MCE
= 0.160 0.23
Dam c/s Area Properties
Density of Concrete = 24.00
Top width of Dam = 12.00 m
Base width of Dam = 90.23 mTotal Height of Dam = 95.00 m
Area of Dam Body = 3804Distance to centroid (x) from heel = 38.33 m
Distance to centroid (y) from base = 27.95 m
Area of Pier = 1462
Distance to centroid (x) from heel = 36.13 m
Distance to centroid (y) from base = 75.90 m
Area factor for pier = 0.33 (width of pier / total width of block)
Area factor for water in pier portion = 0.67
Area of Dam Body + Piers = 4286
Radial Gates
Mass of Radial Gate = 180 t
Width of Radial Gate = 14.50 m
Radius of Gate = 26.00 m
Enclosed Angle = 50.0
Area = 295
Weight of Radial Gate per unit width = 82
Distance to centroid (x) from heel = 24.5 m (gate shut)
Distance to centroid (y) from base = 67.4 m (gate shut)
Total Area of Dam + Gate = 4483
Distance to centroid (x) from heel = 38.07 m
Distance to centroid (x) from toe = 52.16 m
Distance to centroid (y) from base = 33.37 m
Weight of Dam = 102,939 kN per unit width
Moment about heel due to S.W. = 3,918,716 kNm
Material Properties
Angle of internal friction f = 53
Cohesion of the material C = 370
Vertical silt density = 9.07
Horizontal silt density = 3.53
Density of water = 10.00
Q=500 m3/s
Q=26400 m3/s
ah
av
ah
kN/m3
TB
WB
Dam Body #
m2
Piers #
m2
m2
o
m2
kN per unit width of block
m2
o
kN/m2
kN/m3
kN/m3
kN/m3
ANNEXURE 1
Shrinagar Hydroelectric Project – Dam Stability Calculation
Area 1 = 17330
Area 2 = 23461
Area 3 = 3200= 34.25 m
= 22.8 m= 76.9 m
Resultant y = 31.3 m
Table 1 - Calculation of Uplift Forces
DRAINS OPERATIVE DRAINS INOPERATIVE
FRL MWL FRL MWLu/s head 89.5 m 93.8 m 89.5 m 93.8 mReduced uplift head @ gallery 51.8 m 78.5 m 83.8 m 91.5 m
d/s head 32.9 m 70.9 m 32.9 m 70.9 m
4.1 m 4.4 m 4.5 m 4.5 m
46.63 m 48.95 m 43.74 m 47.92 m
Area of U1 force diagram 639.2 779.8 784.3 838.5
Area of U2 force diagram 3436.6 6065.5 4737.8 6591.9
Table 2 - Calculation of Hydrodynamic Forces
DBE MCEHorizontal Forces FRL MWL FRL MWL
Cm 0.673 0.673 0.673 0.673
Cs 0.673 0.673 0.673 0.673
89.5 m 93.8 m 89.5 m 93.8 m
89.5 m 93.8 m 89.5 m 93.8 m
96.3 101.0 136.9 143.5
6,260 kN 6,875 kN 8,894 kN 9,769 kN
230,727 kNm 265,606 kNm 327,824 kNm 377,382 kNm
Vertical Forces FRL MWL FRL MWL
6260 kN 6875 kN 8894 kN 9769 kN24.05 m 28.35 m 24.05 m 28.35 m
Cs 0.386 0.414 0.386 0.414
55.3 62.1 78.5 88.2
965 kN 1277 kN 1371 kN 1815 kN
794 kN 840 kN 1128 kN 1193 kN
h*=(0.4 y) 35.80 m 37.52 m 35.80 m 37.52 m
x* 8.37 m 8.63 m 8.37 m 8.63 m
6648 kNm 7245 kNm 9445 kNm 10294 kNm
Fig C1 - Load Case C
m2
m2
m2
y1
y2
y3
Distance of resultant (U1) from heel
Distance of resultant (U2) from heel
m2 m2 m2 m2
m2 m2 m2 m2
y - depth at which pressure acts
h - depth of reservoir
p - pressure at depth y
Vh
Mh
V2
y1
p - pressure at depth y
V1
Wh
Mh
1
Pw1
MWL
Crest EL
Base EL
2
y1
y2
y
3
y3
ANNEXURE 1
Shrinagar Hydroelectric Project – Dam Stability Calculation
LOAD COMBINATION A
NotationMagnitude of force (kN)
Vertical Horizontal (+) ve (-) ve (m)
Self Weight of Over Flow Section W 102,939 38.07 3,918,716
V Tan (Q) + CA
F =H
F =V = Vertical Reaction (kN)H = Horizontal Reaction (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
F = INFINITY
Check for Stresses:-
Mx = V
3,918,716= 102,939= 38.07 m
e = 7.05 m
B/6 = 15.04 m B/6>e No Tension Develops at the Base
= V (1+ /-(6e/B))B
= 1675.42Normal Stress @ heel = 1.68
= 606.28Normal Stress @ toe = 0.61
Construction Condition - Dam completed but no water in reservoir and no tail water
Name of theForce
LeverArm
Moments about heel (kNmm)Clockwise (+) ve
Anti-clockwise(-) ve
Ff FC
Factor of safety against sliding ( ≥ 1.0)
Ff
FC
σmax/ σmin
σmax kN/m2 N/mm2
σmin kN/m2 N/mm2
ANNEXURE 1
Shrinagar Hydroelectric Project – Dam Stability Calculation
LOAD COMBINATION B
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
3,082 6.41 19,754
5,177 2.60 13,461
795 15.64 12,431
4,009 65.71 263,438
Resultant Water Weight Load13,063 309,084
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
Resultant Silt Load 5,006 24,314
Uplift ForceU1 -6,392 4.12 -26,350
U2 -34,366 586.9 46.63 -1,602,326
Resultant Uplift Force -40,759 -1,628,676
Hydrostatic Force (U/S) 40,051 29.83 1,194,862
Hydrostatic Force (D/S) -5,412 10.97 -59,352
Resultant Hydrostatic Force34,639 1,135,510
Horizontal Silt Pressure (U/S) 8,286 22.83 189,187
Horizontal Silt Pressure (D/S) -7 0.67 -5
Resultant Horizontal Silt Load8,279 189,183
Net Restoring Moment (+ve) 5,636,163 kN-mNet Overturning Moment (-ve) -1,688,032 kN-m
FOS (Overturning) 3.3
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
H = 42,918 kNV = 80,250 kNM = 3,948,131 kN- m
Length Without tension = 90.23 m US Corps FSF = 1.87 >1 (SAFE) 3.26
FOS (Sliding) = 1.87
Check for Stresses:-M
x = V3,948,131
= 80,250= 49.20 m
e = -4.08 mB/6 = 15.04 m B/6>e No Tension Develops At The Base
= V (1+ (6e/B))B
= 1131
= 1.13
= 648
= 0.65
Normal Operating Condition - Full reservoir elevation, normal dry weather, normal tail water, ice and silt (if applicable), normal uplift
Name of theForce
LeverArm(m)
V1 M1
Weight of water in Over-Flow Section (U/S)
Ww1
Ww2
Ww3
Weight of water in Over-Flow Section (D/S)
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
ANNEXURE 1
Shrinagar Hydroelectric Project – Dam Stability Calculation
LOAD COMBINATION B - DRAINS INOPERATIVE
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)
3,082 6.41 19,754
5,177 2.60 13,461
795 15.64 12,431
Weight of water in Over-Flow Section (D/S) 4,009 65.71 263,438
Resultant Water Weight Load 13,063 309,084
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
Resultant Silt Load 5,006 24,314
Uplift ForceU1 -7,843 4.48 -35,102U2 -47,378 586.9 43.74 -2,072,178
Resultant Uplift Force -55,221 -2,107,279
Hydrostatic Force (U/S) 40,051 29.83 1,194,862
Hydrostatic Force (D/S) -5,412 10.97 -59,352
Resultant Hydrostatic Force 34,639 1,135,510
Horizontal Silt Pressure (U/S) 8,286 22.83 189,187
Horizontal Silt Pressure (D/S) -7 0.67 -5
Resultant Horizontal Silt Load 8,279 189,183
Net Restoring Moment (+ve) 5,636,163 kN-m
Net Overturning Moment (-ve) -2,166,636 kN-m
FOS (Overturning) 2.6
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
H = 42,918 kNV = 65,787 kNM = 3,469,527 kN- m
Length Without tension = 90.23 m US Corps FSF = 1.57 >1 (SAFE) 2.81
FOS (Sliding) = 1.53
Check for Stresses:-M
x = V3469527
= 65787= 52.74 m
e = -7.62 mB/6 = 15.04 m B/6>e No Tension Develops At The Base
= V (1+ (6e/B))B
= 1099
= 1.10
= 360
= 0.36
Normal Operating Condition -Full reservoir, normal dry weather, tail water, ice and silt (if applicable) 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
ANNEXURE 1
Shrinagar Hydroelectric Project – Dam Stability Calculation
LOAD COMBINATION C
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
Resultant Silt Load 5,006 24,314
Uplift ForceU1 -7,798 4.39 -34,244
U2 -60,655 48.95 -2,968,993
Resultant Uplift Force -68,453 -3,003,237
Hydrostatic Force (U/S) 41,846 31.27 1,308,399
Hydrostatic Force (D/S) -25,134 23.63 -594,001
Resultant Hydrostatic Force 16,712 714,397
Horizontal Silt Pressure (U/S) 8,286 22.83 189,187
Horizontal Silt Pressure (D/S) -7 0.67 -5
Resultant Horizontal Silt Load 8,279 189,183
Net Restoring Moment (+ve) 6,652,709 kN-m
Net Overturning Moment (-ve) -3,597,243 kN-m
FOS (Overturning) 1.8
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
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
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
Resultant Silt Load 5,006 24,314
Uplift ForceU1 -8385 4.51 -37,785
U2 -65,919 47.92 -3,159,092
Resultant Uplift Force -74,304 -3,196,877
Hydrostatic Force (U/S) 41,846 31.27 1,308,399
Hydrostatic Force (D/S) -25,134 23.63 -594,001
Resultant Hydrostatic Force 16,712 714,397
Horizontal Silt Pressure (U/S) 8,286 22.83 189,187
Horizontal Silt Pressure (D/S) -7 0.67 -5
Resultant Horizontal Silt Load 8,279 189,183
Net Restoring Moment (+ve) 6,654,021 kN-m
Net Overturning Moment (-ve) -3,790,883 kN-m
FOS (Overturning) 1.8
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
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
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
Weight of boulder on d/s side 0 Total 104151 8542
KN/m
Salil-17 5
Vikas -4030
45
Vivek Singh-10
Vineet Srivastav-15
20
25
10
40
Piyus-7 30
D’man -1555
260 0
N. Sahoo. 65
D. K Kaushik-15
Vivek Khere-15
K M singh-9
Moment Vertical EQ Moment V 0.23 SHEAREl
33645 244 6049.9 604 36525616 200 5858.6 599 66527316 226 7449.4 594 100451150 466 17270.1 584.5 170328650 302 13950.8 575.75 215613849 135 2088.9 570.00 2358
102336 1191 36952.9 567 414462556 907 33053.9 557 550541499 769 27445.9 547 665823843 615 22939.3 537 75809010 339 13703.8 530 80883237 197 8446.7 524.00 8384464 44 1961.8 522 8450285 62 2844.6 516 8542
0423454 5695 200016
KNm/m
5
30
60
25
25
10
40
30
90
315
FZ FHZ
4.06 1483.798 1483.798 1483.7982.496 747.8315 3325.397 747.8315 4821.06 4058.967 1483.7982.493 846.0269 5022.202 846.0269 6714.256 8230.391 4058.967
4.75 3316.87 16175.92 3316.87 22809.66 21089.45 8230.3913.471 1572.936 18864.07 1572.936 22009.94 37561.26 21089.45
14.5 2931.604 13558.92 2931.604 19422.13 52889.25 37561.266.3 11251.61 12432.13 11251.61 34935.35 71215.08 52889.25
4.976 6770.421 55046.59 6770.421 68587.43 119425.9 71215.084.977 5740.864 66581.37 5740.864 78063.1 180213.4 119425.94.856 4477.931 75802.81 4477.931 84758.68 251272.7 180213.43.738 1898.62 56617.44 1898.62 60414.68 306233.3 251272.72.959 873.9066 50301.26 873.9066 52049.08 355636.4 306233.30.996 66.03271 16899.68 66.03271 17031.75 372469.5 355636.43.082 284.9926 51253.87 284.9926 51823.86 423453.6 372469.5
42263.45
1483.798 0747.8315 1827.338846.0269 3325.397
3316.87 9542.1841572.936 14898.882931.604 12396.3911251.61 7074.226770.421 41440.445740.864 55046.594477.931 66581.37
1898.62 53061.97873.9066 48529.2366.03271 16767.09284.9926 50699.05
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