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Page 1: Dam Stability Analysis

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)

Page 2: Dam Stability Analysis

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

F62
vibhor.gupta: Modified According to Mr. K C Aggrawal
Page 3: Dam Stability Analysis

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

I34
Smec Limited: refer Cl 5.3.2a) of IS:6512 - 1984
J57
Smec Limited: Taken from Fig 10, IS : 1893 - 1984
L57
Smec Limited: Taken from Fig 10, IS : 1893 - 1984
N57
Smec Limited: Taken from Fig 10, IS : 1893 - 1984
P57
Smec Limited: Taken from Fig 10, IS : 1893 - 1984
I61
Smec Limited: from 7.2.1, IS : 1893 - 1984
I62
Smec Limited: from 7.2.1.3, IS : 1893 - 1984
I63
Smec Limited: from 7.2.1.3, IS : 1893 - 1984
I69
Smec Limited: from 7.2.1, IS : 1893 - 1984
I71
Smec Limited: from 7.2.2, IS : 1893 - 1984
I74
Smec Limited: from 7.2.1.3, IS : 1893 - 1984
Page 4: Dam Stability Analysis

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

Page 5: Dam Stability Analysis

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

Page 6: Dam Stability Analysis

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

Page 7: Dam Stability Analysis

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

F22
Smec Limited: Refer Fig C1
G22
Smec Limited: Refer Fig C1
Page 8: Dam Stability Analysis

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

Page 9: Dam Stability Analysis

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

Page 10: Dam Stability Analysis

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

Page 11: Dam Stability Analysis

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

Page 12: Dam Stability Analysis

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

F22
Smec Limited: Refer Fig C1
G22
Smec Limited: Refer Fig C1
Page 13: Dam Stability Analysis

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

Page 14: Dam Stability Analysis

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

Page 15: Dam Stability Analysis

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

Page 16: Dam Stability Analysis

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

Page 17: Dam Stability Analysis

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

Page 18: Dam Stability Analysis

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

Page 19: Dam Stability Analysis

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

Page 20: Dam Stability Analysis

25

25

10

40

30

90

315

Page 21: Dam Stability Analysis

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

Page 22: Dam Stability Analysis

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