CASE (1)

Consider 1m length of dam. When reservoir is empty, the various forces are worked out. Horizontal earthquake forces acting towards upstream are considered. Stability is examined for two sub cases i.e. (a) when vertical earthquake forces are additive to the wt. of dam (b) when vertical E/equal forces are subtractive to dam wt.

Name of

Forces

Desig-natin

Magnitude of force (ton) Lever arm

(m)

Moments about toe anti-clockwise

(+ve)Vertical Horizontal

Downword wt.of dam

Downward wt. of water

Uplift Forces

W1

W2

W3

W4

W5

W6

U1

U2

(+)

12

×6×60×2.4=432

(+)7×90×2.4=1511

(+)

12

×56×80×2.4=5370

65.0

59.5

37.33

66

65

1.4

34.5

46

(+) 28040

(+) 89900

(+) 200000

∑M 1=317940

∑V 1=7313

(+) 10296

(+) 11700

(+) 17.64

∑M 2=22013 .64

(-) 14283

(-) 126960

∑M 3=−141243

(+) 6 x 26 x 1 x 1= 156

(+) ½ x 60 x 6 = 180

(+) ½ x 4.2 x 6 =

12.6

∑V 2=348 .6

(-) 69 x 6 = 414

(-) ½ x 80 x 69 = 2760

∑V 3=−3174

Horizontal Forces

H1

H2

∑V=44876

28.67

2 (-) 106021.6

(+) 25.2

∑M 4=−105996 .4

∑M=92714 .24

-1/2 x 86 x 86 = 3698

+ ½ x 4.2 x 6 = 12.6

= 92714.24/ 44876 = 2.066

e = B/2 – x = 69/2- 2.066 = 32.434

Normal stresses at toe and heel

Principal Stresses

Intensity of Shear Stress