# Gravity Dams

By Vishwajeet Sinha|Updated : January 7th, 2017

Gravity Dams

Forces Acting on Gravity Dam

(1) Water pressure  Acting at from base

Where = Unit weight of water.

(2) Uplift Pressure

(a) When Drainage Gallery is not Provided  (b) when drainage Gallery is Provided (3) Earthquake Force

αH = 0.1g to 0.2g

Where, αH = Horizontal acceleration

αV = Vertical acceleration

αV = 0.75 αH

α = Seismic coefficient

α = β1α0

β = Soil foundation System factor

l = Importance factor

α0 = Basic seismic coefficient which depends upon seismic zone of country where, Fg = body force

g = Acceleration due to gravity, +ve for upward & -ve for downward.

(a) Hydrodynamic force

(1) FH = Horizontal inertia force

(2) it effect of water pressure due to earthquake distribution of pressure is parabolic.  at 0.424 H from base.

α = 0.1g to 0.2g

(4) Silt Pressure Where, hs = Height of silt from the base.

ka = Coefficient of active earth pressure γsub = Submerged unit weight.

According to U.C.B.R (5) Wave Pressure Acts at from still water level where, Pw = Resultant wave pressure. acts at from still water surface.

Where FW = total wave force. if F < 32 km when F > 32 km.

where, Fm = Length of reservoir in km

hW = Height of wave in meter

V = Wind velocity in lm/hr.

(6) Self weight of dam

W = γcV

Where, γc = Unit weight of concrete

V = Volume of dam body per unit length

#### Modes of Failure & Criteria for Structural Stability of Gravity Dam

(1) Failure by Overturning About toe Where, Fs = Factor of safety

MR = Restoring moment about toe (due to ∑FV)

MO = Overturning moment about toe (due to ∑FH)  Where, FR = Resultant force

e = Eccentricity  = Distance of from toe.

(2) Failure due to sliding = Sliding factor = Factor of safety due to sliding  Case: if shear strength is also accounted then factor of safety is called shear frictional factor (S.F.F)  Where, B = Width in meter.

(3) Failure due to Compression or Crushing When toe failure occurs. When heel failure occurs.  σmax ≤ FC for no failure

where FC = Crushing strength

Case: (1) When shear stress also acts on horizontal plane.  Where, α = Angle of d/s surface with vertival for no failure

σ1 ≤ FC

Where, FC = Crushing strength of concrete.

τ = Magnitude of shear stress on horizontal plane near the toe Case (2): When earthquake force considered then Where, Pe = Earthquake Pressure Failure due to tension Elementary Profile of Gravity Dam Where Pu = Uplift pressure i.e., Force of buoyancy.

C = Uplift pressure coefficient  Where w= Weight of dam body for unit length Where, B = minimum base width required for no tension criteria B’ = Minimum base width for no sliding criteria

G = Sp. gravity of concrete, i.e., that of the material of the dam

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