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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