CONRETE GRAVITY DAMS ?????? ??????????? ???????

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-Concrete gravity dams are constructed such that
their own weight resist the forces exerted upon
it .
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• During design, the following should be checked
• a) No tensile stress should occur in the dam
  body. Compressive stresses should not exceed
• maximum allowable stress in concrete.
• b) Dam is safe against overturning.
• c) Dam is safe against shear and sliding.
• d) Bearing capacity of foundation should not be
  exceeded

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1. Forces Acting on Gravity Dams.
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1. Forces Acting on Gravity Dams.

1. The weight Wc (dead load) of the dam.
2. Hydrostatic forces.
3. Uplift Forces
4. Forces due to sediment accumulation.
5. Ice loads
6. Earthquake force on the dam body, Fd
7. Dynamic force in the reservoir induced by
   Earthquake.
8. Forces on Spillways.

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• 1-The weight Wc (dead load) of the dam.
• Is the dead weight of the dam itself. All forces
  are transferred directly to the foundation.
• 2- Hydrostatic forces.
• Those are the forces applied by water at the
  reservoir and tail water. They are separated by
  Horizontal (Hu and Hd) and Vertical (Fvu and Fvd)
  components. These forces are computed for a unit
  width
• 3-Uplift Forces.
• Those forces are acting under the base of the
  dam.
• 4-Forces due to sediment accumulation.
• It is represented by Fs and may be determined
  from lateral earth pressure expression

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• 5- Ice loads
• It should be considered in cold climates. see the
  table in page 3
• 6-Earthquake force on the dam body, Fd
• It must be assumed to act both horizontally and
  vertically through the center of gravity of the
  dam ,
• F kWc.
• where k is the earthquake coefficient which is
  the ratio of earthquake acceleration to
  gravitational acceleration. The k varies between
  0.1-0.6
• 7- Dynamic force in the reservoir induced by
  Earthquake.
• Fw0.726Ck?h12 ,and
• where ? ' is the angle between the upstream face
  of the dam and vertical line (in degrees). For
• a vertical upstream face the value of C becomes
  0.7. The force Fw acts at a distance 0.412h1
• above the bottom of reservoir
• 8- Forces on Spillways
• Those forces can be calculated by momentum
  equations.
• SF ?Q?V
• where ? is the density of water, Q is the outflow
  rate over the spillway crest and ?V is the
• change in the velocity between sections 1 and 2.

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2. Stability Criteria

• a-Safety against overturning.
• The dam must be safe against overturning for all
  loading conditions
• where F.So is the safety factor against
  overturning, SMr is the resisting moments about
  the toe,
• and SMo is the overturning moments about the toe.
  The minimum value recommended for F.So may be
  taken as 2.0
• b-. Safety against sliding.
• The dam must be safe against sliding over any
  horizontal plane. The safety factor against
• sliding is called F.Ss

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• c-Checked for shear and sliding
• A safety factor against combined shear and
  sliding is defined as
• where A is the area of shear plane and ts is the
  allowable shear stress in concrete in contact
  with foundation. The minimum value recommended
  for FSss may be taken as 5.0.
• d-Contact stress between foundation and the dam.
• This stress must be greater than zero at all
  points or the dam will be unsafe against
  overturning. A linear stress distribution is
  assumed on the base
• which can be computed from
• where s is the base pressure, M is the net moment
  about the centerline of the base (MSV.e),
• e is the eccentricity (B/2 x), c B/2, and I
  is the moment of inertia (1B3/12) for unit width.
  Minimum base pressure smin should be greater than
  zero.
• Maximum base pressure smax should be less than
  the allowable compressive stress of the
  foundation material given
• in the table. (page 5)

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• EXAMPLE
• Analyze the stability of given gravity dam for
  the following conditions. The ice thickness at
  the
• reservoir surface is 25 cm with the increase in
  temperature of 2.5 0C/hr. Friction coefficients
• between concretes and concrete-foundation are
  0.75 and 0.65, respectively. Allowable shear
• stress at the foundation level is 2000 kN/ m2,
  allowable compressive and shear stresses in
• concrete are 2500 kN/m2, and 2200 kN/m2,
  respectively. Allowable compressive stress in
• foundation material is 2500 kN/m2. Relief
  drainage may reduce the uplift force by 50. The
• earthquake coefficient is 0.1. Take specific
  weights of concrete and water as 24 kN/m3, and 10
• kN/m3, respectively
• Solution

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Free body diagram is shown below
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The end
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• Thank you