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بسم الله الرحمن الرحيم. CONRETE GRAVITY DAMS السدود الكونكريتية الوزنية . م.م حيدر فاضل عذاب جامعة الكوفة/ديوان الجامعة/الشؤون الهندسية. -Concrete gravity dams are constructed such that their own weight resist the forces exerted upon it . During design, the following should be checked:
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CONRETE GRAVITY DAMSالسدود الكونكريتية الوزنية • م.م حيدر فاضل عذاب • جامعة الكوفة/ديوان الجامعة/الشؤون الهندسية
-Concrete gravity dams are constructed such that their own weight resist the forces exerted upon it .
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
1. Forces Acting on Gravity Dams. • The weight Wc (dead load) of the dam. • Hydrostatic forces. • Uplift Forces • Forces due to sediment accumulation. • Ice loads • Earthquake force on the dam body, Fd • Dynamic force in the reservoir induced by Earthquake. • Forces on Spillways.
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 `
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. Fw=0.726Ckγh1^2 ,and where θ ' 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. • ΣF = ρQΔV where ρ is the density of water, Q is the outflow rate over the spillway crest and ΔV is the change in the velocity between sections 1 and 2.
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, ΣMr is the resisting moments about the toe, and ΣMo 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
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 τs 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 σ is the base pressure, M is the net moment about the centerline of the base (M=ΣV.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 σmin should be greater than zero. Maximum base pressure σmax should be less than the allowable compressive stress of the foundation material given in the table. (page 5)
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:
