Gravity Dam

Topics:
1. Types of Gravity Dam
2. Forces Acting on a Gravity Dam
3. Causes of failure of Gravity Dam
4. Elementary Profile of Gravity Dam
5. Practical Profile of Gravity Dam
6. Limiting height of Gravity Dam
7. Drainage and Inspection Galleries

1. gravity dam (water resources engineering – ii) Unit – II Rambabu Palaka , Assistant Professor BVRIT

2. Learning Objectives Types of Gravity Dam Forces Acting on a Gravity Dam Causes of failure of Gravity Dam Elementary Profile of Gravity Dam Practical Profile of Gravity Dam Limiting height of Gravity Dam Drainage and Inspection Galleries

3. Types of Gravity Dam A Gravity dam is a structure so proportioned that its own weight resists the forces exerted upon it. Types: Masonry Dam Concrete Dam Suitable across gorges with very steep slopes where earth dams might slip.

4. Advantages of Gravity Dam Advantages: Strong, Stable and Durable Suitable for moderately wide valleys having steep slopes Can be constructed to very great heights Suitable for an overflow spillway section Maintenance cost is very low Does not fail suddenly

5. Disadvantages of Gravity Dam Disadvantages: Gravity dams of great height can be constructed only on sound rock foundations. Initial cost is more than earth dam Takes longer time in construction Require more skilled labor than earth dam Subsequent raise is not possible in a gravity dam

6. Forces acting on Dam Water Pressure Weight of Dam Uplift Pressure Pressure due to earthquake Ice Pressure Wave Pressure Silt Pressure Wind Pressure 1 1 1 2 3 4 6 7 1

7. 1. Water Pressure This is the major external force acting on dam Pressure Components on both upstream and downstream are: Vertical Component Horizontal Component Unit weight of water, γ w =1000 kg/m 3

8. 2. Weight of Dam This is the major resisting force Generally unit length of dam is considered The cross section of dam may be divided into several triangles and rectangles and weights W1, W2, W3 etc., may be computed The total weight W of the dam acts at the C.G. of its section. Weight = Volume per unit length x Density of material

9. 3. Uplift Pressure The uplift pressure is defined as the upward pressure of water as it flows or seeps through the body of the dam or its foundation. Uplift Pressure (No Gallery)

10. 4. Pressure due to Earthquake Earthquake waves imparts accelerations to the foundations under the dam and causes its movement This earthquake wave may travel in any direction For design purpose, Horizontal and Vertical directions are considered. Seismic Force = Mass x Earthquake Acceleration According to IS 1893-2002, India was divided into Four zones: zone II, III, VI, and V.

11. Earthquake Acceleration Earthquake Acceleration is usually designated as fraction of the acceleration due to gravity It is expressed as α .g where α is known as Seismic Coefficient

12. Seismic Coefficient Seismic coefficient is divided into Horizontal Seismic coefficient, α h Vertical Seismic Coefficient, α v = .75 α h α h can be determined by one of the two methods Seismic Coefficient Method < 100m height of the dam Response Spectrum Method > 100m height of the dam

13. Seismic Coefficient Method As per IS: 1893-1984, Horizontal Seismic coefficient, α h = 2 α Where α = Basic Seismic Coefficient Basic Seismic Coefficient as per IS 1893:1984 Seismic Zone II III IV V Basic Seismic Coefficient 0.02 0.04 0.05 0.08

14. Response Spectrum Method As per IS: 1893-1984, Horizontal Seismic coefficient, α h = 2 F (Sa/g) Where F = Seismic Zone Factor Seismic Zone Factor as per IS 1893:1984 Seismic Zone II III IV V Seismic Zone Factor, F 0.10 0.20 0.25 0.40 IS: 1893-1984 recommends a damping of 5% for dams * Damping is an influence within or upon an oscillatory system that has the effect of reducing, restricting or preventing its oscillations.

15. Effect of Earthquake Acceleration Effect of Horizontal Earthquake Acceleration, α h g 1. Inertia Force in the body of the dam Inertia Force = Force x Earthquake Acceleration = (W/g) ( α h g) = W. α h 2. Hydrodynamic Pressure of water P ey = C y α h w h  Equation 8.16 (Page 370) where C y is a dimensionless pressure coefficient The Inertia Force is the product of mass and acceleration and this force acts in the direction opposite to that of the ground motion. If Reservoir is Full  Inertia Force acts in downstream direction If Reservoir is Empty  Inertia Force acts in upstream direction

16. Effect of Earthquake Acceleration… Effect of Horizontal Earthquake Acceleration, α h g Horizontal Shear, P eh = 0.726 P ey h Moment, M eh = 0.299 P ey h 2 Vertical Component of Shear, W h = (P e2 - p e1 ) tan φ where φ = actual slope of the u/s face P e2 = Horizontal shear at elevation of the section being considered P e1 = Horizontal shear at elevation at which the slope of the dam face commences

17. Effect of Vertical Earthquake Acceleration Due to Vertical Earthquake Acceleration, α v g, the dam as well as reservoir water are accelerated vertically upwards or downwards. An acceleration upwards increases the weighs and an acceleration downwards decreases the weighs. Altered weighs = w(1+ α v ) or w(1- α v )

18. 5. Ice Pressure The ice formed on water surface of the reservoir is subjected to expansion and contraction due to temperature variations Coefficient of thermal expansion of ice is 5 times more than concrete The dam face has to resist the force due to expansion of ice

19. 5. Ice Pressure This force acts linearly along the length of the dam, at reservoir level IS: 6512-1984 recommends 250 kN /m 2 applied to the face of dam over the anticipated area of contact of ice with the face of the dam.

20. 6. Wave Pressure Waves are generated on the reservoir surface because of wind blowing over it. Where h w = height of wave in m, V = wind velocity in KMPH, F = Fetch or straight length of water expanse in Km Wave Pressure, P w = 2 w h w 2 and it acts at a distance of 3h w /8 above the reservoir surface

21. 7. Silt Pressure The river brings silt and debris along with it. The dam is, therefore, subjected to silt pressure, P s , in addition to water pressure Where γ ’ = submerged unit weight of silt h = height of silt deposit Φ = Angle of internal friction According to IS : 6512-1972, the silt pressure and water pressure exist together in submerged silt. The following are recommended for calculating forces: P sh = 1360 Kg/m 3 P sv = 1925 Kg/m 3

22. 8. Wind Pressure It is a minor force acting on dam Acts on Superstructure of the dam Normally, wind pressure is taken as 1 to 1.5 kN /m 2

23. Combination of Loading for Design USBR Recommendations: Normal Load Combination Extreme Load Combination Reservoir Empty Condition Normal water surface elevation, ice pressure, silt pressure and normal uplift Normal water surface elevation, earthquake force, silt pressure and normal uplift Maximum water surface level, silt pressure and normal uplift Maximum flood water elevation, silt pressure and extreme uplift with no drain in operation to release the lift

24. Combination of Loading for Design IS Recommendations: (IS: 6512-1984) Gravity dam design shall be based on the most adverse conditions A, B, C, D, E, F, and G Construction Condition (A) Normal Operating Condition (B) Flood Discharge Condition (C) Other Load Combinations such as D,E,F and G

25. Causes of Failure of Dam Overturning Sliding Compression or Crushing Tension

26. Overturning Failure The overturning of the dam section takes place when the resultant force at any section cuts the base of the dam downstream of the toe. Factor of Safety (F.S.) should not be less than 1.5

27. Sliding Failure A dam will fail in sliding at its base, or at any other level, if the horizontal forces causing sliding is more than the resistance available to it that level For Low Gravity Dams, Factor of Safety against Sliding (F.F.S.) should be greater than 1 Coefficient of friction μ varies from 0.65 to 0.75

28. Sliding Failure For Large Gravity Dams, Shear Strength of joint should also be considered for economical design. Shear Friction Factor, Where, c = Shear strength of joint varies from 1300 to 4500 kN /m 2, b = Width of the joint

29. Compression or Crushing The maximum compressive stress occurs at the toe and for safety, this should not be greater than the allowable compressive stress for the foundation material.

30. Tension Failure If eccentricity e >b/6, then Tension will be developed at the heel of the dam. Since concrete can not resist Tension, No tension is permitted at any point of the dam under any circumstances

31. Principal Stresses Where Compressive Stress, Intensity of water Pressure, p = γ h p may change depends upon Earthquake Pressure p = p-p e for downstream and p = p+p e for upstream Intensity of Water Pressure normal to the face of dam Uplift Pressure Principal Stress

32. Elementary Profile of Gravity Dam No any other force except forces due to water such as weight of dam, water pressure and uplift Pressure Same shape as hydrostatic pressure distribution diagram e = b/6 If Reservoir is empty, then c= 0

33. Practical Profile of a Gravity Dam Practical profile has a provision of roadway at top, addition loads due to roadway and free board. Resultant force of the weight of dam and water pressure falls outside the middle third of the base of the dam and causes tension at upstream when the reservoir is full To eliminate tension, some masonry is to be provided to the upstream. Free Board: Free board is the margin provided between top of dam and HFL in the reservoir to prevent the splashing of the waves over the non-overflow dam. Fee Board = 3/2 h w Where h w is wave pressure Modern Practice is to provide a maximum Free Board equal to 3 to 4% of the height of dam and it should not be less than 1m in any case Top Width = 14% of height of water level

34. Limiting Height of Gravity Dam If the height of dam is greater than H, then it is known as High Gravity Dam

35. Drainage and Inspection Galleries A gallery is a formed opening left in a dam It runs in longitudinal direction horizontally or on a slope Purpose: To drained off the seepage water which occurs constantly through the upstream face of the dam To provide access to observe and measure the behavior of structure To provide an access needed for the operation of outlet gates and spillway gates

36. Previous Questions What is a Gravity Dam? Write down the profile of a Gravity Dam? Explain the merits and demerits of Gravity Dam? List out the various forces acting on a Gravity Dam? Explain overturning and sliding of a Gravity Dam? What is the elementary profile of a Gravity Dam and how it is deduced? What should be the maximum depth of a elementary profile of a gravity dam, if safe limit of stress on the Masonry should not exceed 1500 KN/m 2 ? State the general conditions of stability of gravity dams. Explain step wise procedure of analyzing High Gravity Dams? What is a Gallery in a Dam? List out the various purposes for which a gallery is formed in the dams?

37. Reference Chapter 8 Irrigation and Water Power Engineering  By Dr. B. C. Punmia , Dr. Pande Brij Basi Lal , Ashok Kr. Jain, Arun Kr. Jain