1. Concrete (Gravity) Dam Engineering
Module-III
Concrete (Gravity) Dam Engineering

2. Gravity Dam
A gravity dam is a structure which is so designed that its own weight resists all the external forces.

3. Forces Acting on a Gravity Dam
1) Water Pressure (When upstream face is straight)

4. When Upstream face is partly vertical and partly inclined:
Horizontal component PH
Vertical component Pv

5. 2) Uplift Pressure
Without Gallery
With Gallery

6. 3) Pressure due to Earthquake Forces
Horizontal acceleration
Vertical acceleration
Effect of Horizontal acceleration
1) Inertia force:

7. Effect of Horizontal acceleration
2) Hydrodynamic Pressure:
Von-Karman

8. Effect of Vertical acceleration
Case I: (acceleration vertically Upward)
Net weight of dam = W [1 + α]
Case II : (acceleration Vertically downward)
Net weight of dam = W [ 1-α]

9. 4) Wave Pressure
F‹32 km
F›32 km

10. 5) Silt Pressure
Where ф is angle of internal friction of deposited soil

11. 6) Ice Pressure
Consider at could countries
A sheet of ice strikes to the face of dam
Ice melts and expands due to temperature variations

12. 7) Weight of dam itself, as a stabilizing force

13. Ex: Figure shows the section of gravity dam (non-overflow section) built of concrete. Compute the following
Water pressure
Uplift pressure
Earthquake pressure
Weight of the dam
Wave pressure
Consider specific weight of concrete = 24 kN/m3 and fetch = 12 km,
Wind velocity 80 kmph, αh = 0.1 g

14. Water pressure
2)Uplift pressure
3)Earthquake pressure
4)Weight of the dam
5)Wave pressure
Consider specific weight of concrete = 24 kN/m3 and fetch = 12 km,
Wind velocity 80 kmph, αh = 0.1 g
Ans: 1) kN 2) kN 3) 72.10kN/m2 Pe = KN

15. Modes of failure and stability criteria of gravity dams
1) Overturning or rotation about toe

16. 2) Sliding or Shear failure
∑H > resistance available at any level
μ is varies from 0.65 to 0.75
FS> 1

17. 3) Compression or crushing at the toe
Normal Stress > allowable com. Str.
Nor. Str. Pn = Dir. Str + Ben. Str.

19. 4) Tension

20. Stability Analysis
We check the stability of the design again all modes of failure.
Overturning ii) Sliding iii) Compression iv) tension
It can be carried out by
Gravity method or two-dimensional method
a) Analytical Method
b) Graphical Method
2) Trial load twist method
3) Slab analogy Method
4) Lattice analogy Method

21. Gravity method or two-dimensional method
Assumption:
The dam is considered to be composed of number of vertical cantilevers each of 1 m thick. They act independent of each other.
The dam and its foundation behave as a single unit
The external loads are resisted entirely by the weight of individual cantilevers
The dam is composed of isotropic and homogeneous material
The stresses developed in dam’s body and its foundation are within the elastic limits.

22. a) Analytical Method
Consider unit length of the dam
Calculate the magnitude & direction of all V force, ∑ V
All Horizontal force H, ∑ H
Compute all force about toe
Calculate the toe [ Clock & Anti Clock wise]
Find O M [∑ Mo] & R M [∑ toe. Find ∑ M = ∑ MR - ∑ Mo
Location of Resultant force R from toe
8) Find Eccentricity e
9) Normal Stress at toe & Heel

23. 10) Compute the maximum normal stress
11) Find the FS against Overturning
12) Find the FS against sliding
FS> 1.5
SF> 1, SFF within 1.5 to 4

24. Ex: The profile of gravity dam with reservoir as figure
Ex: The profile of gravity dam with reservoir as figure. If the coefficient of friction is 0.75, is the dam safe against sliding & Overturning? Take weight density of concrete = 2.4 tonnes/cum.

25. Ex: Check the stability of given dam section as shown in figure
Calculate the stresses developed at the heel and toe. Assume the unit
Weight of concrete as 24 kN/m3 and that of water = 10 kN/m3. take a value of acceleration due to earthquake αh = 0.1 g for horizontal direction.

27. Ex: A section of concrete gravity dam
Ex: A section of concrete gravity dam. Check the stability of section for reservoir empty and full conditions. A tail water depth of 5 m is assumed to be present when reservoir is full and there is no tail water when reservoir is empty.
The earthquake forces are equal to 0.1 g for horizontal force and 0.05 g for vertical forces. The uplift pressure is taken equal to the hydrostatic pressure at either ends and is assumed to act over 2/3 area of section. Take unit weight of concrete equal to 24 kN/m3. Also find the principal and shear stress at the toe and heel of the dam.

28. b) Graphical Method

29. 1 Divide the entire section of dam into horizontal sections 1-1, 2-2, 3-3, etc. at some suitable interval or at places where slope changes.
2. For each section, compute the sum of all the horizontal forces (∑H) and vertical (∑ V) acting about that particular section
3. Locate the line of action of resultant graphically for each section
4. Join all the points where individual resultant cuts the individual section. Thus a single line is obtained
5. This line represents the resultant force and it should lie within the middle third of base width, for no tension to develop
6. Adopt the same procedure for reservoir full condition as well as reservoir empty condition.
7. The resultant for both the cases must lie in the middle third of the base width.

30. Elementary profile of a Gravity Dam

31. a) Reservoir empty condition

32. b) Reservoir full condition
1) Stress Criterion

34. 2) Stability or Sliding Criterion

35. Normal stress in elementary profile under reservoir full condition

36. Principal stress in elementary profile

37. Practical profile of a Gravity Dam
Free board
2) Top Width

38. Limiting Height of a Gravity Dam: High and low Gravity dam

40. Galleries:
A gallery is an opening or passage left in the body of the dam.

41. Shear keys or Key Ways

42. Foundation Treatment in Gravity Dam
Preparation of Surface
Grouting the foundation

43. Prepared by, Dr. Dhruvesh Patel www.drdhruveshpatel.com
Source:
Sincere thanks to Mahajan Publishing house for photographs and supplement materials.