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

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

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

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

2) Uplift Pressure Without Gallery With Gallery

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

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

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]

4) Wave Pressure F‹32 km F›32 km

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

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

7) Weight of dam itself, as a stabilizing force

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

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) 49050 kN 2) 21295 kN 3) 72.10kN/m2 Pe =5234.7 KN

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

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

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

4) Tension

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

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.

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 Moment @ toe [ Clock & Anti Clock wise] Find O M [∑ Mo] & R M [∑ MR] @ toe. Find ∑ M = ∑ MR - ∑ Mo Location of Resultant force R from toe 8) Find Eccentricity e 9) Normal Stress at toe & Heel

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

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.

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.

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.

b) Graphical Method

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.

Elementary profile of a Gravity Dam

a) Reservoir empty condition

b) Reservoir full condition 1) Stress Criterion

2) Stability or Sliding Criterion

Normal stress in elementary profile under reservoir full condition

Principal stress in elementary profile

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

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

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

Shear keys or Key Ways

Foundation Treatment in Gravity Dam Preparation of Surface Grouting the foundation

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