# FORCES ACTING ON A GRAVITY DAM

- A detailed sketch of a gravity dam is shown in Fig. 13.1.
- All the predominant forces, that act on the dam, have been shown in the figure itself.
- The forces that act on the dam are the following:

- Weight of the dam
- Horizontal hydrostatic pressure due to water
- Uplift pressure due to water percolated under the dam
- Earthquake pressure
- Wind pressure
- Ice pressure
- Wave pressure
- Pressure due to silt deposited on U/S face.

- Out of above eight forces, acting on the dam, first three forces are the major forces that are considered in the design.
- All other forces are not of much significance and are considered only under specific conditions.

**1. Weight of the Dam.**

- It is the most important force, particularly for gravity dams.
- Stability of the dam largely depends upon this force.
- For the design purpose only unit length of the dam is considered.
- Cubic content of the cement concrete is determined for unit length of the dam.
- This cubic content when multiplied by the density, gives the total weight (W) of the dam.
- The total weight (W) is considered acting at the C.G. of the dam section.
- The position of C.G. of the dam section can be found out by dividing the dam section into several triangles, rectangles, and trapeziums and by taking moments of these weights about any point at the base of the dam.

**2. Horizontal Hydrostatic Pressure due to Water.**

- This is the largest external force acting on the dam.
- It has the largest capacity for disturbing the stability of the dam.
- It is a horizontal force which acts at the C.G. of the pressure distribution diagram, due to water.
- The pressure distribution diagram is always triangular with zero value at surface of the water and increasing linearly to maximum at the base of the dam.
- The value of maximum horizontal pressure at base of the dam is wh where w is the density of water in kg/m3 and h the depth of water in meters.
- Since pressure distribution diagram due to water is triangular, the value of the total horizontal pressure (P) due to water, will be area of the triangle.
- This force P will act at C.G. of the pressure distribution triangle i.e. 3/h from the base of the dam.

\[Hence- total- horizontal- pressure- P= wh\times \frac{h}{2}= \frac{wh^{2}}{2}\]

- This force P will act at h/3 from base of the dam.
- Similarly if there is tail water of height h’ on the D/S side, it exerts a horizontal pressure (P’) of opposite nature.

\[P= \frac{wh^{2}}{2}\]

where P’ = Horizontal force due to tail water. h’ = Depth of tail water from the base of the dam.

- P’ would be considered acting at 3 h′ from the base of the dam.
- For water, density is considered as 1000 kg/m3.

**3. Uplift Pressure due Seeping Water under the Dam. **

- The water that seeps through the pores of the material comprising dam and foundation, causes uplift pressure and tries to tilt or topple the dam.

- A part of the weight of the dam would get neutralized by uplift pressure and thus net foundation reaction due to vertical forces will be reduced.
- Intensity of uplift pressure is maximum at U/ S end of the dam and it goes on decreasing towards the D/S end.
- As some water can see into the concrete dam also, the uplift pressure may occur anywhere in the dam also.
- It is very difficult to find out the value of uplift pressure accurately.
- It depends upon the factors like, cut off on U/S side, fissures in the foundation rocks, drainability of the foundation etc.
- There are two schools of thought as to on how much area uplift pressure should be considered as acting.
- According to one thought one-third to two-third area of foundation should be considered effective.

**U.S.B.R. Recommendations. **

- According to U.S.B.R. intensity of uplift pressure at D/S (Toe) and U/S (heal) is taken equal to the hydrostatic pressure of water.
- The variation of uplift pressure from heal to toe is linear or straight line.
- In order to release uplift pressure, drainage galleries are provided in the body of the dam.