In this article, we explain various forces acting on gravity dam like water force, ice pressure, earthquake forces, uplift pressure, etc with formula. components of gravity dam, design criteria of gravity dam like overturning criteria, sliding criteria, tension criteria, etc. therefore read the article till the end.

**What is gravity dam?**

Gravity dam is a types of dam in which all the forces resist by its own weight and transfer to the soil by the action of gravity.

- Gravity dam is most durable.
- Gravity dam require less maintenance.
- Gravity dam require high construction cost.
- Gravity dam easy to construct on any site.

The line of the upstream face in sloping, is taken as the reference line for layout purpose, etc. and is known as the base line of the dam or the **axis of dam.**

The highest gravity dam in the world is **GRAND DIXENCE dam** in Switzerland (284m).

**Components of Gravity Dam:**

- Parapet Wall
- Crest
- Spillway
- Sluice way
- Toe
- Heel
- Free board
- Drainage gallery

**1. Parapet wall:**

Parapet walls are provides on top of the Gravity dam on both side for the safety purpose.

**2. Crest:**

Topmost surface (top level of dam) of the gravity dam is known as crest. In case of overflow dam, water flow over the crest. But in non-overflow dam, water flow below the crest.

**3. Spillway:**

Spillway is a water release concrete structure, constructed across the river within dam or out of dam for the purpose of removing excessive water of reservoir.

**4. Sluice way:**

Sluice way is also known as sluice wall. Sluice way is a special arrangement, constructed near the ground level, for the purpose of removing accumulated silt from the reservoir.

**5. Toe:**

Toe is the foot (lowest portion) of the dam at the downstream side.

**6. Heel:**

Heel is the foot (lowest portion) of the dam at the upstream side.

**7. Free board:**

Free board is the vertical distance between Maximum flood level to top of the dam.

**8. Drainage Gallery:**

A drainage gallery is provided in the dam to tackle with Uplift pressure. Drainage gallery is also provided for the inspection purpose in the dam. A higher dam is necessary required drainage galleries.

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**Forces acting on gravity dam:**

- Water pressure
- Uplift pressure
- Silt pressure
- Earthquake Force
- Ice pressure
- Wave pressure
- Self weight of dam

**1. Water pressure:**

Water pressure is major load of gravity dam which is calculated by hydrostatic pressure law. We separate water pressure in two cases which are explain below.

**Case-1 : No Tail water in Downstream side**

In this case water pressure is equal to

**P _{1 }= (1/2)×(Y_{w}h^{2})**

Where,

P_{1} = Water pressure acting on dam

Y_{w} = Unit weight of water

h = height of water in upstream side.

This water pressure acting on dam at h/3 height from the bottom.

**Case-2 : Tail water in Downstream side**

If the tailwater present on the downstream side, that means it is also developed pressure and acts on the dam. Therefore tail water pressure is also calculated by hydrostatic pressure law.

**Upstream side water pressure**

**P _{1} = (1/2)×(Y_{w}h^{2})**

This water pressure acting on dam at h/3 height from the bottom.

Where,

P_{1} = Water pressure acting on dam

Y_{w} = Unit weight of water

h = height of water in upstream side.

**Tail water pressure**

**P _{2 }= (1/2)×(Y_{w}h’^{2})**

This water pressure acting on dam at h’/3 height from the bottom.

Where,

P_{2} = Tail water pressure acting on dam

Y_{w} = Unit weight of water

h’ = height of tail water in downstream side.

**2. Uplift pressure:**

Water seeping from the pores, fissures, cracks etc, exert uplift pressure on dam. Calculation of uplift pressure explain below.

**Case-1: No drainage gallery in gravity dam with no tail water**

**P _{3} = (1/2)×(Y_{w}h × B)**

**Case-2: No drainage gallery in gravity dam with tail wate**

P_{3} = Area of stress diagram

**P _{3 }= (1/2) × (Y_{w}h × B) + (1/2)×(Y_{w}h’×B)**

**Case-3 : Drainage gallery in gravity dam with tail water**

**P _{3} = area of stress diagram.**

Where,

P_{3} = Uplift pressure on gravity dam

Y_{w} = Unit weight of water

h = height of water

B = base width of dam

h’ = height of tail water

**3. Silt pressure:**

If silt deposited on upstream side, which exert pressure on dam that is known as silt pressure. Silt pressure represent in the form of rankine’s formula which is given below.

**P _{s} = (1/2) × (Y_{sub }× h_{s}^{2 }× K_{a})**

Where,

P_{s }= Silt pressure

Y_{sub } = Submerged density of water

h_{s }= Height of silt deposited in upstream side

K_{a} = Coefficient of active earth pressure

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**4. Earthquake pressure:**

If the gravity dam is constructed in seismic region, then it is necessity to design gravity dam including earthquake forces.

The gravity dam is affect by horizontal acceleration and vertical acceleration generated through earthquake force.

The effect of horizontal acceleration and vertical acceleration explain below.

**Effect of Vertical acceleration:**

Vertical acceleration may be act in downward or upward. If it act as upward direction then foundation of gravity dam lifted upward. Hence the effective weight of dam increases, stress will increase.

If the vertical acceleration act downward then the foundation try to move downward. Hence the effective weight of dam decreases stability of dam decrease.

Such acceleration exerts inertia force. Calculation of inertia force is given below.

**= (W/g) × α _{v}**

Net effective weight of dam

= **W(1 – K _{v})**

Where,

W = total weight of dam

α_{v} = vertical acceleration due to earthquake

K_{v }= Fraction of gravity

**K _{v }= α_{v}/g**

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**Effect of horizontal acceleration:**

- Hydrodynamic Pressure
- Horizontal inertia force

**1. Hydrodynamic pressure:**

Horizontal acceleration acting toward the reservoir causes a momentary increase in water pressure, as the foundation and dam accelerate towards the reservoir and the water resists the movement owing to its inertia. The extra pressure exerted by this process is known as hydrodynamic pressure.

**P _{e }= 0.726 × C_{m} × K_{h} × Y_{w} × h^{2}**

And the moment of the force from the base is

**M _{e } = 0.442 × P_{e} × h^{2}**

Where,

C_{m} = 0.735 (θ/90)

θ = Angle in degree which us side of dam make with horizontal

K_{h} = Fraction of gravity

**= α _{h}/g**

h = height of water

**2. Horizontal inertia force:**

Horizontal acceleration produce inertia force.

**Force = (W/g) × α _{h}**

**5. Wave pressure:**

Waves are generated on the surface of the reservoir by the blowing winds, which causes a pressure toward the downstream of gravity dam.

Wave pressure depends on wave height.

**P _{w} = 2 × Y_{w} × h_{w}**

If F< 32 km

**h _{w} = (0.032(V×F)^(1/2)) + 0.763 – 0.271 (F)^(3/4)**

and if F> 32km

**h _{w} = (0.032(V×F)^(1/2))**

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**6. Ice pressure:**

In cold countries, the ice formed in the reservoir. This ice may be expanded or melt due to temperature variation. Due to the melting or expanding of ice, exerting pressure on the gravity dam.

This force acts linearly along the length of the dam and the reservoir level.

The magnitude of this force varies from **250 to 1000 kN/m3** depending upon the temperature variation.

**7. Self weight of dam:**

Self weight of gravity dam is calculated by multiplying volume (area × 1) of dam with is density.

**Area × 1 **is a volume of dam per meter length.

Self weight of dam is a resisting force of gravity dam that is resist all type of external forces.

**P _{4} = Y_{t} × volume (area × 1)**

**Design criteria of Gravity dam:**

- By overturning about the toe
- By crushing
- By development of tension, crushing ultimate failure by crushing
- Sliding failure

**1. By overturning about the toe**

When the resultant force pass through the toe of dam at that situation dam overturn.

The ratio of anti-clockwise moment about toe to clockwise moment about toe is called as** Factor of Safety against Overturning.**

**2. Crushing:**

If the compressive stress exceed the allowable stress of concrete, which causes failure of dam against crushing.

Generally **allowable stress of concrete is 3000 kN/m2**

**P _{max }= (ΣV/B) × ( 1+( 6e/B))**

**P _{min} = (ΣV/B) × ( 1-( 6e/B))**

Where,

ΣV = Total vertical force

e = eccentricity

B = base width of dam

**3. By development of tension:**

Gravity dam or other concrete structure are design in such a way that no tension developed anywhere. If tensile stress appear in dam causing a cracks in dam.

**The maximum permissible tensile stress for concrete = 500 kN/m2**

In order to ensure that no tension is developed anywhere in dam, **we must ensure that P _{min }is at the most equal to zero.**

Maximum value of eccentricity that can be** permitted on either side of the centre is equal to B/6**

**4. Sliding failure:**

Sliding or shear failure of the dam will occur when the net horizontal force at base of dam exceed the frictional resistance of base of dam.

Simply,

Sliding occur when, **Net horizontal Force > µΣV**

**Factor of safety against sliding** = **(µΣV)/ΣH**

In high dam, for economical design,

**Shear force friction Factor = (µΣV + Bq)/ ΣH**

Where,

µ = poisson’s ratio, Generally varies from 0.65 to 0.75

B = base width of dam

q = Average shear strength

**for poor rock = 1400kN/m2****for good rocks = 4000kN/m2**