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# MODES OF FAILURE OF GRAVITY DAMS

A gravity dam can fail due to the following reasons:

1. Overturning of the dam
2. Sliding of the dam
3. Crushing of the dam or Foundation
4. Development of tension in the dam.

1. Overturning of the Dam.

• If the resultant of all the possible forces (internal as well as external) acting on the dam cuts the base of the dam downstream of the Toe, the darn would overturn unless it can resist tensile stresses.
• To safeguard the dam against overturning, the resultant of the forces should never be allowed to go down stream of the Toe.
• If resultant is maintained within the body of the dam, there will be no overturning.
• All the forces acting on the dam cause moments.
• Some of the forces help maintain stability of the dam, while others try to disturb the stability.
• The moments of the forces, helping dam to maintain its stability are know resisting moments (Mr).
• The moments of the forces that try to disturb the stability of the dam are known as overturning moments (Mo).
• As soon as Mo exceeds Mr overturn of the dam would take place. Factor of safety (F.S.) against overturning can be found out as follows.

$F.S= \frac{Resisting -moment}{Overturning -moment}= \frac{M_{0}}{M_{r}}$

The value of F.S. against overturning should not be less than 1.5.

2. Sliding of the Dam.

• In this mode of failure, the dam fails in sliding.
• The dam as a whole slides over its foundation or one part of the dam may slide over the part of the dam itself, lying below it.
• This failure occurs when the horizontal forces causing sliding are more than the resistance available to it, at that level.
• The resistance against sliding may be due to friction alone or it may be due to a combination of friction and shear strength of the joint. Shear strength develops at the base if benched foundation is provided.
• At other joints the shear strength is developed by laying joints carefully so as to obtain good bond.
• Interlocking of stone blocks in stone masonry also helps increase shear strength.
• In case of low masonry dams shear strength is not taken into account.
• In that case factor of safety against sliding is obtained by dividing net vertical forces by net horizontal forces and multiplying the resultant by coefficient of friction μ.

$Safety-factor -(F.S.)= \frac{\mu \Sigma (V-u)}{\Sigma H}$

where

µ = Coefficient of friction.

∑(V – U) = Net vertical force.

∑H = Sum of the horizontal forces causing sliding

• The value of coefficient of friction varies from 0.65 to 0.75. The value of F.S. should always be greater than one.
• In case of large high dams, the shear strength of the joint should also be considered along with static coefficient of friction.
• In this case factor of safety is know shear friction factor (S.F.F.) Hence

where

µ∑(V – U) and ΣH are the same as stated earlier.

b = Width of the joint or section.

q = Shear strength of the joint which is usually taken as 14 kg/cm2. From a safety point of view, the value of shear friction factor (S.F.F.) should lie between 4 and 5.

The factor of safety against sliding and shear friction factor as per IS: 6512–1972 are as follows.

3. Crushing or Compression Failure.

If the compressive stress developed anywhere in the dam exceeds the safe permissible limit, the dam may fail by crushing of the dam itself or of foundation.

The maximum compressive stress can develop at toe when reservoir is full of water.

If reservoir is empty the maximum compressive stress is likely to develop at the heal of the dam.

The magnitude of maximum compressive and minimum compressive stresses can be found out by using following equation.

$Pn= \frac{V}{b}\left ( 1+\frac{6e}{b} \right )$

where

pn = Value normal stress.

V = Total vertical force.

b = Width of the dam base at level of consideration.

e = Eccentricity of resultant force R from the centre of the base.

H = Total horizontal force.

R = Resultant force.

Plus sign is used to evaluate the amount of maximum compressive stress which will occur at Toe of the dam when reservoir is full and at heel when reservoir is empty.

4. Failure due to Development of Tension.

• Both cement concrete and masonry, are very weak in tension.
• Hence from safety point of view the tension is not allowed to be developed in the dam anywhere.
• We know that minimum compressive stress in the dam.
• The nature of this stress remains
• Negative sign of this stress indicates that nature of this stress is tensile rather than compressive.
• Hence as soon as e exceeds 6 b tension is developed in the dam and dam fails by opening of the joints, as concrete and masonry are almost nil in tension.
• When reservoir is full of water, tension is likely to develop at heal and when reservoir is empty tension is likely to develop at Toe of the dam.
• In other words it can be stated that until resultant of the forces lies within the middle third width of the base tension cannot develop anywhere in the dam.
• In the case of gravity dams, having moderate height, no tension is allowed to be developed anywhere.
• However in case of very high dams, a small tensile stress may be permitted to be developed, but only for short durations during heaving floods or earthquakes.
• Once tensile cracks develop at heel, the dam can not be rendered safe.
• Due to tension cracks, uplift pressure gets increased and consequently net vertical downward force is reduced.
• This causes further shifting of the resultant towards the Toe and this leads to further lengthening of the cracks.
• Due to lengthening of the cracks, effective width of base is further reduced and compressive stress at toe further increases.
• Ultimately compressive stress at toe increases to such an extent that dam fails by crushing at Toe.

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