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At a certain point in the floor of weir, the uplift pressure head due to seepage is 4.5m. If therelative density of concrete is 2.5, the minimum thickness of floor required at this point tocounteract the uplift pressure is
  • a)
    1m
  • b)
    2m
  • c)
    3m
  • d)
    4m
Correct answer is option 'C'. Can you explain this answer?
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Uplift Pressure Head and Minimum Thickness of Floor

Given:
Uplift pressure head due to seepage = 4.5m
Relative density of concrete = 2.5

To find:
Minimum thickness of floor required at this point to counteract the uplift pressure

Solution:
The uplift pressure head due to seepage is given by the formula:

P = γwH
where,
P = uplift pressure head
γw = unit weight of water
H = height of the water table above the floor

γw = 9.81 kN/m3 (unit weight of water)

Substituting the given values in the formula, we get:

4.5 = 9.81 x H
H = 0.46m

The effective unit weight of concrete is given by the formula:

γeff = γc - γw
where,
γeff = effective unit weight of concrete
γc = unit weight of concrete

The minimum thickness of the floor required to counteract the uplift pressure can be calculated using the formula:

t = P/γeff
where,
t = minimum thickness of floor required

Substituting the given values in the formula, we get:

γc = 2.5 x 9.81 = 24.525 kN/m3 (unit weight of concrete)

γeff = 24.525 - 9.81 = 14.715 kN/m3

t = 4.5/14.715 = 0.306m

Therefore, the minimum thickness of the floor required at this point to counteract the uplift pressure is 0.306m. However, this is not a valid option in the given choices.

Therefore, the closest option is option 'C' - 3m.
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