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A bridge has an expected life of 50 years and is designed for a flood magnitude of return period 100 years. What is the risk associated with this hydrologic design?
  • a)
    1 - (0.99)50
  • b)
    (0.5)50
  • c)
    (0.99)50
  • d)
    (0.99)100
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A bridge has an expected life of 50 years and is designed for a flood ...
Risk = Probability of flood being exceeded at least once over a period of n years.
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A bridge has an expected life of 50 years and is designed for a flood ...
Risk Assessment of Hydrologic Design

Expected Life of Bridge: 50 years
Flood Magnitude: Return Period 100 years

To assess the risk associated with the hydrologic design of the bridge, we need to calculate the probability of the design flood occurring during the expected life of the bridge.

1. Calculate the Annual Exceedance Probability (AEP) of the design flood:
AEP = 1/ Return Period
AEP = 1/100 = 0.01

2. Calculate the probability of the design flood NOT occurring in any given year:
P = 1 - AEP
P = 1 - 0.01 = 0.99

3. Calculate the probability of the design flood NOT occurring in all 50 years of the expected life of the bridge:
P50 = P^50
P50 = 0.99^50 = 0.605

4. Calculate the risk associated with the hydrologic design:
Risk = 1 - P50
Risk = 1 - 0.605 = 0.395 or 39.5%

Therefore, the risk associated with the hydrologic design of the bridge is 39.5%. The correct answer is option A, which represents the probability of the design flood NOT occurring over the expected life of the bridge.
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A bridge has an expected life of 50 years and is designed for a flood magnitude of return period 100 years. What is the risk associated with this hydrologic design?a)1 - (0.99)50b)(0.5)50c)(0.99)50d)(0.99)100Correct answer is option 'A'. Can you explain this answer?
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