What is the risk associated with the bridge design in GATE Civil 2026 Set-1 Q55?

The risk is 0.40. With return period T=100 years, the annual exceedance probability p=1/100=0.01. Over a design life of n=50 years, Risk = 1-(1-p)^n = 1-(0.99)^50 = 1-0.605 = 0.395 ≈ 0.40. This means there is a 40% probability that the design flood will be exceeded at least once during the 50-year life of the bridge.

What is the risk formula used in flood hydrology in GATE Civil 2026 Set-1 Q55?

Risk = 1 - (1 - 1/T)^n, where T is the return period and n is the design life. The term (1-1/T)^n is the probability that the design flood is NOT exceeded in any of the n years. Subtracting from 1 gives the probability that the design flood is exceeded at least once during the structure's life.

Why is there a 40% risk even though the bridge is designed for a 100-year flood?

A 100-year return period flood has a 1% chance of occurring in any given year. Over 50 years, the cumulative probability of at least one such event occurring is Risk = 1-(0.99)^50 = 0.40 = 40%. This highlights that designing for a rare flood does not eliminate the risk — it only reduces the annual probability. Longer design lives accumulate higher total risk.

Flood Design Risk Return Period Bridge Life Hydrology | GATE Civil 2026 Set-1 Q55

Civil Engineering > GATE 2026 SET-1 > Hydrology

A bridge with an expected life of 50 years is designed for a flood of 10000 m³/s corresponding to the return period of 100 years. The risk associated with this design is _____________ (rounded off to two decimal places).

Correct : 0.40

Risk in hydrology is the probability that a design flood will be exceeded at least once during the design life of the structure.
The probability of the design flood being exceeded in any single year = 1/T = 1/100 = 0.01
The probability of the flood NOT being exceeded in any single year = 1 − 0.01 = 0.99
The probability of the flood NOT being exceeded in all 50 years = (0.99)⁵⁰ = 0.6050
Therefore the risk — probability of exceedance at least once in 50 years:
Risk = 1 − (0.99)⁵⁰ = 1 − 0.6050 = 0.3950 ≈ 0.40
This means there is a 40% chance that the design flood of 10000 m³/s will be exceeded at least once during the 50-year life of the bridge, even though it was designed for a 100-year return period flood.
Correct answer: 0.40 ✓

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