Question

A bridge has an expected design life of 50 years. It is designed for a flood discharge of 1000 m\(^3\)/s, which corresponds to a return period of 100 years. Determine the risk (probability) that the design flood will be equalled or exceeded at least once during the design life of the bridge. (Enter the numerical value of risk in decimal form, correct up to three decimal places.)

Hint:

Remember the formula for hydrological risk: \(R = 1 - (1 - 1/T)^n\). It's a common application of binomial probability for "at least one success" over \(n\) trials.

Answer 1

Step 1: Define Basic Probabilities.
Return period ($T$) = 100 years. Annual probability of occurrence ($P$) = $1/T = 1/100 = 0.01$. Annual probability of non-occurrence ($q$) = $1 - P = 0.99$.
Step 2: Calculate Reliability.
Reliability is the probability that the event occurs zero times in $n$ years. For $n = 50$ years: Reliability $= q^n = (0.99)^{50} = 0.605006$.
Step 3: Calculate Risk.
Risk is the probability of the event occurring at least once: Risk $= 1 - \text{Reliability}$. Risk $= 1 - 0.605006 = 0.394994$. Rounding to three decimal places, Risk $= 0.395$.