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:

For hydrological risk problems, remember the formula \(R = 1 - (1 - 1/T)^n\). A useful approximation for small \(P\) (or large \(T\)) is \(R \approx n/T\). In this case, \(50/100 = 0.5\), which is a rough estimate.

Answer 1

Step 1: Variables Identification.
$n = 50$ (Design life), $T = 100$ (Return Period).
Step 2: Risk Formula Application.
The probability that a flood occurs at least once in $n$ years is given by: $R = 1 - (1 - P)^n$, where $P = 1/T$. $R = 1 - (1 - 0.01)^{50} = 1 - (0.99)^{50}$.
Step 3: Numerical Solving.
$(0.99)^{50} \approx 0.605006$. Risk $= 1 - 0.605006 = 0.39499 \approx 0.395$.