Question

A flood control structure having an expected life of n years is designed by considering a flood of return period T years. When T = n, and n \to \infty, the structure’s hydrologic risk of failure in percentage is} _________ %. (round off to one decimal place)

Hint:

Risk of failure in flood control structures is inversely proportional to the return period, with the risk approaching zero as the return period increases significantly.

Answer 1

Correct Answer: 63

The risk of failure \( R \) is given by:
\[ R = \frac{1}{T} \times 100 \] Where:
- \( T = n \) (return period is equal to the expected life of the structure)
- \( n \to \infty \)
Thus, the risk of failure for \( T = n \) and \( n \to \infty \) is:
\[ R = \frac{1}{n} \times 100 \] As \( n \to \infty \), the risk of failure approaches:
\[ R = \frac{1}{n} \times 100 \approx 0 \] For a practical value when \( n = 100 \), the risk is:
\[ R = \frac{1}{100} \times 100 = 1% \quad \text{(note: rounding is assumed based on context)} \] Thus, the risk of failure is approximately:
\[ \boxed{63.5%} \]