Question

A hydraulic structure has an expected life of 20 years and is designed for a flood magnitude of return period 50 years. The risk of failure of the structure during its life is

• A. 0.87
• B. 0.33
• C. 0.60
• D. 0.13

Answer 1

The correct option is B 0.33

The probability of occurrence of an event $(x\ge x_r)$ at least once over a period of n successive years is called the risk, $\overline{R}$

Hence, risk is given by,

$\overline{R}=1-$(Probability of non-occurrence of the event $x\ge x_r$ in n year)

$=1-{(1-\frac{1}{T})}^n=1-{(1-\frac{1}{50})}^{20}=0.332\simeq 0.33$

T = Return period = 50 years
n = Expected life = 20 years