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A bridge has an expected life of 25 years and is designed for a flood magnitude of return period 100 years. What is the risk of this hydrologic design ?

A bridge has an expected life of 25 years and is designed for a flood magnitude of return period 100 years. What is the risk of this hydrologic design ? Correct Answer <span class="math-tex">\(1 - \left( \frac{99}{100} \right)^{25} \)</span>

Concept:

Risk = The probability of a flood to occur at least once in n successive years

Risk = 1 – qn = 1 – (1 - p)n

where,

p is the probability of occurrence of an event and it is given by 

p = 1/T

where,

T is the return period, q is the probability of not occurrence of an event

Calculation

Given, n = 25 years,  Risk = ??

Return Period (T) = 100. 

⇒ p = 1/100, q = 1 - 1/100 = 99/100

∴ Risk (R) = 1 – qn = 1 - (99/100)25

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