Question

A culvert is designed for a flood frequency of 100 years and a useful life of 20 years. The risk involved in the design of the culvert (in percentage, up to two decimal places) is ______

Answer 1

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, 

T = 100 years, n = 20 years

\({\rm{P}} = \frac{1}{{\rm{T}}} = \frac{1}{{100}} = 0.01\)

Risk = 1 – (1 - 0.1)²⁰ = 1 – (0.99)²⁰ = 0.1820

Risk (%) = 18.20%

∴ The risk involved in the design of the culvert is 18.20%.