Question

A bridge has an expected life of 50 years and is designed for a flood magnitude of return period 100 years. The risk associated with this hydrologic design is _______ %. Also, the return period in design which would have reduced the risk to 25% will be _____ years.

• A. 55.2% 28 years
• B. 39.8%, 94 years
• C. 39.5%, 16 years
• D. 55.9%, 46 years

Answer 1

The correct option is C 39.5%, 16 years

$\text{Risk (R)}=1-(1-P{)}^n$
$(P=\frac{1}{T})$

$=1-{(1-\frac{1}{100})}^{50}=0.395$

$\simeq 39.5\%$

Now, given R = 25%
$25=1-{(1-\frac{1}{T})}^{50}$
$\ln 25=\ln 1-50\ln (1-\frac{1}{T})$
$\ln 25-\ln 1=-50\ln (1-\frac{1}{T})$

$3.218=-50\ln (1-\frac{1}{T})$

$-0.0644=\ln (1-\frac{1}{T})$

$(1-\frac{1}{T})=e^{-0.644}$

$\frac{1}{T}=1-e^{-0.644}=0.0623$

$T=16.03\simeq 16years$