A bridge with an expected life of 50 years is designed for a flood of 10000 m3/s corresponding to the return period of 100 years. The risk associated with this design is ________(rounded off to two decimal places).

The correct answer is 0.39.

Step-by-step Explanation:

To find the risk associated with the design of the bridge, we calculate the probability that the design flood is exceeded at least once during the expected lifetime of the structure.

We are given the following parameters:
Expected life of the bridge (n) = 50 years
Return period of the design flood (T) = 100 years

1. First, calculate the probability of occurrence (probability of exceedance) of the design flood in any single year, denoted by p:

$$p=\frac{1}{T}=\frac{1}{100}=0.01$$

2. Next, calculate the probability of non-occurrence of the design flood in any single year, denoted by q:

$$q=1-p=1-0.01=0.99$$

3. The risk (R) is defined as the probability that the flood occurs at least once in n years, which is the complement of the probability that the flood does not occur at all in n years:

$$R=1-q^n$$

Substituting the values of q and n into the formula:

$$R=1-{\left(0.99\right)}^{50}$$

Calculating the exponential term:

$${\left(0.99\right)}^{50}\approx 0.605$$

Therefore, the risk is:

$$R=1-0.605=0.395$$

Rounding off to two decimal places, we get:

$$R\approx 0.39$$

Thus, the risk associated with this design is 0.39 (or 39%).