Question

Your professional company is hired to perform a hydrologic-hydraulic study needed for the design of a new bridge. The 75-year historical data (annual maximum series) collected from a nearby station at a river was used to develop the statistical parameters. The expected project life of the bridge is 50 years. Following bridge safety regulations, the 500-year flood (based on annual maximum data series) is used for design purposes. The bridge construction will require five (5) years of work inside the river and the insurance company is only willing to accept the project if the flood recurrence of 25 years is used to calculate the risk probability for their insurance to respond for may flood damage inside the construction area.

Showing all equations and your computations to determine:

a) Probability assigned to the flood with 500-yr recurrence.

b) Risk probability that this 500-year return period flood will be exceeded at least once in the 50-year

project life.

c) The corresponding probability of not exceeding that 25-yr flood during the construction period.

d) Although the building contractor pays the insurance fees, he only builds countermeasures to protect

the construction site equivalent to the 10-yr flood recurrence.

Compute the corresponding probability of not exceeding that 10-yr flood during the construction

period?

Compare, discuss and justify your answer of any risk, ethical, or economic issues associated to the

contractor action as well as present recommendations.

Answer 1

75-year data used for analysis (annual maximum series)

Expected project life of the bridge = 50 years

The bridge construction will require 5-years work inside the river.

The insurance company will accept to provide insurance only if the corresponding risk probability is based on a flood recurrence of 25 years for flood damage inside the construction area.

1. T = 500 years

        Probability assigned (P) = 1/T = 1/500 = 0.002

2. Risk probability that 500 year flood would be exceeded at least once in 50 year project life

= 1- (1-P)ⁿ

=1-(1-0.002)⁵⁰

=0.0952

=9.52 %

3. Probability assigned to 25 year flood = P₂₅ = 1/T = 1/25 = 0.04

Probability that 25 year flood will not be exceeded in the construction period (of 5 years)

= (1-P₂₅)ⁿ

= (1-0.04)⁵

=0.8154

=81.54%

4. However, though contactor pays insurance against 25 year flood agreement, he builds countermeasures for 10- year flood.

Probability assigned to 10 year flood P₁₀ = 1/T =1/10 =0.1

Probability of not exceeding 10 year flood during construction period of 5 years

= (1-P₁₀)ⁿ

=(1-0.1)⁵

=0.5905

=59.05%

Comments:

The contractor is paying for the insurances based on a 25-year flood although he has taken up counter-measured based on a 10-year flood.

A 25-year flood is of greater magnitude than a 10-year flood because smaller floods have smaller return periods.

Hence, the contractor saves cost by not building countermeasures for 25-year flood and using 10-year flood because countermeasures for smaller flood costs less.

However, we see that probability of 25- year flood not occurring is greater than the 10-year flood, as obvious.

We can say, risk of occurrence of the 25-year flood is 100-81.54 = 14.46 % but that of the 10-year flood is 100 – 59.05 =40.95 %.

Hence, ethically, the contractor is taking a risk both with respect to damages to the bridge during construction, as well as risk to the lives of laborers.

Although, the initial investment by the contractor is saving him money, but as he is taking a risk of using 10 year flood, if the insurance company finds out, and a flood of magnitude greater than 10 year flood but less than 25 years flood occurs, then the insurance company may not pay the insurances rightfully based on their agreement. Under such recommendations, the contractor may face greater losses.   

It is thus recommended, that the contractor abides by the agreement made with the insurance company and countermeasures are built for 25-year flood for both ethical and economic safety.