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Sat 12 Nov, 2011 09:08 pm

Project: It is 1963 and your civil engineering firm has been hired by Ameren UE to design and

perform the construction quality assurance (CQA) for the to be Taum Sauk pump-storage project

(FERC 2006, Rizzo 2010). You are considering two options for the design.

Option A: Includes a 90-ft high dam for the reservoir. There is no emergency spillway and the dam will be monitored remotely, so no on-site personnel are necessary. The initial cost to

construct this design is $50 million (M). There is an annual maintenance and operating cost of $5M per year. In 1998, Ameren will upgrade the turbines (from 350 MW to 440 MW) for a cost

of $10M. The revenue from selling the electricity that is produced by the hydraulic turbines is $12M per year beginning in 1964 through and including 1998. Beginning in 1999 and through

and including 2005 the annual revenue from selling the electricity is $47M per year (Ameren increased the number of operating days from about 100/year to 300/year after installing the new

turbines).

Option B: Includes a 91-ft high dam for the reservoir. There is an emergency spillway, on-site personnel and increased maintenance. The initial cost to construct this design is $100 million (M). There is an annual maintenance and operating cost of $7M per year. In 1998, Ameren will upgrade the turbines (from 350 MW to 440 MW) for a cost of $10M. The revenue from selling

the electricity that is produced by the hydraulic turbines is $12M per year beginning in 1964 through and including 1998. Beginning in 1999 and through and including 2005 the annual revenue from selling the electricity is $47M per year.

The high water level in the reservoir varies over the course of the year following a normal distribution with a mean high water level of 88 feet and a standard deviation of 0.6153 ft (Figure

1). If the water level exceeds the height of the dam, failure occurs by overtopping (Rogers & Watkins 2008). The consequence cost of a failure is $1B (= $500M fines, penalties and lawsuits

+ $500M to rebuild the dam).

(Figure 1 – Probability density function of the high water level in Taum Sauk Reservoir over the course of one year. with a mean of 88 ft and Standard Deviation of 0.6153)

Problem (Tasks): Determine the probability (for each option) that the dam will fail one (1) time

in its 42 years of operation (1963 – 2005). Assume that the one failure occurs at the end of the

year (December 31st) 2005 (The dam actually failed on December 14

th, 2005). Considering the dam will be in operation from 1963 through 2005 and the average annual

interest rate over the period 1963-2005 will be 8%:

(a) Which option will you recommend to Ameren, based on expected monetary value

(EMV)?

Baecher and Christian (2003) show that for existing US Dams where the consequence of failure is $1B, a typical acceptable annual level of risk (Pf

) to be between 10-5 to 10-6 or 1/100,000 to 1/1,000,000 (Figure 2). You may use Baecher and Christian 2003 as one of your references.