10

Time, years

FIGURE 36.8 The hazard function for a retaining wall beam over a 20-year period.

warning that something is wrong. The entire wall would need to be replaced, control measures would be installed, and an accelerated schedule would result for an estimated cost of $200,000. (b) There is a 50% chance that the wall will fail catastrophically, slide down the hill, but not spill onto the roadway below. The cost associated with a clean-up, immediate repair, and delaying of traffic while the project is under way is $450,000. (c) There is a 15% chance that the wall would fail catastrophically, extend onto the highway below, and cause accidents. The estimated cost for this scenario is $1.2 million. (d) There is a 5% chance of resulting injuries and fatalities, which raises the estimated cost to $3.6 million. From a purely financial perspective, should the owner replace the wall this year?

Answer

The probability that the wall will fail this year given that it has not failed already is provided by the hazard function in Table 36.3 as H(t) = H(20) = 0.001951. The expected cost of failure is illustrated in the event tree in Figure 36.9 and calculated as

E(Costfaiiure) = 0.30($200,000)+0.50($450,000)+0.15($1,200,000)+0.05($3,600,000) = $645,000

E(Costyear 20) = $645,000(0.001951) + $0(1 - 0.001951) = $1,242

This value represents the annual cost of keeping the retaining wall in service in its present state. In this example, no maintenance is assumed, and thus there is no cost associated with the wall performing as intended.

The annual cost of the support beam replacement is obtained by converting the present value of the $67,000 replacement cost (Cpv) to an annual cost (Cannual) over the expected 20-year life.

The beam replacement is not justified at this time based on the comparative annual costs of the alternatives (i.e., $5841 > $1242). This methodology is used by the Army Corps of Engineers to justify major rehabilitation projects on structures (USACE 1996).

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