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26 do-nothing areas associated with both decreasing and increas- AREADN(RUTTING), and AREADN(ROUGHNESS)) for the previously ing do-nothing curves and the different intersection points presented example. used to define the x-axis boundary conditions. The total do-nothing condition area associated with a decreasing condition indicator relationship [AREADN-TOT(-)] is computed from the following equation: Step 4: Computation of the Overall Expected Service Life of the Do-Nothing Case X2 AREA DN - TOT( - ) = (EQ DN - LBC) While the computed overall expected service life does not X0 (Eq. 2) influence the do-nothing area or benefit computations, it X1 serves as a baseline for determining the expected extension - (EQ DN - UBC) of life. As the extension of service life is often used as a mea- X0 sure of the success of a preventive maintenance treatment, this computed value is included as part of the analysis out- where: put. The expected overall service life for the do-nothing con- EQDN = Equation defining the do-nothing condition indi- dition is selected as the earliest age at which one of the con- cator relationship. sidered condition indicator do-nothing relationships reaches UBC = Upper benefit cutoff value associated with the con- its benefit cutoff value (i.e., the upper benefit cutoff value for dition indicator. increasing relationships or the lower benefit cutoff value for LBC = Lower benefit cutoff value associated with the con- decreasing relationships). This definition is based on the dition indicator. assumption that, in practice, a second treatment would most X0 = Lower limit to the age range (set to zero). likely be applied when the first of the considered condition X1 = Age at which the do-nothing curve intersects the indicator performance curves reaches its benefit cutoff value upper benefit cutoff value (X1 = 0 if there is no as illustrated in the following example. The first assumption intersection with the UBC). in this example is that the benefit from applying preventive X2 = Age at which the do-nothing curve intersects the maintenance lies in its improvement in friction, rutting, and lower benefit cutoff value (X2 = 0 if there is no IRI. Next is that the indicators reach their respective trigger- intersection with the LBC). ing benefit cutoff values at 15, 14, and 17 years. Therefore, The total do-nothing condition area associated with an increas- the overall do-nothing curve expected service life for the ing condition relationship [AREADN-TOT(+)] is computed from analysis session is 14 years--the earliest age of all of the the following equation: triggering conditions. Figure 5 illustrates the process for this determination. X2 AREA DN - TOT( + ) = (UBC - EQ DN ) X0 (Eq. 3) X1 Step 5: Computation of Expected Service Life - (LBC - EQ DN ) of the Post-Treatment Case X0 The next step in the benefit calculation process is to plot the where: post-treatment performance relationships for each condition EQDN = Equation defining the do-nothing condition indi- indicator. The expected service life for the post-treatment case cator relationship. (for a given timing scenario) is then determined as the earliest UBC = Upper benefit cutoff value associated with the age at which any of the post-treatment condition indicators condition indicator. reaches its benefit cutoff value. Unlike the do-nothing case LBC = Lower benefit cutoff value associated with the con- where the area computations are unbounded in the x-direction, dition indicator. the area computations for the post-treatment case are bounded X0 = This lower limit to the age range is set to zero. at this expected post-treatment service life which is also used X1 = Age at which the do-nothing curve intersects the as the analysis period for the LCC computations. lower benefit cutoff value (X1 = 0 if there is no In the previous example, if a preventive maintenance treat- intersection with the LBC). ment is applied at a pavement age of 10 years, the performance X2 = Age at which the do-nothing curve intersects the curves for friction, rutting, and roughness, as shown in Fig- upper benefit cutoff value (X2 = 0 if there is no ure 6, reach their triggering benefit cutoff values at 20, 22, and intersection with the UBC). 24 years, respectively. Therefore, the expected service life (and analysis period) for this timing scenario is 20 years--the Figure 4 illustrates the application of these area boundary con- earliest age of all the triggering conditions. Thus, areas would ditions and the resulting bounded areas (i.e., AREADN(FRICTION), only be computed for the x-range between 0 and 20 years.