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31 where: the computations are slightly more complex in that all post- treatment and do-nothing benefit areas are truncated at the AREAPT(+) = Computed post-treatment area associated expected service life of the post-treatment case computed in with an increasing condition indicator rela- step 5. By truncating these areas, it is ensured that all com- tionship (i.e., area from time zero to the end puted benefit areas for the included condition indicators use of the post-treatment analysis period). the same analysis period. Figure 10 illustrates the benefit EQDN = Equation defining the do-nothing condition areas associated with friction, rutting, and roughness in the indicator relationship. previously presented example. EQPT = Equation defining the post-treatment con- When multiple condition indicators are analyzed simulta- dition indicator relationship (i.e., treatment neously, converting individual condition indicator benefit performance curve). Note that the post- areas into one overall benefit value becomes difficult because treatment equation is a function of treatment different condition indicators are expressed in different units. age (i.e., time since application age) rather To solve this problem, each individual benefit area (i.e., the than the overall pavement age. difference between the post-treatment and associated do- UBC = Upper benefit cutoff value associated with nothing areas) is normalized by dividing each computed ben- the condition indicator. efit area by its associated total do-nothing area computed in LBC = Lower benefit cutoff value associated with step 3. The total do-nothing area is used as the basis for this the condition indicator. comparison so computed benefit areas may be fairly com- X0 = Lower age boundary (equal to zero). pared between different timing scenarios. This normalization X1 = One of the following: (1) pavement age at process results in all individual benefit values being expressed which the do-nothing curve intersects the as a percentage. Equation 6 is used for the individual benefit LBC value, or (2) zero if the do-nothing computations. condition at pavement age zero is greater than the LBC, or (3) the pavement age at %BENEFITi = ( AREA BENEFIT( i ) ) ( AREA DN - TOT( i ) ) (Eq. 6) treatment application (XA) if the do-nothing condition is less than the LBC at the treat- where: ment application age. X2 = Minimum of (1) the pavement age at treat- %BENEFITi = Individual benefit associated with a ment application and (2) the pavement age given condition indicator (benefit area at which the do-nothing curve intersects the expressed as a percentage of the associ- UBC value. Note: X2 is often equal to XA. ated total do-nothing area). XA = Pavement age at treatment application. i = One of i = 1 to n condition indicators X3 = One of the following: (1) overall pavement included in the analysis. age at which the treatment performance curve AREABENEFIT(i) = Computed benefit area associated with intersects the LBC value, or (2) XA if the ini- the jth condition indicator in an analysis tial treatment condition is greater than the = (AREAPT(i) - AREADN(i)) AREAPT(i) = Computed post-treatment area between LBC, or (3) X4 if the treatment condition is time = 0 and the computed post-treatment less than the LBC at the determined X4 age. analysis period (computed in step 6). X4 = The overall post-treatment analysis period AREADN(i) = Do-nothing area between time = 0 and the (in terms of pavement age). computed post-treatment analysis period (computed in step 5). Note: if the analysis Figure 8 illustrates the application of these area boundary period is greater than or equal to the age conditions and the resulting bounded post-treatment areas (i.e., at which the current condition indicator AREAPT(FRICTION), AREAPT(RUTTING), and AREAPT(ROUGHNESS)) for curve intersects the benefit cutoff value, the previously presented example. this area will be the total do-nothing area (i.e., AREADN(i) = AREADN-TOT(i)). AREADN-TOT(i) = Total do-nothing area associated with Step 7: Computation of Benefit Associated the jth condition indicator in an analysis with Each Individual Condition Indicator (i.e., that computed under step 3). When only one condition indicator is included, the individ- ual benefit is determined by comparing the post-treatment area Step 8: Computation of Overall Benefit computed in step 6 with the total area computed in step 3 for the do-nothing case. That is, the benefit is quantified as the When more than one condition indicator is included in an difference in area between the overall post-treatment area analysis, individual condition indicator benefit values are and the associated do-nothing area (see Figure 9). When combined using defined benefit weighting factors. Continuing more than one condition indicator is included in an analysis, with the example, assume that individual benefit values for