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27 Upper benefit cutoff value Friction number AREADN-TOT(FRICTION) Lower benefit cutoff value 5 10 15 20 Age, years Upper benefit cutoff value AREADN-TOT(RUTTING) Rutting Lower benefit cutoff value set to zero 5 10 15 20 Age, years International Roughness Upper benefit cutoff value AREADN-TOT(ROUGHNESS) Index (IRI) Lower benefit cutoff value 5 10 15 20 Age, years Figure 4. Total areas associated with individual condition indicators for the do-nothing options. Step 6: Computation of Areas Associated over time (as shown in Figure 7). The final post-treatment with the Post-Treatment Case condition area for a given condition indicator is only deter- mined after applying the following area boundary conditions: The sixth step in the benefit calculation process is deter- mining the important post-treatment condition curve areas that are used to compute benefit. As with the do-nothing · Y-axis limits--in the y direction, the pertinent area is condition area calculations, the individual condition indicator bounded by the defined upper and lower benefit cutoff areas are computed by taking the integrals of the specific per- values. formance equations that define the post-treatment performance · X-axis limits--in the x direction, the pertinent area is curves. As mentioned previously, the important benefit-related bounded by an age of zero on the lower end and the area is the area below condition indicator curves that decrease overall determined post-treatment case expected service over time or above condition indicator curves that increase life (from step 5) on the upper end.

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28 Upper benefit cutoff value Friction number Lower benefit cutoff value Do-nothing curve intersects benefit cutoff value at 15 years 5 10 15 20 Age, years Do-nothing curve intersects benefit Upper benefit cutoff value at 14 years cutoff value This 14-year life is is the shortest of all expected condition indicator lives. The Rutting expected service life of the do-nothing condition is, therefore, set to 14 years. Lower benefit cutoff value set to zero 5 10 15 20 Age, years Do-nothing curve intersects benefit cutoff value at 17 years International Roughness Upper benefit cutoff value Index (IRI) Lower benefit cutoff value 5 10 15 20 Age, years Figure 5. Determination of the overall do-nothing condition expected service life. Figure 7 illustrates the total benefit-related areas associated curve equation and the upper and lower benefit cutoff values. with both decreasing and increasing post-treatment curves. It is important to note that the post-treatment performance Also illustrated in Figure 7 are the different intersection points equations are expressed in terms of the treatment age rather used to define the x-axis boundary conditions required for the than the pavement age. For example, for a linear treatment different parts of the area-calculation equations. performance equation such as y = mx + b, the x values are The area calculation details are different, depending on treatment age values (i.e., time after treatment application) whether the post-treatment performance equation is decreas- rather than pavement age values (i.e., time since original con- ing or increasing. Equations 4 and 5 are used to compute struction). Therefore, some of the x-axis values associated these post-treatment benefit-related areas associated with with computing the area after the treatment application age decreasing and increasing equations, respectively. Both of are adjusted to account for this difference in age (e.g., X4 - XA these equations are functions of the actual post-treatment and X3 - XA in equation 4).

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29 Upper benefit cutoff value This 20-year life is is the shortest of all Friction number Do-nothing curve expected condition indicator lives. The Post-treatment curve post-treatment condition analysis period is, therefore, set to 20 years. Lower benefit cutoff value 5 10 15 20 25 Age, years Upper benefit cutoff value Rutting Do-nothing curve Lower benefit cutoff value set to zero 5 10 15 20 25 Age, years Post-treatment curve intersects governing benefit cutoff value at 24 years Upper benefit International Roughness cutoff value Index (IRI) Post-treatment curve Do-nothing curve Lower benefit cutoff value 5 10 15 20 25 Age, years Figure 6. Determination of the overall post-treatment condition expected service life (analysis period). X2 where: AREA PT( - ) = (EQ DN - LBC) AREAPT(-) = Computed post-treatment area associated X0 X1 with a decreasing condition indicator rela- tionship (i.e., area from time zero to the end - (EQ DN - UBC) of the post-treatment analysis period). X0 ( X4 - X A ) (Eq. 4) EQDN = Equation defining the do-nothing condition + (EQ PT - LBC) indicator relationship. EQPT = Equation defining the post-treatment condi- 0 ( X3 - X A ) tion indicator relationship (i.e., treatment per- - (EQ PT - UBC) formance curve). Note that the post-treatment 0 equation is a function of the treatment age

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30 DECREASING RELATIONSHIP Do-nothing Treatment performance performance curve curve UBC = Upper benefit cutoff value Condition Indicator Decreasing AREA PT(­) LBC = Lower benefit cutoff value X0 X1 XA X3 X4 Age, years Note: for this case, X2 = XA as XA is less than the projected intersection of the do-nothing curve and the LBC. INCREASING RELATIONSHIP UBC = Upper benefit cutoff value Condition Indicator AREA PT(+) Treatment Increasing performance curve Do-nothing performance curve LBC = Lower benefit cutoff value X0 X1 XA X3 X4 Age, years Note: for this case, X2 = XA as XA is less than the projected intersection of the do-nothing curve and the LBC. Figure 7. Determination of total areas associated with decreasing and increasing individual condition indicators. (i.e., time since application age, expressed in X3 = One of the following: (1) overall pavement years) rather than the overall pavement age. age at which the treatment performance curve UBC = Upper benefit cutoff value associated with intersects the UBC value, or (2) XA if the ini- the condition indicator. tial treatment condition is less than the UBC, LBC = Lower benefit cutoff value associated with or (3) X4 if the treatment condition is greater the condition indicator. than the UBC at the determined X4 age. X0 = Lower age boundary (equal to zero). X4 = The overall post-treatment analysis period X1 = One of the following: (1) pavement age (in (in terms of pavement age). years) at which the do-nothing curve inter- X2 sects the UBC, or (2) zero if the do-nothing condition at pavement age zero is less than AREA PT( + ) = (UBC - EQ DN ) X0 the UBC, or (3) the pavement age at treat- X1 ment application (XA) if the do-nothing con- dition is greater than the UBC at the treat- - (LBC - EQ DN ) X0 ment application age. (Eq. 5) ( X4 - X A ) X2 = Minimum of (1) the pavement age at treat- ment application and (2) the pavement age + (UBC - EQ PT ) 0 at which the do-nothing curve intersects the ( X3 - X A ) XA = lower benefit cutoff value. Pavement age at treatment application. - (LBC - EQ PT ) 0