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OCR for page 27

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