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Although these results appear to contradict engineering Compute Expected Design Lives. The second step of the
judgment, they reflect the accuracy of the provided condition KDOT modeling procedure is to compute an expected design
prediction models. This case study points out the importance life of a selected paving action. Based on the results of a mul-
of not only obtaining representative datasets, but also focus- tiple linear regression process, the following equation is used
ing on compiling separate datasets for different treatment to compute the expected design life for a given paving activ-
application ages. ity on a flexible pavement:
DL_Flex = 8.836 + 1.610 × FDBit
Case Study 2--Kansas
+ 1.201 × EqThick
Introduction - 3.725 × Ln( EqTCR + 1) (Eq. 9)
As part of an ongoing study, the Kansas Department of D_ADL_t
- 0.957 × Ln
Transportation (KDOT) is developing condition indicator EqThick
prediction models based on the historical condition data
available in their pavement management database for nearly where:
11,000 pavement segments. For this case study, only the
transverse cracking models developed by KDOT were used DL_Flex = Flexible pavement design life, years.
to demonstrate the analysis approach. This subsection intro- FDBit = Full-depth bituminous index (value of 1.0 if
the pavement is a full-depth section).
duces the modeling approach used by KDOT and demon-
EqThick = Equivalent thickness of current paving action
strates how such agency-developed models may be used
(construction, rehabilitation, or maintenance
within the analysis approach developed under this project.
activity), in.
EqTCR = Equivalent number of transverse cracks at
time of current paving action. Note: EqTCR is
KDOT Modeling Procedure the equivalent number of "code 3" (rough or
very wide) cracks expected per 30-m (100-ft)
Modeling the performance of a given construction, rehabil- segment.
itation, or maintenance activity is a four-step process. D_ADL_t = Design lane average daily 80 kN (18 kip)
loads.
Estimate Equivalent Asphalt Thickness (EqThick). In an
effort to estimate the expected pavement performance impact In the KDOT study, the limits shown in Table 26 are used to
associated with a specific paving activity, KDOT has esti- "cap" the computed design life if necessary.
mated the equivalent asphalt thicknesses associated with dif-
ferent non-structural, light-structural, and heavy-structural Compute the Condition Indicator Value for the First Sur-
paving actions used in Kansas. Examples of selected equiv- vey Year After a Paving Action. The third step of the KDOT
alent thickness values are listed in Table 25. modeling procedure is to compute the condition indicator
TABLE 25 Examples of equivalent thickness values associated with various
construction actions in Kansas
Action Equivalent Thickness,
Type Paving Action Description mm (in).
Non- Do nothing 0 (0.00)
Structural Modified slurry seal 6 (0.25)
Rout and crack seal on flexible pavement 13 (0.50)
25-mm (1.0-in.) asphalt overlay 25 (1.00)
Light- 38-mm (1.5-in.) asphalt overlay 38 (1.50)
Structural Extensive patching, 38-mm (1.5-in.) asphalt overlay 44 (1.75)
50-mm (2.0-in.) asphalt overlay 50 (2.00)
Heavy- 63-mm (2.5-in.) asphalt overlay 63 (2.50)
Structural Cold recycle 100-mm (4-in.), 38-mm (1.5-in.) asphalt overlay 100 (4.00)
New HMA construction 50, 100, 150, or 200 (2,
50, 100, 150, or 200 mm (2, 4, 6, or 8 in.) depending on 4, 6, or 8 in.) depending
chosen design on chosen design
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TABLE 26 Flexible pavement design life Note: the equivalent transverse cracking value is assumed to
limits for equivalent thickness values drop to zero immediately after a rehabilitation action (i.e.,
Design Life EqTCR = 0 at the year of the paving action).
Equivalent Thickness of Last Projection
Paving Action Limit, yrs Compute the Condition Indicator Values for Subsequent
< 38 mm (1.50 in.) 10 Years. The last step of the KDOT modeling procedure is to
39 to 75 mm (1.51 to 3.00 in.) 10 compute the condition indicator values for all other years
76 to 100 mm (3.01 to 4.00 in.) 15 after the first survey year. In this case study, the following
> 100 mm (> 4.01 in.) 20 equation is used to compute the EqTCR at these subsequent
years regardless of the type of the most recent paving action:
values expected at the first survey year after a paving action.
Different prediction equations are developed for KDOT's EqTCRt + 1 = 0.182 + 1.10 × EqTCRt
structural and non-structural paving actions. The following + 0.282 × CTCRt - 0.0218 × FDBit (Eq. 12)
equations are used to compute the EqTCR value at the first year - 0.0113 × DL_Flex
after a structural or non-structural paving action, respectively.
where:
EqTCRt + 1 = Equivalent number of transverse cracks in
Structural Action any year after the first survey year. Note:
EqTCRt+1 is the maximum of the predicted
EqTCRpost = 0.0973 + 0.0845 × EqTCRprior value from the regression or EqTCRt + 0.05.
(Eq. 10)
+ 0.000394 × D_ADL EqTCRt = Equivalent number of transverse cracks in
the previous year.
where: CTCRt = Change in EqTCR in the previous year (i.e.,
EqTCRpost = Equivalent number of transverse cracks at CTCRt = EqTCRt - EqTCRt - 1).
year 1 after a structural paving action. Note: FDBit = Full-depth bituminous index (value of 1.0 if
EqTCR is the equivalent number of "code 3" the pavement is a full-depth section).
(rough or very wide) cracks expected per DL_Flex = Flexible pavement design life (years) based
30-m (100-ft) segment. on the design life regression model of the
EqTCRprior = Equivalent number of transverse cracks last structural action.
immediately before the paving action.
D_ADL = Design lane average daily 80 kN (18 kip) The following subsections describe an example of how the
loads at the year of the last structural action. KDOT modeling equations are used within the analytical tool.
Treatment Selection
Non-Structural Action
For this case study, routing and sealing cracks on a flexi-
EqTCRpost = 0.376 + 0.239 × EqTCRprior ble pavement is chosen as the preventive maintenance treat-
- 0.351 × EqThick ment. "Rout and Crack Seal" is assigned an effective HMA
(Eq. 11)
+ 0.0943 × FDBit thickness of 13 mm (0.5 in.).
- 0.0190 × DL_Flex
where: Treatment Costs
EqTCRpost = Equivalent number of transverse cracks at The assumed average crack sealing cost is $1,865 per km
year 1 after a non-structural paving action. ($3,000 per mi). A discount rate of 2.0 percent is used for the
EqTCRprior = Equivalent number of transverse cracks analysis (the discount rate typically used by KDOT).
immediately before the paving action.
EqThick = Equivalent thickness of current paving action
(construction, rehabilitation, or maintenance Condition Indicators
activity), in.
FDBit = Full-depth bituminous index (value of 1.0 if The equivalent number of "code 3" (rough or very wide)
the pavement is a full-depth section). cracks expected per 30-m (100-ft) segment (EqTCR) is the
DL_Flex = Flexible pavement design life (years) based sole condition indicator for this treatment. Note that at the
on the design life regression model of the time of initial construction, or the time at which all cracks are
last structural action. routed and sealed, this EqTCR condition indicator is set or
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reset to a value of zero. Also, because the number of devel- construction activity is a structural action, the EqTCR value
oping cracks increases over time, the general trend of this at year 1 is computed using equation 10. The specific inputs
condition indicator is increasing. used in that equation are the following:
· EqTCRprior = 0 at the previous year (initial construction).
Benefit Cutoff Values · D_ADL = 250 for the number of average daily 80kN
(18 kip) loads (average daily ESALs) at the time of ini-
Based on recommendations from KDOT personnel, a tial construction (assumed to be 250).
distress threshold value for EqTCR is identified as 0.62.
Because EqTCR is expected to increase over time, 0.62 is Inserting these input values into equation 10 results in the
set as an upper benefit cutoff; the practical lower limit of following:
EqTCR of zero is used as the lower benefit cutoff value in
the analysis. EqTCRpost = 0.0973 + 0.0845 × (0) + 0.000394 × (250)
= 0.196 (EqTCR at first year after initial
construction)
Do-Nothing Performance Curve
In this example, the do-nothing performance curve is Step 3--Compute Subsequent Year EqTCR Values Used
defined as the EqTCR versus time relationship associated to Define the Performance After Initial Construction (Do-
with the initial pavement construction. An equivalent Nothing Curve). The final step is to determine the expected
asphalt pavement thickness of 200 mm (8.0 in.) represents EqTCR values for years other than years 0 and 1. EqTCR
the do-nothing condition. The following steps are used to values for subsequent years are computed using equation 12.
determine the do-nothing performance curve for the equiv- The following inputs illustrate the case for computing the
alent transverse cracking condition indicator. EqTCR value at year 2:
Step 1--Compute the Expected Design Life Associated · EqTCR1 = 0.196 as computed in step 2.
with the Initial Construction Action. The first step in deter- · CTCR1 = 0.196 is the computed change in EqTCR in the
mining the representative EqTCR do-nothing curve is to previous year. (For this example, CTCR1 = EqTCR1 -
compute the expected service life for the assumed 200-mm EqTCR0 = 0.196 - 0 = 0.196.)
(8.0-in.) equivalent asphalt thickness. The following inputs · FDBit = 1.0 for full-depth bituminous pavement section.
are used in equation 9 to compute the design life associated · DL_Flex = 16.8 years is the expected initial construc-
for the initial construction. tion design life as computed in step 1.
· FDBit = 1.0 for a full-depth bituminous pavement. Inserting these values into equation 12 results in the following:
· EqThick = 200 mm (8.0 in.) for an equivalent asphalt
thickness of 200 mm (8.0 in.) associated with new EqTCR2 = 0.182 + 1.10 × (0.196) + 0.282 × (0.196)
construction paving. - 0.0218 × (1.0) - 0.0113 × (16.8)
· EqTCR = 0 for pavement with no equivalent number = 0.241
of transverse cracks at time zero (initial construction).
· D_ADL_t = 250 for assumed 250 average daily 80kN As explained in equation 12, the EqTCR2 value is the higher
(18 kip) loads (average daily ESALs) in the design of this computed value (i.e., 0.241) or EqTCR1 + 0.05
lane at time of initial construction. (This is reported (i.e., 0.196 + 0.05 = 0.246). Therefore, EqTCR2 is redefined as
by KDOT to be a typical traffic level for a 2-lane high- 0.246.
way in Kansas.) Completing this iterative process for subsequent years (up
to year 20) results in the expected EqTCR values presented
Inserting these values into equation 9 results in the fol- in Table 27. Figure 23 illustrates the plotted EqTCR data and
lowing: the following second-order polynomial equation that repre-
sents the do-nothing condition:
DL_Flex = 8.836 + 1.610 × (1.0) + 1.201 × (8.0)
- 3.725 × Ln(0 + 1) - 0.957 × Ln(250/8.0) EqTCR = 0.0015 × Age2 + 0.0348 × Age + 0.1415 (Eq. 13)
= 16.8 years (design life associated with initial
construction)
Post-Preventive Maintenance Performance
Step 2--Compute the EqTCR Value for the First Survey Relationships
Year (Year 1) After Initial Construction. The next step is
to determine the expected EqTCR value for year 1 (i.e., the In order to test the sensitivity of the timing of routing and
first survey year after initial construction). Since the initial sealing cracks, a wide range of application ages (1, 3, 5, 7, 9,
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TABLE 27 Computed yearly EqTCR values used to define indicated previously, the expected treatment design life is a
the do-nothing curve function of four different variables:
Pavement Computed Equivalent Number of Rough or Very
Age Wide Transverse Cracks per 30 m (100 ft) (EqTCR) · EqTCRprior--the computed values given in Table 27.
0 0.000 · EqThick--the equivalent asphalt thickness of 13 mm
1 0.196 (0.5 in.) associated with the rout and crack seal preven-
2 0.246 tive maintenance treatment.
3 0.296 · FDBit = 1.0--for full-depth bituminous section.
4 0.346 · DL_Flex--the expected design life of the last structural
5 0.396 treatment application. Since the last structural applica-
6 0.446 tion is initial construction, this value is held constant in
7 0.496 the analysis at the calculated 16.8 years.
8 0.546
9 0.596 Table 28 lists all the required inputs and the resulting
10 0.646
expected first survey year EqTCRpost values (computed using
11 0.696
equation 11) for each application age. The following exam-
12 0.750
ple illustrates the computation of the EqTCRpost value for the
13 0.812
application age of 3 years using equation 11.
14 0.881
15 0.959
16 1.048
EqTCRpost = 0.376 + 0.239 × (0.239) - 0.351 × (0.5)
17 1.149 + 0.0943 × (1.0) - 0.0190 × (16.8)
18 1.263 = 0.047 (equivalent number of cracks at the first
19 1.392 survey year after routing and sealing cracks at
20 1.538 a pavement age of 3 years)
Compute Subsequent Year EqTCR Values Used to
Define the Performance After Applying the Rout and
11, and 13 years) were considered. The following two-step Crack Seal Treatment. The second step involves defining
process is used to determine post-treatment performance the post-treatment performance curves for each application
curves for each application age. age by computing EqTCR values for subsequent years (i.e.,
all years after the first survey year after treatment application)
Compute the EqTCR Value for the First Survey Year using equation 12. Table 29 lists all the computed EqTCR val-
After a Treatment Application (for All Application Ages). ues that define the post-treatment performance for the differ-
The first step in determining the representative post-treatment ent application ages. Table 30 lists the EqTCR versus age
performance relationships is to estimate the expected EqTCR second-order polynomial regression equations that are fit
value for the first survey year after each treatment application. through the data for each application age. Also shown in
Since the rout and seal activity is a non-structural action, these Table 30 are the computed times at which each regression
year 1 EqTCR values are computed using equation 11. As equation crosses the previously determined upper benefit
1.8
Very Wide Transverse Cracks
Equivalent No. of Rough or
1.6
per 30 m (100 ft) (EqTCR)
2
EqTCR = 0.0015x + 0.0348x + 0.1415
1.4 2
R = 0.9857
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0 5 10 15 20
Pavement Age, years
Figure 23. Estimated do-nothing curve for Case Study 2--Kansas.
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TABLE 28 Required inputs and computed equivalent cracking values at the first
survey year after a treatment application (at different chosen application ages)
Inputs Equivalent
Equivalent No. of Cracks
Equivalent No. of Cracks at First Year
Asphalt Before Paving Expected After Paving
Application FDBit Index Thickness Action Design Life, Action
Age (FDBit) (EqThick) (EqTCRprior) years (EqTCRpost) 1
1 1.0 13 mm (0.5 in.) 0.196 16.8 (the 0.023
3 (the FDBit (the EqThick 0.296 DL_Flex value 0.047
variable is variable is is held
5 0.396 constant for all 0.071
held constant held constant
7 for all for all 0.496 application 0.095
application application ages)
9 0.596 0.119
ages) ages)
11 0.696 0.143
13 0.812 0.170
1
Equivalent number of cracks at year 1 after paving action (EqTCRpost) are computed using equation 11.
TABLE 29 Computed post-treatment EqTCR values associated with the
different chosen application ages
Treatment Application Age, years
Age, years 1 3 5 7 9 11 13
0 0.000 0.000 0.000 0.000 0.000 0.000 0.000
1 0.023 0.047 0.071 0.095 0.119 0.143 0.170
2 0.073 0.097 0.121 0.145 0.169 0.193 0.220
3 0.123 0.147 0.171 0.195 0.219 0.243 0.270
4 0.173 0.197 0.221 0.245 0.269 0.293 0.320
5 0.223 0.247 0.271 0.295 0.319 0.343 0.370
6 0.273 0.297 0.321 0.345 0.369 0.393 0.420
7 0.323 0.347 0.371 0.395 0.419 0.443 0.470
8 0.373 0.397 0.421 0.445 0.469 0.493 0.520
9 0.423 0.447 0.471 0.495 0.519 0.543 0.570
10 0.473 0.497 0.521 0.545 0.569 0.593 0.620
TABLE 30 Determined post-preventive maintenance performance
relationships for Case Study 2--Kansas
Computed Life Until Equation
Application Reaches Upper Benefit Cutoff
Age Regression Equation Level (EqTCR = 0.62)
1 EqTCR = 0.0492 * AGE - 0.0199 13.0
3 EqTCR = 0.0499 * AGE - 0.0022 12.5
5 EqTCR = 0.0506 * AGE + 0.0156 11.9
7 EqTCR = 0.0515 * AGE + 0.0325 11.4
9 EqTCR = 0.0523 * AGE + 0.0499 10.9
11 EqTCR = 0.0536 * AGE + 0.0653 10.3
13 EqTCR = 0.0555 * AGE + 0.0820 9.7
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Regression Trends Through Selected Post-Treatment Data
0.80
App Age = 1
Upper Benefit Cutoff Value App Age = 3
transverse cracks per 30 m (100 ft) (EqTCR)
0.70
Equivalent No. of rough or very wide
App Age = 5
0.60
App Age = 7
0.50 App Age = 9
App Age = 11
0.40
App Age = 13
Linear (App Age = 1)
0.30
Linear (App Age = 3)
0.20 Linear (App Age = 5)
Linear (App Age = 7)
0.10
Linear (App Age = 9)
0.00 Linear (App Age = 11)
0 2 4 6 8 10 12 14
Linear (App Age = 13)
Age after treatm ent application, years
Figure 24. Illustration of post-treatment performance relationships based on KDOT models.
cutoff value of EqTCR = 0.62. These computed times repre- · Cost Data--Only the cost of routing and sealing cracks
sent the expected ages at treatment failure. Finally, the deter- is included in the analysis (i.e., rehabilitation, user, and
mined post-treatment performance curves associated with routine maintenance costs are excluded). The assumed
different application ages are plotted in Figure 24. average crack sealing cost is $1,865 per km ($3,000 per
mi). A discount rate of 2.0 percent is also chosen for the
analysis based on KDOT's typical practice.
Analysis Setup · Benefit Weighting Factors--Since only one condi-
tion indicator is used in the analysis session, the bene-
The analysis tool is used to evaluate the estimated perfor- fit weighting factor associated with the equivalent
mance data described. The following inputs are used for ana- cracking value (EqTCR) is set to 100 percent.
lyzing the data obtained for this project:
· Analysis Type--A detailed analysis type is selected Analysis Results
because actual data are being analyzed.
· Condition Indicators--A custom condition indicator The results obtained from this analysis are summarized in
for equivalent transverse cracking is defined and labeled Table 31. These results indicate that out of the seven investi-
as EqTCR. gated application ages, application of the treatment at age 11
· Preventive Maintenance Treatment Selection--A is the most cost-effective option as indicated by an EI of 100.
custom treatment, Rout and Seal Cracks, is used. Appli- Also, the application treatment at this age is expected to
cation ages of 1, 3, 5, 7, 9, 11, and 13 years are investi- extend pavement life by 11.6 years (i.e., 11.6 more years than
gated. the expected do-nothing service life of 9.7 years) and an
· Performance Relationships--The do-nothing perfor- EUAC of $140. To help illustrate the results of this analysis,
mance curve from Figure 23 and the post-treatment per- plots of EI, total benefit, extension of life, and EUAC versus
formance relationships defined in Table 30 are entered treatment application age are shown in Figure 25.
directly. It is interesting to note that the highest EI is obtained for
· Project Definition--The sample project is assumed to an application age of 11 years while an application age of
be a 1.6-km (1-mi) segment of a 2-lane (7.3-m [24-ft] 7 years provides the largest total benefit. Therefore, if an
wide) rural highway. Therefore, for this particular con- agency regards the differences in EUAC as insignificant,
dition indicator, the project is defined by setting the proj- the most appropriate option would be the application age of
ect length to 1.6 km (1 mi). 7 years.
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TABLE 31 Analysis results for Case Study 2--Kansas
Output Data
Pavement Surface Type: HMA
Treatment Type: Rout and Seal Cracks
Application Years: 1, 3, 5, 7, 9, 11, 13
Expected Do-Nothing Service Life (yrs): 9.7
Benefit Summary
Individual
Benefit
Summary
Benefit Ranking Factors => 100
Application
Age, yrs Total Benefit EqTCR
1 0.81 0.81
3 1.01 1.01
5 1.15 1.15
7 1.22 1.22
9 1.21 1.21
11 1.12 1.12
13 1.02 1.02
Cost Summary
Other
Application Treatment User Cost, PW Maintenance Rehab. Cost, Total Present
Age, yrs Cost, PW $ $ Cost, PW $ PW $ Worth, $ EUAC, $
1 $2,941 n/a n/a n/a $2,941 $243
3 $2,827 n/a n/a n/a $2,827 $214
5 $2,717 n/a n/a n/a $2,717 $191
7 $2,612 n/a n/a n/a $2,612 $171
9 $2,510 n/a n/a n/a $2,510 $154
11 $2,413 n/a n/a n/a $2,413 $140
13 $2,319 n/a n/a n/a $2,319 $128
Effectiveness Summary
Expected
Application Effectiveness Expected Life, Extension of
Age, yrs Index Total Benefit EUAC, $ yrs Life, yrs
1 41.38 0.81 $243 14.0 4.3
3 58.89 1.01 $214 15.5 5.7
5 75.45 1.15 $191 16.9 7.2
7 89.09 1.22 $171 18.4 8.7
9 97.77 1.21 $154 19.9 10.2
11 100.00 1.12 $140 21.3 11.6
13 99.24 1.02 $128 22.7 13.0
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Effectiveness Index vs. Application Timing
Effectiveness Index
100
80
60
40
20
0
0 2 4 6 8 10 12 14
Timing of First PM Application, years
Total Benefit vs. Application Timing
1.40
Total Benefit, %
1.20
1.00
0.80
0.60
0.40
0.20
0.00
0 2 4 6 8 10 12 14
Timing of First PM Application, years
Extension of Life vs. Application Timing
14.0
Extension of Life,
12.0
10.0
years
8.0
6.0
4.0
2.0
0.0
0 2 4 6 8 10 12 14
Timing of First PM Application, years
EUAC ($) vs. Application Timing
$300
$250
EUAC ($)
$200
$150
$100
$50
$
0 2 4 6 8 10 12 14
Timing of First PM Application, years
Figure 25. Summary charts for Case Study 2--Kansas.
