In the state of Colorado, the Colorado Department of Transportation (CDOT) utilizes their pavement management system (PMS) to manage approximately 9,100 miles of interstate, highways, and lowvolume roads. Three types of deterioration models are currently being used in the existing PMS: sitespecific, family, and expert opinion curves. These curves are developed using deterministic techniques. In the deterministic technique, the uncertainties of pavement deterioration related to traffic and weather are not considered. Probabilistic models that take into account the uncertainties result in more accurate curves. In this study, probabilistic models using the discretetime Markov process were developed for five distress indices: transverse, longitudinal, fatigue, rut, and ride indices, as a case study on lowvolume roads. Regression techniques were used to develop the deterioration paths using the predicted distribution of indices estimated from the Markov process. Results indicated that longitudinal, fatigue, and rut indices had very slow deterioration over time, whereas transverse and ride indices showed faster deterioration. The developed deterioration models had the coefficient of determination (
The Colorado Department of Transportation (CDOT) is responsible for maintaining a highway system that encompasses more than 9,100 centerline miles (about 23,000 total lane miles) and includes 3,437 bridges [
As the performance of each roadway segment is different, the CDOT develops a segmentspecific deterioration curve. These curves are generated to satisfy certain conditions, including at least five years of historical pavement distress data after last rehabilitation, the standard deviation of the data cannot exceed 10, and the minimum coefficient of regression
All these deterioration curves are generated using a deterministic technique [
Predicted maintenance treatments are not fixed, rather depend on how the pavement actually deteriorates.
Because of the uncertainty in selecting maintenance treatments, the treatments should be selected with a high degree of probability.
The success of maintenance decisions can be evaluated by comparing the expected and actual proportions of the miles in a given condition state.
This model has the potential for significant cost saving in selecting projects satisfying the target network performance.
This model can also be incorporated into dynamic programming to produce optimal solutions.
In a probabilistic technique, only two years of historical data are needed to develop a deterioration model. Currently, the Markov process is popular among probabilistic techniques to develop a deterioration model. Michigan DOT already improved their PMS using the Markov process [
The CDOT pavement management software uses five distress indices to model pavement deterioration: three cracking indices (transverse, longitudinal, and fatigue), roughness, and rutting indices. When all the values are loaded into the software, it generates deterioration curves for all roadway segments. For each segment, five performance curves are generated for each of the distress indices. These performance curves are named as the sitespecific curves. There are two other types of performance curves: pavement family and expert opinion. The most desirable of these is the sitespecific curve. When sitespecific curves are not available, family or expert opinion curves can be used.
The length of the CDOT roadway segments ranges from 0.5 mile to 5 miles. For each segment, a sitespecific performance curve is generated using historical distress data as discussed earlier.
The CDOT uses the following criteria to define the family curve:
Pavement types: asphalt, asphalt over concrete, concrete, and concrete over asphalt
Traffic: low, medium, high, very high, and very very high
Climate: very cold, cold, moderate, and hot
Pavement thickness (asphalt: 0 to 4 inches, 4 to 6 inches, and greater than 6 inches; concrete: pavements less than 8 inches and greater than 8 inches)
These categories allow for 200 pavement families. At least 9 points are needed to generate a family curve.
When neither sitespecific nor family curves are available, an expert opinion curve is assigned. The expert opinion curves are generated for each pavement family. As there were 200 pavement families, 200 curves were generated. These curves were not developed from regression analysis of data, rather are derived from expert opinion. These curves are least desirable for any pavement segment [
In the PMS, the pavement deterioration model (PDM) is the key to making maintenance strategies and allocating funding for the future. An accurate and reliable PDM is essential for the optimization model of the PMS [
Deterministic modeling techniques are the most common because of their relative simplicity, ease of use, and familiarity [
Models do not take into account the uncertainties in pavement behavior under variable traffic load and weather conditions.
Developing models require an accurate and abundant dataset. Accuracy of datasets can be greatly affected by regular maintenance or minor rehabilitation activities.
It is necessary to include all confounding variables that affect pavement deterioration.
The critical disadvantage of deterministic models is that it does not take into account the uncertainties [
In the early 1970s, the applications of probabilistic models for modeling pavement performance were first discussed [
According to the CDOT, the distress indices are scaled from 0 to 100, where 100 represents a flawless pavement with no distresses and 0 represents the worst condition. Transverse, longitudinal, and fatigue cracking indices can be calculated for each roadway segment using (
The values of all other parameters in (
The values of parameters for calculating distress indices for asphalt pavement.
Fatigue index  Transverse index  Longitudinal index  Ride index  Rut index  


6230  160  3802  —  — 

3375  111  2492  —  — 

2014  49  1478  —  — 

—  —  —  0  — 

—  —  —  —  0.15 

—  —  —  26  0.95 
The Markov model provides a prediction of pavement performance. Pavement performance can be determined by each distress index or a combined index representing the overall pavement condition. Most commonly used pavement distress indices are transverse, fatigue, longitudinal cracking, roughness, and ride. Usually, these indices range from 0 to 100, where 100 represents the best condition and 0 is for the worst condition. A pavement section begins its life in a nearperfect condition. Over the years, the pavement condition deteriorates due to many factors such as traffic loading and weather conditions. Most states evaluate their pavement condition once a year. In order to develop a capital improvement plan (usually a fiveyear plan), state agencies need to predict their pavement condition for the next five years. In this section, how to predict the pavement condition for the future using the Markov model is discussed.
Markov models start with developing a transition probability matrix (TPM). A TPM represents the probability that a segment will stay in a specific condition for a specific year. For example, Table
Transition probability matrix with five states [
To condition  5  4  3  2  1  

From condition  5 

1 − 
0  0  0 
4  0 

1 − 
0  0  
3  0  0 

1 − 
0  
2  0  0  0 

1 −  
1  0  0  0  0  1 
The next year’s pavement condition can be determined by multiplying the initial state vector
5
4
3
2
1
5
1
0
0
0
0
The next year’s pavement condition can be determined using the following equation:
Figure
Example of a Markovian deterioration model.
In order to develop the deterioration models using the Markov process, a case study was conducted on the lowvolume roads in Colorado. A comprehensive maintenance record of lowvolume roads was collected from the CDOT. There are 116 lowvolume roads in Colorado with 2,022 miles of pavement. These lowvolume roads were segmented by the CDOT, and a total of 342 segments were established. The segments begin and end where there are overlays, new construction, or other changes in the pavement. The database contained information related to road identification number, beginning and ending milepost, and the five distress indices (transverse cracking, longitudinal cracking, fatigue cracking, rut, and ride indices). Five years of maintenance records from 2010 to 2014 were used in this study. The research team had to extract, filter, and combine the datasets from 2010 to 2014 to prepare a single database for lowvolume roads. A sample database for the year 2014 is shown in Table
Maintenance records of lowvolume roads in 2014.
Route  Beg. MP  End. MP  Rehab. year  Ride index  Rut index  Fatigue index  Transverse index  Longitudinal index  Year 

005A  0  14.894  1994  42  99  93  70  99  2014 
006A  11.825  13.867  1985  73  98  73  61  96  2014 
006A  11.179  11.825  1985  73  98  73  61  96  2014 
006A  11.08  11.179  1985  73  98  73  61  96  2014 
In order to implement the Markov process, the values of each distress index were grouped based on Table
Grouping of distress indices.
Index range  Group name  Index range  Group name 

96–100  100  66–70  70 
91–95  95  61–65  65 
86–90  90  56–60  60 
81–85  85  51–55  55 
76–80  80  46–50  50 
71–75  75  41–45  45 
Modified maintenance records of lowvolume roads in 2014.
Route  Beg. MP  End. MP  Rehab. year  Ride index  Rut index  Fatigue index  Transverse index  Longitudinal index  Year 

005A  0  14.894  1994  45  100  100  70  100  2014 
006A  11.825  13.867  1985  75  100  75  65  100  2014 
006A  11.179  11.825  1985  75  100  75  65  100  2014 
006A  11.08  11.179  1985  75  100  75  65  100  2014 
This study intends to develop five separate deterioration models for the five distress indices. In order to do this, a summary matrix for each distress has been developed. A sample summary matrix for the transverse cracking index can be seen in Table
Summary of the database in centerline miles for the transverse cracking index.
Transverse cracking index  

100  95  90  85  80  75  70  65  60  55  50  45  40  35  
Transverse cracking index  100  872  511  117  16  52  6  0  3  16  —  —  2  —  — 
95  —  1018  707  397  238  51  0  2  9  2  —  —  —  —  
90  —  —  488  412  197  172  117  33  5  2  10  7  2  —  
85  —  —  —  438  238  101  92  74  37  8  18  —  10  —  
80  —  —  —  —  175  135  71  43  45  12  10  8  4  0  
75  —  —  —  —  —  20  24  66  35  14  7  5  1  9  
70  —  —  —  —  —  —  18  3  7  4  6  19  5  —  
65  —  —  —  —  —  —  —  24  21  8  —  2  —  —  
60  —  —  —  —  —  —  —  —  —  —  —  25  2  1  
55  —  —  —  —  —  —  —  —  —  —  —  —  2  —  
50  —  —  —  —  —  —  —  —  —  —  —  —  —  —  
45  —  —  —  —  —  —  —  —  —  —  —  —  —  7  
40  —  —  —  —  —  —  —  —  —  —  —  —  —  —  
35  —  —  —  —  —  —  —  —  —  —  —  —  —  — 
Example of the database in centerline miles of the Markov model.
Index ratings (from one year to another)  Length, miles  

Trans.  Ride  Long.  Fatigue  Rut  
100 to 100  872  0  4063  4285  7741 
100 to 95  511  0  964  559  564 
95 to 95  1018  443  340  250  153 
95 to 90  707  149  55  203  5 
90 to 90  488  1670  23  99  42 
90 to 85  412  472  4  40  3 
85 to 85  438  2255  8  55  0 
85 to 80  238  535  1  37  21 
80 to 80  175  1882  0  25  0 
80 to 75  135  263  0  10  0 
75 to 75  20  307  0  56  1 
75 to 70  24  47  0  2  0 
70 to 70  18  65  0  42  0 
70 to 65  3  11  0  43  0 
65 to 65  24  164  0  16  0 
65 to 60  21  3  0  9  0 
60 to 60  0  0  0  0  0 
60 to 55  0  0  0  1  0 
55 to 55  0  0  0  9  0 
The Markovian process has been implemented on all five distress indices using the data shown in Table
Probability distribution values from the Markov model for all five indices.
Transverse cracking index  

Index  Year 1  Year 2  Year 3  Year 4  Year 5 
100 

0.398  0.251  0.158  0.1 
95  0.369 



0.257 
90  0  0.151  0.267  0.314 

85  0  0  0.069  0.167  0.252 
80  0  0  0  0.024  0.072 
75  0  0  0  0  0.011 


100 





95  0.115  0.166  0.182  0.18  0.17 
90  0  0.052  0.111  0.16  0.195 
85  0  0  0.015  0.041  0.071 
80  0  0  0  0.06  0.02 
75  0  0  0  0  0.002 


100 



0.453  0.372 
95  0.18  0.311  0.405 


90  0  0.015  0.039  0.064  0.088 
85  0  0  0.004  0.01  0.016 


100  —  —  —  —  — 
95  —  —  —  —  — 
90 


0.419  0.314  0.235 
85  0.251  0.384 



80  0  0.055  0.129  0.202  0.262 
75  0  0  0.011  0.034  0.069 
70  0  0  0  0.001  0.005 


100 





95  0.068  0.129  0.184  0.234  0.279 
90  0  0.002  0.006  0.01  0.016 
85  0  0  0  0  0.001 
Transition matrix of the transverse cracking index.
Transverse cracking index  

100  95  90  85  80  75  70  65  
Transverse cracking index  100  872  511  —  —  —  —  —  — 
95  —  1018  707  —  —  —  —  —  
90  —  —  488  412  —  —  —  —  
85  —  —  —  438  238  —  —  —  
80  —  —  —  —  175  135  —  —  
75  —  —  —  —  —  20  24  —  
70  —  —  —  —  —  —  18  3  
65  —  —  —  —  —  —  —  24 
Transition probability matrix of the transverse cracking index.
Transverse cracking index  

100  95  90  85  80  75  70  65  
Transverse cracking index  100  0.631  0.369  0  0  0  0  0  0 
95  0  0.590  0.410  0  0  0  0  0  
90  0  0  0.542  0.458  0  0  0  0  
85  0  0  0  0.648  0.352  0  0  0  
80  0  0  0  0  0.564  0.436  0  0  
75  0  0  0  0  0  0.460  0.540  0  
70  0  0  0  0  0  0  0.877  0.123  
65  0  0  0  0  0  0  0  0.454 
Probability distribution values from the transverse cracking index Markov model.
Year 1  Year 2  Year 3  Year 4  Year 5  

Transverse cracking index  100 

0.398  0.251  0.158  0.1 
95  0.369 



0.257  
90  0  0.151  0.267  0.314 


85  0  0  0.069  0.167  0.252  
80  0  0  0  0.024  0.072  
75  0  0  0  0  0.011 
Table
Deterioration models for transverse, longitudinal, fatigue, rut, and ride indices.
In the state of Colorado, the CDOT utilizes their PMS to keep track of approximately 9,100 miles of interstate, highways, and lowvolume roads. Three types of deterioration curves are used in their PMS: sitespecific, family, and expert opinion curves. These curves are developed using deterministic techniques. Within the deterministic technique, the uncertainties of pavement deterioration related to traffic and weather are not considered. Probabilistic models that take into account the uncertainties result in more accurate curves. In this research, probabilistic models have been developed for five distress indices: transverse, longitudinal, fatigue, rut, and ride indices, as a case study on lowvolume roads. Deterioration models were developed for 15 years to investigate the deterioration in longterm durations. As probabilistic models provide more accurate results, it is recommended that these models be used as the family curves in the CDOT PMS after minor modifications.
The developed models can be highlighted as follows:
Tailored specifically to lowvolume roads.
As this methodology incorporates uncertainties, the developed models’ results are more accurate than those currently used by the deterministic technique.
This methodology can also be implemented on other functional classes of roadways in Colorado and for other states with minor changes that reflect local conditions.
DOTs are always shifting practices to better optimize limited resources. It was demonstrated in this paper that the deterioration models using the Markovian probability process can help DOTs better manage their pavements. It is recommended that a comprehensive study be conducted to determine the longterm implications of replacing deterministic models with Markov models in the state of Colorado. It is also recommended that other DOTs consider Markov probability processes when it comes to allocating resources or comparing maintenance and rehabilitation strategies within their jurisdictions.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
The authors would like to thank the CDOT for supporting this research study.