Development of Pavement Deterioration Model for Rigid Pavement (Case Study: Cikopo-Palimanan Toll Road)

. Pavement deterioration will bring disruption to traffic, and it is hoped that the pavement is always on an acceptable condition. If the pavement distresses could be predicted correctly when the repair and maintenance plan was designed, the distresses could be addressed, and preventive steps can be taken to minimize the damage that will occur. This study aims to develop a mathematical model to predict pavement condition, which was represented by using International Roughness Index (IRI) value, for some sections constructed with rigid pavement at Cikopo-Palimanan Toll Road. In this study, there were several parameters that were analysed, including pavement age, traffic volume, and heavy commercial vehicle (HCV), to determine which parameter(s) affect the IRI value. It was found that pavement age has the most significant effect on IRI value. Moreover, a pavement deterioration model that considers pavement age, traffic volume and HCV has been developed .


Introduction
Infrastructure development is a driver of economic growth because it plays a role in regional development.One example of the infrastructure is road pavement.Based on the binding material, there are two types of pavements that are most commonly used, namely flexible and rigid pavements [1], [2].Each type of pavement has advantages and disadvantages.Strength or bearing capacity on concrete roads can reach a service life of more than 20 years if the casting is properly cared for.This value has exceeded the service life of the asphalt road which is only up to 10 years.The durability of asphalt roads is also influenced by external factors, such as temperature and traffic load [3].
During the service period, both asphalt and concrete pavements will be imposed by various number of loads, from both heavy and light vehicles, at varying rates.As a result, pavement performance will decrease and if not treated, over time the pavement will be damaged [1].To repair damaged pavement, it takes a certain amount of maintenance budget to be spent.With a budget, actual costs can be compared with planned costs [4].In its application in the real world, maintenance costs must be planned appropriately according to their needs [5].
This study develops a preliminary mathematical model by using the multilinear regression method, in order to predict the value of the International Roughness Index (IRI) on the rigid pavement of the Cikopo -Palimanan Toll Road, so that later through this value, prevention plans and maintenance actions can be made along with the most appropriate budget design.IRI was used as this the parameter that is most commonly used worldwide to represent the pavement quality [6] - [9].

Pavement Deterioration Model
Pavement deterioration models have become a critical tool for predicting the performance of pavements under various conditions [10].Accurately predicting pavement performance is essential to ensuring the longevity and safety of transportation infrastructure [11].This literature review aims to highlight the importance of pavement deterioration models and their significance in pavement management.
Pavement deterioration models provide a means of predicting the future condition of pavements and assist transportation agencies in developing maintenance and rehabilitation strategies to ensure their longevity and safety [12].These models enable transportation agencies to evaluate the effectiveness of various maintenance and rehabilitation strategies, allowing for better decisionmaking and resource allocation.Additionally, these models can assist in the optimization of pavement design and construction, resulting in longer-lasting and more cost-effective pavements.
Pavement deterioration models are classified into two broad categories: empirical and mechanistic-empirical models.Empirical models are based on statistical analysis of pavement performance data, while mechanisticempirical models utilize mathematical algorithms to represent the complex interaction between the pavement and its environment [13].While both models have their advantages and limitations, the use of mechanistic-empirical models is becoming increasingly prevalent due to their greater accuracy and ability to account for the complex interaction between pavement performance and various factors.
Recent research has shown the effectiveness of pavement deterioration models in predicting pavement performance.There have been a number of research studies that have developed pavement deterioration models [14] - [19].Pavement deterioration models are essential tools for predicting pavement performance and developing maintenance and rehabilitation strategies to ensure the longevity and safety of transportation infrastructure.Recent research has shown the effectiveness of these models in providing more accurate predictions and assisting in decision-making.While both empirical and mechanistic-empirical models have their advantages and limitations, the use of mechanisticempirical models is becoming increasingly prevalent due to their greater accuracy and ability to account for the complex interaction between pavement performance and various factors.Figure 1 shows the research flowchart for this research study.The study began by identifying the problems that occur based on the research background.After the problem was identified, it was continued with the preparation of literature studies that were relevant for the current study to be used as references.The next step is taking data to PT. Lintas Marga Sedaya directly to get traffic volume, repair history of pavement, IRI value.After obtaining the data, an analysis consists of three parts, namely looking for the relationship between parameters, developing a multilinear model to predict the IRI value, and validating and optimizing the model to make it more precise.After obtaining the final model and reassure its validity, conclusions can then be drawn from the analysis.

Data Collection
The data was obtained for Cipali Toll Road KM 72 until KM 188, which are divided into six sections.For all road sections, there were two lanes on each direction.Figure 2 shows the illustration of the road section.The data was available for both flexible and rigid pavements along the selected road sections, but this research only focuses on rigid pavement, and hence, the data was sorted to include only data with rigid pavement.

Data Parameter
Based on the data given, there were a number of parameters analysed, namely Pavement Age, Traffic Volume, Traffic Composition, International Roughness Index (IRI), and Pavement Repair History.Not all the data was available for each year between 2015 and 2021.Table 1 shows the availability of the data, which was used in this research.

Pavement Age
The pavement age calculation is carried out by utilizing the repairment history data that has been obtained from PT. Lintas Marga Sedaya.The repairment history data obtained starts from 2018 to 2021.Therefore, it is assumed in this study that no repairment have been done in 2017.The Cipali Toll Road began operating in the middle of 2015.If no repairs are made until 2017, then the pavement segment will be 2 years old in that year.When the pavement was repaired as an overlay, then the pavement age was considered to be starting at year zero again.Cumulative Single Axle Load (CESAL) The CESAL parameter is the cumulative ESAL value, which is obtained by accumulating the ESAL value in line with the surface age of the pavement.The ESAL values were calculated by multiplying the number of vehicles by the coefficients (E) listed in Table 2. Since the annual average daily traffic data is available from the beginning (in 2015), the CESAL for 2-year-old pavements in 2017 is obtained by summing up the ESAL value from 2015 to 2017.This parameter is the number of heavy vehicles in percent of annual average daily traffic.Heavy vehicles are defined as vehicles that weigh more than 5 tons, so they are separated from light vehicles such as passenger cars and vans because those were considered more influential or giving higher impact in pavement deterioration.

Data Analysis
After all the data was collected and the parameters were calculated.The IRI values were averaged for every 100 meters, every 1 kilometre, and every segment.The relationships between each parameter were analysed and a linear regression model was generated for each parameter.After the strongest relationship between parameter was established, the mathematical model was optimized by using a statistical software SPSS and the Solver Add-on in Microsoft Excel [20].

Relationships between parameters
The analysis process uses a linear regression method that produces an equation that describes the relationship between each parameter with IRI value.From the data, tables and graphs are made in three stages, namely in 100 meters, in 1 kilometre, and in segment to determine the relationship between pavement age and the IRI value, CESAL with the IRI value, and the percentage of heavy vehicles with the IRI value.From the stages done in the research, it was found that the segment stage gave the most reliable outcome due to the small distribution of data.Cipali Toll road consists of four lanes, namely L1A, L2A, L1B, and L2B.Table 3 shows the relationships between parameters and their coefficient of determination (R 2 ).Based on the data shown, it can be seen that the strongest relationship can be found between IRI and Pavement Age and the weakest relationship was found between IRI and HV.The analysis was then continued to combine all the data for each segment.The results can be seen at Figures 3, 4, and 5 for the relationships between IRI and CESAL, between IRI and HV, and between IRI and Pavement Age, respectively.Figure 3 shows a positive relationship between IRI and CESAL with a R 2 values of 0.42.It is important to note there are some outliers in the dataset, which could influence the model.As the CESAL value increases, the IRI value will also increase, which means that pavement became worse as more vehicles passed through.Therefore, it can be said that the CESAL value affects the IRI value.4 shows the relationship between IRI and HV.It can be seen that the variability of the available data was limited and there is almost no relationship between the parameters (by looking at the R 2 value that is almost 0).

Fig. 4. Relationship between HV and IRI Value
Figure 5 shows the relationship between IRI and Pavement Age.It can be seen that there is a strong positive relationship between the parameters.As the Pavement Age increases, the IRI value will also increase.This suggests that as the pavement gets older, the quality of the pavement decreases.Therefore, it can be said that the Pavement Age affects the IRI value.

Development of multilinear model
Based on the results of the first stage of analysis, it is known that from the three parameters tested, the CESAL value and pavement age have the most influence on changes in the IRI value.While the percentage of heavy vehicles does not have a significant role in changes in the IRI value.
The next analysis process will produce a multilinear regression method that produces an equation to predict IRI value from pavement history, CESAL, and percentage of heavy vehicle.The multilinear model produced with help of SPSS 25 software.Table 4 shows the multilinear models developed from SPSS software.
From the data in Table 4, it can be seen that the constant value in L1A was positive, which indicates that the IRI value will remain constant if the independent variables were not given any values.However, the constant values in L2A, L1B, and L2B were negative.This means that the IRI value will be negative if all independent variables have a value of zero.For the Pavement Age parameter, it was found to have a positive coefficient except for L1A.This means that an increase in pavement age in all three lanes will result in an increase in the IRI value.However, in L1A, the coefficient was negative, indicating that a 1% increase in the Pavement Age parameter will result in a 3.8% decrease in the IRI value.For the CESAL parameter, a positive coefficient was found in L1A and L1B.This means that in the other lanes, every increase in the CESAL value will affect a decrease in the IRI value according to its coefficient.This finding was supported by the information given from PT. Lintas Marga Sedaya that Lane 1 is a slow lane, so the load obtained by the pavement will have a greater impact on its damage.The same applies to the percentage of heavy vehicles variable.It was found that only L1A has a negative coefficient, indicating that every increase in the number of heavy vehicles in the other three lanes will have an impact according to its coefficient on an increase in the IRI value.By using the entire data set, the result of multilinear modelling for all lanes from the SPSS program is IRI = 3.647 + 0.145PA + 2.682E-8CESAL -7.15HV with R 2 value of 0.28.Even though the R 2 value was on the low side, but it is important to note that there are some limitations encountered in this research, which will be explained in section 4.4.

Validation and optimization
Validation process was carried out to ensure that the modelling was suitable to the available data.This process was carried out for all modelling results, namely CESAL vs IRI, HV vs IRI, Pavement Age vs IRI, and even multilinear model from SPSS program results.Table 5 shows the validation results.It can be seen that the resulting difference obtained after validation for the four models shows that some equations do not reach zero result.Therefore, further optimization process was needed.Validation process done by matching the IRI value in the initial data with the IRI value calculated using the equations obtained from the SPSS program for multilinear equations, and equations from Microsoft Excel for linear equations.If the total difference from the IRI was still quite large, the model is re-optimized using Microsoft Excel's Solver add-on to minimize the total IRI difference that expected to reach zero.Table 6 shows the results after each model was optimized and it can be seen that the resultants are almost zero.

Research limitations
There are various factors that can affect the variation in data.There is a possibility that the history of repairs was not properly recorded, meaning that the data collection of International Roughness Index (IRI) might have been conducted on different road conditions.Road repairs were not done thoroughly, but are divided into several sections depending on the existing damages.The process of collecting IRI values was also done over a period of years, meaning that it is uncertain whether the IRI values were collected under the same conditions for the entire pavement section.The calculation of Pavement Age was done by looking only at the year when the repair was made or the road was opened.Therefore, this could be source of inaccuracies of the data used.
Moreover, the available IRI values were only from year 2017 to 2021.According to PT. Lintas Marga Sedaya, the IRI values have been collected using a Roughometer device since 2018, which allow the company to conduct the process independently.However, the IRI values measured for 2017 were collected by the Road and Bridge Research Center (Pusjatan), resulting in the available data being in the form of IRI values per 1 kilometer.Therefore, there was a difference between the IRI values in 2017 and 2018, which can affect the graphs generated in the analysis of the relationship between parameters and the development of multilinear models.

Conclusion
Based on the study, it can be concluded that: a. Through parameter analysis, it was found that cumulative ESAL (CESAL), and pavement age had a strong influence on changes in IRI values.However, the parameter of the percentage of heavy vehicles was found to have the least effect on changes in the IRI value.This is evidenced by the correlative coefficient values obtained are as follows: Correlation coefficient (R

Suggestions
Based on results of this research, few suggestions are given to improve and expand the field of knowledge that is directly related to this research: It is necessary to carry out further research on the condition of the subgrade and the existing pavement structure; After obtaining a predictive model, calculations can be made and it is necessary to determine the type of handling and repair of damage that is appropriate for the pavement; Development of IRI value prediction model can be done by considering other factors, such as CBR data, rainfall, and temperature.

2 )
CESAL vs IRI = 0.420; Correlation coefficient (R 2 ) HV vs IRI = 0.004; Correlation coefficient (R 2 ) SA vs IRI = 0.8726; b.The results of the development for the multilinear prediction model of IRI values that are influenced by the three independent variables are: y = 3.647 + 0.145A + 2.678 × 10 -8 CESAL -7.15HV with a correlation coefficient of 0.277 and has met the requirements of the T-test.Based on the test, the variables SA and CESAL have a significant positive effect and HV has a significant negative effect on the IRI value; c.Several factors become obstacles in the development of predictive models, namely: Limited historical data on pavement repairs; Human error in taking IRI scores; Initial data quality, especially IRI scores.

Table 2 .
Coefficients for ESAL Calculation

Table 3 .
Linear Regression Models for the Relationship between Parameters

Table 5 .
Validation Results From SPSS.