Development of a Relationship between Pavement Condition Index and Riding Quality Index on Rural Roads: A Case Study in China

Abstract

The current standard for evaluating road conditions worldwide relies primarily on the Pavement Condition Index (PCI) and the International Roughness Index (IRI). The IRI can be further calculated to obtain the Riding Quality Index (RQI). To assess pavement damage, various imaging equipment is commonly utilized, providing consistent results that align with actual road conditions. For roughness detection, the Laser Profilometer offers excellent results but may not be suitable for rural roads with poor conditions due to its high inspection cost and the need for a stable environmental setting. Therefore, there is a pressing need to develop cost-effective, rapid, and accurate roughness inspection methods for these roads, which constitute a significant portion of the road network. This study examined the relationship between PCI and RQI using nonlinear regression on 30,088 valid pavement inspection records from various regions in China (totaling 24,624.222 km). Our objective was to estimate RQI solely from PCI data, capitalizing on its broad coverage and superior accuracy. Additionally, we explored how PCI levels impact RQI decay rates. The models in this study were compared to several models published in previous studies at last. Our findings indicate that the model performs best for low-grade roads with low PCI scores, achieving over 90% accuracy for both cement concrete and asphalt concrete pavements. Furthermore, different levels of pavement damage have distinct effects on RQI decay rates, with the most significant impact observed when the pavement is severely damaged. The models in this study outperformed all the other available models in the literature. Consequently, under limited inspection conditions in rural areas, pavement damage inspection results can effectively predict riding quality or roughness, thereby reducing inspection costs. Overall, this study offers valuable insights but has limitations, including limited global generalizability and the model’s applicability to high-grade roads. Future research is needed to address these issues and enhance practical applications.

1. Introduction

Pavement technical condition detection and evaluation is one of the basic tasks in road maintenance management, which plays a key role in the scientific allocation of maintenance resources. The road infrastructure in developed countries was built earlier and has entered a stage of large-scale maintenance. Many countries and international organizations have successively established their own pavement evaluation models and further improved the formation of standard specifications for the evaluation of the technical condition of road infrastructures. Representative models include the Present Serviceability Rating (PSR) proposed by AASHTO [1], Japan’s Maintenance Control Index (MCI) model [2,3], the PCI model developed by the U.S. Army Corps of Engineers [4], and the World Bank’s Universal Crack Index (UCI) [5].

The system of road condition indicators used varies from region to region. The evaluation indicators used in Ontario, Canada, are the pavement Distress Rate (DR), International Roughness Index (IRI), and Rutting Depth Index (RDI) [6]. New York State in the United States uses similar indicators [7], including the Pavement Condition Index (PCI), IRI, and RDI. The idea of a comprehensive evaluation of multiple indicators is also adopted in China’s current Highway Performance Assessment Standards (JTG 5210–2018), including PCI, Pavement Riding Quality Index (RQI), RDI, Pavement Skidding Resistance Index (SRI), Pavement Bumping Index (PBI), Pavement Surface Wearing Index (PWI), and Pavement Structural Strength Index (PSSI) [8]. Summarizing the evaluation indicators of different countries (regions), it can be seen that pavement damage, roughness, and rutting are the most frequently used indicators for pavement performance evaluation. Among them, rutting is mainly an indicator of concern for high-grade roads, while pavement damage and roughness are generally applicable for all grades of roads. Especially for low-grade roads, these two indicators are mainly concerned. Therefore, this paper focuses on these two indicators.

1.1. Pavement Damage and Roughness Indicators

PCI is used to characterize pavement damage, which mainly depends on the Distress Rate (DR). It was originally developed by the U.S. Army and later standardized by the ASTM [9]. PCI can comprehensively reflect the damage type, severity, and density of pavement and is considered to be a well-established comprehensive index of pavement damage. China has also incorporated it into the specification and redefined the specific damage types and weights based on the actual situation of Chinese roads. According to the current Chinese standard [8], asphalt pavement damage types include alligator cracking, block cracking, transverse cracking, longitudinal cracking, subsidence, rutting and shoving, potholes, bleeding, raveling, and patching. PCI is a numerical index ranging from 0 to 100 [10]. The higher the score, the better the road condition, and 100 points represents the ideal condition without damage. Both the U.S. and China use the deduction method to calculate the PCI, where the U.S. standard classifies the PCI into seven grades [11], and the Chinese standard divides it into five grades, excellent, good, medium, inferior, and poor [8].

According to ASTM, traveled surface roughness is the vertical deviation of the pavement surface from the ideal plane, which affects the dynamic characteristics of the vehicle, ride quality, dynamic loads on the surface, and drainage [12]. Pavement roughness is usually measured by IRI, a standardized indicator used to characterize the longitudinal profile of a traveled wheel track, measured as the ratio of the cumulative suspension movement to the distance traveled by a standard vehicle [13]. The IRI was initially developed by Gillespie et al. and then adopted and popularized by the World Bank [14,15]. Most highway agencies around the world routinely measure the IRI. AASHTO has stipulated the grading standards for roughness and classified IRI into five grades.

Compared to the IRI, the PCI also includes deformation inspection, which overlaps with the IRI to a certain extent. Therefore, in the case of limited resources, if the relationship between PCI and IRI can be quantified with a high degree of confidence, data on roughness can be obtained easily based on the pavement damage data. This will greatly reduce the cost of pavement condition detection and promote more scientific and reasonable maintenance management and decision-making in transportation departments. Therefore, many scholars have begun to conduct exploratory research on the relationship between pavement damage and roughness. Aultman-Hall et al. [16] studied the correlation between IRI and pavement damage including rutting and cracking based on data from the Connecticut Department of Transportation. The correlation between them was found to be relatively weak, with a maximum coefficient of determination (R²) value of only 0.299. Bryce et al. [17] studied the relationship between PCI and PSR based on LTPP road sections and found that there was little correlation between them. However, the R² reached 0.66 after adding the parameters about the patched area, the lengths of transverse and longitudinal cracks, and the rut depth to the PSR prediction equation. This study proved the speculation that there is a correlation between pavement damage and roughness. Kirbas [18] studied the effect of some typical pavement damages such as cracking, bleeding, and corrugation on IRI through regression analysis and found that the overall R² reached 0.745. Adeli et al. [19] used linear regression analysis to establish a model based on IRI to predict PCI, with an R² of 0.76. Mactutis et al. [20] studied the relationship between IRI and cracks and ruts, and they suggested that better models and methods need to be developed to improve the prediction accuracy of IRI. Park et al. [21] studied the correlation between PCI and IRI using a power regression model based on data from the LTPP database and obtained an R² value of 0.59. Piryonesi and El-Diraby [22] studied the correlation between PCI and IRI in asphalt pavements using linear regression analysis based on the LTPP database, and the overall R² value was only 0.301. However, the R² exceeded 0.7 in some cases after dividing the data into groups based on location and functional class. Makendran and Murugasan [23] used a linear regression analysis to develop the relationship between pavement roughness and cracks and potholes with an R² value of 0.814, but the validity of the model was limited to roads with very low traffic conditions. Amarendra et al. [24] developed the relationship between IRI and a variety of pavement damages by using multiple linear regression analysis. It was found that different pavement distresses affect roughness differently. For Indian roads, potholes and raveling dominated.

In recent years, with the rapid development of various research methods such as deep learning and artificial neural networks, scholars have conducted more quantitative studies on the relationship between pavement damage and roughness. Liu et al. [25] developed the relationship between PCI and IRI using artificial neural network techniques, and the R² reached 0.998. Chandra et al. [26] developed the relationship between pavement roughness and potholes, patching, rutting, raveling, and cracking using linear regression, nonlinear regression, and artificial neural network methods based on the data of four highways in India. The model built by an artificial neural network had the highest accuracy. Elhadidy et al. [27] utilized an artificial neural network to build a model between PCI and IRI based on the LTPP database, and the R² reached 0.86. It showed that IRI could be accurately predicted from the PCI collected in the LTPP database. Ali et al. [28] used multiple linear regression and artificial neural network methods to develop a model for predicting IRI from pavement age and nine types of pavement damage. The results showed that the neural network model has higher accuracy.

Most studies have shown that there is a correlation between pavement damage and roughness, so it should be feasible to predict roughness based on pavement damage data. However, most of the studies use specific pavement damage and IRI to establish a relationship model, and there are very few studies that directly investigate the correlation between PCI and IRI. In addition, most studies usually use data from different regions, and the pavement damage, traffic volume, road grade, etc., are very different, but generally only a single model is established, so the model is not very explanatory to the data.

1.2. Pavement Damage and Roughness Inspection Method

With the development of pavement detection technology and the improvement of pavement performance evaluation methods, many countries have developed pavement inspection methods suitable for their own needs. For example, the Pavement Condition Evaluation Service (PCES) system and the Automated Roadway Inspection System (ARIS) in the U.S. [29,30], the Komatsu system in Japan [31], the Portable Application for Vehicle Underground Evaluation (PAVUE) system in Sweden [32], and the Crack Recognition Holographic System (CREHOS) in Switzerland [33].

In recent years, with the expansion of the road network and the improvement of maintenance and management requirements, road inspection has become more and more popular. The industry’s increasing demand for low-cost inspection techniques has led to the emergence of some simple and fast road inspection methods. For example, Aleadelat et al. [34] used a 3D accelerometer of a smartphone to collect the vertical acceleration data of a vehicle to obtain roughness data. Ersoz et al. [35] developed an Unmanned Aerial Vehicle (UAV)-based pavement crack recognition system to obtain crack features of concrete pavements by capturing images from a UAV, which was used to train the Support Vector Machine (SVM) model. It provides an alternative solution for monitoring the changes of cracks in cement concrete pavements. Yan et al. [36] developed a low-cost Video-based Movement Abnormality Detection System (VPADS) by analyzing video image data collected by a consumer-grade video camera mounted on the front of a car. The VPADS system replaces the traditional on-site inspection or high-end multi-sensor pavement assessment system. Kumar et al. [37] proposed a smartphone-based community sensor network for monitoring pavement conditions. Smartphone applications were distributed to volunteers who participated in acquiring pavement quality data and benefited from information on the general condition of the road. Huang et al. [38] proposed a low-cost data collection system for road condition assessment using an Intel RS-D435 camera, a consumer-grade RGB-D sensor, and an NVIDIA Jetson TX2 computing device that is mounted on a vehicle for data collection. Combined with various deep coding techniques and data fusion methods, potholes can be successfully detected even when the scene is dark (i.e., not bright enough).

The most commonly obtained indicators for these detection methods are pavement damage and roughness, which are also the crucial indicators used in road condition evaluation [39,40]. At present, for pavement damage detection, simple image equipment can provide stable results consistent with the actual road condition trend, and the price is low. For roughness detection, although some low-cost methods can be used, the detection results are obviously not accurate for rural roads with poor conditions. Now, the more mature and stable technology is mainly Laser Profilometer, which is also not suitable for these roads. Moreover, most transportation departments today still rely on IRI for road maintenance and rehabilitation planning [41]. For large-scale inspection, the cost of IRI is relatively high, ranging from $1.40 to $6.20 per kilometer [42]. In addition, IRI inspection requires calibrated equipment and professionally trained personnel. Even with the new and advanced technologies, transportation departments cannot fully afford the time and expense required, much less the cost of inspection at a higher frequency than once a year. For rural roads, the challenges are even more evident. Due to the lack of sophisticated equipment and professionals, accurately measuring road roughness becomes particularly difficult. This not only affects the quality of the data, but also makes the maintenance and management of such roads more challenging. Therefore, finding an economic and accurate method for obtaining road roughness in a resource-limited environment is an important challenge currently facing transportation departments.

In China, compared to specific damage and IRI, PCI and RQI data are often easier to obtain in the actual road maintenance management database, especially when historical data are needed. The RQI includes the content of roughness evaluation, and it can be calculated according to the IRI. The calculation formula of RQI is shown in Equation (1). According to the current Chinese standard, RQI is similar to PCI, which also takes the value of 0–100 and is divided into five grades: excellent, good, medium, inferior, and poor [8]. So, this paper focuses on the relationship between PCI and RQI.

$$RQI=\frac{100}{1+a_0{e}^{a_{1}IRI}}$$

(1)

where $a_0$ and $a_1$ are constants. For expressways and first-class roads, $a_0$ is 0.026, $a_1$ is 0.65, and for other classes of roads, $a_0$ is 0.0185, and $a_1$ is 0.58. In summary, based on a large amount of pavement inspection data from various provinces (cities) in China, this study uses a nonlinear regression analysis method to establish mathematical models of the PCI and RQI for roads with different pavement damage levels and different technical grades. In addition, this paper attempts to quantify the effects of different pavement damage levels on the decay rate of RQI. This study is divided into five sections. Section 1: Data preparation, which mainly includes data profile and data preprocessing. Section 2: Data analysis. Correlation analysis was first performed on PCI and RQI to prove their correlation. Then, regression analysis was carried out to obtain the mathematical model between the two. Section 3: Model prediction effect assessment. The prediction effect of the regression model was evaluated using the reserved sample data. Section 4: Quantitative analysis of the effect of different pavement damage levels on the decay of RQI. Section 5: Model validation. The prediction accuracy of the model proposed in this paper was verified based on actual engineering inspection data.

2. Data Preparation

2.1. Data Profile

This study collected road inspection data from 2008 to 2015 in nine provinces in China, including five southern provinces and four northern provinces. These data are from the national arterial road network database. A total of 51,120 pieces of data were collected, of which 28,467 were for asphalt pavement and 22,653 for cement concrete pavement. After preprocessing, there were 30,088 valid data with a total mileage of 24,624.222 km. Among them, 18,255 sections are asphalt pavement, totaling 17,354.678 km; 11,833 sections are cement concrete pavement, totaling 7269.545 km. These data can be divided into two categories, static data and inspection data. The static data include inspection year, road section ID, road name, section start and end, section length, pavement type, technical grade, management agency, and other basic attribute information of roads. The inspection data include various pavement performance indicators such as PCI, RQI, PSSI, RDI, SRI, and so on. This dataset has sufficient data volume and covers a wide range of areas, which can provide reliable data support for the analysis and modeling of this study.

2.2. Data Preprocessing

Due to the large volume and wide distribution of original data, there may be data noise interference such as missing data, filling errors, and subjective bias in the basic road information and historical inspection data. Therefore, it is necessary to carry out data preprocessing before analyzing and modeling the data, which mainly includes data grouping and outlier processing.

2.2.1. Data Grouping

The analytical-calibration method [43] was first used to determine the reasonable distribution range of PCI and RQI. This method processes the outliers of the overall data and determines a reasonable threshold interval for PCI and RQI based on engineering experience. The analytical-calibration method offers several key advantages in data analysis, particularly in road condition assessment. It is simple, flexible, effective, and practical, making it an invaluable tool for road management applications. Its straightforward nature enables efficient data processing, while its flexibility allows for adaptability to different road types and regional characteristics. The method effectively handles abnormal data values, enhancing data reliability and accuracy. Its practicality lies in producing data that alignss with real-world conditions, supporting informed decision-making in road maintenance management and investment. Overall, the analytical-calibration method offers a robust framework for data analysis in road condition assessment, contributing to more effective and efficient road management practices.

The method mainly consists of the following four steps:

• Data collection and collation. Collect PCI and RQI data for the same road over a period of time. These data usually come from road maintenance management records and field inspection.
• Identifying outliers. Based on engineering experience, determine the general relationship between PCI and RQI. For example, if the PCI score for a certain road is between 98 and 100, it can be expected that its RQI score will generally not be lower than 90. Similarly, if the PCI score is below 60, the RQI score will generally not be higher than 80. These relationships can be used to identify outliers, that is, those data points with PCI and RQI that significantly deviate from the expected range.
• Threshold determination. Determine the reasonable threshold range for PCI and RQI based on the results of outlier identification. For example, if there are too many outliers for a certain PCI score, it may be necessary to adjust the threshold range for that score.
• Data calibration. Calibrating the raw data based on the determined threshold range, which involves removing or correcting outliers to ensure that the data distribution falls within a reasonable range. Calibrated data are more realistic and help to improve the accuracy and reliability of subsequent analysis.

The processed data were further grouped. In the first step, the sample data were categorized into 8 groups based on PCI scores. The grouping here not only referred to the current PCI grade classification standard in China [8] but also considered the relationship between PCI scores and pavement damage distribution [44], as well as the equalization of the amount of data in each group. In the second step, the roads were further grouped according to their technical grades. In China, roads are classified into five levels according to their technical conditions, including expressways, Class I, Class II, Class III, and Class IV and below. Generally, roads of Class III and Class IV and below are defined as low-grade roads. Finally, 24 groups were finally obtained, which are shown in

Table 1. Data grouping based on PCI score.

Group Number	PCI Range
1	100–91
2	91–82
3	82–79
4	79–74
5	74–65
6	65–55
7	55–40
8	40–0

,

Table 2. Data grouping based on road grade.

Group Number	Technical Grade of Roads
1	expressway, Class I
2	Class II
3	Class III, IV and below

and

Table 3. Grouping of sample data.

Group Number	PCI Score	Technical Grade of Roads
1–1	100–91	expressway, Class I
1–2		Class II
1–3		Class III, IV and below
2–1	91–82	expressway, Class I
2–2		Class II
2–3		Class III, IV and below
3–1	82–79	expressway, Class I
3–2		Class II
3–3		Class III, IV and below
4–1	79–74	expressway, Class I
4–2		Class II
4–3		Class III, IV and below
5–1	74–65	expressway, Class I
5–2		Class II
5–3		Class III, IV and below
6–1	65–55	expressway, Class I
6–2		Class II
6–3		Class III, IV and below
7–1	55–40	expressway, Class I
7–2		Class II
7–3		Class III, IV and below
8–1	40–0	expressway, Class I
8–2		Class II
8–3		Class III, IV and below

. Although this paper mainly focuses on low-grade roads, the data on higher-grade roads were still analyzed as a reference.

2.2.2. Outlier Processing

The Isolation Forest (iForest) algorithm was used in this study for outlier processing. The key to this method is to determine the proportion of anomalies in each set of sample data, and frequency analysis was used here. Frequency analysis is a way of counting the frequency of different values of a set of data falling within a specified region to understand its data distribution status. Through frequency analysis, it can reflect to a certain extent whether the samples are representative of the whole and whether there is systematic bias in sampling. In this way, it can prove the representativeness and credibility of the analysis of the relevant issues. After determining the proportion of anomalies in each set of sample data, anomaly detection was performed on each set of data.

The iForest algorithm was first proposed by Zhou et al. in 2008 [45]. In comparison to other anomaly detection algorithms, the iForest algorithm offers significant advantages in detecting outliers. Specifically, it exhibits efficient performance, enabling rapid processing of large-scale datasets. Additionally, it provides high accuracy, automatically selecting the most relevant features to enhance model performance and demonstrate good generalization capabilities, enabling the identification of different types of outliers. The simplicity of implementation offers distinct advantages in practical industrial detection settings, characterized by small memory footprints and fast operational speeds. Furthermore, the algorithm’s applicability to high-dimensional datasets sets it apart from other methods, facilitating the processing of complex datasets. A noteworthy advantage is the algorithm’s ability to operate without labeled data, distinguishing it from other supervised learning algorithms that require labeled datasets for training and prediction. The algorithm also exhibits efficient memory utilization, outperforming some machine learning algorithms by utilizing random subsets instead of storing the entire dataset. Its scalability allows for integration with other machine learning algorithms to further enhance and optimize performance across diverse application scenarios and requirements. Finally, the ease of implementation facilitates implementation in various programming languages, leveraging existing libraries and tools to facilitate deployment.

Below is a breakdown of the steps involved in implementing the isolation forest algorithm to detect and eliminate outliers:

• Constructing Binary Trees. This involves creating binary trees by randomly selecting a feature from the dataset and choosing a random split point within the range of values for that feature. The split partitions the dataset into two halves, and the process is repeated recursively until each data point is isolated in its own leaf node.
• Building the Binary Tree Forest. The next step involves constructing multiple binary trees by repeating the above process multiple times, each time with a different randomly selected subset of the data. The resulting collection of binary trees forms the isolation forest.
• Calculating Path Lengths. Once the isolation forest is complete, the algorithm proceeds to predict the labels of the data points. This prediction is achieved by recursively traversing each binary tree in the forest, recording the path lengths from the root to the leaf nodes. For each data point, the algorithm computes its corresponding path length.
• Identifying Outliers. The final step involves calculating the deviation of each data point’s path length from its expected value. This deviation is computed using statistical methods to determine how far each data point lies from the mean and standard deviation of all path lengths. Data points that exhibit a significant deviation from the expected values are identified as outliers.

Taking 4–2 groups of sample data as an example, according to the relative relationship between PCI and RQI, the processing effect of the iForest method is shown in Figure 1. A total of 30,088 sample data were finally obtained, and 10% of each group of data was reserved as validation data.

3. Regression Modeling and Model Validation

3.1. Correlation Analysis

Correlation analysis can reveal whether and to what extent there is a correlation between PCI and RQI. Considering the different performance characteristics of asphalt and cement concrete pavements, all the following analyses were conducted separately for the sample data of asphalt and cement concrete pavements. The results of the correlation analysis are shown in

Table 4. Results of correlation analysis between PCI and RQI for asphalt pavement.

Group Number	Sample Size	Pearson’s Correlation Coefficient	Coefficient of Significance
1–1	1595	0.416	0.000
1–2	1045	0.527	0.000
1–3	921	0.607	0.000
2–1	1352	0.565	0.000
2–2	916	0.640	0.000
2–3	810	0.687	0.000
3–1	1278	0.722	0.000
3–2	764	0.779	0.000
3–3	580	0.806	0.000
4–1	1260	0.751	0.000
4–2	968	0.812	0.000
4–3	790	0.832	0.000
5–1	959	0.774	0.000
5–2	665	0.830	0.000
5–3	878	0.842	0.000
6–1	434	0.804	0.000
6–2	615	0.840	0.000
6–3	490	0.865	0.000
7–1	264	0.817	0.000
7–2	575	0.844	0.000
7–3	460	0.882	0.000
8–1	81	0.806	0.000
8–2	387	0.824	0.000
8–3	168	0.843	0.000

and

Table 5. Results of correlation analysis between PCI and RQI for cement concrete pavement.

Group Number	Sample Size	Pearson’s Correlation Coefficient	Coefficient of Significance
1–1	1624	0.433	0.000
1–2	3065	0.492	0.000
1–3	708	0.530	0.000
2–1	940	0.617	0.000
2–2	866	0.674	0.000
2–3	205	0.699	0.000
3–1	203	0.680	0.000
3–2	292	0.728	0.000
3–3	41	0.756	0.000
4–1	235	0.713	0.000
4–2	368	0.741	0.000
4–3	47	0.774	0.000
5–1	237	0.734	0.000
5–2	377	0.741	0.000
5–3	60	0.774	0.000
6–1	83	0.768	0.000
6–2	124	0.797	0.000
6–3	37	0.819	0.000
7–1	351	0.803	0.000
7–2	927	0.841	0.000
7–3	157	0.886	0.000
8–1	119	0.611	0.000
8–2	544	0.637	0.000
8–3	223	0.704	0.000

. In this study, the value of the Pearson’s correlation coefficient [46] is defined to be greater than 0.5 to indicate strong correlation, 0.3–0.5 to indicate moderate correlation, and 0.1–0.3 to indicate weak correlation.

The results of the correlation analysis in Table 4 and Table 5 show that for asphalt and concrete pavement, the coefficient of significance for each group of sample data is less than 0.05, and Pearson’s correlation coefficient is greater than 0, which indicates that PCI is significantly and positively correlated with RQI.

However, the strength of the correlation between the two was related to both the PCI score and the technical grade of roads. In groups 6–3 and 7–3 (low-grade roads with PCI ranging from 65 to 55 and 55 to 40), the correlation between PCI and RQI was the strongest, with Pearson’s correlation coefficients of 0.8 or more, showing a strong positive correlation. However, for group 8–3 (low-grade roads with PCI ranging from 40 to 0), Pearson’s correlation coefficient decreased to around 0.7. That is, the Pearson’s correlation coefficients show a tendency to increase and then decrease as the PCI scores and road grade decrease. In other words, when the road performance is very good, the correlation between PCI and RQI is not strong. As the road performance decays, the correlation between the two increases. The reason for this phenomenon may be that the pavement roughness is also negatively affected as the road performance decays, which leads to a decrease in RQI scores. At this point, both the PCI and RQI scores show a downward trend, resulting in the correlation between the two becoming stronger. However, when the road performance deteriorates further, the correlation between the two weakens again. This may be related to the specific types of pavement damage. As the road performance further deteriorates, various types of damage become more serious. At this time, deformation-type damage that has a significant impact on roughness may become insignificant, so the decrease in RQI scores is not obvious, and the correlation between the two weakens. And there are subtle differences in this trend specific to different pavement types. Pearson’s correlation coefficient of the asphalt pavement increases faster with the decrease in PCI score and road grade, while the cement concrete pavement is relatively slower. However, Pearson’s coefficient for asphalt pavements decreases less relative to cement concrete pavements when the PCI decreases below 40 points. It indicates that the correlation between PCI and RQI for asphalt pavement is lower than that for cement concrete pavement for higher-grade roads with better conditions, while the opposite is true for lower-grade roads with poorer conditions.

Overall, there is a significant correlation between PCI and RQI regardless of the pavement type, so the next step of regression analysis can be carried out.

3.2. Regression Analysis

The mathematical relationship between PCI and RQI was further established by regression analysis [47] on 24 sets of sample data for asphalt and cement concrete pavements, respectively. The following are some reasons for using nonlinear regression methods instead of other methods:

• Modeling nonlinear relationships. Nonlinear regression is specifically used to handle data with nonlinear relationships. The relationship between PCI and RQI is complex and cannot be easily described by a linear relationship. In this case, nonlinear regression may be more suitable for modeling.
• Simplicity. Nonlinear regression models are relatively simple and require fewer parameters, making them easier to interpret and debug.
• Computational efficiency. For certain datasets and problems, nonlinear regression may converge faster than artificial neural networks and require fewer computational resources.
• Avoiding overfitting. Artificial neural networks have the ability to fit noise and irrelevant details in the training data, which can lead to overfitting. In contrast, nonlinear regression models are usually simpler and may be less prone to overfitting.
• Explanatory. Nonlinear regression models are often easier to interpret because their parameters (i.e., slopes and intercepts) have intuitive meanings. In contrast, the parameters of artificial neural networks are often difficult to interpret.
• Data volume: The data range of this study is very wide, but the amount of data in each group is not much. Nonlinear regression is more suitable because it does not require a large amount of data for training.

In this study, the use of natural logarithm equations to fit the relationship between PCI and RQI has several advantages:

• Explanatory. In fields such as economics, the coefficients of log regression can be interpreted as elasticities, which are the rates of change of the dependent variable relative to the independent variable. This makes analyzing and interpreting data simpler and more intuitive.
• Emphasis on relative change. The rate of change of the log function is different for different ranges of independent variables. For smaller values, the rate of change of the log function is larger, while for larger values, the rate of change is smaller. This means that the log function is more sensitive to differences in smaller parts of the value than in larger parts, thus more accurately reflecting the relative relationship between data.
• Fitting data. Natural logarithm functions can better fit nonlinear relationships and reduce the impact of outliers or outliers on the model.

Most importantly, in the actual curve-fitting process, compared to other forms of functions, it was found that the best fit between PCI and RQI was achieved when the natural logarithmic function was used, and the residuals were uniformly distributed on both sides of the zero-standard line. Therefore, the functional relationship between PCI and RQI can be defined as shown in Equation (2), where a and b are constants.

$$RQI=a\times \ln PCI+b$$

(2)

The sets of data listed in Table 4 and Table 5 were fitted based on Equation (2). Of these, the fit for low-grade road groups are shown in Figure 2 and Figure 3. The distribution of residuals for low-grade road groups can be found in Appendix A.

The specific regression analysis results for each group of sample data are listed in

Table 6. Regression results for groups of asphalt pavement.

Group Number	R2	RMSE	Constants a,b	95% Confidence Interval		T-Test		F-Test
				Lower Limit	Upper Limit	T-Value	p-Value	F-Value	p-Value
1–1	0.173	0.723	11.242	10.032	12.451	18.228	0.000	332.251	0.000
			42.841	37.318	48.365	15.213	0.000
1–2	0.277	0.932	17.806	16.060	19.551	20.012	0.000	400.495	0.000
			13.755	5.794	21.715	3.391	0.000
1–3	0.369	0.663	16.581	15.176	17.986	23.159	0.001	536.326	0.000
			19.341	12.907	25.776	5.899	0.000
2–1	0.320	1.088	26.226	24.183	28.269	25.182	0.000	634.130	0.000
			−25.999	−35.125	−16.873	−5.589	0.000
2–2	0.410	2.176	67.605	61.841	72.288	25.199	0.000	634.971	0.000
			−209.293	−232.658	−185.929	−17.580	0.000
2–3	0.474	1.989	62.985	58.402	67.568	26.977	0.000	727.738	0.000
			−190.744	−211.175	−170.312	−18.325	0.000
3–1	0.522	2.248	219.334	207.805	230.862	37.325	0.000	1393.126	0.000
			−876.772	−927.360	−826.184	−34.001	0.000
3–2	0.608	2.057	234.717	221.303	248.131	34.350	0.000	1179.946	0.000
			−945.220	−1004.090	−886.350	−31.519	0.000
3–3	0.65	2.046	257.222	241.804	272.639	32.769	0.000	1073.805	0.000
			−1044.892	−1112.539	−977.245	−30.338	0.000
4–1	0.564	2.589	194.988	185.510	204.467	40.358	0.000	1628.762	0.000
			−762.981	−804.143	−721.820	−36.365	0.000
4–2	0.662	2.131	193.746	184.998	202.494	43.464	0.000	1889.157	0.000
			−756.403	−794.379	−718.427	−39.087	0.000
4–3	0.692	2.639	246.039	234.568	257.510	42.104	0.000	1772.743	0.000
			−986.122	−1035.913	−936.330	−38.877	0.000
5–1	0.602	2.959	110.764	105.055	116.474	38.070	0.000	1449.361	0.000
			−393.124	−417.438	−368.810	−31.730	0.000
5–2	0.689	2.989	129.448	122.823	136.073	38.366	0.000	1471.971	0.000
			−477.190	−505.370	−449.011	−33.251	0.000
5–3	0.712	3.221	151.571	145.118	157.964	46.535	0.000	2165.478	0.000
			−568.865	−596.071	−541.659	−41.038	0.000
6–1	0.649	4.64	141.794	131.928	151.659	28.249	0.000	798.024	0.000
			−515.459	−556.116	−474.803	−24.919	0.000
6–2	0.706	4.005	137.474	130.445	144.504	38.406	0.000	1474.991	0.000
			−497.255	−526.175	−468.335	−33.767	0.000
6–3	0.752	3.614	137.278	130.267	144.289	38.472	0.000	1480.131	0.000
			−495.071	−523.872	−466.270	−33.774	0.000
7–1	0.676	5.072	96.215	88.113	104.317	23.383	0.000	546.759	0.000
			−312.546	−344.220	−280.872	−19.430	0.000
7–2	0.721	5.987	117.563	111.561	123.566	38.467	0.000	1479.732	0.000
			−399.532	−422.864	−376.200	−33.633	0.000
7–3	0.785	5.81	128.736	122.547	134.925	40.877	0.000	1670.893	0.000
			−444.551	−468.615	−420.486	−36.303	0.000
8–1	0.716	3.583	22.169	19.039	25.298	14.100	0.000	198.820	0.000
			−27.491	−38.286	−16.697	−5.069	0.000
8–2	0.765	6.569	21.605	20.406	22.803	35.435	0.000	1255.639	0.000
			−34.847	−38.699	−30.994	−17.785	0.000
8–3	0.822	3.586	7.981	7.411	8.550	27.673	0.000	765.795	0.000
			3.179	1.410	4.947	3.548	0.000

and

Table 7. Regression results for groups of cement concrete pavement.

Group Number	R2	RMSE	Constants a,b	95% Confidence Interval		T-Test		F-Test
				Lower Limit	Upper Limit	T-Value	p-Value	F-Value	p-Value
1–1	0.190	3.096	52.030	46.799	57.260	19.512	0.000	380.727	0.000
			−149.397	−173.315	−125.478	−12.251	0.000
1–2	0.242	4.410	85.299	79.957	90.641	31.308	0.000	980.194	0.000
			−301.592	−326.027	−277.156	−24.200	0.001
1–3	0.281	4.689	102.146	90.070	114.221	16.607	0.000	275.802	0.000
			−381.568	−436.683	−326.452	−13.592	0.000
2–1	0.383	4.141	117.531	107.979	127.084	24.146	0.000	583.053	0.000
			−440.297	−483.009	−397.585	−20.231	0.000
2–2	0.457	3.429	119.264	110.580	127.949	26.954	0.000	726.523	0.000
			−451.520	−490.347	−412.693	−22.825	0.000
2–3	0.489	3.634	135.362	116.208	154.516	13.934	0.000	194.159	0.000
			−521.190	−606.698	−435.683	−12.018	0.000
3–1	0.463	4.383	405.568	344.783	466.354	13.156	0.000	173.089	0.000
			−1698.863	−1965.877	−1431.850	−12.546	0.000
3–2	0.531	5.040	536.062	477.784	594.341	18.104	0.000	327.747	0.000
			−2273.467	−2529.457	−2017.478	−17.480	0.000
3–3	0.573	3.904	471.828	339.992	603.663	7.239	0.000	52.403	0.000
			−1990.840	−2569.787	−1411.893	−6.955	0.000
4–1	0.509	4.883	338.299	295.396	381.201	15.535	0.000	241.351	0.000
			−1389.154	−1575.695	−1202.613	−14.672	0.000
4–2	0.549	4.479	284.437	257.943	310.930	21.112	0.000	445.722	0.000
			−1154.783	−1269.901	−1039.665	−19.726	0.000
4–3	0.601	5.140	385.904	291.550	480.259	8.238	0.000	67.858	0.000
			−1569.480	−2006.477	−1186.484	−7.843	0.000
5–1	0.539	7.060	225.902	199.064	252.740	16.583	0.000	274.993	0.000
			−890.327	−1004.681	−775.974	−15.339	0.000
5–2	0.586	5.636	215.020	196.677	233.364	23.049	0.000	531.242	0.000
			−842.745	−920.903	−764.588	−21.202	0.000
5–3	0.616	7.084	279.711	221.709	337.713	9.653	0.000	93.183	0.000
			−1119.030	−1366.044	−872.017	−9.068	0.000
6–1	0.593	7.576	215.007	175.658	254.357	10.872	0.000	118.195	0.000
			−826.796	−988.555	−665.036	−10.170	0.000
6–2	0.636	8.303	253.342	218.994	287.690	14.601	0.000	213.189	0.000
			−987.019	−1128.289	−845.750	−13.831	0.000
6–3	0.671	6.263	219.995	167.083	272.908	8.441	0.000	71.244	0.000
			−835.219	−1053.083	−617.356	−7.783	0.000
7–1	0.653	5.522	94.058	74.391	113.724	9.611	0.000	92.373	0.000
			−321.442	−398.383	−244.501	−8.396	0.000
7–2	0.704	5.561	85.570	70.699	100.441	11.527	0.000	132.871	0.000
			−288.069	−345.907	−230.231	−9.977	0.000
7–3	0.788	6.929	137.446	109.873	165.019	10.211	0.000	104.263	0.000
			−491.169	−597.068	−385.269	−9.501	0.000
8–1	0.404	9.270	24.329	10.910	37.748	3.770	0.000	14.216	0.000
			−51.255	−97.567	−4.944	−2.302	0.000
8–2	0.471	6.050	20.172	14.916	25.429	7.662	0.000	58.705	0.000
			−25.605	−43.548	−7.662	−2.849	0.000
8–3	0.509	10.076	22.750	18.289	27.210	10.121	0.000	102.426	0.000
			−47.298	−59.907	−34.690	−7.443	0.000

.

As can be seen from the results of the regression analysis in Table 6 and Table 7, for asphalt and cement concrete pavements, the p-values corresponding to the F-tests and t-tests are less than 0.05 (significance level of 0.05), indicating that the established regression model is significant and able to adequately explain the relationship between PCI and RQI.

Overall, as PCI scores and road grades decrease, the R² value increases, and the model’s fit validity improves. For both asphalt and cement concrete pavements, the model fit better for low-grade roads. In particular, for asphalt pavements, the best fit was for PCI scores of 0–40, while for cement concrete pavements, the best fit was for PCI scores of 40–55. As a result, it can be found that the regression model developed for low-grade roads with lower PCI scores can better explain the correlation between PCI and RQI at this time.

3.3. Model Validation

The reserved 10% random sample data were used to validate the established regression model. There are a total of 3275 pieces of data reserved, of which 2195 were for asphalt pavement and 1080 for cement concrete pavement. In this study, the regression validation method is used to evaluate the predictive power and accuracy of regression models. Commonly used regression model validation indicators include Mean Absolute Error (MAE), Mean Absolute Relative Error (MARE), and Root-Mean-Squared Error (RMSE). These indicators can objectively evaluate the performance of the model by calculating the difference between the predicted results and the actual results, helping us understand the model’s error conditions and improvement directions. The formulas for these indicators are shown in Equations (3)–(5):

$$MAE=\frac{1}{n}{{\displaystyle \sum }}_{i=1}^n\left|{\gamma }_i-{\tilde{\gamma }}_i\right|,$$

(3)

$$MARE=\frac{1}{n}\frac{{{\displaystyle \sum }}_{i=1}^n\left|{\gamma }_i-{\tilde{\gamma }}_i\right|}{{\gamma }_i}\times 100\%$$

(4)

$$RMSE=\sqrt{\frac{1}{n}{{\displaystyle \sum }}_{i=1}^n{\left|{\gamma }_i-{\tilde{\gamma }}_i\right|}^2},$$

(5)

where ${\gamma }_i$ is the measured value of RQI; ${\tilde{\gamma }}_i$ is the estimated value of RQI based on the regression model.

The evaluation results of each group of regression models for asphalt and cement concrete pavements are shown in

Table 8. The evaluation results of regression models of asphalt pavement.

Group Number	Sample Size	MAE	MARE (%)	RMSE
1–1	180	4.434	4.9%	4.435
1–2	115	4.375	4.8%	4.376
1–3	100	4.166	4.6%	4.166
2–1	150	3.970	4.4%	4.203
2–2	100	3.772	4.0%	4.054
2–3	90	3.427	3.7%	3.911
3–1	150	3.633	4.2%	3.983
3–2	95	3.417	3.9%	3.551
3–3	70	2.872	3.4%	3.076
4–1	160	3.543	4.1%	3.888
4–2	120	3.180	3.7%	3.407
4–3	100	2.690	3.2%	2.887
5–1	120	3.059	3.8%	3.498
5–2	85	2.499	3.3%	2.969
5–3	110	1.913	2.5%	2.316
6–1	55	1.922	2.7%	2.287
6–2	80	1.737	2.5%	1.962
6–3	65	1.347	2.0%	1.571
7–1	35	1.664	2.6%	2.043
7–2	75	1.537	2.4%	1.918
7–3	60	1.063	1.7%	1.317
8–1	10	2.732	4.9%	3.302
8–2	50	1.908	4.3%	2.288
8–3	20	1.406	4.3%	1.640

and

Table 9. The evaluation results of regression models of cement concrete pavement.

Group Number	Sample Size	MAE	MARE (%)	RMSE
1–1	180	4.470	5.3%	4.860
1–2	340	4.318	4.8%	4.598
1–3	80	3.779	4.5%	4.092
2–1	105	3.540	4.2%	3.963
2–2	95	3.245	4.0%	3.562
2–3	20	3.156	3.6%	3.411
3–1	20	2.984	3.5%	3.189
3–2	30	2.918	3.4%	3.122
3–3	5	2.860	3.3%	3.000
4–1	25	2.744	3.1%	2.927
4–2	40	2.550	3.0%	2.791
4–3	5	2.380	2.9%	2.418
5–1	25	2.108	2.8%	2.231
5–2	40	2.001	2.7%	2.165
5–3	5	1.937	2.6%	2.033
6–1	10	1.416	2.3%	1.615
6–2	15	1.267	2.0%	1.506
6–3	5	1.216	1.8%	1.335
7–1	5	0.698	1.6%	0.776
7–2	5	0.633	1.3%	0.760
7–3	5	0.285	1.2%	0.427
8–1	5	2.306	6.2%	2.589
8–2	5	2.279	4.9%	2.466
8–3	10	0.952	3.7%	1.168

.

From the evaluation results in Table 8 and Table 9, it can be seen that for both asphalt and cement concrete pavements, MAE, MARE, and RMSE are reduced with the decreasing PCI scores and road grades. For low-grade roads with a PCI of 40~55 points, MAE, MARE, and RMSE are all minimized, and the corresponding regression model has the highest prediction accuracy. It can be concluded that the prediction accuracy of the model is higher for low-grade roads with poor conditions.

The MAE, MARE, and RMSE of cement concrete pavement are smaller than those of the asphalt pavement in most groups. For example, in group 7–3 (PCI between 40 and 55, low-grade roads), the MAE, MARE, and RMSE of cement concrete pavement are 0.285, 1.2%, and 0.427, respectively, which are about 73%, 0.5%, and 68% smaller than those of asphalt pavement. It can be seen that the model prediction performance of cement concrete pavement is better than that of asphalt pavement. In other words, it is more accurate to predict RQI based on PCI on cement concrete pavement.

3.4. Assessment of the Prediction Effectiveness of Models

The prediction accuracy of the regression model developed in this study was further evaluated based on the pavement inspection data collected from an actual project in China. A total of 414 pieces of data were collected, of which 250 were for asphalt pavement and 164 for cement concrete pavement. The data mainly include the section name, section stake number, PCI, RQI, and the road grade. Based on the grouping criteria proposed in this study, the data for asphalt and cement concrete pavements were separated. Due to the limited amount of measured data, it is not possible to cover all groups, so only groups for which data are available are analyzed here. The prediction accuracy was evaluated using Equation (6).

$$E=\left(1-MARE\right)\times 100\%,$$

(6)

where E is the prediction accuracy.

The RQI prediction accuracy of the regression model for asphalt and cement concrete pavement for different data groups is shown in

Table 10. Prediction accuracy of regression model for asphalt pavement.

Group Number	Sample Size	Prediction Accuracy
1–1	145	81.5%
1–3	4	87.5%
2–1	96	82.5%
3–1	3	86.2%
3–3	1	91.0%
4–1	1	87.2%

and

Table 11. Prediction accuracy of regression model for cement concrete pavement.

Group Number	Sample Size	Prediction Accuracy
1–3	80	70.3%
2–3	50	74.1%
3–3	10	81.1%
4–3	10	85.8%
5–3	10	88.8%
6–3	2	90.2%
7–3	2	95.7%

. It should be noted here that cement concrete pavement is mostly used for low-grade roads in China, so the data in Table 11 are all low-grade roads. The results are also exhibited in the form of a bar chart in Figure 4 for visualizing the prediction accuracy of each model.

It can be seen that the prediction accuracy of the model gradually improved with the reduction of PCI score and road grade. The cement concrete pavement data used for verification are all from low-grade roads, and it can be found that the prediction accuracy of the model gradually increases with the decrease in PCI. When the PCI score is less than 65, the prediction accuracy of the model is about 20% higher than when the PCI score is greater than 82.

In general, the highest prediction accuracy of the established regression model was found for low-grade roads with poor conditions. The potential reasons for this phenomenon may include the following points. Firstly, according to the previous analysis, for low-grade roads with poor conditions, the correlation between PCI and RQI is the strongest, resulting in the highest prediction accuracy for the corresponding relationship model. Secondly, as mentioned earlier, the regression model with the best fitting degree is for low-grade roads with poor conditions, which means that the model can well explain the relationship between PCI and RQI with minimal error and can generalize to new and unseen data, thus achieving higher accuracy in predicting RQI from PCI. Therefore, for such roads, it is quite accurate and reliable to use PCI to predict RQI.

4. Discussion

4.1. Quantitative Analysis of the Contribution of PCI Level to the RQI Decay Rate

From the above analysis, it can be concluded that PCI and RQI have a significant positive correlation. As the PCI decreases, the RQI also becomes lower. However, with the different degrees of PCI reduction, the decay amplitude of RQI also varies, and it shows a certain regularity. Besides, based on the regression analysis above, the theoretical decay curve of the RQI relative to PCI should be in the form of a natural logarithmic, but this is not entirely the case. Therefore, the Decay Contribution Rate (DCR) of RQI by different PCI levels can be explored and quantified, as shown in Equation (7).

$$DCR=\left(\frac{q}{q_0}-1\right)\times 100\%,$$

(7)

where $q$ is the actual degree of RQI decay; $q_0$ is the theoretical degree of RQI decay.

The PCI score can reflect the severity of pavement damage. As shown in Table 1, the pavement damage was divided into 8 levels and characterized by the different PCI range. The relationship between the actual and theoretical values of RQI decay and the DCR with PCI at different PCI levels is shown in Figure 5.

It can be found in Figure 5 that regardless of the type of pavement, with the aggravation of pavement damage, the actual decay of RQI gradually exceeds the theoretical decay, and the gap is greatest when the PCI reaches about level 4 (PCI ranging from 79 to 74). The DCR also abruptly changes at this time. When the PCI level is less than 4, the DCR is less than 50%, indicating that the pavement damage degree has little effect on the decay rate of RQI. When the PCI level is greater than 4, the DCR becomes larger and larger, up to more than 70%. It indicates that the degree of pavement damage begins to strongly affect the decay rate of RQI, and the more serious the pavement damage, the faster the RQI decay. It further explains why there is a strong correlation between PCI and RQI for low-grade roads with poor road conditions. However, when the PCI level increases further, the DCR starts to decrease. It shows that different PCI levels (or extent of pavement damage) have different effects on RQI decay rates, and the RQI decay rate is most affected by the PCI level when the pavement is severely damaged.

The deterioration patterns vary for different types of pavement. When the pavement damage is more severe, for example, the PCI level reaches 4 and 5 (PCI score ranging from 65 to 79), the DCR of RQI is significantly higher for cement concrete pavement than for asphalt pavement. When the pavement deteriorates further, the DCR of asphalt pavement exceeds that of cement concrete pavement. This indicates that when the PCI score is low, e.g., 65 to 79, the PCI of concrete pavement has a greater effect on RQI than that of asphalt pavement. But when the PCI is too low, e.g., below 65, the PCI of asphalt pavements exceeds that of cement concrete pavements in terms of its effect on RQI. The reason may be that there are differences in material properties between asphalt pavement and cement concrete pavement, which leads to different types and degrees of damage. When the PCI score is low, the roughness of cement concrete pavement is more affected by pavement damage than asphalt pavement, which makes the PCI have a greater impact on RQI. However, when the PCI score further decreases and pavement damage becomes more severe, the roughness of cement concrete pavement is no longer significantly affected by pavement damage, while asphalt pavement is instead more affected, which makes the PCI of asphalt pavement have a greater impact on RQI than cement concrete pavement.

Through the above analysis, it was found that although the relationship model between PCI and RQI can be used to simplify road inspection work, it should be noted that the prediction accuracy of RQI based on PCI is also different with different PCI levels. Therefore, maintenance agencies should pay attention to the development of pavement diseases and make reasonable use of the prediction model.

4.2. Comparison between the Models in This Study and Other Models

A comparison was made between the models in this study and published models in previous studies. The asphalt pavement prediction model and cement concrete pavement prediction model established based on nonlinear regression in this study are superior to all models because they have the highest R² (0.822, 0.788) among all models applied, as shown in

Table 12. Comparison between the model in this study and several previous models.

Number	Model	R2	Authors
1	$RQI=7.981\ln \left(PCI\right)+3.179$ (Asphalt)	0.822	This study
	$RQI=137.446\ln \left(PCI\right)-491.169$ (Concrete)	0.788
2	$IRI=0.0171\left(153-PCI\right)$	0.52	Dewan and Smith [48] (2002)
3	$\log PCI=2-0.436\left(\log IRI\right)$	0.59	Park et al. [21] (2007)
4	$\log PCI=-0.115\log \left(IRI\right)+2.131$	0.013	Arhin and Noel [49] (2014)
5	$PCI=-0.224IRI+120.02$ (Asphalt)	0.82	Arhin et al. [50] (2015)
	$PCI=-0.172IRI+110.01$ (Concrete)	0.72
	$PCI=-0.203IRI+113.73$ (Composite)	0.75
6	$IRI=16.074{\exp }^{-0.26PCI}$	0.59	Hasibuan and Surbakti [51] (2019)
7	$PCI=4.354IRI+\frac{15.04}{IRI/5.41}$	0.72	Imam et al. [52] (2021)

. This was followed by Arhin et al.’s model, which had an R² of 0.75 for the comprehensive model, 0.82 for the asphalt pavement prediction model, which is similar to the R² of the model in this study, and 0.72 for the cement pavement prediction model, which is lower than the cement pavement prediction model in this study. The model with the lowest score is Arhin and Noel’s, with an R² of only 0.013. This confirms that the models established in this study are the most accurate in predicting pavement roughness compared to other selected models in previous studies.

Therefore, it is fully demonstrated that the models established in this study can be effectively utilized for predicting roughness in future maintenance and management work. This will greatly reduce the cost of road maintenance. Moreover, it will significantly promote scientific and rational maintenance decisions and extend the service life of rural roads in China scientific and rational maintenance decisions and extend the service life of rural roads in China.

5. Conclusions and Future Work

This study explored the correlation between PCI and RQI under different pavement damage levels and different technical grades based on extensive pavement inspection data from nine provinces in China. The mathematical models between the two were further established using nonlinear regression analysis, and the predictive effect and accuracy of the models were evaluated by actual road inspection data. On this basis, the contribution of the PCI level to the RQI decay rate was quantitatively analyzed. Finally, the models in this study were compared to several models published in previous studies. The main content of the study leads to the following conclusions:

• It was found that the PCI and RQI showed a strong correlation when the road condition was poor, and the lower the technical grade of the road, the stronger the correlation between the two.
• For low-grade roads with poor conditions, the accuracy of RQI prediction by PCI achieves more than 90%, and the prediction effect of cement concrete pavement is better than that of asphalt pavement. In summary, the most applicable RQI prediction models for different types of pavements and their scope of application can be obtained. For asphalt pavements, the prediction model works best when the PCI score is below 65 and the technical grade is below Level II. For concrete pavements, the model works best when the PCI score is between 40 and 65 and the technical grade is also lower than Grade II. In both cases, the predictive accuracy of the model can reach more than 90%.
• The results of the analysis of the pavement damage degree on the decay rate of RQI show that different pavement damage degrees contribute differently to the decay rate of RQI. When pavement damage is more serious, the degree of pavement damage will have a stronger effect on the decay rate of RQI, and RQI will accelerate with the severity of pavement damage.
• The performance of the models in this study was the best by comparing with other models in previous studies. Therefore, it fully proved that the models established in this study can be used for the prediction of roughness in future maintenance and management work.

Overall, the method proposed in this study can greatly reduce the inspection cost and improve the accuracy and reliability of pavement technical condition evaluation. Most of the low-grade roads, especially those with concrete pavements, are rural roads in China. These roads usually have insufficient funds for inspection and restricted inspection conditions. By using the relationship model between PCI and RQI proposed in this study to predict the roughness of the pavement with the results of pavement damage inspection, accurate and reliable technical conditions of highways can be obtained at a low cost. This will help promote scientific and rational maintenance decisions and extend the service life of rural roads in China, which is very important for the economic development of China’s rural areas. Although the relationship model between PCI and RQI can be utilized to simplify road inspection work, it should be noted that the prediction accuracy of RQI based on PCI is also different with different PCI levels. Therefore, maintenance agencies should pay attention to the development of pavement diseases and make reasonable use of the prediction model.

However, some problems were found in this study, for example, for cement concrete pavements, the correlation between PCI and RQI was substantially weakened when the PCI scores were too low, which may be due to the small amount of data in these groups, or due to the poor quality of the data, as cement concrete pavements with very poor road conditions usually have limited inspection conditions as well. In addition, pavement damage encompasses a wide range of specific damage types, and this study only discusses the effect of the composite index PCI on RQI due to time and data collection constraints, so that the effect of pavement-specific damage types on RQI can be investigated in the future.