Introduction

Continuously reinforced concrete pavement (CRCP) is a robust solution for transportation infrastructure, designed to withstand heavy traffic loads and environmental stresses. CRCP features continuous steel reinforcement, minimizing the need for transverse expansion joints and enhancing load distribution to reduce cracking and deterioration1,2. This design reduces maintenance needs and improves ride quality, thereby enhancing safety and comfort for road users3,4. Longitudinal joints in CRCP manage temperature-induced expansion and contraction, which is critical for maintaining pavement integrity5,6.

Spalling along longitudinal joints in CRCP, which involves the detachment of concrete fragments, presents a significant challenge7. Spalling poses safety risks by creating uneven surfaces and potential hazards from dislodged fragments8. It also increases maintenance costs due to frequent repairs, impacting financial resources for transportation agencies9. Addressing spalling is crucial for enhancing CRCP's long-term performance, reducing maintenance costs, and promoting sustainable infrastructure10,11.

Predictive models using advanced analytics and data-driven algorithms are essential tools for managing infrastructure. These models enable early detection of issues and proactive decision-making, minimizing unexpected failures and optimizing maintenance strategies6,12,13. In CRCP, predictive models help identify factors contributing to spalling, allowing for targeted preventive measures and optimized pavement designs14,15,16,17.

The Long-Term Pavement Performance (LTPP) database, established by the Federal Highway Administration (FHWA), provides comprehensive data on pavement performance under various conditions18. This extensive dataset includes details on pavement structure, traffic loads, and climatic conditions, offering valuable insights for understanding CRCP performance and informing effective maintenance strategies19,20,21,22,23.

Existing literature on CRCP provides a foundation for understanding its performance. Previous research has explored design, construction, and maintenance practices, as well as the causes and mitigation strategies for longitudinal joint spalling24,25,26,27. Machine learning applications have gained prominence in pavement engineering for predictive modeling and decision support28,29. Researchers have used machine learning algorithms to analyze and predict pavement performance, leveraging large datasets like the LTPP database30,31,32.

Despite progress in these areas, a notable gap exists in applying machine learning specifically to predict and mitigate longitudinal joint spalling in CRCP33,34,35. This research aims to fill this gap by using machine learning algorithms to analyze factors influencing spalling. By leveraging data from the LTPP database, this study seeks to develop predictive models to identify early indicators of spalling, assess maintenance practices, and enhance CRCP management. This integration of machine learning represents a novel approach, providing practical insights for improving the durability and performance of CRCP.

Research objectives

The primary objective of this research study is to conduct a comparative analysis of six AI/ML approaches for predicting spalling of longitudinal joints in Continuously Reinforced Concrete Pavement (CRCP). The selected methods for investigation are linear regression, regression decision tree, Support Vector Machine (SVM), ensemble tree (bagged and boosted), Gaussian Process Regression (GPR), Artificial Neural Networks (ANN), and Kernel. To achieve this goal, data has been extracted from the comprehensive Long-Term Pavement Performance (LTPP) database, which provides a wealth of time series and variable information. The specific objectives of the study can be summarized as follows:

  1. 1.

    Dataset exploration and description: conduct a comprehensive exploration of the Long-Term Pavement Performance (LTPP) database, providing a detailed description of the dataset's structure, contents, and variables.

  2. 2.

    Statistical analysis: perform statistical analyses on the LTPP dataset to gain insights into the distribution, variability, and central tendencies of the relevant variables related to spalling in CRCP longitudinal joints.

  3. 3.

    Feature importance assessment: evaluate the importance of different features within the dataset concerning the prediction of spalling in CRCP longitudinal joints, utilizing appropriate statistical methods.

  4. 4.

    Machine learning model development: develop machine learning models using six distinct approaches, including regression decision tree, support vector machine (SVM), ensemble tree (bagged and boosted), Gaussian process regression (GPR), and artificial neural networks (ANN) with a kernel, leveraging the extracted data from the LTPP database.

  5. 5.

    Model evaluation: evaluate the performance of each machine learning model using relevant metrics, such as mean squared error, R-squared, or other appropriate indicators, to assess their accuracy and predictive capabilities.

  6. 6.

    Comparison of models: conduct a comparative analysis of the developed machine learning models, considering their strengths and weaknesses, to identify the most effective approach for predicting spalling in CRCP longitudinal joints.

Methodology

The research study adhered to a systematic methodology, delineated in Fig. 1, comprising several stages to ensure robustness. Initially, data retrieval involved extracting CRCP sections from both cold and warm climate zones, culminating in selecting 33 sections. The criteria for section selection were meticulously defined, emphasizing diversity in climatic conditions to capture a comprehensive range of environmental factors. The justification for this selection was rooted in the need to enhance the study's generalizability and account for the varying impacts of climate on pavement performance. After section selection, the raw data underwent rigorous processing, integration, and cleaning to guarantee its suitability for exploration, visualization, and modeling. This study adopted spalling in CRCP longitudinal joints as the pivotal pavement performance indicator, serving as the primary dependent variable for subsequent analysis. The study’s overarching objective was to scrutinize the relationship between spalling in CRCP longitudinal joints and all other independent variables (features) to discern notable patterns. State-of-the-art machine learning techniques were employed to develop highly effective prediction models for spalling in CRCP longitudinal joints. Acknowledging the uncertainty surrounding the optimal machine learning technique for modeling such spalling, the study recommended using multiple techniques. Consequently, six state-of-the-art machine learning techniques were chosen, namely regression tree (RT), support vector machine (SVM), ensembles, Gaussian process regression (GPR), artificial neural network (ANN), and kernel. The forthcoming sections will elaborate on the specific details and intricacies of these six chosen techniques.

Figure 1
figure 1

Methodology framework.

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It is important to note that the data preprocessing, filtering, visualization, and modeling stages were carried out using the following software:

More details of the methodology are mentioned in the subsequent subsections.

Statistical analysis

In the initial phase of our methodology, a comprehensive Descriptive Statistical Analysis is undertaken to illuminate key characteristics of the dataset. This involves calculating fundamental statistical measures such as mean, median, mode, standard deviation, and range for pertinent variables. The presentation of summary statistics will afford a nuanced understanding of the central tendency and dispersion within the dataset. Additionally, graphical representations, such as the Histogram of the Output Variable, specifically the spalling of longitudinal joints, will be constructed. This histogram serves as a visual aid to illuminate the frequency distribution of the output variable and provide insights into the underlying distribution pattern. By scrutinizing the shape of the histogram, we aim to glean valuable information about the distribution characteristics, gaining insights into the prevalence and severity of spalling in CRCP longitudinal joints. This visual assessment is pivotal for identifying potential skewness, kurtosis, or other distributional aspects that can inform subsequent modeling decisions and enhance the overall interpretability of our findings.

Subsequently, we delve into the realm of conventional regression modeling. Leveraging the capabilities of Minitab software, a regression analysis will be conducted to formulate an equation encapsulating the coefficients of predictor variables. An Analysis of Variance (ANOVA) will be employed to scrutinize the significance of the regression model. The results will be visually represented using a Pareto chart, offering a clear depiction of the contribution of each predictor variable to the overall model.

The following step in our methodology involves validating the conventional regression model and its underlying assumptions. Normality, linearity, and homoscedasticity of residuals will be assessed, and diagnostic plots will be employed for validation. Any necessary adjustments or transformations required to meet the model assumptions will be discussed in this section, ensuring the reliability of subsequent analyses.

A thorough interpretation of results will be undertaken to culminate in the statistical analysis phase. This involves a nuanced discussion of the significance of predictor variables based on their coefficients, providing insights into the intricate relationships between predictor variables and the output variable. The findings from the conventional regression model will be summarized, paving the way for the subsequent stages of our methodology.

Correlation matrix and feature importance assessment

In the initial stage of our methodology, we calculate a Correlation Matrix to explore the relationships among input features. The dataset is loaded from an Excel file, and using MATLAB, we compute the correlation matrix by analyzing the relationships between the first 16 variables. Subsequently, to enhance interpretability, a heatmap visualization is generated. This heatmap provides a graphical representation of the correlation matrix, offering insights into the strength and directionality of the relationships among the input features.

Moving forward, our methodology extends to assessing feature importance utilizing the Random Forest algorithm. The dataset, comprising 20 variables, is imported and split into input features and the output variable. Through MATLAB's TreeBagger function, a random forest model is trained with 100 decision trees, adopting a classification method and enabling the assessment of out-of-bag predictor importance. Subsequently, feature importance is calculated based on the model's out-of-bag permuted predictor delta error.

The feature importance values are sorted and displayed in descending order to ensure clarity and ease of interpretation. The variable names and their corresponding importance values are presented, laying the foundation for a comprehensive understanding of each feature's impact on predicting the spalling of longitudinal joints in CRCP.

A bar plot is generated to depict the sorted feature importance values to encapsulate these findings visually. This plot, angled for better readability, clearly represents each feature's relative significance in influencing the Random Forest model's predictions.

Machine learning models

In the machine learning model development phase, we aim to employ diverse algorithms to comprehensively predict the spalling of longitudinal joints in continuously reinforced concrete pavement (CRCP). Six distinct models will be implemented and evaluated, each bringing unique strengths to the predictive task. The models selected for this study include linear regression, regression decision tree, support vector machine (SVM), ensemble tree (bagged and boosted), Gaussian process regression (GPR), artificial neural networks (ANN), and kernel methods.

To initiate the process, the dataset, comprising relevant features and the target variable (spalling of longitudinal joints), is meticulously prepared for model training. Subsequently, we embark on developing a Linear Regression model, which serves as a baseline for predictive performance. The dataset is split into training and testing sets, and a tenfold cross-validation method is employed to ensure robust evaluation.

A regression decision tree is implemented to capture non-linear relationships within the data. The decision tree is trained using the training set, and its performance is assessed through the tenfold cross-validation framework.

The support vector machine (SVM) 's predictive capability is then harnessed, focusing on handling complex relationships within the dataset. Normalization of input features precedes the training of the SVM model, and its effectiveness is rigorously evaluated using the tenfold cross-validation approach.

The ensemble tree models, namely bagged and boosted, are introduced to exploit the benefits of ensemble methods for enhanced predictive accuracy. The random forest (bagged) and gradient boosting (boosted) models undergo training and evaluation within the tenfold cross-validation setup.

Gaussian process regression (GPR) is then employed to explore the flexibility of this probabilistic approach in capturing complex patterns within the data. Input feature normalization precedes the training of the GPR model, and its performance is rigorously evaluated through the tenfold cross-validation methodology.

Artificial neural networks (ANN) and Kernel methods are subsequently introduced, leveraging the capabilities of deep learning and kernelized algorithms. The input features are normalized, and an ANN model is designed and trained for regression. A support vector machine with a kernel, such as the radial basis function (RBF) kernel, is implemented. Both models are subjected to thorough evaluation using the tenfold cross-validation technique.

The final stage involves a comprehensive model comparison, considering relevant metrics such as mean squared error and R-squared. The diverse characteristics of each model, including interpretability, computational efficiency, and predictive accuracy, are considered to inform the selection of the most effective approach. Table 1 presents the specific configurations of the machine learning models utilized in our study, outlining the hyperparameters adjusted to optimize each model’s performance. The hyperparameters for each model were selected based on a combination of empirical evidence, literature review, and preliminary testing to ensure optimal model performance. These settings reflect our commitment to leveraging the strengths of each model to accurately predict spalling, taking into account the complexities of the dataset.

Table 1 Hyperparameter settings for machine learning models.
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This meticulous and systematic methodology thoroughly explores various machine learning approaches, providing valuable insights into their effectiveness for predicting spalling in CRCP longitudinal joints. Using tenfold cross-validation enhances the reliability and robustness of our model evaluations.

Data description, preprocessing, preliminary analysis and visualization

The data employed for our analysis was drawn from the Long-Term Pavement Performance (LTPP) database, established in 1987, primarily focusing on investigating methods for constructing high-performing pavements under diverse conditions. Boasting a comprehensive collection from over 600 pavement sections, including archival data from more than 1900 pavement sections, the LTPP database is a rich and expansive resource. The data collection initiatives, comprising general pavement studies and specific pavement studies (SPS), are integral to the LTPP's mission36. Administered by the Federal Highway Administration (FHWA), the LTPP database aligns seamlessly with our research objectives. Its expansive scope and meticulous data collection protocols provide a relevant and invaluable foundation for our analysis, ensuring a robust exploration of the factors influencing spalling in CRCP longitudinal joints. By leveraging the freely accessible data on the FHWA website (https://infopave.fhwa.dot.gov/), researchers and professionals in the field of pavement engineering can tap into this repository to fortify their analyses and contribute to the advancement of the understanding of pavement performance under varying conditions.

This research study employed a meticulous selection process to extract control asphalt pavement sections from the Long-Term Pavement Performance (LTPP) database. Specifically, sections situated in cold and warm climate regions, with and without freezing conditions, and without any history of maintenance or rehabilitation activities were identified. This careful criteria selection aimed to isolate pavement sections that exhibit a range of climatic conditions, ensuring a comprehensive representation of environmental factors influencing spalling in CRCP longitudinal joints. The chosen criteria contribute directly to the study's focus by encompassing diverse climate scenarios, including freezing conditions, pertinent to understanding spalling phenomena. This data selection process resulted in identifying 33 control pavement sections, totaling 395 individual records that met the specified criteria. Retrieving four primary data types from the LTPP database—structure, climate, traffic, and performance-related information—ensured a holistic dataset for comprehensive analysis. The attributes in Table 2 were chosen based on their relevance and potential influence on spalling in CRCP. Each category includes variables that are critical to understanding the conditions and performance of the pavement. Structural attributes provide insights into the pavement's physical characteristics and include layers such as the subbase (Layer #2), base (Layer #3), and concrete (Layer #4). These layers are essential for analyzing the support and load distribution properties of the pavement. Climate attributes, such as annual average precipitation, temperature, and humidity levels, capture the environmental factors affecting the pavement. Traffic attributes, including the number of lanes and traffic volumes (AADT, AADTT, and KESAL), reflect the load and stress on the pavement. Each traffic-related factor provides unique insights: AADT captures the total volume of daily traffic, reflecting overall load; AADTT measures the volume of truck traffic, which exerts higher loads and contributes significantly to pavement distress; and KESAL represents the cumulative traffic load in terms of equivalent single axle loads, offering a standardized measure of the impact of varying vehicle types and loads over time. Performance-related attributes, such as initial IRI and spalling measurements, are directly related to the pavement's condition and distress. This comprehensive selection ensures that all significant factors influencing spalling are considered in the analysis.

Table 2 Summary of the collected data.
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A map was generated to visually represent the geographic distribution of the selected LTPP pavement sections (see Fig. 2), categorizing them according to their respective states. This map visualization enhances the study's context. It facilitates a spatial understanding of the selected sections, aligning with the research focus on spalling in CRCP longitudinal joints under varied climatic conditions.

Figure 2
figure 2

Mapping the geographic locations of the chosen asphalt pavement sections.

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Results and discussion

Statistical analysis

Descriptive statistics

Table 3 illustrates a comprehensive set of descriptive statistics obtained for various key variables related to the pavement condition and environmental factors. These statistics offer valuable insights into the dataset’s central tendencies, variabilities, and distributions. Let's delve into a detailed discussion of the results.

Table 3 Summary of descriptive statistical analysis.
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The variable "Age" exhibits a wide range, with a mean of 18.506 years and a standard deviation of 10.204 years. The pavement structures span from newly constructed to significantly aged, as evidenced by the minimum age of 0 years and a maximum of 47 years. The quartile values indicate a notable spread in the age distribution. This diversity in "Age" is crucial as it includes pavements at various stages of their lifecycle, providing a comprehensive view of the aging process and its potential impact on spalling in CRCP longitudinal joints. A higher standard deviation in this variable signifies a more diverse dataset, capturing a broader spectrum of pavement ages. This is relevant for understanding how age variability may contribute to spalling patterns.

Regarding the "Number of Lanes," the mean of 2.238 lanes with a standard deviation of 0.5178 suggests a predominantly stable configuration. Most pavements have either two or three lanes, as indicated by the quartile values and the maximum of three lanes. The lower standard deviation, in this case, indicates less variability in the number of lanes, pointing towards a more consistent feature within the dataset. This stability in lane configuration is pertinent as it establishes a baseline for assessing the influence of other variables on spalling, helping to isolate and analyze the specific impact of factors such as climate and traffic on CRCP longitudinal joint spalling. Providing context to the mean and standard deviation of each variable enhances our understanding of the dataset’s characteristics. It sets the stage for more informed analyses of spalling phenomena in CRCP.

Layer thicknesses, particularly "L2 Thickness," "L3 Thickness," and "L4 Thickness," exhibit considerable variability. These thicknesses refer to layers that are on top of each other within the pavement structure: "L2 Thickness" represents the subbase layer, "L3 Thickness" represents the base layer, and "L4 Thickness" represents the concrete layer. The mean values of 169.78 mm for the subbase layer, 155.95 mm for the base layer, and 142.61 mm for the concrete layer showcase the diversity in pavement layer compositions. The significant standard deviations highlight the range of thicknesses present in the dataset. The "Total Thickness" provides an aggregate view of pavement structure, with a mean of 468.33 and a standard deviation of 109.07. The quartile values indicate a substantial variation in the total thickness of pavements, reflecting different construction designs and materials. Meteorological variables, such as "Annual Average Precipitation", "Annual Average Temperature", and "Annual Average Freeze Index", showcase diverse climatic conditions. These variables exhibit varying means and standard deviations, reflecting the geographical diversity of the dataset.

Humidity variables, "Annual Average Humidity min" and "Annual Average Humidity max", demonstrate a moderate range of values, with means of 16.235 and 116.65, respectively. The standard deviations indicate the variability in humidity levels across the dataset. Traffic-related variables, including "AADT" (Average Annual Daily Traffic) and "AADTT" (Average Annual Daily Truck Traffic), show considerable variability, as indicated by the mean, standard deviation, and quartile values. This reflects the diverse traffic conditions experienced by the pavements. The variable "KESAL," representing the cumulative traffic load in terms of equivalent single axle loads (ESALs), also demonstrates substantial variability with a mean of 644 and a standard deviation of 693.9. The quartile values indicate a wide range of KESAL values in the dataset, highlighting the varying impacts of different traffic volumes and compositions on pavement performance.

The "Initial IRI" (International Roughness Index) exhibits a mean of 1.3253, indicating a moderate level of pavement roughness. The standard deviation suggests variability in pavement conditions, with values ranging from 0.576 to 2.314. Finally, the variable "Spalling of Long. Joints," as in Fig. 3, provides information about the extent of spalling in longitudinal joints. The dataset reflects a range of spalling conditions with a mean of 141.21 and a standard deviation of 56.05. The quartile values offer insights into the distribution of spalling severity.

Figure 3
figure 3

Histogram of dependent variable (spalling of longitudinal joint).

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Regression analysis

The regression analysis has yielded a detailed predictive equation for spalling in CRCP longitudinal joints, offering numerical insights into the impact of various predictor variables. The equation is expressed below:

$$ {\text{Spalling}}\, = \,{373}.{5}\, + \,{2}.{\text{745 \,\,\, Age}}{-\!\!-}{3}.0{\text{9\,\,\, No lanes}}{-\!\!-}0.0{\text{238\,\,\, L2 thickness}}\, + \,0.{\text{1991\,\,\, L3 thickness}}\, + \,0.{\text{1467\,\,\, L4 thickness}}{-\!\!-}0.0{3}0{\text{19 \,\,\, Annual precipitation}}{-\!\!-}{5}.{\text{61 \,\,\, Annual temperature}}\, + \,0.00{\text{66 \,\,\, FreezeIndex}}{-\!\!-}0.{\text{733 \,\,\, Min humidity}}{-\!\!-}{1}.{4}0{\text{6\,\,\, Max humidity}}\, + \,0.000{\text{574\,\,\, AADT}}\, + \,0.00{\text{388\,\,\, AADTT}}{-\!\!-}0.0{2}0{\text{28 \,\,\, KESAL}}{-\!\!-}{2}0.0{\text{6 initial IRI}} $$

Table 4 presents the coefficient values of all variables in the developed regression model. To clarify the practical interpretation of the intercept term (373.5), this value represents the estimated spalling in CRCP longitudinal joints when all predictor variables are zero. In this specific regression equation, it implies the baseline level of spalling when all continuous variables are at their reference levels and categorical variables are at their baseline categories.

Table 4 Coefficient values.
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When all the predictor variables are at their zero or reference values, the intercept term represents the estimated starting point for spalling in CRCP longitudinal joints. It is crucial to note that interpretation should be done cautiously, especially if it falls outside the plausible range of values for the predictors. In this case, it serves as the intercept when other factors are not considered, providing a reference point for comparison with the impact of individual predictor variables on spalling.

Pavement age (Coef: 2.745, T-value: 11.37, P-value < 0.05) emerges as a highly significant factor, with a positive coefficient indicating that for each unit increase in pavement age, spalling severity is expected to increase by 2.745 units. The number of lanes (Coef: −3.09, T-value: −0.57, P-value: > 0.05) shows a weak, non-significant negative association with spalling, suggesting that the width of the pavement might not be a significant driver of spalling. Layer thicknesses play a crucial role, with L3 Thickness (Coef: 0.1991, T-value: 2.58, P-value < 0.05) and L4 thickness (Coef: 0.1467, T-value: 2.73, P-value < 0.05) exhibiting positive coefficients, indicating that an increase in the thickness of these layers is associated with an increase in spalling. In contrast, L2 thickness (Coef: −0.0238, T-value: −0.55, P-value > 0.05) shows a weak, non-significant negative association.

Climatic factors demonstrate intriguing effects. Higher annual precipitation (Coef: −0.03019, T-value: −3.76, P-value < 0.05) is associated with a decrease in spalling, contradicting conventional expectations, while higher annual temperatures (Coef: −5.61, T-value: −4.72, P-value < 0.05) show a protective effect against spalling. Humidity variables reveal nuanced relationships. Min humidity (Coef: −0.733, T-value: −1.68, P-value: > 0.05) and Max humidity (Coef: −1.406, T-value: −3.14, P-value < 0.05) exhibit negative coefficients, suggesting that increased humidity is associated with reduced spalling, although the latter is statistically more significant.

Traffic-related variables showcase potential correlations. AADT (Coef: 0.000574, T-value: 1.33, P-value > 0.05) and AADTT (Coef: 0.00388, T-value: 0.80, P-value > 0.05) exhibit positive coefficients, indicating a potential association between higher traffic volumes and increased spalling. The stiffness of the asphalt layer, represented by KESAL, shows a protective effect (Coef: −0.02028, T-value: −2.63, P-value < 0.05), suggesting that higher KESAL values are associated with decreased spalling. Smoother initial pavement conditions, reflected in initial IRI, exhibit a protective effect (Coef: −20.06, T-value: −3.04, P-value < 0.05), indicating that pavements with smoother initial conditions experience reduced spalling.

The model summary indicates that the multiple linear regression model exhibits a significant overall fit. The coefficient of determination (R-squared) is 42.60%, suggesting that the model explains a substantial portion of the variance in the spalling of CRCP longitudinal joints. The adjusted, R-squared and the predicted R-squared stand at 40.49% and 37.00%, respectively, further emphasizing the model's explanatory power.

The Analysis of Variance (ANOVA) results in Table 5 provide a detailed breakdown of the significance of each predictor variable. The overall F-value is 20.15, with a highly significant p-value (0.000), indicating that the regression model as a whole is statistically significant.

Table 5 Analysis of variance results.
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Several variables significantly contribute to explaining the variance in spalling by examining individual predictors. Notably, Age, Annual Precipitation, Annual Temperature, Max Humidity, L3 Thickness, L4 Thickness, KESAL, and initial IRI exhibit highly significant p-values (all < 0.01), emphasizing their substantial impact on spalling severity. Other variables, such as Min Humidity (p < 0.1), also show significance, albeit to a lesser degree. Variables such as No Lanes, L2 Thickness, Freeze Index, AADT, and AADTT do not show significant contributions to the model (p > 0.1).

ANOVA

The ANOVA error analysis reveals that the Lack-of-Fit test is statistically significant (p < 0.001), suggesting that additional factors may not be captured by the model. The Pure Error term represents the variability within the model, with an associated mean square of 673. In the context of ANOVA, the mean square value (673) represents the average variability or error within the model. Specifically, it is the sum of squared deviations from the mean error divided by the degrees of freedom.

In simpler terms, the mean square value of 673 measures the average amount of unexplained variability in the model. A higher mean square value indicates greater dispersion of data points around the model's predictions, suggesting that the model may not fully account for certain factors influencing spalling in CRCP longitudinal joints. Therefore, in the context of this ANOVA error analysis, the mean square value of 673 highlights the presence of unexplained variability within the model, reinforcing the significance of the Lack-of-Fit test and suggesting that additional factors beyond those included in the model may contribute to spalling.

The comprehensive analysis, incorporating both the regression model and Pareto chart insights, reveals the intricate web of factors influencing spalling in CRCP longitudinal joints. The Pareto chart, as in Fig. 4, highlights the most influential variables, with age standing out prominently as the foremost predictor, emphasizing the significant impact of pavement aging on spalling severity. Annual temperature and precipitation are closely followed, with their respective negative correlations suggesting protective effects against spalling in warmer and wetter climates. Max humidity is another crucial factor, indicating that higher maximum humidity is associated with reduced spalling. Furthermore, the Pareto chart underscores the importance of initial pavement conditions (IRI), with smoother surfaces exhibiting a protective effect against spalling. Integrating these Pareto insights with the regression model results reinforces the significance of these variables in predicting spalling. This integrated approach provides actionable insights for pavement management, highlighting the need to address age-related distress, climatic variations, and pavement smoothness in targeted interventions. The findings contribute to a nuanced understanding of the complex interplay between environmental factors and pavement distress, offering valuable guidance for optimizing pavement management strategies and refining predictive models in the context of CRCP longitudinal joint spalling.

Figure 4
figure 4

Pareto chart results.

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Figure 5 presents the residual plots for the spalling of longitudinal joints, encompassing four distinct subplots: (a) Normal Probability Plot, (b) Residuals vs. Fitted Values, (c) Histogram of Residuals, and (d) Residuals vs. Observation Order. In the Normal Probability Plot (a), the residuals generally align along the reference line, indicating that the normality assumption is reasonably satisfied, albeit with some deviation at the tails. The Residuals vs. Fitted Values plot (b) displays a random scatter around the horizontal axis, suggesting that there is no clear pattern or heteroscedasticity, which implies the residuals exhibit constant variance. The Histogram of Residuals (c) shows a roughly symmetrical distribution centered around zero, further supporting the normality of the residuals. Finally, the Residuals vs. Observation Order plot (d) reveals no apparent patterns or trends over time, indicating that the residuals are randomly distributed and independent. Collectively, these plots suggest that the regression model meets the necessary assumptions for residual analysis, lending credibility to the model's predictions of spalling in longitudinal joints.

Figure 5
figure 5

Residual plots for spalling of long. joints.

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Correlation matrix and feature importance assessment

Figure 6 presents a heatmap correlation matrix illustrating the relationships among various variables, including age, lane numbers, layer thicknesses, climatic conditions, traffic data, initial IRI, and spalling. Each cell in the heatmap displays the correlation coefficient between pairs of variables, with values ranging from −1 to 1. Positive values signify a direct relationship, while negative values denote an inverse relationship. This comprehensive matrix provides valuable insights into the intricate relationships between various factors affecting spalling in CRCP.

Figure 6
figure 6

Heatmap correlation matrix result.

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A significant observation from the heatmap is the strong positive correlation between Age and spalling (0.44), indicating that older pavements are more likely to experience spalling. This relationship highlights the importance of considering pavement age in maintenance and rehabilitation planning to mitigate spalling-related issues.

The thickness of various pavement layers also reveals interesting correlations with spalling. L2 Thickness (Subbase Layer) has a very weak positive correlation with spalling (0.016), while L3 Thickness (Base Layer) shows a slightly stronger but still weak positive correlation (0.015). On the other hand, L4 Thickness (Concrete Layer) has a weak negative correlation with spalling (−0.040), suggesting that thicker concrete layers may help reduce the occurrence of spalling. These relationships underscore the complex interplay between different structural layers and spalling in CRCP.

Climatic factors also show notable correlations with spalling. Annual Precipitation has a moderate negative correlation with spalling (−0.214), indicating that higher precipitation levels are associated with lower spalling occurrences. This could be due to the increased moisture potentially aiding in maintaining the integrity of the pavement structure. Conversely, Annual Temperature exhibits a moderate negative correlation with spalling (−0.337), suggesting that higher temperatures may reduce spalling. The Freeze Index shows a moderate positive correlation with spalling (0.314), highlighting that pavements in regions with frequent freezing conditions are more prone to spalling. Additionally, Min Humidity has a weak negative correlation with spalling (−0.148), while Max Humidity shows a very weak positive correlation (0.051). These climatic correlations emphasize the need to consider environmental factors in pavement performance assessments.

Traffic-related variables display significant interrelationships with spalling. AADT (Average Annual Daily Traffic) has a very weak negative correlation with spalling (−0.038), suggesting that total traffic volume alone does not have a strong direct impact on spalling. AADTT (Average Annual Daily Truck Traffic) shows a very weak positive correlation (0.007), indicating that truck traffic volume has a minimal direct effect on spalling. Interestingly, KESAL (cumulative traffic load in terms of equivalent single axle loads) has a weak negative correlation with spalling (−0.034), implying that higher cumulative traffic loads slightly reduce spalling occurrences. This could be due to better pavement designs in areas with higher traffic loads, which are built to withstand such stress.

Initial IRI exhibits a weak negative correlation with spalling (−0.127), suggesting that pavements with higher roughness indices tend to experience slightly more spalling. This finding indicates that while surface roughness is a factor in spalling, it may not be the most critical predictor.

The Random Forest feature importance analysis in Fig. 7 provides valuable insights into the factors influencing spalling in Continuously Reinforced Concrete Pavement (CRCP). The numerical importance scores indicate the significance of each feature in predicting spalling occurrences.

Figure 7
figure 7

Feature importance assessment using random forest algorithm.

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Age, with an importance score of 0.792, emerges as the most crucial predictor, underscoring the profound impact of pavement age on spalling. AADT (Annual Average Daily Traffic) follows closely with a score of 0.761, emphasizing the strong relationship between traffic volume and spalling. Total Thickness, L2 Thickness, and L3 Thickness, with scores of 0.743, 0.729, and 0.700, respectively, highlight the structural importance of pavement layers in influencing spalling.

AADTT (Annual Average Daily Truck Traffic) holds a notable importance score of 0.686, indicating the specific impact of truck traffic on spalling occurrences. Initial IRI (International Roughness Index) is recognized as a relevant factor, scoring 0.569, and signifies the connection between pavement roughness and spalling. KESAL, an indicator of distress, and Annual Precipitation, with scores of 0.440 and 0.428, respectively, contribute to the predictive model, offering insights into the role of distress and environmental conditions.

Considering structural features, L4 Thickness maintains a significance score of 0.427, suggesting its influence on spalling events. Annual Temperature, Min Humidity, and No Lanes exhibit scores of 0.409, 0.384, and 0.365, respectively, indicating their contributions to the model. Other features, such as construction number, L4 Type, L3 Type, L2 Type, Annual Freeze Index, Climate Zone, and Max Humidity, also contribute to varying degrees.

The differences in importance scores between the regression analysis and the Random Forest method arise from the distinct methodologies each employs. Regression analysis typically measures the linear relationship between variables, which may not capture complex interactions or nonlinear dependencies. In contrast, the Random Forest method excels in identifying intricate, nonlinear relationships and interactions among variables. This explains why certain variables might appear more or less important depending on the method used.

Given the nature of our data, which includes various interacting factors influencing spalling, the Random Forest method provides a more comprehensive and nuanced understanding of variable importance. This approach allows us to capture the multifaceted nature of pavement performance and offers more reliable insights for predicting spalling occurrences.

Development of machine learning models

Table 6 and Fig. 8 illustrate the performance evaluation of various machine learning models for predicting spalling in Continuously Reinforced Concrete Pavement (CRCP) that reveals distinctive characteristics and trade-offs. Linear Regression models, both in the linear and robust forms, exhibit moderate performance with RMSE values of 40.15 and 48.07, respectively. Regression Tree models, categorized by granularity (Fine, Medium, Coarse), demonstrate improved R-squared values, with the Fine tree achieving an RMSE of 36.32 and an R-squared of 0.58, indicating better predictive capability.

Table 6 Machine learning results.
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Figure 8
figure 8

Machine learning results.

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Support vector machine (SVM) models exhibit varying performance, including Linear, Quadratic, Cubic, and Gaussian kernels. Quadratic SVM stands out with a lower RMSE of 29.21 and a high R-squared of 0.73, suggesting better accuracy in capturing the spalling variation. Ensemble Trees, represented by Boosted and Bagged trees, demonstrate competitive performance with RMSE values of 28.17 and 29.84, respectively, and high R-squared values.

Gaussian Process Regression models, employing different kernels such as Squared Exponential, Matern 5/2, Exponential, and Rational Quadratic, exhibit strong predictive capabilities with lower RMSE values ranging from 24.65 to 26.04 and high R-squared values ranging from 0.78 to 0.81. Artificial Neural Network models, based on network architectures, display diverse performance. The Narrow Neural Network outperforms others with an RMSE of 35.73 and an R-squared of 0.60, while the Wide Neural Network with 100 neurons presents an RMSE of 43.95 and an R-squared of 0.39.

Kernel models, including SVM Kernel and Least Squares Regression Kernel, show lower performance with higher RMSE values and lower R-squared values, indicating limitations in capturing the complexity of the spalling phenomenon.

Among all models evaluated, the Gaussian Process Regression (GPR) models and certain ensemble tree models demonstrated the most promising predictive accuracy. The Matern 5/2 GPR model, in particular, achieved the best performance with an RMSE of 24.65 and an R-squared of 0.81. The Boosted Trees model also performed well, with an RMSE of 28.17 and an R-squared of 0.75. These models effectively capture the complex relationships between the input variables and spalling, making them highly suitable for this application.

The superior performance of GPR and ensemble tree models can be attributed to their ability to handle non-linear relationships and interactions between variables. GPR models, with their kernel-based approach, can flexibly model complex patterns in the data. Ensemble trees, such as Boosted Trees, improve prediction accuracy by combining multiple weak learners to form a strong learner, thus enhancing the model's robustness.

For practical applications in CRCP management, we recommend using Gaussian Process Regression and Boosted Trees models. These models can provide more accurate and reliable predictions for spalling, helping infrastructure managers to make informed decisions regarding maintenance and rehabilitation. Implementing these advanced predictive models can lead to more effective resource allocation, reduced maintenance costs, and extended pavement service life.

In summary, the comparative analysis highlights the effectiveness of GPR and ensemble tree models in predicting spalling in CRCP. Their superior performance, combined with their ability to capture complex data patterns, makes them invaluable tools for enhancing the durability and performance of CRCP infrastructure.

Sensitivity analysis

The sensitivity analysis of our predictive model, the Matern 5/2 Gaussian Process Regression (GPR), aimed to ascertain the influence of various factors on the spalling of longitudinal joints in Continuously Reinforced Concrete Pavement (CRCP). Four primary variables were considered based on their recognized importance in pavement engineering: age, total thickness, temperature, and Average Annual Daily Truck Traffic (AADTT). The following sections detail the influence of each variable on spalling, as indicated by the trends in the Fig. 9.

Figure 9
figure 9

Sensitivity analysis results.

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The first variable, age, exhibits a monotonically increasing relationship with spalling. As shown in Fig. 9a, the progression of spalling is relatively subdued in the early years, gradually escalating as the pavement ages. The curve suggests a nonlinear increase, potentially indicative of an accelerating deterioration process as the concrete and steel reinforcement undergo cumulative stress and environmental exposure over time. This finding aligns with the intuitive understanding that aging infrastructure is increasingly susceptible to wear and damage, corroborating the importance of age as a predictive factor in the model.

Total pavement thickness demonstrates a non-monotonic influence on spalling, as depicted in Fig. 8b. There is an initial rise in spalling with increased thickness, reaching a peak at an intermediate thickness level before displaying a steep downward trend. This implies an optimal thickness range beyond which additional material significantly reduces spalling. It is possible that beyond this optimal thickness, the benefits of additional material outweigh any potential drawbacks, such as increased stress due to thermal expansion or more significant structural complexities. The model's sensitivity to thickness is critical for understanding how material specifications can be optimized to mitigate spalling effectively.

As revealed in Fig. 9c, temperature shows a complex relationship with spalling. There is an initial increase in spalling with rising temperatures, followed by a plateau and a subsequent decline. This pattern suggests that moderate temperatures may not lead to significant changes in spalling rates, while extremes on either end of the temperature spectrum might. Thermal expansion, freeze–thaw cycles, and other temperature-related stresses are known to affect concrete integrity, which may account for these observations. The impact of temperature on spalling underlines the importance of considering climatic conditions when designing CRCP.

Figure 9d presents a positive correlation between AADTT and spalling, illustrating a nearly linear trend. The increase in spalling with AADTT supports the premise that heavier traffic loads, especially those involving trucks, contribute to pavement distress. The Matern 5/2 GPR's sensitivity to AADTT indicates that traffic parameters are a significant component in the predictive modeling of spalling, underlining the need for robust pavement design that accounts for traffic intensity and load distribution.

The Matern 5/2 GPR model's sensitivity to the examined variables elucidates their individual and collective impact on spalling in CRCP. The nuances captured by the model provide valuable insights into the deterioration mechanisms at play, offering a data-driven basis for intervention strategies. While age and AADTT display a direct and anticipated influence on spalling, the complexities in the relationship between total thickness and temperature underscore the multifaceted nature of pavement behavior. By identifying the varying degrees of sensitivity to these variables, the Matern 5/2 GPR model serves as a sophisticated tool for predictive analysis, contributing significantly to the field of pavement engineering and infrastructure maintenance.

Conclusion

In conclusion, this comprehensive study aimed to assess and predict spalling in Continuously Reinforced Concrete Pavement (CRCP) through a multifaceted analysis incorporating descriptive statistics, regression analysis, correlation matrices, feature importance, and machine learning models. The descriptive statistics provided a detailed dataset overview, highlighting key parameters such as age, thickness, precipitation, temperature, and traffic variables.

The regression analysis, elucidated by a robust equation and coefficient details, offered insights into the relationships between various factors and spalling. The results underscored the significance of age, annual temperature, annual precipitation, max humidity, and initial IRI in influencing spalling. Additionally, the ANOVA results and Pareto chart emphasized the importance of these variables in contributing to spalling variability.

The correlation matrix heat map further elucidated the interdependencies among variables, revealing notable correlations and guiding feature selection. Feature importance analysis reinforced the prominence of certain variables, with age, AADT, and total thickness emerging as key contributors to spalling.

In the context of pavement engineering, understanding these influential factors holds significant practical implications. As a key contributor, age signifies the importance of considering the aging process of CRCP in maintenance strategies. A thorough understanding of the impact of traffic, represented by AADT, provides insights into the role of usage intensity in spalling development. The emphasis on total thickness also underscores the importance of pavement structure and design in mitigating spalling risks. Incorporating this knowledge into maintenance strategies allows for more informed decision-making, facilitating targeted interventions based on the identified critical factors. By addressing age-related issues, managing traffic impacts, and optimizing pavement thickness, maintenance practices can be tailored to enhance the resilience and longevity of CRCP infrastructure.

Machine learning models provided a nuanced understanding of predictive performance. Gaussian Process Regression models and specific ensemble tree models demonstrated superior accuracy, highlighting their potential for robust spalling prediction. However, variations in model performance across different architectures and kernels underscored the importance of model selection based on specific requirements and dataset characteristics.

The study's findings contribute valuable insights for both researchers and practitioners in the field of pavement engineering. The identified influential factors and predictive models can inform maintenance strategies and enhance the durability and longevity of CRCP infrastructure. As advancements in predictive modeling continue, the study sets the stage for ongoing research to refine spalling prediction methodologies and improve the resilience of concrete pavement systems.

Expanding on future research, specific avenues for exploration could include a more in-depth analysis of the temporal evolution of influential factors to capture dynamic changes in spalling patterns over time. Additionally, investigating the impact of emerging technologies, such as real-time monitoring and sensor data, on spalling prediction could further enhance the accuracy of models. Addressing data integration and variability challenges across different geographical regions could improve the generalizability of predictive methodologies. Exploring the potential influence of climate change on spalling and developing adaptive strategies for evolving environmental conditions represents another critical avenue. By delving into these specific aspects, future research can advance the field of pavement engineering, refining predictive methodologies and addressing challenges to bolster the resilience of concrete pavement systems against spalling.

Limitation and future research directions

Limitations

This study presents several limitations that need to be acknowledged. Firstly, the geographic distribution of the CRCP sections used in our analysis is skewed towards Texas and adjacent regions. While this reflects the availability of data in the LTPP database, it may limit the generalizability of the findings to other regions with different environmental and climatic conditions. Although our dataset includes sections covering various climate types, the concentration of data from specific regions means that some climate types are more represented than others.

Future research directions

To address these limitations, future research should aim to incorporate a more geographically diverse set of CRCP sections. Expanding the dataset to include CRCP sections from underrepresented regions will provide a more comprehensive understanding of the influence of different environmental factors on spalling development. Efforts should be made to obtain and integrate data from various climate zones to ensure a uniform geographic distribution.