A Comparative Assessment of Bridge Deck Wearing Surfaces: Performance, Deterioration, and Maintenance

Abstract

Bridge decks deteriorate faster compared to other bridge components, primarily influenced by traffic volume, while previous studies have examined the effect of bridge-wearing surfaces on deterioration, further understanding of the relationship between bridge performance and maintenance is needed for policy-making and planning purposes. In this study, we focus on nine influential variables to unravel the intricate connections among performance, deterioration, and maintenance of six distinct bridge-wearing surfaces: Monolithic Concrete, Gravel, Wood or Timber, Bituminous, Low Surface Concrete, and Other. Statistical analyses were employed to determine associations between variables and concepts, exploring similarities and differences across various wearing surface types. In particular, machine learning algorithms were utilized to model the maintenance considering the performance and deterioration of the six diverse wearing surfaces. This approach allowed for an examination of interactions between those variables and concepts. We further applied a well-performing prediction model (which achieved an accuracy of 0.86 and an AUC score of approximately 0.83) to obtain interpretable insights regarding bridge deck surfaces. Analysis with interpretable methods such as SHAP (Shapley additive explanation) and PDP (partial dependency plot) revealed that deterioration, deck age, deck area, and overall performance were the most influential variables among average daily traffic, average daily truck traffic, and the number of spans significantly influenced the maintenance of bridge deck condition with different wearing surfaces. Notably, a strong relationship between performance and maintenance was observed in specific wearing surface types, such as Monolithic Concrete and Wood or Timber, while Other surface types exhibited different patterns. These findings highlight the need for tailored approaches when assessing bridge health, considering the distinct characteristics of different bridge deck types.

1. Introduction

The condition of bridge decks plays a critical role in supporting traffic connectivity and the efficiency of transportation networks [1]. Proper design, construction, inspection, and maintenance of bridge decks are of utmost importance for ensuring the functionality and longevity of bridges [2]. However, with the average age of bridge decks reaching 50 years, often surpassing their intended design life, deterioration becomes a significant concern [3]. Particularly in the state of Nebraska, we observe that bridge decks tend to deteriorate faster than bridge substructures and superstructures, requiring considerable attention and resources from stakeholders and bridge engineers [2,4].

Effectively managing the performance of bridge decks to extend their service life presents a challenge that necessitates the development of efficient and effective maintenance scheduling strategies [1]. In bridge management, prior research efforts have developed approaches to determine the optimal timing of bridge inspections and predicted future interventions for preserving a bridge’s overall condition. However, these methods generally adhere to strategies that either focus on comprehending the repercussions of bridge failure, relying on the existing rate of bridge condition deterioration [5], or consider the known time elapsed between two consecutive condition assessments of the bridge [6,7]. Overall, a comprehensive understanding of the determinants for selecting the appropriate maintenance type and evaluating the performance of bridge components across time intervals still needs to be addressed.

This research analyzes the influential variables affecting the overall health of the bridge deck, focusing on three key metrics: performance, deterioration, and maintenance. We define the three concepts of bridge health as the following:

• Performance: Performance of a bridge component is measured by comparing its condition rating to that of other bridges relative to age. This metric serves as an indicator of the bridge’s service life.
• Deterioration: Deterioration refers to the degradation of a bridge component over time.
• Maintenance: Maintenance encompasses interventions or actions aimed at significantly improving the condition rating of a bridge component.

It is important to note that we assume each of these bridge health metrics is independent, and focusing on one metric does not necessarily provide information about the others. For instance, while maintenance may improve condition ratings, it may not necessarily enhance performance compared to other bridges of the same age. Similarly, high levels of deterioration may lead to frequent maintenance, but maintenance is not always mandated with respect to deterioration. Furthermore, some essential bridges, such as those within critical highway networks, may undergo regular maintenance regardless of their deterioration levels. Both deterioration and maintenance drive the overall performance of a bridge deck, yet high-performing bridges may not require extensive maintenance and may not be deteriorating rapidly. Understanding the precise dynamics and considering other influential factors can provide further insights into the behavior of different types of bridge decks with wearing surfaces throughout their service life.

The selection and design of a wearing surface consider factors such as traffic weight, volume, speed, construction requirements, and maintenance costs [8]. Understanding the correlation, interaction, and other relationships between these metrics and other factors could assist in guiding decision-making processes and minimizing accumulated costs and disruptions caused by significant repairs and replacements. Although some studies have examined the impact of wearing surfaces on bridge deck deterioration, a comprehensive understanding of the relationship between bridge performance, deterioration, maintenance, and wearing surfaces is still needed [9,10].

In this work, we address this research gap by formulating our analysis for all types of wearing surface areas with respect to maintenance, deterioration, and performance.

This study introduces several novel aspects in the analysis of deck wearing surfaces:

• Our research focuses on assessing bridge deck-wearing surfaces within the state of Nebraska, which was previously an unexplored area in the existing literature.
• In addition to understanding the deterioration of bridge deck wearing surface, a bridge health metric examined extensively in the literature, we broaden our focus to encompass other dimensions, including performance and bridge maintenance.
• While prior studies have examined the influence of wearing surfaces on bridge deck deterioration, there remains a need for a comprehensive understanding of the intricate interaction between variables such as bridge performance, deterioration, maintenance, and other variables in understanding bridge wearing surfaces.
• We explore the relationship between influential variables in predicting bridge deck maintenance to discern whether they exhibit linear or non-linear associations. Moreover, we employ state-of-the-art explainable techniques like partial dependency plots (PDP) and Shapley additive explanation (SHAP) alongside performance metrics to gain further insights into the results of the maintenance of bridge deck-wearing surfaces.

The remainder of this paper is structured as follows: Section 2 reviews prior literature, motivating our research. Section 3 offers an in-depth exploration of the methodology, including data collection and processing, the formulation of bridge health metrics, statistical tests, and machine learning modeling techniques, all aimed at understanding the critical aspects of bridge deck performance, deterioration, and maintenance. Section 4 presents the results of our statistical analysis and machine learning modeling. Section 5 is focused on a comprehensive discussion of our findings and their implications, leveraging state-of-the-art explainable methods. Finally, in Section 6, we conclude the paper by summarizing our findings and outlining potential avenues for future research.

2. Literature Review

Previous research has identified several influential factors in bridge condition, including region, ownership, environmental factors, and the number of spans. Additionally, the wearing surface has been highlighted as a significant factor in the deterioration of bridge decks [2,8,11]. A recent study by Kong et al. [9] suggests that bridges without wearing surfaces, corrugated steel deck structures, wide bridge structures, and long spans are highly associated with faster-deteriorating decks.

In this section, we focus on previous research that explores state-of-the-art bridge health metrics with respect to performance, maintenance, and deterioration. Further, we examine several modeling techniques that take into account bridge health metrics and identify factors that influence bridge health. We also look into challenges with respect to data quality required to compute bridge health metrics. The following subsections present an overview of relevant studies, highlighting the gaps in the existing knowledge and the need for further investigation in this field. Synthesizing the existing literature, this review underscores the need for a detailed understanding of how different types of bridge deck-wearing surfaces perform in relation to other variables beyond performance, deterioration, and maintenance.

2.1. Deterioration

There are several methods for evaluating the deterioration of a bridge’s components. Time In Condition Ratings (TICR) is one of the methods for measuring the bridge condition ratings using bridge inspection records spanning multiple years. The proposed method, TICR, primarily computes a bridge’s time over the observed timeline in a particular condition rating. Nasrollahi et al. [6] computed TICR for bridges based on 20 years of bridge inspection records. Furthermore, TICR, in conjunction with other methods, has been adopted in population analysis to understand the bridge decks nationwide [7]. Similarly, Hazard Ratio (HR) is another method that primarily considers condition ratings to compute the probability of a transition into a higher or lower condition rating [5].

2.2. Performance

In contrast to methods that observe condition ratings over time, the Baseline Difference Score (BDS) considers the bridge’s age and condition rating to understand overall bridge health [3]. BDS accounts for the entire service time of the bridge to compute a baseline for mean condition rating with respect to age. Next, the entire service timeline of each bridge is compared against the baseline to compute a score that indicates how each bridge performs better or worse in comparison to the baseline.

2.3. Maintenance

The nature of the dataset presents the challenge in computing the bridge health metrics. Previous researchers have analyzed only non-increasing segments of a bridge timeline to mitigate bias caused by a lack of maintenance history. Other methods account for unrecorded maintenance activities by assuming that consecutive inspections should not increase condition rating, and hence, the mean of condition rating between the periods of consecutive interventions should be considered [12]. Another strategy uses the Bridge Intervention Matrix (BIM) to address the problem of unrecorded maintenance activity and to map specific interventions for transition into condition ratings. Another feature of BIM is that any consecutive improvement in the bridge’s condition ratings is also implemented [13].

Most of the influential factors have been identified from the perspective of deterioration bridge components such as deck, substructure, and superstructure. There is a need for more understanding of the overall performance of the bridge through the service life of the components. We observed that influential factors vary across different perspectives. Moreover, the findings regarding influential variables differ with the study’s objective and the method used to produce the results. Therefore, findings from other studies are limited to only state-level analysis and may not be applicable to other states [6,12,13]. Moreover, with respect to the role of surface wearing in understanding bridge decks from the perspective of performance, deterioration, and maintenance, individual studies are limited to the effectiveness of particular wearing surfaces on bridge decks. However, a comprehensive insight into how different types of bridge surfaces affect bridge decks is yet to be explored.

3. Methodology

As summarized in Figure 1, our research method can be divided into five steps: Inspection Record Collection, Data Processing, Formulation of Measurement, Statistical Analysis and Modeling, and Evaluation. The following section describes each step in detail.

3.1. Inspection Record Collection (Data Collection)

We downloaded the NBI dataset from the Federal Highway Administration’s (FHWA) National Bridge Inventory for the years from 1992 to 2021 [14]. The collected data comprises all record types categorized in accordance with the FHWA bridge inspection recording guide’s item 5A. A total count of 431,128 inspection records related to a service timeline covering 17,536 observed bridges across the span from 1992 to 2021 were taken into account for our study. The count of bridge records varies annually. Presently, in 2021, the total count of bridges stands at 15,348. We also collect the precipitation data from the Center for Disease Control and Prevention (CDC) [15]—Freeze–thaw and Snowfall dataset from Long-Term Bridge Performance (LTBP) and InfoBridge [16].

3.2. Data Preprocessing

The data preprocessing phase consists of two main phases: data cleaning and preparation, and data transformation. In the data cleaning and preparation (Section 3.2.1), we ensure the dataset’s quality and readiness for analysis. The subsection elucidates the criteria for cleaning the NBI dataset and provides a detailed description of selected variables, presented in

Table 1. Categorization and description of variables.

Category	Factor	Description
Physical	Age/year-built	Year of construction
	Structure length	Length of the structure
	Width	Width of deck
	Number of spans	Number of spans in main unit
	Deck	Condition ratings of the bridge component
Region	Longitude	Longitude
	Latitude	Latitude
Structural Type	Material type	Kind of material used such as Concrete, Steel, Wood or Timber
	Deck protection	Protective system on bridge deck
	Membrane type	Membrane used as a part of protective system on bridge deck
Environmental	Precipitation	Annual mean precipitation in inches or millimeters
	Snowfall	Annual mean snowfall
	Freeze-thaw	Annual mean freeze-thaw
Service	Owner	Maintenance responsibility of bridges

. Furthermore, the section offers summarized results for both numerical (

Table 2. Descriptive summary of numerical variables.

Factor	Mean	Median	Std. Dev	Min	Q1	Q3	Max
Traffic	1820.28	50	7873.3	2	25.50	235	165,270
Deck-age	40.52	34	25.39	1	19	69	122
Area	234.65	100.5	600.18	28.81	61.25	229.99	20,659
Snowfall	57.41	58	7.39	41.97	51.05	62.92	73.315
Freezethaw	105.79	103.81	6.65	98.44	101.97	106.76	133
Precipitation	2.03	2.08	0.265	1.05	1.94	2.18	2.5
Longitude	−94.40	−97.35	18.241	−104.95	−98.58	−96.56	0.0
Latitude	39.74	41.125	7.68	40.0	40.53	41.75	43.16
Deterioration	0.0971	0.045	0.145	0.173	0.0002	0.103	1.5
Length	29.65	15.8	54.06	6.1	9.8	30.8	1644.7
Spans	1.81	1.0	1.57	1	1	3	52
Performance	0.748	0.67	0.51	2.86	0.34	1.06	3.18

) and categorical variables (Table 2). The subsequent subsection (Data Transformation, Section 3.2.2), addresses the challenges encountered in constructing time-series data for bridges. Here, we outline the obstacles faced and detail our approach to overcoming them to create meaningful time-series data for the analysis.

3.2.1. Data Cleaning and Preparation

We created a clean NBI dataset containing information about bridges from LTBP InfoBridge. During the cleaning processing, we observed missing data and inconsistencies in complying with the FHWA coding guide [17]. Specifically, the early years of the Nebraska data have a large percentage of non-compliant data to the FHWA coding guide. For instance, we observed unrecorded previous reconstruction dates and missing data related to condition ratings. These inconsistencies in the dataset affect the analysis of the data, as it is difficult to account for various maintenance activities. Therefore, we addressed several data-related inconsistencies as follows: The data cleaning consists of handling missing data, removing duplicate records, detecting outliers that can skew the model’s understanding of the data, and treating outliers. After the selection of specific attributes, a total of 15,349 bridges belonged to the state of Nebraska from 1992 to 2021.

The following are the detailed steps taken to clean the dataset:

• We removed all missing inspection records with missing deck condition ratings.
• For each bridge time series, we detected the changes in the year of the bridge. To preserve the consistency in the bridge life-cycle, with the change in the year a bridge was built, we reintroduced the remaining bridge time series with a new structure number that contains the original structure with a segment suffix.
• We discarded inspection records for culverts.
• We discarded inspection records of bridges with structure lengths under 20 feet.
• We selected a bridge deck with a wearing surface (NBI item 108A): Monolithic Concrete, Gravel, Bituminous, Wood or Timber, Other, and Low-slump concrete.

After the selection of specific attributes, a total of 9,152 bridges belonged to the state of Nebraska from 1992 to 2021.

This study examines 14 variables from five categories: Physical, Region, Structural Type, Environmental, and Service, as shown in Table 1. These variables can be classified into two types: numerical (either continuous or discrete) and categorical (either nominal or ordinal). We present descriptive statistics for numerical variables to summarize their characteristics in Table 2.

On the other hand, categorical variables such as material, membrane type, deck protection, owner, and maintenance are divided into different categories or levels, as shown in

Table 3. Frequency and percentage breakdown of categorical variables.

Factor	Frequency Count	Percentage
Material
Steel	4684	0.511801
Concrete Continuous	987	0.107845
Wood or Timber	975	0.106534
Pres. Concrete	964	0.105332
Steel Continuous	689	0.075284
Concrete	662	0.072334
Pres. Concrete Continuous	186	0.020323
Other	5	0.000546
Membrane Type
None	8744	0.955420
Preformed Fabric	151	0.016499
Built-up	135	0.014751
Unknown	77	0.008413
Not Applicable	22	0.002404
Other	15	0.001639
Epoxy	8	0.000874
Deck Protection
None	7473	0.816543
Epoxy Coated Reinforcing	1429	0.156141
Unknown	120	0.013112
Galvanized Reinforcing	87	0.009506
Not Applicable	25	0.002732
Other	8	0.000874
Other Coated Reinforcing	4	0.000437
Cathodic Protection	2	0.000219
Internally Sealed	2	0.000219
Polymer Impregnated	2	0.000219
Owner
County Highway	7072	0.772727
State Highway	1664	0.181818
City Highway	294	0.032124
Other Local	62	0.006774
Other State	25	0.002732
Railroad	12	0.001311
Private	10	0.001093
Bureau of Indian Affairs	8	0.000874
Corps of Engineers (Civil)	2	0.000219
Bureau of Reclamation	2	0.000219
National Park Services	1	0.000109
Maintenance
Intervention	3739	0.408
No Intervention	5413	0.591

. By presenting these descriptive statistics and summarizing the categories within each variable, we provide a comprehensive overview of the data, enabling readers to understand the characteristics and distributions of the variables under investigation.

Table 3 reveals an observable imbalance in the distribution of certain categorical variables within the context of Nebraska. Notably, there is a significant preponderance of bridges with “None” for deck protection and membrane type (consisting of 81% of bridge decks). Additionally, the most frequently employed bridge material in Nebraska is steel. Furthermore, the ownership of a majority of the bridges falls under the purview of County Highway authorities, accounting for 77% of bridges.

3.2.2. Data Transformation

During the data cleaning, we discovered inconsistencies in the year-built variable across the time-series data for bridges. These inconsistencies arose when comparing the year a bridge was built from one inspection record to another, resulting in discrepancies among the inspection records.

To address this issue, we consulted with a subject matter expert from the Nebraska Department of Transportation. We learned that a newer year-built than previously reported in the dataset would indicate that a structure has been replaced. In order to maintain consistency in the bridge life-cycle despite changes in the year-built, we divided the existing time series of each bridge. We then introduced the remaining segments of the bridge as separate entities, each assigned a new structure number that included the original structure number with a segment suffix. This allowed us to treat each segment of a bridge as a distinct entity during the computation of bridge metrics, including performance scores, number of maintenance interventions, and deterioration. Ultimately, when calculating bridge health metrics for all bridges, the values were averaged across all segments of each bridge to ensure comprehensive representation.

3.3. Formulation of Measurement

Here, we describe the formulations for three bridge metrics: Baseline Difference Score, Deterioration Score, and Number of Maintenance. This work uses bridge health metrics and measurements interchangeably. Moreover, this section provides a formulation for other derived variables, such as deck age, that are considered in modeling the bridge maintenance.

3.3.1. Deck Age

Unique to this study is our interest in understanding how various deck surface-wearing types perform over their lifetime and the relationship between maintenance, performance, and deterioration of the bridges. Hence, we only consider the deck condition rating in the rest of the study. For this research study, we focus on deck age as opposed to age calculated using year-built. Deck age provides a more specific understanding of the deck performance than the actual age of the bridge. The following is the computation for the deck age of the bridge.

Let,

• $cY$ be the year of the survey of B, when the bridge was inspected.
• $rY$ be the year reconstructed of the survey of B, as mentioned in the survey of the year $cY$.
• $bY$ be the built year of the bridge B, as mentioned in the survey of the year $cY$.

  $$d{Y}_B=cY-max(rY,bY)$$

  (1)

3.3.2. Formulation of Baseline Difference Score

In this section, we describe the method used to calculate the Baseline Difference Score (BDS), also referred to as the performance score in this study. The baseline is determined by averaging the bridge deck condition ratings for all bridges in Nebraska based on the deck age of each bridge. For this work, the terms performance score and BDS are used interchangeably. Further, we also compute the Nebraska average for each bridge deck with different surface-wearing types. Although the bridges are built for a life of 50 years, we continue to compute the baseline until the baseline reaches a mean condition rating of 4.

The following is the overview for the computation of the BDS:

• Compute mean condition rating using records available from Nebraska for each deck age.
• Compare each bridge time-series of condition rating data with baseline.
• The mean difference between the time-series baseline and the bridges is known as the BDS.

In the following subsection, we describe the mathematical formulation of the baseline difference score [3].

To calculate the BDS $S_b$ for Bridge B:

Let

i be the age of Bridge B, when bridge B was first inspected.

k be the age of Bridge B, when bridge B was last inspected.

$\overrightarrow{C}$ be the vector of condition ratings of the Bridge B from age i to age k.

$\overrightarrow{X}$ be the average condition rating of all bridges from age 1 to 60.

$X_y$ is the vector of the average condition rating of all bridges from age i to age j, such that $j\le k$.

$D_b$ be the vector of differences computed from $\overrightarrow{C}$ and $X_y$, such that $j\le k$.

$$D_b=\overrightarrow{C}-\overrightarrow{X_y}$$

(2)

Then, BDS $S_b$ is computed as in Equation (3):

$$S_b=\overline{D_b}$$

(3)

From the formulation above, a BDS is computed for a bridge using a time series of its condition ratings available in the NBI. This computational strategy limits the risk of auto-correlation. In contrast to condition ratings of a particular bridge that is ordinal from 0 to 9 values, the baseline is continuous, as it is the mean condition rating over all bridges in Nebraska at a particular age. For the deck baseline, we compute the baseline using the computed deck age instead of a bridge’s built age. We also observe that the bridge condition ratings may fluctuate above and below the baseline because of improvements from interventions and deterioration of the bridge deck components. Thus, bridges with equal baseline difference scores may have highly varied condition ratings.

3.3.3. Computation Of Deterioration Score

The condition ratings of bridge decks can exhibit consistency, deterioration, or improvement over time. These variations in condition ratings are typically the result of natural deterioration, subjective ratings provided by bridge engineers during inspections, or improvements made through bridge maintenance activities (interventions). To account for the decrease in condition ratings over time (deterioration), we assume that a decrease in condition ratings corresponds to a negative slope with respect to both condition rating and deck age. Thus, in addition to creating separate bridge segments based on the new year-built, we further split each segment into monotonically decreasing segments along the bridge timeline, enabling a comprehensive understanding of bridge deck deterioration.

In order to define the deterioration score of a bridge deck, we focus on the monotonically decreasing segments within the bridge deck’s timeline. By calculating the difference in condition ratings over time, we can determine the deterioration of the bridge component. This deterioration score is derived through a simple calculation of the slope, capturing the extent of deterioration experienced by the bridge deck over its lifespan.

Let

$y_1$ be the condition rating of Bridge B at the start of the segment.

$y_2$ be the condition rating of Bridge B at the end of the segment.

$x_1$ be the deck age of Bridge B at the start of the segment.

$x_2$ be the deck age of Bridge B at the end of the segment.

$$\begin{array}{cc}\hfill \mathrm{Slope}\left(\mathrm{Deterioration}\right)& =\frac{\Delta (\mathrm{deck}\mathrm{condition}\mathrm{rating})}{\Delta (\mathrm{deck}\mathrm{age})}\hfill \\ \hfill & =\frac{y_2-y_1}{x_2-x_1}\hfill \end{array}$$

The slope represents the rate of change in deck condition rating between two points with respect to deck age. The final deterioration score of a bridge deck is the average of all segments and their monotonically decreasing sections of the bridge deck ratings.

3.3.4. Computing Number of Maintenance

To identify the maintenance events within each bridge’s time-series data of deck condition ratings, each bridge deck condition rating is described in the NBI recording guide [17] in

Table 4. Bridge deck condition ratings as described in NBI Recording and Coding Guide for the Structure Inventory and Appraisal of the Nation’s Bridges [17].

Rating	Description
N	Not Applicable
9	Excellent Condition
8	Very Good Condition
7	Good Condition
6	Satisfactory Condition
5	Fair Condition
4	Poor Condition
3	Serious Condition
2	Critical Condition
1	Imminent Failure Condition
0	Failed Condition

, we adopted a Bridge Intervention Matrix (BIM) to map improvement in condition ratings to its appropriate intervention. The implemented BIM in this study is based on the matrix first implemented by Saeed et al. [13] and was customized for the maintenance patterns in Nebraska. Under the guidance and discussion with a subject matter expert from the Nebraska Department of Transportation (DOT), the intervention criteria described in

Table 5. Description of maintenance intervention and abbreviation.

Type	Abbreviation	Criteria
Repair	Rep	If deck transition within 4 condition ratings
Rehab	Rab	If deck goes from 4 or 5 (or less) to 8 or 9
Replace	Rec	If deck all goes from 4, 5, or 6 to 8 or 9
Not applicable	NA	These bridges do not exist
Inspection variance	Var	Allowable inspection tolerance is 1 NBI condition code
None	N	No change in deck condition ratings

were implemented in the new BIM.

Table 6. Bridge Intervention Matrix (BIM) maps the improvement in bridge condition ratings to the possible bridge intervention. The abbreviations used in this table are explained in Table 5 above.

To Condition
From Condition		9	8	7	6	5	4	3	2	1
	9	N
	8	Var	N
	7	Rep	Var	N
	6	Rep	Rep	Var	N
	5	Rab	Rep	Rep	Var	N
	4	Rec	Rec	Rab	Rep	Var	N
	3	Rec	Rec	Rab	Rep	Rep	Var	N
	2	Rec	Rec	Rab	Rab	Rep	Rep	Rep	N
	1	NA	NA	NA	NA	NA	NA	NA	NA	N

describes the entire BIM used for this study.

Considering the Bridge Intervention Matrix (BIM), we encounter three potential categories of bridge intervention. However, in our modeling approach, we simplify the prediction task by transforming it into a binary classification problem. Bridges that exhibit any form of observed maintenance are encoded as “intervened” or “yes”. In contrast, bridges that show no indications of intervention or maintenance are encoded as “non-intervened” or “no”.

3.4. Statistical Analysis and Modeling

Various statistical methods guide in exploring the relationship between bridge health metrics such as performance, deterioration, and maintenance activities of bridge deck-wearing surfaces. Understanding the correlation between bridge health measurements gives stakeholders insights for making effective decisions regarding budget planning and allocation, maintenance scheduling, and policy development.

From visual inspection, the performance and deterioration scores distribution resembles a normal distribution. Therefore, appropriate parametric or non-parametric statistical testing will provide insights into differences between the distribution of bridge health metrics across the bridge deck-wearing surfaces. Moreover, other statistical analyses, such as correlation tests between performance, maintenance, and deterioration among all surface wearing types, will suggest if there is a correlation between the bridge health metrics.

After the data processing phase, it is common to encounter challenges in the dataset, such as class imbalance, outliers, and missing data. To address these challenges effectively, this research study finds tree-based modeling to be a promising approach for several reasons. One advantage is that certain implementations of tree-based models have the ability to handle missing data directly, eliminating the need for imputing missing values. Additionally, tree-based models perform well even when the target classes are imbalanced, which is a prevalent issue in many real-world datasets.

Another benefit is the inherent interpretability of tree-based models, making them accessible even to non-experts. These models can be easily visualized, allowing for clear and concise explanations when presenting the model to stakeholders. Particularly decision trees are considered the most interpretable models [18,19]. Furthermore, tree-based models are non-parametric, meaning they do not rely on specific assumptions about the data distribution [9]. This flexibility enables them to effectively handle outliers and capture non-linear relationships within the data.

By leveraging these features, tree-based models provide a robust and intuitive approach for analyzing datasets with imbalanced classes, outliers, and missing data. Their interpretability and ability to handle diverse data characteristics make them a valuable tool in addressing the challenges often encountered in real-world datasets.

This research study assesses the performance of models and reports metrics like accuracy, precision, recall, F1 score, AUC, and kappa values for the maintenance classification problem.

3.5. Evaluation

In this section, we aim to evaluate the performance of various models by reporting key metrics such as accuracy, precision, recall, F1 score, area under curve (AUC), and kappa values for the maintenance classification problem. Additionally, we delve into the interpretability of the models, examining the explanations the machine learning models provide. Specifically, we leverage SHAP (Shapley additive explanations) for model interpretation. We employ SHAP feature importance implemented in python [20] to identify the significance of different variables and utilize partial dependency plots (PDP) to gain further insights into the relationships between variables and the predicted outcomes of the models. By utilizing these techniques, we aim to enhance our understanding of the model’s predictive performance and gain valuable insights into the factors influencing maintenance classification. Note that these techniques have been previously used to study bridge deck deterioration [9].

3.5.1. SHAP Feature Importance

SHAP assigns each variable an importance value for a particular prediction. Variables with large absolute Shapley values are important. Since we want global importance, we average the absolute Shapley values per variable across the data.

The following is the formulation for SHAP feature (variable) importance [21]:

$$\frac{1}{n}\sum _{i=1}^n\left|\varphi {\left(i\right)}_j\right|$$

In this equation, $\varphi {\left(i\right)}_j$ represents the contribution of variable j to the prediction for instance i. The sum is taken over all instances in the dataset, and the absolute values of the contributions are averaged by dividing by the total number of instances, n. The resulting value represents the variable importance, indicating the magnitude of the contribution of a variable to the model prediction outcome.

By calculating the SHAP feature importance, we can assess the relative importance of different variables in the model’s decision-making process. Higher values indicate stronger influences, while lower values suggest a lesser impact on the model’s predictions. This information helps to understand the significance of each variable and provide insights into the underlying relationships between the variable and the target variable.

3.5.2. Partial Dependency Plot (PDP)

A partial dependency plot (PDP) shows the marginal effect of variables on the predicted outcome of a machine learning model [21]. It is a simple and effective way to visualize interactions of variables and their importance.

The formulation for a partial dependency plot (PDP) involves plotting the average predicted outcome of a model as a function of a specific variable while holding other variable fixed.

The following is the formulation for a PDP [21]:

$$PDP\left(x_j\right)=\frac{1}{n}\sum _{i=1}^n\widehat{f}(x_j,x_{-j}^{\left(i\right)})$$

In this equation, $PDP\left(x_j\right)$ represents the partial dependency for variable $x_j$. $\widehat{f}(x_j,x_{-j}^{\left(i\right)})$ represents the predicted outcome of the model for the given variable value $x_j$ keeping the remaining variables, $x_{-j}^{\left(i\right)}$, fixed. The result is averaged over all n instances in the dataset.

By calculating the PDP for a specific variable, we can analyze how the model’s predictions change as that variable varies. This helps to understand the relationship between the variable and the predicted outcome while controlling for other variable. Another important use of PDPs is for identifying and detecting potential non-linear relationships or interactions between variables.

4. Results

In this section, we first delve into the descriptive statistics of the dataset, specifically focusing on the bridge health metrics: performance, deterioration, and maintenance. We explore the correlation analysis between these health metrics and outline the modeling processes needed to identify the relationships between these metrics and the key factors influencing bridge deck maintenance.

4.1. Descriptive Statistics

The descriptive statistics provide a comprehensive summary of the bridge deck population. This is further analyzed from calculated bridge health metrics such as deterioration, performance, and maintenance, offering a detailed view of their distribution.

4.1.1. Summary of Bridge Deck with Wearing Surfaces

Figure 2 shows the distribution of wearing surfaces across bridge decks in the state of Nebraska, with the majority composed of Monolithic Concrete, which accounts for 57.4% of all bridge surfaces. This is followed by Wood or Timber, which is used in 17.12% of bridges. Gravel surfaces make up 10.07% of the total. The remaining bridge decks are distributed among Bituminous, Other, and Low Slump Concrete surfaces, which constitute 6.54%, 2.85%, and 2.43% of the total, respectively, as shown in

Table 7. Distribution of Bridge Deck Surface Wearing Type by Count and Percentage in the state of Nebraska.

Type	Count	Percent
Wood or Timber	2262	17.12
Gravel	1331	10.07
Monolithic Concrete	7582	57.40
Bituminous	864	6.54
Not applicable	76	0.48
Other	377	2.85
None	76	0.57
Integral Concrete	225	1.70
Latex Concrete	34	0.25
Epoxy Overlay	72	0.54
Low Slump Concrete	321	2.43

. This distribution indicates a clear preference for certain materials in constructing and maintaining bridge decks, with Monolithic Concrete and Wood or Timber being the most prevalent materials.

4.1.2. Deterioration

Figure 3 describes the deterioration scores for various bridge deck surfaces, ranging from 0 (no deterioration) to −0.36 (decreasing condition rating per year). The median scores across all surfaces are similar, with a narrow range. However, we can see that bridge decks with surface wearing of Wood or Timber show a higher range of variability, indicating a higher deterioration score. In contrast, bridge decks with surface wearing of Gravel bridges show the lowest variability, indicating the lowest range of deterioration score.

Low Slump Concrete decks have the best median deterioration score (−0.076), followed by Monolithic Concrete bridges (−0.078), Bituminous and Other (−0.079). Other surfaces like Gravel and Wood or Timber have comparable median scores, all around −0.09 to −0.010. After removing outliers, these scores appear to be normally distributed. However, the normality test (Shapiro–Wilk test) suggests that the distribution is not normal, with a p-value (0.0) less than 0.05. The Kruskal–Wallis (non-parametric) test reveals that minor differences in deterioration scores between bridge decks with different wearing surfaces, while relatively small, are statistically significant.

4.1.3. Maintenance

In analyzing the maintenance distribution across bridge decks with different wearing surfaces, as shown in Figure 4, we excluded bridge decks with more than three interventions, as they represent a small fraction (5%) of all bridges. On average, we found that in the remaining population of the bridge deck, about 80% (79.16%) of bridge decks, regardless of their surface type, have no recorded maintenance interventions. Wood or Timber wearing surfaces required the most interventions, with 49% of bridges needing maintenance, followed by Monolithic Concrete (45.6%), and Low Slump Concrete (19.7%). In contrast, Other and Bituminous wearing surfaces have the fewest interventions, with only 23.8% and 25.6% of bridges needing maintenance respectively. Interestingly, only Monolithic Concrete, Gravel, and Wood or Timber bridge decks had more than 2% of their bridges requiring two maintenance interventions, suggesting lower maintenance needs for these surface types.

4.1.4. Performance

Figure 5 shows the performance of the bridge deck across all bridge-wearing surfaces. The performance of the bridge deck seems to vary significantly with various bridge-wearing surfaces, as reflected by the Baseline Difference Score (BDS). The normality test (Shapiro–Wilk test) suggests that the distribution of performance (BDS) score is not normal, with a p-value (0.0) less than 0.5. The Kruskal–Wallis (non-parametric) test reveals that minor differences in performance scores between bridge decks with different wearing surfaces, while relatively small, are statistically significant. It is essential to note that the BDS indicates the long-term performance of bridge components, considering the average condition rating of bridge decks with specific surface types with respect to their age.

The positive BDS values indicate that certain types of bridge decks with wearing surfaces perform better than the average, with Monolithic Concrete (0.16) and Low Slump Concrete (0.37) demonstrating the highest median baseline difference scores. These high BDS values signify a superior than average performance of bridges with these surface types, possibly due to their durable and resilient nature.

Conversely, the negative BDS values for Bituminous (−0.67) and Gravel (−0.29) deck-wearing surfaces suggest that these bridges perform below the average. These wearing surfaces may be more prone to damage and deterioration due to traffic load, environmental conditions, or maintenance practices. The Bituminous wearing surface shows a low BDS, indicating a much worse performance than the average bridge deck.

The magnitude of the BDS reflects the extent to which a specific bridge-wearing surface’s performance deviates from the baseline, as seen in Figure 6. Therefore, the larger the absolute value of the BDS, the more significant the difference from the average performance of the bridge deck. According to the BDS, this understanding allows for more targeted and effective bridge maintenance strategies, focusing on wearing surfaces that show a tendency to underperform. Conversely, it may also guide future bridge design choices toward materials that have demonstrated superior long-term performance.

Figure 6 presents a comparison of the baselines—defined as the average condition rating relative to age—for all bridge decks in Nebraska, labeled as overall (Deck - Baseline), against individual wearing surface types: Monolithic Concrete, Gravel, Wood or Timber, Bituminous, Other, and Low Slump Concrete. It is important to remember that the overall category may encompass bridges not included in this specific study. When examining individual wearing surface types, bridges with decks composed of Monolithic Concrete and Low Slump Concrete exhibit superior performance compared to the overall deck baseline. This indicates that these surface types may have a better-than-average longevity relative to their age. In contrast, decks with Bituminous and Wood or Timber-wearing surfaces show the lowest performance relative to the deck-baseline. This suggests these bridge decks might not age well or be more susceptible to wear and tear or deterioration.

4.2. Correlation Analysis

Assessing the relationship between a bridge’s performance, deterioration, and maintenance, as they relate to various bridge surface types, can offer valuable insights into the maintenance trends for specific bridge decks. The results of the correlation analysis are shown in

Table 8. Correlation analysis between Performance (P), Deterioration (D), and Maintenance (M) by Surface Wearing Type of Bridge Deck in the state of Nebraska.

Attribute	P-M	P-D	D-M
All	−0.155	0.172	−0.259
Monolithic Concrete	−0.316	−0.270	−0.260
Gravel	−0.075	0.023	−0.239
Wood or Timber	0.080	−0.068	−0.321
Bituminous	0.131	0.050	0.171
Other	0.008	0.128	−0.203
Low Slump Concrete	−0.034	0.371	0.010

. If a strong correlation is found, this would suggest a linear relationship, indicating that most of the variability in how bridge decks are maintained is linked to the deterioration rate and overall performance of the bridge deck. In addition to the correlation between maintenance, performance, and deterioration, understanding the influence of each variable can shed light on their distinct role.

Generally, the correlation between performance and deterioration ranged from non-existent to weak. When examining specific surface wearing types, we found that the impact of deterioration and performance on maintenance was mostly weak. The strongest positive correlations between performance and maintenance were observed in the cases of Bituminous (0.131) and Wood or Timber (0.080). Conversely, the strongest negative correlations between performance and deterioration were seen in Monolithic Concrete (−0.270), followed by Monolithic Concrete for performance and maintenance (−0.316). A strong correlation, if observed, would point to a linear relationship, suggesting that the changes in bridge maintenance were primarily driven by deterioration and overall performance. However, the unique relationships between bridge health metrics and surface-wearing types suggest a non-linear relationship and limited influence on the maintenance patterns of the bridge decks. Such an analysis offers valuable insights that could aid in creating predictive models for future maintenance and bridge performance across varied surface types.

4.3. Model Performance and Evaluation

We opted for linear and non-linear algorithms to model the maintenance of bridge decks with various wearing surfaces. The choice of these models was guided by previous research and informed by the results of our correlation analysis between deterioration, maintenance, and performance. Our selection was also guided by previous research and our assumptions about the relationship between maintenance and these influential variables. The correlation analysis suggested a negligible to weak correlation between bridge health metrics and the influence of other key variables in predicting the maintenance of bridge decks with different surface types. We employed logistic regression to accommodate the potential linear relationships between the key variables affecting maintenance. Meanwhile, to account for the possibility of non-linear relationships, we utilized tree-based models.

4.3.1. Model Performance Scores

We tested four algorithms: Logistic Regression (LR), Decision Tree (DT), Light Boosting (LB), and Extreme Gradient Boosting (XGB). The evaluation of these algorithms was based on metrics such as accuracy, precision, f1-score, and kappa value. We then selected the best-performing model to conduct an interpretable analysis of influential variables using SHAP feature importance. The results presented in

Table 9. Comparative analysis of model performance for Logistic Regression (LR), Decision Tree (DT), XGBoost (XGB), and LightBoost (LB), across different bridge wearing surface types: Monolithic Concrete, Gravel, Wood or Timber, Bituminous, Low Slump Concrete, and Other.

Model	Accuracy	Precision	F1 Score	AUC	Kappa
Monolithic Concrete
LR	0.767	0.725	0.735	0.841	0.735
DT	0.884	0.870	0.865	0.881	0.747
XGB	0.911	0.881	0.897	0.963	0.819
LB	0.905	0.872	0.893	0.964	0.808
Gravel
LR	0.779	0.565	0.568	0.768	0.413
DT	0.859	0.712	0.724	0.818	0.630
XGB	0.881	0.747	0.778	0.939	0.694
LB	0.873	0.737	0.768	0.936	0.669
Wood or Timber
LR	0.673	0.572	0.562	0.696	0.302
DT	0.714	0.616	0.633	0.702	0.399
XGB	0.761	0.675	0.700	0.839	0.501
LB	0.760	0.681	0.689	0.832	0.492
Bituminous
LR	0.647	0.172	0.256	0.565	0.089
DR	0.741	0.227	0.312	0.179	0.179
XGB	0.811	0.375	0.461	0.745	0.326
LB	0.750	0.684	0.456	0.811	0.445
Low Slump Concrete
LR	0.743	0.666	0.603	0.779	0.435
DT	0.820	0.727	0.774	0.821	0.626
XGB	0.884	0.851	0.821	0.862	0.747
LB	0.871	0.851	0.821	0.840	0.721
Other
LR	0.718	0.437	0.341	0.581	0.136
DT	0.700	0.357	0.594	0.180	0.180
XGB	0.772	0.500	0.390	0.831	0.258
LB	0.772	0.571	0.410	0.776	0.207

demonstrate that non-linear models, such as tree-based models, outperformed the linear model (Logistic Regression) across all wearing surface types. In particular, Light boosting yielded the highest performance in modeling deck maintenance across different wearing surfaces, with an average accuracy of 83.6% and AUC of 86.3%. Therefore, our further analysis is based on the Light Booting model.

However, the AUC and kappa values suggest that certain surface-wearing types, such as Monolithic Concrete, Gravel, and Low Slump Concrete, were modeled reasonably well, as indicated by higher Kappa values and AUC scores (above 50%). On the other hand, the modeling of Bituminous and Other surface types showed less-than-ideal performance, possibly due to low and imbalanced sample sizes in the testing data. These findings imply that variations in the performance of the models can be attributed to the specific characteristics of the wearing surface types.

4.3.2. Feature Importance Based on SHAP Values

In Figure 7, we present the influential variables for predicting bridge deck maintenance across various wearing surface types. In the following subsection, we offer a detailed analysis of our results with respect to all wearing surfaces. Additionally, we delve into the interaction among the most influential factors as identified by LightGBM (Light Boosting) using partial dependency plots (PDP). Our discussion further extends the insights from PDP results to understand how variable interactions affect the decision boundaries of the LightGBM model. Furthermore, we validate the LightGBM model’s PDP results through data exploration and a visual examination of variable distributions in relation to the target variables.

4.3.3. Monolithic Concrete

Deck age, deterioration, performance, average daily traffic, and latitude are the most influential factors in predicting maintenance for bridge decks with Monolithic Concrete. The distribution of each of the influential variables is shown in Figure 8 with respect to maintenance type: intervention (Yes) and non-intervention (No) group. Specifically, we observe that the median deck age (19) of the intervened bridges is younger than the older bridges’ deck age (33). Median deterioration scores (−0.0869) are lower in intervened type (−0.076) than the median deterioration score in the non-intervened bridge deck, suggesting that the intervention group of the bridge deck is deteriorating rapidly compared to the non-intervention group. Similarly, the intervention distribution has a lower performance score than the non-intervention distribution.

In understanding the interaction between the two most influential variables, PDP plot Figure 9 shows a complex interaction between the deck age and deterioration.

The two-way PDP is a 3D surface plot where the x and y-axes represent the two variables of interest, and the z-axis (often represented as a color scale or contours in 2D plots) shows the average prediction of the model. In the two-way PDP, each point with respect to the deterioration score and deck age on the plot corresponds to a color or height that represents the maintenance decision for the bridge deck with respect to that of the deterioration score and deck age. The lighter shades or higher contour lines typically represent higher predicted values (Intervened). In Figure 9, the lightest shade or the highest contour line occurs at low deck age; this indicates an interaction between the deck age and deterioration score. The darker shades or lower contour lines represent a non-intervened bridge deck. In the PDP plot, these occur at higher deck ages and higher deterioration scores (slow deterioration rate), meaning bridges with higher deterioration scores and higher deck age are associated with no intervention of the bridge deck.

4.3.4. Gravel

The maintenance model for a bridge deck with a wearing surface is influenced by deterioration, along with location attributes such as deck area, longitude, and latitude, which play pivotal roles in predicting maintenance for a bridge deck with Gravel wearing surface. Additionally, it is evident that bridge decks with Gravel wearing surfaces exhibit a wide range of deterioration scores. Intervened bridge decks have a lower median deterioration score of −0.095 (faster deterioration) than non-intervened bridges (−0.076). The distribution of longitude indicates that intervened bridges have slightly median higher values (−97.43) than non-intervened bridges (−97.67), as seen in Figure 10. Furthermore, considering the deck area reveals that the median deck area is higher within the intervened distribution compared to the non-intervened group.

The two-PDP demonstrates the interaction between deck area and deterioration, the two top influential variables in modeling bridge decks with Gravel wearing surfaces, as shown in Figure 11. The PDP suggests higher deterioration score (low deterioration rate) values are associated with no intervention, whereas lower deterioration score (higher deterioration rate) values are associated with the intervention of the bridge deck; darker shades and lower contour values represent this. Specifically, there is a significant intervention pattern with respect to low deterioration scores for deck areas higher than 50, as represented by lighter shade and higher contour values. Overall, the relationship between the deck area and deterioration across all ranges of values is complex.

4.3.5. Wood or Timber

Maintenance modeling of bridge decks with Wood or Timber surface wearing indicates that location variables: longitude, latitude, and bridge metric variable–deterioration score play influential roles in predicting maintenance. Furthermore, the distribution of deterioration scores suggests that intervened bridges have significantly lower scores (−0.125) compared to non-intervened (−0.076) bridges, implying that a high deterioration rate is influential in making bridge maintenance decisions, as seen in Figure 12. The distribution of latitude and longitude are skewed towards lower values and higher values, respectively, while intervened bridges have higher median values for intervened and non-intervened bridge decks within the distribution of longitude and latitude; the overall distribution is similar.

Understanding the two-way PDP interaction between deterioration and latitude, the PDP reveals a complex relationship, as shown in Figure 13. The PDP plot suggests that specific areas associated with latitude are not indicative of bridge intervention. However, lower deterioration scores across all latitudes are associated with bridge intervention indicated by lighter shade compartments of the plot, while the higher deterioration scores are associated with non-intervened bridge decks. The complex pattern indicates that Wood bridges are concentrated in certain areas and are more frequently intervened. We observe significant interactions across various ranges of deterioration score and latitude.

4.3.6. Bituminous

We identify several influential variables specific to bridge decks with Bituminous wearing surfaces. These variables include deck area, deterioration, membrane type (none), and environmental conditions. Furthermore, variables such as deck area, deterioration score, and membrane type demonstrate significant influence according to the best maintenance model. Generally, the intervened group of Bituminous bridge deck tends to have a higher median deck area (319.4) than the non-intervened (187.88) group, implying that large deck areas are associated with interventions. Interestingly, the intervened group exhibits a slower deterioration rate (−0.06) than the non-intervened (−0.076) bridges, as seen in Figure 14. In contrast, the bridge deck with a Bituminous wearing surface and no membrane has a high concentration of non-intervened bridge decks compared to an equal concentration of intervened and non-intervened bridge decks in other membrane types.

The two-way PDP between deterioration score and deck area suggests complex interaction at higher and lower values of deck area values as shown in Figure 15. The plot suggests that low deterioration scores and high deck area represented by lighter shades are associated with the intervention decision of a bridge deck with a Bituminous wearing surface. Higher deterioration scores with very low deck area values represented by darker shades are associated with non-intervened bridges.

4.3.7. Low Slump Concrete

The top three influential factors in predicting the maintenance of bridge decks with Low Slump Concrete are deck age, average daily traffic, and deck protection. We see a significant difference in the intervened (Yes) and non-intervened (No) distribution of bridge decks with Low Slump Concrete wearing surfaces. Intervened bridge decks with Low Slump Concrete wearing surfaces have a lower median age of 25 than the median age of 35 for the non-intervened bridges. We see a broad range of average daily traffic values for non-intervened bridge decks with a higher median value (1417) than the intervened bridge deck (1390), as seen in Figure 16. Similarly, deck protection plays an influential role in determining bridge deck maintenance. Bridge decks with no protection have a higher concentration of intervened bridge decks (93) than non-intervened bridge decks (44).

In Low Slump Concrete bridges, where deck age and average daily traffic are influential factors as seen in Figure 17, their interaction appears to be indicating that, in general, younger bridge decks are associated with intervention (Yes), represented by the lighter shaded regions. Specifically, older decks with high average daily traffic are associated with no-intervention (No) maintenance decisions, represented by darker shaded regions. Meanwhile, younger decks with low average daily traffic are associated with intervention (Yes) maintenance decisions.

4.3.8. Other

Deterioration, average daily traffic, and longitude are the top three influential variables in predicting bridge deck maintenance with Other wearing surfaces. From Figure 18, we see a significant difference in the distribution of intervened (Yes) and non-intervened (No) distribution of bridge deck with Other wearing surfaces. Intervened bridge deck had a lower deterioration score (−0.111), indicating a faster deterioration rate as compared to the non-intervened bridge deck (−0.076). We see a broad range of longitude values for intervened bridge decks with a higher median value (−97.19) than non-intervened bridge decks (−97.415). Average daily traffic (ADT) plays an influential role in determining bridge deck maintenance. Intervened and non-intervened bridge decks have the same ADT of 30. However, intervened bridge deck distributions have higher ranges of values.

In comparing the interaction between the top two influential variables that shape bridge deck maintenance, the relationship between average daily traffic and deterioration score for bridge decks with Other wearing surface types is less complex. On analyzing the PDP plot in Figure 19, we observe an interaction between the average daily traffic and deterioration score, implying simple boundary conditions as represented by horizontal and vertical contours. Generally, lower deterioration scores (faster deterioration rate) are associated with intervention (Yes) of the bridge deck as represented by lighter shade or high contours. Higher deterioration scores (slow deterioration rate) are associated with decision-making related to non-intervened (No) bridge decks. A lower range of the average daily traffic (lower than 50) and a lower deterioration rate are associated with non-intervened bridges.

5. Discussion

In this work, we present a research methodology for modeling bridge maintenance with the goal of evaluating the relationship between performance, maintenance, deterioration, and other influential variables of bridge decks with various surface wearing types. We analyze six different wearing surfaces of bridge deck: Monolithic Concrete, Gravel, Wood or Timber, Low Slump Concrete, Other, and Bituminous, from the perspective of bridge health metrics. Our approach offers a way to analyze and investigate structural, environmental, and regional variables that shape the health of bridge decks. Our results portray an interaction between such variables through different perspectives of bridge health on different types of bridge wearing surfaces.

We identify relationships across various types of bridge deck surfaces. Statistical and machine learning models indicate that each bridge deck surface type exhibits a distinct pattern that can be characterized by influential variables and bridge health metrics introduced in this work. Although deterioration patterns between all types of bridges seem similar, there is a statistically significant difference between the deterioration rate of bridge decks among wearing surfaces. Moreover, the deterioration rate of a bridge deck across all wearing surfaces is one of the top influential factors. The frequency of maintenance is high for concrete and Wood type surfaces of bridges. Finally, overall performance patterns indicate individual baseline compared with the general baseline of the deck in the state of Nebraska, showing varied influence of deterioration and maintenance patterns. In the following sections, we will discuss findings from previous literature mainly focused on Monolithic Concrete, Gravel, Wood or Timber, Bituminous, and Low Slump Concrete wearing surfaces in light of new results. We do not include a discussion on Other wearing surface type, as previous researchers have not provided a comprehensive understanding of this type of wearing surface and its influential variable in modeling bridge deck maintenance.

5.1. Monolithic Concrete

During our analysis, we discovered that nearly half of bridge decks (approximately 57%) in the state of Nebraska are made of Monolithic Concrete surfaces. This percentage is higher compared to a previous study conducted in the northern hemisphere of the United States, which observed that 33% of the 9809 bridges featured Monolithic Concrete wearing surfaces [10]. Monolithic Concrete bridge decks are generally associated with both good and poor deck conditions [9,10]. Contrary to other studies, we did not observe the interaction between deck protection or membrane type [9,10]. However, our analysis supports the conclusion that average daily traffic is one of the influential factors in bridge maintenance.

Our analysis observed that Monolithic Concrete bridge decks maintain a consistent baseline throughout their service cycle. This pattern is reflected in the high-performance score and slow deterioration rate of bridge decks with Monolithic Concrete wearing surfaces. Moreover, this consistency in performance may be attributed to frequent maintenance intervention, as indicated by the higher rate of intervention for bridge decks and slow deterioration rates.

5.2. Gravel

Gravel wearing surfaces are typically utilized for low-volume roads and temporary bridges, necessitating continuous maintenance and re-graveling to maintain the desired surface quality and level of service [22]. Indicators of deterioration for gravel roads include surface roughness, gravel loss, rut depth, and loose gravel [22]. Bridges with Gravel decks often experience low traffic levels [9]. This lower usage may contribute to the favorable performance of decks with Gravel wearing surfaces [10].

Bridge decks with Gravel wearing surfaces exhibit similar deterioration rates compared to those with concrete wearing surfaces. The baseline difference score also remains below 0, indicating overall performance levels lower than the average for all types of bridge deck wearing surfaces. We observe that the baseline for bridges with Gravel wearing surfaces has consistently remained below the all bridge deck baseline condition rating until the age of 40, typically hovering around condition rating 6. We find that deterioration, along with location variables such as deck area and longitude, plays pivotal roles.

5.3. Wood or Timber

The choice of Wood or Timber as a bridge deck surface is primarily based on load capacity, taking into account factors such as the type of wood, size, and configuration of the deck members [8]. Generally, bridge decks with Wood or Timber surfaces may have shorter lifespans than decks with wearing surfaces made of materials like Monolithic Concrete [2]. However, with proper maintenance, preservation measures, and protective treatments, the performance and longevity of wood bridge decks can be improved [8].

Our analysis supports some of the conclusions and findings observed in the literature. Bridge decks with Wood or Timber wearing surfaces exhibit one of the fastest deterioration rates and lowest performance scores. Additionally, the condition baseline for Wood or Timber bridges consistently remains below the overall bridge deck baseline, indicating lower performance throughout the service life-cycle. Like Gravel wearing surface bridge decks, the maintenance model indicates that variables like longitude, latitude, and deterioration play influential roles in predicting maintenance for bridge decks with Wood or Timber wearing surfaces. Furthermore, the distribution of deterioration scores suggests that intervened bridges have significantly lower scores compared to non-intervened bridges.

5.4. Bituminous

Existing studies on the performance and deterioration of bridge decks with Bituminous wearing surfaces presents inconsistent findings. Two research studies referenced in this work offer diverging perspectives. One study suggests that Bituminous surfaces are associated with superior performance compared to non-Bituminous wearing surface types [9]. However, another study indicates that bridge decks with Bituminous wearing surfaces tend to exhibit poor conditions [10]. Our analysis found that Bituminous surfaces perform similarly to bridge decks with Gravel wearing surfaces. The distribution of performance scores for Bituminous wearing surfaces is consistently lower, as indicated by the difference between the overall deck baseline and the Bituminous baseline in Figure 6. Additionally, bridge decks with Bituminous wearing surfaces display the fastest median deterioration rates. Examining maintenance patterns, we observe that Bituminous bridges have fewer interventions than Monolithic Concrete, Wood or Timber, and Low Slump Concrete bridges.

5.5. Low Slump Concrete

Existing literature emphasizes the importance of proper maintenance practices for maximizing the lifespan of concrete bridges. This involves ensuring adequate curing, protection from extreme conditions, and regular inspections [10]. However, our literature review uncovered limited recent studies specifically addressing influential factors related to the deterioration, maintenance, and performance of Low Slump Concrete bridges. Vibration due to adjacent traffic of the bridge deck did not cause a decrease in concrete strength in the bridge deck surface with Low Slump Concrete [23]. Based on our analysis, Low Slump Concrete bridges exhibit superior performance, with higher median performance and a slower rate of deterioration compared to other bridge deck types. The mean condition rating baseline is also higher for Low Slump Concrete bridges. Notably, there is a significant difference in the distribution of intervened and non-intervened Low Slump Concrete bridge decks. The top three influential factors for predicting bridge deck maintenance in Low Slump Concrete bridges are deck age, average daily traffic, and deck protection.

5.6. Limitation and Biases

The majority of the bridges have Monolithic Concrete as the bridge wearing surface. The other bridge wearing surfaces are not equally represented in the dataset. As a result, the performance of these wearing surface maintenance models needs more data samples for accurate training. The lack of sample size also implies a lack of all possible variations of scenarios for specific bridge surface decks to identify patterns with respect to deterioration, performance, maintenance, and other variables. Therefore, the overall results of the models are limited by the data.

Our modeling of bridge deck maintenance is limited to intervention and non-intervention activities as opposed to the detailed maintenance activities such as repair, reconstruction, and rehabilitation. Moreover, tuning maintenance models is non-trivial and may lead to experimental bias which leads to over fitting, and a possibility of “confirmation bias”. Despite the biases and limitation, the results we present in this work hold strong. We therefore feel the majority of these limitation are artifacts of the data and not limitations in our methodology. By applying this approach to a larger, less biased sample, we believe that future research may provide an even more accurate representation of bridge deck maintenance.

6. Conclusions

This study assesses six commonly used bridge deck wearing surfaces, focusing on performance, deterioration, and maintenance. Our approach involves statistical analysis and machine learning modeling for each wearing surface type, offering valuable insights into the relationships between bridge health metrics and the roles of individual variables in shaping bridge deck maintenance. Each wearing surface model provides a unique perspective on how these variables affect overall bridge deck maintenance.

In summary, our analysis suggests that Low Slump Concrete bridges and Monolithic Concrete bridge wearing surfaces perform best in terms of the performance metric (BDS). However, this could be due to a higher intervention ratio for Monolithic Concrete and Low Slump Concrete compared to other wearing surfaces. Additionally, Low Slump Concrete and Monolithic Concrete bridge decks have the best median deterioration scores, indicating slower deterioration than other wearing surfaces. Among bridge health metrics, deterioration (the decrease in condition rating over time) proves more influential than performance (the average condition of the bridge deck over its service life). Deterioration is the most influential variable in predicting bridge deck maintenance for Gravel, Wood or Timber, and Bituminous deck-wearing surfaces. Besides bridge health metrics, physical attributes of the bridge deck, such as deck age and average daily traffic, also play influential roles in classifying bridge deck maintenance. Regional variables like longitude and latitude are influential in classifying bridge deck maintenance of Wood or Timber, and Gravel wearing surfaces. Notably, the relationship between influential variables and bridge deck maintenance for all wearing surfaces is not linear. Our research findings support this result through statistical analysis, including correlation analysis, and demonstrate the limited capacity of linear models in explaining variables’ impact on bridge deck maintenance. Finally, the results obtained using LightGBM prove useful in modeling bridge deck maintenance for various deck wearing surfaces in Nebraska, as evidenced by high accuracy, AUC, and kappa values.

Several avenues for improvement exist in this study. Future research could incorporate additional environmental factors, such as weather conditions (e.g., temperature transitions per year, water temperature, and days with extreme temperatures), alongside snowfall, freeze–thaw cycles, and precipitation. These variables could offer further insights into the role of environmental factors in evaluating bridge health for deck wearing surfaces. Moreover, the inherent subjectivity of bridge inspector visual assessments highlights the need to enhance the quality of the NBI dataset, including methods for estimating missing values to provide more data points for analysis and modeling. To address these challenges, future work could focus on analyzing data collected using IoT (Internet of Things) devices, which can provide more reliable, frequent, and objective data. Lastly, extending the research to other states and exploring detailed element-level inspection data from the National Bridge Inventory Element data (NBE) could allow for more precise condition assessments in calculating bridge health scores.