Performance Assessment of Existing Asphalt Pavement in China’s Highway Reconstruction and Expansion Project Based on Coupling Weighting Method and Cloud Model Theory

Abstract

In China, a substantial portion of highway asphalt pavements are no longer capable of accommodating increasing traffic volumes and necessitate renovation and expansion. Prior to commencing such activities, it is crucial to evaluate the performance of the existing asphalt pavements. This study developed a novel normal cloud framework integrating a comprehensive weighted indicator system for existing asphalt pavement. Five key performance indicators including riding quality index (RQI), rutting area ratio (R_r), cracking area ratio (C_r), patching area ratio (P_r), and pavement structural strength index (PSSI) were selected to holistically represent the pavement condition in highway renovation and expansion projects. Subsequently, a method was proposed to determine the weights of these indicators by integrating the analytic hierarchy process (AHP) and entropy. A normal cloud model was constructed to address data characteristics and representation of indicator fuzziness/randomness through digital cloud modeling. The model was applied to 12 sections of the **g**tang Expressway (Tian** section). The results revealed only one section where the normal cloud model differed from the pavement maintenance quality assessment (PQI) model. The 3D ground-penetrating radar detection results of this different section indicated that the normal cloud model more closely aligned with the road structure condition. Compared to absolute pass/fail criteria of the traditional PQI model, the cloud model offered enhanced sensitivity to define graded condition assessments essential for reconstruction planning and decision analysis. Therefore, the normal cloud model is more suitable for assessing the performance of existing asphalt pavements in highway reconstruction and extension projects compared to the PQI model.

1. Introduction

With rapid economic development and the increase in traffic volumes in China, many early-built highways now require renovation and expansion due to deteriorating pavement conditions [1,2]. Highway reconstruction aims to improve transportation efficiency, stimulate economic growth, and enhance quality of life for residents. However, current standards for assessing asphalt pavement performance in China, i.e., the Highway Performance Assessment Standards (JTG 5210-2018), are insufficient to guide reconstruction works [3]. Therefore, develo** a performance assessment indicator system and evaluation models for existing asphalt pavements is imperative in highway renovation and expansion projects.

Numerous studies have explored indicator systems and models for assessing existing asphalt pavement in highway renovation and expansion projects in China. ** a corresponding decision-making framework. While these are pioneering detection methods, the main challenge lies in comprehensive analysis and utilization of inspection results. The rapid progress of computer technology has offered a plethora of valuable tools for conducting comprehensive pavement performance evaluations. Notably, fuzzy mathematics [6], grey theory [7], neural networks [8], entropy theory [9,10], and support vector machines [11], among others, were initially applied for the comprehensive evaluation of pavement performance. However, there are still several key issues that require further discussion concerning the proper application of these tools in road surface evaluation [12,13,14,15].

Li Deyi, an academician from the Chinese Academy of Engineering, proposed the cloud model theory based on fuzzy mathematics and statistical mathematics to realize the map** and conversion between uncertain linguistic values and accurate values, better describing the randomness, fuzziness, and relevance of variables [16]. Since their inception, cloud models have achieved success across diverse fields through natural language processing, data mining, decision analysis, and intelligent control [17,18,19]. Fu [17] and Yang et al. [20] reviewed the generality and flexibility of cloud models in dealing with complex problems and multi-indicator system problems. Cloud models have been preliminarily applied in pavement performance assessment. **ao and Fan [21] analyzed the fuzziness, randomness, and discreteness in the process of pavement condition evaluation, established a pavement condition evaluation model based on the comprehensive weight and cloud model, and verified the model’s correctness through engineering applications. Wei et al. [22] established an entropy weight-cloud model for evaluating pavement performance and compared the calculated results of the model with those of the matter element model, confirming the feasibility of the model. He et al. [23] combined the gray level co-occurrence matrix (GLCM) algorithm and the cloud model theory to construct a damage identification and evaluation model for pavements. However, applications of cloud models in evaluating pavement performance remain limited. Moreover, existing studies neglect reconstruction project particulars by not discussing indicator systems tailored for such work.

This study established an evaluation model based on a comprehensive weighting method and the normal cloud model theory for assessing the performance of existing asphalt pavement in highway renovation and expansion projects, taking into account the fuzziness and randomness inherent in the assessment. The application of the normal cloud model in the performance evaluation of existing asphalt pavement for highway renovation and expansion projects necessitated addressing the following two issues:

(1)

A rational performance assessment indicator system.

(2)

Determination of the weights for the evaluation indicators.

Based on a synthesis of existing research results, and expert experience, this study selected five key indicators to construct a performance assessment indicator system for existing asphalt pavement in highway reconstruction and expansion projects. These five indicators were the riding quality index (RQI), rutting area ratio (R_r), cracking area ratio (C_r), patching area ratio (P_r), and the pavement structural strength index (PSSI). The weights of the evaluation indicators were determined through the analytic hierarchy process (AHP) and entropy. Furthermore, the existing asphalt pavement performance assessment model was established based on the AHP–entropy and normal cloud model. Finally, the feasibility of the method was verified using the detection data from the renovation and expansion project of the **g**tang Expressway (Tian** section).

Specifically, this study made the following contributions: It selected indicators suitable for evaluating the performance of existing asphalt pavement in highway renovation and expansion projects and obtained the weights of the indicators through subjective and objective weighting methods. A normal cloud model for evaluating the existing asphalt pavement in highway renovation and expansion projects was established, and the correctness of the model was verified through engineering applications. The applicability of the model for existing asphalt pavement in highway renovation and expansion projects was demonstrated with high confidence when compared with the PQI evaluation results.

2. Comparative Analysis of Old Pavement Evaluation Models

The oldest worldwide model for assessing asphalt pavement performance is the present serviceability index (PSI) established by the American Association of State Highway Officials (AASHO) in the 1960s [24]. The introduction of the PSI marked a significant milestone in the road management sector. The AASHO established threshold indicators for road surface condition, with a PSI of 2.5 for primary roads and 2.0 for secondary roads. If the PSI fell below the specified threshold, remedial technical measures should be considered for maintenance. Subsequently, many countries adopted PSI variations tailored to their contexts, including the ride comfort index (RCI) in Canada, the maintenance condition index (MCI) in Japan, and the pavement quality index (PQI) model in China [25].

While pioneering, these early models primarily relied on limited regression analysis and contemporary expert knowledge, which presents issues when evaluating aged pavements in reconstruction projects. Firstly, evaluation data itself demonstrates randomness, complexity, and fuzziness characteristics difficult to fully capture through single-factor regression. This can induce discrepancies between modeled and actual relationships between factors and outputs. Secondly, the models were mainly developed for maintenance and repair rather than reconstruction, requiring investigation into their suitability given reconstruction’s unique demands.

Notably, the widely used PQI model in China incorporates indices like overall cracking, rutting, depression, and others [24]. However, related research shows cracks and ruts, respectively, account for over 60% and 30% of pavement distress on Chinese highways [23]. The PQI model does not sufficiently prioritize these predominant failure modes. Furthermore, the PQI calculation equally weights all indices, which may not optimally guide decisions if a particular problem drastically worsens. Fixed weights cannot flexibly reflect actual priorities and importance levels for reconstruction projects.

In summary, while pioneering works, conventional models exhibit several shortcomings limiting applicability to aged pavement performance appraisal for major reconstruction projects. A new approach considering data characteristics and project requirements is warranted to scientifically guide engineering decision-making. The proposed normal cloud framework addresses the abovementioned issues by enabling holistic representation of indicators, weights, and condition fuzziness.

3. Construction of Performance Assessment Indicator System for Existing Asphalt Pavement in Highway Renovation and Expansion Project

The current assessment of asphalt pavement performance in China primarily relies on the PQI evaluation model, with the calculation formula of this model shown in Equation (1).

$$\mathrm{PQI}=w_{\mathrm{PCI}}\mathrm{PCI}+w_{\mathrm{RQI}}\mathrm{RQI}+w_{\mathrm{RDI}}\mathrm{RDI}+w_{\mathrm{PBI}}\mathrm{PBI}+w_{\mathrm{PWI}}\mathrm{PWI}+w_{\mathrm{SRI}}\mathrm{SRI}+w_{\mathrm{PSSI}}\mathrm{PSSI}$$

(1)

where PQI, PCI, RQI, RDI, PBI, PWI, SRI, and PSSI, respectively, represent the pavement maintenance quality index, pavement surface condition index, riding quality index, pavement rut depth, pavement bumpiness index, pavement wear index, pavement surface skid resistance index, and pavement structural strength index; w_PCI, w_RQI, w_RDI, w_SRI, w_PBI, w_PWI, and w_PSSI, respectively, represent the weights of PCI, RQI, RDI, PQI, SRI, PBI, PWI, and PSSI in the PQI model; and w_PSSI takes a value of 0.

According to Equation (1), the PQI model incorporates elements such as surface condition, riding quality, skid resistance, rutting, etc. However, further discussion is needed on the following aspects to evaluate the performance of existing asphalt pavement in highway renovation and expansion projects:

(1)

PSSI is not factored into the PQI calculation, rendering the model unable to reflect the pavement’s structural condition.

(2)

Indicators such as PBI, PWI, and SRI, which are associated with pavement safety, are seldom considered in the pavement design of highway renovation and expansion projects, leading to redundant indicators.

(3)

The weights assigned to these indicators are fixed, resulting in a lower PQI evaluation when a particular indicator deteriorates, which may not effectively guide decision-making in the design of the asphalt pavement for highway renovation and expansion projects.

The primary objective of assessing asphalt pavement performance in highway renovation and expansion projects is to gauge the condition of existing asphalt pavement. Thus, when establishing a performance assessment indicator system for existing asphalt pavement in highway renovation and expansion projects, it is crucial to highlight common issues and accurately reflect the pavement’s load-bearing capacity. Based on the aforementioned considerations, it is evident that there is a need to develop a new performance assessment indicator system for existing asphalt pavement in highway renovation and expansion projects. Drawing from existing literature [26,27,28], five asphalt pavement performance evaluation indicators were selected, including RQI, R_r, C_r, P_r, and PSSI, to construct a comprehensive performance assessment indicator system for existing asphalt pavement in highway renovation and expansion projects. These five indicators provide a holistic view of pavement performance across various dimensions, as illustrated in Figure 1.

The calculation methods for RQI and PSSI are based on the Chinese standard (JTG 5210-2018) [3]. The calculation methods for R_r, C_r, and P_r are presented in Equations (2)–(4), respectively.

$$R_{\mathrm{r}}=\frac{{\mathrm{A}}_{\mathrm{R}}}{\mathrm{A}}\times 100\%$$

(2)

$${\mathrm{C}}_{\mathrm{r}}=\frac{{\mathrm{A}}_{\mathrm{C}}}{\mathrm{A}}\times 100\%$$

(3)

$${\mathrm{P}}_r=\frac{{\mathrm{A}}_{\mathrm{P}}}{\mathrm{A}}\times 100\%$$

(4)

where A_R represents the pavement surface area with a rutting depth greater than 7 mm, calculated by multiplying the rutting length (m) by 0.4 m; A_C denotes the crack area, encompassing alligator cracking, block cracking, transverse cracks, and longitudinal cracks, and the area is determined according to the standard JTG 5210-2018 [3]; A_P signifies the patching area; and A represents the survey area.

4. Evaluation Model Based on AH–Entropy and Normal Cloud Model

4.1. Cloud Model-Related Theories

Academician Li Deyi [29] introduced the theory of the cloud model in 1995. The cloud model serves as a framework for converting qualitative concepts into quantitative data, with the cloud digital features and cloud generator playing pivotal roles in its theoretical application. The cloud generator facilitates the bidirectional transformation between qualitative concepts and quantitative data.

4.1.1. Definition of Normal Cloud Model

Definition 1. 

Consider U as the universe of discourse, and let C be a qualitative concept in U. If x∈U is a random instantiation of concept C, where x follows a distribution x~N(Ex, En’²), En’~N(En, He²), then the degree of certainty that x belongs to concept C is satisfied by:

$$\mu (x)=\exp \{-\frac{{(x-Ex)}^2}{2E{x}^{\prime 2}}\}$$

(5)

The distribution of x within the universe U is referred to as a normal cloud or a second-order normal cloud.

From Definition 1, it is evident that the normal cloud model can capture not only the fuzziness of concepts through membership functions u(x) but also the randomness associated with these membership functions u(x). This highlights a key distinction between the normal cloud model and type-2 fuzzy sets: the normal cloud model is capable of characterizing both the fuzziness of uncertain concepts and their inherent randomness.

4.1.2. Digital Features of Normal Cloud Model

According to the definition in Section 4.1.1, the normal cloud model encompasses three numerical features: Ex, En, and He. Among these, Ex represents the expectation, En denotes the entropy, and He signifies the entropy of entropy, known as hyper entropy. A degenerate cloud drops into a normal distribution when Ex = 0. If Ex = 0 and En = 0, then x = Ex and μ(x) = 1. A larger He indicates a heavier tail in the distribution of the random variable x. Ex serves as the central value of the cloud droplet distribution in the domain space, representing the qualitative concepts most accurately. En measures the uncertainty of qualitative concepts, determined by the randomness and fuzziness of the concept. It not only reflects the probability degree of cloud droplets but also mirrors the fuzziness of qualitative concepts. Hyper entropy He is an uncertainty measure of entropy En, determined by the randomness and fuzziness of entropy, primarily reflecting the aggregation of uncertainty in qualitative concepts [30]. The cloud image comprises a specific number of cloud droplets, as shown in Figure 2. In this study, the number of cloud droplets is set at 3000, determined through a comparison of cloud images composed of varying numbers of cloud droplets.

4.1.3. Positive Cloud Generator

The generator is a specific algorithm employed to convert qualitative concepts and quantitative data in cloud models, with two types: positive cloud generator and backward cloud generator. The positive cloud generator facilitates the transformation from qualitative concepts to quantitative values. The cloud is generated from the cloud parameters (Ex, En, and He), as shown in Figure 3.

Utilizing the cloud drops generated by the positive generator of the cloud model, a normal cloud model for pavement condition evaluation can be established through the following main steps:

Step 1: Obtain the digital feature entropy Ex and hyper entropy He of the cloud model based on the measured data of pavement condition evaluation indicators.

Step 2: Generate a normal random number En′ using statistical methods based on the obtained digital features of the cloud model, En′~N(Ex, He²).

Step 3: Calculate the uncertainty value $\mu (x)=\exp \{-\frac{{(x-Ex)}^2}{2E{x}^{\prime 2}}\}$ based on the generated normal random number En′ to generate a cloud drop (x,u).

Step 4: Repeat the aforementioned three steps until n cloud drops are generated, and the normal cloud model is depicted by the cloud drops.

4.2. Determination of Combination Weights

Prior to employing cloud models to assess pavement performance conditions, it is crucial to determine appropriate indicator weights. Weighting methods encompass subjective, objective, and comprehensive approaches. Subjective methods include the AHP [31], the Delphi method [32], and the scoring method [33], among others. Objective methods comprise the entropy method [34], CRITIC method [35], and principal component analysis (PCA) [36], among others. Subjective methods can reasonably establish weights, ensuring alignment with actual importance; however, they may lack objectivity. Objective methods offer clarity in the calculation process and objective weighting but may fail to capture evaluators’ varying degrees of importance placed on different indicators, potentially leading to disparities between attribute weights and actual importance. Upon reviewing existing research findings, the AHP method was selected for subjective weighting, entropy weighting for objective weighting, and a combination of both methods to derive comprehensive weights.

4.2.1. Deriving Subjective Weights with AHP

The calculation procedure of AHP [37] is outlined as follows:

Step 1: Invite experts to conduct pairwise comparisons of the performance evaluation indicators of the current asphalt pavement in highway renovation and expansion projects, assigning scores based on their relative importance. The specific scores and corresponding scale meanings are detailed in

Table 1. Fundamental scale of absolute numbers.

Intensity of Importance	Definition	Explanation
1	Equal Importance	Two indicators contribute equally to the objective
3	Moderate importance	Experience and judgement slightly favor one indicator over another
5	Strong importance	Experience and judgement strongly favor one indicator over another
7	Very strong or demonstrated importance	An indicator is favored very strongly over another; its dominance is demonstrated in practice
9	Extreme importance	The evidence favoring one indicator over another is of the highest possible order of affirmation
2, 4, 6, 8	The median value of the above judgment	—
Reciprocals of above	If indicator i has one of the above non-zero numbers assigned to it when compared with indicator j, then j has the reciprocal value when compared with i	—

.

Step 2: Construct a judgment matrix based on expert scoring. Assuming there are n evaluation indicators, the judgment matrix A = (a_ij)_n×n is as follows:

$$A=\left[\begin{array}{cccc}{a}_{11}& a_{12}& \dots & a_{n1}\\ a_{11}& a_{22}& \dots & a_{n2}\\ \dots & \dots & \dots & \dots \\ a_{n1}& a_{n2}& \dots & a_{nn}\end{array}\right]$$

(6)

where the element a_ij of the judgment matrix is determined from Table 1 based on expert opinions.

Step 3: Compute the maximum eigenvalue λ_max of matrix A according to Equation (7) and derive the weight matrix W accordingly:

$${\lambda }_{\max }={\displaystyle \sum _{i=1}^n\frac{(AW)}{n{W}_i}}=\frac{1}{n}{\displaystyle \sum _{i=1}^n\frac{{(AW)}_i}{W_i}}$$

(7)

where:

$$AW=\left[\begin{array}{c}{(AW)}_1\\ {(AW)}_2\\ \dots \\ {(AW)}_n\end{array}\right]=\left[\begin{array}{cccc}{a}_{11}& a_{12}& \dots & a_{1n}\\ a_{21}& a_{22}& \dots & a_{2n}\\ \dots & \dots & \dots & \dots \\ a_{n1}& a_{n2}& \dots & a_{nm}\end{array}\right]\times \left[\begin{array}{c}{\omega }_1\\ {\omega }_2\\ \dots \\ {\omega }_4\end{array}\right]$$

(8)

Step 4: Consistency verification. This study employed a composite indicator CI for assessing consistency.

4.2.2. Deriving Objective Weights with Entropy

In information theory, the definition of information entropy is as follows:

$$H(x)=-{\displaystyle \sum _{i}p(x_i)\ln p(x_i)}$$

(9)

where, x represents a random variable, and p(x) represents the output probability function, p(x_i) ∈ [0, 1], ∑p(x_i) = 1.

According to Equation (9), a higher variability of the variable corresponds to a greater entropy, signifying that is carries a larger amount of information. Information entropy primarily indicates the extent of variation in indicators. A high entropy for a specific evaluation indicator suggests that the indicator provides more information in the comprehensive evaluation, resulting in a higher corresponding weight. Conversely, a lower weight is assigned. In cases where the evaluation values of an indicator are identical, it conveys no information and is assigned a weight of 0 in the comprehensive evaluation. The weight calculation process for the entropy method is detailed as follows [34,38]:

Step 1: Construct the original matrix. Assuming the number of evaluation indicators is n and the number of evaluation objects is m, an original matrix B = (b_ij)_m×n can be constructed as follows:

$$B=\left[\begin{array}{cccc}{b}_{11}& b_{12}& \dots & b_{1n}\\ b_{21}& b_{22}& \dots & b_{2n}\\ \dots & \dots & \dots & \dots \\ b_{m1}& b_{m2}& \dots & b_{mn}\end{array}\right]$$

(10)

where b_ij represents the jth indicator detection result of the ith evaluation object.

Step 2: The indices B_ij are normalized. The positive indicator is calculated as follows:

$${b^{\prime }}_{ij}=\frac{b_{ij}-\min \left\{b_{ij},\dots ,b_{nj}\right\}}{\max \left\{b_{1j},\dots ,b_{nj}\right\}-\min \left\{b_{ij},\dots ,b_{nj}\right\}}$$

(11)

The negative indicator is calculated as follows:

$${b^{\prime }}_{ij}=\frac{\min \left\{b_{ij},\dots ,b_{nj}\right\}-b_{ij}}{\max \left\{b_{1j},\dots ,b_{nj}\right\}-\min \left\{b_{ij},\dots ,b_{nj}\right\}}$$

(12)

Step 3: Determining the proportion of evaluation indicators in the scheme is achieved as follows:

$$p_{ij}=\frac{{b^{\prime }}_{ij}}{{\displaystyle \sum _{i=1}^m{b^{\prime }}_{ij}}},i=1,2,\dots ,m;j=1,2,\dots ,n$$

(13)

Step 4: Calculate entropy. The computation of entropy for the evaluation indicators is as follows:

$$H_j=-k{\displaystyle \sum _{i=1}^m{p}_{ij}\ln p_{ij}},j=1,2,\dots ,n,k=\frac{1}{\ln m}$$

(14)

where H_j is the entropy of the jth indicator. If p_ij = 0, then p_ijlnp_ij = 0, while ensuring H_j ∈ [0, 1].

Step 5: Calculate entropy weights. The calculation of the entropy weights for the evaluation indicators is as follows:

$${\omega }_j=\frac{1-H_j}{n-{\displaystyle \sum _{i=1}^n{H}_j}},j=1,2,\dots ,n$$

(15)

where w_j is the entropy weight of the jth indicator, w_j ∈ [0, 1], ${\displaystyle \sum _{j=1}^n{\omega }_j=1}$.

4.2.3. Determination of Comprehensive Weights

The formula for calculating the comprehensive weight is as follows [39]:

$${\omega }_i=\frac{\omega 1_i\omega 2_i}{{\displaystyle \sum _{i=1}^n\omega 1_i\omega 2_i}}$$

(16)

where w_i is the combination weight, and w1 and w2 are the weights calculated by the AHP and entropy method, respectively.

4.3. Performance Ratings of Evaluation Indicators for Existing Asphalt Pavement in Highway Renovation and Expansion Projects

The PQI model and its sub-indicators categorize the performance of asphalt pavement into five classifications: excellent, good, average, poor, and failed. This study adopted the PQI level classification approach and also categorized the five evaluation indicators of existing asphalt pavement in highway renovation and expansion projects—namely, RQI, R_r, C_r, P_r, and PSSI—into the same five categories: excellent, good, average, poor, and failed. While the performance ratings for RQI and PSSI can be determined using the Chinese standard JTG 5210-2018 [3], there are currently no relevant references for R_r, C_r, and P_r. This study established the performance ratings of R_r, C_r, and P_r. The specific performance ratings of evaluation indicators are shown in

Table 2. Performance ratings of evaluation indicators for the existing asphalt pavement in highway renovation and expansion project.

Performance Rating	RQI	Rr	Cr	Pr	PSSI
Excellent	≥90, <100	≥0, <1	≥0, ≤0.5	≥0, ≤5	≥90, <100
Good	≥80, <90	≥1, <5	>0.5, ≤3.5	>5, ≤10	≥80, <90
Average	≥70, <80	≥5, <10	>3.5, ≤10	>10, ≤20	≥70, <80
Poor	≥60, <70	≥10, <25	>10, ≤25	>20, ≤50	≥60, <70
Failed	≥0, <60	≥25, <50	>25, ≤50	>50, ≤80	≥0, <60

.

4.4. Calculation of Digital Features for Normal Cloud Model

The digital features of the normal cloud model for evaluating the performance condition of existing asphalt pavement in highway renovation and expansion projects can be calculated according to Equations (17)–(19):

$$Ex=(c_{ij}^1+c_{ij}^2)/2$$

(17)

$$En=(c_{ij}^1-c_{ij}^2)/2.335$$

(18)

$$He=k$$

(19)

where Ex is the expectation; En is the entropy; and He is the entropy of entropy; $c_{ij}^1$ and $c_{ij}^2$ are the upper and lower limits of the corresponding performance ratings for each evaluation indicator; and k is a constant that can be adjusted according to the degree of ambiguity of the actual problem. The value of k in this study uniformly takes 0.1.

The normal cloud model for evaluating the performance condition of existing asphalt pavement in highway renovation and expansion projects is constructed using the positive generator. The calculation procedure for the positive generator is detailed in Section 4.1.3. This study adopted a value of n = 3000.

4.5. Calculation of Membership Degree for Normal Cloud Model

Based on the normal cloud model in Section 4.4, the membership degree μ(x) of each evaluation indicator at different performance levels can be calculated. Utilizing Equation (20), the comprehensive membership degree of the performance evaluation of existing asphalt pavement in highway renovation and expansion projects is determined.

$$F={\displaystyle \sum _{i=1}^{n}u(x_{ij}){\omega }_i,i=1,2,\dots ,n}$$

(20)

where F is the comprehensive membership degree of the performance ratings, u(x_ij) is the membership degree of the ith indicator at the jth evaluation level, and w_i is the comprehensive weight of the ith indicator.

The performance level S for the existing asphalt pavement in highway renovation and expansion projects is determined based on the principle of maximum membership degree.

$$S=\max (F_1,F_2,\dots ,F_n)$$

(21)

4.6. Flow of Evaluation System for Combination Weighting and Normal Cloud Model

The construction process of the evaluation model for existing asphalt pavement in highway renovation and expansion projects, based on AHP–entropy and the normal cloud model, is as follows:

(1)

Determination of the comprehensive weight of evaluation indicators.

(2)

Determination of performance ratings for the indicators.

(3)

Calculation of the comprehensive certainty degree of the normal cloud.

(4)

Determination of the performance rating for existing asphalt pavement.

The flow of the evaluation system for combination weighting and the normal cloud model is shown in Figure 4.

5. Case Study

5.1. Engineering Background

The application project for this model is the renovation and expansion project of the **g**tang Expressway (Tian** section). The **g**tang Expressway, approved as the first expressway by the State Council for construction and the first cross-provincial expressway in China, was fully completed and opened to traffic in September 1993, and has been in operation for nearly 30 years. The Tian** Municipal Transportation Commission approved the application report for the renovation and expansion project of the **g**tang Expressway (Tian** section) on 29 December 2022, signifying the official commencement of the project’s implementation phase. However, before the implementation of the renovation and expansion project, it is essential to analyze and evaluate the current performance of the existing highway pavement, and then systematically formulate the utilization strategy for the existing pavement structure. Against this backdrop, this study selected sections K67 to K70 to conduct pavement performance inspections and verified this model based on the inspection data. The results for RQI, R_r, C_r, P_r, and PSSI are shown in

Table 3. Inspection data of sections K67 to K70.

Number	Stake	Direction	Lane	RQI	Rr	Cr	Pr	PSSI
1	K67–K68	Forward	Light traffic	93.71	0.832	0.311	0.234	99.95
2	K68–K69	Forward	Light traffic	93.06	0.876	0.286	0.167	99.94
3	K69–K70	Forward	Light traffic	93.74	0.756	0.437	0.209	99.99
4	K67–K68	Forward	Heavy traffic	94.01	0.955	0.799	0.289	99.98
5	K68–K69	Forward	Heavy traffic	94.12	0.917	0.741	0.197	99.92
6	K69–K70	Forward	Heavy traffic	94.29	0.866	0.568	0.213	99.98
7	K67–K68	Reverse	Light traffic	94.80	0.452	0.149	0.251	99.73
8	K68–K69	Reverse	Light traffic	94.92	0.291	0.046	0.255	99.82
9	K69–K70	Reverse	Light traffic	95.23	0.856	0.144	0.324	99.81
10	K67–K68	Reverse	Heavy traffic	92.81	0.398	0.091	0.195	99.66
11	K68–K69	Reverse	Heavy traffic	94.50	0.321	0.052	0.312	99.88
12	K69–K70	Reverse	Heavy traffic	93.82	1.672	0.471	0.364	99.89

. The measurement and calculation methods of RQI and PSSI are in accordance with Chinese standard (JTG 5210-2018) [3], while the calculation methods for R_r, C_r, and P_r are based on Equations (2)–(4).

5.2. Evaluation Results of PQI Model

The PQI model, currently the primary pavement performance evaluation approach in China, was applied to the inspection data from section K67 to K70.

Table 4. Evaluation results of the PQI evaluation model.

Number	Stake	Direction	Lane	Sub-Indicators						PQI	Performance Rating
				PCI	RQI	RDI	PBI	SRI	PSSI
1	K67–K68	Forward	Light traffic	87.67	93.71	94.28	100.00	94.74	99.95	92.41	Excellent
2	K68–K69	Forward	Light traffic	88.08	93.06	92.97	100.00	93.88	99.94	92.08	Excellent
3	K69–K70	Forward	Light traffic	85.81	93.74	93.87	100.00	92.46	99.99	91.48	Excellent
4	K67–K68	Forward	Heavy traffic	81.82	94.01	89.67	100.00	96.35	99.98	89.93	Good
5	K68–K69	Forward	Heavy traffic	81.73	94.12	89.71	100.00	96.65	99.92	89.95	Good
6	K69–K70	Forward	Heavy traffic	82.49	94.29	91.16	100.00	96.27	99.98	90.46	Excellent
7	K67–K68	Reverse	Light traffic	90.90	94.80	97.41	100.00	96.18	99.73	94.48	Excellent
8	K68–K69	Reverse	Light traffic	92.58	94.92	97.65	100.00	95.65	99.82	95.09	Excellent
9	K69–K70	Reverse	Light traffic	93.96	95.23	98.00	100.00	94.76	99.88	95.63	Excellent
10	K67–K68	Reverse	Heavy traffic	90.18	92.81	95.09	75.00	95.93	99.66	90.76	Excellent
11	K68–K69	Reverse	Heavy traffic	91.16	94.50	94.09	100.00	97.57	99.81	94.13	Excellent
12	K69–K70	Reverse	Heavy traffic	85.50	93.82	95.91	100.00	95.11	99.89	91.97	Excellent

presents the PQI evaluation results. The PQI rating of the forward heavy traffic lane in sections K67 to K68 and K68 to K69 was good, while the rest of the sections were rated as excellent. Overall, the PQI rating of section K67 to K70 is excellent. Among the various sub-indicators, the PBI and PCI indicators are slightly lower, whereas the RQI, PBI, SRI, and PSSI indicators are better.

The measurement and calculation methods of PCI, RDI, PBI, and SRI are in accordance with Chinese standard (JTG 5210-2018) [3]. Among sub-indicators, PCI and PBI values were slightly lower, while RQI, PWI, SRI, and PSSI performed better. PCI reflects surface distresses like cracking and rutting that predominantly impact Chinese highways [23]. The relatively lower PCI scores, thus, provide useful insight regarding pavement distress conditions. However, the PQI model assigns all sub-indicators equal weighting regardless of predominant distresses or reconstruction priorities.

5.3. Evaluation Results of Normal Cloud Model

Based on the calculation steps outlined in Section 4 and the data presented in Table 3, the calculation results of the combination weighting-normal cloud model can be derived, as illustrated in

Table 5. Evaluation results of normal cloud model.

Number	Membership Degree of Inspection Values in Performance Ratings					Normal Cloud Model	PQI Model
	Excellent	Good	Average	Poor	Failed
1	0.798	0.374	0.042	0.028	0.002	Excellent	Excellent
2	0.815	0.373	0.041	0.028	0.077	Excellent	Excellent
3	0.646	0.399	0.047	0.029	0.002	Excellent	Excellent
4	0.275	0.519	0.062	0.032	0.004	Good	Good
5	0.307	0.500	0.059	0.031	0.002	Good	Good
6	0.449	0.445	0.052	0.030	0.002	Excellent	Excellent
7	0.970	0.254	0.009	0.020	0.001	Excellent	Excellent
8	0.640	0.265	0.033	0.024	0.002	Excellent	Excellent
9	0.734	0.334	0.037	0.027	0.002	Excellent	Excellent
10	0.726	0.283	0.034	0.025	0.002	Excellent	Excellent
11	0.660	0.269	0.033	0.025	0.002	Excellent	Excellent
12	0.093	0.668	0.080	0.037	0.003	Good	Excellent

. Membership degrees at each performance level (“Excellent”, “Good”, etc.) were calculated using Equation (20) to determine comprehensive membership values.

Table 5 shows the membership degrees and resultant model/PQI ratings. Several notable aspects emerged:

(a)

Sections rated “Good” by PQI (forward lanes K67–K68 and K68–K69) exhibited higher membership in the “Good” class using the cloud model (0.519, 0.500).

(b)

Section K69–K70 reverse lane demonstrated higher membership in “Good” (0.668) versus “Excellent” (0.093).

(c)

Other sections generally aligned between the two approaches, with membership heavily favoring the identical rating.

These results demonstrate the cloud model’s ability to more sensitively represent indicator fuzziness and randomness, generating intermediate membership degrees where conventional methods deliver absolute ratings. This continuous evaluation scale is valuable for reconstruction project planning requiring graded condition assessments.

5.4. Results of 3D Radar Detection

To validate the results obtained from the normal cloud model, 3D ground-penetrating radar (GPR) detection was conducted on the reverse heavy traffic lanes of sections K68–K69 and K69–K70. GPR is a well-established nondestructive technique that has seen increasing usage for pavement subsurface investigation to supplement visual condition surveys.

A Malå ProEx 600 MHz shielded antenna system was employed for data collection. This frequency facilitated the necessary 1–1.2 m penetration depth required to evaluate key structural layers like the asphalt–base interface and aggregate base essential for reconstruction decision-making. Continuous profiling was performed at 14 channels spaced 10.5 cm along wheel-paths and between using an integrated positioning console. This configuration ensured collection of high-resolution 3D condition imagery suitable for detailed structural analysis. The 3D radar detection and processing software utilized in this study were provided by Chengdu Guimu Robot Co., Ltd. Chengdu Guimu Robot Co., Ltd. is a supplier of pavement non-destructive testing equipment located in Chengdu, China.

The 3D radar detection results were assessed based on the impact area, with the calculation method for the impact area being the sum of the areas affected by looseness, sub-grade settlement, and cracking. The calculation method for the cracking impact area involved multiplying the cracking length by a width of 0.4 m. All areas represented horizontally projected areas. The data presented in

Table 6. 3D radar detection results (reverse heavy traffic lane).

Stake	Layer	Looseness (m2)	Cracking (m2)	Settlement (m2)	Total Area (m2)
K68–K69	Base layer	1224.6	0.0	/	1326.0
	Subbase layer	32.2	46.4	/
	Subgrade	0.0	/	22.9
K69–K70	Base layer	1667.7	0.0	/	1678.0
	Subbase layer	10.7	0.0	/
	Subgrade	1.5	/	0.0

were automatically computed using the software provided by Chengdu Guimu Robot Co., Ltd.

Results showed that the reverse heavy traffic lane of section K69–K69 exhibited various types of structural issues, including looseness, cracking, and settlement, whereas there was only one type of issue in the reverse heavy traffic lane of section K69–K70. However, in terms of impact area, the total area affected by internal structural issues in the reverse heavy traffic lane of section K69–K70 was 1678 m², while it was 1326 m² in the reverse heavy traffic lane of section K68–K69. The total area affected by internal issues in the reverse heavy traffic lane of section K69–K70 was 126.5% of that in the reverse heavy traffic lane of section K68–K69. Therefore, based on the results of the 3D radar detection, the performance rating of the reverse heavy traffic lane in section K68–K69 was better than that of the reverse heavy traffic lane in section K69–K70.

In summary, these subsurface conditions validated the normal cloud model evaluation of the reverse lane in section K69–K70 as “good” versus the PQI assessment of “excellent”. GPR objectively verifies increased subsurface impact warranting a lower rating than assigned previously. This reinforces the normal cloud approach’s sensitivity in differentiating conditions where conventional methods may overlook subtle deterioration.

6. Conclusions

The AHP and entropy methods are utilized to determine subjective and objective weights, respectively, and a combination of these two methods is employed to derive comprehensive weights for evaluating indicators of existing asphalt pavement in highway reconstruction and expansion projects. Building upon the derived indicator weights, a performance assessment model for existing asphalt pavement in highway renovation and expansion projects is established, integrating combination weighting and the normal cloud model. This model is applied and validated in the renovation and expansion project of the **g**tang Expressway (Tian** section) highway reconstruction and expansion project. The research findings can be summarized as follows:

(a)

The normal cloud framework addressed limitations of conventional methods by addressing input data characteristics and reconstructing the fuzziness and randomness inherent to pavement evaluation.

(b)

Application to a reconstruction project case study yielded evaluation results demonstrating good consistency with objective 3D GPR detection. The cloud model exhibited an enhanced ability to discern marginal variations in condition and generate continuous membership outputs versus absolute ratings. This improves its utility for reconstruction and extension planning demand of graded condition assessments.

In conclusion, the proposed model establishes an innovative and practical means of appraising existing pavement informed by engineering fundamentals. It provides reconstruction and extension project managements with an effective decision support tool capturing input ambiguities. The cloud theoretic methodology also displays potential for continued refinement and wider pavement management applications