Safety Assessment Method of Concrete-Filled Steel Tubular Arch Bridge by Fuzzy Analytic Hierarchy Process

Abstract

The concrete-filled steel tubular (CFST) arch bridge has achieved significant development in recent years due to its unique mechanical performance and technical advantages. However, due to the lagging theoretical research compared to engineering practice, many problems have been exposed in the existing bridges, resulting in adverse social impacts and enormous economic losses. With the increasing prominence of safety issues in CFST arch bridges, it is necessary to assess their safety condition in service. This paper establishes a safety assessment index system for CFST arch bridges using the fuzzy analytic hierarchy process (AHP) based on an exponential scale. The assessment method proposed includes the following main points: (1) Bridge safety assessment is closely related to the load-bearing capacity of components. This study proposes an assessment index that comprehensively considers both the defect conditions and the design load-bearing capacity of components for the safety assessment. (2) The exponential scale method is introduced to safety assessment for the first time, and the AHP based on an exponential scale is applied to calculate the component weights. (3) Considering the specific structural characteristics of CFST arch bridges, this study provides a detailed division of component types and calculates the component weights. By combining the component assessment indexes, a comprehensive safety assessment index system is established, and a safety assessment method for CFST arch bridges is proposed. (4) Taking the Jiantiao Bridge in Zhejiang Province as an engineering case, the load-bearing capacity of components is calculated using finite element software ANSYS 19.1. Based on the established safety assessment index system, the safety of the bridge is assessed by integrating the inspection results. (5) Software for the safety assessment of a CFST arch bridge is developed using Visual Basic, and the assessment results align well with the actual condition of the bridge.

1. Introduction

The concrete-filled steel tubular (CFST) arch bridge has seen significant development in recent years due to its unique mechanical properties and technical advantages [1]. However, due to the lag between theoretical research and engineering practice, many issues have been exposed in existing bridges, resulting in an adverse social impact and significant economic losses. In some cases, these issues have even led to bridges collapse and casualties [1,2,3]. With the increasingly prominent safety concerns regarding CFST arch bridges, it is necessary to assess their safety under service conditions to ensure the operational safety of these bridges.

Currently, major countries in bridge construction around the world have developed bridge maintenance standards that are suitable for their own national conditions [2]. China has a large number of CFST arch bridges and has issued the specifications for the maintenance of highway bridges and culverts [4] and technical standards of maintenance for city bridges [5] domestically. However, both of these standards have shortcomings in the bridge assessment section. For example, they do not fully cover the different bridge types, such as excluding CFST arch bridges. The assignment of component weights is also incomplete; for example, important components such as tie rods, suspenders, and anchorages in CFST arch bridges and steel arch bridges are lacking. This inevitably affects the accuracy and reliability of bridge assessment results, making it unsuitable for conducting safety assessments on CFST arch bridges with diverse component configurations.

Scholars from different countries have developed various assessment theories and models for bridge safety assessment. They primarily utilize the theory of Analytic Hierarchy Process (AHP) to establish assessment models for conducting safety assessments on bridges. For example, Pan [6] emphasizes the importance of choosing the right bridge construction method and introduces a fuzzy AHP model to address uncertainties and vagueness in decision-making. The model, using triangular and trapezoidal fuzzy numbers, is illustrated through a case study evaluating bridge construction methods. Li [7] aims to develop a structural health monitoring (SHM) based bridge rating method for bridge inspection of long-span cable-supported bridges. The fuzzy synthetic decisions for inspection are made in consideration of the synthetic ratings of all structural components. The results show that the proposed method is feasible, and it can be used in practice for long-span cable-supported bridges with SHM systems. Peng [8] presents a safety risk assessment approach with a case study, where a combined AHP-fuzzy clustering-Delphi method is used for the risk assessment of the Jiangshun Suspension Bridge. Li [9] proposes a method using the AHP to figure out which parts of overpass bridges are most at risk from terrorist attacks. That helps prioritize protection efforts and allocate resources effectively, as shown in the analysis of a bridge in Beijing. Darko [10] aims to show how AHP is being used more in construction management for decision-making, especially in areas like risk management and sustainable construction. It is flexible, widely used in Asia, and favored for being simple and user-friendly, making it useful for researchers and practitioners in the field. Contreras-Nieto [11] introduces a GIS-integrated decision-making framework that prioritizes bridge maintenance using aggregated ratings and average daily traffic, employing an AHP for determining weights. The developed framework is validated through a case study with the Oklahoma Department of Transportation, offering a reliable and implementable approach to support state DOTs in decision-making for bridge maintenance without requiring extra data collection. Xu [12] proposes a cloud-based AHP rating system for deciding inspection intervals of long-span suspension bridges, considering uncertainties. Using the Tsing Ma Bridge in Hong Kong as a case study, the system, with its three-level structure and Gaussian cloud model, proves more effective than the current system at providing precise inspection intervals. Yau [13] proposes an AHP-based prioritization model to support bridge officials in establishing the order of priority for post-disaster bridge maintenance actions. Qing [14] takes a typical ancient three-hole stone arch bridge as a research example to establish a quantitative assessment method by improved AHP for structural safety. Das Khan [15] introduces a new method for ranking defects in concrete bridges by integrating AHP and fuzzy-Technique for Order of Preference by Similarity to Ideal Solution. It considers both defects and their underlying causes, providing a more comprehensive approach. The model, demonstrated on a bridge deck in India, identifies ‘cracks’ as the most critical defect, offering a practical decision-making tool for bridge owners.

In addition, there have been efforts to combine fuzzy theory with neural network technology to establish fuzzy neural network assessment models [16,17,18,19,20,21,22,23,24,25]. Additionally, methods that integrate genetic algorithms with neural networks have been developed to create bridge damage fuzzy assessment expert systems [26,27,28,29,30]. Furthermore, bridge safety assessment systems have been developed utilizing the powerful database management capability of the GIS [31,32,33,34,35].

Considering that China has a significant number of CFST arch bridges, research on safety assessment for this type of bridge is primarily concentrated in China. For example, Cui [36] presents a reliability assessment model for long-span CFST arch bridges at a serviceability limit state. Aiming at the implicit and nonlinear characteristics of the bridges, a hybrid logarithm for calculating the reliability index is proposed with a comprehensive combination of the back propagation neural network and the JC method. Guo [37] proposes a method of fuzzy comprehensive assessment based on the AHP and the fuzzy theory. The results show that the state of the long-span CFST arch bridge can be assessed using the method of fuzzy comprehensive assessment. Wei [38] takes a long-span CFST arch bridge as an example and establishes the finite element model of the bridge by MIDAS/civil program. Based on the MATLAB program, the Monte Carlo method is used to analyze the long-span CFST arch bridge. Jiang [39] proposes a novel damage identification method for CFST arch bridges using data fusion based on information allocation theory. This method is actually a data fusion process in which the statistical characteristics of the measured data, such as mean and standard deviation, are calculated first, and then the bad points are excluded from the data set using the Grubbs Guidelines. Xie [40] takes the world’s longest-span CFST arch bridge, the Pingnan Third Bridge in Guangxi Province, as an example to study the safety and stability of the main truss arch structure during the concrete pouring process in a long-span CFST arch bridge.

From the current state of research, it can be observed that there are a variety of theories and methods for bridge safety assessment. Significant progress has been made in the safety assessment of CFST arch bridges, but there are still some challenges that hinder their effective application in engineering practice. This is mainly because CFST arch bridges have numerous components, complex structural forms, and various disease types, making it difficult to calculate the weights of each component accurately. Existing assessment methods mostly use the condition of component defects as assessment indexes while neglecting the design load-bearing capacity of the structural elements. Therefore, assessing the safety of components solely based on the method is not entirely reasonable. Additionally, as a new material and bridge type, research on CFST arch bridges has mostly concentrated on their mechanical performance and construction methods, while the research on maintenance and management theory has been relatively neglected. In order to ensure the safety of bridges during the operational process, it is crucial to develop a rapid and accurate assessment method specifically tailored to the safety assessment of CFST arch bridges.

This paper establishes a hierarchical model for CFST arch bridges, applying the AHP based on the exponential scale to calculate component weights. The design load-bearing capacity and condition of the component defects are used as safety assessment indexes. Moreover, a comprehensive index system for the safety assessment of CFST arch bridges is established, and a safety assessment system is developed. This method offers a comprehensive representation of the structural safety status and improves the efficiency of bridge safety assessment work.

2. Fuzzy AHP Based on Exponential Scale

2.1. Steps of Fuzzy AHP Based on Exponential Scale

The AHP was proposed by the American scholar Y. L. Saaty in 1977 [41]. It is a quantitative method for comprehensive multi-criteria assessment. By determining the initial weights of various assessment indexes within the same hierarchy, the AHP provides a means to translate qualitative factors into quantitative expressions. It systematically structures and organizes various influencing factors in a hierarchical manner, reducing the impact of subjective factors to some extent and making the assessment results more scientifically oriented. The AHP has found widespread application across various fields, including engineering, agriculture, and economic management [9,10,11,12,13,14,15].

The fuzzy comprehensive assessment method quantifies various uncertain information and utilizes fuzzy operations to obtain assessment result matrices. Through these matrices, not only can the judgment levels of the objects be obtained, but their membership to each level can also be determined. Currently, it has been widely applied in multiple fields.

This paper combines the characteristics of the AHP and fuzzy comprehensive assessment method, adopting the fuzzy AHP for the safety assessment of CFST arch bridges. Within this theoretical framework, the exponential scale is introduced to replace the traditional ‘1–9’ scale for establishing the judgment matrix. Additionally, proximity analysis and variable weight processing techniques are employed to adjust the assessment results. Its basic approach is as follows:

(1) Dividing the complex problem into hierarchical levels brings order and organization to the various factors within the problem, making them more systematic and structured.

(2) Based on an assessment of the objective reality, a quantitative representation is assigned to indicate the relative importance of each level.

(3) Mathematical methods are used to determine the weights of all factors at each level.

(4) By utilizing the single-factor assessment results related to the objects, the corresponding assessment vectors are formed.

(5) The assessment vectors corresponding to each factor are integrated to form a fuzzy relationship matrix.

(6) Applying a fuzzy transformation using the weight vector that determines the importance of each factor, the assessment results for the objects are obtained.

When assessing a specific object using the fuzzy AHP based on an exponential scale, its basic process can be seen in Figure 1.

2.2. Constructing the Judgment Matrix by the Exponential Scale

In the AHP, assuming that the elements of the upper level are denoted as B_k, they exert dominance over the elements A₁, A₂, …, A_n of the lower level. This method employs pairwise comparisons to obtain the weights of each element under the criterion B_k, comparing the influence of A_i with A_j on B_k and denoting it as u_ij. In the traditional AHP, experts construct judgment matrices based on the ‘1–9’ scale to determine the importance between two indexes. However, the use of the ‘1–9’ scale can often lead to inconsistencies in the judgment matrix and a lack of equivalence with the thought process, resulting in distorted results for weight calculation. This issue has been extensively discussed in literature [42,43,44].

The exponential scale [45,46] utilizes the Weber–Fechner law from psychology. It assumes that the objective importance ratio between u_i and u_j is given by a^k−1, where a = 1.316 and k is a natural number ranging from 1 to 9. By comparing n elements with each other, we construct a pairwise comparison judgment matrix A = (u_ij)_n×n, where u_ij = a^k−1. In this paper, the exponential scale values and their corresponding interpretation can be found in

Table 1. Contrast of 1–9 scale and exponential scale meaning.

Meaning of the Scale	‘1–9’ Scale	Exponential Scale, a = 1.316
Negligible importance	1	a0 = 1
Very low importance	2	a1 = 1.316
Low importance	3	a2 = 1.732
Moderately low importance	4	a3 = 2.279
Equal importance	5	a4 = 3
Moderately high importance	6	a5 = 3.947
High importance	7	a6 = 5.194
Very high importance	8	a7 = 6.836
Extreme importance	9	a8 = 9

.

Clearly, this judgment matrix is a positive reciprocal matrix and possesses the following properties:

(1)

u_ij > 0        (i, j = 1, 2, …, n).

(2)

u_ij = 1/u_ji   (i, j = 1, 2, …, n).

(3)

u_ii = 1        (i = 1, 2, …, n).

2.3. Determination of Weights

Under the established criteria, to obtain the ranking results of the factors A₁, A₂, …, A_n it is necessary to calculate their weights. The judgment matrix A can be represented as follows:

$$A={\left(u_{ij}\right)}_{n\times n}=\left(\begin{array}{cccc}\frac{W_1}{W_1}& \frac{W_1}{W_2}& \cdots & \frac{W_1}{W_n}\\ \frac{W_2}{W_1}& \frac{W_2}{W_2}& \cdots & \frac{W_2}{W_n}\\ ⋮& ⋮& ⋮& ⋮\\ \frac{W_n}{W_1}& \frac{W_n}{W_2}& \cdots & \frac{W_n}{W_n}\end{array}\right)$$

(1)

Due to the positive reciprocal nature of matrix A, Equation (2) can be obtained as follows:

$$(A-\lambda \cdot E)\cdot W=0$$

(2)

where W represents the eigenvector of matrix A, λ represents its eigenvalue, and E represents the identity matrix. According to matrix theory, it is known that A has a unique non-zero maximum eigenvalue, λ_max.

The general method for solving the eigenvalues of a judgment matrix is as follows: Convert the general matrix to a compressed matrix (Hessenberg matrix), then convert it to a tridiagonal matrix (Frobenius form), and finally obtain the eigenvalues. The meaning of matrix eigenvalues and eigenvectors depends on the composition of the matrix. For a consistent judgment matrix, the ranking vector is indeed the eigenvector of A. Therefore, only by ensuring the consistency of the judgment matrix can its eigenvector be used as weights. The W represents the weight vector of A.

Since the judgment matrix A is non-symmetric, the accurate computation of the maximum eigenvalue λ_max and weight vector W for matrix A becomes tedious. In response to this, Saaty proposed two approximate calculation methods: the sum-product method and the square root method. According to this theory, this study utilizes MATLAB R2020a software to calculate the eigenvalues and eigenvectors of the judgment matrix.

Taking into account the numerous shortcomings of the fixed weight mode [6], the variable weight mode can also be adopted. The original weights are adjusted according to Equation (3).

$$w_j(r_1,\cdots ,r_m)=\frac{w_j^{(0)}{r}_j^{a-1}}{{\displaystyle \sum _{k=1}^m{w}_k^{(0)}{r}_k^{a-1}}},(j=1,2,\dots ,m)$$

(3)

where, w_j represents the weight of the j index, r_j represents the assessment value that belongs to the j index, α is an empirical coefficient. It is commonly believed that α = 0.2 is applicable to most engineering situations.

2.4. Obtaining the Assessment Results

Assuming there is a set of factors consisting of n elements, it is typically represented by the vector U. Similarly, there is a set of judgments consisting of m elements, typically represented by the vector V. The fuzzy relationship matrix R is formed by the combination of n factors and m judgments. The operation of fuzzy transformation is as follows:

$$B=W\circ R=\left(\begin{array}{cccc}{w}_1& w_2& \cdots & w_i\end{array}\right)\circ \left(\begin{array}{cccc}{r}_{11}& r_{12}& \cdots & r_{1j}\\ r_{21}& r_{22}& \cdots & r_{2j}\\ ⋮& ⋮& ⋮& ⋮\\ r_{i1}& r_{i2}& \cdots & r_{ij}\end{array}\right)$$

(4)

where r_ij represents the degree to which factor U_i belongs to grade V_j, and it also represents the single-factor assessment of the i factor on the object. The value of r_ij can be obtained through the use of the membership function. ‘$\circ$’ denotes the fuzzy composition operator.

To align with the current regulations in China, the safety condition of CFST arch bridges is divided into five levels: excellent, good, moderate, poor, and dangerous. In Equation (4), j represents the number of judgments, which is set as 5. Theoretically, there are many methods for generalized fuzzy composition operations. However, for the safety assessment of CFST arch bridges, equation 5 is considered the most appropriate.

$$b_j=\min \left\{\left.{\displaystyle \sum _{i=1}^n{w}_i{r}_{ij}},1\right\}\right.$$

(5)

In the equation, b_j represents the degree to which the assessment result belongs to the grade V_j. The index i represents the number of factors, and its value should be 1, 2, …, n. The index j represents the value of the grade, and its value should be 1, 2, …, 5.

The advantage of this assessment model is that it retains all the information of the individual factors when determining their membership degrees in the assessment grades. It considers the influence of all factors rather than just focusing on the factors with the most significant impact. Therefore, it is particularly suitable for the safety assessment requirements of CFST arch bridges.

3. Index System for Safety Assessment of CFST Arch Bridge

The CFST arch bridge is a complex system, and there are numerous factors that affect the safety of the bridge, for example, numerous components, complex structural forms, bearing capacity, various disease types, and so on. In order to scientifically and comprehensively assess the safety of the CFST arch bridge, the AHP is used to divide the complex structural system and calculate the weights of structural components. The influence of component design load-bearing capacity and defect conditions are comprehensively considered, and the fuzzy assessment theory is introduced to establish a membership function for the assessment indexes. A comprehensive safety assessment index system for the CFST arch bridges has been established.

3.1. Dividing the Hierarchical Structure

3.1.1. Structural Components Subdivision

After conducting detailed investigations and summaries of completed CFST arch bridges both domestically and internationally, the overall structure can be categorized into three major components: the upper structure, the lower structure, and the bridge deck system. Based on this, further subdivisions can be made as follows: (1) Upper structure: arch ribs, arch rib transverse braces, suspenders, tie rods, upper arch pillars, horizontal beams, and longitudinal beams. (2) Lower structure: foundation, abutment, pier, bearing. (3) Bridge deck system: bridge deck pavement, expansion joints, auxiliary facilities.

3.1.2. Assessment Criteria for Structural Components

There are multiple forms of deterioration in CFST arch bridges, and the determination of component defects needs to be combined with their specific forms of deterioration. The focus of this research is not on the study of disease types, causes, and mechanisms. Below is a brief introduction to common forms of structural component deterioration: (1) Arch ribs: hollowing inside the pipes, corrosion of steel pipes, abnormal arch axis shape, and weld cracking. (2) Arch rib transverse braces: corrosion of steel pipes, weld cracking, abnormal alignment. (3) suspenders, tie rods: cracking of protective sleeves, corrosion of anchorages, corrosion of steel strands. (4) Upper arch pillars: corrosion of steel pipes, weld cracking, abnormal alignment. (5) Horizontal beams and longitudinal beams: deterioration of concrete strength, carbonation of concrete, cracks, corrosion of reinforcement, chloride ion content. (6) Foundations: subsidence of the base, scouring of the base. (7) Piers and abutments: deterioration of concrete strength, carbonation of concrete, cracks, corrosion of reinforcement, chloride ion content, settlement, and displacement. (8) Bearings: damage, detachment. (9) Bridge deck system: damage to the bridge deck pavement, abnormal expansion joints, poor drainage, and damage to other auxiliary facilities.

The design load-bearing capacity can be calculated based on the original design documents. By combining the results of regular inspections for bridges and using the methods provided in the following text, the condition of component defects can be assessed. After adjustment, the actual bearing capacity can be obtained.

3.1.3. Hierarchical Structure

The hierarchical structure of the CFST arch bridge, established according to the principles of the AHP, is shown in Figure 2.

3.2. Weight of Indexes

3.2.1. Design of Expert Scoring Sheet

The expert survey uses the method of pairwise comparison with the exponential scale to construct a judgment matrix for the relevant indexes. The exponential scale values and their corresponding interpretation can be found in Table 1. Based on this principle, our research team designed a survey for the analysis of the importance of safety assessment factors for CFST arch bridges. This survey was distributed to 8 well-known experts in the field of bridge structural engineering for scoring, including Jielian Zheng, Shuixing Zhou, Eatherton, and so on. An example related to the upper structure is presented in

Table 2. Expert scoring sheet for CFST arch bridge.

	j	Arch Rib	Arch Rib Transverse Brace	Tie Rod	Suspender	Upper Arch Pillar	Horizontal Beam	Longitudinal Beam
i
Arch rib		1
Arch rib transverse brace		-	1
Tie rod		-	-	1
Suspender		-	-	-	1
Upper arch pillar		-	-	-	-	1
Horizontal beam		-	-	-	-	-	1
Longitudinal beam		-	-	-	-	-	-	1

Note: If i is more important than j, then fill in according to the above scale; if i is less important than j, then fill in the reciprocal of the above scale.

.

3.2.2. Weight Calculation

By distributing survey questionnaires and collecting expert ratings, a judgment matrix is constructed. By using MATLAB software for calculations, the weights of various factors can be obtained.

(1)

Overall bridge

The overall bridge can be divided into the following components: lower structure, upper structure, and bridge deck system. The constructed judgment matrix is as follows:

$$\left(\begin{array}{ccc}1& 1.732& 6.836\\ \frac{1}{1.732}& 1& 5.194\\ \frac{1}{6.836}& \frac{1}{5.194}& 1\end{array}\right)$$

The calculated weights are as follows: W^T = {0.56, 0.33, 0.11}. Therefore, the original weights of the bridge components are: {lower structure, upper structure, bridge deck system} = {0.56, 0.33, 0.11}.

(2)

Upper Structure

The upper structure can be divided into the following components: arch ribs, arch rib transverse braces, tie rods, suspenders, upper arch pillars, horizontal beams, and longitudinal beams. The constructed judgment matrix is as follows:

$$\left(\begin{array}{ccccccc}1& 3& 1.732& 2.279& 3& 3& 3\\ \frac{1}{3}& 1& \frac{1}{2.279}& \frac{1}{1.732}& 1& 1& 1\\ \frac{1}{1.732}& 2.279& 1& 1.316& 1.732& 1.732& 1.732\\ \frac{1}{2.279}& 1.732& \frac{1}{1.316}& 1& 1.316& 1.316& 1.316\\ \frac{1}{3}& 1& \frac{1}{1.732}& \frac{1}{1.316}& 1& 1& 1\\ \frac{1}{3}& 1& \frac{1}{1.732}& \frac{1}{1.316}& 1& 1& 1\\ \frac{1}{3}& 1& \frac{1}{1.732}& \frac{1}{1.316}& 1& 1& 1\end{array}\right)$$

The calculated weights are as follows: W^T = {0.3, 0.1, 0.17, 0.13, 0.1, 0.1, 0.1}. Therefore, the original weights of the upper structure components are: {arch ribs, arch rib transverse braces, tie rods, suspenders, upper arch pillars, horizontal beams, longitudinal beams} = {0.3, 0.1, 0.17, 0.13, 0.1, 0.1, 0.1}.

(3)

Lower Structure

The lower structure can be divided into the following components: foundation, abutment, pier, and bearing. The constructed judgment matrix is as follows:

$$\left(\begin{array}{cccc}1& 1.732& 1.732& 5.194\\ \frac{1}{1.732}& 1& 1& 3.947\\ \frac{1}{1.732}& 1& 1& 3.947\\ \frac{1}{5.194}& \frac{1}{3.947}& \frac{1}{3.947}& 1\end{array}\right)$$

The calculated weights are as follows: W^T = {0.41, 0.26, 0.26, 0.07}. Therefore, the original weights of the lower structure components are: {foundation, abutment, pier, bearing} = {0.41, 0.26, 0.26, 0.07}.

(4)

Bridge deck system

The bridge deck system can be divided into the following components: bridge deck pavement, expansion joints, and auxiliary facilities. The constructed judgment matrix is as follows:

$$\left(\begin{array}{ccc}1& 1.316& 3\\ \frac{1}{1.316}& 1& 2.279\\ \frac{1}{3}& \frac{1}{2.279}& 1\end{array}\right)$$

The calculated weights are as follows: W^T = {0.48, 0.36, 0.16}. Therefore, the original weights of the bridge deck system components are: {bridge deck pavement, expansion joints, and auxiliary facilities} = {0.48, 0.36, 0.16}.

3.3. Component Assessment

When components of a CFST arch bridge experience damage, it is necessary to make appropriate adjustments to their design load-bearing capacity. In this case, reference can be made to the scoring criteria in the literature [4,5] to assess the condition of component defects and obtain the capacity verification factor Z₁. Then, the actual load-bearing capacity can be calculated according to equation 6.

$$C_{\mathrm{r}}=Z_1\cdot C_{\mathrm{d}}$$

(6)

where, C_d represents the design load-bearing capacity, C_r represents the actual load-bearing capacity.

By substituting C_r into the membership function, the safety assessment vector r(r₁,…,r_m) for the primary stressed components can be obtained. The membership function is shown in Figure 3, and for convenience of expression, let n = (C_d − 1)/7.

For non-stressed components or components for which load-bearing capacity is difficult to calculate, only the extent of their visual defects is used as the safety assessment index, directly obtaining a set of judgments.

3.4. Overall Bridge Assessment

The overall bridge assessment is based on the assessment results of the components, combined with the weight coefficients of each component, and obtained through fuzzy transformation, as shown in Equation (4).

4. Example of Safety Assessment Method

4.1. Project Overview

The Jiantiao Bridge is located approximately 1 km southwest of Jiantiao Town in Sanmen County, Zhejiang Province. It spans Jiantiao Harbor and is a long-span CFST arch bridge with a total length of 507.3 m and a main span of 245 m. The Φ800 mm main steel tubes and Φ600 mm transverse braces are made of Q345C spiral-welded pipes, while the Φ351 mm web members and transverse braces are constructed using Q345C seamless steel tubes. The bridge consists of 18 major sections, seven transverse braces, and two horizontal beams between the ribs. The bridge deck system consists of 41 cast-in-place segments and 38 prefabricated horizontal beams. The horizontal beams are manufactured as precast box girders with open ends, and each piece of horizontal beam is equipped with double suspenders. The cast-in-place segments between two adjacent horizontal beams have a length of 2.9 m, and the horizontal beams are connected to form a unified structure through cast-in-place segments. The bridge deck system is equipped with continuous prestressed tendons throughout its length.

4.2. Calculation Model

The calculation of the design load-bearing capacity of the Jiantiao Bridge utilizes the finite element software ANSYS. In the model, the arch ribs, the concrete inside the pipes, the transverse braces, the web members, the horizontal beams, and the columns are modeled using the beam44 element. The suspenders are modeled using the link10 element, and the upper and lower diaphragms, as well as the cast-in-place segments of the bridge deck, are modeled using the shell63 element. The finite element model established is shown in Figure 4.

4.3. Load-Bearing Capacity Calculation

The load effects of the Jiantiao Bridge can be obtained by the ANSYS finite element model, and the load effects are combined according to the specifications. The resistance effects can be calculated separately according to the design specifications corresponding to each component, and they will not be elaborated here. The calculation results can be seen in

Table 3. The safety assessment for components of the Jiantiao Bridge.

Components	Arch Rib	Transverse Brace	Suspender	Pillar	Horizontal Beam	Longitudinal Beam	Foundation	Abutment	Bridge Deck Pavement	Expansion Joint	Auxiliary Facilities
Design load-bearing capacity	2.24	4.26	2.21	4.99	3.36	3.36	-	-	-	-	-
Correction factor	0.90	1.00	0.98	1.00	0.98	0.98	-	-	-	-	-
Actual load-bearing capacity	2.02	4.26	2.17	4.99	3.29	3.29	-	-	-	-	-
Comment	good	excellent	excellent	excellent	excellent	excellent	excellent	excellent	good	good	fair

.

4.4. Bridge Defect Investigation

By combining the regular inspection data of the Jiantiao Bridge, the current condition of the bridge damages can be obtained. Taking the suspender as an example, Figure 5 shows the condition of the disease discovered during the inspection. The load-bearing capacity verification coefficients for the main stressed components are obtained according to the relevant provisions in the literature [4,5]. For the remaining components, the safety assessment comments are directly obtained from the literature. Please refer to Table 3 for details.

4.5. Component Assessment

By following the method described in Section 3, a set of comments on the safety condition of the components can be obtained, as shown in Table 3.

4.6. Overall Bridge Assessment

Due to article length limitations, only the assessment process for the overall bridge will be introduced here. The assessment methods for the upper structure, lower structure, and bridge deck system are similar to the process described.

The overall bridge consists of the upper structure, lower structure, and bridge deck system. The fuzzy relationship matrix was established in the following order:

$$R=\left(\begin{array}{ccccc}0.29& 0.71& 0& 0& 0\\ 1& 0& 0& 0& 0\\ 0& 0.5& 0.5& 0& 0\end{array}\right)$$

For the division of components in the overall bridge, the original weights are: {Upper structure, Lower structure, Bridge deck system} = {0.33, 0.56, 0.11}. After applying variable weighting, the adjusted weights are: {Upper structure, Lower structure, Bridge deck system} = {0.44, 0.13, 0.43}. With the fuzzy relationship matrix and component weights, we can obtain the assessment result for the lower structure.

$$B=\left\{\begin{array}{ccc}0.44& 0.13& 0.43\end{array}\right\}\circ \left(\begin{array}{ccccc}0.29& 0.71& 0& 0& 0\\ 1& 0& 0& 0& 0\\ 0& 0.5& 0.5& 0& 0\end{array}\right)$$

Based on the calculation, it is determined that B = {0.26, 0.52, 0.22, 0, 0}. Based on this fuzzy vector, it can be determined that the safety assessment result for Jiantiao Bridge is ‘good’.

5. Development for Safety Assessment Software of CFST Arch Bridge

5.1. Characteristics of the Software

A safety assessment software for CFST arch bridges has been developed, using this paper’s established safety assessment index system. It utilizes Visual Basic as a tool for visual programming and is closely integrated with the operational processes of bridge management and maintenance. The software achieves automated assessment operations, significantly simplifying the bridge assessment process. It has the following features:

(1)

Collects accurate and comprehensive bridge condition information.

(2)

Implements automation for displaying and managing various data.

(3)

Provides a simple, convenient, and visual data input function.

(4)

Utilizes both fixed weighting and variable weighting methods to quickly and accurately assess the bridge condition.

(5)

The system has a user-friendly interface, clear functionality, reasonable layout, and easy operation. It also possesses maintainability and expandability, allowing for adjustments to adapt to new changes through modifications.

5.2. Module of the Software

According to the overall objectives of the system and the principles of program design, the CFST arch bridge safety assessment system is divided into several modules: the weight input module, the design load-bearing capacity input module, the defect condition input module, and the assessment result module.

(1)

Weight input module

Upon entering the assessment system, default weight values are set for each component. If the weights need to be modified, users must click the ‘Modify weight’ button and then enter the modified weights. If the sum of the component weights is not equal to 1, the software will display an error message.

(2)

Design a load-bearing capacity input module

Similar to the weights, it is not recommended for users to modify the design load-bearing capacity. If modification is necessary, users must click the ‘Modify design load-bearing capacity‘ button.

(3)

Defect condition input module

Before conducting a safety assessment using the software, users must input the defect conditions of the bridge.

(4)

Assessment result module

The assessment result module consists of component assessment results and overall bridge assessment results. After users input the defect conditions and click ‘Start assessment,’ the program will automatically calculate the assessment result. Bridge management and maintenance can assess the bridge’s safety by considering both the component and overall assessment.

Additionally, the software provides options for both fixed weighting and variable weighting based on different methods. To make scientifically reasonable judgments on complex assessment results, a proximity option is also available for users to choose from. The interface of the CFST arch bridge safety assessment software is shown in Figure 6.

5.3. Operation of the Software

During the routine management and maintenance process of CFST arch bridges, a maintenance engineer only needs to conduct targeted inspections based on the various items listed in the software. They can refer to the scoring criteria provided in references [4,5] to rate the components and enter the scores into the assessment software. The program can automatically calculate the assessment results for the bridge and its components based on the data input by the surveyors. By considering the overall bridge assessment results and the fuzzy relationship matrix, management and maintenance engineers can make judgments on the bridge’s safety and decide whether necessary repair and reinforcement measures should be taken to address any structural damage.

The calculation of the design load-bearing capacity involves the use of finite element software ANSYS. The system also adopts a pre-recorded method for entering the design load-bearing capacity, which users can modify if necessary. If a certain index was not tested during a particular routine inspection, the previous test result can be used. The safety assessment results for the Jintao Bridge are shown in Figure 7.

5.4. Applicability of the Assessment Method and Software

This safety assessment software is currently applicable to CFST arch bridges. At present, the database of software only includes the Jianqiao Bridge. As our team conducts more in-depth research and more surveys, we will continue to update the database with additional bridges. Furthermore, this assessment method and software can serve as a reference for the safety assessment of other bridge types, such as beam bridges, suspension bridges, cable-stayed bridges, and so on.

6. Conclusions

This paper establishes a safety assessment index system for CFST arch bridges using the fuzzy AHP based on an exponential scale. The assessment method is proposed and validated on an actual bridge. Software for assessment is developed. The main achievements are summarized as follows:

(1)

Bridge safety assessment aims to assess the ultimate limit state of a bridge, which is closely related to its load-bearing capacity. Existing safety assessment methods for the CFST arch bridges often focus on defect conditions as assessment indexes while neglecting the design load-bearing capacity. This does not fully rationalize the assessment of component safety. This work introduces an assessment index that comprehensively considers both external defects and component design load-bearing capacity, resulting in assessment results that better reflect the safety of the bridge.

(2)

This study applies the exponential scale method to the field of bridge safety assessment for the first time. It determines the importance of each index and calculates the weights of components using the AHP based on an exponential scale, simplifying the solution process and achieving more reasonable weighting.

(3)

The current assessment section of bridge maintenance specifications has many flaws, such as incomplete bridge types, missing component types, and rough weight assignments, leading to significant differences between the assessment results and the actual bridge condition. To address these issues, this work establishes a hierarchical structure based on commonly found components in the CFST arch bridges, provides a detailed classification of component types, and calculates component weights using the AHP based on an exponential scale, effectively compensating for the deficiencies in current bridge maintenance specifications.

(4)

Based on the hierarchical model, combined with component assessment indexes, a comprehensive safety assessment index system is established, and a safety assessment method for the CFST arch bridges is proposed. This method is applied to the safety assessment of the Jiantiao Bridge in Zhejiang Province. The assessment results match well with the conclusions of load tests conducted on the actual bridge [47]. Compared to the load test, this method not only saves a significant amount of time and resources but also offers convenient operation.

(5)

For the daily management and maintenance of bridges, software for the CFST arch bridge safety assessment is developed using Visual Basic. It is applied to the daily management and maintenance of the bridge, facilitating operations for bridge maintenance engineers and reducing the work associated with bridge assessment while improving efficiency.