Bridge Fire Vulnerability Hierarchy Assessment Based on the Weighted Topsis Method

Abstract

With the increasing traffic volume and gradually higher percentage of hazardous goods transport vehicles, bridge fire accidents are more frequent and the resulting losses are striking. Therefore, the assessment of fire risk in bridges has important implications. In this paper, we identify and establish a bridge fire vulnerability indicator system based on vulnerability theory from three aspects: the susceptibility to fire, its resistance to reversal, and its exposure during a fire. On the basis of grading fire vulnerability and making a description of the status of each grade, the corresponding index values of each grade were established by the method of assigning values to the qualitative indexes, and then the empowering TOPSIS method was applied to calculate the relative closeness of each indicator to the ideal status, so as to establish a bridge fire vulnerability grade evaluation model. Finally, using a bridge as an example, it was verified that the assessment method was reasonably feasible by calculating the relative proximity of the bridge to the ideal condition, resulting in a fire vulnerability grade of I for the bridge, which corresponded to its fire history.

1. Introduction

With the growth in car ownership and the rapid development of the logistics industry, the number of vehicles for transporting hazardous chemicals has gradually increased, and the number of large-scale fires on bridges, tunnels, and underground passages has increased. Fire will directly affect the mechanical properties and durability of bridges, greatly increasing the probability of danger. Therefore, it is necessary to establish a risk level model and an effective response plan to minimize the socio-economic losses caused by bridge fires.

Scholars at home and abroad have conducted relevant research into the damage status and safety assessment of bridges after fire. The research found that the degree of fire impact on bridges is mainly related to the height of the fire source from the bottom of the beam. Ju Xiaochen [1] used the large eddy simulation method in FDS to establish the numerical models of three fire scenarios: bridge deck train fire, open bridge fire, and semi-open bridge fire. The fire heating curve, through the analysis, concluded that the fire safety height under the bridge, that is, the bridge bottom height, is greater than two times the flame height, thus the bridge structure is relatively safe. Liu Xuzheng [2] analyzed the variation law of the temperature at the center measuring point of the beam bottom and the temperature field radius of the beam bottom with the height (H) of the beam bottom from the combustion object and the fire source area (S) by establishing the FDS model of the bridge under fire. The different characteristics of the damage state in the interval divide the affected temperature interval at the bottom of the beam and a set of safety assessment procedures for concrete bridges after a fire is established accordingly. Through the analysis of fire cases, Chang J [3] believes that the most serious cause of fire is the transportation of dangerous goods and the most unfavorable position is under the bridge. Through the three-step risk assessment procedure of PRA, SRA, and DRA, the fire risk of bridges is assessed to further identify the locations of high-risk bridges, so as to formulate corresponding countermeasures. Hojune Ann [4] determined the damage degree of the bridge surface based on FDS technology, established the risk level, established the risk level model on this basis, and determined the risk level of the actual bridge through GIS, so as to formulate the corresponding plan. For cable-stayed bridges and suspension bridges, the cables and beams share the load. When the temperature exceeds 500 °C, the strength of the cables will drop to less than 50% of the original strength. Therefore, when a bridge fire occurs, the safety of the cables is more important. Moon Ok Kim [5] proposed a fire risk analysis method for suspension bridges, including quantitative analysis of the installation of fire hydrants on suspension bridges and qualitative analysis of standpipe systems, to ensure that sufficient fire-extinguishing facilities are installed on the bridges.

Most of the existing research is on the assessment of the structural damage status of bridges after fire. How to assess and predict the fire risk of bridges in service and classify the risk levels to achieve the purpose of prevention needs further research. Zhang Xiaodong [6] integrated the probability of vehicle fire and the transcendence probability of bridges with different damages in the disaster domain and calculated the risk probability of bridge fire using a numerical method. This method can effectively evaluate the fire resistance of bridges. The purpose of this paper is to combine the vulnerability theory and bridge fire risk to analyze the factors that lead to bridge fire and use it as an index to evaluate the vulnerability level of bridge fire, and then use the improved TOPSIS method to calculate the relative approximation of different levels compared with the ideal state, so as to establish a set of methods for evaluating the fire vulnerability of bridges. Liu Muyu [7] used the multistage fuzzy comprehensive evaluation method for bridge fire risk evaluation, and provided evaluation results to guide the fire prevention design of Wuhan Yangtze river bridge. Wang Xiaocui [8] showed that, according to the influence factors of bridge fire, the relative connection between bridge fire toughness and ideal state is calculated by the TOPSIS method on this basis, and a bridge fire toughness evaluation model is established.

2. Bridge Fire Vulnerability Theory

Vulnerability is the probability of adverse changes in the system in the face of disasters. Unlike resilience, it emphasizes the possibility that the system cannot restore its original function. The works of [9,10,11] believe that vulnerability is a collection of exposure, sensitivity, adaptability, and resilience. In the field of engineering, vulnerability is mostly used in safety research of buildings and underground engineering. Hou Gongyu [12] calculated the risk probability under single-factor and multi-factor coupling through the N-K model and completed the analysis of the vulnerability of the subway construction safety system. Yang Huiying [13] analyzed the relationship between the vulnerability factors of the prefabricated building construction system through the ISM model and proposed relevant countermeasures to reduce the vulnerability.

The application of vulnerability theory in bridges mainly focuses on the analysis of bridge seismic vulnerability. Djemai, M.C. [14] showed that the application of vulnerability theory in bridges mainly focuses on the analysis of bridge seismic vulnerability. Han Xing [15] adopted the method of numerical integration of failure probability and realized the probability assessment of bridge seismic risk through the numerical integration of the probability density function of seismic acceleration and the probability density function of bridge structure vulnerability. Vulnerability analysis is like a physical examination of the system. Only by finding the crux of the problem can we prescribe the right medicine. Therefore, studying the vulnerability of bridge fires is of great significance to bridge safety in the context of increasing traffic volume. Giuliani L [16] combined vulnerability theory with bridge fire for the first time. Li Jie [17] established a bridge fire vulnerability evaluation model using the fuzzy comprehensive evaluation method. According to the study of relevant literature, this paper defines the bridge fire vulnerability as follows: the probability of the bridge being exposed to fire, the sensitivity of the bridge to fire, and the ability of the bridge to resist the damage caused by fire. Exposure refers to the time the bridge is exposed to fire and the range affected by the fire; sensitivity refers to the degree of response of the bridge when it suffers from fire; and art degrees refers to the fire resistance of a bridge. The mechanism of action of the three is shown in Figure 1.

3. Bridge Fire Vulnerability Assessment Model

3.1. Bridge Fire Vulnerability Index System

According to the definitions of sensitivity, exposure, and stress resistance, combined with the bridge itself and the surrounding environment and other factors, the bridge fire vulnerability index system is constructed as shown in Figure 2. According to the relevant literature [18], each three-level index is divided into four levels; I level corresponds to the safest bridge and then the vulnerability of each level increases in turn, with a corresponding fuzzy description for each level. As shown in

Table 1. Grading and description of indicators of vulnerability to fire in bridges.

First-Level Indicator	Secondary Indicators	I	II	III	IV
Sensitivity	Bridge structure type $I_1$	arch bridge	beam bridge	cable-stayed bridge	suspension bridge
	Bridge material type $I_2$	reinforced concrete bridge	pre-stressed reinforced concrete bridge	steel/concrete composite bridge	steel/wooden bridge
	The length of the bridge in service (years) $I_3$	$<$15	15~30	30~50	$>$50
	Bridge fire history and perception $I_4$	frequent fires	more fires	fewer fires	No fire history
Exposure	Bridge location $I_5$	mountains	rural	suburbs	urban area
	Average number of vehicles per day (vehicle/d) $I_6$	$<$1000	1000~5000	5000~10,000	$>$10,000
	Bridge porous span total length (m) $I_7$	8~30	30~100	100~1000	$>$1000
Art degrees	Ease of repair $I_8$	simpler	general difficulty	difficult	extremely difficult
	Rescue time (min)$I_9$	$<$15 min	15~25	25~35	$>$35
	Impact on the surrounding environment $I_{10}$	basically no impact	less affected	partial loss of function	severe loss of function

, for the convenience of calculation, for quantitative indicators with specific value intervals, the left endpoint of each interval is used. For the qualitative indicators, the method of assignment is adopted and the value of 1~4 is assigned corresponding to the grades I~IV, so as to obtain the values of the three-level indicators corresponding to each grade, as shown in

Table 2. Index level values.

Index Level	${\mathit{I}}_1$	${\mathit{I}}_2$	${\mathit{I}}_3 \left(\mathrm{year}\right)$	${\mathit{I}}_4$	${\mathit{I}}_5$	${\mathit{I}}_6 (\mathbf{Vehicle}/\mathbf{d})$	${\mathit{I}}_7 \left(\mathbf{m}\right)$	${\mathit{I}}_8$	${\mathit{I}}_9 \left(\min \right)$	${\mathit{I}}_{10}$
Level 1	1	1	0	1	1	0	8	1	0	1
Level 2	2	2	15	2	2	1000	30	2	15	2
Level 3	3	3	30	3	3	5000	100	3	25	3
Level 4	4	4	50	4	4	10,000	1000	4	35	4

Note: For the convenience of calculation, I₁, I₂, I₄, I₅, I₈, and I₁₀ are assigned values and 1, 2, 3, and 4 correspond to grades I, II, III, and IV, respectively.

.

3.2. Bridge Fire Vulnerability Rating Assessment

Multi-attribute decision making (MCDM) refers to the use of existing decision information to rank or select the best of a limited number of alternatives. MCDM is a commonly used evaluation method for objects with multiple influencing factors, which can take into account the exclusivity among alternatives and the uncertainty of indicators. Mehdi Keshavarz Ghorabaee [19] improved the fuzziness of the SWARA method and CRITIC method to determine the subjective and objective weights and, combined with the fuzzy EDAS method, proposed a new comprehensive MCDM method to evaluate the harmful impact of construction equipment on the environment. Manman Lu [20] combined the optimal-worst method with IC management, ranked the KPIs by calculating the weight of IC performance, and established the IC measurement system. Ratapol Wudhikarn [21] uses the AHP method to rank the knowledge that enterprises need students to master, so as to efficiently teach relevant knowledge to meet the needs of enterprises.

In the traditional analytic hierarchy process (AHP), the process of constructing the index relation matrix mostly adopts the method of expert investigation, which leads to the calculation result being too subjective and greatly reducing the credibility of the result. The entropy method calculates the weight of each index using objective data and the calculation result is relatively rational. Therefore, the linear combination of the subjective weight calculated by AHP and the objective weight obtained by the entropy method can not only take into account the experience of senior experts, but also avoid excessive influence of subjective factors.

In this paper, the comprehensive weighted TOPSIS method is proposed to evaluate the fire vulnerability of bridges. The TOPSIS method is the approximation to the ideal solution method, which is a method to measure the pros and cons of the evaluated object by calculating the Euclidean distance between the target and the ideal state. The closer it is to the ideal state, the better the evaluated object. It can make full use of the original data information and the results are objective and accurate. The calculation process is relatively simple, does not need to introduce additional functions and variables, and the programming language is easy to implement. The method is designed as a program for engineering projects, which can make the evaluation work more conveniently and has the advantages of economy and efficiency. However, as the influence degree of each index on the result may not be the same, this paper adopts the weighted TOPSIS method to calculate the weight of each index through the AHP and entropy weight method, and then calculates the relative proximity degree. In this way, the importance of each index to bridge fire vulnerability can be considered and the results are more reliable.

3.2.1. Calculation of Subjective Weights by AHP

(1)

To establish the judgment matrix

This article adopts the method of expert scoring, according to the 1–9 scaling method, inviting industry experts on the fire vulnerability index of the bridge between the relative important degree scores, forming the judgment matrix.

$$\mathit{A}=\left[\begin{array}{cccc}{a}_{11}& a_{12}& \dots & a_{1\mathrm{m}}\\ a_{21}& a_{22}& \cdots & a_{2\mathrm{m}}\\ ⋮& ⋮& \ddots & ⋮\\ a_{\mathrm{m}1}& a_{\mathrm{m}2}& \cdots & a_{\mathrm{mm}}\end{array}\right]$$

(1)

where $a_{ij}$ is the importance of index i relative to index j, which is assigned according to the 1–9 scale.

(2)

Normalized judgment matrix

To normalize the elements in the judgment matrix:

$$\begin{gathered} {\omega }_i=\frac{{\omega }_{ij}^{\prime }}{{\sum }_{j=1}^m{\omega }_{ij}^{\prime }},i=1,2,3,\dots ,m \\ {\omega }_{ij}^{\prime }=\raisebox{1ex}{$a_{ij}$}\!\left/ \!\raisebox{-1ex}{${\sum }_{i=1}^m{a}_{ij}$}\right.,j=1,2,3,\dots ,m \end{gathered}$$

(2)

(3)

Consistency check

In the analytic hierarchy process (AHP), the judgment matrix is obtained according to the scores of different experts, and it is likely that the relationship between the importance of the same index is not consistent. Therefore, the consistency test of the judgment matrix is required and the formula is as follows:

$$CI=\frac{{\lambda }_{max}-n}{n-1}$$

(3)

$$CR=\frac{CI}{RI}$$

(4)

where ${\lambda }_{max}$ is the largest characteristic root of the judgment matrix; RI is the consistency index, which can be obtained by looking up the table according to the order of the judgment matrix. If CR > 0.1, the judgment matrix is not a consistency matrix and needs to be reconstructed.

3.2.2. The Entropy Weight Method to Calculate the Index Objective Weights

The entropy weighting method is used to judge the discrete degree of the index by calculating the entropy value of the index. The larger the entropy value, the greater the discrete degree of the index and the greater the corresponding weight. It is an objective weighting method. The calculation steps are as follows:

(1) There are m evaluation indicators and n objects to be evaluated, thus constructing an initial judgment matrix $X$:

$$X=\left[\begin{array}{cccc}{\mathrm{x}}_{11}& {\mathrm{x}}_{12}& \dots & {\mathrm{x}}_{1\mathrm{m}}\\ {\mathrm{x}}_{21}& {\mathrm{x}}_{22}& \cdots & {\mathrm{x}}_{2\mathrm{m}}\\ ⋮& ⋮& \ddots & ⋮\\ {\mathrm{x}}_{\mathrm{n}1}& {\mathrm{x}}_{\mathrm{n}2}& \cdots & {\mathrm{x}}_{\mathrm{nm}}\end{array}\right]$$

(5)

where $x_{\mathrm{ij}}$ represents the value corresponding to the jth index of the ith evaluation object.

(2) Determine positive and negative indicators. A positive index means that, the larger the index value, the more favorable it is to treat the evaluation object, and vice versa if it is a negative index. If it is a negative indicator, it will be converted into a positive indicator through the formula. The conversion formula is as follows:

$$x^{^}=x_{\mathrm{j},\max }-x_{\mathrm{ij}}(i=1,2\dots \dots ,n)$$

(6)

where $x^{^}$ represents the converted value and $x_{\mathrm{j},\max }$ represents the maximum value of the jth column.

(3) The initial judgment matrix $X$ is normalized to obtain the judgment matrix $\mathit{A}$:

$${\tilde{x}}_{\mathrm{ij}}=\frac{x_{\mathrm{ij}}-\min \left(x_{1\mathrm{j}},x_{2\mathrm{j}},\dots ,x_{3\mathrm{j}}\right)}{\max \left(x_{1\mathrm{j}},x_{2\mathrm{j}},\dots ,x_{3\mathrm{j}}\right)-\min \left(x_{1\mathrm{j}},x_{2\mathrm{j}},\dots ,x_{3\mathrm{j}}\right)}$$

(7)

where ${\tilde{x}}_{\mathrm{ij}}$ is the element value in the normalized judgment matrix $\mathit{A}$, $\min \left(x_{1\mathrm{j}},x_{2\mathrm{j}},\dots ,x_{\mathrm{nj}}\right)$ is the minimum value of the element in the jth column of the initial judgment matrix, and $\max \left(x_{1\mathrm{j}},x_{2\mathrm{j}},\dots ,x_{\mathrm{nj}}\right)$ is the maximum value of elements in column j.

(4) To calculate the specific gravity, the formula is as follows:

$$P_{\mathrm{ij}}=\frac{{\tilde{x}}_{\mathrm{ij}}}{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\tilde{x}}_{\mathrm{ij}}} \left(\mathrm{j}=1,2,\dots ,\mathrm{m}\right)$$

(8)

(5) Calculate the entropy value and information entropy redundancy:

$$e_{\mathrm{j}}=-k{\sum }_{i=1}^n{P}_{\mathrm{ij}}\ln P_{\mathrm{ij}}\left(\mathrm{j}=1,2,\dots ,\mathrm{m}\right)$$

(9)

$$d_{\mathrm{j}}=1-e_{\mathrm{j}}$$

(10)

where $e_{\mathrm{j}}$ is the entropy value of the jth index, $k=\frac{1}{\ln \left(\mathrm{n}\right)}$, and if $P_{\mathrm{ij}}$ is 0, then let $P_{\mathrm{ij}}\ln P_{\mathrm{ij}}$ be 0; $d_{\mathrm{j}}$ is the information entropy redundancy of jth indicator.

(6) Calculate the indicator weights:

$${\omega }_{\mathrm{j}}=\frac{d_{\mathrm{j}}}{{\sum }_{\mathrm{j}=1}^{\mathrm{n}}{d}_{\mathrm{j}}}$$

(11)

3.2.3. Comprehensive Weight Calculation

It can be reduced by linear combination of subjective weight calculated by analytic hierarchy process and objective weight calculated by entropy method. The formula for the influence of subjective factors on the results is as follows:

$$W=\beta W_1+\left(1-\beta \right)W_2$$

(12)

where β is the subjective influence coefficient, which is taken as 0.5 in this paper.

3.2.4. TOPSIS Method Calculation Steps

(1) Standardize the initial judgment matrix to get the judgment matrix $Z$. The normalization formula is as follows:

$$Z_{\mathrm{ij}}=\frac{x_{\mathrm{ij}}}{\sqrt{{\sum }_{i=1}^n{x}_{\mathrm{ij}}^2}}\left(\mathrm{j}=1,2,\dots ,\mathrm{m}\right)$$

(13)

(2) Determine the positive ideal solution and the negative ideal solution; the positive ideal solution refers to the most ideal state of the evaluation object and the negative ideal solution refers to the most unfavorable state of the evaluation object.

$$Z^{+}=\left[Z_1^{+},Z_2^{+},\dots ,Z_{\mathrm{m}}^{+}\right]=\max \left\{Z_{\mathrm{ij}}\right\}\left(j=1,2,\dots ,\mathrm{m}\right)$$

(14)

$$Z^{-}=\left[Z_1^{-},Z_2^{-},\dots ,Z_{\mathrm{m}}^{-}\right]=\min \left\{Z_{\mathrm{ij}}\right\}\left(\mathrm{j}=1,2,\dots ,\mathrm{m}\right)$$

(15)

In the formula, $\max \left\{Z_{\mathrm{ij}}\right\}$ is the maximum value of the jth column in the judgment matrix $Z$ and $\min \left\{Z_{\mathrm{ij}}\right\}$ is the minimum value of the jth column.

(3) Calculate the distance to the positive and negative ideal solutions.

$$D_{\mathrm{i}}^{+}=\sqrt{\sum _{\mathrm{j}=1}^{\mathrm{n}}\left[{\omega }_{\mathrm{j}}{\left(Z_{\mathrm{j}}^{+}-Z_{\mathrm{ij}}\right)}^2\right]} \left(\mathrm{i}=1,2,\dots ,\mathrm{m}\right)$$

(16)

$$D_{\mathrm{i}}^{-}=\sqrt{\sum _{\mathrm{j}=1}^{\mathrm{n}}\left[{\omega }_{\mathrm{j}}{\left(Z_{\mathrm{j}}^{-}-Z_{\mathrm{ij}}\right)}^2\right]} \left(\mathrm{i}=1,2,\dots ,\mathrm{m}\right)$$

(17)

(2) Calculate the relative proximity; the greater the relative proximity, the closer to the positive ideal solution.

$$S_{\mathrm{i}}=\frac{D_{\mathrm{i}}^{-}}{D_{\mathrm{i}}^{-}+D_{\mathrm{i}}^{+}}$$

(18)

3.2.5. Build a Rating Model

Establish an initial judgment matrix $X$ according to the index level values in Table 2.

$$\begin{gathered} \mathbf{X}=\left[\begin{array}{cccccccccc}1& 1& 0& 1& 1& 0& 8& 1& 0& 1\\ 2& 2& 15& 2& 2& 1000& 30& 2& 15& 2\\ 3& 3& 30& 3& 3& 5000& 100& 3& 25& 3\\ 4& 4& 50& 4& 4& 10000& 1000& 4& 35& 4\end{array}\right] \\ {A}_1=\left[\begin{array}{ccc}1& 1/2& 2\\ 2& 1& 2\\ 1/2& 1/2& 1\end{array}\right] A_2=\left[\begin{array}{cccc}1& 1/2& 3& 2\\ 2& 1& 4& 2\\ 1/3& 1/4& 1& 2\\ 1/2& 1/2& 1/2& 1\end{array}\right] \\ {A}_3=\left[\begin{array}{ccc}1& 1/3& 1/2\\ 3& 1& 2\\ 2& 1/2& 1\end{array}\right] A_4=\left[\begin{array}{ccc}1& 1/2& 2\\ 2& 1& 3\\ 1/2& 1/3& 1\end{array}\right] \end{gathered}$$

The weight of the indicator $I_1~I_{10}$ is calculated by Formulas (2)~(7) and the results are shown in

Table 3. Weight of each indicator.

Index	${\mathit{I}}_1$	${\mathit{I}}_2$	${\mathit{I}}_3$	${\mathit{I}}_4$	${\mathit{I}}_5$	${\mathit{I}}_6$	${\mathit{I}}_7$	${\mathit{I}}_8$	${\mathit{I}}_9$	${\mathit{I}}_{10}$
$\omega$	0.0953	0.1256	0.0705	0.0719	0.0915	0.1777	0.1126	0.0802	0.1077	0.0672

.

After the weight of each indicator is obtained, the relative proximity of the four levels can be calculated by Formulas (8)~(13). The closer the relative proximity is to 1, the better the result. $S_{\mathrm{i}}$ results are shown in

Table 4. Relative proximity of bridge fire vulnerability ratings.

Bridge Vulnerability Rating	$D_i^{+}$	$D_i^{-}$	$S_i$
I	0	0.7666	1
II	0.2382	0.5535	0.6991
III	0.4777	0.3255	0.4053
IV	0.7666	0	0

. According to the calculated relative proximity of each grade, the bridge vulnerability grade standard can be established; it can be seen in

Table 5. Bridge frailty rating criteria.

Bridge Fire Vulnerability Rating	${\mathit{S}}_{\mathit{i}}$
I	$S_{\mathrm{i}}=1$
II	$0.6991\le S_{\mathrm{i}}<1$
III	$0.4053\le S_{\mathrm{i}}<0.6991$
IV	$0\le S_{\mathrm{i}}<0.4053$

.

4. Case Analysis

A bridge with a total length of 1293 m adopts a two-way, six-lane design with a design speed of 100 km/h. It was completed and opened to traffic in 1998. The bridge structure is a prestressed reinforced concrete box-type continuous beam. With an average daily traffic flow of more than 10,000 vehicles, there is a high possibility of collisions. There was a bridge fire accident caused by the explosion of an oil tanker, so the bridge has little fire history, the database for fire risks is not perfect, and the perception of fire is low. It can be seen from Table 1 that the fire sensitivity and exposure of the bridge are relatively high. Therefore, taking this bridge as an example, the fire vulnerability assessment of the bridge is carried out.

4.1. The Value of the Bridge Fire Vulnerability Index

The bridge to be assessed is recorded as Y₁ and the values of each fire vulnerability index can be obtained according to Table 1 and the relevant data of the bridge, as shown in

Table 6. Vulnerability indicator values of Y₁.

Object	${\mathit{I}}_1$	${\mathit{I}}_2$	${\mathit{I}}_3 \left(\mathbf{year}\right)$	${\mathit{I}}_4$	${\mathit{I}}_5$	${\mathit{I}}_6 (\mathbf{vehicle}/\mathbf{d})$	${\mathit{I}}_7 \left(\mathbf{m}\right)$	${\mathit{I}}_8$	${\mathit{I}}_9 \left(\mathbf{min}\right)$	${\mathit{I}}_{10}$
Y1	2	2	24	3	4	10,000	1000	3	30	3

. In this evaluation model, vulnerability level I is regarded as the most ideal solution and level IV is the worst solution. Therefore, the evaluation model is used to analyze engineering cases; that is, after determining the values of each index of a specific project, the relationship between the index value sequence of the project and the most ideal solution and the worst solution is calculated by Formulas (11) and (12). The Euclidean distance is shown in Figure 3 and the relative proximity is further calculated by formula (13), as shown in

Table 7. Results of relative proximity calculations of Y₁.

Evaluation Object	${\mathit{D}}_{\mathit{i}}^{+}$	${\mathit{D}}_{\mathit{i}}^{-}$	${\mathit{S}}_{\mathit{i}}$
Y1	0.6492	0.4251	0.3957

, and then compared with the grade standard in Table 5 to determine the vulnerability grade of the project.

Comparing the calculated relative proximity results of Y₁ with the rating criteria in Table 5, the bridge has a vulnerability rating of IV. Because the overall length of the bridge is longer, the traffic flow is larger, the rescue response time is longer, and the service time is long, thus it is more at risk to fire. From the fire history of the bridge, it can be seen that the bridge has experienced fires, so the assessment results are more credible. Therefore, the bridge fire vulnerability grade assessment based on the empowered TOPSIS method is a more convenient and feasible assessment method for bridge fire risk. The comparisons in [4,5] using the fuzzy comprehensive evaluation method do not need to find the right transferred membership function, as well as to prevent human subjective judgment in the process of looking for membership function, making the results more objective and reliable. In addition, we do not need to calculate the multistage evaluation result, making the evaluation process more simple and more suitable for engineering application programming.

4.2. Measures to Improve Bridge Fire Vulnerability

(1) In terms of sensitivity: ① Minimize the use of flammable and explosive materials in bridge structures and pay attention to the research and development and popularization of new materials such as refractory materials. ② With the increase in bridge service time, vigilance against bridge fires should also be improved. Commissioners should be regularly arranged to investigate the hidden dangers of bridge fires and timely formulate adjustment measures. ③ For bridges that have experienced fires, a special database should be established to record in detail the time of each fire, the cause of the fire, the loss caused by the fire, and its recovery. It is convenient to carry out bridge fire risk assessment and provide a basis for maintenance work.

(2) In terms of exposure: ① For areas with high traffic flow, a policy of vehicle restriction can be adopted to reduce the average number of vehicles per day. At the same time, the time when hazardous chemicals transport vehicles can drive on the bridge should be staggered from the peak hours of traffic flow on the bridge, and strict screening of hazardous chemicals transport vehicles on the bridge should be carried out to exclude potential explosion risks. ② On the premise of meeting the safety requirements and practical requirements, the bridge span should be shortened as much as possible through route selection to reduce the exposure scope of the bridge in the fire.

(3) In terms of art degrees: ① A fire-resistant coating should be installed on the bridge to reduce the impact of fire on the structure. ② Real-time fire monitoring and alarm devices should be installed and adequate firefighting facilities should be installed, so as to detect and control the further spread of the fire in time and minimize the loss of land caused by the fire. ③ The time required for fire rescue should be considered when selecting the bridge site and the detour distance of the bridge should be shortened. At the same time, the fire rescue emergency response mechanism should be improved. ④ Irreversible components in the ecological environment around the bridge should be reduced and the impact of fire on the entire bridge system should be minimized.

5. Conclusions

In the first quarter of 2022, a total of 219,000 fires were reported across the country, a total of 625 people died due to fires, and the direct property loss was as high as 1.52 billion yuan. Countless shocking facts have made people realize how vulnerable human society is in the face of fire. Fire can have a devastating effect on structural works such as bridges. If the fire risk can be assessed scientifically and accurately, countermeasures and aftermath plans can be prepared in advance to minimize the losses caused by the fire. Through this study, the following conclusions can be drawn:

(1) The combination of vulnerability theory and bridge fire enriches the bridge fire risk theory and brings new ideas for risk identification. This paper analyzes the mechanism of bridge fire vulnerability from three aspects of bridge sensitivity, exposure, and stress resistance, and constructs bridges with 10 bridge fire disaster factors including bridge structure type and repair difficulty. This is called a fire vulnerability indicator system.

(2) By consulting the relevant literature, the bridge fire vulnerability is divided into four grades, the TOPSIS method is used to calculate the relative proximity of the four grades to the ideal state, and the bridge fire vulnerability grade evaluation standard is established according to the calculation results. Considering that the TOPSIS method ignores the different degrees of influence of each index on the evaluation object, the entropy weight method is combined with the TOPSIS method and the weight of each index is first calculated by the entropy weight method, which makes the calculation result of the TOPSIS method more reasonable.

(3) Taking a bridge as an example, according to the actual data of the bridge, the relative proximity to the ideal state is calculated and compared with the grade evaluation standard obtained above; it is concluded that the bridge fire vulnerability grade of the bridge is grade IV. Combined with the fire history of the bridge, it shows that the method in this paper is more feasible.

(4) In this paper, the bridge fire vulnerability is divided into four grades. However, with the analysis of bridge fire accidents and further research into the disaster-causing factors, the index system needs to be better and the grade standards need to be further refined to reflect the actual situation, with complexity and comprehensiveness. The index system of bridge fire vulnerability is established using the Delphi method. Based on the advice of many senior experts in the industry, the index system was established. Accordingly, an unavoidable artificial subjective factor of ground interference appeared. In the process of calculating the relative proximity by the TOPSIS method, the assignment of qualitative indexes still cannot completely avoid the influence of subjective factors, so the objectivity of this method is not ideal. In addition, this method can only provide the vulnerability level of bridge fire of specific engineering projects at present and cannot identify the direct causes of bridge fire. Therefore, the fire treatment module can also be added and the disaster-causing factors can be identified and predicted by grey prediction, least square method, and BP neural network, and the corresponding specific prevention measures can be provided to guide the bridge fire prevention work.