1. Introduction
Bridges are a very important part of the modern transportation network. Urbanization puts forward higher requirements for the sustainable development of bridges in China. Since the 1980s, China’s bridges have gone through a period of large-scale construction. By the end of 2018, China had as many as 851,500 road bridges, and the number is increasing at a rate of 20,000 a year. However, the actual service life of the bridge is far from its design life [
1,
2,
3]. Bridge collapse occurred in the process of bridge construction and operation, which caused huge economic losses and casualties and had major social and economic impact [
4,
5,
6]. Now the bridge construction should change from “Chinese speed” to “Chinese quality” [
7,
8,
9]. This has meant that bridge construction and management gained widespread attention [
10,
11,
12]. The safety of bridges is related to social stability and economic development, and in order to realize the extension of bridge service life, a more scientific and systematic management path is needed [
13,
14].
The degradation mechanism and manifestation of the same kind of bridge have a certain regularity, and finding this rule is helpful for preventing maintenance of such bridges [
3,
15,
16]. It is necessary to adopt a scientific and reasonable analysis method to find out the cause of collapse, since avoiding similar bridge collapse accidents has become an important issue in modern engineering research [
17]. Based on a large number of bridge collapse cases, researchers usually analyze them from three perspectives: (i) the general situation and development trend of bridge collapse are analyzed by means of descriptive statistics, and management measures for the causes that account for a relatively high proportion of bridge collapses are then proposed [
18,
19,
20,
21]; (ii) the causes of collapse of different types of bridges are summarized, and the importance of influencing factors by methods such as analytic hierarchy process (AHP) and fault tree analysis (FTA) etc., are analyzed and corresponding risk assessment methods and prevention strategies based on the importance of factors are proposed [
22,
23,
24,
25,
26]; (iii) the health status of the bridge is assessed through predictive methods and appropriate preventive measures are developed [
27,
28,
29,
30,
31]. However, bridge collapse is a complex problem, which involves many factors in each stage of a bridge’s life [
3]. It is difficult to define the cause of bridge collapse due to the interaction of various factors rather than simple superposition. Therefore, it is necessary to clarify the action mechanism among the influencing factors and then design a scientific and effective bridge management path.
A few studies focused on the correlation between the factors affecting bridge degradation. Deng et al. summarized the collapse modes of several main types of bridges and expounded the mechanism of collapse [
32]. Based on descriptive statistics of bridge collapse data, Zhu et al. analyzed the correlation between collapse factors at various stages [
18]. Zhao et al. used mechanical theory to analyze the relationship between internal and external factors of bridge collapse and believed that the collapse of the bridge was the result of external forces overcoming structural resistance [
33]. Chen et al. analyzed the influence mechanism of natural environmental factors on the durability of concrete bridges and classified the working environment of bridges accordingly [
34]. Zhang et al. used an association analysis technique in data mining to find association rules between influencing factors. According to the support degree, confidence degree and other indexes, the possible causes of bridge damage are judged [
35]. Luo et al. used machine learning method to study the correlation between bridge health monitoring data to improve the identification accuracy of bridge damage [
36]. The existing researches mainly focus on the management of the bridge’s operational stage. They used scientific methods to determine earlier and more accurately what was affecting the health of the bridge, so that maintenance measures could be taken in advance. However, the role of the bridge collapse factor has continuity, and a fault in the design and construction stage is difficult to compensate for by maintenance measures in the operation stage. Therefore, it is necessary to design the management path throughout the whole life cycle of the bridge, strengthen the whole process quality control of the bridge from the starting point and reduce the probability of bridge collapse from the source.
The bridge collapse factors of different materials and structures are different [
32]. Concrete bridges account for more than 90% of China’s total bridges [
34,
37] and beam bridges account for more than 74% [
38]. Taking the sustainable management path of concrete beam bridges as the target, this paper analyzes the collapse characteristics and trends of concrete beam bridges, influencing factors at different stages of its life cycle and influencing relations among the factors. In order to analyze the collapse factors, information about 190 concrete beam bridge collapses in China in the past 30 years was collected. The main contents of this paper are as follows: (i) to study the general characteristics of concrete beam bridge collapse and the influencing factors at each stage; (ii) to analyze the mechanism of action among the influencing factors using the FISM model; (iii) to propose a management path for concrete beam bridges which provides a reference for governments to improve bridge sustainability.
3. Collapse Factors of Concrete Beam Bridge
Bridge engineering is a complex system with many uncertain factors, and the causes of bridge collapse are also diverse [
32]. Based on many existing studies, this paper divides the causes of bridge collapse at various stages into two categories: natural factors and human factors. According to the different time of the accident, the cause of the accident is divided into three stages: the design and construction stage, operation stage and investigation and maintenance stage (see
Figure 4).
Figure 4 shows the cause of the collapse of 190 concrete beam bridges that have been collected. A total of 65 collapses occurred during the design and construction period. As shown in
Figure 4a, human factors (93.85%) are the main causes of bridge collapse in the construction stage. Inadequate design, lack of experience with new technologies, deliberate use of inferior materials or improper construction methods are common causes of bridge collapse at this stage [
42,
43,
44,
45,
46]. Natural factors played a minor role in this phase. Heavy precipitation is a very dangerous factor. Continuous precipitation tends to lead to floods, which will cause the softening of bedrock, foundation instability, equipment failure and other phenomena [
47,
48,
49]. Therefore, strict process control and effective supervision are very important in the design and construction stage, which can effectively reduce the probability of bridge collapse.
As shown in
Figure 4b, 108 collapses occurred during the service of the bridge. Heavy precipitation and flood accounted for 27.08%. Especially for bridges that spanned across water, heavy rainfall and flood will cause serious scour and erosion. The lateral impact of the earthquake may cause the substructure of the bridge to fail. The design and construction problems (28.57%) in the construction stage reduce the durability of the bridge, continuously affect the service stage. 54.29% of the collapsed bridges had long-term vehicle overload. Overloaded vehicles are common in China, where demand for transport is increasing. Vehicle overload will increase the bridge load, accelerate the deterioration of the superstructure and reduce the service life of the bridge components. There are two main reasons for the phenomenon of vehicle overload. The first is the deviation in the prediction of bridge bearing capacity in the design stage, and the second is the ineffective control of vehicle overload by the regulatory authorities. For water bridges, ship collision (26.03%) and illegal sand mining (9.59%) are also important causes of bridge collapse. Ship collision may cause partial structural damage to the bridge, and even irreparable deformation and displacement. Excessive sand mining will change the riverbed topography, resulting in the bridge foundation bearing capacity not being able to meet the original design requirements, forming a great safety hazard.
As shown in
Figure 4c, 17 collapses occurred during the investigation and maintenance stage. Most of the bridges in this stage have a long service time and, due to inadequate maintenance and repair work, have structural diseases that are serious and more dangerous than in the construction period. During maintenance and demolition, bridge collapse can be caused by insufficient cognition of bridge structure, unreasonable demolition plans, irregular construction and negligence of monitoring work.
4. Analysis Methods
The correlation between collapse factors of concrete beam bridges is very important for bridge management.
Figure 5 shows a schematic flow chart for the proposed sustainable management paths of concrete beam bridge. Firstly, the information about bridge collapse is collected, the characteristics of bridge collapse are analyzed and the causes of bridge collapse in each life stage are analyzed. On the basis of statistical data analysis and literature review, the list of collapse factors of concrete beam bridges is determined by expert interviews. Secondly, experts are asked to judge the correlation degree between the factors in the list of collapse factors of a concrete beam bridge. The expert’s judgment results are converted into triangular fuzzy numbers, and the triangular fuzzy numbers adjacency matrix is constructed. According to the accessibility matrix, the collapse factors of concrete beam bridge are divided into different levels, and the multi–layer hierarchical interpretation model of concrete beam bridge collapse is drawn. The establishment of the FISM model can intuitively observe the hierarchical relationship among collapse factors, which is conducive to clarifying the influence mechanism among collapse factors. Finally, the model results are analyzed, and the management path that is beneficial to the sustainable development of the bridge is proposed.
4.1. Step 1: Identifying Collapse Factors
Based on the statistical analysis of concrete beam bridge collapse accidents in the first and second parts of this paper and the collapse factors obtained from the existing research, the initial list of collapse factors is extracted. In order to ensure the effectiveness of collapse factors, the final collapse factors list of concrete beam bridges is obtained by modifying and simplifying the initial factors list through expert interviews.
Different types of bridges have different risk preferences for collapse. The list of collapse factors obtained from the literature review is more comprehensive, but it is aimed at all types of bridges and lacks the characteristics of concrete beam bridges. Due to the limited data, the risk list obtained by data statistics has certain limitations. Therefore, taking the collapse factors identified by the above two approaches into consideration, the final collapse factors list is determined through expert interviews. This was done in order to ensure that risk identification is comprehensive and effective.
4.2. Step 2: Constructing FISM Model
Many factors that lead to the collapse of concrete beam bridges are not simply superimposed but interact with each other. In the 1970s, Warfield proposed a classical Interpretive Structural Model (ISM), which can express the fuzzy relation between several elements in a complex system with a structural matrix and hierarchical topological map [
50]. The idea of fuzzy mathematics is fused with ISM [
51], and fuzzy matrix is introduced to carry out fuzzy processing for the ISM. This kind of improved model is called the Fuzzy Interpretive Structural Model (FISM). The FISM model has been widely used in the analysis of accident-causing mechanisms [
52,
53] and the study of system structure optimization [
54,
55]. In this paper, the relationship between the collapse factors is clarified by building a FISM model.
4.2.1. Construct Fuzzy Direct Relation Matrix
Firstly, the fuzzy triangle numbers of the relationship among the factors are sorted out through the expert’s judgment results. In this paper, the three letters l, m and h are used to represent a triangular fuzzy number (i.e., l ≤ m ≤ h), where l represents the possible lower limit value, m represents the most likely value, and h represents the possible upper limit value [
56]. Referring to existing studies [
57], corresponding tables of expert ratings, language operators and triangular fuzzy numbers are given (as shown in
Table 1).
Table 1 was used to convert expert scores into triangular fuzzy numbers, and then a triangular fuzzy relation matrix (
) was established to show the correlation between each collapse factor. The triangular fuzzy number in the triangular fuzzy matrix is expressed as
, which represents the influence degree of risk factor F
i on F
j.
Secondly, the fuzzy data is transformed according to the following steps to obtain the fuzzy direct relation matrix of collapse factors.
- (1)
Normalized triangular fuzzy Numbers.
- (2)
Calculate the limit of the normalized values
(left) and
(right).
- (3)
Calculate the total value of the normalized values.
- (4)
Calculate the exact value
, according to the triangular fuzzy value judged by each expert.
- (5)
Calculate the accurate value
xij, based on all expert judgment results.
- (6)
Form the fuzzy direct relation matrix
of the collapse factor of a concrete beam bridge.
4.2.2. The Intercept Coefficient is used to Transform the Fuzzy Direct Relation Matrix into skeleton matrix .
The intercept coefficient
d plays a classification role. When the element in the fuzzy direct relation matrix is greater than or equal to
d, the element value is replaced by 1. Otherwise, it is replaced with 0. There is no fixed value for intercept coefficient
d, and the choice of its value depends on circumstances. The selection of intercept coefficient
d is closely related to the construction of the multi-level hierarchical structure model. The smaller the value of
d is, the more fuzzy the relationship among factors will be, and the larger the value of
d is, the stronger the relationship among factors will be. By selecting the appropriate intercept coefficient, the fuzzy direct relation matrix obtained in the previous step can be transformed into the skeleton matrix
S, which can be directly used in a Boolean operation.
4.2.3. Calculating Reachability Matrix
The skeleton matrix first performs the Boolean operation with the identity matrix, and then carries out self-multiplication. When the result no longer changes, it becomes the reachability matrix [
52]. This step is relatively complicated, and MATLAB or Python is usually chosen for calculation.
4.3. Step 3: Using ISM to Hierarchize Collapse Factors
It is an important link of ISM theory to construct multi-level hierarchical structure models. The collapse factors are classified according to the reachability matrix. Take the row in the reachability matrix, the collapse factor in which all elements are 0 except the main diagonal is the first layer; remove the row and column where this factor is located, and then find each layer factor in the same way. A hierarchical ISM chart is obtained by connecting related factors with directed arrow lines. The ISM chart can intuitively show the interaction between collapse factors.
5. Results and Findings
According to the first step described in part 4 of this paper, a preliminary list of collapse factors is obtained through literature review and collapse event statistical analysis.
Existing literature can be roughly divided into three categories. First, according to the stages of the accident, the analysis is divided into a construction stage, operation stage and investigation and maintenance stage [
33,
58,
59,
60]. Second, according to the initiator of the accident, it is divided into human factors and natural factors [
61,
62,
63]. Third, multi-dimensional comprehensive analysis is carried out. For example, taking the year 2000 as the dividing line, vertical and horizontal two-way analysis and comparison are conducted from five aspects, including construction, natural disaster, accidental load, durability and design, to explore the differences in collapse causes [
3]. Meanwhile, to build a risk evaluation index system starting from the four dimensions of people, things, environment and management, we consider the internal environment and external environment comprehensively [
64]. Collapse factors in literatures are shown in
Table 2. More than half of the literatures considered that design, construction, natural disasters, climate, overload, collision, bridge diseases, maintenance and management and accidents (fire, etc.) were the factors influencing bridge collapse. A few literatures have suggested that other factors, such as sabotage, could also lead to bridge collapse.
According to the contents of
Section 2 and
Section 3 of this paper, the collapse factor list based on accident statistics is obtained (as shown in
Table 3). Compared with the list of factors obtained in the literature review, this list adds congenital factors such as bridge characteristics and area characteristics. In addition, material quality and sand mining are added into the human factors. Geological conditions are added into the natural factors. The collapse factor lists from the literature review and case analysis are integrated to form the preliminary list of collapse factors (see
Appendix A).
In order to prevent deficiencies in the preliminary list of collapse factors, we interviewed a total of 15 experts to supplement and modify the contents of the preliminary list. These experts included two managers of the government engineering supervision department, three researchers in the field of bridge engineering, five project managers in a bridge construction company and five managers of the bridge project company, all of whom have extensive experience and rich knowledge in bridge design, construction or management.
First, we sent questionnaires to experts on the factors of bridge collapse (see
Appendix A) via email and WeChat. The feedback is summarized as follows: (1) Accidents and sabotage factors, such as fire, are unexpected and uncontrollable events, which should not be considered in this study. (2) For bridges in service, the information conveyed by “Construction Year” and “Age” overlap, so it was suggested that they merge. (3) “Material Quality” should be included in “Construction”. (4) Bridge diseases are the result of these factors and are not appropriate for this list. (5) Management factors can be added, such as construction specifications, departmental supervision, etc. As the experts hold different opinions, we invited them to discuss it through online meetings in order to, ultimately, achieve agreement. The collapse factors of concrete beam bridges are divided into five categories, “congenital factors”, “construction factors”, “environmental factors”, “service conditions” and “management factors”, according to their characteristics. A final list of collapse factors of concrete beam bridges is formed (as shown in
Table 4).
These experts were invited to participate not only in the identification of collapse factors but also in the determination of the correlation between collapse factors by means of WeChat and email (see
Appendix B).
The scores of 15 experts on the relationship of collapse factors are converted into triangular fuzzy numbers, and the triangular fuzzy relation matrix is constructed. Then, according to formulas 1–7, the triangular fuzzy relation matrix is transformed into the fuzzy direct relation matrix (as shown in
Table 5).
On the basis of the fuzzy direct relation matrix, the intercept coefficient
d = 5 is set to convert it into the skeleton matrix that can be directly used in Boolean calculation, as shown in
Table 6.
The reachability matrix is obtained by Boolean calculation (see in
Table 7). MATLAB was used for calculation.
The construction of a multi-level hierarchical structure model is an important part of ISM theory. The ISM diagram drawing is based on the reachability matrix. In the ISM diagram, the collapse factors of concrete beam bridges are divided into three zones: upper, middle and bottom. Factors in different zones have different driving forces, and lower factors will affect factors of the upper layer. The factors located in the upper position are surface factors with a small driving force, which will have a direct impact on the system. The factors in the bottom position are root factors, which will cause hidden trouble to the system and have a strong driving force. The middle-level factors are limited by the lower-level factors and affect the upper-level factors (as shown in
Figure 6).
The upper collapse factor included F13 (Maintenance). Improper maintenance is the direct cause of bridge collapse.
The middle collapse factors included F1 (Length), F6 (Material), F7 (Natural disaster), F11 (Collision), F12 (Sand mining), F5 (Construction), F10 (Overload), F8 (Climate), F4 (Design) and F9 (Geological condition).
The bottom collapse factors included F3 (Area), F14 (Specification), F15 (Supervise) and F2 (Year), and there was a strong connection between F14 and F15. These factors seem to have little relationship with bridge collapse, but they are the most fundamental factors in the system and have a great impact on the workings of the subsequent sequence.
7. Conclusions
There is a close interaction between collapse factors of concrete beam bridge. However, there are few studies on the interaction between collapse factors at different stages of bridge life. This study has adopted the descriptive statistical analysis and FISM method to discuss the collapse factors of concrete beam bridges and their hierarchical relationship. In addition, according to the relationship between factors shown in ISM chart, a bridge management path based on the whole life of the bridge is proposed, which provides a new idea for the sustainable development of the bridge.
This study started with a statistical analysis of collapse accidents of concrete beam bridges. The present situation of collapse of concrete beam bridges in China was presented intuitively through data. In terms of the identification of collapse factors, three methods, including statistical analysis, literature investigation and expert interview, were comprehensively used to find out 15 factors that had an important impact on the collapse of concrete beam bridges. Based on the experts’ ratings of the correlation degree among the identified factors, the hierarchical relationship among the collapse factors of the concrete beam bridge was analyzed by FISM, and the hierarchical structure chart of the collapse factors was drawn. The chart shows that early stage failures have a lasting impact on the health of the bridge. The earlier risk management is involved, the more effectively the bridge life can be extended. Based on the analysis of the interdependent relationship between the collapse factors, suggestions on bridge management of each stage for each participant are put forward. The participants include government planning departments, government supervision departments, bridge design units, construction units, engineering supervision units and maintenance management departments.
Risk management in the field of infrastructure is a complex problem. On the basis of traditional risk analysis methods [
22,
23,
24,
25,
26], many new risk management techniques and methods have been proposed. OSCAD platform risk identification, risk response, facility recovery, and management process improvement can be realized through computer modeling [
66]. The Critical Risks Method (CRM) applies six key indicators to ensure the suitability of critical infrastructure, which can effectively reduce maintenance costs [
67]. A two-stage stochastic programming approach has been proposed to analyze the probability of adverse events and to contribute to pre- and post-event decision-making [
68,
69]. These methods play an important role in analyzing risk occurrence probability, risk importance and risk response. However, these studies focus on the management of infrastructure operation stages and seldom discuss the interaction between risk factors. The risk factor identification in this paper involves a preparation stage, design stage, construction stage and operation stage. FISM considers fuzziness among risk factors based on the ISM. The hierarchical relationship between factors can be determined according to the driving force of factors [
70]. Triangular fuzzy numbers are used to transform subjective judgment into quantitative analysis, which provides a more scientific theoretical basis for bridge management. In addition, the reachability matrix is obtained by fuzzy processing of the direct relation matrix by using the intercept coefficient, which makes this method flexible to a certain extent [
52]. Managers can get different reachability matrixes according to their own requirements of risk correlation degree by adjusting the intercept coefficient.
In general, this paper is an exploratory and theoretical study that opens up a way of working. Data collection in this study is limited, and experts’ judgment of the interdependent relationship between collapse factors also has certain limitations. Further development will surely need to be supported by big data and advanced computer technology. There are still some deficiencies in this study, which can be further studied in the future: (1) Although the correlation between collapse factors was determined by the FISM model, quantitative analysis such as the degree of correlation need to be further studied; (2) Due to the limited data, this paper only focuses on the collapse factors of concrete beam bridges, and other types of bridges and more detailed data need to be further developed; (3) In this study, human factors and natural factors are considered separately. However, these factors also have a combined effect, which can be further studied.