Management Path of Concrete Beam Bridge in China from the Perspective of Sustainable Development

Abstract

More and more bridges have entered the maintenance stage, which has potential collapse hazards and threatens life and property safety. More attention has been paid to the improvement of maintenance management levels during the operation period in terms of extending the service life of the bridge, but less attention has been paid to it from the perspective of the whole life cycle. One hundred and ninety examples of concrete beam bridges in China were collected, based on which the collapse characteristics and collapse causes of concrete beam bridges were analyzed. The causes of bridge collapse come from all stages of bridge life cycle, including environmental factors and human factors. Moreover, the effects of the previous phase carry over to the next. Superficially, poor maintenance management during an operation led to bridge collapse. However, the root cause may have occurred at an earlier stage. On this basis, a fuzzy interpretation structure model (FISM) for concrete beam bridge deterioration is conducted. The model can decompose the complex and messy relationship among the factors of bridge collapse into a clear, multi–level and hierarchical structure. Compared with qualitative analysis, an ISM chart can directly reflect the relationship between collapse factors, which is convenient for further analysis. Poor maintenance management during operation is the direct cause, while improper planning, imperfect standards and weak supervision in the early stage are the fundamental causes. Finally, in order to improve the sustainability of concrete beam bridges scientifically, management suggestions are put forward for the participants involved in each stage of the bridge’s life cycle.

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.

2. Characteristics of Concrete Beam Bridge Collapse

For a more comprehensive understanding of concrete beam bridge collapse status, 190 reported concrete beam bridge collapses (excluding footbridges) during the period between 1971 and 2019 in China were collected. Data sources include major bridge collapse events reported on the official website of the government, local news and literature review. The statistics include basic information about the bridge, such as the location, structure, length and the age of the bridge, as well as the investigation results of the causes of the bridge collapse and the casualties. Although data collection is limited and incomplete, some features and trends can be analyzed.

2.1. The Number of Collapses

According to the statistical results, the number of concrete bridge collapse accidents is on the rise during the period between 1971 and 2019 in China. As shown in Figure 1, what deserves special attention is that the stage of the collapse has changed significantly; this trend is consistent with existing research [6]. Before 2000, bridge construction level was limited [3,18], and accidents in the construction stage accounted for up to 62% of accidents. After 2000, the accident rate in the construction stage decreased gradually, while the accident rate in the operation stage increased gradually. In the past five years, accidents in the construction stage accounted for about 40% of accidents, and accidents in the operation stage accounted for 60%. The results show that with the improvement in the construction level of concrete beam bridges [39], the impact of construction capacity on collapse accidents is reduced to some extent, and the maintenance and management of bridges is becoming increasingly prominent.

2.2. Age and Length of the Collapsed Bridge

Figure 2 illustrates that the probability of collapse is related to the length and age of the bridge. On the one hand, the longer the span of the bridge, the higher the requirements on the construction level, and the higher the probability of collapse accidents in the construction process. On the other hand, Figure 2 shows that 10–20 years after the bridge is completed is the frequent time of bridge collapse, which is quite different from the design life of the bridge. This phenomenon reflects that there are loopholes in the maintenance and management of bridges and huge hidden dangers in the safety of bridges.

2.3. Environmental Characteristic

According to limited data analysis, bridge collapse accidents are relatively frequent in eastern, central and southern China, especially in the Yangtze River Delta region (as shown in Figure 3). Different social and natural environments in different regions have formed different bridge service environments [34]. Understanding the effect of the environment on the bridge is helpful to improve the durability of the bridge from the aspects of design, construction and maintenance, thus extending the service life of the bridge [34]. Temperature, humidity, precipitation, wind speed, carbon dioxide concentration, precipitation PH value, natural disaster frequency and freight volume all affect the deterioration of concrete structures [40,41]. Statistical results show that freight volume is an important factor affecting bridge collapse [6]: 75% of concrete beam bridge collapses occur in provinces with a high volume (above the national average) of freight traffic. The large number of bridge collapse accidents in the Yangtze River Delta may be related to factors such as the developed economy, large stock of bridges, large freight volume, high precipitation and a pH value of precipitation less than 5 [18].

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. Language operators and triangular fuzzy numbers.

Score	Language Operators	Triangular Fuzzy Numbers
0	No impact	(0, 0, 0)
1	Very low impact	(0, 0, 0.25)
2	Low impact	(0, 0.25, 0.5)
3	Medium impact	(0.25, 0.5, 0.75)
4	High impact	(0.5, 0.75, 1)
5	Very high impact	(0.75, 1, 1)

).

Table 1 was used to convert expert scores into triangular fuzzy numbers, and then a triangular fuzzy relation matrix (${\tilde{X}}^k$) was established to show the correlation between each collapse factor. The triangular fuzzy number in the triangular fuzzy matrix is expressed as ${\tilde{x}}^k=\left(l_{ij}^k,m_{ij}^k,h_{ij}^k\right)$, which represents the influence degree of risk factor F_i on F_j.

$${\tilde{X}}^k=\left[\begin{array}{cccc}0& \widetilde{d_{12}^k}& \cdots & \widetilde{d_{1n}^k}\\ \widetilde{d_{21}^k}& 0& \cdots & \widetilde{d_{2n}^k}\\ ⋮& ⋮& \ddots & ⋮\\ \widetilde{d_{n1}^k}& \widetilde{d_{n2}^k}& \cdots & 0\end{array}\right]$$

(1)

Secondly, the fuzzy data is transformed according to the following steps to obtain the fuzzy direct relation matrix $X$ of collapse factors.

(1)

Normalized triangular fuzzy Numbers.

$$\begin{gathered} a_{ij}^k=\left(l_{ij}^k-min{l}_{ij}^k\right)/\left(max{h}_{ij}^k-min{l}_{ij}^k\right) \\ {b}_{ij}^k=\left(m_{ij}^k-min{m}_{ij}^k\right)/\left(max{h}_{ij}^k-min{l}_{ij}^k\right) \\ {c}_{ij}^k=\left(h_{ij}^k-min{h}_{ij}^k\right)/\left(max{h}_{ij}^k-min{l}_{ij}^k\right) \end{gathered}$$

(2)

(2)

Calculate the limit of the normalized values $u_{ij}^k$(left) and $v_{ij}^k$(right).

$$\begin{gathered} u_{ij}^k=b_{ij}^k/\left(1+b_{ij}^k-a_{ij}^k\right) \\ {v}_{ij}^k=c_{ij}^k/\left(1+c_{ij}^k-b_{ij}^k\right) \end{gathered}$$

(3)

(3)

Calculate the total value of the normalized values.

$$w_{ij}^k=\frac{u_{ij}^k\left(1-u^k\right)+{\left(v^k\right)}^2}{\left(1-u_{ij}^k+v_{ij}^k\right)}$$

(4)

(4)

Calculate the exact value $x_{ij}^k$, according to the triangular fuzzy value judged by each expert.

$$x_{ij}^k=min{l}_{ij}^k+w_{ij}^k·\left(max{h}_{ij}^k-min{l}_{ij}^k\right)$$

(5)

(5)

Calculate the accurate value x_ij, based on all expert judgment results.

$$x_{ij}=\frac{1}{P}·{\displaystyle \sum }_{k=1}^P{x}_{ij}^k$$

(6)

(6)

Form the fuzzy direct relation matrix $X$ of the collapse factor of a concrete beam bridge.

$$X=\left[\begin{array}{cccc}0& x_{12}& \cdots & x_{1n}\\ x_{21}& 0& \dots & x_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ x_{n1}& x_{n2}& \cdots & 0\end{array}\right]$$

(7)

4.2.2. The Intercept Coefficient is used to Transform the Fuzzy Direct Relation Matrix $X$ into skeleton matrix $S_{ij}$.

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.

$$S_{ij}=\{\begin{array}{c}1 \left(x_{ij}\ge d\right)\\ 0 \left(x_{ij}<d\right)\end{array}$$

(8)

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. Collapse factor list obtained from literature review.

Literature		[3]	[6]	[18]	[23]	[24]	[32]	[33]	[59]	[60]	[61]	[62]	[63]	[64]	[65]	Total
Factors
Human factors	Design	√	√	√		√	√	√	√	√	√	√	√	√		12
	Construction	√	√	√	√	√	√	√	√	√	√	√	√	√		13
	Overload		√	√	√	√	√	√	√		√	√	√	√		11
	Collision		√	√	√	√	√	√	√		√		√	√		10
	Maintenance			√			√	√		√	√	√		√		7
	Sabotage						√						√			2
	Accident	√	√	√	√	√	√	√		√		√	√			10
Natural factors	Natural Disaster	√	√	√	√	√	√	√	√		√	√	√	√		12
	–Flood/Scour		√	√	√	√	√				√	√	√	√	√	10
	–Earthquake		√	√	√	√	√					√				6
	–Landslide			√			√									2
	Climate		√		√	√	√				√	√	√	√		8
	–Wind		√		√	√	√				√	√	√	√		8
	–Snow/Ice					√						√	√			3
	Bridge Disease	√		√	√	√		√	√				√			7
Other			√			√			√			√	√			5

. 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. Collapse factor list based on accident statistical analysis.

Classification	Factors	Stages
		Construction	Operation	Maintenance
Congenital factors	Bridge Characteristics	√	√	√
	–Construction Year
	–Length
	–Age
	Area Characteristics	√	√	√
	–Freight
	–Temperature
	–Precipitation PH
	–Disaster
	Frequency
	–Wind Speed
	–Precipitation
	–Humidity
Human factors	Design	√	√
	Construction	√	√	√
	Overload		√
	Collision		√
	Maintenance		√	√
	Accident	√
	Material Quality	√	√	√
	Sand Mining		√
Natural factors	Natural Disaster
	–Flood/Scour	√	√	√
	–Earthquake	√	√
	–Landslide		√
	Climate
	–Wind		√
	Geological Conditions		√
	Bridge Diseases		√	√

). 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. The final collapse factor list of concrete beam bridges.

Classification	Factors	Description
Congenital factors	F1 Length	The total length of the bridge.
	F2 Year	The year the bridge was built.
	F3 Area	Bridge construction area.
Construction factors	F4 Design	Bridge design factors, such as structural design, bearing capacity design, etc.
	F5 Construction	Bridge construction factors, such as construction plan, construction technology, construction quality, etc.
	F6 Material	Construction material quality.
Environmental factors	F7 Natural Disaster	Natural disasters, such as floods, earthquakes, mudslides, etc.
	F8 Climate	Climatic factors, such as precipitation, pH value of precipitation, humidity, temperature, wind speed, etc.
	F9 Geological Conditions	The geological condition of the bridge construction site.
Service conditions	F10 Overload	Overload behavior.
	F11 Collision	Collision of vehicles and ship.
	F12 Sand Mining	Illegal sand mining.
Management factors	F13 Maintenance	Maintenance time and maintenance measures.
	F14 Specification	Design specification, construction specification, maintenance specification, etc.
	F15 Supervise	The intensity, frequency and manner of supervision.

).

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. Fuzzy direct relation matrix of the collapse factors of concrete beam bridges.

Factor	F1	F2	F3	F4	F5	F6	F7	F8	F9	F10	F11	F12	F13	F14	F15
F1	0.0	0.2	0.1	0.2	0.2	0.2	0.0	0.0	0.0	0.1	0.4	0.1	0.5	0.1	0.2
F2	0.2	0.0	0.1	0.4	0.5	0.3	0.1	0.1	0.1	0.4	0.3	0.1	0.3	0.6	0.4
F3	0.2	0.1	0.0	0.3	0.2	0.2	0.4	0.7	0.7	0.3	0.4	0.3	0.3	0.1	0.3
F4	0.5	0.1	0.2	0.0	0.5	0.4	0.1	0.1	0.0	0.5	0.4	0.2	0.3	0.2	0.1
F5	0.0	0.0	0.0	0.0	0.0	0.6	0.1	0.1	0.0	0.2	0.2	0.0	0.3	0.3	0.3
F6	0.1	0.1	0.1	0.1	0.4	0.0	0.0	0.0	0.0	0.1	0.1	0.0	0.5	0.1	0.1
F7	0.1	0.1	0.1	0.4	0.5	0.2	0.0	0.3	0.4	0.4	0.3	0.1	0.5	0.1	0.0
F8	0.1	0.1	0.1	0.3	0.6	0.4	0.2	0.0	0.2	0.4	0.4	0.1	0.3	0.1	0.2
F9	0.4	0.1	0.2	0.5	0.1	0.3	0.4	0.1	0.0	0.0	0.1	0.4	0.2	0.1	0.1
F10	0.1	0.1	0.1	0.4	0.1	0.0	0.0	0.0	0.0	0.0	0.5	0.0	0.6	0.3	0.4
F11	0.0	0.0	0.1	0.3	0.1	0.1	0.0	0.0	0.1	0.1	0.0	0.0	0.5	0.3	0.2
F12	0.0	0.1	0.1	0.1	0.0	0.1	0.0	0.1	0.2	0.0	0.1	0.0	0.5	0.2	0.3
F13	0.1	0.0	0.1	0.0	0.4	0.0	0.0	0.0	0.0	0.4	0.4	0.2	0.0	0.3	0.3
F14	0.3	0.1	0.1	0.4	0.4	0.6	0.0	0.0	0.0	0.5	0.4	0.6	0.5	0.0.	0.6
F15	0.1	0.1	0.1	0.5	0.4	0.5	0.0	0.1	0.1	0.4	0.2	0.7	0.5	0.5	0.0

).

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. Skeleton matrix of the collapse factors of concrete beam bridges.

Factor	F1	F2	F3	F4	F5	F6	F7	F8	F9	F10	F11	F12	F13	F14	F15
F1	1	0	0	0	0	0	0	0	0	0	0	0	1	0	0
F2	0	1	0	0	1	0	0	0	0	0	0	0	0	1	0
F3	0	0	1	0	0	0	0	1	1	0	0	0	0	0	0
F4	1	0	0	1	1	0	0	0	0	1	0	0	0	0	0
F5	0	0	0	0	1	1	0	0	0	0	0	0	1	0	0
F6	0	0	0	0	0	1	0	0	0	0	0	0	1	0	0
F7	0	0	0	0	0	0	1	0	0	0	0	0	1	0	0
F8	0	0	0	0	1	0	0	1	0	0	0	0	0	0	0
F9	0	0	0	1	1	0	0	0	1	0	0	0	0	0	0
F10	0	0	0	0	0	0	0	0	0	1	1	0	1	0	0
F11	0	0	0	0	0	0	0	0	0	0	1	0	1	0	0
F12	0	0	0	0	0	0	0	0	0	0	0	1	1	0	0
F13	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0
F14	0	0	0	0	0	1	0	0	0	1	0	1	1	1	1
F15	0	0	0	1	0	1	0	0	0	0	0	1	1	1	1

.

The reachability matrix is obtained by Boolean calculation (see in

Table 7. Reachability matrix of the collapse factors of concrete beam bridges.

Factor	R13	R1	R6	R7	R11	R12	R5	R10	R8	R4	R9	R3	R14	R15	R2	Dr
R13	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1
R1	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	2
R6	1	0	1	0	0	0	0	0	0	0	0	0	0	0	0	2
R7	1	0	0	1	0	0	0	0	0	0	0	0	0	0	0	2
R11	1	0	0	0	1	0	0	0	0	0	0	0	0	0	0	2
R12	1	0	0	0	0	1	0	0	0	0	0	0	0	0	0	2
R5	1	0	1	0	0	0	1	0	0	0	0	0	0	0	0	3
R10	1	0	0	0	1	0	0	1	0	0	0	0	0	0	0	3
R8	1	0	1	0	0	0	1	0	1	0	0	0	0	0	0	4
R4	1	1	1	0	1	0	1	1	0	1	0	0	0	0	0	7
R9	1	1	1	0	1	0	1	1	0	1	1	0	0	0	0	8
R3	1	1	1	0	1	0	1	1	1	1	1	1	0	0	0	10
R14	1	1	1	0	1	1	1	1	0	1	0	0	1	1	0	10
R15	1	1	1	0	1	1	1	1	0	1	0	0	1	1	0	10
R2	1	1	1	0	1	1	1	1	0	1	0	0	1	1	1	11
De	15	7	9	1	8	4	8	7	2	6	2	1	3	3	1

). 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.

6. Discussion: Sustainable Management Path

6.1. Analysis of FISM Results

The ISM diagram shows that “Maintenance” during bridge operation is the direct factor affecting bridge collapse. To a certain extent, maintenance can make up for the bridge quality problems in the design and construction stage, repair the damage caused by human and natural factors during the use of the bridge and thus extend the service life of the bridge. However, poor maintenance is not the root cause of bridge collapse. To realize the sustainable development of bridges, it is not enough to study how to improve the ability of bridge maintenance only. In addition, early stage failures have a lasting impact on the health of the bridge. Mistakes in the design and construction phase continue to have an impact in the operational phase. Therefore, in order to realize the sustainable development of the bridge, we must focus on the whole life of the bridge.

As shown in Figure 6, the site selection, construction time, design and construction specifications of bridges and the supervision ability of relevant government departments are the root causes of bridge collapse. The location of the bridge determines the environment of the bridge. The construction time of a bridge is closely related to the construction level, specifications perfection and supervision level of the bridge. In general, the length, site selection and construction time of bridges are the objective requirements of social and economic development.

The middle collapse factors are not only restricted by the bottom factors but also affect the upper collapse factors. Specification is the basis of bridge design and construction. To perfect bridge specification and strengthen supervision and management in the process of bridge design and construction can effectively reduce improper behaviors in design and construction. Natural and social environments such as geological conditions, climatic conditions and traffic flow, which are determined by the site selection of the bridge, are objective. The environmental damage to the bridge can only be reduced by means of durability and the bearing capacity design of the bridge in the early stage and preventive management in the operation stage. Human factors such as collision, overloads and sand mining can be reduced by strengthening supervision and other management measures. The occurrence of natural disasters is unpredictable, and the damage to bridges caused by natural disasters can be reduced by strengthening monitoring and making emergency plans as well as through other management means.

6.2. Suggestions to the Government

In China, bridge projects are operated and managed by relevant government departments after completion. The control of bridge collapse factors involves government planning departments, government supervision departments, bridge design units, construction units, engineering supervision units and maintenance management departments. Based on the hierarchical relationship of each factor, a bridge management path is proposed, as shown in Figure 7.

• Preparation stage. When planning bridges, government planning departments should consider the natural environment of the construction site carefully and try to avoid building bridges in areas with frequent natural disasters such as earthquake zones. In addition, the bridge design and construction specifications should be revised in time to ensure that the specifications are compatible with the current situation. New technologies and methods should be adopted to ensure that the probability of bridge collapse is reduced from the source.
• Design stage. Designers of design units should pay attention to the natural environment such as geological conditions, climatic conditions (temperature, humidity, precipitation, PH value, etc.), frequency of natural disasters and social environment such as freight volume. Considering the durability and bearing capacity of the bridge, appropriate construction materials and an appropriate bridge type are selected. In this process, the government supervision departments should ensure that the bridge design strictly conforms to the requirements of the design specifications and that the design scheme is reasonable and feasible through expert verification.
• Construction stage. The engineering quality problems during the construction period of bridges will become the “congenital defects” of bridges in service, which are difficult to repair through maintenance during the operation period. Therefore, bridge construction units, supervision units and government supervision departments should work together to control bridge construction and material quality strictly, which can fundamentally extend the bridge life. The construction unit should carry out the construction in strict accordance with the design drawings and construction specifications. Construction under inclement weather conditions should be avoided. When work needs to be rushed, it should be based on ensuring the quality of the project. Caution should be exercised in adopting new technology and equipment to avoid operational errors. The supervising unit should carefully check whether each working procedure meets the requirements. Government regulators should conduct spot checks.
• Operation stage. The maintenance department should adopt the “active” preventive maintenance method instead of the traditional “passive” maintenance concept. This involves collecting bridge periodic inspection data and relevant environmental information, adopting machine learning and other advanced methods to predict the health status of the bridge and selecting the maintenance time point and maintenance method to minimize the cost and maximize the benefit. This should be done as far as it is possible to improve the bridge health status and extend the bridge service life. In addition, government regulators should strictly investigate illegal sand mining, overloading, collision and other behaviors that threaten the safety of bridges. We should do a good job in popularizing knowledge among the masses to make them aware of the dangers of these behaviors. At the same time, we should formulate strict disciplinary measures to minimize the damage caused by human factors to the bridge.

Bridge management is a complex work that requires the cooperation of multiple parties. The whole process, from the bridge planning stage to bridge collapse, should be vigilantly monitored in order to prolong the bridge life effectively.

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.