# Risk Assessment Method for Cable System Construction of Long-Span Suspension Bridge Based on Cloud Model

Authors: Zhifang Lu; Chaofan Wei; Muyu Liu; Xiaoguang Deng
Journal: Advances in Civil Engineering
 (2019)

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## Abstract

Cable system construction is one of the most risky construction stages of long-span suspension bridges, and a reliable risk assessment is an important means to ensure the construction safety. This study proposes a risk assessment method for cable system construction of suspension bridges based on the cloud model, which can combine randomness and fuzziness of risk information effectively. First, a multilevel evaluation index system is built by disassembling the process of cable system construction. Next, the index weights are calculated by the uncertain analytic hierarchy process (AHP). Then, according to the cloud model, a risk assessment model for cable system construction of the suspension bridge is established by realizing the mutual transformation between qualitative language and quantified data. Finally, an illustrative example concerning the risk of cable system construction of Wuhan Yang-Si-Gang Yangtze River Bridge is provided to demonstrate the feasibility and objectivity of the proposed method.


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## Body

## 1. Introduction

Long-span suspension bridges are a construction project with large investment, long cycle, and many uncertain factors. The problem of safety accidents during construction is very prominent. Cable system construction is the construction stage with the maximal risk of suspension bridge construction. Once the accidents occur, it will cause huge economic losses, even casualties and bad social impact. Therefore, it is important to propose an objective and effective risk assessment theory of bridge construction and to carry out risk management control on cable system construction.At present, many scholars have proposed different evaluation methods in the risk assessment field of bridge construction. Nieto-Morote and Ruz-Vila [1] combined fuzzy theory with analytic hierarchy process to evaluate the risk of a bridge during construction period. Based on neural network finite element Monte Carlo simulation, Gong [2] proposed a risk assessment method of long-span cable-stayed bridge construction. Chen et al. [3] built a construction risk assessment system for building bridges from three aspects of occupational health, safety, and environment (HSE), and the work decomposition structure-risk decomposition structure and the analytic hierarchy process were used to establish and apply to the evaluation model. Ding et al. [4] identified the main risk factors of the bridge construction stage, constructed the evaluation index system, and established the bridge construction risk assessment model based on the Monte Carlo method. Liu et al. [5] studied the construction risk of double-wall steel cofferdam piers and applied fuzzy fault tree theory to propose a fuzzy fault tree-based risk assessment method. To propose the principal component analysis method of bridge open caisson foundation construction risk, Liu et al. [6] studied the construction risk of open caisson foundation by using principal component analysis method. In summary, the current risk assessment methods have been well applied in the field of bridge construction risk assessment, but there are still some shortcomings; for example, the evaluation steps are cumbersome, and the analysis results are much more subjective. How to determine the membership function of a fuzzy concept accurately becomes the key problems in the risk assessment.The cloud model, which can represent the fuzziness and randomness as well as their relations of uncertain concepts well by giving the random determination of the sample points [7], has been applied in the field of safety evaluation and decision analysis in recent years. Wang et al. [8] applied a synthetical cloud in the effectiveness evaluation method for the shortcomings of the cloud gravity center method and cloud model method and justified the capability through a simple example. The research team of Wang and Liu [9, 10] proposed a decision-making method based on cloud model to solve the multicriteria group decision-making problems and also applied the cloud model into the game problems, online recommendation approach, and sustainable energy crop selection problems [11–13]. The results were observed to demonstrate the cloud model could combine the randomness and fuzziness of an uncertain concept effectively.In view of the above advantages, in order to provide an objective and effective risk assessment for cable system construction, this paper applies the cloud model into the risk assessment and proposes a new risk assessment method for cable system construction of suspension bridge based on the cloud model.


## 2. The Index System of Cable System Construction

### 2.1. Determination of Risk Index of Cable System Construction for Long-Span Suspension Bridge

According to the principles of scientificity, system, orientation, feasibility, and relative independence between index, the characteristics and actual conditions of cable system construction for large suspension bridges are analyzed, and the risk factors of the suspension bridge in the construction process are identified. The risk sources in the construction of the cable system are identified to determine the construction risk indicators, mainly including the following:(1)
Saddle installation risk: during the installation process of the saddle, it is prone to hoisting damage, falling from a high altitude, etc. The mounting bracket is an important force structure when the saddle is installed, and its instability is also likely to cause serious safety accidents.(2)
Traction system installation and catwalks construction risks: during the installation of the traction system and the catwalks construction process, frequent high-altitude operations and water above operations are prone to cause accidents such as machine failure, drowning, and falling from high altitude. Gale weather will also have a great impact on catwalks construction.(3)
Main cable erection and cable tightening construction risk: one mistake in the erection of the cable can cause safety accidents such as slipping, lifting damage, and improper machine coordination.(4)
Cable clamp and sling installation risk: there are risks such as sling high-altitude slings, cable clamp deformation, and cable strand extrusion.


### 2.2. Construction of Evaluation Index System

According to the aforesaid established construction risk index, a multilevel suspension bridge cable system construction risk evaluation index system including 20 secondary evaluation indicators such as “saddle installation risk” and 20 three-level evaluation indicators such as “high-altitude falling objects” is established in Figure1, so the foundation for the construction risk assessment is settled.Figure 1
Cable system construction risk evaluation index system of the suspension bridge.


### 2.3. Cable System Construction Risk Assessment Criteria

Combined with corresponding engineering data, on-site investigation, expert experience, and standard [14, 15], the risk assessment level standard for the cable system construction of the long-span suspension bridge is established and [7, 8] is used for all index. The evaluation value, from large to small, is a trend in which the risk gradually decreases. Five standard trust clouds are generated by the expert opinion in the interval, corresponding to different risk levels. The risk level of the comment set is {lower risk, low risk, medium risk, high risk, higher risk}, use the golden section method to calculate the cloud model parameters, and set the superentropy He according to the golden section method [8, 9]. Since the value of the domain is {0, 10}, the value of the superentropy He of the cloud corresponding to the intermediate value of “medium risk” is 0.05, and and the calculation results of the values in the standard cloud moder of each risk level are shown in Table 1, and the cloud model is shown in Figure 2.Table 1
Value form of risk-level reliance cloud.
Risk level
Ex
En
He
Lower risk
0
1.0302
0.1309
Low risk
3.0900
0.6367
0.0809
Medium risk
5.0000
0.3935
0.0500
High risk
6.9100
0.6367
0.0809
Higher risk
10.0000
1.0302
0.1309Figure 2
Cloud model of each risk level.


## 2.1. Determination of Risk Index of Cable System Construction for Long-Span Suspension Bridge

According to the principles of scientificity, system, orientation, feasibility, and relative independence between index, the characteristics and actual conditions of cable system construction for large suspension bridges are analyzed, and the risk factors of the suspension bridge in the construction process are identified. The risk sources in the construction of the cable system are identified to determine the construction risk indicators, mainly including the following:(1)
Saddle installation risk: during the installation process of the saddle, it is prone to hoisting damage, falling from a high altitude, etc. The mounting bracket is an important force structure when the saddle is installed, and its instability is also likely to cause serious safety accidents.(2)
Traction system installation and catwalks construction risks: during the installation of the traction system and the catwalks construction process, frequent high-altitude operations and water above operations are prone to cause accidents such as machine failure, drowning, and falling from high altitude. Gale weather will also have a great impact on catwalks construction.(3)
Main cable erection and cable tightening construction risk: one mistake in the erection of the cable can cause safety accidents such as slipping, lifting damage, and improper machine coordination.(4)
Cable clamp and sling installation risk: there are risks such as sling high-altitude slings, cable clamp deformation, and cable strand extrusion.


## 2.2. Construction of Evaluation Index System

According to the aforesaid established construction risk index, a multilevel suspension bridge cable system construction risk evaluation index system including 20 secondary evaluation indicators such as “saddle installation risk” and 20 three-level evaluation indicators such as “high-altitude falling objects” is established in Figure1, so the foundation for the construction risk assessment is settled.Figure 1
Cable system construction risk evaluation index system of the suspension bridge.


## 2.3. Cable System Construction Risk Assessment Criteria

Combined with corresponding engineering data, on-site investigation, expert experience, and standard [14, 15], the risk assessment level standard for the cable system construction of the long-span suspension bridge is established and [7, 8] is used for all index. The evaluation value, from large to small, is a trend in which the risk gradually decreases. Five standard trust clouds are generated by the expert opinion in the interval, corresponding to different risk levels. The risk level of the comment set is {lower risk, low risk, medium risk, high risk, higher risk}, use the golden section method to calculate the cloud model parameters, and set the superentropy He according to the golden section method [8, 9]. Since the value of the domain is {0, 10}, the value of the superentropy He of the cloud corresponding to the intermediate value of “medium risk” is 0.05, and and the calculation results of the values in the standard cloud moder of each risk level are shown in Table 1, and the cloud model is shown in Figure 2.Table 1
Value form of risk-level reliance cloud.
Risk level
Ex
En
He
Lower risk
0
1.0302
0.1309
Low risk
3.0900
0.6367
0.0809
Medium risk
5.0000
0.3935
0.0500
High risk
6.9100
0.6367
0.0809
Higher risk
10.0000
1.0302
0.1309Figure 2
Cloud model of each risk level.


## 3. Construction Risk Assessment of Suspension Bridge Cable System

In 1995, Li Deyi, an academician of the Chinese Academy of Engineering, proposed the concept and theory of the cloud and unified the randomness, ambiguity, and correlation between these two by giving the random determination of the sample points. Based on this research the cloud model was proposed based on. It has been applied in the field of safety evaluation and decision analysis.


### 3.1. Cable System Risk Assessment Cloud Model

The cloud model theory is to establish the uncertainty conversion model between a qualitative concept and its quantification expressed by natural language values and fully express the ambiguity and randomness of the qualitative concept evaluation information expressed by experts in natural language. It is also a group decision-making individual preference representation method based on natural language evaluation information. The cloud model includes tools such as virtual clouds, forward and reverse cloud generators, and cloud uncertainty prediction. This paper mainly applies forward and reverse cloud generators.Let U be a domain expressed by exact numerical values. For any elementX in the domain, there is a stable random number Y = U(X) as the degree of concept determination of X, the distribution of X on the domain is called the cloud model or simplified as cloud, and each (X, Y) is called a cloud drop. If the domain U is defined as an n-dimensional space, it can be extended to an n-dimensional cloud.The cloud consists of a large number of cloud droplets, each of which represents a specific implementation of this qualitative concept in the number domain space with uncertainty. Separate cloud droplets may not be trivial, but the shape of a large number of cloud droplets can reflect the basic characteristics of the qualitative concept [7].The digital characteristics of the cloud are mainly represented by Ex (expected value), En (entropy), and He (hyper entropy). A schematic diagram of the one-dimensional cloud model is shown in Figure3 with Ex = 5, En = 1, and He = 0.05.Figure 3
Diagram of the cloud model.Ex: the value that best represents this qualitative concept, usually corresponding to the value of cloud center, reflecting the information center value of the corresponding qualitative concept.En: the measure of the ambiguity of the qualitative concept. The number of elements that can be accepted of the qualitative concept in the domain is directly affected by the entropy value, which reflects the margin of the qualitative concept.He: entropy of entropy, reflecting the degree of dispersion of the cloud, that is, the thickness of the cloud. The greater the thickness shows the greater the randomness of the membership.


### 3.2. Weight Determination of Risk Indicator

By the interval form, the two-two importance comparison of the indicators is given. The interval scale is still the 9 scale of the analytic hierarchy process, as shown in Table2.Table 2
Implication of index evaluation scale.
Scale
Implication
1
Indicatori is as important as indicator j
3
Indicatori is slightly more important than indicator j
5
Indicatori is more important than indicator j
7
Indicatori is significantly more important than indicator j
9
Indicatori is far more important than indicator j
2, 4, 6, 8
The intermediate values of two adjacent judgments mentioned above
Reciprocal
The comparison result between indexi and index j is the reciprocal of the comparison between index j and index i(1)
It is assumed that there aren evaluation indicators in a subindicator system of the cable construction risk assessment system, which constitutes a set U=U1,U2,…,Un, invites experts whose number is q to compare the importance of the two pairs of evaluation indicators in the set (according to the scale of 1∼9), and gives a specific comparison interval. Then the judgment interval of the expert whose sequence is k for the indicator Ui and the indicator Uj is as follows:(1)Ak=aijn×n=aijl,aiju.
(2)
The judgment matrix based on the uncertain AHP method is(2)A=1,1a12l,a12u⋯a1nl,a1nu1a12u,1a12l1,1⋯a2nl,a2nu⋮⋮⋱⋮1a1nu,1a1nl1a2nu,1a2nl⋯1,1.
The derived vector of the definition matrix is as follows:(3)vecAk=a11l,…,an1l,a12l,…,an2l,…,a1nl,…,annl,…,a11u,…,an1u,a12u,…,an2u,…,a1nu,…,annu.
Calculate the angle cosineVk of the derived vector between matrices, and normalize Vk to obtain the similarity between the two judgment matrices by defining Vk=∑i≠k,i=1qVik:(4)λk=Vk∑i=1qVi.
(3)
For the calculation of the difference between the judgment matrices, first useek to represent the sum of the absolute values of the elements in the evaluation matrix of the kth expert and all the experts and then normalize the ek to obtain the kth expert. The difference between the judgment and other experts’ judgment is given as follows:(5)Wk=ek∑i=1qei.
The similarity and difference of the judgment matrix are taken as important parameters, and the expert credibilityrk is calculated:(6)rk=λk,∑i=1qλi⋅Wi=1,λk1−Wk1−∑i=1qλi⋅Wi,∑i=1qλi⋅Wi≠1,k=1,2,…,q..
(4)
The calculation of weighted sorting interval is an important part of the uncertain AHP method [16]. Firstly, the judgment matrix is uniformly approximated, and the matrix M = (mij)n×n is constructed:(7)mij=∏k=1naiklaikuajklajku2n.
Weight vector of matrixM is w=w1,w2,…,wnT:(8)wj=1∑i=1nmij=∏k=1najklajku1/2n∑i=1n∏k=1naiklaiku1/2n,j∈N
Construct the level difference matrixΔM1andΔM2 and its matrix weight vector:(9)ΔM1=mij−aijln×n=Δ1mij,ΔM2=aiju−mijn×n=Δ2mij,Δkwj2=∑i=1nΔkmij2∑i=1nmij4,k=1,2.
The weighting interval of the judgment matrix is(10)wj′=wj−Δ1wj,wj−Δ2wj=u1,u2.
(5)
The subjective weightwi1 based on the expert credibility risk factor is determined by the expert’s judgment matrix. The weighted interval of the determined judgment matrix is processed by the fuzzy set-valued statistical method to obtain the subjective weight of the risk factor:(11)wi1=12⋅∑k=1qrku2k2−u1k2∑k=1qrku2k−u1k.
The objective weight mainly reflects the degree of grasp and objectivity of the expert on the risk factor. The objective weightwi2 is(12)wi2=bdi∑i=1nbdi,i=1,2,…,n,bdi=11+gi,gi=13⋅∑k=1qrku2k−wi13−u1k−wi13u2k−u1k.
(6)
Finally, the subjective weightwi1 and the objective weight wi2 are combined to obtain the final weight of the risk factor:(13)wi=wi1⋅wi2∑i=1qwi1⋅wi2,i=1,2,…,n.


### 3.3. Risk Assessment of Cable System Construction Based on Cloud Model

According to the evaluation index system, the uncertain analytic hierarchy process- (AHP-) based weighting method is combined with the cloud model to propose a suspension cable system construction risk assessment model. The specific steps are as follows:(1)
Establish a risk assessment index system for cable systems of long-span suspension bridges(2)
Identify the review set and generate a corresponding standard cloud model for different levels of reviews(3)
Calculate the weightwi of each indicator by using the weighting method based on the uncertain AHP(4)
Collect the expert evaluation data, and the trust attribute cloud of the evaluation index is calculated by the undetermined reverse cloud algorithm [17], and the three characteristic values of the risk trust cloud are calculated by the indicator weight:(14)Ex=∑i=1nExi×wi,En=∑i=1nEni2×wi,He=∑i=1nHei×wi.(5)
Calculate the similarity between the risk trust cloud and the trust clouds of each level. The specific steps are as follows:(1)
Enter the risk trust cloud STC1 and standard trust cloud STC.(2)
Generate a normal random numberEni′=NORMEni,Hei2 with Eni as the expectation and Hei2 as the variance in the risk trust cloud STC1.(3)
Generate a normal random numberxi=NORMExi,Eni′2 with Ex1 as the expectation and Eni′2 as the variance in risk trust cloud STC1.(4)
Substitute the normal random numberxi into the expected equation of the standard trust cloud STC, and calculate δi′=exp−xi−Ex2/2En2.(5)
Repeat steps (1)∼(3) untilδi′ are generated with number as n.(6)
Calculateδ=1/n∑i=1nδi′ and δ is the similarity sought.(7)
Determination of the level of risk. The calculated risk trust cloud is sorted with the similarity degree of the standard trust cloud of different risk levels, and the risk level of the evaluation index is obtained.


## 3.1. Cable System Risk Assessment Cloud Model

The cloud model theory is to establish the uncertainty conversion model between a qualitative concept and its quantification expressed by natural language values and fully express the ambiguity and randomness of the qualitative concept evaluation information expressed by experts in natural language. It is also a group decision-making individual preference representation method based on natural language evaluation information. The cloud model includes tools such as virtual clouds, forward and reverse cloud generators, and cloud uncertainty prediction. This paper mainly applies forward and reverse cloud generators.Let U be a domain expressed by exact numerical values. For any elementX in the domain, there is a stable random number Y = U(X) as the degree of concept determination of X, the distribution of X on the domain is called the cloud model or simplified as cloud, and each (X, Y) is called a cloud drop. If the domain U is defined as an n-dimensional space, it can be extended to an n-dimensional cloud.The cloud consists of a large number of cloud droplets, each of which represents a specific implementation of this qualitative concept in the number domain space with uncertainty. Separate cloud droplets may not be trivial, but the shape of a large number of cloud droplets can reflect the basic characteristics of the qualitative concept [7].The digital characteristics of the cloud are mainly represented by Ex (expected value), En (entropy), and He (hyper entropy). A schematic diagram of the one-dimensional cloud model is shown in Figure3 with Ex = 5, En = 1, and He = 0.05.Figure 3
Diagram of the cloud model.Ex: the value that best represents this qualitative concept, usually corresponding to the value of cloud center, reflecting the information center value of the corresponding qualitative concept.En: the measure of the ambiguity of the qualitative concept. The number of elements that can be accepted of the qualitative concept in the domain is directly affected by the entropy value, which reflects the margin of the qualitative concept.He: entropy of entropy, reflecting the degree of dispersion of the cloud, that is, the thickness of the cloud. The greater the thickness shows the greater the randomness of the membership.


## 3.2. Weight Determination of Risk Indicator

By the interval form, the two-two importance comparison of the indicators is given. The interval scale is still the 9 scale of the analytic hierarchy process, as shown in Table2.Table 2
Implication of index evaluation scale.
Scale
Implication
1
Indicatori is as important as indicator j
3
Indicatori is slightly more important than indicator j
5
Indicatori is more important than indicator j
7
Indicatori is significantly more important than indicator j
9
Indicatori is far more important than indicator j
2, 4, 6, 8
The intermediate values of two adjacent judgments mentioned above
Reciprocal
The comparison result between indexi and index j is the reciprocal of the comparison between index j and index i(1)
It is assumed that there aren evaluation indicators in a subindicator system of the cable construction risk assessment system, which constitutes a set U=U1,U2,…,Un, invites experts whose number is q to compare the importance of the two pairs of evaluation indicators in the set (according to the scale of 1∼9), and gives a specific comparison interval. Then the judgment interval of the expert whose sequence is k for the indicator Ui and the indicator Uj is as follows:(1)Ak=aijn×n=aijl,aiju.
(2)
The judgment matrix based on the uncertain AHP method is(2)A=1,1a12l,a12u⋯a1nl,a1nu1a12u,1a12l1,1⋯a2nl,a2nu⋮⋮⋱⋮1a1nu,1a1nl1a2nu,1a2nl⋯1,1.
The derived vector of the definition matrix is as follows:(3)vecAk=a11l,…,an1l,a12l,…,an2l,…,a1nl,…,annl,…,a11u,…,an1u,a12u,…,an2u,…,a1nu,…,annu.
Calculate the angle cosineVk of the derived vector between matrices, and normalize Vk to obtain the similarity between the two judgment matrices by defining Vk=∑i≠k,i=1qVik:(4)λk=Vk∑i=1qVi.
(3)
For the calculation of the difference between the judgment matrices, first useek to represent the sum of the absolute values of the elements in the evaluation matrix of the kth expert and all the experts and then normalize the ek to obtain the kth expert. The difference between the judgment and other experts’ judgment is given as follows:(5)Wk=ek∑i=1qei.
The similarity and difference of the judgment matrix are taken as important parameters, and the expert credibilityrk is calculated:(6)rk=λk,∑i=1qλi⋅Wi=1,λk1−Wk1−∑i=1qλi⋅Wi,∑i=1qλi⋅Wi≠1,k=1,2,…,q..
(4)
The calculation of weighted sorting interval is an important part of the uncertain AHP method [16]. Firstly, the judgment matrix is uniformly approximated, and the matrix M = (mij)n×n is constructed:(7)mij=∏k=1naiklaikuajklajku2n.
Weight vector of matrixM is w=w1,w2,…,wnT:(8)wj=1∑i=1nmij=∏k=1najklajku1/2n∑i=1n∏k=1naiklaiku1/2n,j∈N
Construct the level difference matrixΔM1andΔM2 and its matrix weight vector:(9)ΔM1=mij−aijln×n=Δ1mij,ΔM2=aiju−mijn×n=Δ2mij,Δkwj2=∑i=1nΔkmij2∑i=1nmij4,k=1,2.
The weighting interval of the judgment matrix is(10)wj′=wj−Δ1wj,wj−Δ2wj=u1,u2.
(5)
The subjective weightwi1 based on the expert credibility risk factor is determined by the expert’s judgment matrix. The weighted interval of the determined judgment matrix is processed by the fuzzy set-valued statistical method to obtain the subjective weight of the risk factor:(11)wi1=12⋅∑k=1qrku2k2−u1k2∑k=1qrku2k−u1k.
The objective weight mainly reflects the degree of grasp and objectivity of the expert on the risk factor. The objective weightwi2 is(12)wi2=bdi∑i=1nbdi,i=1,2,…,n,bdi=11+gi,gi=13⋅∑k=1qrku2k−wi13−u1k−wi13u2k−u1k.
(6)
Finally, the subjective weightwi1 and the objective weight wi2 are combined to obtain the final weight of the risk factor:(13)wi=wi1⋅wi2∑i=1qwi1⋅wi2,i=1,2,…,n.


## 3.3. Risk Assessment of Cable System Construction Based on Cloud Model

According to the evaluation index system, the uncertain analytic hierarchy process- (AHP-) based weighting method is combined with the cloud model to propose a suspension cable system construction risk assessment model. The specific steps are as follows:(1)
Establish a risk assessment index system for cable systems of long-span suspension bridges(2)
Identify the review set and generate a corresponding standard cloud model for different levels of reviews(3)
Calculate the weightwi of each indicator by using the weighting method based on the uncertain AHP(4)
Collect the expert evaluation data, and the trust attribute cloud of the evaluation index is calculated by the undetermined reverse cloud algorithm [17], and the three characteristic values of the risk trust cloud are calculated by the indicator weight:(14)Ex=∑i=1nExi×wi,En=∑i=1nEni2×wi,He=∑i=1nHei×wi.(5)
Calculate the similarity between the risk trust cloud and the trust clouds of each level. The specific steps are as follows:(1)
Enter the risk trust cloud STC1 and standard trust cloud STC.(2)
Generate a normal random numberEni′=NORMEni,Hei2 with Eni as the expectation and Hei2 as the variance in the risk trust cloud STC1.(3)
Generate a normal random numberxi=NORMExi,Eni′2 with Ex1 as the expectation and Eni′2 as the variance in risk trust cloud STC1.(4)
Substitute the normal random numberxi into the expected equation of the standard trust cloud STC, and calculate δi′=exp−xi−Ex2/2En2.(5)
Repeat steps (1)∼(3) untilδi′ are generated with number as n.(6)
Calculateδ=1/n∑i=1nδi′ and δ is the similarity sought.(7)
Determination of the level of risk. The calculated risk trust cloud is sorted with the similarity degree of the standard trust cloud of different risk levels, and the risk level of the evaluation index is obtained.


## 4. Case Analysis of Cable Construction Risk of Suspension Bridge

### 4.1. Engineering Background

Wuhan Yang-Si-Gang Yangtze River Bridge is a double-layer suspension bridge connecting Hanyang and Wuchang. The total length of the bridge is 4134 m, as shown in Figure4. The length of main span is 1700 m, the side span is 465 m, and the rise-span ratio is 1/9. The design load is 47 tons per meter, the main cable tension is 65,000 tons, and the sling tension is 500 tons, which are the largest in the world. It is necessary to carry out cable system construction risk analysis and propose corresponding risk prevention measures.Figure 4
General arrangement diagram of main bridge.


### 4.2. Cable System Risk Index System of the Suspension Bridge

Based on the construction risk index of the cable system of the long-span suspension bridge, the risk evaluation index system for the cable system of the Yang-Si-Gang Yangtze River Bridge in Wuhan is constructed, as shown in Figure1.


### 4.3. Determination of Indicator Weight

Five experts were invited to compare the importance of each level of the indicators, and the interval number was scored to form the judgment matrix of each expert. The calculation was carried out by using Matlab software programming.Take the “main cable erection and tight cable entanglement construction riskU3” of the criterion layer as an example. The six evaluation indicators are “hoist parts are loose U31,” “winch and entanglement machine mismatch U32,” “lifting accident U33,” “traction of the cable strand or strapping damage U34,” “strand slip U35,” and “windy weather during the process of erection process U36,” and five experts compare their importance and get the judgment matrix as follows:(15)A1=1,11,22,313,1214,1214,1312,11,11,215,1416,1515,1313,1212,11,115,1417,1616,152,32,44,51,114,1213,12,45,66,72,41,11,33,43,55,61,313,11,1,A2=1,11,22,413,1213,1214,1212,11,11,315,1316,1515,1414,1213,11,115,1417,1516,152,33,54,51,113,1214,12,35,65,72,31,11,22,44,65,61,413,11,1,A3=1,11,22,413,113,1214,1312,11,11,214,1316,1515,1414,1212,11,115,1417,1516,151,33,44,51,114,1213,12,35,66,72,41,11,22,44,65,61,413,11,1,A4=1,11,32,413,1214,1214,1213,11,11,214,1316,1516,1414,1212,11,115,1318,1616,142,33,43,51,113,1212,12,45,66,82,31,11,22,44,64,61,212,11,1,A5=1,11,22,513,1214,1215,1312,11,11,414,1318,1516,1415,1214,11,115,1317,1517,132,33,43,51,115,1213,12,45,86,72,51,11,33,54,63,71,313,11,1.Calculate the similarity between each expert’s judgment matrix according to equations (3) and (4):(16)λk=0.2002,0.2000,0.2005,0.2000,0.1990.The degree of difference between the judgment matrices is(17)Wk=0.1889,0.1956,0.1719,0.1973,0.2463.Expert credibility is(18)rk=0.2030,0.2012,0.2076,0.2007,0.1875.Based on the expert credibility, the weights of uncertain AHP are calculated. Firstly, the judgment matrix is uniformly approximated, and the consistency matrixM is constructed with calculating weight vector (each column corresponds to the weight vector of each expert):(19)wj=0.09290.10130.10330.10230.09340.06480.06150.06120.05860.06120.04480.04310.04320.04540.04200.17450.18460.17030.18760.16960.36040.32860.34020.34570.36900.26250.28090.28180.26040.2649.After constructing the level difference matrixesΔM1 and ΔM2, calculate the weight vectors Δ1w and Δ2w and determine the weight interval of the judgment matrix as(20)wj′=0.0764,0.10720.0860,0.11940.0874,0.12380.0864,0.12340.0760,0.11510.0587,0.07240.0577,0.07120.0570,0.06650.0541,0.06600.0563,0.07210.0403,0.04860.0374,0.04780.0386,0.04740.0399,0.04980.0341,0.04960.1573,0.24900.1635,0.27890.1495,0.24130.1709,0.23380.1513,0.26090.3007,0.40810.2828,0.35640.2922,0.37090.3061,0.38470.3054,0.42100.2273,0.37730.2448,0.35280.2531,0.35230.2316,0.31060.2280,0.3811.The risk factor weights include the subjective weightwi1 and the objective weight wi2 of each element:(21)wi1=0.1004,0.0634,0.0432,0.2066,0.3451,0.2980,wi2=0.1668,0.1668,0.1668,0.1666,0.1665,0.1663.Through the coupling of subjective weight and objective weight by using equation (13), the final weights of the six risk factors in the construction risk of main cable erection and tight cable entanglement construction risk are as follows:(22)wi=0.0952,0.0601,0.0409,0.1956,0.3266,0.2817.Due to the limited space, the weight calculation methods of the other indicator layers and the criterion layer are the same as above, and the calculation results are shown in Table3.Table 3
Index weight of the cable system construction risk evaluation system.
Criteria layer
Weights
Indicator layer
Weights
Comprehensive weight
Saddle installation riskU1
0.2734
Falling objectsU11
0.0801
0.0219
Mounting bracket instabilityU12
0.2696
0.0737
Cable saddle fallingU13
0.5004
0.1368
Lifting damageU14
0.1499
0.0410
Traction system installation and catwalk construction riskU2
0.3678
Commander signal is not uniformU21
0.0413
0.0152
Catwalk load-bearing cable anchoring embedded parts are not strongU22
0.0594
0.0218
Drowning accidentU23
0.0967
0.0356
Traction system failureU24
0.2081
0.0765
Catwalk construction falls highU25
0.2660
0.0978
Catwalk construction encounters strong windsU26
0.3285
0.1208
Main cable erection and cable tightening construction riskU3
0.2980
Hoist parts are looseU31
0.0952
0.0284
Winch and entanglement machine mismatchedU32
0.0601
0.0179
Lifting accidentU33
0.0409
0.0122
Traction of the cable strand or strapping damageU34
0.1956
0.0583
Strand slipU35
0.3266
0.0973
Windy weather during the erection processU36
0.2817
0.0839
Cable clamp and sling installation riskU4
0.0608
Wire strand extrusionU41
0.0660
0.0040
Cable clamp deformationU42
0.1277
0.0078
Sling installation is tilted and biasedU43
0.3423
0.0208
Sling falling from high altitudeU44
0.4640
0.0282


### 4.4. Comprehensive Synthesis of Risk Trust Clouds

Based on the actual situation of the Yang-Si-Gang Yangtze River Bridge, and considering the risk occurrence probability and the degree of risk impact comprehensively, the five experts give a score to the indicators at the index level. According to these score, the reversed cloud calculation is carried out, and the index layer attributes are synthesized based on formula (14). Then, the characteristic value of the criterion layer cloud model can be obtained, as shown as Table 4.Table 4
Calculation results of the criterion layer attribute cloud characteristic value.
Criterion layer
Ex
En
He
Saddle installation riskU1
5.0600
0.5738
0.2977
Traction system installation and catwalk construction riskU2
4.9907
0.7981
0.3483
Main cable erection and cable tightening construction riskU3
4.6661
0.7564
0.2771
Cable clamp and sling installation riskU4
3.9789
0.7252
0.2666The criterion layer is synthesized again to obtain the characteristic value of the risk trust cloud of the target layer:(23)Ex=4.8514,En=0.7258,He=0.3083.


### 4.5. Comprehensive Evaluation of Cable System Construction Risk

According to the similarity calculation method between the cloud models in Section2.3, the similarity between the risk trust cloud and each standard trust clouds of every level is calculated and sorted. The cloud model is shown in Figure 5, and the calculation results are shown in Table 5.Figure 5
Diagram of the risk reliance cloud and criterion reliance cloud of each risk level.Table 5
Similarity between criterion reliance cloud of each risk level and risk reliance cloud.
Risk level
Lower risk
Low risk
Medium risk
High risk
Higher risk
Connection number
2.3417 × 10−4
0.0841
0.5869
0.0389
8.5316 × 10−4Table5 shows that the risk trust cloud has the greatest similarity with the medium-risk standard trust cloud. Therefore, the comprehensive judgment result of the cable system construction risk of the Yang-Si-Gang Yangtze River Bridge is “medium risk”. According to the construction risk decision criteria, the risk level is subject to conditional acceptance, but further risk management measures are needed to improve project safety.


### 4.6. Construction Risk Prevention Measures

According to the calculation results of the characteristic values of each attribute cloud in the criterion layer in Table5, the corresponding risk prevention measures are proposed for the cable saddle construction, the traction system and catwalk construction, the main cable erection and the cable tightening construction. The risk of cable clamp and sling installation construction is low and no need to take precautions.


#### 4.6.1. Saddle Construction Safety Measures

The tower top construction platform shall be provided with protective railings and safety nets, and operators shall strictly wear safe labor insurance products. Before the sling is lifted, a special project should be formulated for demonstration.


#### 4.6.2. Risk Prevention Measures for Catwalk Construction and Traction System

Before construction, the quality of the cable should be strictly checked. Wire breaking and rust is strictly forbidden. The impact of bad weather should be regarded. It is strictly forbidden to carry out the construction of the catwalk and the main cable under high wind conditions.


#### 4.6.3. Risk Prevention Measures of Main Cable Erection and Cable Tightening Construction

Pay attention to monitoring the displacement of the main tower during construction. The displacement should be adjusted in time and always within the allowable range. The wire bundle should be tracked and inspected during the traction process to prevent the wire bundle from twisting, wearing, bulging, or breaking the bandage.


## 4.1. Engineering Background

Wuhan Yang-Si-Gang Yangtze River Bridge is a double-layer suspension bridge connecting Hanyang and Wuchang. The total length of the bridge is 4134 m, as shown in Figure4. The length of main span is 1700 m, the side span is 465 m, and the rise-span ratio is 1/9. The design load is 47 tons per meter, the main cable tension is 65,000 tons, and the sling tension is 500 tons, which are the largest in the world. It is necessary to carry out cable system construction risk analysis and propose corresponding risk prevention measures.Figure 4
General arrangement diagram of main bridge.


## 4.2. Cable System Risk Index System of the Suspension Bridge

Based on the construction risk index of the cable system of the long-span suspension bridge, the risk evaluation index system for the cable system of the Yang-Si-Gang Yangtze River Bridge in Wuhan is constructed, as shown in Figure1.


## 4.3. Determination of Indicator Weight

Five experts were invited to compare the importance of each level of the indicators, and the interval number was scored to form the judgment matrix of each expert. The calculation was carried out by using Matlab software programming.Take the “main cable erection and tight cable entanglement construction riskU3” of the criterion layer as an example. The six evaluation indicators are “hoist parts are loose U31,” “winch and entanglement machine mismatch U32,” “lifting accident U33,” “traction of the cable strand or strapping damage U34,” “strand slip U35,” and “windy weather during the process of erection process U36,” and five experts compare their importance and get the judgment matrix as follows:(15)A1=1,11,22,313,1214,1214,1312,11,11,215,1416,1515,1313,1212,11,115,1417,1616,152,32,44,51,114,1213,12,45,66,72,41,11,33,43,55,61,313,11,1,A2=1,11,22,413,1213,1214,1212,11,11,315,1316,1515,1414,1213,11,115,1417,1516,152,33,54,51,113,1214,12,35,65,72,31,11,22,44,65,61,413,11,1,A3=1,11,22,413,113,1214,1312,11,11,214,1316,1515,1414,1212,11,115,1417,1516,151,33,44,51,114,1213,12,35,66,72,41,11,22,44,65,61,413,11,1,A4=1,11,32,413,1214,1214,1213,11,11,214,1316,1516,1414,1212,11,115,1318,1616,142,33,43,51,113,1212,12,45,66,82,31,11,22,44,64,61,212,11,1,A5=1,11,22,513,1214,1215,1312,11,11,414,1318,1516,1415,1214,11,115,1317,1517,132,33,43,51,115,1213,12,45,86,72,51,11,33,54,63,71,313,11,1.Calculate the similarity between each expert’s judgment matrix according to equations (3) and (4):(16)λk=0.2002,0.2000,0.2005,0.2000,0.1990.The degree of difference between the judgment matrices is(17)Wk=0.1889,0.1956,0.1719,0.1973,0.2463.Expert credibility is(18)rk=0.2030,0.2012,0.2076,0.2007,0.1875.Based on the expert credibility, the weights of uncertain AHP are calculated. Firstly, the judgment matrix is uniformly approximated, and the consistency matrixM is constructed with calculating weight vector (each column corresponds to the weight vector of each expert):(19)wj=0.09290.10130.10330.10230.09340.06480.06150.06120.05860.06120.04480.04310.04320.04540.04200.17450.18460.17030.18760.16960.36040.32860.34020.34570.36900.26250.28090.28180.26040.2649.After constructing the level difference matrixesΔM1 and ΔM2, calculate the weight vectors Δ1w and Δ2w and determine the weight interval of the judgment matrix as(20)wj′=0.0764,0.10720.0860,0.11940.0874,0.12380.0864,0.12340.0760,0.11510.0587,0.07240.0577,0.07120.0570,0.06650.0541,0.06600.0563,0.07210.0403,0.04860.0374,0.04780.0386,0.04740.0399,0.04980.0341,0.04960.1573,0.24900.1635,0.27890.1495,0.24130.1709,0.23380.1513,0.26090.3007,0.40810.2828,0.35640.2922,0.37090.3061,0.38470.3054,0.42100.2273,0.37730.2448,0.35280.2531,0.35230.2316,0.31060.2280,0.3811.The risk factor weights include the subjective weightwi1 and the objective weight wi2 of each element:(21)wi1=0.1004,0.0634,0.0432,0.2066,0.3451,0.2980,wi2=0.1668,0.1668,0.1668,0.1666,0.1665,0.1663.Through the coupling of subjective weight and objective weight by using equation (13), the final weights of the six risk factors in the construction risk of main cable erection and tight cable entanglement construction risk are as follows:(22)wi=0.0952,0.0601,0.0409,0.1956,0.3266,0.2817.Due to the limited space, the weight calculation methods of the other indicator layers and the criterion layer are the same as above, and the calculation results are shown in Table3.Table 3
Index weight of the cable system construction risk evaluation system.
Criteria layer
Weights
Indicator layer
Weights
Comprehensive weight
Saddle installation riskU1
0.2734
Falling objectsU11
0.0801
0.0219
Mounting bracket instabilityU12
0.2696
0.0737
Cable saddle fallingU13
0.5004
0.1368
Lifting damageU14
0.1499
0.0410
Traction system installation and catwalk construction riskU2
0.3678
Commander signal is not uniformU21
0.0413
0.0152
Catwalk load-bearing cable anchoring embedded parts are not strongU22
0.0594
0.0218
Drowning accidentU23
0.0967
0.0356
Traction system failureU24
0.2081
0.0765
Catwalk construction falls highU25
0.2660
0.0978
Catwalk construction encounters strong windsU26
0.3285
0.1208
Main cable erection and cable tightening construction riskU3
0.2980
Hoist parts are looseU31
0.0952
0.0284
Winch and entanglement machine mismatchedU32
0.0601
0.0179
Lifting accidentU33
0.0409
0.0122
Traction of the cable strand or strapping damageU34
0.1956
0.0583
Strand slipU35
0.3266
0.0973
Windy weather during the erection processU36
0.2817
0.0839
Cable clamp and sling installation riskU4
0.0608
Wire strand extrusionU41
0.0660
0.0040
Cable clamp deformationU42
0.1277
0.0078
Sling installation is tilted and biasedU43
0.3423
0.0208
Sling falling from high altitudeU44
0.4640
0.0282


## 4.4. Comprehensive Synthesis of Risk Trust Clouds

Based on the actual situation of the Yang-Si-Gang Yangtze River Bridge, and considering the risk occurrence probability and the degree of risk impact comprehensively, the five experts give a score to the indicators at the index level. According to these score, the reversed cloud calculation is carried out, and the index layer attributes are synthesized based on formula (14). Then, the characteristic value of the criterion layer cloud model can be obtained, as shown as Table 4.Table 4
Calculation results of the criterion layer attribute cloud characteristic value.
Criterion layer
Ex
En
He
Saddle installation riskU1
5.0600
0.5738
0.2977
Traction system installation and catwalk construction riskU2
4.9907
0.7981
0.3483
Main cable erection and cable tightening construction riskU3
4.6661
0.7564
0.2771
Cable clamp and sling installation riskU4
3.9789
0.7252
0.2666The criterion layer is synthesized again to obtain the characteristic value of the risk trust cloud of the target layer:(23)Ex=4.8514,En=0.7258,He=0.3083.


## 4.5. Comprehensive Evaluation of Cable System Construction Risk

According to the similarity calculation method between the cloud models in Section2.3, the similarity between the risk trust cloud and each standard trust clouds of every level is calculated and sorted. The cloud model is shown in Figure 5, and the calculation results are shown in Table 5.Figure 5
Diagram of the risk reliance cloud and criterion reliance cloud of each risk level.Table 5
Similarity between criterion reliance cloud of each risk level and risk reliance cloud.
Risk level
Lower risk
Low risk
Medium risk
High risk
Higher risk
Connection number
2.3417 × 10−4
0.0841
0.5869
0.0389
8.5316 × 10−4Table5 shows that the risk trust cloud has the greatest similarity with the medium-risk standard trust cloud. Therefore, the comprehensive judgment result of the cable system construction risk of the Yang-Si-Gang Yangtze River Bridge is “medium risk”. According to the construction risk decision criteria, the risk level is subject to conditional acceptance, but further risk management measures are needed to improve project safety.


## 4.6. Construction Risk Prevention Measures

According to the calculation results of the characteristic values of each attribute cloud in the criterion layer in Table5, the corresponding risk prevention measures are proposed for the cable saddle construction, the traction system and catwalk construction, the main cable erection and the cable tightening construction. The risk of cable clamp and sling installation construction is low and no need to take precautions.


### 4.6.1. Saddle Construction Safety Measures

The tower top construction platform shall be provided with protective railings and safety nets, and operators shall strictly wear safe labor insurance products. Before the sling is lifted, a special project should be formulated for demonstration.


### 4.6.2. Risk Prevention Measures for Catwalk Construction and Traction System

Before construction, the quality of the cable should be strictly checked. Wire breaking and rust is strictly forbidden. The impact of bad weather should be regarded. It is strictly forbidden to carry out the construction of the catwalk and the main cable under high wind conditions.


### 4.6.3. Risk Prevention Measures of Main Cable Erection and Cable Tightening Construction

Pay attention to monitoring the displacement of the main tower during construction. The displacement should be adjusted in time and always within the allowable range. The wire bundle should be tracked and inspected during the traction process to prevent the wire bundle from twisting, wearing, bulging, or breaking the bandage.


## 4.6.1. Saddle Construction Safety Measures

The tower top construction platform shall be provided with protective railings and safety nets, and operators shall strictly wear safe labor insurance products. Before the sling is lifted, a special project should be formulated for demonstration.


## 4.6.2. Risk Prevention Measures for Catwalk Construction and Traction System

Before construction, the quality of the cable should be strictly checked. Wire breaking and rust is strictly forbidden. The impact of bad weather should be regarded. It is strictly forbidden to carry out the construction of the catwalk and the main cable under high wind conditions.


## 4.6.3. Risk Prevention Measures of Main Cable Erection and Cable Tightening Construction

Pay attention to monitoring the displacement of the main tower during construction. The displacement should be adjusted in time and always within the allowable range. The wire bundle should be tracked and inspected during the traction process to prevent the wire bundle from twisting, wearing, bulging, or breaking the bandage.


## 5. Conclusion

To solve the problems that the common risk assessment methods have their limitations with complicated operation and insufficient objectivity at present, this paper proposes a risk assessment method for cable system construction of suspension bridge based on the cloud model, and the research results are as follows. First, through the decomposition of the cable system construction and the identity of risk sources, a multilevel evaluation index systems including 4 secondary evaluation indicators and 20 three-level evaluation indicators is established. Second, according to the index weights determined by the uncertain AHP weighting method, as well as the expert evaluation data, the three characteristic values of risk trust cloud are calculated by using the undetermined reverse cloud algorithm, consequently the risk evaluation model based on cloud model is obtained. Finally, an illustrative example concerning the risk of cable system construction of Wuhan Yang-Si-Gang Yangtze River Bridge is provided, and the results show that the risk grade of the cable system is “medium risk”; simultaneously, the preventive measures for each construction risk are proposed accordingly. In conclusion, the risk assessment method proposed in this study can provide safety assurance and technical support for cable system construction of long-span suspension bridge feasibly and objectively.



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*Source: 5720637-2019-04-01.xml*