RESEARCH ON SAFETY RISK COUPLING OF METRO CONSTRUCTION BASED ON N-K MODEL

Meifang SHEN1，Huitao LIU2，Xianguo WU1，Kebao WU3

1School of Civil Engineering and Mechanics，Huazhong University of Science and Technology，Wuhan 430074

2Infrastructure Section of Tongji Hospital，Tongji Medical College Huazhong University of Science & Technology，Wuhan 430030

3Civil Engineering Testing Center，Huazhong University of Science and Technology，Wuhan 430074

Abstract：In order to study metro construction safety risk management and probability of accidents because of interaction between various risk factors，this thesis analyzed the risk coupling from the aspects of personnel factors，equipment factors，management factors and environmental factors.N-K model was built to calculate the polarity and risk value of different types of risk coupling.The result shows that multi-factor risk coupling increases the probability of accident.Security risks increase when human factors and management factors involve in risk coupling.The conclusions can provide reference for improving metro construction safety management.

Keywords：metro construction，complex network，risk coupling，N-K model，safety management

Email：smf0812@163.com

1　Introduction

In recent years，a large number of metro engineering is widely developed to reduce the pressure on ground transportation.However，there are several problems，such as the overlarge scale of metro construction，the lack of technology capacity，and the low level of construction management，which cause the high risks of metro construction.Since the effect of complex risk system in metro construction，accidents always happen because of the interaction of different risk factors.The probabilities of accidents happening are usually hard to be determined by the coupling effect of different risk factors.Hence，it is quite necessary to investigate the coupling effect of different risk factors，which can commendably help improving the safety management level in metro construction.

There are several studies focus on the accidents happened in metro construction.Xie[1]investigated several typical accident in metro construction，and discovered some useful characters and regularities.Hu[2]compared the characters of accident in metro construction and proposed effective advices to reduce the casualty ratio of accidents.Fan[3]proposed the suggestion of multi-participation in metro construction to control the source of risk.The previous studies investigated factors（e.g.，the moments，types，and deaths of accidents），however，which lack of the analysis from causes of accidents.Only Wang[4]discovered the causes of accidents in metro construction，however，the interaction of the factors were neglected in the study.

N-K model[5]was originated from information theory，which is used in estimating the information transmission quantity and developed into a generalized model to elucidate complex system.It is mainly used to investigate the effect of elements within complex on the adaptability of overall system，and widely applied in economy and finance，which is lack of investigations in safety management of metro construction.Based on the N-K model，this study discovered the effect of risk coupling on the safety management of metro construction.The probability and risk-value of accidents happened are calculated by the N-K model，and the safety state of metro construction is evaluated by the risk-value，which can provide some useful suggests in the safety management of metro construction.

2　Risk Analysis of Metro Construction

2.1　Risk analysis and factor analysis

According to the definition of risk in study[4-5]，the safety risk is the probability and damage extent of unsafe incidents occurrence on certain conditions，and it profoundly reflects the correlation interaction of inside and outside factors on metro construction.Meanwhile，the main safety risk in metro construction can be divided into four categories as follow：human behaviors risk，equipment risk，management risk，and environment risk.

（1）Human is most active factor and the direct source of accidents in metro construction.The human behaviors risk includes physical defects risk，the risk of poor the safety knowledge，the risk of weak safety consciousness，and the risk of poor technology ability，etc.

（2）Equipment risk reflects to the flaws-induced risk exist in the mechanical and construction equipment of metro construction，which mainly includes the disqualification of equipment quality，performance degradation caused by equipment aging，and improper transportation of construction materials.

（3）Management risk reflects to the risk induced by unscientific management scheme，improper design of construction organization，and poor supervision of actual production management in metro construction.Management risk includes faults of personnel management，poor security check，loopholes in the rules and regulation，incomplete management system，etc.4）Environment risk reflects to the risk induced by environmental factors（e.g.，geology and hydrology environment，buildings and pipelines around the tunnel，and the internal work environment）.Environment risk includes the risk of poor geological conditions，the risk of complex traffic conditions around construction site，the risk of complex pipelines，and the risk of bad weather，etc.

2.2　Mechanism of risk coupling

Coupling is a phenomenon of tend to be coordinated by interaction in a system（with two or above element）or movement types[6，7].In the concept of system dynamics，all things are not isolated in the world，which must be the part of a system.Coupling is a mutual dependence，coordination and promotion process between each subsystem.In the field of risk management，coupling is defined as the dependence degree of risk occurrence and influence to other risk，and the influence degree of this risk impact on other risk.In the metro construction，the interaction among risks factors may eventually change the probability of risk occurring，and form the risk coupling in the process of risk evolution.

3　Coupling Analysis by N-K Model

N-K model is a general model to investigate the complicated dynamic system，which includes two parameters：N is the number of elements of the system，and K is the number of interdependent relationship in a network.If there are N elements in system，each element has n different state，and there are nN possible compound modes in total.Network is combined by the system elements，which the minimum value of K is 0，and the minimum value of K is N-1.The substeps of safety risk measure coupling by N-K model in metro construction includes the following steps：the classification of coupling risk in metro construction；determine the risk coupling interaction information and formula；building a calculation formula of multi-factor coupling risk.

3.1　Risk coupling classification of metro construction

According to the number of risk factors，the metro construction safety risk can be divided into the following three categories：

（1）Coupling of single risk factor.Single factor coupling risk refers to the individual risk factors affecting the safety of metro construction which contains multiple risk factors and the internal interaction in these risk factors.Single factor coupling including coupling of human factors risk，coupling of equipment risk factors，coupling of environment risk factors and coupling of management risk factors，i.e.，T11（a），T12（b），T13（c），T14（d），and the coupling of whole risk（T1）.

（2）Coupling of double risk factors.Coupling of double risk factors refers to the coupling influence of the two risk factors in the metro construction.Coupling of double risk factors includes coupling of human-equipment risk factors，coupling of human-environment risk factors，coupling of human-management risk factors，coupling of equipment-environment risk factors，coupling of equipment-management risk factors，coupling of environment-management risk factors，i.e.，T21（a，b），T22（a，c），T23（a，d），T24（b，c），T25（b，d），T26（c，d），and the coupling of whole risk（T2）.

（3）Coupling of multi-risk factors.Coupling of multi-risk factors refers to the coupling influence of the three risk factors in the metro construction.Coupling of multi-risk factors including coupling of human-equipment-environment risk factors，coupling of human-environment-management risk factors，coupling of human-environment-management risk factors，coupling of equipment-environment-management risk factors，i.e.，T31（a，b，c），T32（a，b，d），T33（a，c，d），T34（b，c，d），and the coupling of whole risk（T3）.The coupling of four risk factors is T41（a，b，c，d），and the total value of coupling risk is T4.The model of coupling is shown in Figure 1.

3.2　Determining interaction formula of coupling risk

This paper calculated the interaction information of four kinds of risk factors in the metro construction，and evaluated the updated risk state by considering the coupling effect.The probabilities of the coupling way occurring are measured by the number of coupling effect，i.e.，the larger the number of the coupling，the greater probability of the coupling way.The size of coupling risks and probability of risk occurring are measured by the coupling values，namely the more coupling the values obtained in some way，the greater the coupling risk，and the greater probability of the accident occurring.The calculating formula of mutual information is as follows：

where，Phijkrefers to the probability of the coupling risks occurring，in which the human are in the h status，the equipment are in the i status，the environment are in the j status，the management are in the k status.The greater T value，the greater safety risk of the metro construction，T is safety quantitative assessment of coupling risk in the metro construction.

3.3　Formula establishment of coupling by double risk factors

Most safety risk coupling of metro construction is in local，which includes single factor risk coupling，double factors coupling and multi-factor risk coupling.Local coupling can be referred as the coupling within interaction of internal risk factors，which can be regarded as a special case of multi-factor risk coupling.The coupling between two risk factors can produce six kinds of different situations，such as when the factors of equipment and environmental are coupled，which means the accident happened at a less relationship with human risk factors，and it is called partial risk coupling.Therefore，the coupling of local risk can be investigated by calculating the information interaction of two risks.And the formula of double risk factors coupling is as follows：

3.4　Formula establishment of coupling by multi-factor

The same as section 2.3，there are four coupling ways of three risk factors，such as coupling the human-equipment-environment factors，which has a less relationship with management risk factors，and it is called partial risk coupling.And the formula of three risk factors coupling is as follows：

4　Case Study

4.1　Project background

In recent years，there are several significant development in metro construction，due to the complexity of metro construction（e.g.，geographical position and construction environment），different types and levels of construction safety accident appear constantly，which has caused great economic losses and adverse social impact.According to relevant data[2]，a total of 183accident happened in the metro construction from 2002 to 2014.Part of the safety accident information is shown in Table 1.

4.2　Calculation of risk coupling

Not happened and happened in 0 and 1，respectively，in N-K model.Thus，there are 16kinds of potential risk coupling，then through the analysis on the statistical data of safety accident in the metro construction，the times of risk coupling and the frequency of each coupling can be concluded，and the results are shown in Table 2.

（1）The analysis of single factor risk coupling.In order to calculate the valueof T，the probability of risk coupling is calculated by the different coupling ways.

According to the Equation（1），the values of Ph，Pi，Pj，Pkcan be calculated.And the probability without considering human factors is P0…=P0000+P0100+P0010+P0001+P0110+P0101+P0011+P0111=0.2514.In the same way，the P1…，P.0..，P.1..，P..0.，P..1.，P…0，and P…1can be calculated，and the results are shown in Table 3.

（2）The analysis of double factor risks coupling.According to the Equation 2-7，the values of Phi，Phj，Phk，Pij，Pik，and Pjkcan be calculated.And the probability without considering human factors and equipment factors is P00..=P0000+P0010+P0001+P0011=0.0656.In the same way，the other values can be calculated，and the results are shown in Table 4.

（3）The analysis of multi-factor risks coupling.According to the Equation 8-11，the values of Phij，Phik，Phjk，and Pijkcan be calculated.And the probability without considering human factors，equipment factors and environmental factors is P000.=P0000+P0001=0+0.0109=0.0109.In the same way，the other values can be calculated，and the results are shown in Table 5

According to the Equation 1-11，the values of T can be calculated.T4=0.1431；T21=0.0158；T22=0.0248；T23=0.0253；T24=0.0191；T25=0.0107；T26=0.0152；T31=0.0678；T32=0.0586；T33=0.0749；T34=0.0527.

T4>T33>T31>T32>T34>T23>T22>T24>T21>T26>T25

3.3　Comprehensive analysis

（1）With the increase of coupling risk factors，the risk also increases.The calculated result shows that the coupling risk of four factors is greater than the coupling risk of three factors；the coupling risk of three factors is more than the coupling risk of double factors，which are in conformity with the actual construction.

（2）In the coupling of three risk factors，the coupling values of human-environment-management factors are the most；meanwhile，the coupling risk of human-equipment-management and human-environment-management factors is great than the coupling risk of human-equipment-environment and equipment-environment-management factors.This suggests that the fully risk coupling of subjective factors（human factors and management factors）is greater than the incomplete coupling，and the fully coupling of the subjective factors and environmental factors has the most risk.

（3）In the coupling of double risk factors，the coupling risk of human-environmentfactors is the most，and the coupling risk of equipment-environment and human-equipment factors are the medium，and coupling risk of equipment-management factors is the least.This suggests that the coupling probability of human factors and management factors is the most，which means the inappropriate operation of constructors and inaccurate management of administrator easy to cause the safety accidents.

5　Conclusions

（1）This paper investigated the typical accident cases data of metro construction in our country on the last decade.The coupling risk value in the process of metro construction is calculated by N-K model，and there are some regularities of the risk coupling are discovered，which can provide theoretical basis for metro construction safety management.

（2）From the calculation results，the human factors，management factors and environmental factors showed activity in the process of the risk coupling.In the human-equipment-environment-management system，human factors is the main factors，therefore，paying attention on the people’s subjective initiative is useful to improve the management level.And strengthening the control of environmental factors and equipment factors is useful to reduce the frequency of the metro construction accident In addition，it is necessary to avoid the multi-risk coupling，especially the coupling of four risk factors.

（3）Because the N-K model have strict request for the integrity of the data and sample size，therefore，it is necessary to improve the integrity of data and enlarge the size of sample，which can improve the accuracy of calculated results，and the results can be more tally with the actual project.

Acknowledgement

This work was financially supported by the National Natural Science Foundation of China（No.51378235 and No.71571078），Hubei Provincial Natural Science Fund（No.2014CFA117），and Wuhan City Construction Committee Support Project（No.201334）.

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